diff --git a/texk/web2c/mplibdir/ChangeLog b/texk/web2c/mplibdir/ChangeLog index d549ebf828..749c01682f 100644 --- a/texk/web2c/mplibdir/ChangeLog +++ b/texk/web2c/mplibdir/ChangeLog @@ -1,3 +1,8 @@ +2023-09-10 TANAKA Takuji + + * decContext.{c,h}, decNumber.{c,h}, decNumberLocal.h: + Convert newline from CRLF to LF. + 2023-08-20 TANAKA Takuji * {dvitomp,mptraptest}.test: diff --git a/texk/web2c/mplibdir/decContext.c b/texk/web2c/mplibdir/decContext.c index 9f99759336..6db29be034 100644 --- a/texk/web2c/mplibdir/decContext.c +++ b/texk/web2c/mplibdir/decContext.c @@ -1,437 +1,437 @@ -/* ------------------------------------------------------------------ */ -/* Decimal Context module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for handling arithmetic */ -/* context structures. */ -/* ------------------------------------------------------------------ */ - -#include // for strcmp -#include // for printf if DECCHECK -#include "decContext.h" // context and base types -#include "decNumberLocal.h" // decNumber local types, etc. - -/* compile-time endian tester [assumes sizeof(Int)>1] */ -static const Int mfcone=1; // constant 1 -static const Flag *mfctop=(const Flag *)&mfcone; // -> top byte -#define LITEND *mfctop // named flag; 1=little-endian - -/* ------------------------------------------------------------------ */ -/* round-for-reround digits */ -/* ------------------------------------------------------------------ */ -const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */ - -/* ------------------------------------------------------------------ */ -/* Powers of ten (powers[n]==10**n, 0<=n<=9) */ -/* ------------------------------------------------------------------ */ -const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000, - 10000000, 100000000, 1000000000}; - -/* ------------------------------------------------------------------ */ -/* decContextClearStatus -- clear bits in current status */ -/* */ -/* context is the context structure to be queried */ -/* mask indicates the bits to be cleared (the status bit that */ -/* corresponds to each 1 bit in the mask is cleared) */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextClearStatus(decContext *context, uInt mask) { - context->status&=~mask; - return context; - } // decContextClearStatus - -/* ------------------------------------------------------------------ */ -/* decContextDefault -- initialize a context structure */ -/* */ -/* context is the structure to be initialized */ -/* kind selects the required set of default values, one of: */ -/* DEC_INIT_BASE -- select ANSI X3-274 defaults */ -/* DEC_INIT_DECIMAL32 -- select IEEE 754 defaults, 32-bit */ -/* DEC_INIT_DECIMAL64 -- select IEEE 754 defaults, 64-bit */ -/* DEC_INIT_DECIMAL128 -- select IEEE 754 defaults, 128-bit */ -/* For any other value a valid context is returned, but with */ -/* Invalid_operation set in the status field. */ -/* returns a context structure with the appropriate initial values. */ -/* ------------------------------------------------------------------ */ -decContext * decContextDefault(decContext *context, Int kind) { - // set defaults... - context->digits=9; // 9 digits - context->emax=DEC_MAX_EMAX; // 9-digit exponents - context->emin=DEC_MIN_EMIN; // .. balanced - context->round=DEC_ROUND_HALF_UP; // 0.5 rises - context->traps=DEC_Errors; // all but informational - context->status=0; // cleared - context->clamp=0; // no clamping - #if DECSUBSET - context->extended=0; // cleared - #endif - switch (kind) { - case DEC_INIT_BASE: - // [use defaults] - break; - case DEC_INIT_DECIMAL32: - context->digits=7; // digits - context->emax=96; // Emax - context->emin=-95; // Emin - context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even - context->traps=0; // no traps set - context->clamp=1; // clamp exponents - #if DECSUBSET - context->extended=1; // set - #endif - break; - case DEC_INIT_DECIMAL64: - context->digits=16; // digits - context->emax=384; // Emax - context->emin=-383; // Emin - context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even - context->traps=0; // no traps set - context->clamp=1; // clamp exponents - #if DECSUBSET - context->extended=1; // set - #endif - break; - case DEC_INIT_DECIMAL128: - context->digits=34; // digits - context->emax=6144; // Emax - context->emin=-6143; // Emin - context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even - context->traps=0; // no traps set - context->clamp=1; // clamp exponents - #if DECSUBSET - context->extended=1; // set - #endif - break; - - default: // invalid Kind - // use defaults, and .. - decContextSetStatus(context, DEC_Invalid_operation); // trap - } - - return context;} // decContextDefault - -/* ------------------------------------------------------------------ */ -/* decContextGetRounding -- return current rounding mode */ -/* */ -/* context is the context structure to be queried */ -/* returns the rounding mode */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -enum rounding decContextGetRounding(decContext *context) { - return context->round; - } // decContextGetRounding - -/* ------------------------------------------------------------------ */ -/* decContextGetStatus -- return current status */ -/* */ -/* context is the context structure to be queried */ -/* returns status */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextGetStatus(decContext *context) { - return context->status; - } // decContextGetStatus - -/* ------------------------------------------------------------------ */ -/* decContextRestoreStatus -- restore bits in current status */ -/* */ -/* context is the context structure to be updated */ -/* newstatus is the source for the bits to be restored */ -/* mask indicates the bits to be restored (the status bit that */ -/* corresponds to each 1 bit in the mask is set to the value of */ -/* the correspnding bit in newstatus) */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextRestoreStatus(decContext *context, - uInt newstatus, uInt mask) { - context->status&=~mask; // clear the selected bits - context->status|=(mask&newstatus); // or in the new bits - return context; - } // decContextRestoreStatus - -/* ------------------------------------------------------------------ */ -/* decContextSaveStatus -- save bits in current status */ -/* */ -/* context is the context structure to be queried */ -/* mask indicates the bits to be saved (the status bits that */ -/* correspond to each 1 bit in the mask are saved) */ -/* returns the AND of the mask and the current status */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextSaveStatus(decContext *context, uInt mask) { - return context->status&mask; - } // decContextSaveStatus - -/* ------------------------------------------------------------------ */ -/* decContextSetRounding -- set current rounding mode */ -/* */ -/* context is the context structure to be updated */ -/* newround is the value which will replace the current mode */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextSetRounding(decContext *context, - enum rounding newround) { - context->round=newround; - return context; - } // decContextSetRounding - -/* ------------------------------------------------------------------ */ -/* decContextSetStatus -- set status and raise trap if appropriate */ -/* */ -/* context is the context structure to be updated */ -/* status is the DEC_ exception code */ -/* returns the context structure */ -/* */ -/* Control may never return from this routine, if there is a signal */ -/* handler and it takes a long jump. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatus(decContext *context, uInt status) { - context->status|=status; - if (status & context->traps) raise(SIGFPE); - return context;} // decContextSetStatus - -/* ------------------------------------------------------------------ */ -/* decContextSetStatusFromString -- set status from a string + trap */ -/* */ -/* context is the context structure to be updated */ -/* string is a string exactly equal to one that might be returned */ -/* by decContextStatusToString */ -/* */ -/* The status bit corresponding to the string is set, and a trap */ -/* is raised if appropriate. */ -/* */ -/* returns the context structure, unless the string is equal to */ -/* DEC_Condition_MU or is not recognized. In these cases NULL is */ -/* returned. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatusFromString(decContext *context, - const char *string) { - if (strcmp(string, DEC_Condition_CS)==0) - return decContextSetStatus(context, DEC_Conversion_syntax); - if (strcmp(string, DEC_Condition_DZ)==0) - return decContextSetStatus(context, DEC_Division_by_zero); - if (strcmp(string, DEC_Condition_DI)==0) - return decContextSetStatus(context, DEC_Division_impossible); - if (strcmp(string, DEC_Condition_DU)==0) - return decContextSetStatus(context, DEC_Division_undefined); - if (strcmp(string, DEC_Condition_IE)==0) - return decContextSetStatus(context, DEC_Inexact); - if (strcmp(string, DEC_Condition_IS)==0) - return decContextSetStatus(context, DEC_Insufficient_storage); - if (strcmp(string, DEC_Condition_IC)==0) - return decContextSetStatus(context, DEC_Invalid_context); - if (strcmp(string, DEC_Condition_IO)==0) - return decContextSetStatus(context, DEC_Invalid_operation); - #if DECSUBSET - if (strcmp(string, DEC_Condition_LD)==0) - return decContextSetStatus(context, DEC_Lost_digits); - #endif - if (strcmp(string, DEC_Condition_OV)==0) - return decContextSetStatus(context, DEC_Overflow); - if (strcmp(string, DEC_Condition_PA)==0) - return decContextSetStatus(context, DEC_Clamped); - if (strcmp(string, DEC_Condition_RO)==0) - return decContextSetStatus(context, DEC_Rounded); - if (strcmp(string, DEC_Condition_SU)==0) - return decContextSetStatus(context, DEC_Subnormal); - if (strcmp(string, DEC_Condition_UN)==0) - return decContextSetStatus(context, DEC_Underflow); - if (strcmp(string, DEC_Condition_ZE)==0) - return context; - return NULL; // Multiple status, or unknown - } // decContextSetStatusFromString - -/* ------------------------------------------------------------------ */ -/* decContextSetStatusFromStringQuiet -- set status from a string */ -/* */ -/* context is the context structure to be updated */ -/* string is a string exactly equal to one that might be returned */ -/* by decContextStatusToString */ -/* */ -/* The status bit corresponding to the string is set; no trap is */ -/* raised. */ -/* */ -/* returns the context structure, unless the string is equal to */ -/* DEC_Condition_MU or is not recognized. In these cases NULL is */ -/* returned. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatusFromStringQuiet(decContext *context, - const char *string) { - if (strcmp(string, DEC_Condition_CS)==0) - return decContextSetStatusQuiet(context, DEC_Conversion_syntax); - if (strcmp(string, DEC_Condition_DZ)==0) - return decContextSetStatusQuiet(context, DEC_Division_by_zero); - if (strcmp(string, DEC_Condition_DI)==0) - return decContextSetStatusQuiet(context, DEC_Division_impossible); - if (strcmp(string, DEC_Condition_DU)==0) - return decContextSetStatusQuiet(context, DEC_Division_undefined); - if (strcmp(string, DEC_Condition_IE)==0) - return decContextSetStatusQuiet(context, DEC_Inexact); - if (strcmp(string, DEC_Condition_IS)==0) - return decContextSetStatusQuiet(context, DEC_Insufficient_storage); - if (strcmp(string, DEC_Condition_IC)==0) - return decContextSetStatusQuiet(context, DEC_Invalid_context); - if (strcmp(string, DEC_Condition_IO)==0) - return decContextSetStatusQuiet(context, DEC_Invalid_operation); - #if DECSUBSET - if (strcmp(string, DEC_Condition_LD)==0) - return decContextSetStatusQuiet(context, DEC_Lost_digits); - #endif - if (strcmp(string, DEC_Condition_OV)==0) - return decContextSetStatusQuiet(context, DEC_Overflow); - if (strcmp(string, DEC_Condition_PA)==0) - return decContextSetStatusQuiet(context, DEC_Clamped); - if (strcmp(string, DEC_Condition_RO)==0) - return decContextSetStatusQuiet(context, DEC_Rounded); - if (strcmp(string, DEC_Condition_SU)==0) - return decContextSetStatusQuiet(context, DEC_Subnormal); - if (strcmp(string, DEC_Condition_UN)==0) - return decContextSetStatusQuiet(context, DEC_Underflow); - if (strcmp(string, DEC_Condition_ZE)==0) - return context; - return NULL; // Multiple status, or unknown - } // decContextSetStatusFromStringQuiet - -/* ------------------------------------------------------------------ */ -/* decContextSetStatusQuiet -- set status without trap */ -/* */ -/* context is the context structure to be updated */ -/* status is the DEC_ exception code */ -/* returns the context structure */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext * decContextSetStatusQuiet(decContext *context, uInt status) { - context->status|=status; - return context;} // decContextSetStatusQuiet - -/* ------------------------------------------------------------------ */ -/* decContextStatusToString -- convert status flags to a string */ -/* */ -/* context is a context with valid status field */ -/* */ -/* returns a constant string describing the condition. If multiple */ -/* (or no) flags are set, a generic constant message is returned. */ -/* ------------------------------------------------------------------ */ -const char *decContextStatusToString(const decContext *context) { - Int status=context->status; - - // test the five IEEE first, as some of the others are ambiguous when - // DECEXTFLAG=0 - if (status==DEC_Invalid_operation ) return DEC_Condition_IO; - if (status==DEC_Division_by_zero ) return DEC_Condition_DZ; - if (status==DEC_Overflow ) return DEC_Condition_OV; - if (status==DEC_Underflow ) return DEC_Condition_UN; - if (status==DEC_Inexact ) return DEC_Condition_IE; - - if (status==DEC_Division_impossible ) return DEC_Condition_DI; - if (status==DEC_Division_undefined ) return DEC_Condition_DU; - if (status==DEC_Rounded ) return DEC_Condition_RO; - if (status==DEC_Clamped ) return DEC_Condition_PA; - if (status==DEC_Subnormal ) return DEC_Condition_SU; - if (status==DEC_Conversion_syntax ) return DEC_Condition_CS; - if (status==DEC_Insufficient_storage ) return DEC_Condition_IS; - if (status==DEC_Invalid_context ) return DEC_Condition_IC; - #if DECSUBSET - if (status==DEC_Lost_digits ) return DEC_Condition_LD; - #endif - if (status==0 ) return DEC_Condition_ZE; - return DEC_Condition_MU; // Multiple errors - } // decContextStatusToString - -/* ------------------------------------------------------------------ */ -/* decContextTestEndian -- test whether DECLITEND is set correctly */ -/* */ -/* quiet is 1 to suppress message; 0 otherwise */ -/* returns 0 if DECLITEND is correct */ -/* 1 if DECLITEND is incorrect and should be 1 */ -/* -1 if DECLITEND is incorrect and should be 0 */ -/* */ -/* A message is displayed if the return value is not 0 and quiet==0. */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -Int decContextTestEndian(Flag quiet) { - Int res=0; // optimist - uInt dle=(uInt)DECLITEND; // unsign - if (dle>1) dle=1; // ensure 0 or 1 - - if (LITEND!=DECLITEND) { - if (!quiet) { // always refer to this - #if DECPRINT - const char *adj; - if (LITEND) adj="little"; - else adj="big"; - printf("Warning: DECLITEND is set to %d, but this computer appears to be %s-endian\n", - DECLITEND, adj); - #endif - } - res=(Int)LITEND-dle; - } - return res; - } // decContextTestEndian - -/* ------------------------------------------------------------------ */ -/* decContextTestSavedStatus -- test bits in saved status */ -/* */ -/* oldstatus is the status word to be tested */ -/* mask indicates the bits to be tested (the oldstatus bits that */ -/* correspond to each 1 bit in the mask are tested) */ -/* returns 1 if any of the tested bits are 1, or 0 otherwise */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextTestSavedStatus(uInt oldstatus, uInt mask) { - return (oldstatus&mask)!=0; - } // decContextTestSavedStatus - -/* ------------------------------------------------------------------ */ -/* decContextTestStatus -- test bits in current status */ -/* */ -/* context is the context structure to be updated */ -/* mask indicates the bits to be tested (the status bits that */ -/* correspond to each 1 bit in the mask are tested) */ -/* returns 1 if any of the tested bits are 1, or 0 otherwise */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -uInt decContextTestStatus(decContext *context, uInt mask) { - return (context->status&mask)!=0; - } // decContextTestStatus - -/* ------------------------------------------------------------------ */ -/* decContextZeroStatus -- clear all status bits */ -/* */ -/* context is the context structure to be updated */ -/* returns context */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decContext *decContextZeroStatus(decContext *context) { - context->status=0; - return context; - } // decContextZeroStatus - +/* ------------------------------------------------------------------ */ +/* Decimal Context module */ +/* ------------------------------------------------------------------ */ +/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */ +/* */ +/* This software is made available under the terms of the */ +/* ICU License -- ICU 1.8.1 and later. */ +/* */ +/* The description and User's Guide ("The decNumber C Library") for */ +/* this software is called decNumber.pdf. This document is */ +/* available, together with arithmetic and format specifications, */ +/* testcases, and Web links, on the General Decimal Arithmetic page. */ +/* */ +/* Please send comments, suggestions, and corrections to the author: */ +/* mfc@uk.ibm.com */ +/* Mike Cowlishaw, IBM Fellow */ +/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ +/* ------------------------------------------------------------------ */ +/* This module comprises the routines for handling arithmetic */ +/* context structures. */ +/* ------------------------------------------------------------------ */ + +#include // for strcmp +#include // for printf if DECCHECK +#include "decContext.h" // context and base types +#include "decNumberLocal.h" // decNumber local types, etc. + +/* compile-time endian tester [assumes sizeof(Int)>1] */ +static const Int mfcone=1; // constant 1 +static const Flag *mfctop=(const Flag *)&mfcone; // -> top byte +#define LITEND *mfctop // named flag; 1=little-endian + +/* ------------------------------------------------------------------ */ +/* round-for-reround digits */ +/* ------------------------------------------------------------------ */ +const uByte DECSTICKYTAB[10]={1,1,2,3,4,6,6,7,8,9}; /* used if sticky */ + +/* ------------------------------------------------------------------ */ +/* Powers of ten (powers[n]==10**n, 0<=n<=9) */ +/* ------------------------------------------------------------------ */ +const uInt DECPOWERS[10]={1, 10, 100, 1000, 10000, 100000, 1000000, + 10000000, 100000000, 1000000000}; + +/* ------------------------------------------------------------------ */ +/* decContextClearStatus -- clear bits in current status */ +/* */ +/* context is the context structure to be queried */ +/* mask indicates the bits to be cleared (the status bit that */ +/* corresponds to each 1 bit in the mask is cleared) */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextClearStatus(decContext *context, uInt mask) { + context->status&=~mask; + return context; + } // decContextClearStatus + +/* ------------------------------------------------------------------ */ +/* decContextDefault -- initialize a context structure */ +/* */ +/* context is the structure to be initialized */ +/* kind selects the required set of default values, one of: */ +/* DEC_INIT_BASE -- select ANSI X3-274 defaults */ +/* DEC_INIT_DECIMAL32 -- select IEEE 754 defaults, 32-bit */ +/* DEC_INIT_DECIMAL64 -- select IEEE 754 defaults, 64-bit */ +/* DEC_INIT_DECIMAL128 -- select IEEE 754 defaults, 128-bit */ +/* For any other value a valid context is returned, but with */ +/* Invalid_operation set in the status field. */ +/* returns a context structure with the appropriate initial values. */ +/* ------------------------------------------------------------------ */ +decContext * decContextDefault(decContext *context, Int kind) { + // set defaults... + context->digits=9; // 9 digits + context->emax=DEC_MAX_EMAX; // 9-digit exponents + context->emin=DEC_MIN_EMIN; // .. balanced + context->round=DEC_ROUND_HALF_UP; // 0.5 rises + context->traps=DEC_Errors; // all but informational + context->status=0; // cleared + context->clamp=0; // no clamping + #if DECSUBSET + context->extended=0; // cleared + #endif + switch (kind) { + case DEC_INIT_BASE: + // [use defaults] + break; + case DEC_INIT_DECIMAL32: + context->digits=7; // digits + context->emax=96; // Emax + context->emin=-95; // Emin + context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even + context->traps=0; // no traps set + context->clamp=1; // clamp exponents + #if DECSUBSET + context->extended=1; // set + #endif + break; + case DEC_INIT_DECIMAL64: + context->digits=16; // digits + context->emax=384; // Emax + context->emin=-383; // Emin + context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even + context->traps=0; // no traps set + context->clamp=1; // clamp exponents + #if DECSUBSET + context->extended=1; // set + #endif + break; + case DEC_INIT_DECIMAL128: + context->digits=34; // digits + context->emax=6144; // Emax + context->emin=-6143; // Emin + context->round=DEC_ROUND_HALF_EVEN; // 0.5 to nearest even + context->traps=0; // no traps set + context->clamp=1; // clamp exponents + #if DECSUBSET + context->extended=1; // set + #endif + break; + + default: // invalid Kind + // use defaults, and .. + decContextSetStatus(context, DEC_Invalid_operation); // trap + } + + return context;} // decContextDefault + +/* ------------------------------------------------------------------ */ +/* decContextGetRounding -- return current rounding mode */ +/* */ +/* context is the context structure to be queried */ +/* returns the rounding mode */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +enum rounding decContextGetRounding(decContext *context) { + return context->round; + } // decContextGetRounding + +/* ------------------------------------------------------------------ */ +/* decContextGetStatus -- return current status */ +/* */ +/* context is the context structure to be queried */ +/* returns status */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextGetStatus(decContext *context) { + return context->status; + } // decContextGetStatus + +/* ------------------------------------------------------------------ */ +/* decContextRestoreStatus -- restore bits in current status */ +/* */ +/* context is the context structure to be updated */ +/* newstatus is the source for the bits to be restored */ +/* mask indicates the bits to be restored (the status bit that */ +/* corresponds to each 1 bit in the mask is set to the value of */ +/* the correspnding bit in newstatus) */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextRestoreStatus(decContext *context, + uInt newstatus, uInt mask) { + context->status&=~mask; // clear the selected bits + context->status|=(mask&newstatus); // or in the new bits + return context; + } // decContextRestoreStatus + +/* ------------------------------------------------------------------ */ +/* decContextSaveStatus -- save bits in current status */ +/* */ +/* context is the context structure to be queried */ +/* mask indicates the bits to be saved (the status bits that */ +/* correspond to each 1 bit in the mask are saved) */ +/* returns the AND of the mask and the current status */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextSaveStatus(decContext *context, uInt mask) { + return context->status&mask; + } // decContextSaveStatus + +/* ------------------------------------------------------------------ */ +/* decContextSetRounding -- set current rounding mode */ +/* */ +/* context is the context structure to be updated */ +/* newround is the value which will replace the current mode */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextSetRounding(decContext *context, + enum rounding newround) { + context->round=newround; + return context; + } // decContextSetRounding + +/* ------------------------------------------------------------------ */ +/* decContextSetStatus -- set status and raise trap if appropriate */ +/* */ +/* context is the context structure to be updated */ +/* status is the DEC_ exception code */ +/* returns the context structure */ +/* */ +/* Control may never return from this routine, if there is a signal */ +/* handler and it takes a long jump. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatus(decContext *context, uInt status) { + context->status|=status; + if (status & context->traps) raise(SIGFPE); + return context;} // decContextSetStatus + +/* ------------------------------------------------------------------ */ +/* decContextSetStatusFromString -- set status from a string + trap */ +/* */ +/* context is the context structure to be updated */ +/* string is a string exactly equal to one that might be returned */ +/* by decContextStatusToString */ +/* */ +/* The status bit corresponding to the string is set, and a trap */ +/* is raised if appropriate. */ +/* */ +/* returns the context structure, unless the string is equal to */ +/* DEC_Condition_MU or is not recognized. In these cases NULL is */ +/* returned. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatusFromString(decContext *context, + const char *string) { + if (strcmp(string, DEC_Condition_CS)==0) + return decContextSetStatus(context, DEC_Conversion_syntax); + if (strcmp(string, DEC_Condition_DZ)==0) + return decContextSetStatus(context, DEC_Division_by_zero); + if (strcmp(string, DEC_Condition_DI)==0) + return decContextSetStatus(context, DEC_Division_impossible); + if (strcmp(string, DEC_Condition_DU)==0) + return decContextSetStatus(context, DEC_Division_undefined); + if (strcmp(string, DEC_Condition_IE)==0) + return decContextSetStatus(context, DEC_Inexact); + if (strcmp(string, DEC_Condition_IS)==0) + return decContextSetStatus(context, DEC_Insufficient_storage); + if (strcmp(string, DEC_Condition_IC)==0) + return decContextSetStatus(context, DEC_Invalid_context); + if (strcmp(string, DEC_Condition_IO)==0) + return decContextSetStatus(context, DEC_Invalid_operation); + #if DECSUBSET + if (strcmp(string, DEC_Condition_LD)==0) + return decContextSetStatus(context, DEC_Lost_digits); + #endif + if (strcmp(string, DEC_Condition_OV)==0) + return decContextSetStatus(context, DEC_Overflow); + if (strcmp(string, DEC_Condition_PA)==0) + return decContextSetStatus(context, DEC_Clamped); + if (strcmp(string, DEC_Condition_RO)==0) + return decContextSetStatus(context, DEC_Rounded); + if (strcmp(string, DEC_Condition_SU)==0) + return decContextSetStatus(context, DEC_Subnormal); + if (strcmp(string, DEC_Condition_UN)==0) + return decContextSetStatus(context, DEC_Underflow); + if (strcmp(string, DEC_Condition_ZE)==0) + return context; + return NULL; // Multiple status, or unknown + } // decContextSetStatusFromString + +/* ------------------------------------------------------------------ */ +/* decContextSetStatusFromStringQuiet -- set status from a string */ +/* */ +/* context is the context structure to be updated */ +/* string is a string exactly equal to one that might be returned */ +/* by decContextStatusToString */ +/* */ +/* The status bit corresponding to the string is set; no trap is */ +/* raised. */ +/* */ +/* returns the context structure, unless the string is equal to */ +/* DEC_Condition_MU or is not recognized. In these cases NULL is */ +/* returned. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatusFromStringQuiet(decContext *context, + const char *string) { + if (strcmp(string, DEC_Condition_CS)==0) + return decContextSetStatusQuiet(context, DEC_Conversion_syntax); + if (strcmp(string, DEC_Condition_DZ)==0) + return decContextSetStatusQuiet(context, DEC_Division_by_zero); + if (strcmp(string, DEC_Condition_DI)==0) + return decContextSetStatusQuiet(context, DEC_Division_impossible); + if (strcmp(string, DEC_Condition_DU)==0) + return decContextSetStatusQuiet(context, DEC_Division_undefined); + if (strcmp(string, DEC_Condition_IE)==0) + return decContextSetStatusQuiet(context, DEC_Inexact); + if (strcmp(string, DEC_Condition_IS)==0) + return decContextSetStatusQuiet(context, DEC_Insufficient_storage); + if (strcmp(string, DEC_Condition_IC)==0) + return decContextSetStatusQuiet(context, DEC_Invalid_context); + if (strcmp(string, DEC_Condition_IO)==0) + return decContextSetStatusQuiet(context, DEC_Invalid_operation); + #if DECSUBSET + if (strcmp(string, DEC_Condition_LD)==0) + return decContextSetStatusQuiet(context, DEC_Lost_digits); + #endif + if (strcmp(string, DEC_Condition_OV)==0) + return decContextSetStatusQuiet(context, DEC_Overflow); + if (strcmp(string, DEC_Condition_PA)==0) + return decContextSetStatusQuiet(context, DEC_Clamped); + if (strcmp(string, DEC_Condition_RO)==0) + return decContextSetStatusQuiet(context, DEC_Rounded); + if (strcmp(string, DEC_Condition_SU)==0) + return decContextSetStatusQuiet(context, DEC_Subnormal); + if (strcmp(string, DEC_Condition_UN)==0) + return decContextSetStatusQuiet(context, DEC_Underflow); + if (strcmp(string, DEC_Condition_ZE)==0) + return context; + return NULL; // Multiple status, or unknown + } // decContextSetStatusFromStringQuiet + +/* ------------------------------------------------------------------ */ +/* decContextSetStatusQuiet -- set status without trap */ +/* */ +/* context is the context structure to be updated */ +/* status is the DEC_ exception code */ +/* returns the context structure */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext * decContextSetStatusQuiet(decContext *context, uInt status) { + context->status|=status; + return context;} // decContextSetStatusQuiet + +/* ------------------------------------------------------------------ */ +/* decContextStatusToString -- convert status flags to a string */ +/* */ +/* context is a context with valid status field */ +/* */ +/* returns a constant string describing the condition. If multiple */ +/* (or no) flags are set, a generic constant message is returned. */ +/* ------------------------------------------------------------------ */ +const char *decContextStatusToString(const decContext *context) { + Int status=context->status; + + // test the five IEEE first, as some of the others are ambiguous when + // DECEXTFLAG=0 + if (status==DEC_Invalid_operation ) return DEC_Condition_IO; + if (status==DEC_Division_by_zero ) return DEC_Condition_DZ; + if (status==DEC_Overflow ) return DEC_Condition_OV; + if (status==DEC_Underflow ) return DEC_Condition_UN; + if (status==DEC_Inexact ) return DEC_Condition_IE; + + if (status==DEC_Division_impossible ) return DEC_Condition_DI; + if (status==DEC_Division_undefined ) return DEC_Condition_DU; + if (status==DEC_Rounded ) return DEC_Condition_RO; + if (status==DEC_Clamped ) return DEC_Condition_PA; + if (status==DEC_Subnormal ) return DEC_Condition_SU; + if (status==DEC_Conversion_syntax ) return DEC_Condition_CS; + if (status==DEC_Insufficient_storage ) return DEC_Condition_IS; + if (status==DEC_Invalid_context ) return DEC_Condition_IC; + #if DECSUBSET + if (status==DEC_Lost_digits ) return DEC_Condition_LD; + #endif + if (status==0 ) return DEC_Condition_ZE; + return DEC_Condition_MU; // Multiple errors + } // decContextStatusToString + +/* ------------------------------------------------------------------ */ +/* decContextTestEndian -- test whether DECLITEND is set correctly */ +/* */ +/* quiet is 1 to suppress message; 0 otherwise */ +/* returns 0 if DECLITEND is correct */ +/* 1 if DECLITEND is incorrect and should be 1 */ +/* -1 if DECLITEND is incorrect and should be 0 */ +/* */ +/* A message is displayed if the return value is not 0 and quiet==0. */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +Int decContextTestEndian(Flag quiet) { + Int res=0; // optimist + uInt dle=(uInt)DECLITEND; // unsign + if (dle>1) dle=1; // ensure 0 or 1 + + if (LITEND!=DECLITEND) { + if (!quiet) { // always refer to this + #if DECPRINT + const char *adj; + if (LITEND) adj="little"; + else adj="big"; + printf("Warning: DECLITEND is set to %d, but this computer appears to be %s-endian\n", + DECLITEND, adj); + #endif + } + res=(Int)LITEND-dle; + } + return res; + } // decContextTestEndian + +/* ------------------------------------------------------------------ */ +/* decContextTestSavedStatus -- test bits in saved status */ +/* */ +/* oldstatus is the status word to be tested */ +/* mask indicates the bits to be tested (the oldstatus bits that */ +/* correspond to each 1 bit in the mask are tested) */ +/* returns 1 if any of the tested bits are 1, or 0 otherwise */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextTestSavedStatus(uInt oldstatus, uInt mask) { + return (oldstatus&mask)!=0; + } // decContextTestSavedStatus + +/* ------------------------------------------------------------------ */ +/* decContextTestStatus -- test bits in current status */ +/* */ +/* context is the context structure to be updated */ +/* mask indicates the bits to be tested (the status bits that */ +/* correspond to each 1 bit in the mask are tested) */ +/* returns 1 if any of the tested bits are 1, or 0 otherwise */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +uInt decContextTestStatus(decContext *context, uInt mask) { + return (context->status&mask)!=0; + } // decContextTestStatus + +/* ------------------------------------------------------------------ */ +/* decContextZeroStatus -- clear all status bits */ +/* */ +/* context is the context structure to be updated */ +/* returns context */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decContext *decContextZeroStatus(decContext *context) { + context->status=0; + return context; + } // decContextZeroStatus + diff --git a/texk/web2c/mplibdir/decContext.h b/texk/web2c/mplibdir/decContext.h index 82e4fcf2db..f5dca1d305 100644 --- a/texk/web2c/mplibdir/decContext.h +++ b/texk/web2c/mplibdir/decContext.h @@ -1,254 +1,254 @@ -/* ------------------------------------------------------------------ */ -/* Decimal Context module header */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* */ -/* Context variables must always have valid values: */ -/* */ -/* status -- [any bits may be cleared, but not set, by user] */ -/* round -- must be one of the enumerated rounding modes */ -/* */ -/* The following variables are implied for fixed size formats (i.e., */ -/* they are ignored) but should still be set correctly in case used */ -/* with decNumber functions: */ -/* */ -/* clamp -- must be either 0 or 1 */ -/* digits -- must be in the range 1 through 999999999 */ -/* emax -- must be in the range 0 through 999999999 */ -/* emin -- must be in the range 0 through -999999999 */ -/* extended -- must be either 0 or 1 [present only if DECSUBSET] */ -/* traps -- only defined bits may be set */ -/* */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECCONTEXT) - #define DECCONTEXT - #define DECCNAME "decContext" /* Short name */ - #define DECCFULLNAME "Decimal Context Descriptor" /* Verbose name */ - #define DECCAUTHOR "Mike Cowlishaw" /* Who to blame */ - - #if !defined(int32_t) - #include /* C99 standard integers */ - #endif - #include /* for printf, etc. */ - #include /* for traps */ - - /* Extended flags setting -- set this to 0 to use only IEEE flags */ - #if !defined(DECEXTFLAG) - #define DECEXTFLAG 1 /* 1=enable extended flags */ - #endif - - /* Conditional code flag -- set this to 0 for best performance */ - #if !defined(DECSUBSET) - #define DECSUBSET 0 /* 1=enable subset arithmetic */ - #endif - - /* Context for operations, with associated constants */ - enum rounding { - DEC_ROUND_CEILING, /* round towards +infinity */ - DEC_ROUND_UP, /* round away from 0 */ - DEC_ROUND_HALF_UP, /* 0.5 rounds up */ - DEC_ROUND_HALF_EVEN, /* 0.5 rounds to nearest even */ - DEC_ROUND_HALF_DOWN, /* 0.5 rounds down */ - DEC_ROUND_DOWN, /* round towards 0 (truncate) */ - DEC_ROUND_FLOOR, /* round towards -infinity */ - DEC_ROUND_05UP, /* round for reround */ - DEC_ROUND_MAX /* enum must be less than this */ - }; - #define DEC_ROUND_DEFAULT DEC_ROUND_HALF_EVEN; - - typedef struct { - int32_t digits; /* working precision */ - int32_t emax; /* maximum positive exponent */ - int32_t emin; /* minimum negative exponent */ - enum rounding round; /* rounding mode */ - uint32_t traps; /* trap-enabler flags */ - uint32_t status; /* status flags */ - uint8_t clamp; /* flag: apply IEEE exponent clamp */ - #if DECSUBSET - uint8_t extended; /* flag: special-values allowed */ - #endif - } decContext; - - /* Maxima and Minima for context settings */ - #define DEC_MAX_DIGITS 999999999 - #define DEC_MIN_DIGITS 1 - #define DEC_MAX_EMAX 999999999 - #define DEC_MIN_EMAX 0 - #define DEC_MAX_EMIN 0 - #define DEC_MIN_EMIN -999999999 - #define DEC_MAX_MATH 999999 /* max emax, etc., for math funcs. */ - - /* Classifications for decimal numbers, aligned with 754 (note that */ - /* 'normal' and 'subnormal' are meaningful only with a decContext */ - /* or a fixed size format). */ - enum decClass { - DEC_CLASS_SNAN, - DEC_CLASS_QNAN, - DEC_CLASS_NEG_INF, - DEC_CLASS_NEG_NORMAL, - DEC_CLASS_NEG_SUBNORMAL, - DEC_CLASS_NEG_ZERO, - DEC_CLASS_POS_ZERO, - DEC_CLASS_POS_SUBNORMAL, - DEC_CLASS_POS_NORMAL, - DEC_CLASS_POS_INF - }; - /* Strings for the decClasses */ - #define DEC_ClassString_SN "sNaN" - #define DEC_ClassString_QN "NaN" - #define DEC_ClassString_NI "-Infinity" - #define DEC_ClassString_NN "-Normal" - #define DEC_ClassString_NS "-Subnormal" - #define DEC_ClassString_NZ "-Zero" - #define DEC_ClassString_PZ "+Zero" - #define DEC_ClassString_PS "+Subnormal" - #define DEC_ClassString_PN "+Normal" - #define DEC_ClassString_PI "+Infinity" - #define DEC_ClassString_UN "Invalid" - - /* Trap-enabler and Status flags (exceptional conditions), and */ - /* their names. The top byte is reserved for internal use */ - #if DECEXTFLAG - /* Extended flags */ - #define DEC_Conversion_syntax 0x00000001 - #define DEC_Division_by_zero 0x00000002 - #define DEC_Division_impossible 0x00000004 - #define DEC_Division_undefined 0x00000008 - #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ - #define DEC_Inexact 0x00000020 - #define DEC_Invalid_context 0x00000040 - #define DEC_Invalid_operation 0x00000080 - #if DECSUBSET - #define DEC_Lost_digits 0x00000100 - #endif - #define DEC_Overflow 0x00000200 - #define DEC_Clamped 0x00000400 - #define DEC_Rounded 0x00000800 - #define DEC_Subnormal 0x00001000 - #define DEC_Underflow 0x00002000 - #else - /* IEEE flags only */ - #define DEC_Conversion_syntax 0x00000010 - #define DEC_Division_by_zero 0x00000002 - #define DEC_Division_impossible 0x00000010 - #define DEC_Division_undefined 0x00000010 - #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ - #define DEC_Inexact 0x00000001 - #define DEC_Invalid_context 0x00000010 - #define DEC_Invalid_operation 0x00000010 - #if DECSUBSET - #define DEC_Lost_digits 0x00000000 - #endif - #define DEC_Overflow 0x00000008 - #define DEC_Clamped 0x00000000 - #define DEC_Rounded 0x00000000 - #define DEC_Subnormal 0x00000000 - #define DEC_Underflow 0x00000004 - #endif - - /* IEEE 754 groupings for the flags */ - /* [DEC_Clamped, DEC_Lost_digits, DEC_Rounded, and DEC_Subnormal */ - /* are not in IEEE 754] */ - #define DEC_IEEE_754_Division_by_zero (DEC_Division_by_zero) - #if DECSUBSET - #define DEC_IEEE_754_Inexact (DEC_Inexact | DEC_Lost_digits) - #else - #define DEC_IEEE_754_Inexact (DEC_Inexact) - #endif - #define DEC_IEEE_754_Invalid_operation (DEC_Conversion_syntax | \ - DEC_Division_impossible | \ - DEC_Division_undefined | \ - DEC_Insufficient_storage | \ - DEC_Invalid_context | \ - DEC_Invalid_operation) - #define DEC_IEEE_754_Overflow (DEC_Overflow) - #define DEC_IEEE_754_Underflow (DEC_Underflow) - - /* flags which are normally errors (result is qNaN, infinite, or 0) */ - #define DEC_Errors (DEC_IEEE_754_Division_by_zero | \ - DEC_IEEE_754_Invalid_operation | \ - DEC_IEEE_754_Overflow | DEC_IEEE_754_Underflow) - /* flags which cause a result to become qNaN */ - #define DEC_NaNs DEC_IEEE_754_Invalid_operation - - /* flags which are normally for information only (finite results) */ - #if DECSUBSET - #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact \ - | DEC_Lost_digits) - #else - #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact) - #endif - - /* IEEE 854 names (for compatibility with older decNumber versions) */ - #define DEC_IEEE_854_Division_by_zero DEC_IEEE_754_Division_by_zero - #define DEC_IEEE_854_Inexact DEC_IEEE_754_Inexact - #define DEC_IEEE_854_Invalid_operation DEC_IEEE_754_Invalid_operation - #define DEC_IEEE_854_Overflow DEC_IEEE_754_Overflow - #define DEC_IEEE_854_Underflow DEC_IEEE_754_Underflow - - /* Name strings for the exceptional conditions */ - #define DEC_Condition_CS "Conversion syntax" - #define DEC_Condition_DZ "Division by zero" - #define DEC_Condition_DI "Division impossible" - #define DEC_Condition_DU "Division undefined" - #define DEC_Condition_IE "Inexact" - #define DEC_Condition_IS "Insufficient storage" - #define DEC_Condition_IC "Invalid context" - #define DEC_Condition_IO "Invalid operation" - #if DECSUBSET - #define DEC_Condition_LD "Lost digits" - #endif - #define DEC_Condition_OV "Overflow" - #define DEC_Condition_PA "Clamped" - #define DEC_Condition_RO "Rounded" - #define DEC_Condition_SU "Subnormal" - #define DEC_Condition_UN "Underflow" - #define DEC_Condition_ZE "No status" - #define DEC_Condition_MU "Multiple status" - #define DEC_Condition_Length 21 /* length of the longest string, */ - /* including terminator */ - - /* Initialization descriptors, used by decContextDefault */ - #define DEC_INIT_BASE 0 - #define DEC_INIT_DECIMAL32 32 - #define DEC_INIT_DECIMAL64 64 - #define DEC_INIT_DECIMAL128 128 - /* Synonyms */ - #define DEC_INIT_DECSINGLE DEC_INIT_DECIMAL32 - #define DEC_INIT_DECDOUBLE DEC_INIT_DECIMAL64 - #define DEC_INIT_DECQUAD DEC_INIT_DECIMAL128 - - /* decContext routines */ - extern decContext * decContextClearStatus(decContext *, uint32_t); - extern decContext * decContextDefault(decContext *, int32_t); - extern enum rounding decContextGetRounding(decContext *); - extern uint32_t decContextGetStatus(decContext *); - extern decContext * decContextRestoreStatus(decContext *, uint32_t, uint32_t); - extern uint32_t decContextSaveStatus(decContext *, uint32_t); - extern decContext * decContextSetRounding(decContext *, enum rounding); - extern decContext * decContextSetStatus(decContext *, uint32_t); - extern decContext * decContextSetStatusFromString(decContext *, const char *); - extern decContext * decContextSetStatusFromStringQuiet(decContext *, const char *); - extern decContext * decContextSetStatusQuiet(decContext *, uint32_t); - extern const char * decContextStatusToString(const decContext *); - extern int32_t decContextTestEndian(uint8_t); - extern uint32_t decContextTestSavedStatus(uint32_t, uint32_t); - extern uint32_t decContextTestStatus(decContext *, uint32_t); - extern decContext * decContextZeroStatus(decContext *); - -#endif +/* ------------------------------------------------------------------ */ +/* Decimal Context module header */ +/* ------------------------------------------------------------------ */ +/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ +/* */ +/* This software is made available under the terms of the */ +/* ICU License -- ICU 1.8.1 and later. */ +/* */ +/* The description and User's Guide ("The decNumber C Library") for */ +/* this software is called decNumber.pdf. This document is */ +/* available, together with arithmetic and format specifications, */ +/* testcases, and Web links, on the General Decimal Arithmetic page. */ +/* */ +/* Please send comments, suggestions, and corrections to the author: */ +/* mfc@uk.ibm.com */ +/* Mike Cowlishaw, IBM Fellow */ +/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ +/* ------------------------------------------------------------------ */ +/* */ +/* Context variables must always have valid values: */ +/* */ +/* status -- [any bits may be cleared, but not set, by user] */ +/* round -- must be one of the enumerated rounding modes */ +/* */ +/* The following variables are implied for fixed size formats (i.e., */ +/* they are ignored) but should still be set correctly in case used */ +/* with decNumber functions: */ +/* */ +/* clamp -- must be either 0 or 1 */ +/* digits -- must be in the range 1 through 999999999 */ +/* emax -- must be in the range 0 through 999999999 */ +/* emin -- must be in the range 0 through -999999999 */ +/* extended -- must be either 0 or 1 [present only if DECSUBSET] */ +/* traps -- only defined bits may be set */ +/* */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECCONTEXT) + #define DECCONTEXT + #define DECCNAME "decContext" /* Short name */ + #define DECCFULLNAME "Decimal Context Descriptor" /* Verbose name */ + #define DECCAUTHOR "Mike Cowlishaw" /* Who to blame */ + + #if !defined(int32_t) + #include /* C99 standard integers */ + #endif + #include /* for printf, etc. */ + #include /* for traps */ + + /* Extended flags setting -- set this to 0 to use only IEEE flags */ + #if !defined(DECEXTFLAG) + #define DECEXTFLAG 1 /* 1=enable extended flags */ + #endif + + /* Conditional code flag -- set this to 0 for best performance */ + #if !defined(DECSUBSET) + #define DECSUBSET 0 /* 1=enable subset arithmetic */ + #endif + + /* Context for operations, with associated constants */ + enum rounding { + DEC_ROUND_CEILING, /* round towards +infinity */ + DEC_ROUND_UP, /* round away from 0 */ + DEC_ROUND_HALF_UP, /* 0.5 rounds up */ + DEC_ROUND_HALF_EVEN, /* 0.5 rounds to nearest even */ + DEC_ROUND_HALF_DOWN, /* 0.5 rounds down */ + DEC_ROUND_DOWN, /* round towards 0 (truncate) */ + DEC_ROUND_FLOOR, /* round towards -infinity */ + DEC_ROUND_05UP, /* round for reround */ + DEC_ROUND_MAX /* enum must be less than this */ + }; + #define DEC_ROUND_DEFAULT DEC_ROUND_HALF_EVEN; + + typedef struct { + int32_t digits; /* working precision */ + int32_t emax; /* maximum positive exponent */ + int32_t emin; /* minimum negative exponent */ + enum rounding round; /* rounding mode */ + uint32_t traps; /* trap-enabler flags */ + uint32_t status; /* status flags */ + uint8_t clamp; /* flag: apply IEEE exponent clamp */ + #if DECSUBSET + uint8_t extended; /* flag: special-values allowed */ + #endif + } decContext; + + /* Maxima and Minima for context settings */ + #define DEC_MAX_DIGITS 999999999 + #define DEC_MIN_DIGITS 1 + #define DEC_MAX_EMAX 999999999 + #define DEC_MIN_EMAX 0 + #define DEC_MAX_EMIN 0 + #define DEC_MIN_EMIN -999999999 + #define DEC_MAX_MATH 999999 /* max emax, etc., for math funcs. */ + + /* Classifications for decimal numbers, aligned with 754 (note that */ + /* 'normal' and 'subnormal' are meaningful only with a decContext */ + /* or a fixed size format). */ + enum decClass { + DEC_CLASS_SNAN, + DEC_CLASS_QNAN, + DEC_CLASS_NEG_INF, + DEC_CLASS_NEG_NORMAL, + DEC_CLASS_NEG_SUBNORMAL, + DEC_CLASS_NEG_ZERO, + DEC_CLASS_POS_ZERO, + DEC_CLASS_POS_SUBNORMAL, + DEC_CLASS_POS_NORMAL, + DEC_CLASS_POS_INF + }; + /* Strings for the decClasses */ + #define DEC_ClassString_SN "sNaN" + #define DEC_ClassString_QN "NaN" + #define DEC_ClassString_NI "-Infinity" + #define DEC_ClassString_NN "-Normal" + #define DEC_ClassString_NS "-Subnormal" + #define DEC_ClassString_NZ "-Zero" + #define DEC_ClassString_PZ "+Zero" + #define DEC_ClassString_PS "+Subnormal" + #define DEC_ClassString_PN "+Normal" + #define DEC_ClassString_PI "+Infinity" + #define DEC_ClassString_UN "Invalid" + + /* Trap-enabler and Status flags (exceptional conditions), and */ + /* their names. The top byte is reserved for internal use */ + #if DECEXTFLAG + /* Extended flags */ + #define DEC_Conversion_syntax 0x00000001 + #define DEC_Division_by_zero 0x00000002 + #define DEC_Division_impossible 0x00000004 + #define DEC_Division_undefined 0x00000008 + #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ + #define DEC_Inexact 0x00000020 + #define DEC_Invalid_context 0x00000040 + #define DEC_Invalid_operation 0x00000080 + #if DECSUBSET + #define DEC_Lost_digits 0x00000100 + #endif + #define DEC_Overflow 0x00000200 + #define DEC_Clamped 0x00000400 + #define DEC_Rounded 0x00000800 + #define DEC_Subnormal 0x00001000 + #define DEC_Underflow 0x00002000 + #else + /* IEEE flags only */ + #define DEC_Conversion_syntax 0x00000010 + #define DEC_Division_by_zero 0x00000002 + #define DEC_Division_impossible 0x00000010 + #define DEC_Division_undefined 0x00000010 + #define DEC_Insufficient_storage 0x00000010 /* [when malloc fails] */ + #define DEC_Inexact 0x00000001 + #define DEC_Invalid_context 0x00000010 + #define DEC_Invalid_operation 0x00000010 + #if DECSUBSET + #define DEC_Lost_digits 0x00000000 + #endif + #define DEC_Overflow 0x00000008 + #define DEC_Clamped 0x00000000 + #define DEC_Rounded 0x00000000 + #define DEC_Subnormal 0x00000000 + #define DEC_Underflow 0x00000004 + #endif + + /* IEEE 754 groupings for the flags */ + /* [DEC_Clamped, DEC_Lost_digits, DEC_Rounded, and DEC_Subnormal */ + /* are not in IEEE 754] */ + #define DEC_IEEE_754_Division_by_zero (DEC_Division_by_zero) + #if DECSUBSET + #define DEC_IEEE_754_Inexact (DEC_Inexact | DEC_Lost_digits) + #else + #define DEC_IEEE_754_Inexact (DEC_Inexact) + #endif + #define DEC_IEEE_754_Invalid_operation (DEC_Conversion_syntax | \ + DEC_Division_impossible | \ + DEC_Division_undefined | \ + DEC_Insufficient_storage | \ + DEC_Invalid_context | \ + DEC_Invalid_operation) + #define DEC_IEEE_754_Overflow (DEC_Overflow) + #define DEC_IEEE_754_Underflow (DEC_Underflow) + + /* flags which are normally errors (result is qNaN, infinite, or 0) */ + #define DEC_Errors (DEC_IEEE_754_Division_by_zero | \ + DEC_IEEE_754_Invalid_operation | \ + DEC_IEEE_754_Overflow | DEC_IEEE_754_Underflow) + /* flags which cause a result to become qNaN */ + #define DEC_NaNs DEC_IEEE_754_Invalid_operation + + /* flags which are normally for information only (finite results) */ + #if DECSUBSET + #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact \ + | DEC_Lost_digits) + #else + #define DEC_Information (DEC_Clamped | DEC_Rounded | DEC_Inexact) + #endif + + /* IEEE 854 names (for compatibility with older decNumber versions) */ + #define DEC_IEEE_854_Division_by_zero DEC_IEEE_754_Division_by_zero + #define DEC_IEEE_854_Inexact DEC_IEEE_754_Inexact + #define DEC_IEEE_854_Invalid_operation DEC_IEEE_754_Invalid_operation + #define DEC_IEEE_854_Overflow DEC_IEEE_754_Overflow + #define DEC_IEEE_854_Underflow DEC_IEEE_754_Underflow + + /* Name strings for the exceptional conditions */ + #define DEC_Condition_CS "Conversion syntax" + #define DEC_Condition_DZ "Division by zero" + #define DEC_Condition_DI "Division impossible" + #define DEC_Condition_DU "Division undefined" + #define DEC_Condition_IE "Inexact" + #define DEC_Condition_IS "Insufficient storage" + #define DEC_Condition_IC "Invalid context" + #define DEC_Condition_IO "Invalid operation" + #if DECSUBSET + #define DEC_Condition_LD "Lost digits" + #endif + #define DEC_Condition_OV "Overflow" + #define DEC_Condition_PA "Clamped" + #define DEC_Condition_RO "Rounded" + #define DEC_Condition_SU "Subnormal" + #define DEC_Condition_UN "Underflow" + #define DEC_Condition_ZE "No status" + #define DEC_Condition_MU "Multiple status" + #define DEC_Condition_Length 21 /* length of the longest string, */ + /* including terminator */ + + /* Initialization descriptors, used by decContextDefault */ + #define DEC_INIT_BASE 0 + #define DEC_INIT_DECIMAL32 32 + #define DEC_INIT_DECIMAL64 64 + #define DEC_INIT_DECIMAL128 128 + /* Synonyms */ + #define DEC_INIT_DECSINGLE DEC_INIT_DECIMAL32 + #define DEC_INIT_DECDOUBLE DEC_INIT_DECIMAL64 + #define DEC_INIT_DECQUAD DEC_INIT_DECIMAL128 + + /* decContext routines */ + extern decContext * decContextClearStatus(decContext *, uint32_t); + extern decContext * decContextDefault(decContext *, int32_t); + extern enum rounding decContextGetRounding(decContext *); + extern uint32_t decContextGetStatus(decContext *); + extern decContext * decContextRestoreStatus(decContext *, uint32_t, uint32_t); + extern uint32_t decContextSaveStatus(decContext *, uint32_t); + extern decContext * decContextSetRounding(decContext *, enum rounding); + extern decContext * decContextSetStatus(decContext *, uint32_t); + extern decContext * decContextSetStatusFromString(decContext *, const char *); + extern decContext * decContextSetStatusFromStringQuiet(decContext *, const char *); + extern decContext * decContextSetStatusQuiet(decContext *, uint32_t); + extern const char * decContextStatusToString(const decContext *); + extern int32_t decContextTestEndian(uint8_t); + extern uint32_t decContextTestSavedStatus(uint32_t, uint32_t); + extern uint32_t decContextTestStatus(decContext *, uint32_t); + extern decContext * decContextZeroStatus(decContext *); + +#endif diff --git a/texk/web2c/mplibdir/decNumber.c b/texk/web2c/mplibdir/decNumber.c index 19230b8957..2572fac5b1 100644 --- a/texk/web2c/mplibdir/decNumber.c +++ b/texk/web2c/mplibdir/decNumber.c @@ -1,8141 +1,8141 @@ -/* ------------------------------------------------------------------ */ -/* Decimal Number arithmetic module */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This module comprises the routines for arbitrary-precision General */ -/* Decimal Arithmetic as defined in the specification which may be */ -/* found on the General Decimal Arithmetic pages. It implements both */ -/* the full ('extended') arithmetic and the simpler ('subset') */ -/* arithmetic. */ -/* */ -/* Usage notes: */ -/* */ -/* 1. This code is ANSI C89 except: */ -/* */ -/* a) C99 line comments (double forward slash) are used. (Most C */ -/* compilers accept these. If yours does not, a simple script */ -/* can be used to convert them to ANSI C comments.) */ -/* */ -/* b) Types from C99 stdint.h are used. If you do not have this */ -/* header file, see the User's Guide section of the decNumber */ -/* documentation; this lists the necessary definitions. */ -/* */ -/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */ -/* uint64_t types may be used. To avoid these, set DECUSE64=0 */ -/* and DECDPUN<=4 (see documentation). */ -/* */ -/* The code also conforms to C99 restrictions; in particular, */ -/* strict aliasing rules are observed. */ -/* */ -/* 2. The decNumber format which this library uses is optimized for */ -/* efficient processing of relatively short numbers; in particular */ -/* it allows the use of fixed sized structures and minimizes copy */ -/* and move operations. It does, however, support arbitrary */ -/* precision (up to 999,999,999 digits) and arbitrary exponent */ -/* range (Emax in the range 0 through 999,999,999 and Emin in the */ -/* range -999,999,999 through 0). Mathematical functions (for */ -/* example decNumberExp) as identified below are restricted more */ -/* tightly: digits, emax, and -emin in the context must be <= */ -/* DEC_MAX_MATH (999999), and their operand(s) must be within */ -/* these bounds. */ -/* */ -/* 3. Logical functions are further restricted; their operands must */ -/* be finite, positive, have an exponent of zero, and all digits */ -/* must be either 0 or 1. The result will only contain digits */ -/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ -/* */ -/* 4. Operands to operator functions are never modified unless they */ -/* are also specified to be the result number (which is always */ -/* permitted). Other than that case, operands must not overlap. */ -/* */ -/* 5. Error handling: the type of the error is ORed into the status */ -/* flags in the current context (decContext structure). The */ -/* SIGFPE signal is then raised if the corresponding trap-enabler */ -/* flag in the decContext is set (is 1). */ -/* */ -/* It is the responsibility of the caller to clear the status */ -/* flags as required. */ -/* */ -/* The result of any routine which returns a number will always */ -/* be a valid number (which may be a special value, such as an */ -/* Infinity or NaN). */ -/* */ -/* 6. The decNumber format is not an exchangeable concrete */ -/* representation as it comprises fields which may be machine- */ -/* dependent (packed or unpacked, or special length, for example). */ -/* Canonical conversions to and from strings are provided; other */ -/* conversions are available in separate modules. */ -/* */ -/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ -/* to 1 for extended operand checking (including NULL operands). */ -/* Results are undefined if a badly-formed structure (or a NULL */ -/* pointer to a structure) is provided, though with DECCHECK */ -/* enabled the operator routines are protected against exceptions. */ -/* (Except if the result pointer is NULL, which is unrecoverable.) */ -/* */ -/* However, the routines will never cause exceptions if they are */ -/* given well-formed operands, even if the value of the operands */ -/* is inappropriate for the operation and DECCHECK is not set. */ -/* (Except for SIGFPE, as and where documented.) */ -/* */ -/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ -/* ------------------------------------------------------------------ */ -/* Implementation notes for maintenance of this module: */ -/* */ -/* 1. Storage leak protection: Routines which use malloc are not */ -/* permitted to use return for fastpath or error exits (i.e., */ -/* they follow strict structured programming conventions). */ -/* Instead they have a do{}while(0); construct surrounding the */ -/* code which is protected -- break may be used to exit this. */ -/* Other routines can safely use the return statement inline. */ -/* */ -/* Storage leak accounting can be enabled using DECALLOC. */ -/* */ -/* 2. All loops use the for(;;) construct. Any do construct does */ -/* not loop; it is for allocation protection as just described. */ -/* */ -/* 3. Setting status in the context must always be the very last */ -/* action in a routine, as non-0 status may raise a trap and hence */ -/* the call to set status may not return (if the handler uses long */ -/* jump). Therefore all cleanup must be done first. In general, */ -/* to achieve this status is accumulated and is only applied just */ -/* before return by calling decContextSetStatus (via decStatus). */ -/* */ -/* Routines which allocate storage cannot, in general, use the */ -/* 'top level' routines which could cause a non-returning */ -/* transfer of control. The decXxxxOp routines are safe (do not */ -/* call decStatus even if traps are set in the context) and should */ -/* be used instead (they are also a little faster). */ -/* */ -/* 4. Exponent checking is minimized by allowing the exponent to */ -/* grow outside its limits during calculations, provided that */ -/* the decFinalize function is called later. Multiplication and */ -/* division, and intermediate calculations in exponentiation, */ -/* require more careful checks because of the risk of 31-bit */ -/* overflow (the most negative valid exponent is -1999999997, for */ -/* a 999999999-digit number with adjusted exponent of -999999999). */ -/* */ -/* 5. Rounding is deferred until finalization of results, with any */ -/* 'off to the right' data being represented as a single digit */ -/* residue (in the range -1 through 9). This avoids any double- */ -/* rounding when more than one shortening takes place (for */ -/* example, when a result is subnormal). */ -/* */ -/* 6. The digits count is allowed to rise to a multiple of DECDPUN */ -/* during many operations, so whole Units are handled and exact */ -/* accounting of digits is not needed. The correct digits value */ -/* is found by decGetDigits, which accounts for leading zeros. */ -/* This must be called before any rounding if the number of digits */ -/* is not known exactly. */ -/* */ -/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ -/* numbers up to four digits, using appropriate constants. This */ -/* is not useful for longer numbers because overflow of 32 bits */ -/* would lead to 4 multiplies, which is almost as expensive as */ -/* a divide (unless a floating-point or 64-bit multiply is */ -/* assumed to be available). */ -/* */ -/* 8. Unusual abbreviations that may be used in the commentary: */ -/* lhs -- left hand side (operand, of an operation) */ -/* lsd -- least significant digit (of coefficient) */ -/* lsu -- least significant Unit (of coefficient) */ -/* msd -- most significant digit (of coefficient) */ -/* msi -- most significant item (in an array) */ -/* msu -- most significant Unit (of coefficient) */ -/* rhs -- right hand side (operand, of an operation) */ -/* +ve -- positive */ -/* -ve -- negative */ -/* ** -- raise to the power */ -/* ------------------------------------------------------------------ */ - -#include // for malloc, free, etc. -#include // for printf [if needed] -#include // for strcpy -#include // for lower -#include "decNumber.h" // base number library -#include "decNumberLocal.h" // decNumber local types, etc. - -/* Constants */ -// Public lookup table used by the D2U macro -const uByte d2utable[DECMAXD2U+1]=D2UTABLE; - -#define DECVERB 1 // set to 1 for verbose DECCHECK -#define powers DECPOWERS // old internal name - -// Local constants -#define DIVIDE 0x80 // Divide operators -#define REMAINDER 0x40 // .. -#define DIVIDEINT 0x20 // .. -#define REMNEAR 0x10 // .. -#define COMPARE 0x01 // Compare operators -#define COMPMAX 0x02 // .. -#define COMPMIN 0x03 // .. -#define COMPTOTAL 0x04 // .. -#define COMPNAN 0x05 // .. [NaN processing] -#define COMPSIG 0x06 // .. [signaling COMPARE] -#define COMPMAXMAG 0x07 // .. -#define COMPMINMAG 0x08 // .. - -#define DEC_sNaN 0x40000000 // local status: sNaN signal -#define BADINT (Int)0x80000000 // most-negative Int; error indicator -// Next two indicate an integer >= 10**6, and its parity (bottom bit) -#define BIGEVEN (Int)0x80000002 -#define BIGODD (Int)0x80000003 - -static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing - -/* Granularity-dependent code */ -#if DECDPUN<=4 - #define eInt Int // extended integer - #define ueInt uInt // unsigned extended integer - // Constant multipliers for divide-by-power-of five using reciprocal - // multiply, after removing powers of 2 by shifting, and final shift - // of 17 [we only need up to **4] - static const uInt multies[]={131073, 26215, 5243, 1049, 210}; - // QUOT10 -- macro to return the quotient of unit u divided by 10**n - #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) -#else - // For DECDPUN>4 non-ANSI-89 64-bit types are needed. - #if !DECUSE64 - #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 - #endif - #define eInt Long // extended integer - #define ueInt uLong // unsigned extended integer -#endif - -/* Local routines */ -static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, - decContext *, uByte, uInt *); -static Flag decBiStr(const char *, const char *, const char *); -static uInt decCheckMath(const decNumber *, decContext *, uInt *); -static void decApplyRound(decNumber *, decContext *, Int, uInt *); -static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); -static decNumber * decCompareOp(decNumber *, const decNumber *, - const decNumber *, decContext *, - Flag, uInt *); -static void decCopyFit(decNumber *, const decNumber *, decContext *, - Int *, uInt *); -static decNumber * decDecap(decNumber *, Int); -static decNumber * decDivideOp(decNumber *, const decNumber *, - const decNumber *, decContext *, Flag, uInt *); -static decNumber * decExpOp(decNumber *, const decNumber *, - decContext *, uInt *); -static void decFinalize(decNumber *, decContext *, Int *, uInt *); -static Int decGetDigits(Unit *, Int); -static Int decGetInt(const decNumber *); -static decNumber * decLnOp(decNumber *, const decNumber *, - decContext *, uInt *); -static decNumber * decMultiplyOp(decNumber *, const decNumber *, - const decNumber *, decContext *, - uInt *); -static decNumber * decNaNs(decNumber *, const decNumber *, - const decNumber *, decContext *, uInt *); -static decNumber * decQuantizeOp(decNumber *, const decNumber *, - const decNumber *, decContext *, Flag, - uInt *); -static void decReverse(Unit *, Unit *); -static void decSetCoeff(decNumber *, decContext *, const Unit *, - Int, Int *, uInt *); -static void decSetMaxValue(decNumber *, decContext *); -static void decSetOverflow(decNumber *, decContext *, uInt *); -static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); -static Int decShiftToLeast(Unit *, Int, Int); -static Int decShiftToMost(Unit *, Int, Int); -static void decStatus(decNumber *, uInt, decContext *); -static void decToString(const decNumber *, char[], Flag); -static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); -static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, - Unit *, Int); -static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); - -#if !DECSUBSET -/* decFinish == decFinalize when no subset arithmetic needed */ -#define decFinish(a,b,c,d) decFinalize(a,b,c,d) -#else -static void decFinish(decNumber *, decContext *, Int *, uInt *); -static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); -#endif - -/* Local macros */ -// masked special-values bits -#define SPECIALARG (rhs->bits & DECSPECIAL) -#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) - -/* Diagnostic macros, etc. */ -#if DECALLOC -// Handle malloc/free accounting. If enabled, our accountable routines -// are used; otherwise the code just goes straight to the system malloc -// and free routines. -#define malloc(a) decMalloc(a) -#define free(a) decFree(a) -#define DECFENCE 0x5a // corruption detector -// 'Our' malloc and free: -static void *decMalloc(size_t); -static void decFree(void *); -uInt decAllocBytes=0; // count of bytes allocated -// Note that DECALLOC code only checks for storage buffer overflow. -// To check for memory leaks, the decAllocBytes variable must be -// checked to be 0 at appropriate times (e.g., after the test -// harness completes a set of tests). This checking may be unreliable -// if the testing is done in a multi-thread environment. -#endif - -#if DECCHECK -// Optional checking routines. Enabling these means that decNumber -// and decContext operands to operator routines are checked for -// correctness. This roughly doubles the execution time of the -// fastest routines (and adds 600+ bytes), so should not normally be -// used in 'production'. -// decCheckInexact is used to check that inexact results have a full -// complement of digits (where appropriate -- this is not the case -// for Quantize, for example) -#define DECUNRESU ((decNumber *)(void *)0xffffffff) -#define DECUNUSED ((const decNumber *)(void *)0xffffffff) -#define DECUNCONT ((decContext *)(void *)(0xffffffff)) -static Flag decCheckOperands(decNumber *, const decNumber *, - const decNumber *, decContext *); -static Flag decCheckNumber(const decNumber *); -static void decCheckInexact(const decNumber *, decContext *); -#endif - -#if DECTRACE || DECCHECK -// Optional trace/debugging routines (may or may not be used) -void decNumberShow(const decNumber *); // displays the components of a number -static void decDumpAr(char, const Unit *, Int); -#endif - -/* ================================================================== */ -/* Conversions */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* from-int32 -- conversion from Int or uInt */ -/* */ -/* dn is the decNumber to receive the integer */ -/* in or uin is the integer to be converted */ -/* returns dn */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberFromInt32(decNumber *dn, Int in) { - uInt unsig; - if (in>=0) unsig=in; - else { // negative (possibly BADINT) - if (in==BADINT) unsig=(uInt)1073741824*2; // special case - else unsig=-in; // invert - } - // in is now positive - decNumberFromUInt32(dn, unsig); - if (in<0) dn->bits=DECNEG; // sign needed - return dn; - } // decNumberFromInt32 - -decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { - Unit *up; // work pointer - decNumberZero(dn); // clean - if (uin==0) return dn; // [or decGetDigits bad call] - for (up=dn->lsu; uin>0; up++) { - *up=(Unit)(uin%(DECDPUNMAX+1)); - uin=uin/(DECDPUNMAX+1); - } - dn->digits=decGetDigits(dn->lsu, up-dn->lsu); - return dn; - } // decNumberFromUInt32 - -/* ------------------------------------------------------------------ */ -/* to-int32 -- conversion to Int or uInt */ -/* */ -/* dn is the decNumber to convert */ -/* set is the context for reporting errors */ -/* returns the converted decNumber, or 0 if Invalid is set */ -/* */ -/* Invalid is set if the decNumber does not have exponent==0 or if */ -/* it is a NaN, Infinite, or out-of-range. */ -/* ------------------------------------------------------------------ */ -Int decNumberToInt32(const decNumber *dn, decContext *set) { - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; - #endif - - // special or too many digits, or bad exponent - if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad - else { // is a finite integer with 10 or fewer digits - Int d; // work - const Unit *up; // .. - uInt hi=0, lo; // .. - up=dn->lsu; // -> lsu - lo=*up; // get 1 to 9 digits - #if DECDPUN>1 // split to higher - hi=lo/10; - lo=lo%10; - #endif - up++; - // collect remaining Units, if any, into hi - for (d=DECDPUN; ddigits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; - // now low has the lsd, hi the remainder - if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range? - // most-negative is a reprieve - if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; - // bad -- drop through - } - else { // in-range always - Int i=X10(hi)+lo; - if (dn->bits&DECNEG) return -i; - return i; - } - } // integer - decContextSetStatus(set, DEC_Invalid_operation); // [may not return] - return 0; - } // decNumberToInt32 - -uInt decNumberToUInt32(const decNumber *dn, decContext *set) { - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; - #endif - // special or too many digits, or bad exponent, or negative (<0) - if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 - || (dn->bits&DECNEG && !ISZERO(dn))); // bad - else { // is a finite integer with 10 or fewer digits - Int d; // work - const Unit *up; // .. - uInt hi=0, lo; // .. - up=dn->lsu; // -> lsu - lo=*up; // get 1 to 9 digits - #if DECDPUN>1 // split to higher - hi=lo/10; - lo=lo%10; - #endif - up++; - // collect remaining Units, if any, into hi - for (d=DECDPUN; ddigits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; - - // now low has the lsd, hi the remainder - if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible - else return X10(hi)+lo; - } // integer - decContextSetStatus(set, DEC_Invalid_operation); // [may not return] - return 0; - } // decNumberToUInt32 - -/* ------------------------------------------------------------------ */ -/* to-scientific-string -- conversion to numeric string */ -/* to-engineering-string -- conversion to numeric string */ -/* */ -/* decNumberToString(dn, string); */ -/* decNumberToEngString(dn, string); */ -/* */ -/* dn is the decNumber to convert */ -/* string is the string where the result will be laid out */ -/* */ -/* string must be at least dn->digits+14 characters long */ -/* */ -/* No error is possible, and no status can be set. */ -/* ------------------------------------------------------------------ */ -char * decNumberToString(const decNumber *dn, char *string){ - decToString(dn, string, 0); - return string; - } // DecNumberToString - -char * decNumberToEngString(const decNumber *dn, char *string){ - decToString(dn, string, 1); - return string; - } // DecNumberToEngString - -/* ------------------------------------------------------------------ */ -/* to-number -- conversion from numeric string */ -/* */ -/* decNumberFromString -- convert string to decNumber */ -/* dn -- the number structure to fill */ -/* chars[] -- the string to convert ('\0' terminated) */ -/* set -- the context used for processing any error, */ -/* determining the maximum precision available */ -/* (set.digits), determining the maximum and minimum */ -/* exponent (set.emax and set.emin), determining if */ -/* extended values are allowed, and checking the */ -/* rounding mode if overflow occurs or rounding is */ -/* needed. */ -/* */ -/* The length of the coefficient and the size of the exponent are */ -/* checked by this routine, so the correct error (Underflow or */ -/* Overflow) can be reported or rounding applied, as necessary. */ -/* */ -/* If bad syntax is detected, the result will be a quiet NaN. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberFromString(decNumber *dn, const char chars[], - decContext *set) { - Int exponent=0; // working exponent [assume 0] - uByte bits=0; // working flags [assume +ve] - Unit *res; // where result will be built - Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary - // [+9 allows for ln() constants] - Unit *allocres=NULL; // -> allocated result, iff allocated - Int d=0; // count of digits found in decimal part - const char *dotchar=NULL; // where dot was found - const char *cfirst=chars; // -> first character of decimal part - const char *last=NULL; // -> last digit of decimal part - const char *c; // work - Unit *up; // .. - #if DECDPUN>1 - Int cut, out; // .. - #endif - Int residue; // rounding residue - uInt status=0; // error code - - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) - return decNumberZero(dn); - #endif - - do { // status & malloc protection - for (c=chars;; c++) { // -> input character - if (*c>='0' && *c<='9') { // test for Arabic digit - last=c; - d++; // count of real digits - continue; // still in decimal part - } - if (*c=='.' && dotchar==NULL) { // first '.' - dotchar=c; // record offset into decimal part - if (c==cfirst) cfirst++; // first digit must follow - continue;} - if (c==chars) { // first in string... - if (*c=='-') { // valid - sign - cfirst++; - bits=DECNEG; - continue;} - if (*c=='+') { // valid + sign - cfirst++; - continue;} - } - // *c is not a digit, or a valid +, -, or '.' - break; - } // c - - if (last==NULL) { // no digits yet - status=DEC_Conversion_syntax;// assume the worst - if (*c=='\0') break; // and no more to come... - #if DECSUBSET - // if subset then infinities and NaNs are not allowed - if (!set->extended) break; // hopeless - #endif - // Infinities and NaNs are possible, here - if (dotchar!=NULL) break; // .. unless had a dot - decNumberZero(dn); // be optimistic - if (decBiStr(c, "infinity", "INFINITY") - || decBiStr(c, "inf", "INF")) { - dn->bits=bits | DECINF; - status=0; // is OK - break; // all done - } - // a NaN expected - // 2003.09.10 NaNs are now permitted to have a sign - dn->bits=bits | DECNAN; // assume simple NaN - if (*c=='s' || *c=='S') { // looks like an sNaN - c++; - dn->bits=bits | DECSNAN; - } - if (*c!='n' && *c!='N') break; // check caseless "NaN" - c++; - if (*c!='a' && *c!='A') break; // .. - c++; - if (*c!='n' && *c!='N') break; // .. - c++; - // now either nothing, or nnnn payload, expected - // -> start of integer and skip leading 0s [including plain 0] - for (cfirst=c; *cfirst=='0';) cfirst++; - if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s - status=0; // it's good - break; // .. - } - // something other than 0s; setup last and d as usual [no dots] - for (c=cfirst;; c++, d++) { - if (*c<'0' || *c>'9') break; // test for Arabic digit - last=c; - } - if (*c!='\0') break; // not all digits - if (d>set->digits-1) { - // [NB: payload in a decNumber can be full length unless - // clamped, in which case can only be digits-1] - if (set->clamp) break; - if (d>set->digits) break; - } // too many digits? - // good; drop through to convert the integer to coefficient - status=0; // syntax is OK - bits=dn->bits; // for copy-back - } // last==NULL - - else if (*c!='\0') { // more to process... - // had some digits; exponent is only valid sequence now - Flag nege; // 1=negative exponent - const char *firstexp; // -> first significant exponent digit - status=DEC_Conversion_syntax;// assume the worst - if (*c!='e' && *c!='E') break; - /* Found 'e' or 'E' -- now process explicit exponent */ - // 1998.07.11: sign no longer required - nege=0; - c++; // to (possible) sign - if (*c=='-') {nege=1; c++;} - else if (*c=='+') c++; - if (*c=='\0') break; - - for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros - firstexp=c; // save exponent digit place - for (; ;c++) { - if (*c<'0' || *c>'9') break; // not a digit - exponent=X10(exponent)+(Int)*c-(Int)'0'; - } // c - // if not now on a '\0', *c must not be a digit - if (*c!='\0') break; - - // (this next test must be after the syntax checks) - // if it was too long the exponent may have wrapped, so check - // carefully and set it to a certain overflow if wrap possible - if (c>=firstexp+9+1) { - if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; - // [up to 1999999999 is OK, for example 1E-1000000998] - } - if (nege) exponent=-exponent; // was negative - status=0; // is OK - } // stuff after digits - - // Here when whole string has been inspected; syntax is good - // cfirst->first digit (never dot), last->last digit (ditto) - - // strip leading zeros/dot [leave final 0 if all 0's] - if (*cfirst=='0') { // [cfirst has stepped over .] - for (c=cfirst; cextended) { - decNumberZero(dn); // clean result - break; // [could be return] - } - #endif - } // at least one leading 0 - - // Handle decimal point... - if (dotchar!=NULL && dotchardigits) res=dn->lsu; // fits into supplied decNumber - else { // rounding needed - Int needbytes=D2U(d)*sizeof(Unit);// bytes needed - res=resbuff; // assume use local buffer - if (needbytes>(Int)sizeof(resbuff)) { // too big for local - allocres=(Unit *)malloc(needbytes); - if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} - res=allocres; - } - } - // res now -> number lsu, buffer, or allocated storage for Unit array - - // Place the coefficient into the selected Unit array - // [this is often 70% of the cost of this function when DECDPUN>1] - #if DECDPUN>1 - out=0; // accumulator - up=res+D2U(d)-1; // -> msu - cut=d-(up-res)*DECDPUN; // digits in top unit - for (c=cfirst;; c++) { // along the digits - if (*c=='.') continue; // ignore '.' [don't decrement cut] - out=X10(out)+(Int)*c-(Int)'0'; - if (c==last) break; // done [never get to trailing '.'] - cut--; - if (cut>0) continue; // more for this unit - *up=(Unit)out; // write unit - up--; // prepare for unit below.. - cut=DECDPUN; // .. - out=0; // .. - } // c - *up=(Unit)out; // write lsu - - #else - // DECDPUN==1 - up=res; // -> lsu - for (c=last; c>=cfirst; c--) { // over each character, from least - if (*c=='.') continue; // ignore . [don't step up] - *up=(Unit)((Int)*c-(Int)'0'); - up++; - } // c - #endif - - dn->bits=bits; - dn->exponent=exponent; - dn->digits=d; - - // if not in number (too long) shorten into the number - if (d>set->digits) { - residue=0; - decSetCoeff(dn, set, res, d, &residue, &status); - // always check for overflow or subnormal and round as needed - decFinalize(dn, set, &residue, &status); - } - else { // no rounding, but may still have overflow or subnormal - // [these tests are just for performance; finalize repeats them] - if ((dn->exponent-1emin-dn->digits) - || (dn->exponent-1>set->emax-set->digits)) { - residue=0; - decFinalize(dn, set, &residue, &status); - } - } - // decNumberShow(dn); - } while(0); // [for break] - - if (allocres!=NULL) free(allocres); // drop any storage used - if (status!=0) decStatus(dn, status, set); - return dn; - } /* decNumberFromString */ - -/* ================================================================== */ -/* Operators */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* decNumberAbs -- absolute value operator */ -/* */ -/* This computes C = abs(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* See also decNumberCopyAbs for a quiet bitwise version of this. */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This has the same effect as decNumberPlus unless A is negative, */ -/* in which case it has the same effect as decNumberMinus. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dzero; // for 0 - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - decNumberZero(&dzero); // set 0 - dzero.exponent=rhs->exponent; // [no coefficient expansion] - decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberAbs - -/* ------------------------------------------------------------------ */ -/* decNumberAdd -- add two Numbers */ -/* */ -/* This computes C = A + B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This just calls the routine shared with Subtract */ -decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decAddOp(res, lhs, rhs, set, 0, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberAdd - -/* ------------------------------------------------------------------ */ -/* decNumberAnd -- AND two Numbers, digitwise */ -/* */ -/* This computes C = A & B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - const Unit *ua, *ub; // -> operands - const Unit *msua, *msub; // -> operand msus - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) - || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - - // operands are valid - ua=lhs->lsu; // bottom-up - ub=rhs->lsu; // .. - uc=res->lsu; // .. - msua=ua+D2U(lhs->digits)-1; // -> msu of lhs - msub=ub+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop - Unit a, b; // extract units - if (ua>msua) a=0; - else a=*ua; - if (ub>msub) b=0; - else b=*ub; - *uc=0; // can now write back - if (a|b) { // maybe 1 bits to examine - Int i, j; - *uc=0; // can now write back - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // both OK - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberAnd - -/* ------------------------------------------------------------------ */ -/* decNumberCompare -- compare two Numbers */ -/* */ -/* This computes C = A ? B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit (or NaN). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPARE, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompare - -/* ------------------------------------------------------------------ */ -/* decNumberCompareSignal -- compare, signalling on all NaNs */ -/* */ -/* This computes C = A ? B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit (or NaN). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPSIG, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompareSignal - -/* ------------------------------------------------------------------ */ -/* decNumberCompareTotal -- compare two Numbers, using total ordering */ -/* */ -/* This computes C = A ? B, under total ordering */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit; the result will always be one of */ -/* -1, 0, or 1. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompareTotal - -/* ------------------------------------------------------------------ */ -/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ -/* */ -/* This computes C = |A| ? |B|, under total ordering */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for one digit; the result will always be one of */ -/* -1, 0, or 1. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - uInt needbytes; // for space calculations - decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0 - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber bufb[D2N(DECBUFFER+1)]; - decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated - decNumber *a, *b; // temporary pointers - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - // if either is negative, take a copy and absolute - if (decNumberIsNegative(lhs)) { // lhs<0 - a=bufa; - needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - decNumberCopy(a, lhs); // copy content - a->bits&=~DECNEG; // .. and clear the sign - lhs=a; // use copy from here on - } - if (decNumberIsNegative(rhs)) { // rhs<0 - b=bufb; - needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufb)) { // need malloc space - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufb==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - b=allocbufb; // use the allocated space - } - decNumberCopy(b, rhs); // copy content - b->bits&=~DECNEG; // .. and clear the sign - rhs=b; // use copy from here on - } - decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); - } while(0); // end protected - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (allocbufb!=NULL) free(allocbufb); // .. - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberCompareTotalMag - -/* ------------------------------------------------------------------ */ -/* decNumberDivide -- divide one number by another */ -/* */ -/* This computes C = A / B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, DIVIDE, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberDivide - -/* ------------------------------------------------------------------ */ -/* decNumberDivideInteger -- divide and return integer quotient */ -/* */ -/* This computes C = A # B, where # is the integer divide operator */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberDivideInteger - -/* ------------------------------------------------------------------ */ -/* decNumberExp -- exponentiation */ -/* */ -/* This computes C = exp(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* Finite results will always be full precision and Inexact, except */ -/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ -/* */ -/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* This is a wrapper for decExpOp which can handle the slightly wider */ -/* (double) range needed by Ln (which has to be able to calculate */ -/* exp(-a) where a can be the tiniest number (Ntiny). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberExp(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0; // accumulator - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // Check restrictions; these restrictions ensure that if h=8 (see - // decExpOp) then the result will either overflow or underflow to 0. - // Other math functions restrict the input range, too, for inverses. - // If not violated then carry out the operation. - if (!decCheckMath(rhs, set, &status)) do { // protect allocation - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - decExpOp(res, rhs, set, &status); - } while(0); // end protected - - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // drop any storage used - #endif - // apply significant status - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberExp - -/* ------------------------------------------------------------------ */ -/* decNumberFMA -- fused multiply add */ -/* */ -/* This computes D = (A * B) + C with only one rounding */ -/* */ -/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ -/* lhs is A */ -/* rhs is B */ -/* fhs is C [far hand side] */ -/* set is the context */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, - const decNumber *rhs, const decNumber *fhs, - decContext *set) { - uInt status=0; // accumulator - decContext dcmul; // context for the multiplication - uInt needbytes; // for space calculations - decNumber bufa[D2N(DECBUFFER*2+1)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *acc; // accumulator pointer - decNumber dzero; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { // [undefined if subset] - status|=DEC_Invalid_operation; - break;} - #endif - // Check math restrictions [these ensure no overflow or underflow] - if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) - || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) - || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; - // set up context for multiply - dcmul=*set; - dcmul.digits=lhs->digits+rhs->digits; // just enough - // [The above may be an over-estimate for subset arithmetic, but that's OK] - dcmul.emax=DEC_MAX_EMAX; // effectively unbounded .. - dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions] - // set up decNumber space to receive the result of the multiply - acc=bufa; // may fit - needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - acc=allocbufa; // use the allocated space - } - // multiply with extended range and necessary precision - //printf("emin=%ld\n", dcmul.emin); - decMultiplyOp(acc, lhs, rhs, &dcmul, &status); - // Only Invalid operation (from sNaN or Inf * 0) is possible in - // status; if either is seen than ignore fhs (in case it is - // another sNaN) and set acc to NaN unless we had an sNaN - // [decMultiplyOp leaves that to caller] - // Note sNaN has to go through addOp to shorten payload if - // necessary - if ((status&DEC_Invalid_operation)!=0) { - if (!(status&DEC_sNaN)) { // but be true invalid - decNumberZero(res); // acc not yet set - res->bits=DECNAN; - break; - } - decNumberZero(&dzero); // make 0 (any non-NaN would do) - fhs=&dzero; // use that - } - #if DECCHECK - else { // multiply was OK - if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); - } - #endif - // add the third operand and result -> res, and all is done - decAddOp(res, acc, fhs, set, 0, &status); - } while(0); // end protected - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberFMA - -/* ------------------------------------------------------------------ */ -/* decNumberInvert -- invert a Number, digitwise */ -/* */ -/* This computes C = ~A */ -/* */ -/* res is C, the result. C may be A (e.g., X=~X) */ -/* rhs is A */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, - decContext *set) { - const Unit *ua, *msua; // -> operand and its msu - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - // operand is valid - ua=rhs->lsu; // bottom-up - uc=res->lsu; // .. - msua=ua+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, uc++) { // Unit loop - Unit a; // extract unit - Int i, j; // work - if (ua>msua) a=0; - else a=*ua; - *uc=0; // can now write back - // always need to examine all bits in rhs - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberInvert - -/* ------------------------------------------------------------------ */ -/* decNumberLn -- natural logarithm */ -/* */ -/* This computes C = ln(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Notable cases: */ -/* A<0 -> Invalid */ -/* A=0 -> -Infinity (Exact) */ -/* A=+Infinity -> +Infinity (Exact) */ -/* A=1 exactly -> 0 (Exact) */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* This is a wrapper for decLnOp which can handle the slightly wider */ -/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ -/* to calculate at p+e+2). */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberLn(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0; // accumulator - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // Check restrictions; this is a math function; if not violated - // then carry out the operation. - if (!decCheckMath(rhs, set, &status)) do { // protect allocation - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - // special check in subset for rhs=0 - if (ISZERO(rhs)) { // +/- zeros -> error - status|=DEC_Invalid_operation; - break;} - } // extended=0 - #endif - decLnOp(res, rhs, set, &status); - } while(0); // end protected - - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // drop any storage used - #endif - // apply significant status - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberLn - -/* ------------------------------------------------------------------ */ -/* decNumberLogB - get adjusted exponent, by 754 rules */ -/* */ -/* This computes C = adjustedexponent(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context, used only for digits and status */ -/* */ -/* For an unrounded result, digits may need to be 10 (A might have */ -/* 10**9 digits and an exponent of +999999999, or one digit and an */ -/* exponent of -1999999999). */ -/* */ -/* This returns the adjusted exponent of A after (in theory) padding */ -/* with zeros on the right to set->digits digits while keeping the */ -/* same value. The exponent is not limited by emin/emax. */ -/* */ -/* Notable cases: */ -/* A<0 -> Use |A| */ -/* A=0 -> -Infinity (Division by zero) */ -/* A=Infinite -> +Infinity (Exact) */ -/* A=1 exactly -> 0 (Exact) */ -/* NaNs are propagated as usual */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberLogB(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // NaNs as usual; Infinities return +Infinity; 0->oops - if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); - else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs); - else if (decNumberIsZero(rhs)) { - decNumberZero(res); // prepare for Infinity - res->bits=DECNEG|DECINF; // -Infinity - status|=DEC_Division_by_zero; // as per 754 - } - else { // finite non-zero - Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent - if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out - else { - decNumber buft[D2N(10)]; // temporary number - decNumber *t=buft; // .. - decNumberFromInt32(t, ae); // lay it out - decNumberPlus(res, t, set); // round as necessary - } - } - - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberLogB - -/* ------------------------------------------------------------------ */ -/* decNumberLog10 -- logarithm in base 10 */ -/* */ -/* This computes C = log10(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Notable cases: */ -/* A<0 -> Invalid */ -/* A=0 -> -Infinity (Exact) */ -/* A=+Infinity -> +Infinity (Exact) */ -/* A=10**n (if n is an integer) -> n (Exact) */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* This calculates ln(A)/ln(10) using appropriate precision. For */ -/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ -/* requested digits and t is the number of digits in the exponent */ -/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ -/* fastpath in decLnOp. The final division is done to the requested */ -/* precision. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberLog10(decNumber *res, const decNumber *rhs, - decContext *set) { - uInt status=0, ignore=0; // status accumulators - uInt needbytes; // for space calculations - Int p; // working precision - Int t; // digits in exponent of A - - // buffers for a and b working decimals - // (adjustment calculator, same size) - decNumber bufa[D2N(DECBUFFER+2)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *a=bufa; // temporary a - decNumber bufb[D2N(DECBUFFER+2)]; - decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated - decNumber *b=bufb; // temporary b - decNumber bufw[D2N(10)]; // working 2-10 digit number - decNumber *w=bufw; // .. - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - - decContext aset; // working context - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // Check restrictions; this is a math function; if not violated - // then carry out the operation. - if (!decCheckMath(rhs, set, &status)) do { // protect malloc - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - // special check in subset for rhs=0 - if (ISZERO(rhs)) { // +/- zeros -> error - status|=DEC_Invalid_operation; - break;} - } // extended=0 - #endif - - decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context - - // handle exact powers of 10; only check if +ve finite - if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { - Int residue=0; // (no residue) - uInt copystat=0; // clean status - - // round to a single digit... - aset.digits=1; - decCopyFit(w, rhs, &aset, &residue, ©stat); // copy & shorten - // if exact and the digit is 1, rhs is a power of 10 - if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { - // the exponent, conveniently, is the power of 10; making - // this the result needs a little care as it might not fit, - // so first convert it into the working number, and then move - // to res - decNumberFromInt32(w, w->exponent); - residue=0; - decCopyFit(res, w, set, &residue, &status); // copy & round - decFinish(res, set, &residue, &status); // cleanup/set flags - break; - } // not a power of 10 - } // not a candidate for exact - - // simplify the information-content calculation to use 'total - // number of digits in a, including exponent' as compared to the - // requested digits, as increasing this will only rarely cost an - // iteration in ln(a) anyway - t=6; // it can never be >6 - - // allocate space when needed... - p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; - needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - aset.digits=p; // as calculated - aset.emax=DEC_MAX_MATH; // usual bounds - aset.emin=-DEC_MAX_MATH; // .. - aset.clamp=0; // and no concrete format - decLnOp(a, rhs, &aset, &status); // a=ln(rhs) - - // skip the division if the result so far is infinite, NaN, or - // zero, or there was an error; note NaN from sNaN needs copy - if (status&DEC_NaNs && !(status&DEC_sNaN)) break; - if (a->bits&DECSPECIAL || ISZERO(a)) { - decNumberCopy(res, a); // [will fit] - break;} - - // for ln(10) an extra 3 digits of precision are needed - p=set->digits+3; - needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); - if (needbytes>sizeof(bufb)) { // need malloc space - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufb==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - b=allocbufb; // use the allocated space - } - decNumberZero(w); // set up 10... - #if DECDPUN==1 - w->lsu[1]=1; w->lsu[0]=0; // .. - #else - w->lsu[0]=10; // .. - #endif - w->digits=2; // .. - - aset.digits=p; - decLnOp(b, w, &aset, &ignore); // b=ln(10) - - aset.digits=set->digits; // for final divide - decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result - } while(0); // [for break] - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (allocbufb!=NULL) free(allocbufb); // .. - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // .. - #endif - // apply significant status - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberLog10 - -/* ------------------------------------------------------------------ */ -/* decNumberMax -- compare two Numbers and return the maximum */ -/* */ -/* This computes C = A ? B, returning the maximum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMax(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMAX, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMax - -/* ------------------------------------------------------------------ */ -/* decNumberMaxMag -- compare and return the maximum by magnitude */ -/* */ -/* This computes C = A ? B, returning the maximum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMaxMag - -/* ------------------------------------------------------------------ */ -/* decNumberMin -- compare two Numbers and return the minimum */ -/* */ -/* This computes C = A ? B, returning the minimum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMin(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMIN, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMin - -/* ------------------------------------------------------------------ */ -/* decNumberMinMag -- compare and return the minimum by magnitude */ -/* */ -/* This computes C = A ? B, returning the minimum by 754 rules */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMinMag - -/* ------------------------------------------------------------------ */ -/* decNumberMinus -- prefix minus operator */ -/* */ -/* This computes C = 0 - A */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* See also decNumberCopyNegate for a quiet bitwise version of this. */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* Simply use AddOp for the subtract, which will do the necessary. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMinus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dzero; - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - decNumberZero(&dzero); // make 0 - dzero.exponent=rhs->exponent; // [no coefficient expansion] - decAddOp(res, &dzero, rhs, set, DECNEG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMinus - -/* ------------------------------------------------------------------ */ -/* decNumberNextMinus -- next towards -Infinity */ -/* */ -/* This computes C = A - infinitesimal, rounded towards -Infinity */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* This is a generalization of 754 NextDown. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dtiny; // constant - decContext workset=*set; // work - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // +Infinity is the special case - if ((rhs->bits&(DECINF|DECNEG))==DECINF) { - decSetMaxValue(res, set); // is +ve - // there is no status to set - return res; - } - decNumberZero(&dtiny); // start with 0 - dtiny.lsu[0]=1; // make number that is .. - dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest - workset.round=DEC_ROUND_FLOOR; - decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); - status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberNextMinus - -/* ------------------------------------------------------------------ */ -/* decNumberNextPlus -- next towards +Infinity */ -/* */ -/* This computes C = A + infinitesimal, rounded towards +Infinity */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* This is a generalization of 754 NextUp. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dtiny; // constant - decContext workset=*set; // work - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // -Infinity is the special case - if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { - decSetMaxValue(res, set); - res->bits=DECNEG; // negative - // there is no status to set - return res; - } - decNumberZero(&dtiny); // start with 0 - dtiny.lsu[0]=1; // make number that is .. - dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest - workset.round=DEC_ROUND_CEILING; - decAddOp(res, rhs, &dtiny, &workset, 0, &status); - status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberNextPlus - -/* ------------------------------------------------------------------ */ -/* decNumberNextToward -- next towards rhs */ -/* */ -/* This computes C = A +/- infinitesimal, rounded towards */ -/* +/-Infinity in the direction of B, as per 754-1985 nextafter */ -/* modified during revision but dropped from 754-2008. */ -/* */ -/* res is C, the result. C may be A or B. */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* This is a generalization of 754-1985 NextAfter. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - decNumber dtiny; // constant - decContext workset=*set; // work - Int result; // .. - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { - decNaNs(res, lhs, rhs, set, &status); - } - else { // Is numeric, so no chance of sNaN Invalid, etc. - result=decCompare(lhs, rhs, 0); // sign matters - if (result==BADINT) status|=DEC_Insufficient_storage; // rare - else { // valid compare - if (result==0) decNumberCopySign(res, lhs, rhs); // easy - else { // differ: need NextPlus or NextMinus - uByte sub; // add or subtract - if (result<0) { // lhsbits&(DECINF|DECNEG))==(DECINF|DECNEG)) { - decSetMaxValue(res, set); - res->bits=DECNEG; // negative - return res; // there is no status to set - } - workset.round=DEC_ROUND_CEILING; - sub=0; // add, please - } // plus - else { // lhs>rhs, do nextminus - // +Infinity is the special case - if ((lhs->bits&(DECINF|DECNEG))==DECINF) { - decSetMaxValue(res, set); - return res; // there is no status to set - } - workset.round=DEC_ROUND_FLOOR; - sub=DECNEG; // subtract, please - } // minus - decNumberZero(&dtiny); // start with 0 - dtiny.lsu[0]=1; // make number that is .. - dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest - decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or - - // turn off exceptions if the result is a normal number - // (including Nmin), otherwise let all status through - if (decNumberIsNormal(res, set)) status=0; - } // unequal - } // compare OK - } // numeric - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberNextToward - -/* ------------------------------------------------------------------ */ -/* decNumberOr -- OR two Numbers, digitwise */ -/* */ -/* This computes C = A | B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X|X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberOr(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - const Unit *ua, *ub; // -> operands - const Unit *msua, *msub; // -> operand msus - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) - || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - // operands are valid - ua=lhs->lsu; // bottom-up - ub=rhs->lsu; // .. - uc=res->lsu; // .. - msua=ua+D2U(lhs->digits)-1; // -> msu of lhs - msub=ub+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop - Unit a, b; // extract units - if (ua>msua) a=0; - else a=*ua; - if (ub>msub) b=0; - else b=*ub; - *uc=0; // can now write back - if (a|b) { // maybe 1 bits to examine - Int i, j; - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // non-zero - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberOr - -/* ------------------------------------------------------------------ */ -/* decNumberPlus -- prefix plus operator */ -/* */ -/* This computes C = 0 + A */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* See also decNumberCopy for a quiet bitwise version of this. */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This simply uses AddOp; Add will take fast path after preparing A. */ -/* Performance is a concern here, as this routine is often used to */ -/* check operands and apply rounding and overflow/underflow testing. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberPlus(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dzero; - uInt status=0; // accumulator - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - decNumberZero(&dzero); // make 0 - dzero.exponent=rhs->exponent; // [no coefficient expansion] - decAddOp(res, &dzero, rhs, set, 0, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberPlus - -/* ------------------------------------------------------------------ */ -/* decNumberMultiply -- multiply two Numbers */ -/* */ -/* This computes C = A x B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decMultiplyOp(res, lhs, rhs, set, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberMultiply - -/* ------------------------------------------------------------------ */ -/* decNumberPower -- raise a number to a power */ -/* */ -/* This computes C = A ** B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X**X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Mathematical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* */ -/* However, if 1999999997<=B<=999999999 and B is an integer then the */ -/* restrictions on A and the context are relaxed to the usual bounds, */ -/* for compatibility with the earlier (integer power only) version */ -/* of this function. */ -/* */ -/* When B is an integer, the result may be exact, even if rounded. */ -/* */ -/* The final result is rounded according to the context; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberPower(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - decNumber *allocdac=NULL; // -> allocated acc buffer, iff used - decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used - Int reqdigits=set->digits; // requested DIGITS - Int n; // rhs in binary - Flag rhsint=0; // 1 if rhs is an integer - Flag useint=0; // 1 if can use integer calculation - Flag isoddint=0; // 1 if rhs is an integer and odd - Int i; // work - #if DECSUBSET - Int dropped; // .. - #endif - uInt needbytes; // buffer size needed - Flag seenbit; // seen a bit while powering - Int residue=0; // rounding residue - uInt status=0; // accumulators - uByte bits=0; // result sign if errors - decContext aset; // working context - decNumber dnOne; // work value 1... - // local accumulator buffer [a decNumber, with digits+elength+1 digits] - decNumber dacbuff[D2N(DECBUFFER+9)]; - decNumber *dac=dacbuff; // -> result accumulator - // same again for possible 1/lhs calculation - decNumber invbuff[D2N(DECBUFFER+9)]; - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { // reduce operands and set status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, &status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // handle NaNs and rhs Infinity (lhs infinity is harder) - if (SPECIALARGS) { - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs - decNaNs(res, lhs, rhs, set, &status); - break;} - if (decNumberIsInfinite(rhs)) { // rhs Infinity - Flag rhsneg=rhs->bits&DECNEG; // save rhs sign - if (decNumberIsNegative(lhs) // lhs<0 - && !decNumberIsZero(lhs)) // .. - status|=DEC_Invalid_operation; - else { // lhs >=0 - decNumberZero(&dnOne); // set up 1 - dnOne.lsu[0]=1; - decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1 - decNumberZero(res); // prepare for 0/1/Infinity - if (decNumberIsNegative(dac)) { // lhs<1 - if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0] - } - else if (dac->lsu[0]==0) { // lhs=1 - // 1**Infinity is inexact, so return fully-padded 1.0000 - Int shift=set->digits-1; - *res->lsu=1; // was 0, make int 1 - res->digits=decShiftToMost(res->lsu, 1, shift); - res->exponent=-shift; // make 1.0000... - status|=DEC_Inexact|DEC_Rounded; // deemed inexact - } - else { // lhs>1 - if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0] - } - } // lhs>=0 - break;} - // [lhs infinity drops through] - } // specials - - // Original rhs may be an integer that fits and is in range - n=decGetInt(rhs); - if (n!=BADINT) { // it is an integer - rhsint=1; // record the fact for 1**n - isoddint=(Flag)n&1; // [works even if big] - if (n!=BIGEVEN && n!=BIGODD) // can use integer path? - useint=1; // looks good - } - - if (decNumberIsNegative(lhs) // -x .. - && isoddint) bits=DECNEG; // .. to an odd power - - // handle LHS infinity - if (decNumberIsInfinite(lhs)) { // [NaNs already handled] - uByte rbits=rhs->bits; // save - decNumberZero(res); // prepare - if (n==0) *res->lsu=1; // [-]Inf**0 => 1 - else { - // -Inf**nonint -> error - if (!rhsint && decNumberIsNegative(lhs)) { - status|=DEC_Invalid_operation; // -Inf**nonint is error - break;} - if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n - // [otherwise will be 0 or -0] - res->bits=bits; - } - break;} - - // similarly handle LHS zero - if (decNumberIsZero(lhs)) { - if (n==0) { // 0**0 => Error - #if DECSUBSET - if (!set->extended) { // [unless subset] - decNumberZero(res); - *res->lsu=1; // return 1 - break;} - #endif - status|=DEC_Invalid_operation; - } - else { // 0**x - uByte rbits=rhs->bits; // save - if (rbits & DECNEG) { // was a 0**(-n) - #if DECSUBSET - if (!set->extended) { // [bad if subset] - status|=DEC_Invalid_operation; - break;} - #endif - bits|=DECINF; - } - decNumberZero(res); // prepare - // [otherwise will be 0 or -0] - res->bits=bits; - } - break;} - - // here both lhs and rhs are finite; rhs==0 is handled in the - // integer path. Next handle the non-integer cases - if (!useint) { // non-integral rhs - // any -ve lhs is bad, as is either operand or context out of - // bounds - if (decNumberIsNegative(lhs)) { - status|=DEC_Invalid_operation; - break;} - if (decCheckMath(lhs, set, &status) - || decCheckMath(rhs, set, &status)) break; // variable status - - decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context - aset.emax=DEC_MAX_MATH; // usual bounds - aset.emin=-DEC_MAX_MATH; // .. - aset.clamp=0; // and no concrete format - - // calculate the result using exp(ln(lhs)*rhs), which can - // all be done into the accumulator, dac. The precision needed - // is enough to contain the full information in the lhs (which - // is the total digits, including exponent), or the requested - // precision, if larger, + 4; 6 is used for the exponent - // maximum length, and this is also used when it is shorter - // than the requested digits as it greatly reduces the >0.5 ulp - // cases at little cost (because Ln doubles digits each - // iteration so a few extra digits rarely causes an extra - // iteration) - aset.digits=MAXI(lhs->digits, set->digits)+6+4; - } // non-integer rhs - - else { // rhs is in-range integer - if (n==0) { // x**0 = 1 - // (0**0 was handled above) - decNumberZero(res); // result=1 - *res->lsu=1; // .. - break;} - // rhs is a non-zero integer - if (n<0) n=-n; // use abs(n) - - aset=*set; // clone the context - aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced - // calculate the working DIGITS - aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; - #if DECSUBSET - if (!set->extended) aset.digits--; // use classic precision - #endif - // it's an error if this is more than can be handled - if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} - } // integer path - - // aset.digits is the count of digits for the accumulator needed - // if accumulator is too long for local storage, then allocate - needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); - // [needbytes also used below if 1/lhs needed] - if (needbytes>sizeof(dacbuff)) { - allocdac=(decNumber *)malloc(needbytes); - if (allocdac==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - dac=allocdac; // use the allocated space - } - // here, aset is set up and accumulator is ready for use - - if (!useint) { // non-integral rhs - // x ** y; special-case x=1 here as it will otherwise always - // reduce to integer 1; decLnOp has a fastpath which detects - // the case of x=1 - decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs) - // [no error possible, as lhs 0 already handled] - if (ISZERO(dac)) { // x==1, 1.0, etc. - // need to return fully-padded 1.0000 etc., but rhsint->1 - *dac->lsu=1; // was 0, make int 1 - if (!rhsint) { // add padding - Int shift=set->digits-1; - dac->digits=decShiftToMost(dac->lsu, 1, shift); - dac->exponent=-shift; // make 1.0000... - status|=DEC_Inexact|DEC_Rounded; // deemed inexact - } - } - else { - decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs - decExpOp(dac, dac, &aset, &status); // dac=exp(dac) - } - // and drop through for final rounding - } // non-integer rhs - - else { // carry on with integer - decNumberZero(dac); // acc=1 - *dac->lsu=1; // .. - - // if a negative power the constant 1 is needed, and if not subset - // invert the lhs now rather than inverting the result later - if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] - decNumber *inv=invbuff; // asssume use fixed buffer - decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later] - #if DECSUBSET - if (set->extended) { // need to calculate 1/lhs - #endif - // divide lhs into 1, putting result in dac [dac=1/dac] - decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); - // now locate or allocate space for the inverted lhs - if (needbytes>sizeof(invbuff)) { - allocinv=(decNumber *)malloc(needbytes); - if (allocinv==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - inv=allocinv; // use the allocated space - } - // [inv now points to big-enough buffer or allocated storage] - decNumberCopy(inv, dac); // copy the 1/lhs - decNumberCopy(dac, &dnOne); // restore acc=1 - lhs=inv; // .. and go forward with new lhs - #if DECSUBSET - } - #endif - } - - // Raise-to-the-power loop... - seenbit=0; // set once a 1-bit is encountered - for (i=1;;i++){ // for each bit [top bit ignored] - // abandon if had overflow or terminal underflow - if (status & (DEC_Overflow|DEC_Underflow)) { // interesting? - if (status&DEC_Overflow || ISZERO(dac)) break; - } - // [the following two lines revealed an optimizer bug in a C++ - // compiler, with symptom: 5**3 -> 25, when n=n+n was used] - n=n<<1; // move next bit to testable position - if (n<0) { // top bit is set - seenbit=1; // OK, significant bit seen - decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x - } - if (i==31) break; // that was the last bit - if (!seenbit) continue; // no need to square 1 - decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square] - } /*i*/ // 32 bits - - // complete internal overflow or underflow processing - if (status & (DEC_Overflow|DEC_Underflow)) { - #if DECSUBSET - // If subset, and power was negative, reverse the kind of -erflow - // [1/x not yet done] - if (!set->extended && decNumberIsNegative(rhs)) { - if (status & DEC_Overflow) - status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; - else { // trickier -- Underflow may or may not be set - status&=~(DEC_Underflow | DEC_Subnormal); // [one or both] - status|=DEC_Overflow; - } - } - #endif - dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign - // round subnormals [to set.digits rather than aset.digits] - // or set overflow result similarly as required - decFinalize(dac, set, &residue, &status); - decNumberCopy(res, dac); // copy to result (is now OK length) - break; - } - - #if DECSUBSET - if (!set->extended && // subset math - decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] - // so divide result into 1 [dac=1/dac] - decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); - } - #endif - } // rhs integer path - - // reduce result to the requested length and copy to result - decCopyFit(res, dac, set, &residue, &status); - decFinish(res, set, &residue, &status); // final cleanup - #if DECSUBSET - if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros - #endif - } while(0); // end protected - - if (allocdac!=NULL) free(allocdac); // drop any storage used - if (allocinv!=NULL) free(allocinv); // .. - #if DECSUBSET - if (alloclhs!=NULL) free(alloclhs); // .. - if (allocrhs!=NULL) free(allocrhs); // .. - #endif - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberPower - -/* ------------------------------------------------------------------ */ -/* decNumberQuantize -- force exponent to requested value */ -/* */ -/* This computes C = op(A, B), where op adjusts the coefficient */ -/* of C (by rounding or shifting) such that the exponent (-scale) */ -/* of C has exponent of B. The numerical value of C will equal A, */ -/* except for the effects of any rounding that occurred. */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the number with exponent to match */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Unless there is an error or the result is infinite, the exponent */ -/* after the operation is guaranteed to be equal to that of B. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decQuantizeOp(res, lhs, rhs, set, 1, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberQuantize - -/* ------------------------------------------------------------------ */ -/* decNumberReduce -- remove trailing zeros */ -/* */ -/* This computes C = 0 + A, and normalizes the result */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -// Previously known as Normalize -decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, - decContext *set) { - return decNumberReduce(res, rhs, set); - } // decNumberNormalize - -decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, - decContext *set) { - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - uInt status=0; // as usual - Int residue=0; // as usual - Int dropped; // work - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // Infinities copy through; NaNs need usual treatment - if (decNumberIsNaN(rhs)) { - decNaNs(res, rhs, NULL, set, &status); - break; - } - - // reduce result to the requested length and copy to result - decCopyFit(res, rhs, set, &residue, &status); // copy & round - decFinish(res, set, &residue, &status); // cleanup/set flags - decTrim(res, set, 1, 0, &dropped); // normalize in place - // [may clamp] - } while(0); // end protected - - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // .. - #endif - if (status!=0) decStatus(res, status, set);// then report status - return res; - } // decNumberReduce - -/* ------------------------------------------------------------------ */ -/* decNumberRescale -- force exponent to requested value */ -/* */ -/* This computes C = op(A, B), where op adjusts the coefficient */ -/* of C (by rounding or shifting) such that the exponent (-scale) */ -/* of C has the value B. The numerical value of C will equal A, */ -/* except for the effects of any rounding that occurred. */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the requested exponent */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Unless there is an error or the result is infinite, the exponent */ -/* after the operation is guaranteed to be equal to B. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decQuantizeOp(res, lhs, rhs, set, 0, &status); - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberRescale - -/* ------------------------------------------------------------------ */ -/* decNumberRemainder -- divide and return remainder */ -/* */ -/* This computes C = A % B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, REMAINDER, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberRemainder - -/* ------------------------------------------------------------------ */ -/* decNumberRemainderNear -- divide and return remainder from nearest */ -/* */ -/* This computes C = A % B, where % is the IEEE remainder operator */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - decDivideOp(res, lhs, rhs, set, REMNEAR, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberRemainderNear - -/* ------------------------------------------------------------------ */ -/* decNumberRotate -- rotate the coefficient of a Number left/right */ -/* */ -/* This computes C = A rot B (in base ten and rotating set->digits */ -/* digits). */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ -/* lhs is A */ -/* rhs is B, the number of digits to rotate (-ve to right) */ -/* set is the context */ -/* */ -/* The digits of the coefficient of A are rotated to the left (if B */ -/* is positive) or to the right (if B is negative) without adjusting */ -/* the exponent or the sign of A. If lhs->digits is less than */ -/* set->digits the coefficient is padded with zeros on the left */ -/* before the rotate. Any leading zeros in the result are removed */ -/* as usual. */ -/* */ -/* B must be an integer (q=0) and in the range -set->digits through */ -/* +set->digits. */ -/* C must have space for set->digits digits. */ -/* NaNs are propagated as usual. Infinities are unaffected (but */ -/* B must be valid). No status is set unless B is invalid or an */ -/* operand is an sNaN. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - Int rotate; // rhs as an Int - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // NaNs propagate as normal - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) - decNaNs(res, lhs, rhs, set, &status); - // rhs must be an integer - else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) - status=DEC_Invalid_operation; - else { // both numeric, rhs is an integer - rotate=decGetInt(rhs); // [cannot fail] - if (rotate==BADINT // something bad .. - || rotate==BIGODD || rotate==BIGEVEN // .. very big .. - || abs(rotate)>set->digits) // .. or out of range - status=DEC_Invalid_operation; - else { // rhs is OK - decNumberCopy(res, lhs); - // convert -ve rotate to equivalent positive rotation - if (rotate<0) rotate=set->digits+rotate; - if (rotate!=0 && rotate!=set->digits // zero or full rotation - && !decNumberIsInfinite(res)) { // lhs was infinite - // left-rotate to do; 0 < rotate < set->digits - uInt units, shift; // work - uInt msudigits; // digits in result msu - Unit *msu=res->lsu+D2U(res->digits)-1; // current msu - Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu - for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0 - res->digits=set->digits; // now full-length - msudigits=MSUDIGITS(res->digits); // actual digits in msu - - // rotation here is done in-place, in three steps - // 1. shift all to least up to one unit to unit-align final - // lsd [any digits shifted out are rotated to the left, - // abutted to the original msd (which may require split)] - // - // [if there are no whole units left to rotate, the - // rotation is now complete] - // - // 2. shift to least, from below the split point only, so that - // the final msd is in the right place in its Unit [any - // digits shifted out will fit exactly in the current msu, - // left aligned, no split required] - // - // 3. rotate all the units by reversing left part, right - // part, and then whole - // - // example: rotate right 8 digits (2 units + 2), DECDPUN=3. - // - // start: 00a bcd efg hij klm npq - // - // 1a 000 0ab cde fgh|ijk lmn [pq saved] - // 1b 00p qab cde fgh|ijk lmn - // - // 2a 00p qab cde fgh|00i jkl [mn saved] - // 2b mnp qab cde fgh|00i jkl - // - // 3a fgh cde qab mnp|00i jkl - // 3b fgh cde qab mnp|jkl 00i - // 3c 00i jkl mnp qab cde fgh - - // Step 1: amount to shift is the partial right-rotate count - rotate=set->digits-rotate; // make it right-rotate - units=rotate/DECDPUN; // whole units to rotate - shift=rotate%DECDPUN; // left-over digits count - if (shift>0) { // not an exact number of units - uInt save=res->lsu[0]%powers[shift]; // save low digit(s) - decShiftToLeast(res->lsu, D2U(res->digits), shift); - if (shift>msudigits) { // msumax-1 needs >0 digits - uInt rem=save%powers[shift-msudigits];// split save - *msumax=(Unit)(save/powers[shift-msudigits]); // and insert - *(msumax-1)=*(msumax-1) - +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // .. - } - else { // all fits in msumax - *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1] - } - } // digits shift needed - - // If whole units to rotate... - if (units>0) { // some to do - // Step 2: the units to touch are the whole ones in rotate, - // if any, and the shift is DECDPUN-msudigits (which may be - // 0, again) - shift=DECDPUN-msudigits; - if (shift>0) { // not an exact number of units - uInt save=res->lsu[0]%powers[shift]; // save low digit(s) - decShiftToLeast(res->lsu, units, shift); - *msumax=*msumax+(Unit)(save*powers[msudigits]); - } // partial shift needed - - // Step 3: rotate the units array using triple reverse - // (reversing is easy and fast) - decReverse(res->lsu+units, msumax); // left part - decReverse(res->lsu, res->lsu+units-1); // right part - decReverse(res->lsu, msumax); // whole - } // whole units to rotate - // the rotation may have left an undetermined number of zeros - // on the left, so true length needs to be calculated - res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); - } // rotate needed - } // rhs OK - } // numerics - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberRotate - -/* ------------------------------------------------------------------ */ -/* decNumberSameQuantum -- test for equal exponents */ -/* */ -/* res is the result number, which will contain either 0 or 1 */ -/* lhs is a number to test */ -/* rhs is the second (usually a pattern) */ -/* */ -/* No errors are possible and no context is needed. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, - const decNumber *rhs) { - Unit ret=0; // return value - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; - #endif - - if (SPECIALARGS) { - if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; - else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; - // [anything else with a special gives 0] - } - else if (lhs->exponent==rhs->exponent) ret=1; - - decNumberZero(res); // OK to overwrite an operand now - *res->lsu=ret; - return res; - } // decNumberSameQuantum - -/* ------------------------------------------------------------------ */ -/* decNumberScaleB -- multiply by a power of 10 */ -/* */ -/* This computes C = A x 10**B where B is an integer (q=0) with */ -/* maximum magnitude 2*(emax+digits) */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the requested power of ten to use */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* The result may underflow or overflow. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - Int reqexp; // requested exponent change [B] - uInt status=0; // accumulator - Int residue; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // Handle special values except lhs infinite - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) - decNaNs(res, lhs, rhs, set, &status); - // rhs must be an integer - else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) - status=DEC_Invalid_operation; - else { - // lhs is a number; rhs is a finite with q==0 - reqexp=decGetInt(rhs); // [cannot fail] - // maximum range is larger than getInt can handle, so this is - // more restrictive than the specification - if (reqexp==BADINT // something bad .. - || reqexp==BIGODD || reqexp==BIGEVEN // it was huge - || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range - status=DEC_Invalid_operation; - else { // rhs is OK - decNumberCopy(res, lhs); // all done if infinite lhs - if (!decNumberIsInfinite(res)) { // prepare to scale - Int exp=res->exponent; // save for overflow test - res->exponent+=reqexp; // adjust the exponent - if (((exp^reqexp)>=0) // same sign ... - && ((exp^res->exponent)<0)) { // .. but result had different - // the calculation overflowed, so force right treatment - if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS; - else res->exponent=DEC_MAX_EMAX+1; - } - residue=0; - decFinalize(res, set, &residue, &status); // final check - } // finite LHS - } // rhs OK - } // rhs finite - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberScaleB - -/* ------------------------------------------------------------------ */ -/* decNumberShift -- shift the coefficient of a Number left or right */ -/* */ -/* This computes C = A << B or C = A >> -B (in base ten). */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X<digits through */ -/* +set->digits. */ -/* C must have space for set->digits digits. */ -/* NaNs are propagated as usual. Infinities are unaffected (but */ -/* B must be valid). No status is set unless B is invalid or an */ -/* operand is an sNaN. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberShift(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - Int shift; // rhs as an Int - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // NaNs propagate as normal - if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) - decNaNs(res, lhs, rhs, set, &status); - // rhs must be an integer - else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) - status=DEC_Invalid_operation; - else { // both numeric, rhs is an integer - shift=decGetInt(rhs); // [cannot fail] - if (shift==BADINT // something bad .. - || shift==BIGODD || shift==BIGEVEN // .. very big .. - || abs(shift)>set->digits) // .. or out of range - status=DEC_Invalid_operation; - else { // rhs is OK - decNumberCopy(res, lhs); - if (shift!=0 && !decNumberIsInfinite(res)) { // something to do - if (shift>0) { // to left - if (shift==set->digits) { // removing all - *res->lsu=0; // so place 0 - res->digits=1; // .. - } - else { // - // first remove leading digits if necessary - if (res->digits+shift>set->digits) { - decDecap(res, res->digits+shift-set->digits); - // that updated res->digits; may have gone to 1 (for a - // single digit or for zero - } - if (res->digits>1 || *res->lsu) // if non-zero.. - res->digits=decShiftToMost(res->lsu, res->digits, shift); - } // partial left - } // left - else { // to right - if (-shift>=res->digits) { // discarding all - *res->lsu=0; // so place 0 - res->digits=1; // .. - } - else { - decShiftToLeast(res->lsu, D2U(res->digits), -shift); - res->digits-=(-shift); - } - } // to right - } // non-0 non-Inf shift - } // rhs OK - } // numerics - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberShift - -/* ------------------------------------------------------------------ */ -/* decNumberSquareRoot -- square root operator */ -/* */ -/* This computes C = squareroot(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -/* This uses the following varying-precision algorithm in: */ -/* */ -/* Properly Rounded Variable Precision Square Root, T. E. Hull and */ -/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ -/* pp229-237, ACM, September 1985. */ -/* */ -/* The square-root is calculated using Newton's method, after which */ -/* a check is made to ensure the result is correctly rounded. */ -/* */ -/* % [Reformatted original Numerical Turing source code follows.] */ -/* function sqrt(x : real) : real */ -/* % sqrt(x) returns the properly rounded approximation to the square */ -/* % root of x, in the precision of the calling environment, or it */ -/* % fails if x < 0. */ -/* % t e hull and a abrham, august, 1984 */ -/* if x <= 0 then */ -/* if x < 0 then */ -/* assert false */ -/* else */ -/* result 0 */ -/* end if */ -/* end if */ -/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ -/* var e := getexp(x) % exponent part of x */ -/* var approx : real */ -/* if e mod 2 = 0 then */ -/* approx := .259 + .819 * f % approx to root of f */ -/* else */ -/* f := f/l0 % adjustments */ -/* e := e + 1 % for odd */ -/* approx := .0819 + 2.59 * f % exponent */ -/* end if */ -/* */ -/* var p:= 3 */ -/* const maxp := currentprecision + 2 */ -/* loop */ -/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ -/* precision p */ -/* approx := .5 * (approx + f/approx) */ -/* exit when p = maxp */ -/* end loop */ -/* */ -/* % approx is now within 1 ulp of the properly rounded square root */ -/* % of f; to ensure proper rounding, compare squares of (approx - */ -/* % l/2 ulp) and (approx + l/2 ulp) with f. */ -/* p := currentprecision */ -/* begin */ -/* precision p + 2 */ -/* const approxsubhalf := approx - setexp(.5, -p) */ -/* if mulru(approxsubhalf, approxsubhalf) > f then */ -/* approx := approx - setexp(.l, -p + 1) */ -/* else */ -/* const approxaddhalf := approx + setexp(.5, -p) */ -/* if mulrd(approxaddhalf, approxaddhalf) < f then */ -/* approx := approx + setexp(.l, -p + 1) */ -/* end if */ -/* end if */ -/* end */ -/* result setexp(approx, e div 2) % fix exponent */ -/* end sqrt */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs, - decContext *set) { - decContext workset, approxset; // work contexts - decNumber dzero; // used for constant zero - Int maxp; // largest working precision - Int workp; // working precision - Int residue=0; // rounding residue - uInt status=0, ignore=0; // status accumulators - uInt rstatus; // .. - Int exp; // working exponent - Int ideal; // ideal (preferred) exponent - Int needbytes; // work - Int dropped; // .. - - #if DECSUBSET - decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated - #endif - // buffer for f [needs +1 in case DECBUFFER 0] - decNumber buff[D2N(DECBUFFER+1)]; - // buffer for a [needs +2 to match likely maxp] - decNumber bufa[D2N(DECBUFFER+2)]; - // buffer for temporary, b [must be same size as a] - decNumber bufb[D2N(DECBUFFER+2)]; - decNumber *allocbuff=NULL; // -> allocated buff, iff allocated - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated - decNumber *f=buff; // reduced fraction - decNumber *a=bufa; // approximation to result - decNumber *b=bufb; // intermediate result - // buffer for temporary variable, up to 3 digits - decNumber buft[D2N(3)]; - decNumber *t=buft; // up-to-3-digit constant or work - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operand and set lostDigits status, as needed - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, &status); - if (allocrhs==NULL) break; - // [Note: 'f' allocation below could reuse this buffer if - // used, but as this is rare they are kept separate for clarity.] - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // handle infinities and NaNs - if (SPECIALARG) { - if (decNumberIsInfinite(rhs)) { // an infinity - if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; - else decNumberCopy(res, rhs); // +Infinity - } - else decNaNs(res, rhs, NULL, set, &status); // a NaN - break; - } - - // calculate the ideal (preferred) exponent [floor(exp/2)] - // [It would be nicer to write: ideal=rhs->exponent>>1, but this - // generates a compiler warning. Generated code is the same.] - ideal=(rhs->exponent&~1)/2; // target - - // handle zeros - if (ISZERO(rhs)) { - decNumberCopy(res, rhs); // could be 0 or -0 - res->exponent=ideal; // use the ideal [safe] - // use decFinish to clamp any out-of-range exponent, etc. - decFinish(res, set, &residue, &status); - break; - } - - // any other -x is an oops - if (decNumberIsNegative(rhs)) { - status|=DEC_Invalid_operation; - break; - } - - // space is needed for three working variables - // f -- the same precision as the RHS, reduced to 0.01->0.99... - // a -- Hull's approximation -- precision, when assigned, is - // currentprecision+1 or the input argument precision, - // whichever is larger (+2 for use as temporary) - // b -- intermediate temporary result (same size as a) - // if any is too long for local storage, then allocate - workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision - workp=MAXI(workp, 7); // at least 7 for low cases - maxp=workp+2; // largest working precision - - needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); - if (needbytes>(Int)sizeof(buff)) { - allocbuff=(decNumber *)malloc(needbytes); - if (allocbuff==NULL) { // hopeless -- abandon - status|=DEC_Insufficient_storage; - break;} - f=allocbuff; // use the allocated space - } - // a and b both need to be able to hold a maxp-length number - needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); - if (needbytes>(Int)sizeof(bufa)) { // [same applies to b] - allocbufa=(decNumber *)malloc(needbytes); - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufa==NULL || allocbufb==NULL) { // hopeless - status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated spaces - b=allocbufb; // .. - } - - // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 - decNumberCopy(f, rhs); - exp=f->exponent+f->digits; // adjusted to Hull rules - f->exponent=-(f->digits); // to range - - // set up working context - decContextDefault(&workset, DEC_INIT_DECIMAL64); - workset.emax=DEC_MAX_EMAX; - workset.emin=DEC_MIN_EMIN; - - // [Until further notice, no error is possible and status bits - // (Rounded, etc.) should be ignored, not accumulated.] - - // Calculate initial approximation, and allow for odd exponent - workset.digits=workp; // p for initial calculation - t->bits=0; t->digits=3; - a->bits=0; a->digits=3; - if ((exp & 1)==0) { // even exponent - // Set t=0.259, a=0.819 - t->exponent=-3; - a->exponent=-3; - #if DECDPUN>=3 - t->lsu[0]=259; - a->lsu[0]=819; - #elif DECDPUN==2 - t->lsu[0]=59; t->lsu[1]=2; - a->lsu[0]=19; a->lsu[1]=8; - #else - t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; - a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; - #endif - } - else { // odd exponent - // Set t=0.0819, a=2.59 - f->exponent--; // f=f/10 - exp++; // e=e+1 - t->exponent=-4; - a->exponent=-2; - #if DECDPUN>=3 - t->lsu[0]=819; - a->lsu[0]=259; - #elif DECDPUN==2 - t->lsu[0]=19; t->lsu[1]=8; - a->lsu[0]=59; a->lsu[1]=2; - #else - t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; - a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; - #endif - } - - decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f - decAddOp(a, a, t, &workset, 0, &ignore); // ..+t - // [a is now the initial approximation for sqrt(f), calculated with - // currentprecision, which is also a's precision.] - - // the main calculation loop - decNumberZero(&dzero); // make 0 - decNumberZero(t); // set t = 0.5 - t->lsu[0]=5; // .. - t->exponent=-1; // .. - workset.digits=3; // initial p - for (; workset.digitsexponent+=exp/2; // set correct exponent - rstatus=0; // clear status - residue=0; // .. and accumulator - decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed) - decFinish(a, &approxset, &residue, &rstatus); // clean and finalize - - // Overflow was possible if the input exponent was out-of-range, - // in which case quit - if (rstatus&DEC_Overflow) { - status=rstatus; // use the status as-is - decNumberCopy(res, a); // copy to result - break; - } - - // Preserve status except Inexact/Rounded - status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); - - // Carry out the Hull correction - a->exponent-=exp/2; // back to 0.1->1 - - // a is now at final precision and within 1 ulp of the properly - // rounded square root of f; to ensure proper rounding, compare - // squares of (a - l/2 ulp) and (a + l/2 ulp) with f. - // Here workset.digits=maxp and t=0.5, and a->digits determines - // the ulp - workset.digits--; // maxp-1 is OK now - t->exponent=-a->digits-1; // make 0.5 ulp - decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp - workset.round=DEC_ROUND_UP; - decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b) - decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed - if (decNumberIsNegative(b)) { // f < b [i.e., b > f] - // this is the more common adjustment, though both are rare - t->exponent++; // make 1.0 ulp - t->lsu[0]=1; // .. - decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp - // assign to approx [round to length] - approxset.emin-=exp/2; // adjust to match a - approxset.emax-=exp/2; - decAddOp(a, &dzero, a, &approxset, 0, &ignore); - } - else { - decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp - workset.round=DEC_ROUND_DOWN; - decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b) - decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f - if (decNumberIsNegative(b)) { // b < f - t->exponent++; // make 1.0 ulp - t->lsu[0]=1; // .. - decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp - // assign to approx [round to length] - approxset.emin-=exp/2; // adjust to match a - approxset.emax-=exp/2; - decAddOp(a, &dzero, a, &approxset, 0, &ignore); - } - } - // [no errors are possible in the above, and rounding/inexact during - // estimation are irrelevant, so status was not accumulated] - - // Here, 0.1 <= a < 1 (still), so adjust back - a->exponent+=exp/2; // set correct exponent - - // count droppable zeros [after any subnormal rounding] by - // trimming a copy - decNumberCopy(b, a); - decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros] - - // Set Inexact and Rounded. The answer can only be exact if - // it is short enough so that squaring it could fit in workp - // digits, so this is the only (relatively rare) condition that - // a careful check is needed - if (b->digits*2-1 > workp) { // cannot fit - status|=DEC_Inexact|DEC_Rounded; - } - else { // could be exact/unrounded - uInt mstatus=0; // local status - decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply - if (mstatus&DEC_Overflow) { // result just won't fit - status|=DEC_Inexact|DEC_Rounded; - } - else { // plausible - decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs - if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal - else { // is Exact - // here, dropped is the count of trailing zeros in 'a' - // use closest exponent to ideal... - Int todrop=ideal-a->exponent; // most that can be dropped - if (todrop<0) status|=DEC_Rounded; // ideally would add 0s - else { // unrounded - // there are some to drop, but emax may not allow all - Int maxexp=set->emax-set->digits+1; - Int maxdrop=maxexp-a->exponent; - if (todrop>maxdrop && set->clamp) { // apply clamping - todrop=maxdrop; - status|=DEC_Clamped; - } - if (dropped0) { // have some to drop - decShiftToLeast(a->lsu, D2U(a->digits), todrop); - a->exponent+=todrop; // maintain numerical value - a->digits-=todrop; // new length - } - } - } - } - } - - // double-check Underflow, as perhaps the result could not have - // been subnormal (initial argument too big), or it is now Exact - if (status&DEC_Underflow) { - Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent - // check if truly subnormal - #if DECEXTFLAG // DEC_Subnormal too - if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); - #else - if (ae>=set->emin*2) status&=~DEC_Underflow; - #endif - // check if truly inexact - if (!(status&DEC_Inexact)) status&=~DEC_Underflow; - } - - decNumberCopy(res, a); // a is now the result - } while(0); // end protected - - if (allocbuff!=NULL) free(allocbuff); // drop any storage used - if (allocbufa!=NULL) free(allocbufa); // .. - if (allocbufb!=NULL) free(allocbufb); // .. - #if DECSUBSET - if (allocrhs !=NULL) free(allocrhs); // .. - #endif - if (status!=0) decStatus(res, status, set);// then report status - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberSquareRoot - -/* ------------------------------------------------------------------ */ -/* decNumberSubtract -- subtract two Numbers */ -/* */ -/* This computes C = A - B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* */ -/* C must have space for set->digits digits. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - uInt status=0; // accumulator - - decAddOp(res, lhs, rhs, set, DECNEG, &status); - if (status!=0) decStatus(res, status, set); - #if DECCHECK - decCheckInexact(res, set); - #endif - return res; - } // decNumberSubtract - -/* ------------------------------------------------------------------ */ -/* decNumberToIntegralExact -- round-to-integral-value with InExact */ -/* decNumberToIntegralValue -- round-to-integral-value */ -/* */ -/* res is the result */ -/* rhs is input number */ -/* set is the context */ -/* */ -/* res must have space for any value of rhs. */ -/* */ -/* This implements the IEEE special operators and therefore treats */ -/* special values as valid. For finite numbers it returns */ -/* rescale(rhs, 0) if rhs->exponent is <0. */ -/* Otherwise the result is rhs (so no error is possible, except for */ -/* sNaN). */ -/* */ -/* The context is used for rounding mode and status after sNaN, but */ -/* the digits setting is ignored. The Exact version will signal */ -/* Inexact if the result differs numerically from rhs; the other */ -/* never signals Inexact. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, - decContext *set) { - decNumber dn; - decContext workset; // working context - uInt status=0; // accumulator - - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - // handle infinities and NaNs - if (SPECIALARG) { - if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity - else decNaNs(res, rhs, NULL, set, &status); // a NaN - } - else { // finite - // have a finite number; no error possible (res must be big enough) - if (rhs->exponent>=0) return decNumberCopy(res, rhs); - // that was easy, but if negative exponent there is work to do... - workset=*set; // clone rounding, etc. - workset.digits=rhs->digits; // no length rounding - workset.traps=0; // no traps - decNumberZero(&dn); // make a number with exponent 0 - decNumberQuantize(res, rhs, &dn, &workset); - status|=workset.status; - } - if (status!=0) decStatus(res, status, set); - return res; - } // decNumberToIntegralExact - -decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, - decContext *set) { - decContext workset=*set; // working context - workset.traps=0; // no traps - decNumberToIntegralExact(res, rhs, &workset); - // this never affects set, except for sNaNs; NaN will have been set - // or propagated already, so no need to call decStatus - set->status|=workset.status&DEC_Invalid_operation; - return res; - } // decNumberToIntegralValue - -/* ------------------------------------------------------------------ */ -/* decNumberXor -- XOR two Numbers, digitwise */ -/* */ -/* This computes C = A ^ B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context (used for result length and error report) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Logical function restrictions apply (see above); a NaN is */ -/* returned with Invalid_operation if a restriction is violated. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberXor(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - const Unit *ua, *ub; // -> operands - const Unit *msua, *msub; // -> operand msus - Unit *uc, *msuc; // -> result and its msu - Int msudigs; // digits in res msu - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) - || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - // operands are valid - ua=lhs->lsu; // bottom-up - ub=rhs->lsu; // .. - uc=res->lsu; // .. - msua=ua+D2U(lhs->digits)-1; // -> msu of lhs - msub=ub+D2U(rhs->digits)-1; // -> msu of rhs - msuc=uc+D2U(set->digits)-1; // -> msu of result - msudigs=MSUDIGITS(set->digits); // [faster than remainder] - for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop - Unit a, b; // extract units - if (ua>msua) a=0; - else a=*ua; - if (ub>msub) b=0; - else b=*ub; - *uc=0; // can now write back - if (a|b) { // maybe 1 bits to examine - Int i, j; - // This loop could be unrolled and/or use BIN2BCD tables - for (i=0; i1) { - decStatus(res, DEC_Invalid_operation, set); - return res; - } - if (uc==msuc && i==msudigs-1) break; // just did final digit - } // each digit - } // non-zero - } // each unit - // [here uc-1 is the msu of the result] - res->digits=decGetDigits(res->lsu, uc-res->lsu); - res->exponent=0; // integer - res->bits=0; // sign=0 - return res; // [no status to set] - } // decNumberXor - - -/* ================================================================== */ -/* Utility routines */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* decNumberClass -- return the decClass of a decNumber */ -/* dn -- the decNumber to test */ -/* set -- the context to use for Emin */ -/* returns the decClass enum */ -/* ------------------------------------------------------------------ */ -enum decClass decNumberClass(const decNumber *dn, decContext *set) { - if (decNumberIsSpecial(dn)) { - if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; - if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; - // must be an infinity - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; - return DEC_CLASS_POS_INF; - } - // is finite - if (decNumberIsNormal(dn, set)) { // most common - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; - return DEC_CLASS_POS_NORMAL; - } - // is subnormal or zero - if (decNumberIsZero(dn)) { // most common - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; - return DEC_CLASS_POS_ZERO; - } - if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; - return DEC_CLASS_POS_SUBNORMAL; - } // decNumberClass - -/* ------------------------------------------------------------------ */ -/* decNumberClassToString -- convert decClass to a string */ -/* */ -/* eclass is a valid decClass */ -/* returns a constant string describing the class (max 13+1 chars) */ -/* ------------------------------------------------------------------ */ -const char *decNumberClassToString(enum decClass eclass) { - if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; - if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; - if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; - if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; - if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; - if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; - if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; - if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; - if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; - if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; - return DEC_ClassString_UN; // Unknown - } // decNumberClassToString - -/* ------------------------------------------------------------------ */ -/* decNumberCopy -- copy a number */ -/* */ -/* dest is the target decNumber */ -/* src is the source decNumber */ -/* returns dest */ -/* */ -/* (dest==src is allowed and is a no-op) */ -/* All fields are updated as required. This is a utility operation, */ -/* so special values are unchanged and no error is possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { - - #if DECCHECK - if (src==NULL) return decNumberZero(dest); - #endif - - if (dest==src) return dest; // no copy required - - // Use explicit assignments here as structure assignment could copy - // more than just the lsu (for small DECDPUN). This would not affect - // the value of the results, but could disturb test harness spill - // checking. - dest->bits=src->bits; - dest->exponent=src->exponent; - dest->digits=src->digits; - dest->lsu[0]=src->lsu[0]; - if (src->digits>DECDPUN) { // more Units to come - const Unit *smsup, *s; // work - Unit *d; // .. - // memcpy for the remaining Units would be safe as they cannot - // overlap. However, this explicit loop is faster in short cases. - d=dest->lsu+1; // -> first destination - smsup=src->lsu+D2U(src->digits); // -> source msu+1 - for (s=src->lsu+1; sdigits digits. */ -/* No exception or error can occur; this is a quiet bitwise operation.*/ -/* See also decNumberAbs for a checking version of this. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; - #endif - decNumberCopy(res, rhs); - res->bits&=~DECNEG; // turn off sign - return res; - } // decNumberCopyAbs - -/* ------------------------------------------------------------------ */ -/* decNumberCopyNegate -- quiet negate value operator */ -/* */ -/* This sets C = negate(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* */ -/* C must have space for set->digits digits. */ -/* No exception or error can occur; this is a quiet bitwise operation.*/ -/* See also decNumberMinus for a checking version of this. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; - #endif - decNumberCopy(res, rhs); - res->bits^=DECNEG; // invert the sign - return res; - } // decNumberCopyNegate - -/* ------------------------------------------------------------------ */ -/* decNumberCopySign -- quiet copy and set sign operator */ -/* */ -/* This sets C = A with the sign of B */ -/* */ -/* res is C, the result. C may be A */ -/* lhs is A */ -/* rhs is B */ -/* */ -/* C must have space for set->digits digits. */ -/* No exception or error can occur; this is a quiet bitwise operation.*/ -/* ------------------------------------------------------------------ */ -decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, - const decNumber *rhs) { - uByte sign; // rhs sign - #if DECCHECK - if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; - #endif - sign=rhs->bits & DECNEG; // save sign bit - decNumberCopy(res, lhs); - res->bits&=~DECNEG; // clear the sign - res->bits|=sign; // set from rhs - return res; - } // decNumberCopySign - -/* ------------------------------------------------------------------ */ -/* decNumberGetBCD -- get the coefficient in BCD8 */ -/* dn is the source decNumber */ -/* bcd is the uInt array that will receive dn->digits BCD bytes, */ -/* most-significant at offset 0 */ -/* returns bcd */ -/* */ -/* bcd must have at least dn->digits bytes. No error is possible; if */ -/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ -/* ------------------------------------------------------------------ */ -uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) { - uByte *ub=bcd+dn->digits-1; // -> lsd - const Unit *up=dn->lsu; // Unit pointer, -> lsu - - #if DECDPUN==1 // trivial simple copy - for (; ub>=bcd; ub--, up++) *ub=*up; - #else // chopping needed - uInt u=*up; // work - uInt cut=DECDPUN; // downcounter through unit - for (; ub>=bcd; ub--) { - *ub=(uByte)(u%10); // [*6554 trick inhibits, here] - u=u/10; - cut--; - if (cut>0) continue; // more in this unit - up++; - u=*up; - cut=DECDPUN; - } - #endif - return bcd; - } // decNumberGetBCD - -/* ------------------------------------------------------------------ */ -/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ -/* dn is the target decNumber */ -/* bcd is the uInt array that will source n BCD bytes, most- */ -/* significant at offset 0 */ -/* n is the number of digits in the source BCD array (bcd) */ -/* returns dn */ -/* */ -/* dn must have space for at least n digits. No error is possible; */ -/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ -/* and bcd[0] zero. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { - Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer] - const uByte *ub=bcd; // -> source msd - - #if DECDPUN==1 // trivial simple copy - for (; ub=dn->lsu; up--) { // each Unit from msu - *up=0; // will take <=DECDPUN digits - for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; - cut=DECDPUN; // next Unit has all digits - } - #endif - dn->digits=n; // set digit count - return dn; - } // decNumberSetBCD - -/* ------------------------------------------------------------------ */ -/* decNumberIsNormal -- test normality of a decNumber */ -/* dn is the decNumber to test */ -/* set is the context to use for Emin */ -/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ -/* ------------------------------------------------------------------ */ -Int decNumberIsNormal(const decNumber *dn, decContext *set) { - Int ae; // adjusted exponent - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; - #endif - - if (decNumberIsSpecial(dn)) return 0; // not finite - if (decNumberIsZero(dn)) return 0; // not non-zero - - ae=dn->exponent+dn->digits-1; // adjusted exponent - if (aeemin) return 0; // is subnormal - return 1; - } // decNumberIsNormal - -/* ------------------------------------------------------------------ */ -/* decNumberIsSubnormal -- test subnormality of a decNumber */ -/* dn is the decNumber to test */ -/* set is the context to use for Emin */ -/* returns 1 if |dn| is finite, non-zero, and exponent+dn->digits-1; // adjusted exponent - if (aeemin) return 1; // is subnormal - return 0; - } // decNumberIsSubnormal - -/* ------------------------------------------------------------------ */ -/* decNumberTrim -- remove insignificant zeros */ -/* */ -/* dn is the number to trim */ -/* returns dn */ -/* */ -/* All fields are updated as required. This is a utility operation, */ -/* so special values are unchanged and no error is possible. The */ -/* zeros are removed unconditionally. */ -/* ------------------------------------------------------------------ */ -decNumber * decNumberTrim(decNumber *dn) { - Int dropped; // work - decContext set; // .. - #if DECCHECK - if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; - #endif - decContextDefault(&set, DEC_INIT_BASE); // clamp=0 - return decTrim(dn, &set, 0, 1, &dropped); - } // decNumberTrim - -/* ------------------------------------------------------------------ */ -/* decNumberVersion -- return the name and version of this module */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -const char * decNumberVersion(void) { - return DECVERSION; - } // decNumberVersion - -/* ------------------------------------------------------------------ */ -/* decNumberZero -- set a number to 0 */ -/* */ -/* dn is the number to set, with space for one digit */ -/* returns dn */ -/* */ -/* No error is possible. */ -/* ------------------------------------------------------------------ */ -// Memset is not used as it is much slower in some environments. -decNumber * decNumberZero(decNumber *dn) { - - #if DECCHECK - if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; - #endif - - dn->bits=0; - dn->exponent=0; - dn->digits=1; - dn->lsu[0]=0; - return dn; - } // decNumberZero - -/* ================================================================== */ -/* Local routines */ -/* ================================================================== */ - -/* ------------------------------------------------------------------ */ -/* decToString -- lay out a number into a string */ -/* */ -/* dn is the number to lay out */ -/* string is where to lay out the number */ -/* eng is 1 if Engineering, 0 if Scientific */ -/* */ -/* string must be at least dn->digits+14 characters long */ -/* No error is possible. */ -/* */ -/* Note that this routine can generate a -0 or 0.000. These are */ -/* never generated in subset to-number or arithmetic, but can occur */ -/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ -/* ------------------------------------------------------------------ */ -// If DECCHECK is enabled the string "?" is returned if a number is -// invalid. -static void decToString(const decNumber *dn, char *string, Flag eng) { - Int exp=dn->exponent; // local copy - Int e; // E-part value - Int pre; // digits before the '.' - Int cut; // for counting digits in a Unit - char *c=string; // work [output pointer] - const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer] - uInt u, pow; // work - - #if DECCHECK - if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { - strcpy(string, "?"); - return;} - #endif - - if (decNumberIsNegative(dn)) { // Negatives get a minus - *c='-'; - c++; - } - if (dn->bits&DECSPECIAL) { // Is a special value - if (decNumberIsInfinite(dn)) { - strcpy(c, "Inf"); - strcpy(c+3, "inity"); - return;} - // a NaN - if (dn->bits&DECSNAN) { // signalling NaN - *c='s'; - c++; - } - strcpy(c, "NaN"); - c+=3; // step past - // if not a clean non-zero coefficient, that's all there is in a - // NaN string - if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; - // [drop through to add integer] - } - - // calculate how many digits in msu, and hence first cut - cut=MSUDIGITS(dn->digits); // [faster than remainder] - cut--; // power of ten for digit - - if (exp==0) { // simple integer [common fastpath] - for (;up>=dn->lsu; up--) { // each Unit from msu - u=*up; // contains DECDPUN digits to lay out - for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); - cut=DECDPUN-1; // next Unit has all digits - } - *c='\0'; // terminate the string - return;} - - /* non-0 exponent -- assume plain form */ - pre=dn->digits+exp; // digits before '.' - e=0; // no E - if ((exp>0) || (pre<-5)) { // need exponential form - e=exp+dn->digits-1; // calculate E value - pre=1; // assume one digit before '.' - if (eng && (e!=0)) { // engineering: may need to adjust - Int adj; // adjustment - // The C remainder operator is undefined for negative numbers, so - // a positive remainder calculation must be used here - if (e<0) { - adj=(-e)%3; - if (adj!=0) adj=3-adj; - } - else { // e>0 - adj=e%3; - } - e=e-adj; - // if dealing with zero still produce an exponent which is a - // multiple of three, as expected, but there will only be the - // one zero before the E, still. Otherwise note the padding. - if (!ISZERO(dn)) pre+=adj; - else { // is zero - if (adj!=0) { // 0.00Esnn needed - e=e+3; - pre=-(2-adj); - } - } // zero - } // eng - } // need exponent - - /* lay out the digits of the coefficient, adding 0s and . as needed */ - u=*up; - if (pre>0) { // xxx.xxx or xx00 (engineering) form - Int n=pre; - for (; pre>0; pre--, c++, cut--) { - if (cut<0) { // need new Unit - if (up==dn->lsu) break; // out of input digits (pre>digits) - up--; - cut=DECDPUN-1; - u=*up; - } - TODIGIT(u, cut, c, pow); - } - if (ndigits) { // more to come, after '.' - *c='.'; c++; - for (;; c++, cut--) { - if (cut<0) { // need new Unit - if (up==dn->lsu) break; // out of input digits - up--; - cut=DECDPUN-1; - u=*up; - } - TODIGIT(u, cut, c, pow); - } - } - else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed - } - else { // 0.xxx or 0.000xxx form - *c='0'; c++; - *c='.'; c++; - for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.' - for (; ; c++, cut--) { - if (cut<0) { // need new Unit - if (up==dn->lsu) break; // out of input digits - up--; - cut=DECDPUN-1; - u=*up; - } - TODIGIT(u, cut, c, pow); - } - } - - /* Finally add the E-part, if needed. It will never be 0, has a - base maximum and minimum of +999999999 through -999999999, but - could range down to -1999999998 for anormal numbers */ - if (e!=0) { - Flag had=0; // 1=had non-zero - *c='E'; c++; - *c='+'; c++; // assume positive - u=e; // .. - if (e<0) { - *(c-1)='-'; // oops, need - - u=-e; // uInt, please - } - // lay out the exponent [_itoa or equivalent is not ANSI C] - for (cut=9; cut>=0; cut--) { - TODIGIT(u, cut, c, pow); - if (*c=='0' && !had) continue; // skip leading zeros - had=1; // had non-0 - c++; // step for next - } // cut - } - *c='\0'; // terminate the string (all paths) - return; - } // decToString - -/* ------------------------------------------------------------------ */ -/* decAddOp -- add/subtract operation */ -/* */ -/* This computes C = A + B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* negate is DECNEG if rhs should be negated, or 0 otherwise */ -/* status accumulates status for the caller */ -/* */ -/* C must have space for set->digits digits. */ -/* Inexact in status must be 0 for correct Exact zero sign in result */ -/* ------------------------------------------------------------------ */ -/* If possible, the coefficient is calculated directly into C. */ -/* However, if: */ -/* -- a digits+1 calculation is needed because the numbers are */ -/* unaligned and span more than set->digits digits */ -/* -- a carry to digits+1 digits looks possible */ -/* -- C is the same as A or B, and the result would destructively */ -/* overlap the A or B coefficient */ -/* then the result must be calculated into a temporary buffer. In */ -/* this case a local (stack) buffer is used if possible, and only if */ -/* too long for that does malloc become the final resort. */ -/* */ -/* Misalignment is handled as follows: */ -/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ -/* BPad: Apply the padding by a combination of shifting (whole */ -/* units) and multiplication (part units). */ -/* */ -/* Addition, especially x=x+1, is speed-critical. */ -/* The static buffer is larger than might be expected to allow for */ -/* calls from higher-level funtions (notable exp). */ -/* ------------------------------------------------------------------ */ -static decNumber * decAddOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - uByte negate, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - Int rhsshift; // working shift (in Units) - Int maxdigits; // longest logical length - Int mult; // multiplier - Int residue; // rounding accumulator - uByte bits; // result bits - Flag diffsign; // non-0 if arguments have different sign - Unit *acc; // accumulator for result - Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many - // allocations when called from - // other operations, notable exp] - Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated - Int reqdigits=set->digits; // local copy; requested DIGITS - Int padding; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // note whether signs differ [used all paths] - diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); - - // handle infinities and NaNs - if (SPECIALARGS) { // a special bit set - if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN - decNaNs(res, lhs, rhs, set, status); - else { // one or two infinities - if (decNumberIsInfinite(lhs)) { // LHS is infinity - // two infinities with different signs is invalid - if (decNumberIsInfinite(rhs) && diffsign) { - *status|=DEC_Invalid_operation; - break; - } - bits=lhs->bits & DECNEG; // get sign from LHS - } - else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity - bits|=DECINF; - decNumberZero(res); - res->bits=bits; // set +/- infinity - } // an infinity - break; - } - - // Quick exit for add 0s; return the non-0, modified as need be - if (ISZERO(lhs)) { - Int adjust; // work - Int lexp=lhs->exponent; // save in case LHS==RES - bits=lhs->bits; // .. - residue=0; // clear accumulator - decCopyFit(res, rhs, set, &residue, status); // copy (as needed) - res->bits^=negate; // flip if rhs was negated - #if DECSUBSET - if (set->extended) { // exponents on zeros count - #endif - // exponent will be the lower of the two - adjust=lexp-res->exponent; // adjustment needed [if -ve] - if (ISZERO(res)) { // both 0: special IEEE 754 rules - if (adjust<0) res->exponent=lexp; // set exponent - // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 - if (diffsign) { - if (set->round!=DEC_ROUND_FLOOR) res->bits=0; - else res->bits=DECNEG; // preserve 0 sign - } - } - else { // non-0 res - if (adjust<0) { // 0-padding needed - if ((res->digits-adjust)>set->digits) { - adjust=res->digits-set->digits; // to fit exactly - *status|=DEC_Rounded; // [but exact] - } - res->digits=decShiftToMost(res->lsu, res->digits, -adjust); - res->exponent+=adjust; // set the exponent. - } - } // non-0 res - #if DECSUBSET - } // extended - #endif - decFinish(res, set, &residue, status); // clean and finalize - break;} - - if (ISZERO(rhs)) { // [lhs is non-zero] - Int adjust; // work - Int rexp=rhs->exponent; // save in case RHS==RES - bits=rhs->bits; // be clean - residue=0; // clear accumulator - decCopyFit(res, lhs, set, &residue, status); // copy (as needed) - #if DECSUBSET - if (set->extended) { // exponents on zeros count - #endif - // exponent will be the lower of the two - // [0-0 case handled above] - adjust=rexp-res->exponent; // adjustment needed [if -ve] - if (adjust<0) { // 0-padding needed - if ((res->digits-adjust)>set->digits) { - adjust=res->digits-set->digits; // to fit exactly - *status|=DEC_Rounded; // [but exact] - } - res->digits=decShiftToMost(res->lsu, res->digits, -adjust); - res->exponent+=adjust; // set the exponent. - } - #if DECSUBSET - } // extended - #endif - decFinish(res, set, &residue, status); // clean and finalize - break;} - - // [NB: both fastpath and mainpath code below assume these cases - // (notably 0-0) have already been handled] - - // calculate the padding needed to align the operands - padding=rhs->exponent-lhs->exponent; - - // Fastpath cases where the numbers are aligned and normal, the RHS - // is all in one unit, no operand rounding is needed, and no carry, - // lengthening, or borrow is needed - if (padding==0 - && rhs->digits<=DECDPUN - && rhs->exponent>=set->emin // [some normals drop through] - && rhs->exponent<=set->emax-set->digits+1 // [could clamp] - && rhs->digits<=reqdigits - && lhs->digits<=reqdigits) { - Int partial=*lhs->lsu; - if (!diffsign) { // adding - partial+=*rhs->lsu; - if ((partial<=DECDPUNMAX) // result fits in unit - && (lhs->digits>=DECDPUN || // .. and no digits-count change - partial<(Int)powers[lhs->digits])) { // .. - if (res!=lhs) decNumberCopy(res, lhs); // not in place - *res->lsu=(Unit)partial; // [copy could have overwritten RHS] - break; - } - // else drop out for careful add - } - else { // signs differ - partial-=*rhs->lsu; - if (partial>0) { // no borrow needed, and non-0 result - if (res!=lhs) decNumberCopy(res, lhs); // not in place - *res->lsu=(Unit)partial; - // this could have reduced digits [but result>0] - res->digits=decGetDigits(res->lsu, D2U(res->digits)); - break; - } - // else drop out for careful subtract - } - } - - // Now align (pad) the lhs or rhs so they can be added or - // subtracted, as necessary. If one number is much larger than - // the other (that is, if in plain form there is a least one - // digit between the lowest digit of one and the highest of the - // other) padding with up to DIGITS-1 trailing zeros may be - // needed; then apply rounding (as exotic rounding modes may be - // affected by the residue). - rhsshift=0; // rhs shift to left (padding) in Units - bits=lhs->bits; // assume sign is that of LHS - mult=1; // likely multiplier - - // [if padding==0 the operands are aligned; no padding is needed] - if (padding!=0) { - // some padding needed; always pad the RHS, as any required - // padding can then be effected by a simple combination of - // shifts and a multiply - Flag swapped=0; - if (padding<0) { // LHS needs the padding - const decNumber *t; - padding=-padding; // will be +ve - bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS - t=lhs; lhs=rhs; rhs=t; - swapped=1; - } - - // If, after pad, rhs would be longer than lhs by digits+1 or - // more then lhs cannot affect the answer, except as a residue, - // so only need to pad up to a length of DIGITS+1. - if (rhs->digits+padding > lhs->digits+reqdigits+1) { - // The RHS is sufficient - // for residue use the relative sign indication... - Int shift=reqdigits-rhs->digits; // left shift needed - residue=1; // residue for rounding - if (diffsign) residue=-residue; // signs differ - // copy, shortening if necessary - decCopyFit(res, rhs, set, &residue, status); - // if it was already shorter, then need to pad with zeros - if (shift>0) { - res->digits=decShiftToMost(res->lsu, res->digits, shift); - res->exponent-=shift; // adjust the exponent. - } - // flip the result sign if unswapped and rhs was negated - if (!swapped) res->bits^=negate; - decFinish(res, set, &residue, status); // done - break;} - - // LHS digits may affect result - rhsshift=D2U(padding+1)-1; // this much by Unit shift .. - mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication - } // padding needed - - if (diffsign) mult=-mult; // signs differ - - // determine the longer operand - maxdigits=rhs->digits+padding; // virtual length of RHS - if (lhs->digits>maxdigits) maxdigits=lhs->digits; - - // Decide on the result buffer to use; if possible place directly - // into result. - acc=res->lsu; // assume add direct to result - // If destructive overlap, or the number is too long, or a carry or - // borrow to DIGITS+1 might be possible, a buffer must be used. - // [Might be worth more sophisticated tests when maxdigits==reqdigits] - if ((maxdigits>=reqdigits) // is, or could be, too large - || (res==rhs && rhsshift>0)) { // destructive overlap - // buffer needed, choose it; units for maxdigits digits will be - // needed, +1 Unit for carry or borrow - Int need=D2U(maxdigits)+1; - acc=accbuff; // assume use local buffer - if (need*sizeof(Unit)>sizeof(accbuff)) { - // printf("malloc add %ld %ld\n", need, sizeof(accbuff)); - allocacc=(Unit *)malloc(need*sizeof(Unit)); - if (allocacc==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - acc=allocacc; - } - } - - res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite.. - res->exponent=lhs->exponent; // .. operands (even if aliased) - - #if DECTRACE - decDumpAr('A', lhs->lsu, D2U(lhs->digits)); - decDumpAr('B', rhs->lsu, D2U(rhs->digits)); - printf(" :h: %ld %ld\n", rhsshift, mult); - #endif - - // add [A+B*m] or subtract [A+B*(-m)] - res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), - rhs->lsu, D2U(rhs->digits), - rhsshift, acc, mult) - *DECDPUN; // [units -> digits] - if (res->digits<0) { // borrowed... - res->digits=-res->digits; - res->bits^=DECNEG; // flip the sign - } - #if DECTRACE - decDumpAr('+', acc, D2U(res->digits)); - #endif - - // If a buffer was used the result must be copied back, possibly - // shortening. (If no buffer was used then the result must have - // fit, so can't need rounding and residue must be 0.) - residue=0; // clear accumulator - if (acc!=res->lsu) { - #if DECSUBSET - if (set->extended) { // round from first significant digit - #endif - // remove leading zeros that were added due to rounding up to - // integral Units -- before the test for rounding. - if (res->digits>reqdigits) - res->digits=decGetDigits(acc, D2U(res->digits)); - decSetCoeff(res, set, acc, res->digits, &residue, status); - #if DECSUBSET - } - else { // subset arithmetic rounds from original significant digit - // May have an underestimate. This only occurs when both - // numbers fit in DECDPUN digits and are padding with a - // negative multiple (-10, -100...) and the top digit(s) become - // 0. (This only matters when using X3.274 rules where the - // leading zero could be included in the rounding.) - if (res->digitsdigits))=0; // ensure leading 0 is there - res->digits=maxdigits; - } - else { - // remove leading zeros that added due to rounding up to - // integral Units (but only those in excess of the original - // maxdigits length, unless extended) before test for rounding. - if (res->digits>reqdigits) { - res->digits=decGetDigits(acc, D2U(res->digits)); - if (res->digitsdigits=maxdigits; - } - } - decSetCoeff(res, set, acc, res->digits, &residue, status); - // Now apply rounding if needed before removing leading zeros. - // This is safe because subnormals are not a possibility - if (residue!=0) { - decApplyRound(res, set, residue, status); - residue=0; // did what needed to be done - } - } // subset - #endif - } // used buffer - - // strip leading zeros [these were left on in case of subset subtract] - res->digits=decGetDigits(res->lsu, D2U(res->digits)); - - // apply checks and rounding - decFinish(res, set, &residue, status); - - // "When the sum of two operands with opposite signs is exactly - // zero, the sign of that sum shall be '+' in all rounding modes - // except round toward -Infinity, in which mode that sign shall be - // '-'." [Subset zeros also never have '-', set by decFinish.] - if (ISZERO(res) && diffsign - #if DECSUBSET - && set->extended - #endif - && (*status&DEC_Inexact)==0) { - if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign - - else res->bits&=~DECNEG; // sign + - } - } while(0); // end protected - - if (allocacc!=NULL) free(allocacc); // drop any storage used - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // .. - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decAddOp - -/* ------------------------------------------------------------------ */ -/* decDivideOp -- division operation */ -/* */ -/* This routine performs the calculations for all four division */ -/* operators (divide, divideInteger, remainder, remainderNear). */ -/* */ -/* C=A op B */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ -/* status is the usual accumulator */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* ------------------------------------------------------------------ */ -/* The underlying algorithm of this routine is the same as in the */ -/* 1981 S/370 implementation, that is, non-restoring long division */ -/* with bi-unit (rather than bi-digit) estimation for each unit */ -/* multiplier. In this pseudocode overview, complications for the */ -/* Remainder operators and division residues for exact rounding are */ -/* omitted for clarity. */ -/* */ -/* Prepare operands and handle special values */ -/* Test for x/0 and then 0/x */ -/* Exp =Exp1 - Exp2 */ -/* Exp =Exp +len(var1) -len(var2) */ -/* Sign=Sign1 * Sign2 */ -/* Pad accumulator (Var1) to double-length with 0's (pad1) */ -/* Pad Var2 to same length as Var1 */ -/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ -/* have=0 */ -/* Do until (have=digits+1 OR residue=0) */ -/* if exp<0 then if integer divide/residue then leave */ -/* this_unit=0 */ -/* Do forever */ -/* compare numbers */ -/* if <0 then leave inner_loop */ -/* if =0 then (* quick exit without subtract *) do */ -/* this_unit=this_unit+1; output this_unit */ -/* leave outer_loop; end */ -/* Compare lengths of numbers (mantissae): */ -/* If same then tops2=msu2pair -- {units 1&2 of var2} */ -/* else tops2=msu2plus -- {0, unit 1 of var2} */ -/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ -/* mult=tops1/tops2 -- Good and safe guess at divisor */ -/* if mult=0 then mult=1 */ -/* this_unit=this_unit+mult */ -/* subtract */ -/* end inner_loop */ -/* if have\=0 | this_unit\=0 then do */ -/* output this_unit */ -/* have=have+1; end */ -/* var2=var2/10 */ -/* exp=exp-1 */ -/* end outer_loop */ -/* exp=exp+1 -- set the proper exponent */ -/* if have=0 then generate answer=0 */ -/* Return (Result is defined by Var1) */ -/* */ -/* ------------------------------------------------------------------ */ -/* Two working buffers are needed during the division; one (digits+ */ -/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ -/* long subtractions. These are acc and var1 respectively. */ -/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ -/* The static buffers may be larger than might be expected to allow */ -/* for calls from higher-level funtions (notable exp). */ -/* ------------------------------------------------------------------ */ -static decNumber * decDivideOp(decNumber *res, - const decNumber *lhs, const decNumber *rhs, - decContext *set, Flag op, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer - Unit *acc=accbuff; // -> accumulator array for result - Unit *allocacc=NULL; // -> allocated buffer, iff allocated - Unit *accnext; // -> where next digit will go - Int acclength; // length of acc needed [Units] - Int accunits; // count of units accumulated - Int accdigits; // count of digits accumulated - - Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1 - Unit *var1=varbuff; // -> var1 array for long subtraction - Unit *varalloc=NULL; // -> allocated buffer, iff used - Unit *msu1; // -> msu of var1 - - const Unit *var2; // -> var2 array - const Unit *msu2; // -> msu of var2 - Int msu2plus; // msu2 plus one [does not vary] - eInt msu2pair; // msu2 pair plus one [does not vary] - - Int var1units, var2units; // actual lengths - Int var2ulen; // logical length (units) - Int var1initpad=0; // var1 initial padding (digits) - Int maxdigits; // longest LHS or required acc length - Int mult; // multiplier for subtraction - Unit thisunit; // current unit being accumulated - Int residue; // for rounding - Int reqdigits=set->digits; // requested DIGITS - Int exponent; // working exponent - Int maxexponent=0; // DIVIDE maximum exponent if unrounded - uByte bits; // working sign - Unit *target; // work - const Unit *source; // .. - uInt const *pow; // .. - Int shift, cut; // .. - #if DECSUBSET - Int dropped; // work - #endif - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions - - // handle infinities and NaNs - if (SPECIALARGS) { // a special bit set - if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs - decNaNs(res, lhs, rhs, set, status); - break; - } - // one or two infinities - if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite - if (decNumberIsInfinite(rhs) || // two infinities are invalid .. - op & (REMAINDER | REMNEAR)) { // as is remainder of infinity - *status|=DEC_Invalid_operation; - break; - } - // [Note that infinity/0 raises no exceptions] - decNumberZero(res); - res->bits=bits|DECINF; // set +/- infinity - break; - } - else { // RHS (divisor) is infinite - residue=0; - if (op&(REMAINDER|REMNEAR)) { - // result is [finished clone of] lhs - decCopyFit(res, lhs, set, &residue, status); - } - else { // a division - decNumberZero(res); - res->bits=bits; // set +/- zero - // for DIVIDEINT the exponent is always 0. For DIVIDE, result - // is a 0 with infinitely negative exponent, clamped to minimum - if (op&DIVIDE) { - res->exponent=set->emin-set->digits+1; - *status|=DEC_Clamped; - } - } - decFinish(res, set, &residue, status); - break; - } - } - - // handle 0 rhs (x/0) - if (ISZERO(rhs)) { // x/0 is always exceptional - if (ISZERO(lhs)) { - decNumberZero(res); // [after lhs test] - *status|=DEC_Division_undefined;// 0/0 will become NaN - } - else { - decNumberZero(res); - if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; - else { - *status|=DEC_Division_by_zero; // x/0 - res->bits=bits|DECINF; // .. is +/- Infinity - } - } - break;} - - // handle 0 lhs (0/x) - if (ISZERO(lhs)) { // 0/x [x!=0] - #if DECSUBSET - if (!set->extended) decNumberZero(res); - else { - #endif - if (op&DIVIDE) { - residue=0; - exponent=lhs->exponent-rhs->exponent; // ideal exponent - decNumberCopy(res, lhs); // [zeros always fit] - res->bits=bits; // sign as computed - res->exponent=exponent; // exponent, too - decFinalize(res, set, &residue, status); // check exponent - } - else if (op&DIVIDEINT) { - decNumberZero(res); // integer 0 - res->bits=bits; // sign as computed - } - else { // a remainder - exponent=rhs->exponent; // [save in case overwrite] - decNumberCopy(res, lhs); // [zeros always fit] - if (exponentexponent) res->exponent=exponent; // use lower - } - #if DECSUBSET - } - #endif - break;} - - // Precalculate exponent. This starts off adjusted (and hence fits - // in 31 bits) and becomes the usual unadjusted exponent as the - // division proceeds. The order of evaluation is important, here, - // to avoid wrap. - exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); - - // If the working exponent is -ve, then some quick exits are - // possible because the quotient is known to be <1 - // [for REMNEAR, it needs to be < -1, as -0.5 could need work] - if (exponent<0 && !(op==DIVIDE)) { - if (op&DIVIDEINT) { - decNumberZero(res); // integer part is 0 - #if DECSUBSET - if (set->extended) - #endif - res->bits=bits; // set +/- zero - break;} - // fastpath remainders so long as the lhs has the smaller - // (or equal) exponent - if (lhs->exponent<=rhs->exponent) { - if (op&REMAINDER || exponent<-1) { - // It is REMAINDER or safe REMNEAR; result is [finished - // clone of] lhs (r = x - 0*y) - residue=0; - decCopyFit(res, lhs, set, &residue, status); - decFinish(res, set, &residue, status); - break; - } - // [unsafe REMNEAR drops through] - } - } // fastpaths - - /* Long (slow) division is needed; roll up the sleeves... */ - - // The accumulator will hold the quotient of the division. - // If it needs to be too long for stack storage, then allocate. - acclength=D2U(reqdigits+DECDPUN); // in Units - if (acclength*sizeof(Unit)>sizeof(accbuff)) { - // printf("malloc dvacc %ld units\n", acclength); - allocacc=(Unit *)malloc(acclength*sizeof(Unit)); - if (allocacc==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - acc=allocacc; // use the allocated space - } - - // var1 is the padded LHS ready for subtractions. - // If it needs to be too long for stack storage, then allocate. - // The maximum units needed for var1 (long subtraction) is: - // Enough for - // (rhs->digits+reqdigits-1) -- to allow full slide to right - // or (lhs->digits) -- to allow for long lhs - // whichever is larger - // +1 -- for rounding of slide to right - // +1 -- for leading 0s - // +1 -- for pre-adjust if a remainder or DIVIDEINT - // [Note: unused units do not participate in decUnitAddSub data] - maxdigits=rhs->digits+reqdigits-1; - if (lhs->digits>maxdigits) maxdigits=lhs->digits; - var1units=D2U(maxdigits)+2; - // allocate a guard unit above msu1 for REMAINDERNEAR - if (!(op&DIVIDE)) var1units++; - if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { - // printf("malloc dvvar %ld units\n", var1units+1); - varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); - if (varalloc==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - var1=varalloc; // use the allocated space - } - - // Extend the lhs and rhs to full long subtraction length. The lhs - // is truly extended into the var1 buffer, with 0 padding, so a - // subtract in place is always possible. The rhs (var2) has - // virtual padding (implemented by decUnitAddSub). - // One guard unit was allocated above msu1 for rem=rem+rem in - // REMAINDERNEAR. - msu1=var1+var1units-1; // msu of var1 - source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array - for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; - for (; target>=var1; target--) *target=0; - - // rhs (var2) is left-aligned with var1 at the start - var2ulen=var1units; // rhs logical length (units) - var2units=D2U(rhs->digits); // rhs actual length (units) - var2=rhs->lsu; // -> rhs array - msu2=var2+var2units-1; // -> msu of var2 [never changes] - // now set up the variables which will be used for estimating the - // multiplication factor. If these variables are not exact, add - // 1 to make sure that the multiplier is never overestimated. - msu2plus=*msu2; // it's value .. - if (var2units>1) msu2plus++; // .. +1 if any more - msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair .. - if (var2units>1) { // .. [else treat 2nd as 0] - msu2pair+=*(msu2-1); // .. - if (var2units>2) msu2pair++; // .. +1 if any more - } - - // The calculation is working in units, which may have leading zeros, - // but the exponent was calculated on the assumption that they are - // both left-aligned. Adjust the exponent to compensate: add the - // number of leading zeros in var1 msu and subtract those in var2 msu. - // [This is actually done by counting the digits and negating, as - // lead1=DECDPUN-digits1, and similarly for lead2.] - for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; - for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; - - // Now, if doing an integer divide or remainder, ensure that - // the result will be Unit-aligned. To do this, shift the var1 - // accumulator towards least if need be. (It's much easier to - // do this now than to reassemble the residue afterwards, if - // doing a remainder.) Also ensure the exponent is not negative. - if (!(op&DIVIDE)) { - Unit *u; // work - // save the initial 'false' padding of var1, in digits - var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; - // Determine the shift to do. - if (exponent<0) cut=-exponent; - else cut=DECDPUN-exponent%DECDPUN; - decShiftToLeast(var1, var1units, cut); - exponent+=cut; // maintain numerical value - var1initpad-=cut; // .. and reduce padding - // clean any most-significant units which were just emptied - for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; - } // align - else { // is DIVIDE - maxexponent=lhs->exponent-rhs->exponent; // save - // optimization: if the first iteration will just produce 0, - // preadjust to skip it [valid for DIVIDE only] - if (*msu1<*msu2) { - var2ulen--; // shift down - exponent-=DECDPUN; // update the exponent - } - } - - // ---- start the long-division loops ------------------------------ - accunits=0; // no units accumulated yet - accdigits=0; // .. or digits - accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1] - for (;;) { // outer forever loop - thisunit=0; // current unit assumed 0 - // find the next unit - for (;;) { // inner forever loop - // strip leading zero units [from either pre-adjust or from - // subtract last time around]. Leave at least one unit. - for (; *msu1==0 && msu1>var1; msu1--) var1units--; - - if (var1units msu - for (pv1=msu1; ; pv1--, pv2--) { - // v1=*pv1 -- always OK - v2=0; // assume in padding - if (pv2>=var2) v2=*pv2; // in range - if (*pv1!=v2) break; // no longer the same - if (pv1==var1) break; // done; leave pv1 as is - } - // here when all inspected or a difference seen - if (*pv1v2. Prepare for real subtraction; the lengths are equal - // Estimate the multiplier (there's always a msu1-1)... - // Bring in two units of var2 to provide a good estimate. - mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); - } // lengths the same - else { // var1units > var2ulen, so subtraction is safe - // The var2 msu is one unit towards the lsu of the var1 msu, - // so only one unit for var2 can be used. - mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); - } - if (mult==0) mult=1; // must always be at least 1 - // subtraction needed; var1 is > var2 - thisunit=(Unit)(thisunit+mult); // accumulate - // subtract var1-var2, into var1; only the overlap needs - // processing, as this is an in-place calculation - shift=var2ulen-var2units; - #if DECTRACE - decDumpAr('1', &var1[shift], var1units-shift); - decDumpAr('2', var2, var2units); - printf("m=%ld\n", -mult); - #endif - decUnitAddSub(&var1[shift], var1units-shift, - var2, var2units, 0, - &var1[shift], -mult); - #if DECTRACE - decDumpAr('#', &var1[shift], var1units-shift); - #endif - // var1 now probably has leading zeros; these are removed at the - // top of the inner loop. - } // inner loop - - // The next unit has been calculated in full; unless it's a - // leading zero, add to acc - if (accunits!=0 || thisunit!=0) { // is first or non-zero - *accnext=thisunit; // store in accumulator - // account exactly for the new digits - if (accunits==0) { - accdigits++; // at least one - for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; - } - else accdigits+=DECDPUN; - accunits++; // update count - accnext--; // ready for next - if (accdigits>reqdigits) break; // have enough digits - } - - // if the residue is zero, the operation is done (unless divide - // or divideInteger and still not enough digits yet) - if (*var1==0 && var1units==1) { // residue is 0 - if (op&(REMAINDER|REMNEAR)) break; - if ((op&DIVIDE) && (exponent<=maxexponent)) break; - // [drop through if divideInteger] - } - // also done enough if calculating remainder or integer - // divide and just did the last ('units') unit - if (exponent==0 && !(op&DIVIDE)) break; - - // to get here, var1 is less than var2, so divide var2 by the per- - // Unit power of ten and go for the next digit - var2ulen--; // shift down - exponent-=DECDPUN; // update the exponent - } // outer loop - - // ---- division is complete --------------------------------------- - // here: acc has at least reqdigits+1 of good results (or fewer - // if early stop), starting at accnext+1 (its lsu) - // var1 has any residue at the stopping point - // accunits is the number of digits collected in acc - if (accunits==0) { // acc is 0 - accunits=1; // show have a unit .. - accdigits=1; // .. - *accnext=0; // .. whose value is 0 - } - else accnext++; // back to last placed - // accnext now -> lowest unit of result - - residue=0; // assume no residue - if (op&DIVIDE) { - // record the presence of any residue, for rounding - if (*var1!=0 || var1units>1) residue=1; - else { // no residue - // Had an exact division; clean up spurious trailing 0s. - // There will be at most DECDPUN-1, from the final multiply, - // and then only if the result is non-0 (and even) and the - // exponent is 'loose'. - #if DECDPUN>1 - Unit lsu=*accnext; - if (!(lsu&0x01) && (lsu!=0)) { - // count the trailing zeros - Int drop=0; - for (;; drop++) { // [will terminate because lsu!=0] - if (exponent>=maxexponent) break; // don't chop real 0s - #if DECDPUN<=4 - if ((lsu-QUOT10(lsu, drop+1) - *powers[drop+1])!=0) break; // found non-0 digit - #else - if (lsu%powers[drop+1]!=0) break; // found non-0 digit - #endif - exponent++; - } - if (drop>0) { - accunits=decShiftToLeast(accnext, accunits, drop); - accdigits=decGetDigits(accnext, accunits); - accunits=D2U(accdigits); - // [exponent was adjusted in the loop] - } - } // neither odd nor 0 - #endif - } // exact divide - } // divide - else /* op!=DIVIDE */ { - // check for coefficient overflow - if (accdigits+exponent>reqdigits) { - *status|=DEC_Division_impossible; - break; - } - if (op & (REMAINDER|REMNEAR)) { - // [Here, the exponent will be 0, because var1 was adjusted - // appropriately.] - Int postshift; // work - Flag wasodd=0; // integer was odd - Unit *quotlsu; // for save - Int quotdigits; // .. - - bits=lhs->bits; // remainder sign is always as lhs - - // Fastpath when residue is truly 0 is worthwhile [and - // simplifies the code below] - if (*var1==0 && var1units==1) { // residue is 0 - Int exp=lhs->exponent; // save min(exponents) - if (rhs->exponentexponent; - decNumberZero(res); // 0 coefficient - #if DECSUBSET - if (set->extended) - #endif - res->exponent=exp; // .. with proper exponent - res->bits=(uByte)(bits&DECNEG); // [cleaned] - decFinish(res, set, &residue, status); // might clamp - break; - } - // note if the quotient was odd - if (*accnext & 0x01) wasodd=1; // acc is odd - quotlsu=accnext; // save in case need to reinspect - quotdigits=accdigits; // .. - - // treat the residue, in var1, as the value to return, via acc - // calculate the unused zero digits. This is the smaller of: - // var1 initial padding (saved above) - // var2 residual padding, which happens to be given by: - postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; - // [the 'exponent' term accounts for the shifts during divide] - if (var1initpadexponent; // exponent is smaller of lhs & rhs - if (rhs->exponentexponent; - - // Now correct the result if doing remainderNear; if it - // (looking just at coefficients) is > rhs/2, or == rhs/2 and - // the integer was odd then the result should be rem-rhs. - if (op&REMNEAR) { - Int compare, tarunits; // work - Unit *up; // .. - // calculate remainder*2 into the var1 buffer (which has - // 'headroom' of an extra unit and hence enough space) - // [a dedicated 'double' loop would be faster, here] - tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, - 0, accnext, 1); - // decDumpAr('r', accnext, tarunits); - - // Here, accnext (var1) holds tarunits Units with twice the - // remainder's coefficient, which must now be compared to the - // RHS. The remainder's exponent may be smaller than the RHS's. - compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), - rhs->exponent-exponent); - if (compare==BADINT) { // deep trouble - *status|=DEC_Insufficient_storage; - break;} - - // now restore the remainder by dividing by two; the lsu - // is known to be even. - for (up=accnext; up0 || (compare==0 && wasodd)) { // adjustment needed - Int exp, expunits, exprem; // work - // This is effectively causing round-up of the quotient, - // so if it was the rare case where it was full and all - // nines, it would overflow and hence division-impossible - // should be raised - Flag allnines=0; // 1 if quotient all nines - if (quotdigits==reqdigits) { // could be borderline - for (up=quotlsu; ; up++) { - if (quotdigits>DECDPUN) { - if (*up!=DECDPUNMAX) break;// non-nines - } - else { // this is the last Unit - if (*up==powers[quotdigits]-1) allnines=1; - break; - } - quotdigits-=DECDPUN; // checked those digits - } // up - } // borderline check - if (allnines) { - *status|=DEC_Division_impossible; - break;} - - // rem-rhs is needed; the sign will invert. Again, var1 - // can safely be used for the working Units array. - exp=rhs->exponent-exponent; // RHS padding needed - // Calculate units and remainder from exponent. - expunits=exp/DECDPUN; - exprem=exp%DECDPUN; - // subtract [A+B*(-m)]; the result will always be negative - accunits=-decUnitAddSub(accnext, accunits, - rhs->lsu, D2U(rhs->digits), - expunits, accnext, -(Int)powers[exprem]); - accdigits=decGetDigits(accnext, accunits); // count digits exactly - accunits=D2U(accdigits); // and recalculate the units for copy - // [exponent is as for original remainder] - bits^=DECNEG; // flip the sign - } - } // REMNEAR - } // REMAINDER or REMNEAR - } // not DIVIDE - - // Set exponent and bits - res->exponent=exponent; - res->bits=(uByte)(bits&DECNEG); // [cleaned] - - // Now the coefficient. - decSetCoeff(res, set, accnext, accdigits, &residue, status); - - decFinish(res, set, &residue, status); // final cleanup - - #if DECSUBSET - // If a divide then strip trailing zeros if subset [after round] - if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); - #endif - } while(0); // end protected - - if (varalloc!=NULL) free(varalloc); // drop any storage used - if (allocacc!=NULL) free(allocacc); // .. - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // .. - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decDivideOp - -/* ------------------------------------------------------------------ */ -/* decMultiplyOp -- multiplication operation */ -/* */ -/* This routine performs the multiplication C=A x B. */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* status is the usual accumulator */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* ------------------------------------------------------------------ */ -/* 'Classic' multiplication is used rather than Karatsuba, as the */ -/* latter would give only a minor improvement for the short numbers */ -/* expected to be handled most (and uses much more memory). */ -/* */ -/* There are two major paths here: the general-purpose ('old code') */ -/* path which handles all DECDPUN values, and a fastpath version */ -/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ -/* than two calls to decUnitAddSub would be made. */ -/* */ -/* The fastpath version lumps units together into 8-digit or 9-digit */ -/* chunks, and also uses a lazy carry strategy to minimise expensive */ -/* 64-bit divisions. The chunks are then broken apart again into */ -/* units for continuing processing. Despite this overhead, the */ -/* fastpath can speed up some 16-digit operations by 10x (and much */ -/* more for higher-precision calculations). */ -/* */ -/* A buffer always has to be used for the accumulator; in the */ -/* fastpath, buffers are also always needed for the chunked copies of */ -/* of the operand coefficients. */ -/* Static buffers are larger than needed just for multiply, to allow */ -/* for calls from other operations (notably exp). */ -/* ------------------------------------------------------------------ */ -#define FASTMUL (DECUSE64 && DECDPUN<5) -static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - uInt *status) { - Int accunits; // Units of accumulator in use - Int exponent; // work - Int residue=0; // rounding residue - uByte bits; // result sign - Unit *acc; // -> accumulator Unit array - Int needbytes; // size calculator - void *allocacc=NULL; // -> allocated accumulator, iff allocated - Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0, - // *4 for calls from other operations) - const Unit *mer, *mermsup; // work - Int madlength; // Units in multiplicand - Int shift; // Units to shift multiplicand by - - #if FASTMUL - // if DECDPUN is 1 or 3 work in base 10**9, otherwise - // (DECDPUN is 2 or 4) then work in base 10**8 - #if DECDPUN & 1 // odd - #define FASTBASE 1000000000 // base - #define FASTDIGS 9 // digits in base - #define FASTLAZY 18 // carry resolution point [1->18] - #else - #define FASTBASE 100000000 - #define FASTDIGS 8 - #define FASTLAZY 1844 // carry resolution point [1->1844] - #endif - // three buffers are used, two for chunked copies of the operands - // (base 10**8 or base 10**9) and one base 2**64 accumulator with - // lazy carry evaluation - uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) - uInt *zlhi=zlhibuff; // -> lhs array - uInt *alloclhi=NULL; // -> allocated buffer, iff allocated - uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) - uInt *zrhi=zrhibuff; // -> rhs array - uInt *allocrhi=NULL; // -> allocated buffer, iff allocated - uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0) - // [allocacc is shared for both paths, as only one will run] - uLong *zacc=zaccbuff; // -> accumulator array for exact result - #if DECDPUN==1 - Int zoff; // accumulator offset - #endif - uInt *lip, *rip; // item pointers - uInt *lmsi, *rmsi; // most significant items - Int ilhs, irhs, iacc; // item counts in the arrays - Int lazy; // lazy carry counter - uLong lcarry; // uLong carry - uInt carry; // carry (NB not uLong) - Int count; // work - const Unit *cup; // .. - Unit *up; // .. - uLong *lp; // .. - Int p; // .. - #endif - - #if DECSUBSET - decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated - decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated - #endif - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - // precalculate result sign - bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); - - // handle infinities and NaNs - if (SPECIALARGS) { // a special bit set - if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs - decNaNs(res, lhs, rhs, set, status); - return res;} - // one or two infinities; Infinity * 0 is invalid - if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) - ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { - *status|=DEC_Invalid_operation; - return res;} - decNumberZero(res); - res->bits=bits|DECINF; // infinity - return res;} - - // For best speed, as in DMSRCN [the original Rexx numerics - // module], use the shorter number as the multiplier (rhs) and - // the longer as the multiplicand (lhs) to minimise the number of - // adds (partial products) - if (lhs->digitsdigits) { // swap... - const decNumber *hold=lhs; - lhs=rhs; - rhs=hold; - } - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>set->digits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - #if FASTMUL // fastpath can be used - // use the fast path if there are enough digits in the shorter - // operand to make the setup and takedown worthwhile - #define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls - if (rhs->digits>NEEDTWO) { // use fastpath... - // calculate the number of elements in each array - ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling] - irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // .. - iacc=ilhs+irhs; - - // allocate buffers if required, as usual - needbytes=ilhs*sizeof(uInt); - if (needbytes>(Int)sizeof(zlhibuff)) { - alloclhi=(uInt *)malloc(needbytes); - zlhi=alloclhi;} - needbytes=irhs*sizeof(uInt); - if (needbytes>(Int)sizeof(zrhibuff)) { - allocrhi=(uInt *)malloc(needbytes); - zrhi=allocrhi;} - - // Allocating the accumulator space needs a special case when - // DECDPUN=1 because when converting the accumulator to Units - // after the multiplication each 8-byte item becomes 9 1-byte - // units. Therefore iacc extra bytes are needed at the front - // (rounded up to a multiple of 8 bytes), and the uLong - // accumulator starts offset the appropriate number of units - // to the right to avoid overwrite during the unchunking. - needbytes=iacc*sizeof(uLong); - #if DECDPUN==1 - zoff=(iacc+7)/8; // items to offset by - needbytes+=zoff*8; - #endif - if (needbytes>(Int)sizeof(zaccbuff)) { - allocacc=(uLong *)malloc(needbytes); - zacc=(uLong *)allocacc;} - if (zlhi==NULL||zrhi==NULL||zacc==NULL) { - *status|=DEC_Insufficient_storage; - break;} - - acc=(Unit *)zacc; // -> target Unit array - #if DECDPUN==1 - zacc+=zoff; // start uLong accumulator to right - #endif - - // assemble the chunked copies of the left and right sides - for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) - for (p=0, *lip=0; p0; - p+=DECDPUN, cup++, count-=DECDPUN) - *lip+=*cup*powers[p]; - lmsi=lip-1; // save -> msi - for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) - for (p=0, *rip=0; p0; - p+=DECDPUN, cup++, count-=DECDPUN) - *rip+=*cup*powers[p]; - rmsi=rip-1; // save -> msi - - // zero the accumulator - for (lp=zacc; lp0 && rip!=rmsi) continue; - lazy=FASTLAZY; // reset delay count - // spin up the accumulator resolving overflows - for (lp=zacc; lp assume buffer for accumulator - needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); - if (needbytes>(Int)sizeof(accbuff)) { - allocacc=(Unit *)malloc(needbytes); - if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} - acc=(Unit *)allocacc; // use the allocated space - } - - /* Now the main long multiplication loop */ - // Unlike the equivalent in the IBM Java implementation, there - // is no advantage in calculating from msu to lsu. So, do it - // by the book, as it were. - // Each iteration calculates ACC=ACC+MULTAND*MULT - accunits=1; // accumulator starts at '0' - *acc=0; // .. (lsu=0) - shift=0; // no multiplicand shift at first - madlength=D2U(lhs->digits); // this won't change - mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier - - for (mer=rhs->lsu; merlsu, madlength, 0, - &acc[shift], *mer) - + shift; - else { // extend acc with a 0; it will be used shortly - *(acc+accunits)=0; // [this avoids length of <=0 later] - accunits++; - } - // multiply multiplicand by 10**DECDPUN for next Unit to left - shift++; // add this for 'logical length' - } // n - #if FASTMUL - } // unchunked units - #endif - // common end-path - #if DECTRACE - decDumpAr('*', acc, accunits); // Show exact result - #endif - - // acc now contains the exact result of the multiplication, - // possibly with a leading zero unit; build the decNumber from - // it, noting if any residue - res->bits=bits; // set sign - res->digits=decGetDigits(acc, accunits); // count digits exactly - - // There can be a 31-bit wrap in calculating the exponent. - // This can only happen if both input exponents are negative and - // both their magnitudes are large. If there was a wrap, set a - // safe very negative exponent, from which decFinalize() will - // raise a hard underflow shortly. - exponent=lhs->exponent+rhs->exponent; // calculate exponent - if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) - exponent=-2*DECNUMMAXE; // force underflow - res->exponent=exponent; // OK to overwrite now - - - // Set the coefficient. If any rounding, residue records - decSetCoeff(res, set, acc, res->digits, &residue, status); - decFinish(res, set, &residue, status); // final cleanup - } while(0); // end protected - - if (allocacc!=NULL) free(allocacc); // drop any storage used - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // .. - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - #if FASTMUL - if (allocrhi!=NULL) free(allocrhi); // .. - if (alloclhi!=NULL) free(alloclhi); // .. - #endif - return res; - } // decMultiplyOp - -/* ------------------------------------------------------------------ */ -/* decExpOp -- effect exponentiation */ -/* */ -/* This computes C = exp(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. status is updated but */ -/* not set. */ -/* */ -/* Restrictions: */ -/* */ -/* digits, emax, and -emin in the context must be less than */ -/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ -/* bounds or a zero. This is an internal routine, so these */ -/* restrictions are contractual and not enforced. */ -/* */ -/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* */ -/* Finite results will always be full precision and Inexact, except */ -/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ -/* ------------------------------------------------------------------ */ -/* This approach used here is similar to the algorithm described in */ -/* */ -/* Variable Precision Exponential Function, T. E. Hull and */ -/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ -/* pp79-91, ACM, June 1986. */ -/* */ -/* with the main difference being that the iterations in the series */ -/* evaluation are terminated dynamically (which does not require the */ -/* extra variable-precision variables which are expensive in this */ -/* context). */ -/* */ -/* The error analysis in Hull & Abrham's paper applies except for the */ -/* round-off error accumulation during the series evaluation. This */ -/* code does not precalculate the number of iterations and so cannot */ -/* use Horner's scheme. Instead, the accumulation is done at double- */ -/* precision, which ensures that the additions of the terms are exact */ -/* and do not accumulate round-off (and any round-off errors in the */ -/* terms themselves move 'to the right' faster than they can */ -/* accumulate). This code also extends the calculation by allowing, */ -/* in the spirit of other decNumber operators, the input to be more */ -/* precise than the result (the precision used is based on the more */ -/* precise of the input or requested result). */ -/* */ -/* Implementation notes: */ -/* */ -/* 1. This is separated out as decExpOp so it can be called from */ -/* other Mathematical functions (notably Ln) with a wider range */ -/* than normal. In particular, it can handle the slightly wider */ -/* (double) range needed by Ln (which has to be able to calculate */ -/* exp(-x) where x can be the tiniest number (Ntiny). */ -/* */ -/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ -/* iterations by appoximately a third with additional (although */ -/* diminishing) returns as the range is reduced to even smaller */ -/* fractions. However, h (the power of 10 used to correct the */ -/* result at the end, see below) must be kept <=8 as otherwise */ -/* the final result cannot be computed. Hence the leverage is a */ -/* sliding value (8-h), where potentially the range is reduced */ -/* more for smaller values. */ -/* */ -/* The leverage that can be applied in this way is severely */ -/* limited by the cost of the raise-to-the power at the end, */ -/* which dominates when the number of iterations is small (less */ -/* than ten) or when rhs is short. As an example, the adjustment */ -/* x**10,000,000 needs 31 multiplications, all but one full-width. */ -/* */ -/* 3. The restrictions (especially precision) could be raised with */ -/* care, but the full decNumber range seems very hard within the */ -/* 32-bit limits. */ -/* */ -/* 4. The working precisions for the static buffers are twice the */ -/* obvious size to allow for calls from decNumberPower. */ -/* ------------------------------------------------------------------ */ -decNumber * decExpOp(decNumber *res, const decNumber *rhs, - decContext *set, uInt *status) { - uInt ignore=0; // working status - Int h; // adjusted exponent for 0.xxxx - Int p; // working precision - Int residue; // rounding residue - uInt needbytes; // for space calculations - const decNumber *x=rhs; // (may point to safe copy later) - decContext aset, tset, dset; // working contexts - Int comp; // work - - // the argument is often copied to normalize it, so (unusually) it - // is treated like other buffers, using DECBUFFER, +1 in case - // DECBUFFER is 0 - decNumber bufr[D2N(DECBUFFER*2+1)]; - decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated - - // the working precision will be no more than set->digits+8+1 - // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER - // is 0 (and twice that for the accumulator) - - // buffer for t, term (working precision plus) - decNumber buft[D2N(DECBUFFER*2+9+1)]; - decNumber *allocbuft=NULL; // -> allocated buft, iff allocated - decNumber *t=buft; // term - // buffer for a, accumulator (working precision * 2), at least 9 - decNumber bufa[D2N(DECBUFFER*4+18+1)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *a=bufa; // accumulator - // decNumber for the divisor term; this needs at most 9 digits - // and so can be fixed size [16 so can use standard context] - decNumber bufd[D2N(16)]; - decNumber *d=bufd; // divisor - decNumber numone; // constant 1 - - #if DECCHECK - Int iterations=0; // for later sanity check - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - if (SPECIALARG) { // handle infinities and NaNs - if (decNumberIsInfinite(rhs)) { // an infinity - if (decNumberIsNegative(rhs)) // -Infinity -> +0 - decNumberZero(res); - else decNumberCopy(res, rhs); // +Infinity -> self - } - else decNaNs(res, rhs, NULL, set, status); // a NaN - break;} - - if (ISZERO(rhs)) { // zeros -> exact 1 - decNumberZero(res); // make clean 1 - *res->lsu=1; // .. - break;} // [no status to set] - - // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path - // positive and negative tiny cases which will result in inexact - // 1. This also allows the later add-accumulate to always be - // exact (because its length will never be more than twice the - // working precision). - // The comparator (tiny) needs just one digit, so use the - // decNumber d for it (reused as the divisor, etc., below); its - // exponent is such that if x is positive it will have - // set->digits-1 zeros between the decimal point and the digit, - // which is 4, and if x is negative one more zero there as the - // more precise result will be of the form 0.9999999 rather than - // 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 - // or 0.00000004 if digits=7 and x<0. If RHS not larger than - // this then the result will be 1.000000 - decNumberZero(d); // clean - *d->lsu=4; // set 4 .. - d->exponent=-set->digits; // * 10**(-d) - if (decNumberIsNegative(rhs)) d->exponent--; // negative case - comp=decCompare(d, rhs, 1); // signless compare - if (comp==BADINT) { - *status|=DEC_Insufficient_storage; - break;} - if (comp>=0) { // rhs < d - Int shift=set->digits-1; - decNumberZero(res); // set 1 - *res->lsu=1; // .. - res->digits=decShiftToMost(res->lsu, 1, shift); - res->exponent=-shift; // make 1.0000... - *status|=DEC_Inexact | DEC_Rounded; // .. inexactly - break;} // tiny - - // set up the context to be used for calculating a, as this is - // used on both paths below - decContextDefault(&aset, DEC_INIT_DECIMAL64); - // accumulator bounds are as requested (could underflow) - aset.emax=set->emax; // usual bounds - aset.emin=set->emin; // .. - aset.clamp=0; // and no concrete format - - // calculate the adjusted (Hull & Abrham) exponent (where the - // decimal point is just to the left of the coefficient msd) - h=rhs->exponent+rhs->digits; - // if h>8 then 10**h cannot be calculated safely; however, when - // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at - // least 6.59E+4342944, so (due to the restriction on Emax/Emin) - // overflow (or underflow to 0) is guaranteed -- so this case can - // be handled by simply forcing the appropriate excess - if (h>8) { // overflow/underflow - // set up here so Power call below will over or underflow to - // zero; set accumulator to either 2 or 0.02 - // [stack buffer for a is always big enough for this] - decNumberZero(a); - *a->lsu=2; // not 1 but < exp(1) - if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02 - h=8; // clamp so 10**h computable - p=9; // set a working precision - } - else { // h<=8 - Int maxlever=(rhs->digits>8?1:0); - // [could/should increase this for precisions >40 or so, too] - - // if h is 8, cannot normalize to a lower upper limit because - // the final result will not be computable (see notes above), - // but leverage can be applied whenever h is less than 8. - // Apply as much as possible, up to a MAXLEVER digits, which - // sets the tradeoff against the cost of the later a**(10**h). - // As h is increased, the working precision below also - // increases to compensate for the "constant digits at the - // front" effect. - Int lever=MINI(8-h, maxlever); // leverage attainable - Int use=-rhs->digits-lever; // exponent to use for RHS - h+=lever; // apply leverage selected - if (h<0) { // clamp - use+=h; // [may end up subnormal] - h=0; - } - // Take a copy of RHS if it needs normalization (true whenever x>=1) - if (rhs->exponent!=use) { - decNumber *newrhs=bufr; // assume will fit on stack - needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); - if (needbytes>sizeof(bufr)) { // need malloc space - allocrhs=(decNumber *)malloc(needbytes); - if (allocrhs==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - newrhs=allocrhs; // use the allocated space - } - decNumberCopy(newrhs, rhs); // copy to safe space - newrhs->exponent=use; // normalize; now <1 - x=newrhs; // ready for use - // decNumberShow(x); - } - - // Now use the usual power series to evaluate exp(x). The - // series starts as 1 + x + x^2/2 ... so prime ready for the - // third term by setting the term variable t=x, the accumulator - // a=1, and the divisor d=2. - - // First determine the working precision. From Hull & Abrham - // this is set->digits+h+2. However, if x is 'over-precise' we - // need to allow for all its digits to potentially participate - // (consider an x where all the excess digits are 9s) so in - // this case use x->digits+h+2 - p=MAXI(x->digits, set->digits)+h+2; // [h<=8] - - // a and t are variable precision, and depend on p, so space - // must be allocated for them if necessary - - // the accumulator needs to be able to hold 2p digits so that - // the additions on the second and subsequent iterations are - // sufficiently exact. - needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - // the term needs to be able to hold p digits (which is - // guaranteed to be larger than x->digits, so the initial copy - // is safe); it may also be used for the raise-to-power - // calculation below, which needs an extra two digits - needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); - if (needbytes>sizeof(buft)) { // need malloc space - allocbuft=(decNumber *)malloc(needbytes); - if (allocbuft==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - t=allocbuft; // use the allocated space - } - - decNumberCopy(t, x); // term=x - decNumberZero(a); *a->lsu=1; // accumulator=1 - decNumberZero(d); *d->lsu=2; // divisor=2 - decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment - - // set up the contexts for calculating a, t, and d - decContextDefault(&tset, DEC_INIT_DECIMAL64); - dset=tset; - // accumulator bounds are set above, set precision now - aset.digits=p*2; // double - // term bounds avoid any underflow or overflow - tset.digits=p; - tset.emin=DEC_MIN_EMIN; // [emax is plenty] - // [dset.digits=16, etc., are sufficient] - - // finally ready to roll - for (;;) { - #if DECCHECK - iterations++; - #endif - // only the status from the accumulation is interesting - // [but it should remain unchanged after first add] - decAddOp(a, a, t, &aset, 0, status); // a=a+t - decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x - decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d - // the iteration ends when the term cannot affect the result, - // if rounded to p digits, which is when its value is smaller - // than the accumulator by p+1 digits. There must also be - // full precision in a. - if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) - && (a->digits>=p)) break; - decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1 - } // iterate - - #if DECCHECK - // just a sanity check; comment out test to show always - if (iterations>p+3) - printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", - (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); - #endif - } // h<=8 - - // apply postconditioning: a=a**(10**h) -- this is calculated - // at a slightly higher precision than Hull & Abrham suggest - if (h>0) { - Int seenbit=0; // set once a 1-bit is seen - Int i; // counter - Int n=powers[h]; // always positive - aset.digits=p+2; // sufficient precision - // avoid the overhead and many extra digits of decNumberPower - // as all that is needed is the short 'multipliers' loop; here - // accumulate the answer into t - decNumberZero(t); *t->lsu=1; // acc=1 - for (i=1;;i++){ // for each bit [top bit ignored] - // abandon if have had overflow or terminal underflow - if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting? - if (*status&DEC_Overflow || ISZERO(t)) break;} - n=n<<1; // move next bit to testable position - if (n<0) { // top bit is set - seenbit=1; // OK, have a significant bit - decMultiplyOp(t, t, a, &aset, status); // acc=acc*x - } - if (i==31) break; // that was the last bit - if (!seenbit) continue; // no need to square 1 - decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square] - } /*i*/ // 32 bits - // decNumberShow(t); - a=t; // and carry on using t instead of a - } - - // Copy and round the result to res - residue=1; // indicate dirt to right .. - if (ISZERO(a)) residue=0; // .. unless underflowed to 0 - aset.digits=set->digits; // [use default rounding] - decCopyFit(res, a, &aset, &residue, status); // copy & shorten - decFinish(res, set, &residue, status); // cleanup/set flags - } while(0); // end protected - - if (allocrhs !=NULL) free(allocrhs); // drop any storage used - if (allocbufa!=NULL) free(allocbufa); // .. - if (allocbuft!=NULL) free(allocbuft); // .. - // [status is handled by caller] - return res; - } // decExpOp - -/* ------------------------------------------------------------------ */ -/* Initial-estimate natural logarithm table */ -/* */ -/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ -/* The result is a 4-digit encode of the coefficient (c=the */ -/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ -/* exponent (e=the bottom 2 bits encoding 0-3) */ -/* */ -/* The resulting value is given by: */ -/* */ -/* v = -c * 10**(-e-3) */ -/* */ -/* where e and c are extracted from entry k = LNnn[x-10] */ -/* where x is truncated (NB) into the range 10 through 99, */ -/* and then c = k>>2 and e = k&3. */ -/* ------------------------------------------------------------------ */ -const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, - 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, - 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, - 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, - 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, - 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, - 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, - 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, - 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, - 10130, 6046, 20055}; - -/* ------------------------------------------------------------------ */ -/* decLnOp -- effect natural logarithm */ -/* */ -/* This computes C = ln(A) */ -/* */ -/* res is C, the result. C may be A */ -/* rhs is A */ -/* set is the context; note that rounding mode has no effect */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Notable cases: */ -/* A<0 -> Invalid */ -/* A=0 -> -Infinity (Exact) */ -/* A=+Infinity -> +Infinity (Exact) */ -/* A=1 exactly -> 0 (Exact) */ -/* */ -/* Restrictions (as for Exp): */ -/* */ -/* digits, emax, and -emin in the context must be less than */ -/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ -/* bounds or a zero. This is an internal routine, so these */ -/* restrictions are contractual and not enforced. */ -/* */ -/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ -/* almost always be correctly rounded, but may be up to 1 ulp in */ -/* error in rare cases. */ -/* ------------------------------------------------------------------ */ -/* The result is calculated using Newton's method, with each */ -/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ -/* Epperson 1989. */ -/* */ -/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ -/* This has to be calculated at the sum of the precision of x and the */ -/* working precision. */ -/* */ -/* Implementation notes: */ -/* */ -/* 1. This is separated out as decLnOp so it can be called from */ -/* other Mathematical functions (e.g., Log 10) with a wider range */ -/* than normal. In particular, it can handle the slightly wider */ -/* (+9+2) range needed by a power function. */ -/* */ -/* 2. The speed of this function is about 10x slower than exp, as */ -/* it typically needs 4-6 iterations for short numbers, and the */ -/* extra precision needed adds a squaring effect, twice. */ -/* */ -/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ -/* as these are common requests. ln(10) is used by log10(x). */ -/* */ -/* 4. An iteration might be saved by widening the LNnn table, and */ -/* would certainly save at least one if it were made ten times */ -/* bigger, too (for truncated fractions 0.100 through 0.999). */ -/* However, for most practical evaluations, at least four or five */ -/* iterations will be neede -- so this would only speed up by */ -/* 20-25% and that probably does not justify increasing the table */ -/* size. */ -/* */ -/* 5. The static buffers are larger than might be expected to allow */ -/* for calls from decNumberPower. */ -/* ------------------------------------------------------------------ */ -decNumber * decLnOp(decNumber *res, const decNumber *rhs, - decContext *set, uInt *status) { - uInt ignore=0; // working status accumulator - uInt needbytes; // for space calculations - Int residue; // rounding residue - Int r; // rhs=f*10**r [see below] - Int p; // working precision - Int pp; // precision for iteration - Int t; // work - - // buffers for a (accumulator, typically precision+2) and b - // (adjustment calculator, same size) - decNumber bufa[D2N(DECBUFFER+12)]; - decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated - decNumber *a=bufa; // accumulator/work - decNumber bufb[D2N(DECBUFFER*2+2)]; - decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated - decNumber *b=bufb; // adjustment/work - - decNumber numone; // constant 1 - decNumber cmp; // work - decContext aset, bset; // working contexts - - #if DECCHECK - Int iterations=0; // for later sanity check - if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; - #endif - - do { // protect allocated storage - if (SPECIALARG) { // handle infinities and NaNs - if (decNumberIsInfinite(rhs)) { // an infinity - if (decNumberIsNegative(rhs)) // -Infinity -> error - *status|=DEC_Invalid_operation; - else decNumberCopy(res, rhs); // +Infinity -> self - } - else decNaNs(res, rhs, NULL, set, status); // a NaN - break;} - - if (ISZERO(rhs)) { // +/- zeros -> -Infinity - decNumberZero(res); // make clean - res->bits=DECINF|DECNEG; // set - infinity - break;} // [no status to set] - - // Non-zero negatives are bad... - if (decNumberIsNegative(rhs)) { // -x -> error - *status|=DEC_Invalid_operation; - break;} - - // Here, rhs is positive, finite, and in range - - // lookaside fastpath code for ln(2) and ln(10) at common lengths - if (rhs->exponent==0 && set->digits<=40) { - #if DECDPUN==1 - if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10) - #else - if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10) - #endif - aset=*set; aset.round=DEC_ROUND_HALF_EVEN; - #define LN10 "2.302585092994045684017991454684364207601" - decNumberFromString(res, LN10, &aset); - *status|=(DEC_Inexact | DEC_Rounded); // is inexact - break;} - if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2) - aset=*set; aset.round=DEC_ROUND_HALF_EVEN; - #define LN2 "0.6931471805599453094172321214581765680755" - decNumberFromString(res, LN2, &aset); - *status|=(DEC_Inexact | DEC_Rounded); - break;} - } // integer and short - - // Determine the working precision. This is normally the - // requested precision + 2, with a minimum of 9. However, if - // the rhs is 'over-precise' then allow for all its digits to - // potentially participate (consider an rhs where all the excess - // digits are 9s) so in this case use rhs->digits+2. - p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; - - // Allocate space for the accumulator and the high-precision - // adjustment calculator, if necessary. The accumulator must - // be able to hold p digits, and the adjustment up to - // rhs->digits+p digits. They are also made big enough for 16 - // digits so that they can be used for calculating the initial - // estimate. - needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); - if (needbytes>sizeof(bufa)) { // need malloc space - allocbufa=(decNumber *)malloc(needbytes); - if (allocbufa==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - a=allocbufa; // use the allocated space - } - pp=p+rhs->digits; - needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); - if (needbytes>sizeof(bufb)) { // need malloc space - allocbufb=(decNumber *)malloc(needbytes); - if (allocbufb==NULL) { // hopeless -- abandon - *status|=DEC_Insufficient_storage; - break;} - b=allocbufb; // use the allocated space - } - - // Prepare an initial estimate in acc. Calculate this by - // considering the coefficient of x to be a normalized fraction, - // f, with the decimal point at far left and multiplied by - // 10**r. Then, rhs=f*10**r and 0.1<=f<1, and - // ln(x) = ln(f) + ln(10)*r - // Get the initial estimate for ln(f) from a small lookup - // table (see above) indexed by the first two digits of f, - // truncated. - - decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended - r=rhs->exponent+rhs->digits; // 'normalised' exponent - decNumberFromInt32(a, r); // a=r - decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585) - b->exponent=-6; // .. - decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b - // now get top two digits of rhs into b by simple truncate and - // force to integer - residue=0; // (no residue) - aset.digits=2; aset.round=DEC_ROUND_DOWN; - decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten - b->exponent=0; // make integer - t=decGetInt(b); // [cannot fail] - if (t<10) t=X10(t); // adjust single-digit b - t=LNnn[t-10]; // look up ln(b) - decNumberFromInt32(b, t>>2); // b=ln(b) coefficient - b->exponent=-(t&3)-3; // set exponent - b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve - aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore - decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b - // the initial estimate is now in a, with up to 4 digits correct. - // When rhs is at or near Nmax the estimate will be low, so we - // will approach it from below, avoiding overflow when calling exp. - - decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment - - // accumulator bounds are as requested (could underflow, but - // cannot overflow) - aset.emax=set->emax; - aset.emin=set->emin; - aset.clamp=0; // no concrete format - // set up a context to be used for the multiply and subtract - bset=aset; - bset.emax=DEC_MAX_MATH*2; // use double bounds for the - bset.emin=-DEC_MAX_MATH*2; // adjustment calculation - // [see decExpOp call below] - // for each iteration double the number of digits to calculate, - // up to a maximum of p - pp=9; // initial precision - // [initially 9 as then the sequence starts 7+2, 16+2, and - // 34+2, which is ideal for standard-sized numbers] - aset.digits=pp; // working context - bset.digits=pp+rhs->digits; // wider context - for (;;) { // iterate - #if DECCHECK - iterations++; - if (iterations>24) break; // consider 9 * 2**24 - #endif - // calculate the adjustment (exp(-a)*x-1) into b. This is a - // catastrophic subtraction but it really is the difference - // from 1 that is of interest. - // Use the internal entry point to Exp as it allows the double - // range for calculating exp(-a) when a is the tiniest subnormal. - a->bits^=DECNEG; // make -a - decExpOp(b, a, &bset, &ignore); // b=exp(-a) - a->bits^=DECNEG; // restore sign of a - // now multiply by rhs and subtract 1, at the wider precision - decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs - decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1 - - // the iteration ends when the adjustment cannot affect the - // result by >=0.5 ulp (at the requested digits), which - // is when its value is smaller than the accumulator by - // set->digits+1 digits (or it is zero) -- this is a looser - // requirement than for Exp because all that happens to the - // accumulator after this is the final rounding (but note that - // there must also be full precision in a, or a=0). - - if (decNumberIsZero(b) || - (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { - if (a->digits==p) break; - if (decNumberIsZero(a)) { - decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ? - if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0 - else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact - break; - } - // force padding if adjustment has gone to 0 before full length - if (decNumberIsZero(b)) b->exponent=a->exponent-p; - } - - // not done yet ... - decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate - if (pp==p) continue; // precision is at maximum - // lengthen the next calculation - pp=pp*2; // double precision - if (pp>p) pp=p; // clamp to maximum - aset.digits=pp; // working context - bset.digits=pp+rhs->digits; // wider context - } // Newton's iteration - - #if DECCHECK - // just a sanity check; remove the test to show always - if (iterations>24) - printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", - (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); - #endif - - // Copy and round the result to res - residue=1; // indicate dirt to right - if (ISZERO(a)) residue=0; // .. unless underflowed to 0 - aset.digits=set->digits; // [use default rounding] - decCopyFit(res, a, &aset, &residue, status); // copy & shorten - decFinish(res, set, &residue, status); // cleanup/set flags - } while(0); // end protected - - if (allocbufa!=NULL) free(allocbufa); // drop any storage used - if (allocbufb!=NULL) free(allocbufb); // .. - // [status is handled by caller] - return res; - } // decLnOp - -/* ------------------------------------------------------------------ */ -/* decQuantizeOp -- force exponent to requested value */ -/* */ -/* This computes C = op(A, B), where op adjusts the coefficient */ -/* of C (by rounding or shifting) such that the exponent (-scale) */ -/* of C has the value B or matches the exponent of B. */ -/* The numerical value of C will equal A, except for the effects of */ -/* any rounding that occurred. */ -/* */ -/* res is C, the result. C may be A or B */ -/* lhs is A, the number to adjust */ -/* rhs is B, the requested exponent */ -/* set is the context */ -/* quant is 1 for quantize or 0 for rescale */ -/* status is the status accumulator (this can be called without */ -/* risk of control loss) */ -/* */ -/* C must have space for set->digits digits. */ -/* */ -/* Unless there is an error or the result is infinite, the exponent */ -/* after the operation is guaranteed to be that requested. */ -/* ------------------------------------------------------------------ */ -static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - Flag quant, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - const decNumber *inrhs=rhs; // save original rhs - Int reqdigits=set->digits; // requested DIGITS - Int reqexp; // requested exponent [-scale] - Int residue=0; // rounding residue - Int etiny=set->emin-(reqdigits-1); - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>reqdigits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) break; - lhs=alloclhs; - } - if (rhs->digits>reqdigits) { // [this only checks lostDigits] - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) break; - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // Handle special values - if (SPECIALARGS) { - // NaNs get usual processing - if (SPECIALARGS & (DECSNAN | DECNAN)) - decNaNs(res, lhs, rhs, set, status); - // one infinity but not both is bad - else if ((lhs->bits ^ rhs->bits) & DECINF) - *status|=DEC_Invalid_operation; - // both infinity: return lhs - else decNumberCopy(res, lhs); // [nop if in place] - break; - } - - // set requested exponent - if (quant) reqexp=inrhs->exponent; // quantize -- match exponents - else { // rescale -- use value of rhs - // Original rhs must be an integer that fits and is in range, - // which could be from -1999999997 to +999999999, thanks to - // subnormals - reqexp=decGetInt(inrhs); // [cannot fail] - } - - #if DECSUBSET - if (!set->extended) etiny=set->emin; // no subnormals - #endif - - if (reqexp==BADINT // bad (rescale only) or .. - || reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or .. - || (reqexpset->emax)) { // > emax - *status|=DEC_Invalid_operation; - break;} - - // the RHS has been processed, so it can be overwritten now if necessary - if (ISZERO(lhs)) { // zero coefficient unchanged - decNumberCopy(res, lhs); // [nop if in place] - res->exponent=reqexp; // .. just set exponent - #if DECSUBSET - if (!set->extended) res->bits=0; // subset specification; no -0 - #endif - } - else { // non-zero lhs - Int adjust=reqexp-lhs->exponent; // digit adjustment needed - // if adjusted coefficient will definitely not fit, give up now - if ((lhs->digits-adjust)>reqdigits) { - *status|=DEC_Invalid_operation; - break; - } - - if (adjust>0) { // increasing exponent - // this will decrease the length of the coefficient by adjust - // digits, and must round as it does so - decContext workset; // work - workset=*set; // clone rounding, etc. - workset.digits=lhs->digits-adjust; // set requested length - // [note that the latter can be <1, here] - decCopyFit(res, lhs, &workset, &residue, status); // fit to result - decApplyRound(res, &workset, residue, status); // .. and round - residue=0; // [used] - // If just rounded a 999s case, exponent will be off by one; - // adjust back (after checking space), if so. - if (res->exponent>reqexp) { - // re-check needed, e.g., for quantize(0.9999, 0.001) under - // set->digits==3 - if (res->digits==reqdigits) { // cannot shift by 1 - *status&=~(DEC_Inexact | DEC_Rounded); // [clean these] - *status|=DEC_Invalid_operation; - break; - } - res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift - res->exponent--; // (re)adjust the exponent. - } - #if DECSUBSET - if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0 - #endif - } // increase - else /* adjust<=0 */ { // decreasing or = exponent - // this will increase the length of the coefficient by -adjust - // digits, by adding zero or more trailing zeros; this is - // already checked for fit, above - decNumberCopy(res, lhs); // [it will fit] - // if padding needed (adjust<0), add it now... - if (adjust<0) { - res->digits=decShiftToMost(res->lsu, res->digits, -adjust); - res->exponent+=adjust; // adjust the exponent - } - } // decrease - } // non-zero - - // Check for overflow [do not use Finalize in this case, as an - // overflow here is a "don't fit" situation] - if (res->exponent>set->emax-res->digits+1) { // too big - *status|=DEC_Invalid_operation; - break; - } - else { - decFinalize(res, set, &residue, status); // set subnormal flags - *status&=~DEC_Underflow; // suppress Underflow [as per 754] - } - } while(0); // end protected - - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // drop any storage used - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decQuantizeOp - -/* ------------------------------------------------------------------ */ -/* decCompareOp -- compare, min, or max two Numbers */ -/* */ -/* This computes C = A ? B and carries out one of four operations: */ -/* COMPARE -- returns the signum (as a number) giving the */ -/* result of a comparison unless one or both */ -/* operands is a NaN (in which case a NaN results) */ -/* COMPSIG -- as COMPARE except that a quiet NaN raises */ -/* Invalid operation. */ -/* COMPMAX -- returns the larger of the operands, using the */ -/* 754 maxnum operation */ -/* COMPMAXMAG -- ditto, comparing absolute values */ -/* COMPMIN -- the 754 minnum operation */ -/* COMPMINMAG -- ditto, comparing absolute values */ -/* COMTOTAL -- returns the signum (as a number) giving the */ -/* result of a comparison using 754 total ordering */ -/* */ -/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ -/* lhs is A */ -/* rhs is B */ -/* set is the context */ -/* op is the operation flag */ -/* status is the usual accumulator */ -/* */ -/* C must have space for one digit for COMPARE or set->digits for */ -/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ -/* ------------------------------------------------------------------ */ -/* The emphasis here is on speed for common cases, and avoiding */ -/* coefficient comparison if possible. */ -/* ------------------------------------------------------------------ */ -decNumber * decCompareOp(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - Flag op, uInt *status) { - #if DECSUBSET - decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated - decNumber *allocrhs=NULL; // .., rhs - #endif - Int result=0; // default result value - uByte merged; // work - - #if DECCHECK - if (decCheckOperands(res, lhs, rhs, set)) return res; - #endif - - do { // protect allocated storage - #if DECSUBSET - if (!set->extended) { - // reduce operands and set lostDigits status, as needed - if (lhs->digits>set->digits) { - alloclhs=decRoundOperand(lhs, set, status); - if (alloclhs==NULL) {result=BADINT; break;} - lhs=alloclhs; - } - if (rhs->digits>set->digits) { - allocrhs=decRoundOperand(rhs, set, status); - if (allocrhs==NULL) {result=BADINT; break;} - rhs=allocrhs; - } - } - #endif - // [following code does not require input rounding] - - // If total ordering then handle differing signs 'up front' - if (op==COMPTOTAL) { // total ordering - if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { - result=-1; - break; - } - if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { - result=+1; - break; - } - } - - // handle NaNs specially; let infinities drop through - // This assumes sNaN (even just one) leads to NaN. - merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); - if (merged) { // a NaN bit set - if (op==COMPARE); // result will be NaN - else if (op==COMPSIG) // treat qNaN as sNaN - *status|=DEC_Invalid_operation | DEC_sNaN; - else if (op==COMPTOTAL) { // total ordering, always finite - // signs are known to be the same; compute the ordering here - // as if the signs are both positive, then invert for negatives - if (!decNumberIsNaN(lhs)) result=-1; - else if (!decNumberIsNaN(rhs)) result=+1; - // here if both NaNs - else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; - else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; - else { // both NaN or both sNaN - // now it just depends on the payload - result=decUnitCompare(lhs->lsu, D2U(lhs->digits), - rhs->lsu, D2U(rhs->digits), 0); - // [Error not possible, as these are 'aligned'] - } // both same NaNs - if (decNumberIsNegative(lhs)) result=-result; - break; - } // total order - - else if (merged & DECSNAN); // sNaN -> qNaN - else { // here if MIN or MAX and one or two quiet NaNs - // min or max -- 754 rules ignore single NaN - if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { - // just one NaN; force choice to be the non-NaN operand - op=COMPMAX; - if (lhs->bits & DECNAN) result=-1; // pick rhs - else result=+1; // pick lhs - break; - } - } // max or min - op=COMPNAN; // use special path - decNaNs(res, lhs, rhs, set, status); // propagate NaN - break; - } - // have numbers - if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); - else result=decCompare(lhs, rhs, 0); // sign matters - } while(0); // end protected - - if (result==BADINT) *status|=DEC_Insufficient_storage; // rare - else { - if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum - if (op==COMPTOTAL && result==0) { - // operands are numerically equal or same NaN (and same sign, - // tested first); if identical, leave result 0 - if (lhs->exponent!=rhs->exponent) { - if (lhs->exponentexponent) result=-1; - else result=+1; - if (decNumberIsNegative(lhs)) result=-result; - } // lexp!=rexp - } // total-order by exponent - decNumberZero(res); // [always a valid result] - if (result!=0) { // must be -1 or +1 - *res->lsu=1; - if (result<0) res->bits=DECNEG; - } - } - else if (op==COMPNAN); // special, drop through - else { // MAX or MIN, non-NaN result - Int residue=0; // rounding accumulator - // choose the operand for the result - const decNumber *choice; - if (result==0) { // operands are numerically equal - // choose according to sign then exponent (see 754) - uByte slhs=(lhs->bits & DECNEG); - uByte srhs=(rhs->bits & DECNEG); - #if DECSUBSET - if (!set->extended) { // subset: force left-hand - op=COMPMAX; - result=+1; - } - else - #endif - if (slhs!=srhs) { // signs differ - if (slhs) result=-1; // rhs is max - else result=+1; // lhs is max - } - else if (slhs && srhs) { // both negative - if (lhs->exponentexponent) result=+1; - else result=-1; - // [if equal, use lhs, technically identical] - } - else { // both positive - if (lhs->exponent>rhs->exponent) result=+1; - else result=-1; - // [ditto] - } - } // numerically equal - // here result will be non-0; reverse if looking for MIN - if (op==COMPMIN || op==COMPMINMAG) result=-result; - choice=(result>0 ? lhs : rhs); // choose - // copy chosen to result, rounding if need be - decCopyFit(res, choice, set, &residue, status); - decFinish(res, set, &residue, status); - } - } - #if DECSUBSET - if (allocrhs!=NULL) free(allocrhs); // free any storage used - if (alloclhs!=NULL) free(alloclhs); // .. - #endif - return res; - } // decCompareOp - -/* ------------------------------------------------------------------ */ -/* decCompare -- compare two decNumbers by numerical value */ -/* */ -/* This routine compares A ? B without altering them. */ -/* */ -/* Arg1 is A, a decNumber which is not a NaN */ -/* Arg2 is B, a decNumber which is not a NaN */ -/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ -/* */ -/* returns -1, 0, or 1 for AB, or BADINT if failure */ -/* (the only possible failure is an allocation error) */ -/* ------------------------------------------------------------------ */ -static Int decCompare(const decNumber *lhs, const decNumber *rhs, - Flag abs) { - Int result; // result value - Int sigr; // rhs signum - Int compare; // work - - result=1; // assume signum(lhs) - if (ISZERO(lhs)) result=0; - if (abs) { - if (ISZERO(rhs)) return result; // LHS wins or both 0 - // RHS is non-zero - if (result==0) return -1; // LHS is 0; RHS wins - // [here, both non-zero, result=1] - } - else { // signs matter - if (result && decNumberIsNegative(lhs)) result=-1; - sigr=1; // compute signum(rhs) - if (ISZERO(rhs)) sigr=0; - else if (decNumberIsNegative(rhs)) sigr=-1; - if (result > sigr) return +1; // L > R, return 1 - if (result < sigr) return -1; // L < R, return -1 - if (result==0) return 0; // both 0 - } - - // signums are the same; both are non-zero - if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities - if (decNumberIsInfinite(rhs)) { - if (decNumberIsInfinite(lhs)) result=0;// both infinite - else result=-result; // only rhs infinite - } - return result; - } - // must compare the coefficients, allowing for exponents - if (lhs->exponent>rhs->exponent) { // LHS exponent larger - // swap sides, and sign - const decNumber *temp=lhs; - lhs=rhs; - rhs=temp; - result=-result; - } - compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), - rhs->lsu, D2U(rhs->digits), - rhs->exponent-lhs->exponent); - if (compare!=BADINT) compare*=result; // comparison succeeded - return compare; - } // decCompare - -/* ------------------------------------------------------------------ */ -/* decUnitCompare -- compare two >=0 integers in Unit arrays */ -/* */ -/* This routine compares A ? B*10**E where A and B are unit arrays */ -/* A is a plain integer */ -/* B has an exponent of E (which must be non-negative) */ -/* */ -/* Arg1 is A first Unit (lsu) */ -/* Arg2 is A length in Units */ -/* Arg3 is B first Unit (lsu) */ -/* Arg4 is B length in Units */ -/* Arg5 is E (0 if the units are aligned) */ -/* */ -/* returns -1, 0, or 1 for AB, or BADINT if failure */ -/* (the only possible failure is an allocation error, which can */ -/* only occur if E!=0) */ -/* ------------------------------------------------------------------ */ -static Int decUnitCompare(const Unit *a, Int alength, - const Unit *b, Int blength, Int exp) { - Unit *acc; // accumulator for result - Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer - Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated - Int accunits, need; // units in use or needed for acc - const Unit *l, *r, *u; // work - Int expunits, exprem, result; // .. - - if (exp==0) { // aligned; fastpath - if (alength>blength) return 1; - if (alength=a; l--, r--) { - if (*l>*r) return 1; - if (*l<*r) return -1; - } - return 0; // all units match - } // aligned - - // Unaligned. If one is >1 unit longer than the other, padded - // approximately, then can return easily - if (alength>blength+(Int)D2U(exp)) return 1; - if (alength+1sizeof(accbuff)) { - allocacc=(Unit *)malloc(need*sizeof(Unit)); - if (allocacc==NULL) return BADINT; // hopeless -- abandon - acc=allocacc; - } - // Calculate units and remainder from exponent. - expunits=exp/DECDPUN; - exprem=exp%DECDPUN; - // subtract [A+B*(-m)] - accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, - -(Int)powers[exprem]); - // [UnitAddSub result may have leading zeros, even on zero] - if (accunits<0) result=-1; // negative result - else { // non-negative result - // check units of the result before freeing any storage - for (u=acc; u=0 integers in Unit arrays */ -/* */ -/* This routine performs the calculation: */ -/* */ -/* C=A+(B*M) */ -/* */ -/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ -/* */ -/* A may be shorter or longer than B. */ -/* */ -/* Leading zeros are not removed after a calculation. The result is */ -/* either the same length as the longer of A and B (adding any */ -/* shift), or one Unit longer than that (if a Unit carry occurred). */ -/* */ -/* A and B content are not altered unless C is also A or B. */ -/* C may be the same array as A or B, but only if no zero padding is */ -/* requested (that is, C may be B only if bshift==0). */ -/* C is filled from the lsu; only those units necessary to complete */ -/* the calculation are referenced. */ -/* */ -/* Arg1 is A first Unit (lsu) */ -/* Arg2 is A length in Units */ -/* Arg3 is B first Unit (lsu) */ -/* Arg4 is B length in Units */ -/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ -/* Arg6 is C first Unit (lsu) */ -/* Arg7 is M, the multiplier */ -/* */ -/* returns the count of Units written to C, which will be non-zero */ -/* and negated if the result is negative. That is, the sign of the */ -/* returned Int is the sign of the result (positive for zero) and */ -/* the absolute value of the Int is the count of Units. */ -/* */ -/* It is the caller's responsibility to make sure that C size is */ -/* safe, allowing space if necessary for a one-Unit carry. */ -/* */ -/* This routine is severely performance-critical; *any* change here */ -/* must be measured (timed) to assure no performance degradation. */ -/* In particular, trickery here tends to be counter-productive, as */ -/* increased complexity of code hurts register optimizations on */ -/* register-poor architectures. Avoiding divisions is nearly */ -/* always a Good Idea, however. */ -/* */ -/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ -/* (IBM Warwick, UK) for some of the ideas used in this routine. */ -/* ------------------------------------------------------------------ */ -static Int decUnitAddSub(const Unit *a, Int alength, - const Unit *b, Int blength, Int bshift, - Unit *c, Int m) { - const Unit *alsu=a; // A lsu [need to remember it] - Unit *clsu=c; // C ditto - Unit *minC; // low water mark for C - Unit *maxC; // high water mark for C - eInt carry=0; // carry integer (could be Long) - Int add; // work - #if DECDPUN<=4 // myriadal, millenary, etc. - Int est; // estimated quotient - #endif - - #if DECTRACE - if (alength<1 || blength<1) - printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); - #endif - - maxC=c+alength; // A is usually the longer - minC=c+blength; // .. and B the shorter - if (bshift!=0) { // B is shifted; low As copy across - minC+=bshift; - // if in place [common], skip copy unless there's a gap [rare] - if (a==c && bshift<=alength) { - c+=bshift; - a+=bshift; - } - else for (; cmaxC) { // swap - Unit *hold=minC; - minC=maxC; - maxC=hold; - } - - // For speed, do the addition as two loops; the first where both A - // and B contribute, and the second (if necessary) where only one or - // other of the numbers contribute. - // Carry handling is the same (i.e., duplicated) in each case. - for (; c=0) { - est=(((ueInt)carry>>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [89%] - if (*c>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c=0) { - est=(((ueInt)carry>>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [99%] - if (*c>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c=0) { - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // quotient - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - #else - // remainder operator is undefined if negative, so must test - if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1 - *c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions] - carry=1; - continue; - } - if (carry>=0) { - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1); - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); - #endif - } // c - - // now may have one or other to complete - // [pretest to avoid loop setup/shutdown] - if (cDECDPUNMAX - #if DECDPUN==4 // use divide-by-multiply - if (carry>=0) { - est=(((ueInt)carry>>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [79.7%] - if (*c>11)*53687)>>18; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c=0) { - est=(((ueInt)carry>>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // likely quotient [99%] - if (*c>3)*16777)>>21; - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - if (*c=0) { - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder - carry=est; // quotient - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - est=QUOT10(carry, DECDPUN); - *c=(Unit)(carry-est*(DECDPUNMAX+1)); - carry=est-(DECDPUNMAX+1); // correctly negative - #else - if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1 - *c=(Unit)(carry-(DECDPUNMAX+1)); - carry=1; - continue; - } - // remainder operator is undefined if negative, so must test - if (carry>=0) { - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1); - continue; - } - // negative case - carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive - *c=(Unit)(carry%(DECDPUNMAX+1)); - carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); - #endif - } // c - - // OK, all A and B processed; might still have carry or borrow - // return number of Units in the result, negated if a borrow - if (carry==0) return c-clsu; // no carry, so no more to do - if (carry>0) { // positive carry - *c=(Unit)carry; // place as new unit - c++; // .. - return c-clsu; - } - // -ve carry: it's a borrow; complement needed - add=1; // temporary carry... - for (c=clsu; c current Unit - - #if DECCHECK - if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; - #endif - - *dropped=0; // assume no zeros dropped - if ((dn->bits & DECSPECIAL) // fast exit if special .. - || (*dn->lsu & 0x01)) return dn; // .. or odd - if (ISZERO(dn)) { // .. or 0 - dn->exponent=0; // (sign is preserved) - return dn; - } - - // have a finite number which is even - exp=dn->exponent; - cut=1; // digit (1-DECDPUN) in Unit - up=dn->lsu; // -> current Unit - for (d=0; ddigits-1; d++) { // [don't strip the final digit] - // slice by powers - #if DECDPUN<=4 - uInt quot=QUOT10(*up, cut); - if ((*up-quot*powers[cut])!=0) break; // found non-0 digit - #else - if (*up%powers[cut]!=0) break; // found non-0 digit - #endif - // have a trailing 0 - if (!all) { // trimming - // [if exp>0 then all trailing 0s are significant for trim] - if (exp<=0) { // if digit might be significant - if (exp==0) break; // then quit - exp++; // next digit might be significant - } - } - cut++; // next power - if (cut>DECDPUN) { // need new Unit - up++; - cut=1; - } - } // d - if (d==0) return dn; // none to drop - - // may need to limit drop if clamping - if (set->clamp && !noclamp) { - Int maxd=set->emax-set->digits+1-dn->exponent; - if (maxd<=0) return dn; // nothing possible - if (d>maxd) d=maxd; - } - - // effect the drop - decShiftToLeast(dn->lsu, D2U(dn->digits), d); - dn->exponent+=d; // maintain numerical value - dn->digits-=d; // new length - *dropped=d; // report the count - return dn; - } // decTrim - -/* ------------------------------------------------------------------ */ -/* decReverse -- reverse a Unit array in place */ -/* */ -/* ulo is the start of the array */ -/* uhi is the end of the array (highest Unit to include) */ -/* */ -/* The units ulo through uhi are reversed in place (if the number */ -/* of units is odd, the middle one is untouched). Note that the */ -/* digit(s) in each unit are unaffected. */ -/* ------------------------------------------------------------------ */ -static void decReverse(Unit *ulo, Unit *uhi) { - Unit temp; - for (; ulo=uar; source--, target--) *target=*source; - } - else { - first=uar+D2U(digits+shift)-1; // where msu of source will end up - for (; source>=uar; source--, target--) { - // split the source Unit and accumulate remainder for next - #if DECDPUN<=4 - uInt quot=QUOT10(*source, cut); - uInt rem=*source-quot*powers[cut]; - next+=quot; - #else - uInt rem=*source%powers[cut]; - next+=*source/powers[cut]; - #endif - if (target<=first) *target=(Unit)next; // write to target iff valid - next=rem*powers[DECDPUN-cut]; // save remainder for next Unit - } - } // shift-move - - // propagate any partial unit to one below and clear the rest - for (; target>=uar; target--) { - *target=(Unit)next; - next=0; - } - return digits+shift; - } // decShiftToMost - -/* ------------------------------------------------------------------ */ -/* decShiftToLeast -- shift digits in array towards least significant */ -/* */ -/* uar is the array */ -/* units is length of the array, in units */ -/* shift is the number of digits to remove from the lsu end; it */ -/* must be zero or positive and <= than units*DECDPUN. */ -/* */ -/* returns the new length of the integer in the array, in units */ -/* */ -/* Removed digits are discarded (lost). Units not required to hold */ -/* the final result are unchanged. */ -/* ------------------------------------------------------------------ */ -static Int decShiftToLeast(Unit *uar, Int units, Int shift) { - Unit *target, *up; // work - Int cut, count; // work - Int quot, rem; // for division - - if (shift==0) return units; // [fastpath] nothing to do - if (shift==units*DECDPUN) { // [fastpath] little to do - *uar=0; // all digits cleared gives zero - return 1; // leaves just the one - } - - target=uar; // both paths - cut=MSUDIGITS(shift); - if (cut==DECDPUN) { // unit-boundary case; easy - up=uar+D2U(shift); - for (; updigits is > set->digits) */ -/* set is the relevant context */ -/* status is the status accumulator */ -/* */ -/* returns an allocated decNumber with the rounded result. */ -/* */ -/* lostDigits and other status may be set by this. */ -/* */ -/* Since the input is an operand, it must not be modified. */ -/* Instead, return an allocated decNumber, rounded as required. */ -/* It is the caller's responsibility to free the allocated storage. */ -/* */ -/* If no storage is available then the result cannot be used, so NULL */ -/* is returned. */ -/* ------------------------------------------------------------------ */ -static decNumber *decRoundOperand(const decNumber *dn, decContext *set, - uInt *status) { - decNumber *res; // result structure - uInt newstatus=0; // status from round - Int residue=0; // rounding accumulator - - // Allocate storage for the returned decNumber, big enough for the - // length specified by the context - res=(decNumber *)malloc(sizeof(decNumber) - +(D2U(set->digits)-1)*sizeof(Unit)); - if (res==NULL) { - *status|=DEC_Insufficient_storage; - return NULL; - } - decCopyFit(res, dn, set, &residue, &newstatus); - decApplyRound(res, set, residue, &newstatus); - - // If that set Inexact then "lost digits" is raised... - if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; - *status|=newstatus; - return res; - } // decRoundOperand -#endif - -/* ------------------------------------------------------------------ */ -/* decCopyFit -- copy a number, truncating the coefficient if needed */ -/* */ -/* dest is the target decNumber */ -/* src is the source decNumber */ -/* set is the context [used for length (digits) and rounding mode] */ -/* residue is the residue accumulator */ -/* status contains the current status to be updated */ -/* */ -/* (dest==src is allowed and will be a no-op if fits) */ -/* All fields are updated as required. */ -/* ------------------------------------------------------------------ */ -static void decCopyFit(decNumber *dest, const decNumber *src, - decContext *set, Int *residue, uInt *status) { - dest->bits=src->bits; - dest->exponent=src->exponent; - decSetCoeff(dest, set, src->lsu, src->digits, residue, status); - } // decCopyFit - -/* ------------------------------------------------------------------ */ -/* decSetCoeff -- set the coefficient of a number */ -/* */ -/* dn is the number whose coefficient array is to be set. */ -/* It must have space for set->digits digits */ -/* set is the context [for size] */ -/* lsu -> lsu of the source coefficient [may be dn->lsu] */ -/* len is digits in the source coefficient [may be dn->digits] */ -/* residue is the residue accumulator. This has values as in */ -/* decApplyRound, and will be unchanged unless the */ -/* target size is less than len. In this case, the */ -/* coefficient is truncated and the residue is updated to */ -/* reflect the previous residue and the dropped digits. */ -/* status is the status accumulator, as usual */ -/* */ -/* The coefficient may already be in the number, or it can be an */ -/* external intermediate array. If it is in the number, lsu must == */ -/* dn->lsu and len must == dn->digits. */ -/* */ -/* Note that the coefficient length (len) may be < set->digits, and */ -/* in this case this merely copies the coefficient (or is a no-op */ -/* if dn->lsu==lsu). */ -/* */ -/* Note also that (only internally, from decQuantizeOp and */ -/* decSetSubnormal) the value of set->digits may be less than one, */ -/* indicating a round to left. This routine handles that case */ -/* correctly; caller ensures space. */ -/* */ -/* dn->digits, dn->lsu (and as required), and dn->exponent are */ -/* updated as necessary. dn->bits (sign) is unchanged. */ -/* */ -/* DEC_Rounded status is set if any digits are discarded. */ -/* DEC_Inexact status is set if any non-zero digits are discarded, or */ -/* incoming residue was non-0 (implies rounded) */ -/* ------------------------------------------------------------------ */ -// mapping array: maps 0-9 to canonical residues, so that a residue -// can be adjusted in the range [-1, +1] and achieve correct rounding -// 0 1 2 3 4 5 6 7 8 9 -static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; -static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, - Int len, Int *residue, uInt *status) { - Int discard; // number of digits to discard - uInt cut; // cut point in Unit - const Unit *up; // work - Unit *target; // .. - Int count; // .. - #if DECDPUN<=4 - uInt temp; // .. - #endif - - discard=len-set->digits; // digits to discard - if (discard<=0) { // no digits are being discarded - if (dn->lsu!=lsu) { // copy needed - // copy the coefficient array to the result number; no shift needed - count=len; // avoids D2U - up=lsu; - for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) - *target=*up; - dn->digits=len; // set the new length - } - // dn->exponent and residue are unchanged, record any inexactitude - if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); - return; - } - - // some digits must be discarded ... - dn->exponent+=discard; // maintain numerical value - *status|=DEC_Rounded; // accumulate Rounded status - if (*residue>1) *residue=1; // previous residue now to right, so reduce - - if (discard>len) { // everything, +1, is being discarded - // guard digit is 0 - // residue is all the number [NB could be all 0s] - if (*residue<=0) { // not already positive - count=len; // avoids D2U - for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0 - *residue=1; - break; // no need to check any others - } - } - if (*residue!=0) *status|=DEC_Inexact; // record inexactitude - *dn->lsu=0; // coefficient will now be 0 - dn->digits=1; // .. - return; - } // total discard - - // partial discard [most common case] - // here, at least the first (most significant) discarded digit exists - - // spin up the number, noting residue during the spin, until get to - // the Unit with the first discarded digit. When reach it, extract - // it and remember its position - count=0; - for (up=lsu;; up++) { - count+=DECDPUN; - if (count>=discard) break; // full ones all checked - if (*up!=0) *residue=1; - } // up - - // here up -> Unit with first discarded digit - cut=discard-(count-DECDPUN)-1; - if (cut==DECDPUN-1) { // unit-boundary case (fast) - Unit half=(Unit)powers[DECDPUN]>>1; - // set residue directly - if (*up>=half) { - if (*up>half) *residue=7; - else *residue+=5; // add sticky bit - } - else { // digits<=0) { // special for Quantize/Subnormal :-( - *dn->lsu=0; // .. result is 0 - dn->digits=1; // .. - } - else { // shift to least - count=set->digits; // now digits to end up with - dn->digits=count; // set the new length - up++; // move to next - // on unit boundary, so shift-down copy loop is simple - for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) - *target=*up; - } - } // unit-boundary case - - else { // discard digit is in low digit(s), and not top digit - uInt discard1; // first discarded digit - uInt quot, rem; // for divisions - if (cut==0) quot=*up; // is at bottom of unit - else /* cut>0 */ { // it's not at bottom of unit - #if DECDPUN<=4 - quot=QUOT10(*up, cut); - rem=*up-quot*powers[cut]; - #else - rem=*up%powers[cut]; - quot=*up/powers[cut]; - #endif - if (rem!=0) *residue=1; - } - // discard digit is now at bottom of quot - #if DECDPUN<=4 - temp=(quot*6554)>>16; // fast /10 - // Vowels algorithm here not a win (9 instructions) - discard1=quot-X10(temp); - quot=temp; - #else - discard1=quot%10; - quot=quot/10; - #endif - // here, discard1 is the guard digit, and residue is everything - // else [use mapping array to accumulate residue safely] - *residue+=resmap[discard1]; - cut++; // update cut - // here: up -> Unit of the array with bottom digit - // cut is the division point for each Unit - // quot holds the uncut high-order digits for the current unit - if (set->digits<=0) { // special for Quantize/Subnormal :-( - *dn->lsu=0; // .. result is 0 - dn->digits=1; // .. - } - else { // shift to least needed - count=set->digits; // now digits to end up with - dn->digits=count; // set the new length - // shift-copy the coefficient array to the result number - for (target=dn->lsu; ; target++) { - *target=(Unit)quot; - count-=(DECDPUN-cut); - if (count<=0) break; - up++; - quot=*up; - #if DECDPUN<=4 - quot=QUOT10(quot, cut); - rem=*up-quot*powers[cut]; - #else - rem=quot%powers[cut]; - quot=quot/powers[cut]; - #endif - *target=(Unit)(*target+rem*powers[DECDPUN-cut]); - count-=cut; - if (count<=0) break; - } // shift-copy loop - } // shift to least - } // not unit boundary - - if (*residue!=0) *status|=DEC_Inexact; // record inexactitude - return; - } // decSetCoeff - -/* ------------------------------------------------------------------ */ -/* decApplyRound -- apply pending rounding to a number */ -/* */ -/* dn is the number, with space for set->digits digits */ -/* set is the context [for size and rounding mode] */ -/* residue indicates pending rounding, being any accumulated */ -/* guard and sticky information. It may be: */ -/* 6-9: rounding digit is >5 */ -/* 5: rounding digit is exactly half-way */ -/* 1-4: rounding digit is <5 and >0 */ -/* 0: the coefficient is exact */ -/* -1: as 1, but the hidden digits are subtractive, that */ -/* is, of the opposite sign to dn. In this case the */ -/* coefficient must be non-0. This case occurs when */ -/* subtracting a small number (which can be reduced to */ -/* a sticky bit); see decAddOp. */ -/* status is the status accumulator, as usual */ -/* */ -/* This routine applies rounding while keeping the length of the */ -/* coefficient constant. The exponent and status are unchanged */ -/* except if: */ -/* */ -/* -- the coefficient was increased and is all nines (in which */ -/* case Overflow could occur, and is handled directly here so */ -/* the caller does not need to re-test for overflow) */ -/* */ -/* -- the coefficient was decreased and becomes all nines (in which */ -/* case Underflow could occur, and is also handled directly). */ -/* */ -/* All fields in dn are updated as required. */ -/* */ -/* ------------------------------------------------------------------ */ -static void decApplyRound(decNumber *dn, decContext *set, Int residue, - uInt *status) { - Int bump; // 1 if coefficient needs to be incremented - // -1 if coefficient needs to be decremented - - if (residue==0) return; // nothing to apply - - bump=0; // assume a smooth ride - - // now decide whether, and how, to round, depending on mode - switch (set->round) { - case DEC_ROUND_05UP: { // round zero or five up (for reround) - // This is the same as DEC_ROUND_DOWN unless there is a - // positive residue and the lsd of dn is 0 or 5, in which case - // it is bumped; when residue is <0, the number is therefore - // bumped down unless the final digit was 1 or 6 (in which - // case it is bumped down and then up -- a no-op) - Int lsd5=*dn->lsu%5; // get lsd and quintate - if (residue<0 && lsd5!=1) bump=-1; - else if (residue>0 && lsd5==0) bump=1; - // [bump==1 could be applied directly; use common path for clarity] - break;} // r-05 - - case DEC_ROUND_DOWN: { - // no change, except if negative residue - if (residue<0) bump=-1; - break;} // r-d - - case DEC_ROUND_HALF_DOWN: { - if (residue>5) bump=1; - break;} // r-h-d - - case DEC_ROUND_HALF_EVEN: { - if (residue>5) bump=1; // >0.5 goes up - else if (residue==5) { // exactly 0.5000... - // 0.5 goes up iff [new] lsd is odd - if (*dn->lsu & 0x01) bump=1; - } - break;} // r-h-e - - case DEC_ROUND_HALF_UP: { - if (residue>=5) bump=1; - break;} // r-h-u - - case DEC_ROUND_UP: { - if (residue>0) bump=1; - break;} // r-u - - case DEC_ROUND_CEILING: { - // same as _UP for positive numbers, and as _DOWN for negatives - // [negative residue cannot occur on 0] - if (decNumberIsNegative(dn)) { - if (residue<0) bump=-1; - } - else { - if (residue>0) bump=1; - } - break;} // r-c - - case DEC_ROUND_FLOOR: { - // same as _UP for negative numbers, and as _DOWN for positive - // [negative residue cannot occur on 0] - if (!decNumberIsNegative(dn)) { - if (residue<0) bump=-1; - } - else { - if (residue>0) bump=1; - } - break;} // r-f - - default: { // e.g., DEC_ROUND_MAX - *status|=DEC_Invalid_context; - #if DECTRACE || (DECCHECK && DECVERB) - printf("Unknown rounding mode: %d\n", set->round); - #endif - break;} - } // switch - - // now bump the number, up or down, if need be - if (bump==0) return; // no action required - - // Simply use decUnitAddSub unless bumping up and the number is - // all nines. In this special case set to 100... explicitly - // and adjust the exponent by one (as otherwise could overflow - // the array) - // Similarly handle all-nines result if bumping down. - if (bump>0) { - Unit *up; // work - uInt count=dn->digits; // digits to be checked - for (up=dn->lsu; ; up++) { - if (count<=DECDPUN) { - // this is the last Unit (the msu) - if (*up!=powers[count]-1) break; // not still 9s - // here if it, too, is all nines - *up=(Unit)powers[count-1]; // here 999 -> 100 etc. - for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0 - dn->exponent++; // and bump exponent - // [which, very rarely, could cause Overflow...] - if ((dn->exponent+dn->digits)>set->emax+1) { - decSetOverflow(dn, set, status); - } - return; // done - } - // a full unit to check, with more to come - if (*up!=DECDPUNMAX) break; // not still 9s - count-=DECDPUN; - } // up - } // bump>0 - else { // -1 - // here checking for a pre-bump of 1000... (leading 1, all - // other digits zero) - Unit *up, *sup; // work - uInt count=dn->digits; // digits to be checked - for (up=dn->lsu; ; up++) { - if (count<=DECDPUN) { - // this is the last Unit (the msu) - if (*up!=powers[count-1]) break; // not 100.. - // here if have the 1000... case - sup=up; // save msu pointer - *up=(Unit)powers[count]-1; // here 100 in msu -> 999 - // others all to all-nines, too - for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; - dn->exponent--; // and bump exponent - - // iff the number was at the subnormal boundary (exponent=etiny) - // then the exponent is now out of range, so it will in fact get - // clamped to etiny and the final 9 dropped. - // printf(">> emin=%d exp=%d sdig=%d\n", set->emin, - // dn->exponent, set->digits); - if (dn->exponent+1==set->emin-set->digits+1) { - if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9] - else { - *sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99.. - dn->digits--; - } - dn->exponent++; - *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; - } - return; // done - } - - // a full unit to check, with more to come - if (*up!=0) break; // not still 0s - count-=DECDPUN; - } // up - - } // bump<0 - - // Actual bump needed. Do it. - decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); - } // decApplyRound - -#if DECSUBSET -/* ------------------------------------------------------------------ */ -/* decFinish -- finish processing a number */ -/* */ -/* dn is the number */ -/* set is the context */ -/* residue is the rounding accumulator (as in decApplyRound) */ -/* status is the accumulator */ -/* */ -/* This finishes off the current number by: */ -/* 1. If not extended: */ -/* a. Converting a zero result to clean '0' */ -/* b. Reducing positive exponents to 0, if would fit in digits */ -/* 2. Checking for overflow and subnormals (always) */ -/* Note this is just Finalize when no subset arithmetic. */ -/* All fields are updated as required. */ -/* ------------------------------------------------------------------ */ -static void decFinish(decNumber *dn, decContext *set, Int *residue, - uInt *status) { - if (!set->extended) { - if ISZERO(dn) { // value is zero - dn->exponent=0; // clean exponent .. - dn->bits=0; // .. and sign - return; // no error possible - } - if (dn->exponent>=0) { // non-negative exponent - // >0; reduce to integer if possible - if (set->digits >= (dn->exponent+dn->digits)) { - dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); - dn->exponent=0; - } - } - } // !extended - - decFinalize(dn, set, residue, status); - } // decFinish -#endif - -/* ------------------------------------------------------------------ */ -/* decFinalize -- final check, clamp, and round of a number */ -/* */ -/* dn is the number */ -/* set is the context */ -/* residue is the rounding accumulator (as in decApplyRound) */ -/* status is the status accumulator */ -/* */ -/* This finishes off the current number by checking for subnormal */ -/* results, applying any pending rounding, checking for overflow, */ -/* and applying any clamping. */ -/* Underflow and overflow conditions are raised as appropriate. */ -/* All fields are updated as required. */ -/* ------------------------------------------------------------------ */ -static void decFinalize(decNumber *dn, decContext *set, Int *residue, - uInt *status) { - Int shift; // shift needed if clamping - Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary - - // Must be careful, here, when checking the exponent as the - // adjusted exponent could overflow 31 bits [because it may already - // be up to twice the expected]. - - // First test for subnormal. This must be done before any final - // round as the result could be rounded to Nmin or 0. - if (dn->exponent<=tinyexp) { // prefilter - Int comp; - decNumber nmin; - // A very nasty case here is dn == Nmin and residue<0 - if (dn->exponentemin; - comp=decCompare(dn, &nmin, 1); // (signless compare) - if (comp==BADINT) { // oops - *status|=DEC_Insufficient_storage; // abandon... - return; - } - if (*residue<0 && comp==0) { // neg residue and dn==Nmin - decApplyRound(dn, set, *residue, status); // might force down - decSetSubnormal(dn, set, residue, status); - return; - } - } - - // now apply any pending round (this could raise overflow). - if (*residue!=0) decApplyRound(dn, set, *residue, status); - - // Check for overflow [redundant in the 'rare' case] or clamp - if (dn->exponent<=set->emax-set->digits+1) return; // neither needed - - - // here when might have an overflow or clamp to do - if (dn->exponent>set->emax-dn->digits+1) { // too big - decSetOverflow(dn, set, status); - return; - } - // here when the result is normal but in clamp range - if (!set->clamp) return; - - // here when need to apply the IEEE exponent clamp (fold-down) - shift=dn->exponent-(set->emax-set->digits+1); - - // shift coefficient (if non-zero) - if (!ISZERO(dn)) { - dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); - } - dn->exponent-=shift; // adjust the exponent to match - *status|=DEC_Clamped; // and record the dirty deed - return; - } // decFinalize - -/* ------------------------------------------------------------------ */ -/* decSetOverflow -- set number to proper overflow value */ -/* */ -/* dn is the number (used for sign [only] and result) */ -/* set is the context [used for the rounding mode, etc.] */ -/* status contains the current status to be updated */ -/* */ -/* This sets the sign of a number and sets its value to either */ -/* Infinity or the maximum finite value, depending on the sign of */ -/* dn and the rounding mode, following IEEE 754 rules. */ -/* ------------------------------------------------------------------ */ -static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { - Flag needmax=0; // result is maximum finite value - uByte sign=dn->bits&DECNEG; // clean and save sign bit - - if (ISZERO(dn)) { // zero does not overflow magnitude - Int emax=set->emax; // limit value - if (set->clamp) emax-=set->digits-1; // lower if clamping - if (dn->exponent>emax) { // clamp required - dn->exponent=emax; - *status|=DEC_Clamped; - } - return; - } - - decNumberZero(dn); - switch (set->round) { - case DEC_ROUND_DOWN: { - needmax=1; // never Infinity - break;} // r-d - case DEC_ROUND_05UP: { - needmax=1; // never Infinity - break;} // r-05 - case DEC_ROUND_CEILING: { - if (sign) needmax=1; // Infinity if non-negative - break;} // r-c - case DEC_ROUND_FLOOR: { - if (!sign) needmax=1; // Infinity if negative - break;} // r-f - default: break; // Infinity in all other cases - } - if (needmax) { - decSetMaxValue(dn, set); - dn->bits=sign; // set sign - } - else dn->bits=sign|DECINF; // Value is +/-Infinity - *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; - } // decSetOverflow - -/* ------------------------------------------------------------------ */ -/* decSetMaxValue -- set number to +Nmax (maximum normal value) */ -/* */ -/* dn is the number to set */ -/* set is the context [used for digits and emax] */ -/* */ -/* This sets the number to the maximum positive value. */ -/* ------------------------------------------------------------------ */ -static void decSetMaxValue(decNumber *dn, decContext *set) { - Unit *up; // work - Int count=set->digits; // nines to add - dn->digits=count; - // fill in all nines to set maximum value - for (up=dn->lsu; ; up++) { - if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines - else { // this is the msu - *up=(Unit)(powers[count]-1); - break; - } - count-=DECDPUN; // filled those digits - } // up - dn->bits=0; // + sign - dn->exponent=set->emax-set->digits+1; - } // decSetMaxValue - -/* ------------------------------------------------------------------ */ -/* decSetSubnormal -- process value whose exponent is extended) { - decNumberZero(dn); - // always full overflow - *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; - return; - } - #endif - - // Full arithmetic -- allow subnormals, rounded to minimum exponent - // (Etiny) if needed - etiny=set->emin-(set->digits-1); // smallest allowed exponent - - if ISZERO(dn) { // value is zero - // residue can never be non-zero here - #if DECCHECK - if (*residue!=0) { - printf("++ Subnormal 0 residue %ld\n", (LI)*residue); - *status|=DEC_Invalid_operation; - } - #endif - if (dn->exponentexponent=etiny; - *status|=DEC_Clamped; - } - return; - } - - *status|=DEC_Subnormal; // have a non-zero subnormal - adjust=etiny-dn->exponent; // calculate digits to remove - if (adjust<=0) { // not out of range; unrounded - // residue can never be non-zero here, except in the Nmin-residue - // case (which is a subnormal result), so can take fast-path here - // it may already be inexact (from setting the coefficient) - if (*status&DEC_Inexact) *status|=DEC_Underflow; - return; - } - - // adjust>0, so need to rescale the result so exponent becomes Etiny - // [this code is similar to that in rescale] - workset=*set; // clone rounding, etc. - workset.digits=dn->digits-adjust; // set requested length - workset.emin-=adjust; // and adjust emin to match - // [note that the latter can be <1, here, similar to Rescale case] - decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); - decApplyRound(dn, &workset, *residue, status); - - // Use 754 default rule: Underflow is set iff Inexact - // [independent of whether trapped] - if (*status&DEC_Inexact) *status|=DEC_Underflow; - - // if rounded up a 999s case, exponent will be off by one; adjust - // back if so [it will fit, because it was shortened earlier] - if (dn->exponent>etiny) { - dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); - dn->exponent--; // (re)adjust the exponent. - } - - // if rounded to zero, it is by definition clamped... - if (ISZERO(dn)) *status|=DEC_Clamped; - } // decSetSubnormal - -/* ------------------------------------------------------------------ */ -/* decCheckMath - check entry conditions for a math function */ -/* */ -/* This checks the context and the operand */ -/* */ -/* rhs is the operand to check */ -/* set is the context to check */ -/* status is unchanged if both are good */ -/* */ -/* returns non-zero if status is changed, 0 otherwise */ -/* */ -/* Restrictions enforced: */ -/* */ -/* digits, emax, and -emin in the context must be less than */ -/* DEC_MAX_MATH (999999), and A must be within these bounds if */ -/* non-zero. Invalid_operation is set in the status if a */ -/* restriction is violated. */ -/* ------------------------------------------------------------------ */ -static uInt decCheckMath(const decNumber *rhs, decContext *set, - uInt *status) { - uInt save=*status; // record - if (set->digits>DEC_MAX_MATH - || set->emax>DEC_MAX_MATH - || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; - else if ((rhs->digits>DEC_MAX_MATH - || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 - || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) - && !ISZERO(rhs)) *status|=DEC_Invalid_operation; - return (*status!=save); - } // decCheckMath - -/* ------------------------------------------------------------------ */ -/* decGetInt -- get integer from a number */ -/* */ -/* dn is the number [which will not be altered] */ -/* */ -/* returns one of: */ -/* BADINT if there is a non-zero fraction */ -/* the converted integer */ -/* BIGEVEN if the integer is even and magnitude > 2*10**9 */ -/* BIGODD if the integer is odd and magnitude > 2*10**9 */ -/* */ -/* This checks and gets a whole number from the input decNumber. */ -/* The sign can be determined from dn by the caller when BIGEVEN or */ -/* BIGODD is returned. */ -/* ------------------------------------------------------------------ */ -static Int decGetInt(const decNumber *dn) { - Int theInt; // result accumulator - const Unit *up; // work - Int got; // digits (real or not) processed - Int ilength=dn->digits+dn->exponent; // integral length - Flag neg=decNumberIsNegative(dn); // 1 if -ve - - // The number must be an integer that fits in 10 digits - // Assert, here, that 10 is enough for any rescale Etiny - #if DEC_MAX_EMAX > 999999999 - #error GetInt may need updating [for Emax] - #endif - #if DEC_MIN_EMIN < -999999999 - #error GetInt may need updating [for Emin] - #endif - if (ISZERO(dn)) return 0; // zeros are OK, with any exponent - - up=dn->lsu; // ready for lsu - theInt=0; // ready to accumulate - if (dn->exponent>=0) { // relatively easy - // no fractional part [usual]; allow for positive exponent - got=dn->exponent; - } - else { // -ve exponent; some fractional part to check and discard - Int count=-dn->exponent; // digits to discard - // spin up whole units until reach the Unit with the unit digit - for (; count>=DECDPUN; up++) { - if (*up!=0) return BADINT; // non-zero Unit to discard - count-=DECDPUN; - } - if (count==0) got=0; // [a multiple of DECDPUN] - else { // [not multiple of DECDPUN] - Int rem; // work - // slice off fraction digits and check for non-zero - #if DECDPUN<=4 - theInt=QUOT10(*up, count); - rem=*up-theInt*powers[count]; - #else - rem=*up%powers[count]; // slice off discards - theInt=*up/powers[count]; - #endif - if (rem!=0) return BADINT; // non-zero fraction - // it looks good - got=DECDPUN-count; // number of digits so far - up++; // ready for next - } - } - // now it's known there's no fractional part - - // tricky code now, to accumulate up to 9.3 digits - if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there - - if (ilength<11) { - Int save=theInt; - // collect any remaining unit(s) - for (; got1999999997) ilength=11; - else if (!neg && theInt>999999999) ilength=11; - if (ilength==11) theInt=save; // restore correct low bit - } - } - - if (ilength>10) { // too big - if (theInt&1) return BIGODD; // bottom bit 1 - return BIGEVEN; // bottom bit 0 - } - - if (neg) theInt=-theInt; // apply sign - return theInt; - } // decGetInt - -/* ------------------------------------------------------------------ */ -/* decDecap -- decapitate the coefficient of a number */ -/* */ -/* dn is the number to be decapitated */ -/* drop is the number of digits to be removed from the left of dn; */ -/* this must be <= dn->digits (if equal, the coefficient is */ -/* set to 0) */ -/* */ -/* Returns dn; dn->digits will be <= the initial digits less drop */ -/* (after removing drop digits there may be leading zero digits */ -/* which will also be removed). Only dn->lsu and dn->digits change. */ -/* ------------------------------------------------------------------ */ -static decNumber *decDecap(decNumber *dn, Int drop) { - Unit *msu; // -> target cut point - Int cut; // work - if (drop>=dn->digits) { // losing the whole thing - #if DECCHECK - if (drop>dn->digits) - printf("decDecap called with drop>digits [%ld>%ld]\n", - (LI)drop, (LI)dn->digits); - #endif - dn->lsu[0]=0; - dn->digits=1; - return dn; - } - msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu - cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu - if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits - // that may have left leading zero digits, so do a proper count... - dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); - return dn; - } // decDecap - -/* ------------------------------------------------------------------ */ -/* decBiStr -- compare string with pairwise options */ -/* */ -/* targ is the string to compare */ -/* str1 is one of the strings to compare against (length may be 0) */ -/* str2 is the other; it must be the same length as str1 */ -/* */ -/* returns 1 if strings compare equal, (that is, it is the same */ -/* length as str1 and str2, and each character of targ is in either */ -/* str1 or str2 in the corresponding position), or 0 otherwise */ -/* */ -/* This is used for generic caseless compare, including the awkward */ -/* case of the Turkish dotted and dotless Is. Use as (for example): */ -/* if (decBiStr(test, "mike", "MIKE")) ... */ -/* ------------------------------------------------------------------ */ -static Flag decBiStr(const char *targ, const char *str1, const char *str2) { - for (;;targ++, str1++, str2++) { - if (*targ!=*str1 && *targ!=*str2) return 0; - // *targ has a match in one (or both, if terminator) - if (*targ=='\0') break; - } // forever - return 1; - } // decBiStr - -/* ------------------------------------------------------------------ */ -/* decNaNs -- handle NaN operand or operands */ -/* */ -/* res is the result number */ -/* lhs is the first operand */ -/* rhs is the second operand, or NULL if none */ -/* context is used to limit payload length */ -/* status contains the current status */ -/* returns res in case convenient */ -/* */ -/* Called when one or both operands is a NaN, and propagates the */ -/* appropriate result to res. When an sNaN is found, it is changed */ -/* to a qNaN and Invalid operation is set. */ -/* ------------------------------------------------------------------ */ -static decNumber * decNaNs(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set, - uInt *status) { - // This decision tree ends up with LHS being the source pointer, - // and status updated if need be - if (lhs->bits & DECSNAN) - *status|=DEC_Invalid_operation | DEC_sNaN; - else if (rhs==NULL); - else if (rhs->bits & DECSNAN) { - lhs=rhs; - *status|=DEC_Invalid_operation | DEC_sNaN; - } - else if (lhs->bits & DECNAN); - else lhs=rhs; - - // propagate the payload - if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy - else { // too long - const Unit *ul; - Unit *ur, *uresp1; - // copy safe number of units, then decapitate - res->bits=lhs->bits; // need sign etc. - uresp1=res->lsu+D2U(set->digits); - for (ur=res->lsu, ul=lhs->lsu; urdigits=D2U(set->digits)*DECDPUN; - // maybe still too long - if (res->digits>set->digits) decDecap(res, res->digits-set->digits); - } - - res->bits&=~DECSNAN; // convert any sNaN to NaN, while - res->bits|=DECNAN; // .. preserving sign - res->exponent=0; // clean exponent - // [coefficient was copied/decapitated] - return res; - } // decNaNs - -/* ------------------------------------------------------------------ */ -/* decStatus -- apply non-zero status */ -/* */ -/* dn is the number to set if error */ -/* status contains the current status (not yet in context) */ -/* set is the context */ -/* */ -/* If the status is an error status, the number is set to a NaN, */ -/* unless the error was an overflow, divide-by-zero, or underflow, */ -/* in which case the number will have already been set. */ -/* */ -/* The context status is then updated with the new status. Note that */ -/* this may raise a signal, so control may never return from this */ -/* routine (hence resources must be recovered before it is called). */ -/* ------------------------------------------------------------------ */ -static void decStatus(decNumber *dn, uInt status, decContext *set) { - if (status & DEC_NaNs) { // error status -> NaN - // if cause was an sNaN, clear and propagate [NaN is already set up] - if (status & DEC_sNaN) status&=~DEC_sNaN; - else { - decNumberZero(dn); // other error: clean throughout - dn->bits=DECNAN; // and make a quiet NaN - } - } - decContextSetStatus(set, status); // [may not return] - return; - } // decStatus - -/* ------------------------------------------------------------------ */ -/* decGetDigits -- count digits in a Units array */ -/* */ -/* uar is the Unit array holding the number (this is often an */ -/* accumulator of some sort) */ -/* len is the length of the array in units [>=1] */ -/* */ -/* returns the number of (significant) digits in the array */ -/* */ -/* All leading zeros are excluded, except the last if the array has */ -/* only zero Units. */ -/* ------------------------------------------------------------------ */ -// This may be called twice during some operations. -static Int decGetDigits(Unit *uar, Int len) { - Unit *up=uar+(len-1); // -> msu - Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu - #if DECDPUN>4 - uInt const *pow; // work - #endif - // (at least 1 in final msu) - #if DECCHECK - if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); - #endif - - for (; up>=uar; up--) { - if (*up==0) { // unit is all 0s - if (digits==1) break; // a zero has one digit - digits-=DECDPUN; // adjust for 0 unit - continue;} - // found the first (most significant) non-zero Unit - #if DECDPUN>1 // not done yet - if (*up<10) break; // is 1-9 - digits++; - #if DECDPUN>2 // not done yet - if (*up<100) break; // is 10-99 - digits++; - #if DECDPUN>3 // not done yet - if (*up<1000) break; // is 100-999 - digits++; - #if DECDPUN>4 // count the rest ... - for (pow=&powers[4]; *up>=*pow; pow++) digits++; - #endif - #endif - #endif - #endif - break; - } // up - return digits; - } // decGetDigits - -#if DECTRACE | DECCHECK -/* ------------------------------------------------------------------ */ -/* decNumberShow -- display a number [debug aid] */ -/* dn is the number to show */ -/* */ -/* Shows: sign, exponent, coefficient (msu first), digits */ -/* or: sign, special-value */ -/* ------------------------------------------------------------------ */ -// this is public so other modules can use it -void decNumberShow(const decNumber *dn) { - const Unit *up; // work - uInt u, d; // .. - Int cut; // .. - char isign='+'; // main sign - if (dn==NULL) { - printf("NULL\n"); - return;} - if (decNumberIsNegative(dn)) isign='-'; - printf(" >> %c ", isign); - if (dn->bits&DECSPECIAL) { // Is a special value - if (decNumberIsInfinite(dn)) printf("Infinity"); - else { // a NaN - if (dn->bits&DECSNAN) printf("sNaN"); // signalling NaN - else printf("NaN"); - } - // if coefficient and exponent are 0, no more to do - if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { - printf("\n"); - return;} - // drop through to report other information - printf(" "); - } - - // now carefully display the coefficient - up=dn->lsu+D2U(dn->digits)-1; // msu - printf("%ld", (LI)*up); - for (up=up-1; up>=dn->lsu; up--) { - u=*up; - printf(":"); - for (cut=DECDPUN-1; cut>=0; cut--) { - d=u/powers[cut]; - u-=d*powers[cut]; - printf("%ld", (LI)d); - } // cut - } // up - if (dn->exponent!=0) { - char esign='+'; - if (dn->exponent<0) esign='-'; - printf(" E%c%ld", esign, (LI)abs(dn->exponent)); - } - printf(" [%ld]\n", (LI)dn->digits); - } // decNumberShow -#endif - -#if DECTRACE || DECCHECK -/* ------------------------------------------------------------------ */ -/* decDumpAr -- display a unit array [debug/check aid] */ -/* name is a single-character tag name */ -/* ar is the array to display */ -/* len is the length of the array in Units */ -/* ------------------------------------------------------------------ */ -static void decDumpAr(char name, const Unit *ar, Int len) { - Int i; - const char *spec; - #if DECDPUN==9 - spec="%09d "; - #elif DECDPUN==8 - spec="%08d "; - #elif DECDPUN==7 - spec="%07d "; - #elif DECDPUN==6 - spec="%06d "; - #elif DECDPUN==5 - spec="%05d "; - #elif DECDPUN==4 - spec="%04d "; - #elif DECDPUN==3 - spec="%03d "; - #elif DECDPUN==2 - spec="%02d "; - #else - spec="%d "; - #endif - printf(" :%c: ", name); - for (i=len-1; i>=0; i--) { - if (i==len-1) printf("%ld ", (LI)ar[i]); - else printf(spec, ar[i]); - } - printf("\n"); - return;} -#endif - -#if DECCHECK -/* ------------------------------------------------------------------ */ -/* decCheckOperands -- check operand(s) to a routine */ -/* res is the result structure (not checked; it will be set to */ -/* quiet NaN if error found (and it is not NULL)) */ -/* lhs is the first operand (may be DECUNRESU) */ -/* rhs is the second (may be DECUNUSED) */ -/* set is the context (may be DECUNCONT) */ -/* returns 0 if both operands, and the context are clean, or 1 */ -/* otherwise (in which case the context will show an error, */ -/* unless NULL). Note that res is not cleaned; caller should */ -/* handle this so res=NULL case is safe. */ -/* The caller is expected to abandon immediately if 1 is returned. */ -/* ------------------------------------------------------------------ */ -static Flag decCheckOperands(decNumber *res, const decNumber *lhs, - const decNumber *rhs, decContext *set) { - Flag bad=0; - if (set==NULL) { // oops; hopeless - #if DECTRACE || DECVERB - printf("Reference to context is NULL.\n"); - #endif - bad=1; - return 1;} - else if (set!=DECUNCONT - && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { - bad=1; - #if DECTRACE || DECVERB - printf("Bad context [digits=%ld round=%ld].\n", - (LI)set->digits, (LI)set->round); - #endif - } - else { - if (res==NULL) { - bad=1; - #if DECTRACE - // this one not DECVERB as standard tests include NULL - printf("Reference to result is NULL.\n"); - #endif - } - if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); - if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); - } - if (bad) { - if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation); - if (res!=DECUNRESU && res!=NULL) { - decNumberZero(res); - res->bits=DECNAN; // qNaN - } - } - return bad; - } // decCheckOperands - -/* ------------------------------------------------------------------ */ -/* decCheckNumber -- check a number */ -/* dn is the number to check */ -/* returns 0 if the number is clean, or 1 otherwise */ -/* */ -/* The number is considered valid if it could be a result from some */ -/* operation in some valid context. */ -/* ------------------------------------------------------------------ */ -static Flag decCheckNumber(const decNumber *dn) { - const Unit *up; // work - uInt maxuint; // .. - Int ae, d, digits; // .. - Int emin, emax; // .. - - if (dn==NULL) { // hopeless - #if DECTRACE - // this one not DECVERB as standard tests include NULL - printf("Reference to decNumber is NULL.\n"); - #endif - return 1;} - - // check special values - if (dn->bits & DECSPECIAL) { - if (dn->exponent!=0) { - #if DECTRACE || DECVERB - printf("Exponent %ld (not 0) for a special value [%02x].\n", - (LI)dn->exponent, dn->bits); - #endif - return 1;} - - // 2003.09.08: NaNs may now have coefficients, so next tests Inf only - if (decNumberIsInfinite(dn)) { - if (dn->digits!=1) { - #if DECTRACE || DECVERB - printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); - #endif - return 1;} - if (*dn->lsu!=0) { - #if DECTRACE || DECVERB - printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); - #endif - decDumpAr('I', dn->lsu, D2U(dn->digits)); - return 1;} - } // Inf - // 2002.12.26: negative NaNs can now appear through proposed IEEE - // concrete formats (decimal64, etc.). - return 0; - } - - // check the coefficient - if (dn->digits<1 || dn->digits>DECNUMMAXP) { - #if DECTRACE || DECVERB - printf("Digits %ld in number.\n", (LI)dn->digits); - #endif - return 1;} - - d=dn->digits; - - for (up=dn->lsu; d>0; up++) { - if (d>DECDPUN) maxuint=DECDPUNMAX; - else { // reached the msu - maxuint=powers[d]-1; - if (dn->digits>1 && *upmaxuint) { - #if DECTRACE || DECVERB - printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", - (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); - #endif - return 1;} - d-=DECDPUN; - } - - // check the exponent. Note that input operands can have exponents - // which are out of the set->emin/set->emax and set->digits range - // (just as they can have more digits than set->digits). - ae=dn->exponent+dn->digits-1; // adjusted exponent - emax=DECNUMMAXE; - emin=DECNUMMINE; - digits=DECNUMMAXP; - if (ae+emax) { - #if DECTRACE || DECVERB - printf("Adjusted exponent overflow [%ld].\n", (LI)ae); - decNumberShow(dn); - #endif - return 1;} - - return 0; // it's OK - } // decCheckNumber - -/* ------------------------------------------------------------------ */ -/* decCheckInexact -- check a normal finite inexact result has digits */ -/* dn is the number to check */ -/* set is the context (for status and precision) */ -/* sets Invalid operation, etc., if some digits are missing */ -/* [this check is not made for DECSUBSET compilation or when */ -/* subnormal is not set] */ -/* ------------------------------------------------------------------ */ -static void decCheckInexact(const decNumber *dn, decContext *set) { - #if !DECSUBSET && DECEXTFLAG - if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact - && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { - #if DECTRACE || DECVERB - printf("Insufficient digits [%ld] on normal Inexact result.\n", - (LI)dn->digits); - decNumberShow(dn); - #endif - decContextSetStatus(set, DEC_Invalid_operation); - } - #else - // next is a noop for quiet compiler - if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; - #endif - return; - } // decCheckInexact -#endif - -#if DECALLOC -#undef malloc -#undef free -/* ------------------------------------------------------------------ */ -/* decMalloc -- accountable allocation routine */ -/* n is the number of bytes to allocate */ -/* */ -/* Semantics is the same as the stdlib malloc routine, but bytes */ -/* allocated are accounted for globally, and corruption fences are */ -/* added before and after the 'actual' storage. */ -/* ------------------------------------------------------------------ */ -/* This routine allocates storage with an extra twelve bytes; 8 are */ -/* at the start and hold: */ -/* 0-3 the original length requested */ -/* 4-7 buffer corruption detection fence (DECFENCE, x4) */ -/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ -/* ------------------------------------------------------------------ */ -static void *decMalloc(size_t n) { - uInt size=n+12; // true size - void *alloc; // -> allocated storage - uByte *b, *b0; // work - uInt uiwork; // for macros - - alloc=malloc(size); // -> allocated storage - if (alloc==NULL) return NULL; // out of strorage - b0=(uByte *)alloc; // as bytes - decAllocBytes+=n; // account for storage - UBFROMUI(alloc, n); // save n - // printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); - for (b=b0+4; b play area - } // decMalloc - -/* ------------------------------------------------------------------ */ -/* decFree -- accountable free routine */ -/* alloc is the storage to free */ -/* */ -/* Semantics is the same as the stdlib malloc routine, except that */ -/* the global storage accounting is updated and the fences are */ -/* checked to ensure that no routine has written 'out of bounds'. */ -/* ------------------------------------------------------------------ */ -/* This routine first checks that the fences have not been corrupted. */ -/* It then frees the storage using the 'truw' storage address (that */ -/* is, offset by 8). */ -/* ------------------------------------------------------------------ */ -static void decFree(void *alloc) { - uInt n; // original length - uByte *b, *b0; // work - uInt uiwork; // for macros - - if (alloc==NULL) return; // allowed; it's a nop - b0=(uByte *)alloc; // as bytes - b0-=8; // -> true start of storage - n=UBTOUI(b0); // lift length - for (b=b0+4; b4 or DECUSE64=1, the C99 64-bit int64_t and */ +/* uint64_t types may be used. To avoid these, set DECUSE64=0 */ +/* and DECDPUN<=4 (see documentation). */ +/* */ +/* The code also conforms to C99 restrictions; in particular, */ +/* strict aliasing rules are observed. */ +/* */ +/* 2. The decNumber format which this library uses is optimized for */ +/* efficient processing of relatively short numbers; in particular */ +/* it allows the use of fixed sized structures and minimizes copy */ +/* and move operations. It does, however, support arbitrary */ +/* precision (up to 999,999,999 digits) and arbitrary exponent */ +/* range (Emax in the range 0 through 999,999,999 and Emin in the */ +/* range -999,999,999 through 0). Mathematical functions (for */ +/* example decNumberExp) as identified below are restricted more */ +/* tightly: digits, emax, and -emin in the context must be <= */ +/* DEC_MAX_MATH (999999), and their operand(s) must be within */ +/* these bounds. */ +/* */ +/* 3. Logical functions are further restricted; their operands must */ +/* be finite, positive, have an exponent of zero, and all digits */ +/* must be either 0 or 1. The result will only contain digits */ +/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */ +/* */ +/* 4. Operands to operator functions are never modified unless they */ +/* are also specified to be the result number (which is always */ +/* permitted). Other than that case, operands must not overlap. */ +/* */ +/* 5. Error handling: the type of the error is ORed into the status */ +/* flags in the current context (decContext structure). The */ +/* SIGFPE signal is then raised if the corresponding trap-enabler */ +/* flag in the decContext is set (is 1). */ +/* */ +/* It is the responsibility of the caller to clear the status */ +/* flags as required. */ +/* */ +/* The result of any routine which returns a number will always */ +/* be a valid number (which may be a special value, such as an */ +/* Infinity or NaN). */ +/* */ +/* 6. The decNumber format is not an exchangeable concrete */ +/* representation as it comprises fields which may be machine- */ +/* dependent (packed or unpacked, or special length, for example). */ +/* Canonical conversions to and from strings are provided; other */ +/* conversions are available in separate modules. */ +/* */ +/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */ +/* to 1 for extended operand checking (including NULL operands). */ +/* Results are undefined if a badly-formed structure (or a NULL */ +/* pointer to a structure) is provided, though with DECCHECK */ +/* enabled the operator routines are protected against exceptions. */ +/* (Except if the result pointer is NULL, which is unrecoverable.) */ +/* */ +/* However, the routines will never cause exceptions if they are */ +/* given well-formed operands, even if the value of the operands */ +/* is inappropriate for the operation and DECCHECK is not set. */ +/* (Except for SIGFPE, as and where documented.) */ +/* */ +/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */ +/* ------------------------------------------------------------------ */ +/* Implementation notes for maintenance of this module: */ +/* */ +/* 1. Storage leak protection: Routines which use malloc are not */ +/* permitted to use return for fastpath or error exits (i.e., */ +/* they follow strict structured programming conventions). */ +/* Instead they have a do{}while(0); construct surrounding the */ +/* code which is protected -- break may be used to exit this. */ +/* Other routines can safely use the return statement inline. */ +/* */ +/* Storage leak accounting can be enabled using DECALLOC. */ +/* */ +/* 2. All loops use the for(;;) construct. Any do construct does */ +/* not loop; it is for allocation protection as just described. */ +/* */ +/* 3. Setting status in the context must always be the very last */ +/* action in a routine, as non-0 status may raise a trap and hence */ +/* the call to set status may not return (if the handler uses long */ +/* jump). Therefore all cleanup must be done first. In general, */ +/* to achieve this status is accumulated and is only applied just */ +/* before return by calling decContextSetStatus (via decStatus). */ +/* */ +/* Routines which allocate storage cannot, in general, use the */ +/* 'top level' routines which could cause a non-returning */ +/* transfer of control. The decXxxxOp routines are safe (do not */ +/* call decStatus even if traps are set in the context) and should */ +/* be used instead (they are also a little faster). */ +/* */ +/* 4. Exponent checking is minimized by allowing the exponent to */ +/* grow outside its limits during calculations, provided that */ +/* the decFinalize function is called later. Multiplication and */ +/* division, and intermediate calculations in exponentiation, */ +/* require more careful checks because of the risk of 31-bit */ +/* overflow (the most negative valid exponent is -1999999997, for */ +/* a 999999999-digit number with adjusted exponent of -999999999). */ +/* */ +/* 5. Rounding is deferred until finalization of results, with any */ +/* 'off to the right' data being represented as a single digit */ +/* residue (in the range -1 through 9). This avoids any double- */ +/* rounding when more than one shortening takes place (for */ +/* example, when a result is subnormal). */ +/* */ +/* 6. The digits count is allowed to rise to a multiple of DECDPUN */ +/* during many operations, so whole Units are handled and exact */ +/* accounting of digits is not needed. The correct digits value */ +/* is found by decGetDigits, which accounts for leading zeros. */ +/* This must be called before any rounding if the number of digits */ +/* is not known exactly. */ +/* */ +/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */ +/* numbers up to four digits, using appropriate constants. This */ +/* is not useful for longer numbers because overflow of 32 bits */ +/* would lead to 4 multiplies, which is almost as expensive as */ +/* a divide (unless a floating-point or 64-bit multiply is */ +/* assumed to be available). */ +/* */ +/* 8. Unusual abbreviations that may be used in the commentary: */ +/* lhs -- left hand side (operand, of an operation) */ +/* lsd -- least significant digit (of coefficient) */ +/* lsu -- least significant Unit (of coefficient) */ +/* msd -- most significant digit (of coefficient) */ +/* msi -- most significant item (in an array) */ +/* msu -- most significant Unit (of coefficient) */ +/* rhs -- right hand side (operand, of an operation) */ +/* +ve -- positive */ +/* -ve -- negative */ +/* ** -- raise to the power */ +/* ------------------------------------------------------------------ */ + +#include // for malloc, free, etc. +#include // for printf [if needed] +#include // for strcpy +#include // for lower +#include "decNumber.h" // base number library +#include "decNumberLocal.h" // decNumber local types, etc. + +/* Constants */ +// Public lookup table used by the D2U macro +const uByte d2utable[DECMAXD2U+1]=D2UTABLE; + +#define DECVERB 1 // set to 1 for verbose DECCHECK +#define powers DECPOWERS // old internal name + +// Local constants +#define DIVIDE 0x80 // Divide operators +#define REMAINDER 0x40 // .. +#define DIVIDEINT 0x20 // .. +#define REMNEAR 0x10 // .. +#define COMPARE 0x01 // Compare operators +#define COMPMAX 0x02 // .. +#define COMPMIN 0x03 // .. +#define COMPTOTAL 0x04 // .. +#define COMPNAN 0x05 // .. [NaN processing] +#define COMPSIG 0x06 // .. [signaling COMPARE] +#define COMPMAXMAG 0x07 // .. +#define COMPMINMAG 0x08 // .. + +#define DEC_sNaN 0x40000000 // local status: sNaN signal +#define BADINT (Int)0x80000000 // most-negative Int; error indicator +// Next two indicate an integer >= 10**6, and its parity (bottom bit) +#define BIGEVEN (Int)0x80000002 +#define BIGODD (Int)0x80000003 + +static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing + +/* Granularity-dependent code */ +#if DECDPUN<=4 + #define eInt Int // extended integer + #define ueInt uInt // unsigned extended integer + // Constant multipliers for divide-by-power-of five using reciprocal + // multiply, after removing powers of 2 by shifting, and final shift + // of 17 [we only need up to **4] + static const uInt multies[]={131073, 26215, 5243, 1049, 210}; + // QUOT10 -- macro to return the quotient of unit u divided by 10**n + #define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17) +#else + // For DECDPUN>4 non-ANSI-89 64-bit types are needed. + #if !DECUSE64 + #error decNumber.c: DECUSE64 must be 1 when DECDPUN>4 + #endif + #define eInt Long // extended integer + #define ueInt uLong // unsigned extended integer +#endif + +/* Local routines */ +static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *, + decContext *, uByte, uInt *); +static Flag decBiStr(const char *, const char *, const char *); +static uInt decCheckMath(const decNumber *, decContext *, uInt *); +static void decApplyRound(decNumber *, decContext *, Int, uInt *); +static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag); +static decNumber * decCompareOp(decNumber *, const decNumber *, + const decNumber *, decContext *, + Flag, uInt *); +static void decCopyFit(decNumber *, const decNumber *, decContext *, + Int *, uInt *); +static decNumber * decDecap(decNumber *, Int); +static decNumber * decDivideOp(decNumber *, const decNumber *, + const decNumber *, decContext *, Flag, uInt *); +static decNumber * decExpOp(decNumber *, const decNumber *, + decContext *, uInt *); +static void decFinalize(decNumber *, decContext *, Int *, uInt *); +static Int decGetDigits(Unit *, Int); +static Int decGetInt(const decNumber *); +static decNumber * decLnOp(decNumber *, const decNumber *, + decContext *, uInt *); +static decNumber * decMultiplyOp(decNumber *, const decNumber *, + const decNumber *, decContext *, + uInt *); +static decNumber * decNaNs(decNumber *, const decNumber *, + const decNumber *, decContext *, uInt *); +static decNumber * decQuantizeOp(decNumber *, const decNumber *, + const decNumber *, decContext *, Flag, + uInt *); +static void decReverse(Unit *, Unit *); +static void decSetCoeff(decNumber *, decContext *, const Unit *, + Int, Int *, uInt *); +static void decSetMaxValue(decNumber *, decContext *); +static void decSetOverflow(decNumber *, decContext *, uInt *); +static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *); +static Int decShiftToLeast(Unit *, Int, Int); +static Int decShiftToMost(Unit *, Int, Int); +static void decStatus(decNumber *, uInt, decContext *); +static void decToString(const decNumber *, char[], Flag); +static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *); +static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int, + Unit *, Int); +static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int); + +#if !DECSUBSET +/* decFinish == decFinalize when no subset arithmetic needed */ +#define decFinish(a,b,c,d) decFinalize(a,b,c,d) +#else +static void decFinish(decNumber *, decContext *, Int *, uInt *); +static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *); +#endif + +/* Local macros */ +// masked special-values bits +#define SPECIALARG (rhs->bits & DECSPECIAL) +#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL) + +/* Diagnostic macros, etc. */ +#if DECALLOC +// Handle malloc/free accounting. If enabled, our accountable routines +// are used; otherwise the code just goes straight to the system malloc +// and free routines. +#define malloc(a) decMalloc(a) +#define free(a) decFree(a) +#define DECFENCE 0x5a // corruption detector +// 'Our' malloc and free: +static void *decMalloc(size_t); +static void decFree(void *); +uInt decAllocBytes=0; // count of bytes allocated +// Note that DECALLOC code only checks for storage buffer overflow. +// To check for memory leaks, the decAllocBytes variable must be +// checked to be 0 at appropriate times (e.g., after the test +// harness completes a set of tests). This checking may be unreliable +// if the testing is done in a multi-thread environment. +#endif + +#if DECCHECK +// Optional checking routines. Enabling these means that decNumber +// and decContext operands to operator routines are checked for +// correctness. This roughly doubles the execution time of the +// fastest routines (and adds 600+ bytes), so should not normally be +// used in 'production'. +// decCheckInexact is used to check that inexact results have a full +// complement of digits (where appropriate -- this is not the case +// for Quantize, for example) +#define DECUNRESU ((decNumber *)(void *)0xffffffff) +#define DECUNUSED ((const decNumber *)(void *)0xffffffff) +#define DECUNCONT ((decContext *)(void *)(0xffffffff)) +static Flag decCheckOperands(decNumber *, const decNumber *, + const decNumber *, decContext *); +static Flag decCheckNumber(const decNumber *); +static void decCheckInexact(const decNumber *, decContext *); +#endif + +#if DECTRACE || DECCHECK +// Optional trace/debugging routines (may or may not be used) +void decNumberShow(const decNumber *); // displays the components of a number +static void decDumpAr(char, const Unit *, Int); +#endif + +/* ================================================================== */ +/* Conversions */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* from-int32 -- conversion from Int or uInt */ +/* */ +/* dn is the decNumber to receive the integer */ +/* in or uin is the integer to be converted */ +/* returns dn */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFromInt32(decNumber *dn, Int in) { + uInt unsig; + if (in>=0) unsig=in; + else { // negative (possibly BADINT) + if (in==BADINT) unsig=(uInt)1073741824*2; // special case + else unsig=-in; // invert + } + // in is now positive + decNumberFromUInt32(dn, unsig); + if (in<0) dn->bits=DECNEG; // sign needed + return dn; + } // decNumberFromInt32 + +decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) { + Unit *up; // work pointer + decNumberZero(dn); // clean + if (uin==0) return dn; // [or decGetDigits bad call] + for (up=dn->lsu; uin>0; up++) { + *up=(Unit)(uin%(DECDPUNMAX+1)); + uin=uin/(DECDPUNMAX+1); + } + dn->digits=decGetDigits(dn->lsu, up-dn->lsu); + return dn; + } // decNumberFromUInt32 + +/* ------------------------------------------------------------------ */ +/* to-int32 -- conversion to Int or uInt */ +/* */ +/* dn is the decNumber to convert */ +/* set is the context for reporting errors */ +/* returns the converted decNumber, or 0 if Invalid is set */ +/* */ +/* Invalid is set if the decNumber does not have exponent==0 or if */ +/* it is a NaN, Infinite, or out-of-range. */ +/* ------------------------------------------------------------------ */ +Int decNumberToInt32(const decNumber *dn, decContext *set) { + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + // special or too many digits, or bad exponent + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad + else { // is a finite integer with 10 or fewer digits + Int d; // work + const Unit *up; // .. + uInt hi=0, lo; // .. + up=dn->lsu; // -> lsu + lo=*up; // get 1 to 9 digits + #if DECDPUN>1 // split to higher + hi=lo/10; + lo=lo%10; + #endif + up++; + // collect remaining Units, if any, into hi + for (d=DECDPUN; ddigits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; + // now low has the lsd, hi the remainder + if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range? + // most-negative is a reprieve + if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000; + // bad -- drop through + } + else { // in-range always + Int i=X10(hi)+lo; + if (dn->bits&DECNEG) return -i; + return i; + } + } // integer + decContextSetStatus(set, DEC_Invalid_operation); // [may not return] + return 0; + } // decNumberToInt32 + +uInt decNumberToUInt32(const decNumber *dn, decContext *set) { + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + // special or too many digits, or bad exponent, or negative (<0) + if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0 + || (dn->bits&DECNEG && !ISZERO(dn))); // bad + else { // is a finite integer with 10 or fewer digits + Int d; // work + const Unit *up; // .. + uInt hi=0, lo; // .. + up=dn->lsu; // -> lsu + lo=*up; // get 1 to 9 digits + #if DECDPUN>1 // split to higher + hi=lo/10; + lo=lo%10; + #endif + up++; + // collect remaining Units, if any, into hi + for (d=DECDPUN; ddigits; up++, d+=DECDPUN) hi+=*up*powers[d-1]; + + // now low has the lsd, hi the remainder + if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible + else return X10(hi)+lo; + } // integer + decContextSetStatus(set, DEC_Invalid_operation); // [may not return] + return 0; + } // decNumberToUInt32 + +/* ------------------------------------------------------------------ */ +/* to-scientific-string -- conversion to numeric string */ +/* to-engineering-string -- conversion to numeric string */ +/* */ +/* decNumberToString(dn, string); */ +/* decNumberToEngString(dn, string); */ +/* */ +/* dn is the decNumber to convert */ +/* string is the string where the result will be laid out */ +/* */ +/* string must be at least dn->digits+14 characters long */ +/* */ +/* No error is possible, and no status can be set. */ +/* ------------------------------------------------------------------ */ +char * decNumberToString(const decNumber *dn, char *string){ + decToString(dn, string, 0); + return string; + } // DecNumberToString + +char * decNumberToEngString(const decNumber *dn, char *string){ + decToString(dn, string, 1); + return string; + } // DecNumberToEngString + +/* ------------------------------------------------------------------ */ +/* to-number -- conversion from numeric string */ +/* */ +/* decNumberFromString -- convert string to decNumber */ +/* dn -- the number structure to fill */ +/* chars[] -- the string to convert ('\0' terminated) */ +/* set -- the context used for processing any error, */ +/* determining the maximum precision available */ +/* (set.digits), determining the maximum and minimum */ +/* exponent (set.emax and set.emin), determining if */ +/* extended values are allowed, and checking the */ +/* rounding mode if overflow occurs or rounding is */ +/* needed. */ +/* */ +/* The length of the coefficient and the size of the exponent are */ +/* checked by this routine, so the correct error (Underflow or */ +/* Overflow) can be reported or rounding applied, as necessary. */ +/* */ +/* If bad syntax is detected, the result will be a quiet NaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFromString(decNumber *dn, const char chars[], + decContext *set) { + Int exponent=0; // working exponent [assume 0] + uByte bits=0; // working flags [assume +ve] + Unit *res; // where result will be built + Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary + // [+9 allows for ln() constants] + Unit *allocres=NULL; // -> allocated result, iff allocated + Int d=0; // count of digits found in decimal part + const char *dotchar=NULL; // where dot was found + const char *cfirst=chars; // -> first character of decimal part + const char *last=NULL; // -> last digit of decimal part + const char *c; // work + Unit *up; // .. + #if DECDPUN>1 + Int cut, out; // .. + #endif + Int residue; // rounding residue + uInt status=0; // error code + + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set)) + return decNumberZero(dn); + #endif + + do { // status & malloc protection + for (c=chars;; c++) { // -> input character + if (*c>='0' && *c<='9') { // test for Arabic digit + last=c; + d++; // count of real digits + continue; // still in decimal part + } + if (*c=='.' && dotchar==NULL) { // first '.' + dotchar=c; // record offset into decimal part + if (c==cfirst) cfirst++; // first digit must follow + continue;} + if (c==chars) { // first in string... + if (*c=='-') { // valid - sign + cfirst++; + bits=DECNEG; + continue;} + if (*c=='+') { // valid + sign + cfirst++; + continue;} + } + // *c is not a digit, or a valid +, -, or '.' + break; + } // c + + if (last==NULL) { // no digits yet + status=DEC_Conversion_syntax;// assume the worst + if (*c=='\0') break; // and no more to come... + #if DECSUBSET + // if subset then infinities and NaNs are not allowed + if (!set->extended) break; // hopeless + #endif + // Infinities and NaNs are possible, here + if (dotchar!=NULL) break; // .. unless had a dot + decNumberZero(dn); // be optimistic + if (decBiStr(c, "infinity", "INFINITY") + || decBiStr(c, "inf", "INF")) { + dn->bits=bits | DECINF; + status=0; // is OK + break; // all done + } + // a NaN expected + // 2003.09.10 NaNs are now permitted to have a sign + dn->bits=bits | DECNAN; // assume simple NaN + if (*c=='s' || *c=='S') { // looks like an sNaN + c++; + dn->bits=bits | DECSNAN; + } + if (*c!='n' && *c!='N') break; // check caseless "NaN" + c++; + if (*c!='a' && *c!='A') break; // .. + c++; + if (*c!='n' && *c!='N') break; // .. + c++; + // now either nothing, or nnnn payload, expected + // -> start of integer and skip leading 0s [including plain 0] + for (cfirst=c; *cfirst=='0';) cfirst++; + if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s + status=0; // it's good + break; // .. + } + // something other than 0s; setup last and d as usual [no dots] + for (c=cfirst;; c++, d++) { + if (*c<'0' || *c>'9') break; // test for Arabic digit + last=c; + } + if (*c!='\0') break; // not all digits + if (d>set->digits-1) { + // [NB: payload in a decNumber can be full length unless + // clamped, in which case can only be digits-1] + if (set->clamp) break; + if (d>set->digits) break; + } // too many digits? + // good; drop through to convert the integer to coefficient + status=0; // syntax is OK + bits=dn->bits; // for copy-back + } // last==NULL + + else if (*c!='\0') { // more to process... + // had some digits; exponent is only valid sequence now + Flag nege; // 1=negative exponent + const char *firstexp; // -> first significant exponent digit + status=DEC_Conversion_syntax;// assume the worst + if (*c!='e' && *c!='E') break; + /* Found 'e' or 'E' -- now process explicit exponent */ + // 1998.07.11: sign no longer required + nege=0; + c++; // to (possible) sign + if (*c=='-') {nege=1; c++;} + else if (*c=='+') c++; + if (*c=='\0') break; + + for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros + firstexp=c; // save exponent digit place + for (; ;c++) { + if (*c<'0' || *c>'9') break; // not a digit + exponent=X10(exponent)+(Int)*c-(Int)'0'; + } // c + // if not now on a '\0', *c must not be a digit + if (*c!='\0') break; + + // (this next test must be after the syntax checks) + // if it was too long the exponent may have wrapped, so check + // carefully and set it to a certain overflow if wrap possible + if (c>=firstexp+9+1) { + if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2; + // [up to 1999999999 is OK, for example 1E-1000000998] + } + if (nege) exponent=-exponent; // was negative + status=0; // is OK + } // stuff after digits + + // Here when whole string has been inspected; syntax is good + // cfirst->first digit (never dot), last->last digit (ditto) + + // strip leading zeros/dot [leave final 0 if all 0's] + if (*cfirst=='0') { // [cfirst has stepped over .] + for (c=cfirst; cextended) { + decNumberZero(dn); // clean result + break; // [could be return] + } + #endif + } // at least one leading 0 + + // Handle decimal point... + if (dotchar!=NULL && dotchardigits) res=dn->lsu; // fits into supplied decNumber + else { // rounding needed + Int needbytes=D2U(d)*sizeof(Unit);// bytes needed + res=resbuff; // assume use local buffer + if (needbytes>(Int)sizeof(resbuff)) { // too big for local + allocres=(Unit *)malloc(needbytes); + if (allocres==NULL) {status|=DEC_Insufficient_storage; break;} + res=allocres; + } + } + // res now -> number lsu, buffer, or allocated storage for Unit array + + // Place the coefficient into the selected Unit array + // [this is often 70% of the cost of this function when DECDPUN>1] + #if DECDPUN>1 + out=0; // accumulator + up=res+D2U(d)-1; // -> msu + cut=d-(up-res)*DECDPUN; // digits in top unit + for (c=cfirst;; c++) { // along the digits + if (*c=='.') continue; // ignore '.' [don't decrement cut] + out=X10(out)+(Int)*c-(Int)'0'; + if (c==last) break; // done [never get to trailing '.'] + cut--; + if (cut>0) continue; // more for this unit + *up=(Unit)out; // write unit + up--; // prepare for unit below.. + cut=DECDPUN; // .. + out=0; // .. + } // c + *up=(Unit)out; // write lsu + + #else + // DECDPUN==1 + up=res; // -> lsu + for (c=last; c>=cfirst; c--) { // over each character, from least + if (*c=='.') continue; // ignore . [don't step up] + *up=(Unit)((Int)*c-(Int)'0'); + up++; + } // c + #endif + + dn->bits=bits; + dn->exponent=exponent; + dn->digits=d; + + // if not in number (too long) shorten into the number + if (d>set->digits) { + residue=0; + decSetCoeff(dn, set, res, d, &residue, &status); + // always check for overflow or subnormal and round as needed + decFinalize(dn, set, &residue, &status); + } + else { // no rounding, but may still have overflow or subnormal + // [these tests are just for performance; finalize repeats them] + if ((dn->exponent-1emin-dn->digits) + || (dn->exponent-1>set->emax-set->digits)) { + residue=0; + decFinalize(dn, set, &residue, &status); + } + } + // decNumberShow(dn); + } while(0); // [for break] + + if (allocres!=NULL) free(allocres); // drop any storage used + if (status!=0) decStatus(dn, status, set); + return dn; + } /* decNumberFromString */ + +/* ================================================================== */ +/* Operators */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberAbs -- absolute value operator */ +/* */ +/* This computes C = abs(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopyAbs for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This has the same effect as decNumberPlus unless A is negative, */ +/* in which case it has the same effect as decNumberMinus. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAbs(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; // for 0 + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); // set 0 + dzero.exponent=rhs->exponent; // [no coefficient expansion] + decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberAbs + +/* ------------------------------------------------------------------ */ +/* decNumberAdd -- add two Numbers */ +/* */ +/* This computes C = A + B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This just calls the routine shared with Subtract */ +decNumber * decNumberAdd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decAddOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberAdd + +/* ------------------------------------------------------------------ */ +/* decNumberAnd -- AND two Numbers, digitwise */ +/* */ +/* This computes C = A & B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X&X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberAnd(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; // -> operands + const Unit *msua, *msub; // -> operand msus + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + + // operands are valid + ua=lhs->lsu; // bottom-up + ub=rhs->lsu; // .. + uc=res->lsu; // .. + msua=ua+D2U(lhs->digits)-1; // -> msu of lhs + msub=ub+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop + Unit a, b; // extract units + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; // can now write back + if (a|b) { // maybe 1 bits to examine + Int i, j; + *uc=0; // can now write back + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // both OK + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberAnd + +/* ------------------------------------------------------------------ */ +/* decNumberCompare -- compare two Numbers */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompare(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPARE, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompare + +/* ------------------------------------------------------------------ */ +/* decNumberCompareSignal -- compare, signalling on all NaNs */ +/* */ +/* This computes C = A ? B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit (or NaN). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPSIG, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompareSignal + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotal -- compare two Numbers, using total ordering */ +/* */ +/* This computes C = A ? B, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompareTotal + +/* ------------------------------------------------------------------ */ +/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */ +/* */ +/* This computes C = |A| ? |B|, under total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for one digit; the result will always be one of */ +/* -1, 0, or 1. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + uInt needbytes; // for space calculations + decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0 + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber bufb[D2N(DECBUFFER+1)]; + decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated + decNumber *a, *b; // temporary pointers + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + // if either is negative, take a copy and absolute + if (decNumberIsNegative(lhs)) { // lhs<0 + a=bufa; + needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + decNumberCopy(a, lhs); // copy content + a->bits&=~DECNEG; // .. and clear the sign + lhs=a; // use copy from here on + } + if (decNumberIsNegative(rhs)) { // rhs<0 + b=bufb; + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { // need malloc space + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; // use the allocated space + } + decNumberCopy(b, rhs); // copy content + b->bits&=~DECNEG; // .. and clear the sign + rhs=b; // use copy from here on + } + decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status); + } while(0); // end protected + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (allocbufb!=NULL) free(allocbufb); // .. + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberCompareTotalMag + +/* ------------------------------------------------------------------ */ +/* decNumberDivide -- divide one number by another */ +/* */ +/* This computes C = A / B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivide(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, DIVIDE, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberDivide + +/* ------------------------------------------------------------------ */ +/* decNumberDivideInteger -- divide and return integer quotient */ +/* */ +/* This computes C = A # B, where # is the integer divide operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X#X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberDivideInteger + +/* ------------------------------------------------------------------ */ +/* decNumberExp -- exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decExpOp which can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-a) where a can be the tiniest number (Ntiny). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberExp(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; // accumulator + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // Check restrictions; these restrictions ensure that if h=8 (see + // decExpOp) then the result will either overflow or underflow to 0. + // Other math functions restrict the input range, too, for inverses. + // If not violated then carry out the operation. + if (!decCheckMath(rhs, set, &status)) do { // protect allocation + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + decExpOp(res, rhs, set, &status); + } while(0); // end protected + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // drop any storage used + #endif + // apply significant status + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberExp + +/* ------------------------------------------------------------------ */ +/* decNumberFMA -- fused multiply add */ +/* */ +/* This computes D = (A * B) + C with only one rounding */ +/* */ +/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */ +/* lhs is A */ +/* rhs is B */ +/* fhs is C [far hand side] */ +/* set is the context */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberFMA(decNumber *res, const decNumber *lhs, + const decNumber *rhs, const decNumber *fhs, + decContext *set) { + uInt status=0; // accumulator + decContext dcmul; // context for the multiplication + uInt needbytes; // for space calculations + decNumber bufa[D2N(DECBUFFER*2+1)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *acc; // accumulator pointer + decNumber dzero; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + if (decCheckOperands(res, fhs, DECUNUSED, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { // [undefined if subset] + status|=DEC_Invalid_operation; + break;} + #endif + // Check math restrictions [these ensure no overflow or underflow] + if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status)) + || (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status)) + || (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break; + // set up context for multiply + dcmul=*set; + dcmul.digits=lhs->digits+rhs->digits; // just enough + // [The above may be an over-estimate for subset arithmetic, but that's OK] + dcmul.emax=DEC_MAX_EMAX; // effectively unbounded .. + dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions] + // set up decNumber space to receive the result of the multiply + acc=bufa; // may fit + needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + acc=allocbufa; // use the allocated space + } + // multiply with extended range and necessary precision + //printf("emin=%ld\n", dcmul.emin); + decMultiplyOp(acc, lhs, rhs, &dcmul, &status); + // Only Invalid operation (from sNaN or Inf * 0) is possible in + // status; if either is seen than ignore fhs (in case it is + // another sNaN) and set acc to NaN unless we had an sNaN + // [decMultiplyOp leaves that to caller] + // Note sNaN has to go through addOp to shorten payload if + // necessary + if ((status&DEC_Invalid_operation)!=0) { + if (!(status&DEC_sNaN)) { // but be true invalid + decNumberZero(res); // acc not yet set + res->bits=DECNAN; + break; + } + decNumberZero(&dzero); // make 0 (any non-NaN would do) + fhs=&dzero; // use that + } + #if DECCHECK + else { // multiply was OK + if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status); + } + #endif + // add the third operand and result -> res, and all is done + decAddOp(res, acc, fhs, set, 0, &status); + } while(0); // end protected + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberFMA + +/* ------------------------------------------------------------------ */ +/* decNumberInvert -- invert a Number, digitwise */ +/* */ +/* This computes C = ~A */ +/* */ +/* res is C, the result. C may be A (e.g., X=~X) */ +/* rhs is A */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberInvert(decNumber *res, const decNumber *rhs, + decContext *set) { + const Unit *ua, *msua; // -> operand and its msu + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + // operand is valid + ua=rhs->lsu; // bottom-up + uc=res->lsu; // .. + msua=ua+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, uc++) { // Unit loop + Unit a; // extract unit + Int i, j; // work + if (ua>msua) a=0; + else a=*ua; + *uc=0; // can now write back + // always need to examine all bits in rhs + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberInvert + +/* ------------------------------------------------------------------ */ +/* decNumberLn -- natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This is a wrapper for decLnOp which can handle the slightly wider */ +/* (+11) range needed by Ln, Log10, etc. (which may have to be able */ +/* to calculate at p+e+2). */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLn(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; // accumulator + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // Check restrictions; this is a math function; if not violated + // then carry out the operation. + if (!decCheckMath(rhs, set, &status)) do { // protect allocation + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + // special check in subset for rhs=0 + if (ISZERO(rhs)) { // +/- zeros -> error + status|=DEC_Invalid_operation; + break;} + } // extended=0 + #endif + decLnOp(res, rhs, set, &status); + } while(0); // end protected + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // drop any storage used + #endif + // apply significant status + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberLn + +/* ------------------------------------------------------------------ */ +/* decNumberLogB - get adjusted exponent, by 754 rules */ +/* */ +/* This computes C = adjustedexponent(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context, used only for digits and status */ +/* */ +/* For an unrounded result, digits may need to be 10 (A might have */ +/* 10**9 digits and an exponent of +999999999, or one digit and an */ +/* exponent of -1999999999). */ +/* */ +/* This returns the adjusted exponent of A after (in theory) padding */ +/* with zeros on the right to set->digits digits while keeping the */ +/* same value. The exponent is not limited by emin/emax. */ +/* */ +/* Notable cases: */ +/* A<0 -> Use |A| */ +/* A=0 -> -Infinity (Division by zero) */ +/* A=Infinite -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* NaNs are propagated as usual */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLogB(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // NaNs as usual; Infinities return +Infinity; 0->oops + if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status); + else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs); + else if (decNumberIsZero(rhs)) { + decNumberZero(res); // prepare for Infinity + res->bits=DECNEG|DECINF; // -Infinity + status|=DEC_Division_by_zero; // as per 754 + } + else { // finite non-zero + Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent + if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out + else { + decNumber buft[D2N(10)]; // temporary number + decNumber *t=buft; // .. + decNumberFromInt32(t, ae); // lay it out + decNumberPlus(res, t, set); // round as necessary + } + } + + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberLogB + +/* ------------------------------------------------------------------ */ +/* decNumberLog10 -- logarithm in base 10 */ +/* */ +/* This computes C = log10(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=10**n (if n is an integer) -> n (Exact) */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* This calculates ln(A)/ln(10) using appropriate precision. For */ +/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */ +/* requested digits and t is the number of digits in the exponent */ +/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */ +/* fastpath in decLnOp. The final division is done to the requested */ +/* precision. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberLog10(decNumber *res, const decNumber *rhs, + decContext *set) { + uInt status=0, ignore=0; // status accumulators + uInt needbytes; // for space calculations + Int p; // working precision + Int t; // digits in exponent of A + + // buffers for a and b working decimals + // (adjustment calculator, same size) + decNumber bufa[D2N(DECBUFFER+2)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *a=bufa; // temporary a + decNumber bufb[D2N(DECBUFFER+2)]; + decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated + decNumber *b=bufb; // temporary b + decNumber bufw[D2N(10)]; // working 2-10 digit number + decNumber *w=bufw; // .. + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + + decContext aset; // working context + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // Check restrictions; this is a math function; if not violated + // then carry out the operation. + if (!decCheckMath(rhs, set, &status)) do { // protect malloc + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + // special check in subset for rhs=0 + if (ISZERO(rhs)) { // +/- zeros -> error + status|=DEC_Invalid_operation; + break;} + } // extended=0 + #endif + + decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context + + // handle exact powers of 10; only check if +ve finite + if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) { + Int residue=0; // (no residue) + uInt copystat=0; // clean status + + // round to a single digit... + aset.digits=1; + decCopyFit(w, rhs, &aset, &residue, ©stat); // copy & shorten + // if exact and the digit is 1, rhs is a power of 10 + if (!(copystat&DEC_Inexact) && w->lsu[0]==1) { + // the exponent, conveniently, is the power of 10; making + // this the result needs a little care as it might not fit, + // so first convert it into the working number, and then move + // to res + decNumberFromInt32(w, w->exponent); + residue=0; + decCopyFit(res, w, set, &residue, &status); // copy & round + decFinish(res, set, &residue, &status); // cleanup/set flags + break; + } // not a power of 10 + } // not a candidate for exact + + // simplify the information-content calculation to use 'total + // number of digits in a, including exponent' as compared to the + // requested digits, as increasing this will only rarely cost an + // iteration in ln(a) anyway + t=6; // it can never be >6 + + // allocate space when needed... + p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + aset.digits=p; // as calculated + aset.emax=DEC_MAX_MATH; // usual bounds + aset.emin=-DEC_MAX_MATH; // .. + aset.clamp=0; // and no concrete format + decLnOp(a, rhs, &aset, &status); // a=ln(rhs) + + // skip the division if the result so far is infinite, NaN, or + // zero, or there was an error; note NaN from sNaN needs copy + if (status&DEC_NaNs && !(status&DEC_sNaN)) break; + if (a->bits&DECSPECIAL || ISZERO(a)) { + decNumberCopy(res, a); // [will fit] + break;} + + // for ln(10) an extra 3 digits of precision are needed + p=set->digits+3; + needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { // need malloc space + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + b=allocbufb; // use the allocated space + } + decNumberZero(w); // set up 10... + #if DECDPUN==1 + w->lsu[1]=1; w->lsu[0]=0; // .. + #else + w->lsu[0]=10; // .. + #endif + w->digits=2; // .. + + aset.digits=p; + decLnOp(b, w, &aset, &ignore); // b=ln(10) + + aset.digits=set->digits; // for final divide + decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result + } while(0); // [for break] + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (allocbufb!=NULL) free(allocbufb); // .. + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // .. + #endif + // apply significant status + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberLog10 + +/* ------------------------------------------------------------------ */ +/* decNumberMax -- compare two Numbers and return the maximum */ +/* */ +/* This computes C = A ? B, returning the maximum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMax(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMAX, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMax + +/* ------------------------------------------------------------------ */ +/* decNumberMaxMag -- compare and return the maximum by magnitude */ +/* */ +/* This computes C = A ? B, returning the maximum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMaxMag + +/* ------------------------------------------------------------------ */ +/* decNumberMin -- compare two Numbers and return the minimum */ +/* */ +/* This computes C = A ? B, returning the minimum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMin(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMIN, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMin + +/* ------------------------------------------------------------------ */ +/* decNumberMinMag -- compare and return the minimum by magnitude */ +/* */ +/* This computes C = A ? B, returning the minimum by 754 rules */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMinMag + +/* ------------------------------------------------------------------ */ +/* decNumberMinus -- prefix minus operator */ +/* */ +/* This computes C = 0 - A */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopyNegate for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* Simply use AddOp for the subtract, which will do the necessary. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMinus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); // make 0 + dzero.exponent=rhs->exponent; // [no coefficient expansion] + decAddOp(res, &dzero, rhs, set, DECNEG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMinus + +/* ------------------------------------------------------------------ */ +/* decNumberNextMinus -- next towards -Infinity */ +/* */ +/* This computes C = A - infinitesimal, rounded towards -Infinity */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* This is a generalization of 754 NextDown. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dtiny; // constant + decContext workset=*set; // work + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // +Infinity is the special case + if ((rhs->bits&(DECINF|DECNEG))==DECINF) { + decSetMaxValue(res, set); // is +ve + // there is no status to set + return res; + } + decNumberZero(&dtiny); // start with 0 + dtiny.lsu[0]=1; // make number that is .. + dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest + workset.round=DEC_ROUND_FLOOR; + decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status); + status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberNextMinus + +/* ------------------------------------------------------------------ */ +/* decNumberNextPlus -- next towards +Infinity */ +/* */ +/* This computes C = A + infinitesimal, rounded towards +Infinity */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* This is a generalization of 754 NextUp. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dtiny; // constant + decContext workset=*set; // work + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // -Infinity is the special case + if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) { + decSetMaxValue(res, set); + res->bits=DECNEG; // negative + // there is no status to set + return res; + } + decNumberZero(&dtiny); // start with 0 + dtiny.lsu[0]=1; // make number that is .. + dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest + workset.round=DEC_ROUND_CEILING; + decAddOp(res, rhs, &dtiny, &workset, 0, &status); + status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberNextPlus + +/* ------------------------------------------------------------------ */ +/* decNumberNextToward -- next towards rhs */ +/* */ +/* This computes C = A +/- infinitesimal, rounded towards */ +/* +/-Infinity in the direction of B, as per 754-1985 nextafter */ +/* modified during revision but dropped from 754-2008. */ +/* */ +/* res is C, the result. C may be A or B. */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* This is a generalization of 754-1985 NextAfter. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + decNumber dtiny; // constant + decContext workset=*set; // work + Int result; // .. + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { + decNaNs(res, lhs, rhs, set, &status); + } + else { // Is numeric, so no chance of sNaN Invalid, etc. + result=decCompare(lhs, rhs, 0); // sign matters + if (result==BADINT) status|=DEC_Insufficient_storage; // rare + else { // valid compare + if (result==0) decNumberCopySign(res, lhs, rhs); // easy + else { // differ: need NextPlus or NextMinus + uByte sub; // add or subtract + if (result<0) { // lhsbits&(DECINF|DECNEG))==(DECINF|DECNEG)) { + decSetMaxValue(res, set); + res->bits=DECNEG; // negative + return res; // there is no status to set + } + workset.round=DEC_ROUND_CEILING; + sub=0; // add, please + } // plus + else { // lhs>rhs, do nextminus + // +Infinity is the special case + if ((lhs->bits&(DECINF|DECNEG))==DECINF) { + decSetMaxValue(res, set); + return res; // there is no status to set + } + workset.round=DEC_ROUND_FLOOR; + sub=DECNEG; // subtract, please + } // minus + decNumberZero(&dtiny); // start with 0 + dtiny.lsu[0]=1; // make number that is .. + dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest + decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or - + // turn off exceptions if the result is a normal number + // (including Nmin), otherwise let all status through + if (decNumberIsNormal(res, set)) status=0; + } // unequal + } // compare OK + } // numeric + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberNextToward + +/* ------------------------------------------------------------------ */ +/* decNumberOr -- OR two Numbers, digitwise */ +/* */ +/* This computes C = A | B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X|X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberOr(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; // -> operands + const Unit *msua, *msub; // -> operand msus + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + // operands are valid + ua=lhs->lsu; // bottom-up + ub=rhs->lsu; // .. + uc=res->lsu; // .. + msua=ua+D2U(lhs->digits)-1; // -> msu of lhs + msub=ub+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop + Unit a, b; // extract units + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; // can now write back + if (a|b) { // maybe 1 bits to examine + Int i, j; + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // non-zero + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberOr + +/* ------------------------------------------------------------------ */ +/* decNumberPlus -- prefix plus operator */ +/* */ +/* This computes C = 0 + A */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* See also decNumberCopy for a quiet bitwise version of this. */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This simply uses AddOp; Add will take fast path after preparing A. */ +/* Performance is a concern here, as this routine is often used to */ +/* check operands and apply rounding and overflow/underflow testing. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberPlus(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dzero; + uInt status=0; // accumulator + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + decNumberZero(&dzero); // make 0 + dzero.exponent=rhs->exponent; // [no coefficient expansion] + decAddOp(res, &dzero, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberPlus + +/* ------------------------------------------------------------------ */ +/* decNumberMultiply -- multiply two Numbers */ +/* */ +/* This computes C = A x B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decMultiplyOp(res, lhs, rhs, set, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberMultiply + +/* ------------------------------------------------------------------ */ +/* decNumberPower -- raise a number to a power */ +/* */ +/* This computes C = A ** B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X**X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Mathematical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* */ +/* However, if 1999999997<=B<=999999999 and B is an integer then the */ +/* restrictions on A and the context are relaxed to the usual bounds, */ +/* for compatibility with the earlier (integer power only) version */ +/* of this function. */ +/* */ +/* When B is an integer, the result may be exact, even if rounded. */ +/* */ +/* The final result is rounded according to the context; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberPower(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + decNumber *allocdac=NULL; // -> allocated acc buffer, iff used + decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used + Int reqdigits=set->digits; // requested DIGITS + Int n; // rhs in binary + Flag rhsint=0; // 1 if rhs is an integer + Flag useint=0; // 1 if can use integer calculation + Flag isoddint=0; // 1 if rhs is an integer and odd + Int i; // work + #if DECSUBSET + Int dropped; // .. + #endif + uInt needbytes; // buffer size needed + Flag seenbit; // seen a bit while powering + Int residue=0; // rounding residue + uInt status=0; // accumulators + uByte bits=0; // result sign if errors + decContext aset; // working context + decNumber dnOne; // work value 1... + // local accumulator buffer [a decNumber, with digits+elength+1 digits] + decNumber dacbuff[D2N(DECBUFFER+9)]; + decNumber *dac=dacbuff; // -> result accumulator + // same again for possible 1/lhs calculation + decNumber invbuff[D2N(DECBUFFER+9)]; + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { // reduce operands and set status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, &status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // handle NaNs and rhs Infinity (lhs infinity is harder) + if (SPECIALARGS) { + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs + decNaNs(res, lhs, rhs, set, &status); + break;} + if (decNumberIsInfinite(rhs)) { // rhs Infinity + Flag rhsneg=rhs->bits&DECNEG; // save rhs sign + if (decNumberIsNegative(lhs) // lhs<0 + && !decNumberIsZero(lhs)) // .. + status|=DEC_Invalid_operation; + else { // lhs >=0 + decNumberZero(&dnOne); // set up 1 + dnOne.lsu[0]=1; + decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1 + decNumberZero(res); // prepare for 0/1/Infinity + if (decNumberIsNegative(dac)) { // lhs<1 + if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0] + } + else if (dac->lsu[0]==0) { // lhs=1 + // 1**Infinity is inexact, so return fully-padded 1.0000 + Int shift=set->digits-1; + *res->lsu=1; // was 0, make int 1 + res->digits=decShiftToMost(res->lsu, 1, shift); + res->exponent=-shift; // make 1.0000... + status|=DEC_Inexact|DEC_Rounded; // deemed inexact + } + else { // lhs>1 + if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0] + } + } // lhs>=0 + break;} + // [lhs infinity drops through] + } // specials + + // Original rhs may be an integer that fits and is in range + n=decGetInt(rhs); + if (n!=BADINT) { // it is an integer + rhsint=1; // record the fact for 1**n + isoddint=(Flag)n&1; // [works even if big] + if (n!=BIGEVEN && n!=BIGODD) // can use integer path? + useint=1; // looks good + } + + if (decNumberIsNegative(lhs) // -x .. + && isoddint) bits=DECNEG; // .. to an odd power + + // handle LHS infinity + if (decNumberIsInfinite(lhs)) { // [NaNs already handled] + uByte rbits=rhs->bits; // save + decNumberZero(res); // prepare + if (n==0) *res->lsu=1; // [-]Inf**0 => 1 + else { + // -Inf**nonint -> error + if (!rhsint && decNumberIsNegative(lhs)) { + status|=DEC_Invalid_operation; // -Inf**nonint is error + break;} + if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n + // [otherwise will be 0 or -0] + res->bits=bits; + } + break;} + + // similarly handle LHS zero + if (decNumberIsZero(lhs)) { + if (n==0) { // 0**0 => Error + #if DECSUBSET + if (!set->extended) { // [unless subset] + decNumberZero(res); + *res->lsu=1; // return 1 + break;} + #endif + status|=DEC_Invalid_operation; + } + else { // 0**x + uByte rbits=rhs->bits; // save + if (rbits & DECNEG) { // was a 0**(-n) + #if DECSUBSET + if (!set->extended) { // [bad if subset] + status|=DEC_Invalid_operation; + break;} + #endif + bits|=DECINF; + } + decNumberZero(res); // prepare + // [otherwise will be 0 or -0] + res->bits=bits; + } + break;} + + // here both lhs and rhs are finite; rhs==0 is handled in the + // integer path. Next handle the non-integer cases + if (!useint) { // non-integral rhs + // any -ve lhs is bad, as is either operand or context out of + // bounds + if (decNumberIsNegative(lhs)) { + status|=DEC_Invalid_operation; + break;} + if (decCheckMath(lhs, set, &status) + || decCheckMath(rhs, set, &status)) break; // variable status + + decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context + aset.emax=DEC_MAX_MATH; // usual bounds + aset.emin=-DEC_MAX_MATH; // .. + aset.clamp=0; // and no concrete format + + // calculate the result using exp(ln(lhs)*rhs), which can + // all be done into the accumulator, dac. The precision needed + // is enough to contain the full information in the lhs (which + // is the total digits, including exponent), or the requested + // precision, if larger, + 4; 6 is used for the exponent + // maximum length, and this is also used when it is shorter + // than the requested digits as it greatly reduces the >0.5 ulp + // cases at little cost (because Ln doubles digits each + // iteration so a few extra digits rarely causes an extra + // iteration) + aset.digits=MAXI(lhs->digits, set->digits)+6+4; + } // non-integer rhs + + else { // rhs is in-range integer + if (n==0) { // x**0 = 1 + // (0**0 was handled above) + decNumberZero(res); // result=1 + *res->lsu=1; // .. + break;} + // rhs is a non-zero integer + if (n<0) n=-n; // use abs(n) + + aset=*set; // clone the context + aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced + // calculate the working DIGITS + aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2; + #if DECSUBSET + if (!set->extended) aset.digits--; // use classic precision + #endif + // it's an error if this is more than can be handled + if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;} + } // integer path + + // aset.digits is the count of digits for the accumulator needed + // if accumulator is too long for local storage, then allocate + needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit); + // [needbytes also used below if 1/lhs needed] + if (needbytes>sizeof(dacbuff)) { + allocdac=(decNumber *)malloc(needbytes); + if (allocdac==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + dac=allocdac; // use the allocated space + } + // here, aset is set up and accumulator is ready for use + + if (!useint) { // non-integral rhs + // x ** y; special-case x=1 here as it will otherwise always + // reduce to integer 1; decLnOp has a fastpath which detects + // the case of x=1 + decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs) + // [no error possible, as lhs 0 already handled] + if (ISZERO(dac)) { // x==1, 1.0, etc. + // need to return fully-padded 1.0000 etc., but rhsint->1 + *dac->lsu=1; // was 0, make int 1 + if (!rhsint) { // add padding + Int shift=set->digits-1; + dac->digits=decShiftToMost(dac->lsu, 1, shift); + dac->exponent=-shift; // make 1.0000... + status|=DEC_Inexact|DEC_Rounded; // deemed inexact + } + } + else { + decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs + decExpOp(dac, dac, &aset, &status); // dac=exp(dac) + } + // and drop through for final rounding + } // non-integer rhs + + else { // carry on with integer + decNumberZero(dac); // acc=1 + *dac->lsu=1; // .. + + // if a negative power the constant 1 is needed, and if not subset + // invert the lhs now rather than inverting the result later + if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] + decNumber *inv=invbuff; // asssume use fixed buffer + decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later] + #if DECSUBSET + if (set->extended) { // need to calculate 1/lhs + #endif + // divide lhs into 1, putting result in dac [dac=1/dac] + decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status); + // now locate or allocate space for the inverted lhs + if (needbytes>sizeof(invbuff)) { + allocinv=(decNumber *)malloc(needbytes); + if (allocinv==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + inv=allocinv; // use the allocated space + } + // [inv now points to big-enough buffer or allocated storage] + decNumberCopy(inv, dac); // copy the 1/lhs + decNumberCopy(dac, &dnOne); // restore acc=1 + lhs=inv; // .. and go forward with new lhs + #if DECSUBSET + } + #endif + } + + // Raise-to-the-power loop... + seenbit=0; // set once a 1-bit is encountered + for (i=1;;i++){ // for each bit [top bit ignored] + // abandon if had overflow or terminal underflow + if (status & (DEC_Overflow|DEC_Underflow)) { // interesting? + if (status&DEC_Overflow || ISZERO(dac)) break; + } + // [the following two lines revealed an optimizer bug in a C++ + // compiler, with symptom: 5**3 -> 25, when n=n+n was used] + n=n<<1; // move next bit to testable position + if (n<0) { // top bit is set + seenbit=1; // OK, significant bit seen + decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x + } + if (i==31) break; // that was the last bit + if (!seenbit) continue; // no need to square 1 + decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square] + } /*i*/ // 32 bits + + // complete internal overflow or underflow processing + if (status & (DEC_Overflow|DEC_Underflow)) { + #if DECSUBSET + // If subset, and power was negative, reverse the kind of -erflow + // [1/x not yet done] + if (!set->extended && decNumberIsNegative(rhs)) { + if (status & DEC_Overflow) + status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal; + else { // trickier -- Underflow may or may not be set + status&=~(DEC_Underflow | DEC_Subnormal); // [one or both] + status|=DEC_Overflow; + } + } + #endif + dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign + // round subnormals [to set.digits rather than aset.digits] + // or set overflow result similarly as required + decFinalize(dac, set, &residue, &status); + decNumberCopy(res, dac); // copy to result (is now OK length) + break; + } + + #if DECSUBSET + if (!set->extended && // subset math + decNumberIsNegative(rhs)) { // was a **-n [hence digits>0] + // so divide result into 1 [dac=1/dac] + decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status); + } + #endif + } // rhs integer path + + // reduce result to the requested length and copy to result + decCopyFit(res, dac, set, &residue, &status); + decFinish(res, set, &residue, &status); // final cleanup + #if DECSUBSET + if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros + #endif + } while(0); // end protected + + if (allocdac!=NULL) free(allocdac); // drop any storage used + if (allocinv!=NULL) free(allocinv); // .. + #if DECSUBSET + if (alloclhs!=NULL) free(alloclhs); // .. + if (allocrhs!=NULL) free(allocrhs); // .. + #endif + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberPower + +/* ------------------------------------------------------------------ */ +/* decNumberQuantize -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has exponent of B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the number with exponent to match */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to that of B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decQuantizeOp(res, lhs, rhs, set, 1, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberQuantize + +/* ------------------------------------------------------------------ */ +/* decNumberReduce -- remove trailing zeros */ +/* */ +/* This computes C = 0 + A, and normalizes the result */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +// Previously known as Normalize +decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs, + decContext *set) { + return decNumberReduce(res, rhs, set); + } // decNumberNormalize + +decNumber * decNumberReduce(decNumber *res, const decNumber *rhs, + decContext *set) { + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + uInt status=0; // as usual + Int residue=0; // as usual + Int dropped; // work + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // Infinities copy through; NaNs need usual treatment + if (decNumberIsNaN(rhs)) { + decNaNs(res, rhs, NULL, set, &status); + break; + } + + // reduce result to the requested length and copy to result + decCopyFit(res, rhs, set, &residue, &status); // copy & round + decFinish(res, set, &residue, &status); // cleanup/set flags + decTrim(res, set, 1, 0, &dropped); // normalize in place + // [may clamp] + } while(0); // end protected + + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // .. + #endif + if (status!=0) decStatus(res, status, set);// then report status + return res; + } // decNumberReduce + +/* ------------------------------------------------------------------ */ +/* decNumberRescale -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B. The numerical value of C will equal A, */ +/* except for the effects of any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be equal to B. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRescale(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decQuantizeOp(res, lhs, rhs, set, 0, &status); + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberRescale + +/* ------------------------------------------------------------------ */ +/* decNumberRemainder -- divide and return remainder */ +/* */ +/* This computes C = A % B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, REMAINDER, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberRemainder + +/* ------------------------------------------------------------------ */ +/* decNumberRemainderNear -- divide and return remainder from nearest */ +/* */ +/* This computes C = A % B, where % is the IEEE remainder operator */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X%X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + decDivideOp(res, lhs, rhs, set, REMNEAR, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberRemainderNear + +/* ------------------------------------------------------------------ */ +/* decNumberRotate -- rotate the coefficient of a Number left/right */ +/* */ +/* This computes C = A rot B (in base ten and rotating set->digits */ +/* digits). */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */ +/* lhs is A */ +/* rhs is B, the number of digits to rotate (-ve to right) */ +/* set is the context */ +/* */ +/* The digits of the coefficient of A are rotated to the left (if B */ +/* is positive) or to the right (if B is negative) without adjusting */ +/* the exponent or the sign of A. If lhs->digits is less than */ +/* set->digits the coefficient is padded with zeros on the left */ +/* before the rotate. Any leading zeros in the result are removed */ +/* as usual. */ +/* */ +/* B must be an integer (q=0) and in the range -set->digits through */ +/* +set->digits. */ +/* C must have space for set->digits digits. */ +/* NaNs are propagated as usual. Infinities are unaffected (but */ +/* B must be valid). No status is set unless B is invalid or an */ +/* operand is an sNaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberRotate(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + Int rotate; // rhs as an Int + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // NaNs propagate as normal + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + // rhs must be an integer + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { // both numeric, rhs is an integer + rotate=decGetInt(rhs); // [cannot fail] + if (rotate==BADINT // something bad .. + || rotate==BIGODD || rotate==BIGEVEN // .. very big .. + || abs(rotate)>set->digits) // .. or out of range + status=DEC_Invalid_operation; + else { // rhs is OK + decNumberCopy(res, lhs); + // convert -ve rotate to equivalent positive rotation + if (rotate<0) rotate=set->digits+rotate; + if (rotate!=0 && rotate!=set->digits // zero or full rotation + && !decNumberIsInfinite(res)) { // lhs was infinite + // left-rotate to do; 0 < rotate < set->digits + uInt units, shift; // work + uInt msudigits; // digits in result msu + Unit *msu=res->lsu+D2U(res->digits)-1; // current msu + Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu + for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0 + res->digits=set->digits; // now full-length + msudigits=MSUDIGITS(res->digits); // actual digits in msu + + // rotation here is done in-place, in three steps + // 1. shift all to least up to one unit to unit-align final + // lsd [any digits shifted out are rotated to the left, + // abutted to the original msd (which may require split)] + // + // [if there are no whole units left to rotate, the + // rotation is now complete] + // + // 2. shift to least, from below the split point only, so that + // the final msd is in the right place in its Unit [any + // digits shifted out will fit exactly in the current msu, + // left aligned, no split required] + // + // 3. rotate all the units by reversing left part, right + // part, and then whole + // + // example: rotate right 8 digits (2 units + 2), DECDPUN=3. + // + // start: 00a bcd efg hij klm npq + // + // 1a 000 0ab cde fgh|ijk lmn [pq saved] + // 1b 00p qab cde fgh|ijk lmn + // + // 2a 00p qab cde fgh|00i jkl [mn saved] + // 2b mnp qab cde fgh|00i jkl + // + // 3a fgh cde qab mnp|00i jkl + // 3b fgh cde qab mnp|jkl 00i + // 3c 00i jkl mnp qab cde fgh + + // Step 1: amount to shift is the partial right-rotate count + rotate=set->digits-rotate; // make it right-rotate + units=rotate/DECDPUN; // whole units to rotate + shift=rotate%DECDPUN; // left-over digits count + if (shift>0) { // not an exact number of units + uInt save=res->lsu[0]%powers[shift]; // save low digit(s) + decShiftToLeast(res->lsu, D2U(res->digits), shift); + if (shift>msudigits) { // msumax-1 needs >0 digits + uInt rem=save%powers[shift-msudigits];// split save + *msumax=(Unit)(save/powers[shift-msudigits]); // and insert + *(msumax-1)=*(msumax-1) + +(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // .. + } + else { // all fits in msumax + *msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1] + } + } // digits shift needed + + // If whole units to rotate... + if (units>0) { // some to do + // Step 2: the units to touch are the whole ones in rotate, + // if any, and the shift is DECDPUN-msudigits (which may be + // 0, again) + shift=DECDPUN-msudigits; + if (shift>0) { // not an exact number of units + uInt save=res->lsu[0]%powers[shift]; // save low digit(s) + decShiftToLeast(res->lsu, units, shift); + *msumax=*msumax+(Unit)(save*powers[msudigits]); + } // partial shift needed + + // Step 3: rotate the units array using triple reverse + // (reversing is easy and fast) + decReverse(res->lsu+units, msumax); // left part + decReverse(res->lsu, res->lsu+units-1); // right part + decReverse(res->lsu, msumax); // whole + } // whole units to rotate + // the rotation may have left an undetermined number of zeros + // on the left, so true length needs to be calculated + res->digits=decGetDigits(res->lsu, msumax-res->lsu+1); + } // rotate needed + } // rhs OK + } // numerics + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberRotate + +/* ------------------------------------------------------------------ */ +/* decNumberSameQuantum -- test for equal exponents */ +/* */ +/* res is the result number, which will contain either 0 or 1 */ +/* lhs is a number to test */ +/* rhs is the second (usually a pattern) */ +/* */ +/* No errors are possible and no context is needed. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + Unit ret=0; // return value + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res; + #endif + + if (SPECIALARGS) { + if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1; + else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1; + // [anything else with a special gives 0] + } + else if (lhs->exponent==rhs->exponent) ret=1; + + decNumberZero(res); // OK to overwrite an operand now + *res->lsu=ret; + return res; + } // decNumberSameQuantum + +/* ------------------------------------------------------------------ */ +/* decNumberScaleB -- multiply by a power of 10 */ +/* */ +/* This computes C = A x 10**B where B is an integer (q=0) with */ +/* maximum magnitude 2*(emax+digits) */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested power of ten to use */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* The result may underflow or overflow. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + Int reqexp; // requested exponent change [B] + uInt status=0; // accumulator + Int residue; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // Handle special values except lhs infinite + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + // rhs must be an integer + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { + // lhs is a number; rhs is a finite with q==0 + reqexp=decGetInt(rhs); // [cannot fail] + // maximum range is larger than getInt can handle, so this is + // more restrictive than the specification + if (reqexp==BADINT // something bad .. + || reqexp==BIGODD || reqexp==BIGEVEN // it was huge + || (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range + status=DEC_Invalid_operation; + else { // rhs is OK + decNumberCopy(res, lhs); // all done if infinite lhs + if (!decNumberIsInfinite(res)) { // prepare to scale + Int exp=res->exponent; // save for overflow test + res->exponent+=reqexp; // adjust the exponent + if (((exp^reqexp)>=0) // same sign ... + && ((exp^res->exponent)<0)) { // .. but result had different + // the calculation overflowed, so force right treatment + if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS; + else res->exponent=DEC_MAX_EMAX+1; + } + residue=0; + decFinalize(res, set, &residue, &status); // final check + } // finite LHS + } // rhs OK + } // rhs finite + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberScaleB + +/* ------------------------------------------------------------------ */ +/* decNumberShift -- shift the coefficient of a Number left or right */ +/* */ +/* This computes C = A << B or C = A >> -B (in base ten). */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X<digits through */ +/* +set->digits. */ +/* C must have space for set->digits digits. */ +/* NaNs are propagated as usual. Infinities are unaffected (but */ +/* B must be valid). No status is set unless B is invalid or an */ +/* operand is an sNaN. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberShift(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + Int shift; // rhs as an Int + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // NaNs propagate as normal + if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) + decNaNs(res, lhs, rhs, set, &status); + // rhs must be an integer + else if (decNumberIsInfinite(rhs) || rhs->exponent!=0) + status=DEC_Invalid_operation; + else { // both numeric, rhs is an integer + shift=decGetInt(rhs); // [cannot fail] + if (shift==BADINT // something bad .. + || shift==BIGODD || shift==BIGEVEN // .. very big .. + || abs(shift)>set->digits) // .. or out of range + status=DEC_Invalid_operation; + else { // rhs is OK + decNumberCopy(res, lhs); + if (shift!=0 && !decNumberIsInfinite(res)) { // something to do + if (shift>0) { // to left + if (shift==set->digits) { // removing all + *res->lsu=0; // so place 0 + res->digits=1; // .. + } + else { // + // first remove leading digits if necessary + if (res->digits+shift>set->digits) { + decDecap(res, res->digits+shift-set->digits); + // that updated res->digits; may have gone to 1 (for a + // single digit or for zero + } + if (res->digits>1 || *res->lsu) // if non-zero.. + res->digits=decShiftToMost(res->lsu, res->digits, shift); + } // partial left + } // left + else { // to right + if (-shift>=res->digits) { // discarding all + *res->lsu=0; // so place 0 + res->digits=1; // .. + } + else { + decShiftToLeast(res->lsu, D2U(res->digits), -shift); + res->digits-=(-shift); + } + } // to right + } // non-0 non-Inf shift + } // rhs OK + } // numerics + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberShift + +/* ------------------------------------------------------------------ */ +/* decNumberSquareRoot -- square root operator */ +/* */ +/* This computes C = squareroot(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +/* This uses the following varying-precision algorithm in: */ +/* */ +/* Properly Rounded Variable Precision Square Root, T. E. Hull and */ +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */ +/* pp229-237, ACM, September 1985. */ +/* */ +/* The square-root is calculated using Newton's method, after which */ +/* a check is made to ensure the result is correctly rounded. */ +/* */ +/* % [Reformatted original Numerical Turing source code follows.] */ +/* function sqrt(x : real) : real */ +/* % sqrt(x) returns the properly rounded approximation to the square */ +/* % root of x, in the precision of the calling environment, or it */ +/* % fails if x < 0. */ +/* % t e hull and a abrham, august, 1984 */ +/* if x <= 0 then */ +/* if x < 0 then */ +/* assert false */ +/* else */ +/* result 0 */ +/* end if */ +/* end if */ +/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */ +/* var e := getexp(x) % exponent part of x */ +/* var approx : real */ +/* if e mod 2 = 0 then */ +/* approx := .259 + .819 * f % approx to root of f */ +/* else */ +/* f := f/l0 % adjustments */ +/* e := e + 1 % for odd */ +/* approx := .0819 + 2.59 * f % exponent */ +/* end if */ +/* */ +/* var p:= 3 */ +/* const maxp := currentprecision + 2 */ +/* loop */ +/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */ +/* precision p */ +/* approx := .5 * (approx + f/approx) */ +/* exit when p = maxp */ +/* end loop */ +/* */ +/* % approx is now within 1 ulp of the properly rounded square root */ +/* % of f; to ensure proper rounding, compare squares of (approx - */ +/* % l/2 ulp) and (approx + l/2 ulp) with f. */ +/* p := currentprecision */ +/* begin */ +/* precision p + 2 */ +/* const approxsubhalf := approx - setexp(.5, -p) */ +/* if mulru(approxsubhalf, approxsubhalf) > f then */ +/* approx := approx - setexp(.l, -p + 1) */ +/* else */ +/* const approxaddhalf := approx + setexp(.5, -p) */ +/* if mulrd(approxaddhalf, approxaddhalf) < f then */ +/* approx := approx + setexp(.l, -p + 1) */ +/* end if */ +/* end if */ +/* end */ +/* result setexp(approx, e div 2) % fix exponent */ +/* end sqrt */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs, + decContext *set) { + decContext workset, approxset; // work contexts + decNumber dzero; // used for constant zero + Int maxp; // largest working precision + Int workp; // working precision + Int residue=0; // rounding residue + uInt status=0, ignore=0; // status accumulators + uInt rstatus; // .. + Int exp; // working exponent + Int ideal; // ideal (preferred) exponent + Int needbytes; // work + Int dropped; // .. + + #if DECSUBSET + decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated + #endif + // buffer for f [needs +1 in case DECBUFFER 0] + decNumber buff[D2N(DECBUFFER+1)]; + // buffer for a [needs +2 to match likely maxp] + decNumber bufa[D2N(DECBUFFER+2)]; + // buffer for temporary, b [must be same size as a] + decNumber bufb[D2N(DECBUFFER+2)]; + decNumber *allocbuff=NULL; // -> allocated buff, iff allocated + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated + decNumber *f=buff; // reduced fraction + decNumber *a=bufa; // approximation to result + decNumber *b=bufb; // intermediate result + // buffer for temporary variable, up to 3 digits + decNumber buft[D2N(3)]; + decNumber *t=buft; // up-to-3-digit constant or work + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operand and set lostDigits status, as needed + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, &status); + if (allocrhs==NULL) break; + // [Note: 'f' allocation below could reuse this buffer if + // used, but as this is rare they are kept separate for clarity.] + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // handle infinities and NaNs + if (SPECIALARG) { + if (decNumberIsInfinite(rhs)) { // an infinity + if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation; + else decNumberCopy(res, rhs); // +Infinity + } + else decNaNs(res, rhs, NULL, set, &status); // a NaN + break; + } + + // calculate the ideal (preferred) exponent [floor(exp/2)] + // [It would be nicer to write: ideal=rhs->exponent>>1, but this + // generates a compiler warning. Generated code is the same.] + ideal=(rhs->exponent&~1)/2; // target + + // handle zeros + if (ISZERO(rhs)) { + decNumberCopy(res, rhs); // could be 0 or -0 + res->exponent=ideal; // use the ideal [safe] + // use decFinish to clamp any out-of-range exponent, etc. + decFinish(res, set, &residue, &status); + break; + } + + // any other -x is an oops + if (decNumberIsNegative(rhs)) { + status|=DEC_Invalid_operation; + break; + } + + // space is needed for three working variables + // f -- the same precision as the RHS, reduced to 0.01->0.99... + // a -- Hull's approximation -- precision, when assigned, is + // currentprecision+1 or the input argument precision, + // whichever is larger (+2 for use as temporary) + // b -- intermediate temporary result (same size as a) + // if any is too long for local storage, then allocate + workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision + workp=MAXI(workp, 7); // at least 7 for low cases + maxp=workp+2; // largest working precision + + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>(Int)sizeof(buff)) { + allocbuff=(decNumber *)malloc(needbytes); + if (allocbuff==NULL) { // hopeless -- abandon + status|=DEC_Insufficient_storage; + break;} + f=allocbuff; // use the allocated space + } + // a and b both need to be able to hold a maxp-length number + needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit); + if (needbytes>(Int)sizeof(bufa)) { // [same applies to b] + allocbufa=(decNumber *)malloc(needbytes); + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufa==NULL || allocbufb==NULL) { // hopeless + status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated spaces + b=allocbufb; // .. + } + + // copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1 + decNumberCopy(f, rhs); + exp=f->exponent+f->digits; // adjusted to Hull rules + f->exponent=-(f->digits); // to range + + // set up working context + decContextDefault(&workset, DEC_INIT_DECIMAL64); + workset.emax=DEC_MAX_EMAX; + workset.emin=DEC_MIN_EMIN; + + // [Until further notice, no error is possible and status bits + // (Rounded, etc.) should be ignored, not accumulated.] + + // Calculate initial approximation, and allow for odd exponent + workset.digits=workp; // p for initial calculation + t->bits=0; t->digits=3; + a->bits=0; a->digits=3; + if ((exp & 1)==0) { // even exponent + // Set t=0.259, a=0.819 + t->exponent=-3; + a->exponent=-3; + #if DECDPUN>=3 + t->lsu[0]=259; + a->lsu[0]=819; + #elif DECDPUN==2 + t->lsu[0]=59; t->lsu[1]=2; + a->lsu[0]=19; a->lsu[1]=8; + #else + t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2; + a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8; + #endif + } + else { // odd exponent + // Set t=0.0819, a=2.59 + f->exponent--; // f=f/10 + exp++; // e=e+1 + t->exponent=-4; + a->exponent=-2; + #if DECDPUN>=3 + t->lsu[0]=819; + a->lsu[0]=259; + #elif DECDPUN==2 + t->lsu[0]=19; t->lsu[1]=8; + a->lsu[0]=59; a->lsu[1]=2; + #else + t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8; + a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2; + #endif + } + + decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f + decAddOp(a, a, t, &workset, 0, &ignore); // ..+t + // [a is now the initial approximation for sqrt(f), calculated with + // currentprecision, which is also a's precision.] + + // the main calculation loop + decNumberZero(&dzero); // make 0 + decNumberZero(t); // set t = 0.5 + t->lsu[0]=5; // .. + t->exponent=-1; // .. + workset.digits=3; // initial p + for (; workset.digitsexponent+=exp/2; // set correct exponent + rstatus=0; // clear status + residue=0; // .. and accumulator + decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed) + decFinish(a, &approxset, &residue, &rstatus); // clean and finalize + + // Overflow was possible if the input exponent was out-of-range, + // in which case quit + if (rstatus&DEC_Overflow) { + status=rstatus; // use the status as-is + decNumberCopy(res, a); // copy to result + break; + } + + // Preserve status except Inexact/Rounded + status|=(rstatus & ~(DEC_Rounded|DEC_Inexact)); + + // Carry out the Hull correction + a->exponent-=exp/2; // back to 0.1->1 + + // a is now at final precision and within 1 ulp of the properly + // rounded square root of f; to ensure proper rounding, compare + // squares of (a - l/2 ulp) and (a + l/2 ulp) with f. + // Here workset.digits=maxp and t=0.5, and a->digits determines + // the ulp + workset.digits--; // maxp-1 is OK now + t->exponent=-a->digits-1; // make 0.5 ulp + decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp + workset.round=DEC_ROUND_UP; + decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b) + decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed + if (decNumberIsNegative(b)) { // f < b [i.e., b > f] + // this is the more common adjustment, though both are rare + t->exponent++; // make 1.0 ulp + t->lsu[0]=1; // .. + decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp + // assign to approx [round to length] + approxset.emin-=exp/2; // adjust to match a + approxset.emax-=exp/2; + decAddOp(a, &dzero, a, &approxset, 0, &ignore); + } + else { + decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp + workset.round=DEC_ROUND_DOWN; + decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b) + decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f + if (decNumberIsNegative(b)) { // b < f + t->exponent++; // make 1.0 ulp + t->lsu[0]=1; // .. + decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp + // assign to approx [round to length] + approxset.emin-=exp/2; // adjust to match a + approxset.emax-=exp/2; + decAddOp(a, &dzero, a, &approxset, 0, &ignore); + } + } + // [no errors are possible in the above, and rounding/inexact during + // estimation are irrelevant, so status was not accumulated] + + // Here, 0.1 <= a < 1 (still), so adjust back + a->exponent+=exp/2; // set correct exponent + + // count droppable zeros [after any subnormal rounding] by + // trimming a copy + decNumberCopy(b, a); + decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros] + + // Set Inexact and Rounded. The answer can only be exact if + // it is short enough so that squaring it could fit in workp + // digits, so this is the only (relatively rare) condition that + // a careful check is needed + if (b->digits*2-1 > workp) { // cannot fit + status|=DEC_Inexact|DEC_Rounded; + } + else { // could be exact/unrounded + uInt mstatus=0; // local status + decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply + if (mstatus&DEC_Overflow) { // result just won't fit + status|=DEC_Inexact|DEC_Rounded; + } + else { // plausible + decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs + if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal + else { // is Exact + // here, dropped is the count of trailing zeros in 'a' + // use closest exponent to ideal... + Int todrop=ideal-a->exponent; // most that can be dropped + if (todrop<0) status|=DEC_Rounded; // ideally would add 0s + else { // unrounded + // there are some to drop, but emax may not allow all + Int maxexp=set->emax-set->digits+1; + Int maxdrop=maxexp-a->exponent; + if (todrop>maxdrop && set->clamp) { // apply clamping + todrop=maxdrop; + status|=DEC_Clamped; + } + if (dropped0) { // have some to drop + decShiftToLeast(a->lsu, D2U(a->digits), todrop); + a->exponent+=todrop; // maintain numerical value + a->digits-=todrop; // new length + } + } + } + } + } + + // double-check Underflow, as perhaps the result could not have + // been subnormal (initial argument too big), or it is now Exact + if (status&DEC_Underflow) { + Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent + // check if truly subnormal + #if DECEXTFLAG // DEC_Subnormal too + if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow); + #else + if (ae>=set->emin*2) status&=~DEC_Underflow; + #endif + // check if truly inexact + if (!(status&DEC_Inexact)) status&=~DEC_Underflow; + } + + decNumberCopy(res, a); // a is now the result + } while(0); // end protected + + if (allocbuff!=NULL) free(allocbuff); // drop any storage used + if (allocbufa!=NULL) free(allocbufa); // .. + if (allocbufb!=NULL) free(allocbufb); // .. + #if DECSUBSET + if (allocrhs !=NULL) free(allocrhs); // .. + #endif + if (status!=0) decStatus(res, status, set);// then report status + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberSquareRoot + +/* ------------------------------------------------------------------ */ +/* decNumberSubtract -- subtract two Numbers */ +/* */ +/* This computes C = A - B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X-X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* */ +/* C must have space for set->digits digits. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + uInt status=0; // accumulator + + decAddOp(res, lhs, rhs, set, DECNEG, &status); + if (status!=0) decStatus(res, status, set); + #if DECCHECK + decCheckInexact(res, set); + #endif + return res; + } // decNumberSubtract + +/* ------------------------------------------------------------------ */ +/* decNumberToIntegralExact -- round-to-integral-value with InExact */ +/* decNumberToIntegralValue -- round-to-integral-value */ +/* */ +/* res is the result */ +/* rhs is input number */ +/* set is the context */ +/* */ +/* res must have space for any value of rhs. */ +/* */ +/* This implements the IEEE special operators and therefore treats */ +/* special values as valid. For finite numbers it returns */ +/* rescale(rhs, 0) if rhs->exponent is <0. */ +/* Otherwise the result is rhs (so no error is possible, except for */ +/* sNaN). */ +/* */ +/* The context is used for rounding mode and status after sNaN, but */ +/* the digits setting is ignored. The Exact version will signal */ +/* Inexact if the result differs numerically from rhs; the other */ +/* never signals Inexact. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs, + decContext *set) { + decNumber dn; + decContext workset; // working context + uInt status=0; // accumulator + + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + // handle infinities and NaNs + if (SPECIALARG) { + if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity + else decNaNs(res, rhs, NULL, set, &status); // a NaN + } + else { // finite + // have a finite number; no error possible (res must be big enough) + if (rhs->exponent>=0) return decNumberCopy(res, rhs); + // that was easy, but if negative exponent there is work to do... + workset=*set; // clone rounding, etc. + workset.digits=rhs->digits; // no length rounding + workset.traps=0; // no traps + decNumberZero(&dn); // make a number with exponent 0 + decNumberQuantize(res, rhs, &dn, &workset); + status|=workset.status; + } + if (status!=0) decStatus(res, status, set); + return res; + } // decNumberToIntegralExact + +decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs, + decContext *set) { + decContext workset=*set; // working context + workset.traps=0; // no traps + decNumberToIntegralExact(res, rhs, &workset); + // this never affects set, except for sNaNs; NaN will have been set + // or propagated already, so no need to call decStatus + set->status|=workset.status&DEC_Invalid_operation; + return res; + } // decNumberToIntegralValue + +/* ------------------------------------------------------------------ */ +/* decNumberXor -- XOR two Numbers, digitwise */ +/* */ +/* This computes C = A ^ B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X^X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context (used for result length and error report) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Logical function restrictions apply (see above); a NaN is */ +/* returned with Invalid_operation if a restriction is violated. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberXor(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + const Unit *ua, *ub; // -> operands + const Unit *msua, *msub; // -> operand msus + Unit *uc, *msuc; // -> result and its msu + Int msudigs; // digits in res msu + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs) + || rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + // operands are valid + ua=lhs->lsu; // bottom-up + ub=rhs->lsu; // .. + uc=res->lsu; // .. + msua=ua+D2U(lhs->digits)-1; // -> msu of lhs + msub=ub+D2U(rhs->digits)-1; // -> msu of rhs + msuc=uc+D2U(set->digits)-1; // -> msu of result + msudigs=MSUDIGITS(set->digits); // [faster than remainder] + for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop + Unit a, b; // extract units + if (ua>msua) a=0; + else a=*ua; + if (ub>msub) b=0; + else b=*ub; + *uc=0; // can now write back + if (a|b) { // maybe 1 bits to examine + Int i, j; + // This loop could be unrolled and/or use BIN2BCD tables + for (i=0; i1) { + decStatus(res, DEC_Invalid_operation, set); + return res; + } + if (uc==msuc && i==msudigs-1) break; // just did final digit + } // each digit + } // non-zero + } // each unit + // [here uc-1 is the msu of the result] + res->digits=decGetDigits(res->lsu, uc-res->lsu); + res->exponent=0; // integer + res->bits=0; // sign=0 + return res; // [no status to set] + } // decNumberXor + + +/* ================================================================== */ +/* Utility routines */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decNumberClass -- return the decClass of a decNumber */ +/* dn -- the decNumber to test */ +/* set -- the context to use for Emin */ +/* returns the decClass enum */ +/* ------------------------------------------------------------------ */ +enum decClass decNumberClass(const decNumber *dn, decContext *set) { + if (decNumberIsSpecial(dn)) { + if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN; + if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN; + // must be an infinity + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF; + return DEC_CLASS_POS_INF; + } + // is finite + if (decNumberIsNormal(dn, set)) { // most common + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL; + return DEC_CLASS_POS_NORMAL; + } + // is subnormal or zero + if (decNumberIsZero(dn)) { // most common + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO; + return DEC_CLASS_POS_ZERO; + } + if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL; + return DEC_CLASS_POS_SUBNORMAL; + } // decNumberClass + +/* ------------------------------------------------------------------ */ +/* decNumberClassToString -- convert decClass to a string */ +/* */ +/* eclass is a valid decClass */ +/* returns a constant string describing the class (max 13+1 chars) */ +/* ------------------------------------------------------------------ */ +const char *decNumberClassToString(enum decClass eclass) { + if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN; + if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN; + if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ; + if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ; + if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS; + if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS; + if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI; + if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI; + if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN; + if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN; + return DEC_ClassString_UN; // Unknown + } // decNumberClassToString + +/* ------------------------------------------------------------------ */ +/* decNumberCopy -- copy a number */ +/* */ +/* dest is the target decNumber */ +/* src is the source decNumber */ +/* returns dest */ +/* */ +/* (dest==src is allowed and is a no-op) */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopy(decNumber *dest, const decNumber *src) { + + #if DECCHECK + if (src==NULL) return decNumberZero(dest); + #endif + + if (dest==src) return dest; // no copy required + + // Use explicit assignments here as structure assignment could copy + // more than just the lsu (for small DECDPUN). This would not affect + // the value of the results, but could disturb test harness spill + // checking. + dest->bits=src->bits; + dest->exponent=src->exponent; + dest->digits=src->digits; + dest->lsu[0]=src->lsu[0]; + if (src->digits>DECDPUN) { // more Units to come + const Unit *smsup, *s; // work + Unit *d; // .. + // memcpy for the remaining Units would be safe as they cannot + // overlap. However, this explicit loop is faster in short cases. + d=dest->lsu+1; // -> first destination + smsup=src->lsu+D2U(src->digits); // -> source msu+1 + for (s=src->lsu+1; sdigits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberAbs for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits&=~DECNEG; // turn off sign + return res; + } // decNumberCopyAbs + +/* ------------------------------------------------------------------ */ +/* decNumberCopyNegate -- quiet negate value operator */ +/* */ +/* This sets C = negate(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* See also decNumberMinus for a checking version of this. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) { + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + decNumberCopy(res, rhs); + res->bits^=DECNEG; // invert the sign + return res; + } // decNumberCopyNegate + +/* ------------------------------------------------------------------ */ +/* decNumberCopySign -- quiet copy and set sign operator */ +/* */ +/* This sets C = A with the sign of B */ +/* */ +/* res is C, the result. C may be A */ +/* lhs is A */ +/* rhs is B */ +/* */ +/* C must have space for set->digits digits. */ +/* No exception or error can occur; this is a quiet bitwise operation.*/ +/* ------------------------------------------------------------------ */ +decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs, + const decNumber *rhs) { + uByte sign; // rhs sign + #if DECCHECK + if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res; + #endif + sign=rhs->bits & DECNEG; // save sign bit + decNumberCopy(res, lhs); + res->bits&=~DECNEG; // clear the sign + res->bits|=sign; // set from rhs + return res; + } // decNumberCopySign + +/* ------------------------------------------------------------------ */ +/* decNumberGetBCD -- get the coefficient in BCD8 */ +/* dn is the source decNumber */ +/* bcd is the uInt array that will receive dn->digits BCD bytes, */ +/* most-significant at offset 0 */ +/* returns bcd */ +/* */ +/* bcd must have at least dn->digits bytes. No error is possible; if */ +/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */ +/* ------------------------------------------------------------------ */ +uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) { + uByte *ub=bcd+dn->digits-1; // -> lsd + const Unit *up=dn->lsu; // Unit pointer, -> lsu + + #if DECDPUN==1 // trivial simple copy + for (; ub>=bcd; ub--, up++) *ub=*up; + #else // chopping needed + uInt u=*up; // work + uInt cut=DECDPUN; // downcounter through unit + for (; ub>=bcd; ub--) { + *ub=(uByte)(u%10); // [*6554 trick inhibits, here] + u=u/10; + cut--; + if (cut>0) continue; // more in this unit + up++; + u=*up; + cut=DECDPUN; + } + #endif + return bcd; + } // decNumberGetBCD + +/* ------------------------------------------------------------------ */ +/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */ +/* dn is the target decNumber */ +/* bcd is the uInt array that will source n BCD bytes, most- */ +/* significant at offset 0 */ +/* n is the number of digits in the source BCD array (bcd) */ +/* returns dn */ +/* */ +/* dn must have space for at least n digits. No error is possible; */ +/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */ +/* and bcd[0] zero. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) { + Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer] + const uByte *ub=bcd; // -> source msd + + #if DECDPUN==1 // trivial simple copy + for (; ub=dn->lsu; up--) { // each Unit from msu + *up=0; // will take <=DECDPUN digits + for (; cut>0; ub++, cut--) *up=X10(*up)+*ub; + cut=DECDPUN; // next Unit has all digits + } + #endif + dn->digits=n; // set digit count + return dn; + } // decNumberSetBCD + +/* ------------------------------------------------------------------ */ +/* decNumberIsNormal -- test normality of a decNumber */ +/* dn is the decNumber to test */ +/* set is the context to use for Emin */ +/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */ +/* ------------------------------------------------------------------ */ +Int decNumberIsNormal(const decNumber *dn, decContext *set) { + Int ae; // adjusted exponent + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0; + #endif + + if (decNumberIsSpecial(dn)) return 0; // not finite + if (decNumberIsZero(dn)) return 0; // not non-zero + + ae=dn->exponent+dn->digits-1; // adjusted exponent + if (aeemin) return 0; // is subnormal + return 1; + } // decNumberIsNormal + +/* ------------------------------------------------------------------ */ +/* decNumberIsSubnormal -- test subnormality of a decNumber */ +/* dn is the decNumber to test */ +/* set is the context to use for Emin */ +/* returns 1 if |dn| is finite, non-zero, and exponent+dn->digits-1; // adjusted exponent + if (aeemin) return 1; // is subnormal + return 0; + } // decNumberIsSubnormal + +/* ------------------------------------------------------------------ */ +/* decNumberTrim -- remove insignificant zeros */ +/* */ +/* dn is the number to trim */ +/* returns dn */ +/* */ +/* All fields are updated as required. This is a utility operation, */ +/* so special values are unchanged and no error is possible. The */ +/* zeros are removed unconditionally. */ +/* ------------------------------------------------------------------ */ +decNumber * decNumberTrim(decNumber *dn) { + Int dropped; // work + decContext set; // .. + #if DECCHECK + if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn; + #endif + decContextDefault(&set, DEC_INIT_BASE); // clamp=0 + return decTrim(dn, &set, 0, 1, &dropped); + } // decNumberTrim + +/* ------------------------------------------------------------------ */ +/* decNumberVersion -- return the name and version of this module */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +const char * decNumberVersion(void) { + return DECVERSION; + } // decNumberVersion + +/* ------------------------------------------------------------------ */ +/* decNumberZero -- set a number to 0 */ +/* */ +/* dn is the number to set, with space for one digit */ +/* returns dn */ +/* */ +/* No error is possible. */ +/* ------------------------------------------------------------------ */ +// Memset is not used as it is much slower in some environments. +decNumber * decNumberZero(decNumber *dn) { + + #if DECCHECK + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; + #endif + + dn->bits=0; + dn->exponent=0; + dn->digits=1; + dn->lsu[0]=0; + return dn; + } // decNumberZero + +/* ================================================================== */ +/* Local routines */ +/* ================================================================== */ + +/* ------------------------------------------------------------------ */ +/* decToString -- lay out a number into a string */ +/* */ +/* dn is the number to lay out */ +/* string is where to lay out the number */ +/* eng is 1 if Engineering, 0 if Scientific */ +/* */ +/* string must be at least dn->digits+14 characters long */ +/* No error is possible. */ +/* */ +/* Note that this routine can generate a -0 or 0.000. These are */ +/* never generated in subset to-number or arithmetic, but can occur */ +/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */ +/* ------------------------------------------------------------------ */ +// If DECCHECK is enabled the string "?" is returned if a number is +// invalid. +static void decToString(const decNumber *dn, char *string, Flag eng) { + Int exp=dn->exponent; // local copy + Int e; // E-part value + Int pre; // digits before the '.' + Int cut; // for counting digits in a Unit + char *c=string; // work [output pointer] + const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer] + uInt u, pow; // work + + #if DECCHECK + if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) { + strcpy(string, "?"); + return;} + #endif + + if (decNumberIsNegative(dn)) { // Negatives get a minus + *c='-'; + c++; + } + if (dn->bits&DECSPECIAL) { // Is a special value + if (decNumberIsInfinite(dn)) { + strcpy(c, "Inf"); + strcpy(c+3, "inity"); + return;} + // a NaN + if (dn->bits&DECSNAN) { // signalling NaN + *c='s'; + c++; + } + strcpy(c, "NaN"); + c+=3; // step past + // if not a clean non-zero coefficient, that's all there is in a + // NaN string + if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return; + // [drop through to add integer] + } + + // calculate how many digits in msu, and hence first cut + cut=MSUDIGITS(dn->digits); // [faster than remainder] + cut--; // power of ten for digit + + if (exp==0) { // simple integer [common fastpath] + for (;up>=dn->lsu; up--) { // each Unit from msu + u=*up; // contains DECDPUN digits to lay out + for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow); + cut=DECDPUN-1; // next Unit has all digits + } + *c='\0'; // terminate the string + return;} + + /* non-0 exponent -- assume plain form */ + pre=dn->digits+exp; // digits before '.' + e=0; // no E + if ((exp>0) || (pre<-5)) { // need exponential form + e=exp+dn->digits-1; // calculate E value + pre=1; // assume one digit before '.' + if (eng && (e!=0)) { // engineering: may need to adjust + Int adj; // adjustment + // The C remainder operator is undefined for negative numbers, so + // a positive remainder calculation must be used here + if (e<0) { + adj=(-e)%3; + if (adj!=0) adj=3-adj; + } + else { // e>0 + adj=e%3; + } + e=e-adj; + // if dealing with zero still produce an exponent which is a + // multiple of three, as expected, but there will only be the + // one zero before the E, still. Otherwise note the padding. + if (!ISZERO(dn)) pre+=adj; + else { // is zero + if (adj!=0) { // 0.00Esnn needed + e=e+3; + pre=-(2-adj); + } + } // zero + } // eng + } // need exponent + + /* lay out the digits of the coefficient, adding 0s and . as needed */ + u=*up; + if (pre>0) { // xxx.xxx or xx00 (engineering) form + Int n=pre; + for (; pre>0; pre--, c++, cut--) { + if (cut<0) { // need new Unit + if (up==dn->lsu) break; // out of input digits (pre>digits) + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + if (ndigits) { // more to come, after '.' + *c='.'; c++; + for (;; c++, cut--) { + if (cut<0) { // need new Unit + if (up==dn->lsu) break; // out of input digits + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + } + else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed + } + else { // 0.xxx or 0.000xxx form + *c='0'; c++; + *c='.'; c++; + for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.' + for (; ; c++, cut--) { + if (cut<0) { // need new Unit + if (up==dn->lsu) break; // out of input digits + up--; + cut=DECDPUN-1; + u=*up; + } + TODIGIT(u, cut, c, pow); + } + } + + /* Finally add the E-part, if needed. It will never be 0, has a + base maximum and minimum of +999999999 through -999999999, but + could range down to -1999999998 for anormal numbers */ + if (e!=0) { + Flag had=0; // 1=had non-zero + *c='E'; c++; + *c='+'; c++; // assume positive + u=e; // .. + if (e<0) { + *(c-1)='-'; // oops, need - + u=-e; // uInt, please + } + // lay out the exponent [_itoa or equivalent is not ANSI C] + for (cut=9; cut>=0; cut--) { + TODIGIT(u, cut, c, pow); + if (*c=='0' && !had) continue; // skip leading zeros + had=1; // had non-0 + c++; // step for next + } // cut + } + *c='\0'; // terminate the string (all paths) + return; + } // decToString + +/* ------------------------------------------------------------------ */ +/* decAddOp -- add/subtract operation */ +/* */ +/* This computes C = A + B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X+X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* negate is DECNEG if rhs should be negated, or 0 otherwise */ +/* status accumulates status for the caller */ +/* */ +/* C must have space for set->digits digits. */ +/* Inexact in status must be 0 for correct Exact zero sign in result */ +/* ------------------------------------------------------------------ */ +/* If possible, the coefficient is calculated directly into C. */ +/* However, if: */ +/* -- a digits+1 calculation is needed because the numbers are */ +/* unaligned and span more than set->digits digits */ +/* -- a carry to digits+1 digits looks possible */ +/* -- C is the same as A or B, and the result would destructively */ +/* overlap the A or B coefficient */ +/* then the result must be calculated into a temporary buffer. In */ +/* this case a local (stack) buffer is used if possible, and only if */ +/* too long for that does malloc become the final resort. */ +/* */ +/* Misalignment is handled as follows: */ +/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */ +/* BPad: Apply the padding by a combination of shifting (whole */ +/* units) and multiplication (part units). */ +/* */ +/* Addition, especially x=x+1, is speed-critical. */ +/* The static buffer is larger than might be expected to allow for */ +/* calls from higher-level funtions (notable exp). */ +/* ------------------------------------------------------------------ */ +static decNumber * decAddOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uByte negate, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + Int rhsshift; // working shift (in Units) + Int maxdigits; // longest logical length + Int mult; // multiplier + Int residue; // rounding accumulator + uByte bits; // result bits + Flag diffsign; // non-0 if arguments have different sign + Unit *acc; // accumulator for result + Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many + // allocations when called from + // other operations, notable exp] + Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated + Int reqdigits=set->digits; // local copy; requested DIGITS + Int padding; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // note whether signs differ [used all paths] + diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG); + + // handle infinities and NaNs + if (SPECIALARGS) { // a special bit set + if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN + decNaNs(res, lhs, rhs, set, status); + else { // one or two infinities + if (decNumberIsInfinite(lhs)) { // LHS is infinity + // two infinities with different signs is invalid + if (decNumberIsInfinite(rhs) && diffsign) { + *status|=DEC_Invalid_operation; + break; + } + bits=lhs->bits & DECNEG; // get sign from LHS + } + else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity + bits|=DECINF; + decNumberZero(res); + res->bits=bits; // set +/- infinity + } // an infinity + break; + } + + // Quick exit for add 0s; return the non-0, modified as need be + if (ISZERO(lhs)) { + Int adjust; // work + Int lexp=lhs->exponent; // save in case LHS==RES + bits=lhs->bits; // .. + residue=0; // clear accumulator + decCopyFit(res, rhs, set, &residue, status); // copy (as needed) + res->bits^=negate; // flip if rhs was negated + #if DECSUBSET + if (set->extended) { // exponents on zeros count + #endif + // exponent will be the lower of the two + adjust=lexp-res->exponent; // adjustment needed [if -ve] + if (ISZERO(res)) { // both 0: special IEEE 754 rules + if (adjust<0) res->exponent=lexp; // set exponent + // 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0 + if (diffsign) { + if (set->round!=DEC_ROUND_FLOOR) res->bits=0; + else res->bits=DECNEG; // preserve 0 sign + } + } + else { // non-0 res + if (adjust<0) { // 0-padding needed + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; // to fit exactly + *status|=DEC_Rounded; // [but exact] + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; // set the exponent. + } + } // non-0 res + #if DECSUBSET + } // extended + #endif + decFinish(res, set, &residue, status); // clean and finalize + break;} + + if (ISZERO(rhs)) { // [lhs is non-zero] + Int adjust; // work + Int rexp=rhs->exponent; // save in case RHS==RES + bits=rhs->bits; // be clean + residue=0; // clear accumulator + decCopyFit(res, lhs, set, &residue, status); // copy (as needed) + #if DECSUBSET + if (set->extended) { // exponents on zeros count + #endif + // exponent will be the lower of the two + // [0-0 case handled above] + adjust=rexp-res->exponent; // adjustment needed [if -ve] + if (adjust<0) { // 0-padding needed + if ((res->digits-adjust)>set->digits) { + adjust=res->digits-set->digits; // to fit exactly + *status|=DEC_Rounded; // [but exact] + } + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; // set the exponent. + } + #if DECSUBSET + } // extended + #endif + decFinish(res, set, &residue, status); // clean and finalize + break;} + + // [NB: both fastpath and mainpath code below assume these cases + // (notably 0-0) have already been handled] + + // calculate the padding needed to align the operands + padding=rhs->exponent-lhs->exponent; + + // Fastpath cases where the numbers are aligned and normal, the RHS + // is all in one unit, no operand rounding is needed, and no carry, + // lengthening, or borrow is needed + if (padding==0 + && rhs->digits<=DECDPUN + && rhs->exponent>=set->emin // [some normals drop through] + && rhs->exponent<=set->emax-set->digits+1 // [could clamp] + && rhs->digits<=reqdigits + && lhs->digits<=reqdigits) { + Int partial=*lhs->lsu; + if (!diffsign) { // adding + partial+=*rhs->lsu; + if ((partial<=DECDPUNMAX) // result fits in unit + && (lhs->digits>=DECDPUN || // .. and no digits-count change + partial<(Int)powers[lhs->digits])) { // .. + if (res!=lhs) decNumberCopy(res, lhs); // not in place + *res->lsu=(Unit)partial; // [copy could have overwritten RHS] + break; + } + // else drop out for careful add + } + else { // signs differ + partial-=*rhs->lsu; + if (partial>0) { // no borrow needed, and non-0 result + if (res!=lhs) decNumberCopy(res, lhs); // not in place + *res->lsu=(Unit)partial; + // this could have reduced digits [but result>0] + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + break; + } + // else drop out for careful subtract + } + } + + // Now align (pad) the lhs or rhs so they can be added or + // subtracted, as necessary. If one number is much larger than + // the other (that is, if in plain form there is a least one + // digit between the lowest digit of one and the highest of the + // other) padding with up to DIGITS-1 trailing zeros may be + // needed; then apply rounding (as exotic rounding modes may be + // affected by the residue). + rhsshift=0; // rhs shift to left (padding) in Units + bits=lhs->bits; // assume sign is that of LHS + mult=1; // likely multiplier + + // [if padding==0 the operands are aligned; no padding is needed] + if (padding!=0) { + // some padding needed; always pad the RHS, as any required + // padding can then be effected by a simple combination of + // shifts and a multiply + Flag swapped=0; + if (padding<0) { // LHS needs the padding + const decNumber *t; + padding=-padding; // will be +ve + bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS + t=lhs; lhs=rhs; rhs=t; + swapped=1; + } + + // If, after pad, rhs would be longer than lhs by digits+1 or + // more then lhs cannot affect the answer, except as a residue, + // so only need to pad up to a length of DIGITS+1. + if (rhs->digits+padding > lhs->digits+reqdigits+1) { + // The RHS is sufficient + // for residue use the relative sign indication... + Int shift=reqdigits-rhs->digits; // left shift needed + residue=1; // residue for rounding + if (diffsign) residue=-residue; // signs differ + // copy, shortening if necessary + decCopyFit(res, rhs, set, &residue, status); + // if it was already shorter, then need to pad with zeros + if (shift>0) { + res->digits=decShiftToMost(res->lsu, res->digits, shift); + res->exponent-=shift; // adjust the exponent. + } + // flip the result sign if unswapped and rhs was negated + if (!swapped) res->bits^=negate; + decFinish(res, set, &residue, status); // done + break;} + + // LHS digits may affect result + rhsshift=D2U(padding+1)-1; // this much by Unit shift .. + mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication + } // padding needed + + if (diffsign) mult=-mult; // signs differ + + // determine the longer operand + maxdigits=rhs->digits+padding; // virtual length of RHS + if (lhs->digits>maxdigits) maxdigits=lhs->digits; + + // Decide on the result buffer to use; if possible place directly + // into result. + acc=res->lsu; // assume add direct to result + // If destructive overlap, or the number is too long, or a carry or + // borrow to DIGITS+1 might be possible, a buffer must be used. + // [Might be worth more sophisticated tests when maxdigits==reqdigits] + if ((maxdigits>=reqdigits) // is, or could be, too large + || (res==rhs && rhsshift>0)) { // destructive overlap + // buffer needed, choose it; units for maxdigits digits will be + // needed, +1 Unit for carry or borrow + Int need=D2U(maxdigits)+1; + acc=accbuff; // assume use local buffer + if (need*sizeof(Unit)>sizeof(accbuff)) { + // printf("malloc add %ld %ld\n", need, sizeof(accbuff)); + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + acc=allocacc; + } + } + + res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite.. + res->exponent=lhs->exponent; // .. operands (even if aliased) + + #if DECTRACE + decDumpAr('A', lhs->lsu, D2U(lhs->digits)); + decDumpAr('B', rhs->lsu, D2U(rhs->digits)); + printf(" :h: %ld %ld\n", rhsshift, mult); + #endif + + // add [A+B*m] or subtract [A+B*(-m)] + res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhsshift, acc, mult) + *DECDPUN; // [units -> digits] + if (res->digits<0) { // borrowed... + res->digits=-res->digits; + res->bits^=DECNEG; // flip the sign + } + #if DECTRACE + decDumpAr('+', acc, D2U(res->digits)); + #endif + + // If a buffer was used the result must be copied back, possibly + // shortening. (If no buffer was used then the result must have + // fit, so can't need rounding and residue must be 0.) + residue=0; // clear accumulator + if (acc!=res->lsu) { + #if DECSUBSET + if (set->extended) { // round from first significant digit + #endif + // remove leading zeros that were added due to rounding up to + // integral Units -- before the test for rounding. + if (res->digits>reqdigits) + res->digits=decGetDigits(acc, D2U(res->digits)); + decSetCoeff(res, set, acc, res->digits, &residue, status); + #if DECSUBSET + } + else { // subset arithmetic rounds from original significant digit + // May have an underestimate. This only occurs when both + // numbers fit in DECDPUN digits and are padding with a + // negative multiple (-10, -100...) and the top digit(s) become + // 0. (This only matters when using X3.274 rules where the + // leading zero could be included in the rounding.) + if (res->digitsdigits))=0; // ensure leading 0 is there + res->digits=maxdigits; + } + else { + // remove leading zeros that added due to rounding up to + // integral Units (but only those in excess of the original + // maxdigits length, unless extended) before test for rounding. + if (res->digits>reqdigits) { + res->digits=decGetDigits(acc, D2U(res->digits)); + if (res->digitsdigits=maxdigits; + } + } + decSetCoeff(res, set, acc, res->digits, &residue, status); + // Now apply rounding if needed before removing leading zeros. + // This is safe because subnormals are not a possibility + if (residue!=0) { + decApplyRound(res, set, residue, status); + residue=0; // did what needed to be done + } + } // subset + #endif + } // used buffer + + // strip leading zeros [these were left on in case of subset subtract] + res->digits=decGetDigits(res->lsu, D2U(res->digits)); + + // apply checks and rounding + decFinish(res, set, &residue, status); + + // "When the sum of two operands with opposite signs is exactly + // zero, the sign of that sum shall be '+' in all rounding modes + // except round toward -Infinity, in which mode that sign shall be + // '-'." [Subset zeros also never have '-', set by decFinish.] + if (ISZERO(res) && diffsign + #if DECSUBSET + && set->extended + #endif + && (*status&DEC_Inexact)==0) { + if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign - + else res->bits&=~DECNEG; // sign + + } + } while(0); // end protected + + if (allocacc!=NULL) free(allocacc); // drop any storage used + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // .. + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decAddOp + +/* ------------------------------------------------------------------ */ +/* decDivideOp -- division operation */ +/* */ +/* This routine performs the calculations for all four division */ +/* operators (divide, divideInteger, remainder, remainderNear). */ +/* */ +/* C=A op B */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X/X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* The underlying algorithm of this routine is the same as in the */ +/* 1981 S/370 implementation, that is, non-restoring long division */ +/* with bi-unit (rather than bi-digit) estimation for each unit */ +/* multiplier. In this pseudocode overview, complications for the */ +/* Remainder operators and division residues for exact rounding are */ +/* omitted for clarity. */ +/* */ +/* Prepare operands and handle special values */ +/* Test for x/0 and then 0/x */ +/* Exp =Exp1 - Exp2 */ +/* Exp =Exp +len(var1) -len(var2) */ +/* Sign=Sign1 * Sign2 */ +/* Pad accumulator (Var1) to double-length with 0's (pad1) */ +/* Pad Var2 to same length as Var1 */ +/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */ +/* have=0 */ +/* Do until (have=digits+1 OR residue=0) */ +/* if exp<0 then if integer divide/residue then leave */ +/* this_unit=0 */ +/* Do forever */ +/* compare numbers */ +/* if <0 then leave inner_loop */ +/* if =0 then (* quick exit without subtract *) do */ +/* this_unit=this_unit+1; output this_unit */ +/* leave outer_loop; end */ +/* Compare lengths of numbers (mantissae): */ +/* If same then tops2=msu2pair -- {units 1&2 of var2} */ +/* else tops2=msu2plus -- {0, unit 1 of var2} */ +/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */ +/* mult=tops1/tops2 -- Good and safe guess at divisor */ +/* if mult=0 then mult=1 */ +/* this_unit=this_unit+mult */ +/* subtract */ +/* end inner_loop */ +/* if have\=0 | this_unit\=0 then do */ +/* output this_unit */ +/* have=have+1; end */ +/* var2=var2/10 */ +/* exp=exp-1 */ +/* end outer_loop */ +/* exp=exp+1 -- set the proper exponent */ +/* if have=0 then generate answer=0 */ +/* Return (Result is defined by Var1) */ +/* */ +/* ------------------------------------------------------------------ */ +/* Two working buffers are needed during the division; one (digits+ */ +/* 1) to accumulate the result, and the other (up to 2*digits+1) for */ +/* long subtractions. These are acc and var1 respectively. */ +/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/ +/* The static buffers may be larger than might be expected to allow */ +/* for calls from higher-level funtions (notable exp). */ +/* ------------------------------------------------------------------ */ +static decNumber * decDivideOp(decNumber *res, + const decNumber *lhs, const decNumber *rhs, + decContext *set, Flag op, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer + Unit *acc=accbuff; // -> accumulator array for result + Unit *allocacc=NULL; // -> allocated buffer, iff allocated + Unit *accnext; // -> where next digit will go + Int acclength; // length of acc needed [Units] + Int accunits; // count of units accumulated + Int accdigits; // count of digits accumulated + + Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1 + Unit *var1=varbuff; // -> var1 array for long subtraction + Unit *varalloc=NULL; // -> allocated buffer, iff used + Unit *msu1; // -> msu of var1 + + const Unit *var2; // -> var2 array + const Unit *msu2; // -> msu of var2 + Int msu2plus; // msu2 plus one [does not vary] + eInt msu2pair; // msu2 pair plus one [does not vary] + + Int var1units, var2units; // actual lengths + Int var2ulen; // logical length (units) + Int var1initpad=0; // var1 initial padding (digits) + Int maxdigits; // longest LHS or required acc length + Int mult; // multiplier for subtraction + Unit thisunit; // current unit being accumulated + Int residue; // for rounding + Int reqdigits=set->digits; // requested DIGITS + Int exponent; // working exponent + Int maxexponent=0; // DIVIDE maximum exponent if unrounded + uByte bits; // working sign + Unit *target; // work + const Unit *source; // .. + uInt const *pow; // .. + Int shift, cut; // .. + #if DECSUBSET + Int dropped; // work + #endif + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions + + // handle infinities and NaNs + if (SPECIALARGS) { // a special bit set + if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs + decNaNs(res, lhs, rhs, set, status); + break; + } + // one or two infinities + if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite + if (decNumberIsInfinite(rhs) || // two infinities are invalid .. + op & (REMAINDER | REMNEAR)) { // as is remainder of infinity + *status|=DEC_Invalid_operation; + break; + } + // [Note that infinity/0 raises no exceptions] + decNumberZero(res); + res->bits=bits|DECINF; // set +/- infinity + break; + } + else { // RHS (divisor) is infinite + residue=0; + if (op&(REMAINDER|REMNEAR)) { + // result is [finished clone of] lhs + decCopyFit(res, lhs, set, &residue, status); + } + else { // a division + decNumberZero(res); + res->bits=bits; // set +/- zero + // for DIVIDEINT the exponent is always 0. For DIVIDE, result + // is a 0 with infinitely negative exponent, clamped to minimum + if (op&DIVIDE) { + res->exponent=set->emin-set->digits+1; + *status|=DEC_Clamped; + } + } + decFinish(res, set, &residue, status); + break; + } + } + + // handle 0 rhs (x/0) + if (ISZERO(rhs)) { // x/0 is always exceptional + if (ISZERO(lhs)) { + decNumberZero(res); // [after lhs test] + *status|=DEC_Division_undefined;// 0/0 will become NaN + } + else { + decNumberZero(res); + if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation; + else { + *status|=DEC_Division_by_zero; // x/0 + res->bits=bits|DECINF; // .. is +/- Infinity + } + } + break;} + + // handle 0 lhs (0/x) + if (ISZERO(lhs)) { // 0/x [x!=0] + #if DECSUBSET + if (!set->extended) decNumberZero(res); + else { + #endif + if (op&DIVIDE) { + residue=0; + exponent=lhs->exponent-rhs->exponent; // ideal exponent + decNumberCopy(res, lhs); // [zeros always fit] + res->bits=bits; // sign as computed + res->exponent=exponent; // exponent, too + decFinalize(res, set, &residue, status); // check exponent + } + else if (op&DIVIDEINT) { + decNumberZero(res); // integer 0 + res->bits=bits; // sign as computed + } + else { // a remainder + exponent=rhs->exponent; // [save in case overwrite] + decNumberCopy(res, lhs); // [zeros always fit] + if (exponentexponent) res->exponent=exponent; // use lower + } + #if DECSUBSET + } + #endif + break;} + + // Precalculate exponent. This starts off adjusted (and hence fits + // in 31 bits) and becomes the usual unadjusted exponent as the + // division proceeds. The order of evaluation is important, here, + // to avoid wrap. + exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits); + + // If the working exponent is -ve, then some quick exits are + // possible because the quotient is known to be <1 + // [for REMNEAR, it needs to be < -1, as -0.5 could need work] + if (exponent<0 && !(op==DIVIDE)) { + if (op&DIVIDEINT) { + decNumberZero(res); // integer part is 0 + #if DECSUBSET + if (set->extended) + #endif + res->bits=bits; // set +/- zero + break;} + // fastpath remainders so long as the lhs has the smaller + // (or equal) exponent + if (lhs->exponent<=rhs->exponent) { + if (op&REMAINDER || exponent<-1) { + // It is REMAINDER or safe REMNEAR; result is [finished + // clone of] lhs (r = x - 0*y) + residue=0; + decCopyFit(res, lhs, set, &residue, status); + decFinish(res, set, &residue, status); + break; + } + // [unsafe REMNEAR drops through] + } + } // fastpaths + + /* Long (slow) division is needed; roll up the sleeves... */ + + // The accumulator will hold the quotient of the division. + // If it needs to be too long for stack storage, then allocate. + acclength=D2U(reqdigits+DECDPUN); // in Units + if (acclength*sizeof(Unit)>sizeof(accbuff)) { + // printf("malloc dvacc %ld units\n", acclength); + allocacc=(Unit *)malloc(acclength*sizeof(Unit)); + if (allocacc==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + acc=allocacc; // use the allocated space + } + + // var1 is the padded LHS ready for subtractions. + // If it needs to be too long for stack storage, then allocate. + // The maximum units needed for var1 (long subtraction) is: + // Enough for + // (rhs->digits+reqdigits-1) -- to allow full slide to right + // or (lhs->digits) -- to allow for long lhs + // whichever is larger + // +1 -- for rounding of slide to right + // +1 -- for leading 0s + // +1 -- for pre-adjust if a remainder or DIVIDEINT + // [Note: unused units do not participate in decUnitAddSub data] + maxdigits=rhs->digits+reqdigits-1; + if (lhs->digits>maxdigits) maxdigits=lhs->digits; + var1units=D2U(maxdigits)+2; + // allocate a guard unit above msu1 for REMAINDERNEAR + if (!(op&DIVIDE)) var1units++; + if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) { + // printf("malloc dvvar %ld units\n", var1units+1); + varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit)); + if (varalloc==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + var1=varalloc; // use the allocated space + } + + // Extend the lhs and rhs to full long subtraction length. The lhs + // is truly extended into the var1 buffer, with 0 padding, so a + // subtract in place is always possible. The rhs (var2) has + // virtual padding (implemented by decUnitAddSub). + // One guard unit was allocated above msu1 for rem=rem+rem in + // REMAINDERNEAR. + msu1=var1+var1units-1; // msu of var1 + source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array + for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source; + for (; target>=var1; target--) *target=0; + + // rhs (var2) is left-aligned with var1 at the start + var2ulen=var1units; // rhs logical length (units) + var2units=D2U(rhs->digits); // rhs actual length (units) + var2=rhs->lsu; // -> rhs array + msu2=var2+var2units-1; // -> msu of var2 [never changes] + // now set up the variables which will be used for estimating the + // multiplication factor. If these variables are not exact, add + // 1 to make sure that the multiplier is never overestimated. + msu2plus=*msu2; // it's value .. + if (var2units>1) msu2plus++; // .. +1 if any more + msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair .. + if (var2units>1) { // .. [else treat 2nd as 0] + msu2pair+=*(msu2-1); // .. + if (var2units>2) msu2pair++; // .. +1 if any more + } + + // The calculation is working in units, which may have leading zeros, + // but the exponent was calculated on the assumption that they are + // both left-aligned. Adjust the exponent to compensate: add the + // number of leading zeros in var1 msu and subtract those in var2 msu. + // [This is actually done by counting the digits and negating, as + // lead1=DECDPUN-digits1, and similarly for lead2.] + for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--; + for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++; + + // Now, if doing an integer divide or remainder, ensure that + // the result will be Unit-aligned. To do this, shift the var1 + // accumulator towards least if need be. (It's much easier to + // do this now than to reassemble the residue afterwards, if + // doing a remainder.) Also ensure the exponent is not negative. + if (!(op&DIVIDE)) { + Unit *u; // work + // save the initial 'false' padding of var1, in digits + var1initpad=(var1units-D2U(lhs->digits))*DECDPUN; + // Determine the shift to do. + if (exponent<0) cut=-exponent; + else cut=DECDPUN-exponent%DECDPUN; + decShiftToLeast(var1, var1units, cut); + exponent+=cut; // maintain numerical value + var1initpad-=cut; // .. and reduce padding + // clean any most-significant units which were just emptied + for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0; + } // align + else { // is DIVIDE + maxexponent=lhs->exponent-rhs->exponent; // save + // optimization: if the first iteration will just produce 0, + // preadjust to skip it [valid for DIVIDE only] + if (*msu1<*msu2) { + var2ulen--; // shift down + exponent-=DECDPUN; // update the exponent + } + } + + // ---- start the long-division loops ------------------------------ + accunits=0; // no units accumulated yet + accdigits=0; // .. or digits + accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1] + for (;;) { // outer forever loop + thisunit=0; // current unit assumed 0 + // find the next unit + for (;;) { // inner forever loop + // strip leading zero units [from either pre-adjust or from + // subtract last time around]. Leave at least one unit. + for (; *msu1==0 && msu1>var1; msu1--) var1units--; + + if (var1units msu + for (pv1=msu1; ; pv1--, pv2--) { + // v1=*pv1 -- always OK + v2=0; // assume in padding + if (pv2>=var2) v2=*pv2; // in range + if (*pv1!=v2) break; // no longer the same + if (pv1==var1) break; // done; leave pv1 as is + } + // here when all inspected or a difference seen + if (*pv1v2. Prepare for real subtraction; the lengths are equal + // Estimate the multiplier (there's always a msu1-1)... + // Bring in two units of var2 to provide a good estimate. + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair); + } // lengths the same + else { // var1units > var2ulen, so subtraction is safe + // The var2 msu is one unit towards the lsu of the var1 msu, + // so only one unit for var2 can be used. + mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus); + } + if (mult==0) mult=1; // must always be at least 1 + // subtraction needed; var1 is > var2 + thisunit=(Unit)(thisunit+mult); // accumulate + // subtract var1-var2, into var1; only the overlap needs + // processing, as this is an in-place calculation + shift=var2ulen-var2units; + #if DECTRACE + decDumpAr('1', &var1[shift], var1units-shift); + decDumpAr('2', var2, var2units); + printf("m=%ld\n", -mult); + #endif + decUnitAddSub(&var1[shift], var1units-shift, + var2, var2units, 0, + &var1[shift], -mult); + #if DECTRACE + decDumpAr('#', &var1[shift], var1units-shift); + #endif + // var1 now probably has leading zeros; these are removed at the + // top of the inner loop. + } // inner loop + + // The next unit has been calculated in full; unless it's a + // leading zero, add to acc + if (accunits!=0 || thisunit!=0) { // is first or non-zero + *accnext=thisunit; // store in accumulator + // account exactly for the new digits + if (accunits==0) { + accdigits++; // at least one + for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++; + } + else accdigits+=DECDPUN; + accunits++; // update count + accnext--; // ready for next + if (accdigits>reqdigits) break; // have enough digits + } + + // if the residue is zero, the operation is done (unless divide + // or divideInteger and still not enough digits yet) + if (*var1==0 && var1units==1) { // residue is 0 + if (op&(REMAINDER|REMNEAR)) break; + if ((op&DIVIDE) && (exponent<=maxexponent)) break; + // [drop through if divideInteger] + } + // also done enough if calculating remainder or integer + // divide and just did the last ('units') unit + if (exponent==0 && !(op&DIVIDE)) break; + + // to get here, var1 is less than var2, so divide var2 by the per- + // Unit power of ten and go for the next digit + var2ulen--; // shift down + exponent-=DECDPUN; // update the exponent + } // outer loop + + // ---- division is complete --------------------------------------- + // here: acc has at least reqdigits+1 of good results (or fewer + // if early stop), starting at accnext+1 (its lsu) + // var1 has any residue at the stopping point + // accunits is the number of digits collected in acc + if (accunits==0) { // acc is 0 + accunits=1; // show have a unit .. + accdigits=1; // .. + *accnext=0; // .. whose value is 0 + } + else accnext++; // back to last placed + // accnext now -> lowest unit of result + + residue=0; // assume no residue + if (op&DIVIDE) { + // record the presence of any residue, for rounding + if (*var1!=0 || var1units>1) residue=1; + else { // no residue + // Had an exact division; clean up spurious trailing 0s. + // There will be at most DECDPUN-1, from the final multiply, + // and then only if the result is non-0 (and even) and the + // exponent is 'loose'. + #if DECDPUN>1 + Unit lsu=*accnext; + if (!(lsu&0x01) && (lsu!=0)) { + // count the trailing zeros + Int drop=0; + for (;; drop++) { // [will terminate because lsu!=0] + if (exponent>=maxexponent) break; // don't chop real 0s + #if DECDPUN<=4 + if ((lsu-QUOT10(lsu, drop+1) + *powers[drop+1])!=0) break; // found non-0 digit + #else + if (lsu%powers[drop+1]!=0) break; // found non-0 digit + #endif + exponent++; + } + if (drop>0) { + accunits=decShiftToLeast(accnext, accunits, drop); + accdigits=decGetDigits(accnext, accunits); + accunits=D2U(accdigits); + // [exponent was adjusted in the loop] + } + } // neither odd nor 0 + #endif + } // exact divide + } // divide + else /* op!=DIVIDE */ { + // check for coefficient overflow + if (accdigits+exponent>reqdigits) { + *status|=DEC_Division_impossible; + break; + } + if (op & (REMAINDER|REMNEAR)) { + // [Here, the exponent will be 0, because var1 was adjusted + // appropriately.] + Int postshift; // work + Flag wasodd=0; // integer was odd + Unit *quotlsu; // for save + Int quotdigits; // .. + + bits=lhs->bits; // remainder sign is always as lhs + + // Fastpath when residue is truly 0 is worthwhile [and + // simplifies the code below] + if (*var1==0 && var1units==1) { // residue is 0 + Int exp=lhs->exponent; // save min(exponents) + if (rhs->exponentexponent; + decNumberZero(res); // 0 coefficient + #if DECSUBSET + if (set->extended) + #endif + res->exponent=exp; // .. with proper exponent + res->bits=(uByte)(bits&DECNEG); // [cleaned] + decFinish(res, set, &residue, status); // might clamp + break; + } + // note if the quotient was odd + if (*accnext & 0x01) wasodd=1; // acc is odd + quotlsu=accnext; // save in case need to reinspect + quotdigits=accdigits; // .. + + // treat the residue, in var1, as the value to return, via acc + // calculate the unused zero digits. This is the smaller of: + // var1 initial padding (saved above) + // var2 residual padding, which happens to be given by: + postshift=var1initpad+exponent-lhs->exponent+rhs->exponent; + // [the 'exponent' term accounts for the shifts during divide] + if (var1initpadexponent; // exponent is smaller of lhs & rhs + if (rhs->exponentexponent; + + // Now correct the result if doing remainderNear; if it + // (looking just at coefficients) is > rhs/2, or == rhs/2 and + // the integer was odd then the result should be rem-rhs. + if (op&REMNEAR) { + Int compare, tarunits; // work + Unit *up; // .. + // calculate remainder*2 into the var1 buffer (which has + // 'headroom' of an extra unit and hence enough space) + // [a dedicated 'double' loop would be faster, here] + tarunits=decUnitAddSub(accnext, accunits, accnext, accunits, + 0, accnext, 1); + // decDumpAr('r', accnext, tarunits); + + // Here, accnext (var1) holds tarunits Units with twice the + // remainder's coefficient, which must now be compared to the + // RHS. The remainder's exponent may be smaller than the RHS's. + compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits), + rhs->exponent-exponent); + if (compare==BADINT) { // deep trouble + *status|=DEC_Insufficient_storage; + break;} + + // now restore the remainder by dividing by two; the lsu + // is known to be even. + for (up=accnext; up0 || (compare==0 && wasodd)) { // adjustment needed + Int exp, expunits, exprem; // work + // This is effectively causing round-up of the quotient, + // so if it was the rare case where it was full and all + // nines, it would overflow and hence division-impossible + // should be raised + Flag allnines=0; // 1 if quotient all nines + if (quotdigits==reqdigits) { // could be borderline + for (up=quotlsu; ; up++) { + if (quotdigits>DECDPUN) { + if (*up!=DECDPUNMAX) break;// non-nines + } + else { // this is the last Unit + if (*up==powers[quotdigits]-1) allnines=1; + break; + } + quotdigits-=DECDPUN; // checked those digits + } // up + } // borderline check + if (allnines) { + *status|=DEC_Division_impossible; + break;} + + // rem-rhs is needed; the sign will invert. Again, var1 + // can safely be used for the working Units array. + exp=rhs->exponent-exponent; // RHS padding needed + // Calculate units and remainder from exponent. + expunits=exp/DECDPUN; + exprem=exp%DECDPUN; + // subtract [A+B*(-m)]; the result will always be negative + accunits=-decUnitAddSub(accnext, accunits, + rhs->lsu, D2U(rhs->digits), + expunits, accnext, -(Int)powers[exprem]); + accdigits=decGetDigits(accnext, accunits); // count digits exactly + accunits=D2U(accdigits); // and recalculate the units for copy + // [exponent is as for original remainder] + bits^=DECNEG; // flip the sign + } + } // REMNEAR + } // REMAINDER or REMNEAR + } // not DIVIDE + + // Set exponent and bits + res->exponent=exponent; + res->bits=(uByte)(bits&DECNEG); // [cleaned] + + // Now the coefficient. + decSetCoeff(res, set, accnext, accdigits, &residue, status); + + decFinish(res, set, &residue, status); // final cleanup + + #if DECSUBSET + // If a divide then strip trailing zeros if subset [after round] + if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped); + #endif + } while(0); // end protected + + if (varalloc!=NULL) free(varalloc); // drop any storage used + if (allocacc!=NULL) free(allocacc); // .. + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // .. + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decDivideOp + +/* ------------------------------------------------------------------ */ +/* decMultiplyOp -- multiplication operation */ +/* */ +/* This routine performs the multiplication C=A x B. */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X*X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* status is the usual accumulator */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* ------------------------------------------------------------------ */ +/* 'Classic' multiplication is used rather than Karatsuba, as the */ +/* latter would give only a minor improvement for the short numbers */ +/* expected to be handled most (and uses much more memory). */ +/* */ +/* There are two major paths here: the general-purpose ('old code') */ +/* path which handles all DECDPUN values, and a fastpath version */ +/* which is used if 64-bit ints are available, DECDPUN<=4, and more */ +/* than two calls to decUnitAddSub would be made. */ +/* */ +/* The fastpath version lumps units together into 8-digit or 9-digit */ +/* chunks, and also uses a lazy carry strategy to minimise expensive */ +/* 64-bit divisions. The chunks are then broken apart again into */ +/* units for continuing processing. Despite this overhead, the */ +/* fastpath can speed up some 16-digit operations by 10x (and much */ +/* more for higher-precision calculations). */ +/* */ +/* A buffer always has to be used for the accumulator; in the */ +/* fastpath, buffers are also always needed for the chunked copies of */ +/* of the operand coefficients. */ +/* Static buffers are larger than needed just for multiply, to allow */ +/* for calls from other operations (notably exp). */ +/* ------------------------------------------------------------------ */ +#define FASTMUL (DECUSE64 && DECDPUN<5) +static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uInt *status) { + Int accunits; // Units of accumulator in use + Int exponent; // work + Int residue=0; // rounding residue + uByte bits; // result sign + Unit *acc; // -> accumulator Unit array + Int needbytes; // size calculator + void *allocacc=NULL; // -> allocated accumulator, iff allocated + Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0, + // *4 for calls from other operations) + const Unit *mer, *mermsup; // work + Int madlength; // Units in multiplicand + Int shift; // Units to shift multiplicand by + + #if FASTMUL + // if DECDPUN is 1 or 3 work in base 10**9, otherwise + // (DECDPUN is 2 or 4) then work in base 10**8 + #if DECDPUN & 1 // odd + #define FASTBASE 1000000000 // base + #define FASTDIGS 9 // digits in base + #define FASTLAZY 18 // carry resolution point [1->18] + #else + #define FASTBASE 100000000 + #define FASTDIGS 8 + #define FASTLAZY 1844 // carry resolution point [1->1844] + #endif + // three buffers are used, two for chunked copies of the operands + // (base 10**8 or base 10**9) and one base 2**64 accumulator with + // lazy carry evaluation + uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) + uInt *zlhi=zlhibuff; // -> lhs array + uInt *alloclhi=NULL; // -> allocated buffer, iff allocated + uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0) + uInt *zrhi=zrhibuff; // -> rhs array + uInt *allocrhi=NULL; // -> allocated buffer, iff allocated + uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0) + // [allocacc is shared for both paths, as only one will run] + uLong *zacc=zaccbuff; // -> accumulator array for exact result + #if DECDPUN==1 + Int zoff; // accumulator offset + #endif + uInt *lip, *rip; // item pointers + uInt *lmsi, *rmsi; // most significant items + Int ilhs, irhs, iacc; // item counts in the arrays + Int lazy; // lazy carry counter + uLong lcarry; // uLong carry + uInt carry; // carry (NB not uLong) + Int count; // work + const Unit *cup; // .. + Unit *up; // .. + uLong *lp; // .. + Int p; // .. + #endif + + #if DECSUBSET + decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated + decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated + #endif + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + // precalculate result sign + bits=(uByte)((lhs->bits^rhs->bits)&DECNEG); + + // handle infinities and NaNs + if (SPECIALARGS) { // a special bit set + if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs + decNaNs(res, lhs, rhs, set, status); + return res;} + // one or two infinities; Infinity * 0 is invalid + if (((lhs->bits & DECINF)==0 && ISZERO(lhs)) + ||((rhs->bits & DECINF)==0 && ISZERO(rhs))) { + *status|=DEC_Invalid_operation; + return res;} + decNumberZero(res); + res->bits=bits|DECINF; // infinity + return res;} + + // For best speed, as in DMSRCN [the original Rexx numerics + // module], use the shorter number as the multiplier (rhs) and + // the longer as the multiplicand (lhs) to minimise the number of + // adds (partial products) + if (lhs->digitsdigits) { // swap... + const decNumber *hold=lhs; + lhs=rhs; + rhs=hold; + } + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>set->digits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + #if FASTMUL // fastpath can be used + // use the fast path if there are enough digits in the shorter + // operand to make the setup and takedown worthwhile + #define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls + if (rhs->digits>NEEDTWO) { // use fastpath... + // calculate the number of elements in each array + ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling] + irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // .. + iacc=ilhs+irhs; + + // allocate buffers if required, as usual + needbytes=ilhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zlhibuff)) { + alloclhi=(uInt *)malloc(needbytes); + zlhi=alloclhi;} + needbytes=irhs*sizeof(uInt); + if (needbytes>(Int)sizeof(zrhibuff)) { + allocrhi=(uInt *)malloc(needbytes); + zrhi=allocrhi;} + + // Allocating the accumulator space needs a special case when + // DECDPUN=1 because when converting the accumulator to Units + // after the multiplication each 8-byte item becomes 9 1-byte + // units. Therefore iacc extra bytes are needed at the front + // (rounded up to a multiple of 8 bytes), and the uLong + // accumulator starts offset the appropriate number of units + // to the right to avoid overwrite during the unchunking. + needbytes=iacc*sizeof(uLong); + #if DECDPUN==1 + zoff=(iacc+7)/8; // items to offset by + needbytes+=zoff*8; + #endif + if (needbytes>(Int)sizeof(zaccbuff)) { + allocacc=(uLong *)malloc(needbytes); + zacc=(uLong *)allocacc;} + if (zlhi==NULL||zrhi==NULL||zacc==NULL) { + *status|=DEC_Insufficient_storage; + break;} + + acc=(Unit *)zacc; // -> target Unit array + #if DECDPUN==1 + zacc+=zoff; // start uLong accumulator to right + #endif + + // assemble the chunked copies of the left and right sides + for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++) + for (p=0, *lip=0; p0; + p+=DECDPUN, cup++, count-=DECDPUN) + *lip+=*cup*powers[p]; + lmsi=lip-1; // save -> msi + for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++) + for (p=0, *rip=0; p0; + p+=DECDPUN, cup++, count-=DECDPUN) + *rip+=*cup*powers[p]; + rmsi=rip-1; // save -> msi + + // zero the accumulator + for (lp=zacc; lp0 && rip!=rmsi) continue; + lazy=FASTLAZY; // reset delay count + // spin up the accumulator resolving overflows + for (lp=zacc; lp assume buffer for accumulator + needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit); + if (needbytes>(Int)sizeof(accbuff)) { + allocacc=(Unit *)malloc(needbytes); + if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;} + acc=(Unit *)allocacc; // use the allocated space + } + + /* Now the main long multiplication loop */ + // Unlike the equivalent in the IBM Java implementation, there + // is no advantage in calculating from msu to lsu. So, do it + // by the book, as it were. + // Each iteration calculates ACC=ACC+MULTAND*MULT + accunits=1; // accumulator starts at '0' + *acc=0; // .. (lsu=0) + shift=0; // no multiplicand shift at first + madlength=D2U(lhs->digits); // this won't change + mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier + + for (mer=rhs->lsu; merlsu, madlength, 0, + &acc[shift], *mer) + + shift; + else { // extend acc with a 0; it will be used shortly + *(acc+accunits)=0; // [this avoids length of <=0 later] + accunits++; + } + // multiply multiplicand by 10**DECDPUN for next Unit to left + shift++; // add this for 'logical length' + } // n + #if FASTMUL + } // unchunked units + #endif + // common end-path + #if DECTRACE + decDumpAr('*', acc, accunits); // Show exact result + #endif + + // acc now contains the exact result of the multiplication, + // possibly with a leading zero unit; build the decNumber from + // it, noting if any residue + res->bits=bits; // set sign + res->digits=decGetDigits(acc, accunits); // count digits exactly + + // There can be a 31-bit wrap in calculating the exponent. + // This can only happen if both input exponents are negative and + // both their magnitudes are large. If there was a wrap, set a + // safe very negative exponent, from which decFinalize() will + // raise a hard underflow shortly. + exponent=lhs->exponent+rhs->exponent; // calculate exponent + if (lhs->exponent<0 && rhs->exponent<0 && exponent>0) + exponent=-2*DECNUMMAXE; // force underflow + res->exponent=exponent; // OK to overwrite now + + + // Set the coefficient. If any rounding, residue records + decSetCoeff(res, set, acc, res->digits, &residue, status); + decFinish(res, set, &residue, status); // final cleanup + } while(0); // end protected + + if (allocacc!=NULL) free(allocacc); // drop any storage used + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // .. + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + #if FASTMUL + if (allocrhi!=NULL) free(allocrhi); // .. + if (alloclhi!=NULL) free(alloclhi); // .. + #endif + return res; + } // decMultiplyOp + +/* ------------------------------------------------------------------ */ +/* decExpOp -- effect exponentiation */ +/* */ +/* This computes C = exp(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. status is updated but */ +/* not set. */ +/* */ +/* Restrictions: */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* */ +/* Finite results will always be full precision and Inexact, except */ +/* when A is a zero or -Infinity (giving 1 or 0 respectively). */ +/* ------------------------------------------------------------------ */ +/* This approach used here is similar to the algorithm described in */ +/* */ +/* Variable Precision Exponential Function, T. E. Hull and */ +/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */ +/* pp79-91, ACM, June 1986. */ +/* */ +/* with the main difference being that the iterations in the series */ +/* evaluation are terminated dynamically (which does not require the */ +/* extra variable-precision variables which are expensive in this */ +/* context). */ +/* */ +/* The error analysis in Hull & Abrham's paper applies except for the */ +/* round-off error accumulation during the series evaluation. This */ +/* code does not precalculate the number of iterations and so cannot */ +/* use Horner's scheme. Instead, the accumulation is done at double- */ +/* precision, which ensures that the additions of the terms are exact */ +/* and do not accumulate round-off (and any round-off errors in the */ +/* terms themselves move 'to the right' faster than they can */ +/* accumulate). This code also extends the calculation by allowing, */ +/* in the spirit of other decNumber operators, the input to be more */ +/* precise than the result (the precision used is based on the more */ +/* precise of the input or requested result). */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decExpOp so it can be called from */ +/* other Mathematical functions (notably Ln) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (double) range needed by Ln (which has to be able to calculate */ +/* exp(-x) where x can be the tiniest number (Ntiny). */ +/* */ +/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */ +/* iterations by appoximately a third with additional (although */ +/* diminishing) returns as the range is reduced to even smaller */ +/* fractions. However, h (the power of 10 used to correct the */ +/* result at the end, see below) must be kept <=8 as otherwise */ +/* the final result cannot be computed. Hence the leverage is a */ +/* sliding value (8-h), where potentially the range is reduced */ +/* more for smaller values. */ +/* */ +/* The leverage that can be applied in this way is severely */ +/* limited by the cost of the raise-to-the power at the end, */ +/* which dominates when the number of iterations is small (less */ +/* than ten) or when rhs is short. As an example, the adjustment */ +/* x**10,000,000 needs 31 multiplications, all but one full-width. */ +/* */ +/* 3. The restrictions (especially precision) could be raised with */ +/* care, but the full decNumber range seems very hard within the */ +/* 32-bit limits. */ +/* */ +/* 4. The working precisions for the static buffers are twice the */ +/* obvious size to allow for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decExpOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; // working status + Int h; // adjusted exponent for 0.xxxx + Int p; // working precision + Int residue; // rounding residue + uInt needbytes; // for space calculations + const decNumber *x=rhs; // (may point to safe copy later) + decContext aset, tset, dset; // working contexts + Int comp; // work + + // the argument is often copied to normalize it, so (unusually) it + // is treated like other buffers, using DECBUFFER, +1 in case + // DECBUFFER is 0 + decNumber bufr[D2N(DECBUFFER*2+1)]; + decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated + + // the working precision will be no more than set->digits+8+1 + // so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER + // is 0 (and twice that for the accumulator) + + // buffer for t, term (working precision plus) + decNumber buft[D2N(DECBUFFER*2+9+1)]; + decNumber *allocbuft=NULL; // -> allocated buft, iff allocated + decNumber *t=buft; // term + // buffer for a, accumulator (working precision * 2), at least 9 + decNumber bufa[D2N(DECBUFFER*4+18+1)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *a=bufa; // accumulator + // decNumber for the divisor term; this needs at most 9 digits + // and so can be fixed size [16 so can use standard context] + decNumber bufd[D2N(16)]; + decNumber *d=bufd; // divisor + decNumber numone; // constant 1 + + #if DECCHECK + Int iterations=0; // for later sanity check + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + if (SPECIALARG) { // handle infinities and NaNs + if (decNumberIsInfinite(rhs)) { // an infinity + if (decNumberIsNegative(rhs)) // -Infinity -> +0 + decNumberZero(res); + else decNumberCopy(res, rhs); // +Infinity -> self + } + else decNaNs(res, rhs, NULL, set, status); // a NaN + break;} + + if (ISZERO(rhs)) { // zeros -> exact 1 + decNumberZero(res); // make clean 1 + *res->lsu=1; // .. + break;} // [no status to set] + + // e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path + // positive and negative tiny cases which will result in inexact + // 1. This also allows the later add-accumulate to always be + // exact (because its length will never be more than twice the + // working precision). + // The comparator (tiny) needs just one digit, so use the + // decNumber d for it (reused as the divisor, etc., below); its + // exponent is such that if x is positive it will have + // set->digits-1 zeros between the decimal point and the digit, + // which is 4, and if x is negative one more zero there as the + // more precise result will be of the form 0.9999999 rather than + // 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0 + // or 0.00000004 if digits=7 and x<0. If RHS not larger than + // this then the result will be 1.000000 + decNumberZero(d); // clean + *d->lsu=4; // set 4 .. + d->exponent=-set->digits; // * 10**(-d) + if (decNumberIsNegative(rhs)) d->exponent--; // negative case + comp=decCompare(d, rhs, 1); // signless compare + if (comp==BADINT) { + *status|=DEC_Insufficient_storage; + break;} + if (comp>=0) { // rhs < d + Int shift=set->digits-1; + decNumberZero(res); // set 1 + *res->lsu=1; // .. + res->digits=decShiftToMost(res->lsu, 1, shift); + res->exponent=-shift; // make 1.0000... + *status|=DEC_Inexact | DEC_Rounded; // .. inexactly + break;} // tiny + + // set up the context to be used for calculating a, as this is + // used on both paths below + decContextDefault(&aset, DEC_INIT_DECIMAL64); + // accumulator bounds are as requested (could underflow) + aset.emax=set->emax; // usual bounds + aset.emin=set->emin; // .. + aset.clamp=0; // and no concrete format + + // calculate the adjusted (Hull & Abrham) exponent (where the + // decimal point is just to the left of the coefficient msd) + h=rhs->exponent+rhs->digits; + // if h>8 then 10**h cannot be calculated safely; however, when + // h=8 then exp(|rhs|) will be at least exp(1E+7) which is at + // least 6.59E+4342944, so (due to the restriction on Emax/Emin) + // overflow (or underflow to 0) is guaranteed -- so this case can + // be handled by simply forcing the appropriate excess + if (h>8) { // overflow/underflow + // set up here so Power call below will over or underflow to + // zero; set accumulator to either 2 or 0.02 + // [stack buffer for a is always big enough for this] + decNumberZero(a); + *a->lsu=2; // not 1 but < exp(1) + if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02 + h=8; // clamp so 10**h computable + p=9; // set a working precision + } + else { // h<=8 + Int maxlever=(rhs->digits>8?1:0); + // [could/should increase this for precisions >40 or so, too] + + // if h is 8, cannot normalize to a lower upper limit because + // the final result will not be computable (see notes above), + // but leverage can be applied whenever h is less than 8. + // Apply as much as possible, up to a MAXLEVER digits, which + // sets the tradeoff against the cost of the later a**(10**h). + // As h is increased, the working precision below also + // increases to compensate for the "constant digits at the + // front" effect. + Int lever=MINI(8-h, maxlever); // leverage attainable + Int use=-rhs->digits-lever; // exponent to use for RHS + h+=lever; // apply leverage selected + if (h<0) { // clamp + use+=h; // [may end up subnormal] + h=0; + } + // Take a copy of RHS if it needs normalization (true whenever x>=1) + if (rhs->exponent!=use) { + decNumber *newrhs=bufr; // assume will fit on stack + needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit); + if (needbytes>sizeof(bufr)) { // need malloc space + allocrhs=(decNumber *)malloc(needbytes); + if (allocrhs==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + newrhs=allocrhs; // use the allocated space + } + decNumberCopy(newrhs, rhs); // copy to safe space + newrhs->exponent=use; // normalize; now <1 + x=newrhs; // ready for use + // decNumberShow(x); + } + + // Now use the usual power series to evaluate exp(x). The + // series starts as 1 + x + x^2/2 ... so prime ready for the + // third term by setting the term variable t=x, the accumulator + // a=1, and the divisor d=2. + + // First determine the working precision. From Hull & Abrham + // this is set->digits+h+2. However, if x is 'over-precise' we + // need to allow for all its digits to potentially participate + // (consider an x where all the excess digits are 9s) so in + // this case use x->digits+h+2 + p=MAXI(x->digits, set->digits)+h+2; // [h<=8] + + // a and t are variable precision, and depend on p, so space + // must be allocated for them if necessary + + // the accumulator needs to be able to hold 2p digits so that + // the additions on the second and subsequent iterations are + // sufficiently exact. + needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + // the term needs to be able to hold p digits (which is + // guaranteed to be larger than x->digits, so the initial copy + // is safe); it may also be used for the raise-to-power + // calculation below, which needs an extra two digits + needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit); + if (needbytes>sizeof(buft)) { // need malloc space + allocbuft=(decNumber *)malloc(needbytes); + if (allocbuft==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + t=allocbuft; // use the allocated space + } + + decNumberCopy(t, x); // term=x + decNumberZero(a); *a->lsu=1; // accumulator=1 + decNumberZero(d); *d->lsu=2; // divisor=2 + decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment + + // set up the contexts for calculating a, t, and d + decContextDefault(&tset, DEC_INIT_DECIMAL64); + dset=tset; + // accumulator bounds are set above, set precision now + aset.digits=p*2; // double + // term bounds avoid any underflow or overflow + tset.digits=p; + tset.emin=DEC_MIN_EMIN; // [emax is plenty] + // [dset.digits=16, etc., are sufficient] + + // finally ready to roll + for (;;) { + #if DECCHECK + iterations++; + #endif + // only the status from the accumulation is interesting + // [but it should remain unchanged after first add] + decAddOp(a, a, t, &aset, 0, status); // a=a+t + decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x + decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d + // the iteration ends when the term cannot affect the result, + // if rounded to p digits, which is when its value is smaller + // than the accumulator by p+1 digits. There must also be + // full precision in a. + if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1)) + && (a->digits>=p)) break; + decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1 + } // iterate + + #if DECCHECK + // just a sanity check; comment out test to show always + if (iterations>p+3) + printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + (LI)iterations, (LI)*status, (LI)p, (LI)x->digits); + #endif + } // h<=8 + + // apply postconditioning: a=a**(10**h) -- this is calculated + // at a slightly higher precision than Hull & Abrham suggest + if (h>0) { + Int seenbit=0; // set once a 1-bit is seen + Int i; // counter + Int n=powers[h]; // always positive + aset.digits=p+2; // sufficient precision + // avoid the overhead and many extra digits of decNumberPower + // as all that is needed is the short 'multipliers' loop; here + // accumulate the answer into t + decNumberZero(t); *t->lsu=1; // acc=1 + for (i=1;;i++){ // for each bit [top bit ignored] + // abandon if have had overflow or terminal underflow + if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting? + if (*status&DEC_Overflow || ISZERO(t)) break;} + n=n<<1; // move next bit to testable position + if (n<0) { // top bit is set + seenbit=1; // OK, have a significant bit + decMultiplyOp(t, t, a, &aset, status); // acc=acc*x + } + if (i==31) break; // that was the last bit + if (!seenbit) continue; // no need to square 1 + decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square] + } /*i*/ // 32 bits + // decNumberShow(t); + a=t; // and carry on using t instead of a + } + + // Copy and round the result to res + residue=1; // indicate dirt to right .. + if (ISZERO(a)) residue=0; // .. unless underflowed to 0 + aset.digits=set->digits; // [use default rounding] + decCopyFit(res, a, &aset, &residue, status); // copy & shorten + decFinish(res, set, &residue, status); // cleanup/set flags + } while(0); // end protected + + if (allocrhs !=NULL) free(allocrhs); // drop any storage used + if (allocbufa!=NULL) free(allocbufa); // .. + if (allocbuft!=NULL) free(allocbuft); // .. + // [status is handled by caller] + return res; + } // decExpOp + +/* ------------------------------------------------------------------ */ +/* Initial-estimate natural logarithm table */ +/* */ +/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */ +/* The result is a 4-digit encode of the coefficient (c=the */ +/* top 14 bits encoding 0-9999) and a 2-digit encode of the */ +/* exponent (e=the bottom 2 bits encoding 0-3) */ +/* */ +/* The resulting value is given by: */ +/* */ +/* v = -c * 10**(-e-3) */ +/* */ +/* where e and c are extracted from entry k = LNnn[x-10] */ +/* where x is truncated (NB) into the range 10 through 99, */ +/* and then c = k>>2 and e = k&3. */ +/* ------------------------------------------------------------------ */ +const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208, + 6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312, + 5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032, + 39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629, + 29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837, + 22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321, + 15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717, + 10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801, + 5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254, + 10130, 6046, 20055}; + +/* ------------------------------------------------------------------ */ +/* decLnOp -- effect natural logarithm */ +/* */ +/* This computes C = ln(A) */ +/* */ +/* res is C, the result. C may be A */ +/* rhs is A */ +/* set is the context; note that rounding mode has no effect */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Notable cases: */ +/* A<0 -> Invalid */ +/* A=0 -> -Infinity (Exact) */ +/* A=+Infinity -> +Infinity (Exact) */ +/* A=1 exactly -> 0 (Exact) */ +/* */ +/* Restrictions (as for Exp): */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */ +/* bounds or a zero. This is an internal routine, so these */ +/* restrictions are contractual and not enforced. */ +/* */ +/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */ +/* almost always be correctly rounded, but may be up to 1 ulp in */ +/* error in rare cases. */ +/* ------------------------------------------------------------------ */ +/* The result is calculated using Newton's method, with each */ +/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */ +/* Epperson 1989. */ +/* */ +/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */ +/* This has to be calculated at the sum of the precision of x and the */ +/* working precision. */ +/* */ +/* Implementation notes: */ +/* */ +/* 1. This is separated out as decLnOp so it can be called from */ +/* other Mathematical functions (e.g., Log 10) with a wider range */ +/* than normal. In particular, it can handle the slightly wider */ +/* (+9+2) range needed by a power function. */ +/* */ +/* 2. The speed of this function is about 10x slower than exp, as */ +/* it typically needs 4-6 iterations for short numbers, and the */ +/* extra precision needed adds a squaring effect, twice. */ +/* */ +/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */ +/* as these are common requests. ln(10) is used by log10(x). */ +/* */ +/* 4. An iteration might be saved by widening the LNnn table, and */ +/* would certainly save at least one if it were made ten times */ +/* bigger, too (for truncated fractions 0.100 through 0.999). */ +/* However, for most practical evaluations, at least four or five */ +/* iterations will be neede -- so this would only speed up by */ +/* 20-25% and that probably does not justify increasing the table */ +/* size. */ +/* */ +/* 5. The static buffers are larger than might be expected to allow */ +/* for calls from decNumberPower. */ +/* ------------------------------------------------------------------ */ +decNumber * decLnOp(decNumber *res, const decNumber *rhs, + decContext *set, uInt *status) { + uInt ignore=0; // working status accumulator + uInt needbytes; // for space calculations + Int residue; // rounding residue + Int r; // rhs=f*10**r [see below] + Int p; // working precision + Int pp; // precision for iteration + Int t; // work + + // buffers for a (accumulator, typically precision+2) and b + // (adjustment calculator, same size) + decNumber bufa[D2N(DECBUFFER+12)]; + decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated + decNumber *a=bufa; // accumulator/work + decNumber bufb[D2N(DECBUFFER*2+2)]; + decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated + decNumber *b=bufb; // adjustment/work + + decNumber numone; // constant 1 + decNumber cmp; // work + decContext aset, bset; // working contexts + + #if DECCHECK + Int iterations=0; // for later sanity check + if (decCheckOperands(res, DECUNUSED, rhs, set)) return res; + #endif + + do { // protect allocated storage + if (SPECIALARG) { // handle infinities and NaNs + if (decNumberIsInfinite(rhs)) { // an infinity + if (decNumberIsNegative(rhs)) // -Infinity -> error + *status|=DEC_Invalid_operation; + else decNumberCopy(res, rhs); // +Infinity -> self + } + else decNaNs(res, rhs, NULL, set, status); // a NaN + break;} + + if (ISZERO(rhs)) { // +/- zeros -> -Infinity + decNumberZero(res); // make clean + res->bits=DECINF|DECNEG; // set - infinity + break;} // [no status to set] + + // Non-zero negatives are bad... + if (decNumberIsNegative(rhs)) { // -x -> error + *status|=DEC_Invalid_operation; + break;} + + // Here, rhs is positive, finite, and in range + + // lookaside fastpath code for ln(2) and ln(10) at common lengths + if (rhs->exponent==0 && set->digits<=40) { + #if DECDPUN==1 + if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10) + #else + if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10) + #endif + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN10 "2.302585092994045684017991454684364207601" + decNumberFromString(res, LN10, &aset); + *status|=(DEC_Inexact | DEC_Rounded); // is inexact + break;} + if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2) + aset=*set; aset.round=DEC_ROUND_HALF_EVEN; + #define LN2 "0.6931471805599453094172321214581765680755" + decNumberFromString(res, LN2, &aset); + *status|=(DEC_Inexact | DEC_Rounded); + break;} + } // integer and short + + // Determine the working precision. This is normally the + // requested precision + 2, with a minimum of 9. However, if + // the rhs is 'over-precise' then allow for all its digits to + // potentially participate (consider an rhs where all the excess + // digits are 9s) so in this case use rhs->digits+2. + p=MAXI(rhs->digits, MAXI(set->digits, 7))+2; + + // Allocate space for the accumulator and the high-precision + // adjustment calculator, if necessary. The accumulator must + // be able to hold p digits, and the adjustment up to + // rhs->digits+p digits. They are also made big enough for 16 + // digits so that they can be used for calculating the initial + // estimate. + needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufa)) { // need malloc space + allocbufa=(decNumber *)malloc(needbytes); + if (allocbufa==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + a=allocbufa; // use the allocated space + } + pp=p+rhs->digits; + needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit); + if (needbytes>sizeof(bufb)) { // need malloc space + allocbufb=(decNumber *)malloc(needbytes); + if (allocbufb==NULL) { // hopeless -- abandon + *status|=DEC_Insufficient_storage; + break;} + b=allocbufb; // use the allocated space + } + + // Prepare an initial estimate in acc. Calculate this by + // considering the coefficient of x to be a normalized fraction, + // f, with the decimal point at far left and multiplied by + // 10**r. Then, rhs=f*10**r and 0.1<=f<1, and + // ln(x) = ln(f) + ln(10)*r + // Get the initial estimate for ln(f) from a small lookup + // table (see above) indexed by the first two digits of f, + // truncated. + + decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended + r=rhs->exponent+rhs->digits; // 'normalised' exponent + decNumberFromInt32(a, r); // a=r + decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585) + b->exponent=-6; // .. + decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b + // now get top two digits of rhs into b by simple truncate and + // force to integer + residue=0; // (no residue) + aset.digits=2; aset.round=DEC_ROUND_DOWN; + decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten + b->exponent=0; // make integer + t=decGetInt(b); // [cannot fail] + if (t<10) t=X10(t); // adjust single-digit b + t=LNnn[t-10]; // look up ln(b) + decNumberFromInt32(b, t>>2); // b=ln(b) coefficient + b->exponent=-(t&3)-3; // set exponent + b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve + aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore + decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b + // the initial estimate is now in a, with up to 4 digits correct. + // When rhs is at or near Nmax the estimate will be low, so we + // will approach it from below, avoiding overflow when calling exp. + + decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment + + // accumulator bounds are as requested (could underflow, but + // cannot overflow) + aset.emax=set->emax; + aset.emin=set->emin; + aset.clamp=0; // no concrete format + // set up a context to be used for the multiply and subtract + bset=aset; + bset.emax=DEC_MAX_MATH*2; // use double bounds for the + bset.emin=-DEC_MAX_MATH*2; // adjustment calculation + // [see decExpOp call below] + // for each iteration double the number of digits to calculate, + // up to a maximum of p + pp=9; // initial precision + // [initially 9 as then the sequence starts 7+2, 16+2, and + // 34+2, which is ideal for standard-sized numbers] + aset.digits=pp; // working context + bset.digits=pp+rhs->digits; // wider context + for (;;) { // iterate + #if DECCHECK + iterations++; + if (iterations>24) break; // consider 9 * 2**24 + #endif + // calculate the adjustment (exp(-a)*x-1) into b. This is a + // catastrophic subtraction but it really is the difference + // from 1 that is of interest. + // Use the internal entry point to Exp as it allows the double + // range for calculating exp(-a) when a is the tiniest subnormal. + a->bits^=DECNEG; // make -a + decExpOp(b, a, &bset, &ignore); // b=exp(-a) + a->bits^=DECNEG; // restore sign of a + // now multiply by rhs and subtract 1, at the wider precision + decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs + decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1 + + // the iteration ends when the adjustment cannot affect the + // result by >=0.5 ulp (at the requested digits), which + // is when its value is smaller than the accumulator by + // set->digits+1 digits (or it is zero) -- this is a looser + // requirement than for Exp because all that happens to the + // accumulator after this is the final rounding (but note that + // there must also be full precision in a, or a=0). + + if (decNumberIsZero(b) || + (a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) { + if (a->digits==p) break; + if (decNumberIsZero(a)) { + decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ? + if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0 + else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact + break; + } + // force padding if adjustment has gone to 0 before full length + if (decNumberIsZero(b)) b->exponent=a->exponent-p; + } + + // not done yet ... + decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate + if (pp==p) continue; // precision is at maximum + // lengthen the next calculation + pp=pp*2; // double precision + if (pp>p) pp=p; // clamp to maximum + aset.digits=pp; // working context + bset.digits=pp+rhs->digits; // wider context + } // Newton's iteration + + #if DECCHECK + // just a sanity check; remove the test to show always + if (iterations>24) + printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n", + (LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits); + #endif + + // Copy and round the result to res + residue=1; // indicate dirt to right + if (ISZERO(a)) residue=0; // .. unless underflowed to 0 + aset.digits=set->digits; // [use default rounding] + decCopyFit(res, a, &aset, &residue, status); // copy & shorten + decFinish(res, set, &residue, status); // cleanup/set flags + } while(0); // end protected + + if (allocbufa!=NULL) free(allocbufa); // drop any storage used + if (allocbufb!=NULL) free(allocbufb); // .. + // [status is handled by caller] + return res; + } // decLnOp + +/* ------------------------------------------------------------------ */ +/* decQuantizeOp -- force exponent to requested value */ +/* */ +/* This computes C = op(A, B), where op adjusts the coefficient */ +/* of C (by rounding or shifting) such that the exponent (-scale) */ +/* of C has the value B or matches the exponent of B. */ +/* The numerical value of C will equal A, except for the effects of */ +/* any rounding that occurred. */ +/* */ +/* res is C, the result. C may be A or B */ +/* lhs is A, the number to adjust */ +/* rhs is B, the requested exponent */ +/* set is the context */ +/* quant is 1 for quantize or 0 for rescale */ +/* status is the status accumulator (this can be called without */ +/* risk of control loss) */ +/* */ +/* C must have space for set->digits digits. */ +/* */ +/* Unless there is an error or the result is infinite, the exponent */ +/* after the operation is guaranteed to be that requested. */ +/* ------------------------------------------------------------------ */ +static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + Flag quant, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + const decNumber *inrhs=rhs; // save original rhs + Int reqdigits=set->digits; // requested DIGITS + Int reqexp; // requested exponent [-scale] + Int residue=0; // rounding residue + Int etiny=set->emin-(reqdigits-1); + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>reqdigits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) break; + lhs=alloclhs; + } + if (rhs->digits>reqdigits) { // [this only checks lostDigits] + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) break; + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // Handle special values + if (SPECIALARGS) { + // NaNs get usual processing + if (SPECIALARGS & (DECSNAN | DECNAN)) + decNaNs(res, lhs, rhs, set, status); + // one infinity but not both is bad + else if ((lhs->bits ^ rhs->bits) & DECINF) + *status|=DEC_Invalid_operation; + // both infinity: return lhs + else decNumberCopy(res, lhs); // [nop if in place] + break; + } + + // set requested exponent + if (quant) reqexp=inrhs->exponent; // quantize -- match exponents + else { // rescale -- use value of rhs + // Original rhs must be an integer that fits and is in range, + // which could be from -1999999997 to +999999999, thanks to + // subnormals + reqexp=decGetInt(inrhs); // [cannot fail] + } + + #if DECSUBSET + if (!set->extended) etiny=set->emin; // no subnormals + #endif + + if (reqexp==BADINT // bad (rescale only) or .. + || reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or .. + || (reqexpset->emax)) { // > emax + *status|=DEC_Invalid_operation; + break;} + + // the RHS has been processed, so it can be overwritten now if necessary + if (ISZERO(lhs)) { // zero coefficient unchanged + decNumberCopy(res, lhs); // [nop if in place] + res->exponent=reqexp; // .. just set exponent + #if DECSUBSET + if (!set->extended) res->bits=0; // subset specification; no -0 + #endif + } + else { // non-zero lhs + Int adjust=reqexp-lhs->exponent; // digit adjustment needed + // if adjusted coefficient will definitely not fit, give up now + if ((lhs->digits-adjust)>reqdigits) { + *status|=DEC_Invalid_operation; + break; + } + + if (adjust>0) { // increasing exponent + // this will decrease the length of the coefficient by adjust + // digits, and must round as it does so + decContext workset; // work + workset=*set; // clone rounding, etc. + workset.digits=lhs->digits-adjust; // set requested length + // [note that the latter can be <1, here] + decCopyFit(res, lhs, &workset, &residue, status); // fit to result + decApplyRound(res, &workset, residue, status); // .. and round + residue=0; // [used] + // If just rounded a 999s case, exponent will be off by one; + // adjust back (after checking space), if so. + if (res->exponent>reqexp) { + // re-check needed, e.g., for quantize(0.9999, 0.001) under + // set->digits==3 + if (res->digits==reqdigits) { // cannot shift by 1 + *status&=~(DEC_Inexact | DEC_Rounded); // [clean these] + *status|=DEC_Invalid_operation; + break; + } + res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift + res->exponent--; // (re)adjust the exponent. + } + #if DECSUBSET + if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0 + #endif + } // increase + else /* adjust<=0 */ { // decreasing or = exponent + // this will increase the length of the coefficient by -adjust + // digits, by adding zero or more trailing zeros; this is + // already checked for fit, above + decNumberCopy(res, lhs); // [it will fit] + // if padding needed (adjust<0), add it now... + if (adjust<0) { + res->digits=decShiftToMost(res->lsu, res->digits, -adjust); + res->exponent+=adjust; // adjust the exponent + } + } // decrease + } // non-zero + + // Check for overflow [do not use Finalize in this case, as an + // overflow here is a "don't fit" situation] + if (res->exponent>set->emax-res->digits+1) { // too big + *status|=DEC_Invalid_operation; + break; + } + else { + decFinalize(res, set, &residue, status); // set subnormal flags + *status&=~DEC_Underflow; // suppress Underflow [as per 754] + } + } while(0); // end protected + + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // drop any storage used + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decQuantizeOp + +/* ------------------------------------------------------------------ */ +/* decCompareOp -- compare, min, or max two Numbers */ +/* */ +/* This computes C = A ? B and carries out one of four operations: */ +/* COMPARE -- returns the signum (as a number) giving the */ +/* result of a comparison unless one or both */ +/* operands is a NaN (in which case a NaN results) */ +/* COMPSIG -- as COMPARE except that a quiet NaN raises */ +/* Invalid operation. */ +/* COMPMAX -- returns the larger of the operands, using the */ +/* 754 maxnum operation */ +/* COMPMAXMAG -- ditto, comparing absolute values */ +/* COMPMIN -- the 754 minnum operation */ +/* COMPMINMAG -- ditto, comparing absolute values */ +/* COMTOTAL -- returns the signum (as a number) giving the */ +/* result of a comparison using 754 total ordering */ +/* */ +/* res is C, the result. C may be A and/or B (e.g., X=X?X) */ +/* lhs is A */ +/* rhs is B */ +/* set is the context */ +/* op is the operation flag */ +/* status is the usual accumulator */ +/* */ +/* C must have space for one digit for COMPARE or set->digits for */ +/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */ +/* ------------------------------------------------------------------ */ +/* The emphasis here is on speed for common cases, and avoiding */ +/* coefficient comparison if possible. */ +/* ------------------------------------------------------------------ */ +decNumber * decCompareOp(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + Flag op, uInt *status) { + #if DECSUBSET + decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated + decNumber *allocrhs=NULL; // .., rhs + #endif + Int result=0; // default result value + uByte merged; // work + + #if DECCHECK + if (decCheckOperands(res, lhs, rhs, set)) return res; + #endif + + do { // protect allocated storage + #if DECSUBSET + if (!set->extended) { + // reduce operands and set lostDigits status, as needed + if (lhs->digits>set->digits) { + alloclhs=decRoundOperand(lhs, set, status); + if (alloclhs==NULL) {result=BADINT; break;} + lhs=alloclhs; + } + if (rhs->digits>set->digits) { + allocrhs=decRoundOperand(rhs, set, status); + if (allocrhs==NULL) {result=BADINT; break;} + rhs=allocrhs; + } + } + #endif + // [following code does not require input rounding] + + // If total ordering then handle differing signs 'up front' + if (op==COMPTOTAL) { // total ordering + if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) { + result=-1; + break; + } + if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) { + result=+1; + break; + } + } + + // handle NaNs specially; let infinities drop through + // This assumes sNaN (even just one) leads to NaN. + merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN); + if (merged) { // a NaN bit set + if (op==COMPARE); // result will be NaN + else if (op==COMPSIG) // treat qNaN as sNaN + *status|=DEC_Invalid_operation | DEC_sNaN; + else if (op==COMPTOTAL) { // total ordering, always finite + // signs are known to be the same; compute the ordering here + // as if the signs are both positive, then invert for negatives + if (!decNumberIsNaN(lhs)) result=-1; + else if (!decNumberIsNaN(rhs)) result=+1; + // here if both NaNs + else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1; + else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1; + else { // both NaN or both sNaN + // now it just depends on the payload + result=decUnitCompare(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), 0); + // [Error not possible, as these are 'aligned'] + } // both same NaNs + if (decNumberIsNegative(lhs)) result=-result; + break; + } // total order + + else if (merged & DECSNAN); // sNaN -> qNaN + else { // here if MIN or MAX and one or two quiet NaNs + // min or max -- 754 rules ignore single NaN + if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) { + // just one NaN; force choice to be the non-NaN operand + op=COMPMAX; + if (lhs->bits & DECNAN) result=-1; // pick rhs + else result=+1; // pick lhs + break; + } + } // max or min + op=COMPNAN; // use special path + decNaNs(res, lhs, rhs, set, status); // propagate NaN + break; + } + // have numbers + if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1); + else result=decCompare(lhs, rhs, 0); // sign matters + } while(0); // end protected + + if (result==BADINT) *status|=DEC_Insufficient_storage; // rare + else { + if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum + if (op==COMPTOTAL && result==0) { + // operands are numerically equal or same NaN (and same sign, + // tested first); if identical, leave result 0 + if (lhs->exponent!=rhs->exponent) { + if (lhs->exponentexponent) result=-1; + else result=+1; + if (decNumberIsNegative(lhs)) result=-result; + } // lexp!=rexp + } // total-order by exponent + decNumberZero(res); // [always a valid result] + if (result!=0) { // must be -1 or +1 + *res->lsu=1; + if (result<0) res->bits=DECNEG; + } + } + else if (op==COMPNAN); // special, drop through + else { // MAX or MIN, non-NaN result + Int residue=0; // rounding accumulator + // choose the operand for the result + const decNumber *choice; + if (result==0) { // operands are numerically equal + // choose according to sign then exponent (see 754) + uByte slhs=(lhs->bits & DECNEG); + uByte srhs=(rhs->bits & DECNEG); + #if DECSUBSET + if (!set->extended) { // subset: force left-hand + op=COMPMAX; + result=+1; + } + else + #endif + if (slhs!=srhs) { // signs differ + if (slhs) result=-1; // rhs is max + else result=+1; // lhs is max + } + else if (slhs && srhs) { // both negative + if (lhs->exponentexponent) result=+1; + else result=-1; + // [if equal, use lhs, technically identical] + } + else { // both positive + if (lhs->exponent>rhs->exponent) result=+1; + else result=-1; + // [ditto] + } + } // numerically equal + // here result will be non-0; reverse if looking for MIN + if (op==COMPMIN || op==COMPMINMAG) result=-result; + choice=(result>0 ? lhs : rhs); // choose + // copy chosen to result, rounding if need be + decCopyFit(res, choice, set, &residue, status); + decFinish(res, set, &residue, status); + } + } + #if DECSUBSET + if (allocrhs!=NULL) free(allocrhs); // free any storage used + if (alloclhs!=NULL) free(alloclhs); // .. + #endif + return res; + } // decCompareOp + +/* ------------------------------------------------------------------ */ +/* decCompare -- compare two decNumbers by numerical value */ +/* */ +/* This routine compares A ? B without altering them. */ +/* */ +/* Arg1 is A, a decNumber which is not a NaN */ +/* Arg2 is B, a decNumber which is not a NaN */ +/* Arg3 is 1 for a sign-independent compare, 0 otherwise */ +/* */ +/* returns -1, 0, or 1 for AB, or BADINT if failure */ +/* (the only possible failure is an allocation error) */ +/* ------------------------------------------------------------------ */ +static Int decCompare(const decNumber *lhs, const decNumber *rhs, + Flag abs) { + Int result; // result value + Int sigr; // rhs signum + Int compare; // work + + result=1; // assume signum(lhs) + if (ISZERO(lhs)) result=0; + if (abs) { + if (ISZERO(rhs)) return result; // LHS wins or both 0 + // RHS is non-zero + if (result==0) return -1; // LHS is 0; RHS wins + // [here, both non-zero, result=1] + } + else { // signs matter + if (result && decNumberIsNegative(lhs)) result=-1; + sigr=1; // compute signum(rhs) + if (ISZERO(rhs)) sigr=0; + else if (decNumberIsNegative(rhs)) sigr=-1; + if (result > sigr) return +1; // L > R, return 1 + if (result < sigr) return -1; // L < R, return -1 + if (result==0) return 0; // both 0 + } + + // signums are the same; both are non-zero + if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities + if (decNumberIsInfinite(rhs)) { + if (decNumberIsInfinite(lhs)) result=0;// both infinite + else result=-result; // only rhs infinite + } + return result; + } + // must compare the coefficients, allowing for exponents + if (lhs->exponent>rhs->exponent) { // LHS exponent larger + // swap sides, and sign + const decNumber *temp=lhs; + lhs=rhs; + rhs=temp; + result=-result; + } + compare=decUnitCompare(lhs->lsu, D2U(lhs->digits), + rhs->lsu, D2U(rhs->digits), + rhs->exponent-lhs->exponent); + if (compare!=BADINT) compare*=result; // comparison succeeded + return compare; + } // decCompare + +/* ------------------------------------------------------------------ */ +/* decUnitCompare -- compare two >=0 integers in Unit arrays */ +/* */ +/* This routine compares A ? B*10**E where A and B are unit arrays */ +/* A is a plain integer */ +/* B has an exponent of E (which must be non-negative) */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is E (0 if the units are aligned) */ +/* */ +/* returns -1, 0, or 1 for AB, or BADINT if failure */ +/* (the only possible failure is an allocation error, which can */ +/* only occur if E!=0) */ +/* ------------------------------------------------------------------ */ +static Int decUnitCompare(const Unit *a, Int alength, + const Unit *b, Int blength, Int exp) { + Unit *acc; // accumulator for result + Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer + Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated + Int accunits, need; // units in use or needed for acc + const Unit *l, *r, *u; // work + Int expunits, exprem, result; // .. + + if (exp==0) { // aligned; fastpath + if (alength>blength) return 1; + if (alength=a; l--, r--) { + if (*l>*r) return 1; + if (*l<*r) return -1; + } + return 0; // all units match + } // aligned + + // Unaligned. If one is >1 unit longer than the other, padded + // approximately, then can return easily + if (alength>blength+(Int)D2U(exp)) return 1; + if (alength+1sizeof(accbuff)) { + allocacc=(Unit *)malloc(need*sizeof(Unit)); + if (allocacc==NULL) return BADINT; // hopeless -- abandon + acc=allocacc; + } + // Calculate units and remainder from exponent. + expunits=exp/DECDPUN; + exprem=exp%DECDPUN; + // subtract [A+B*(-m)] + accunits=decUnitAddSub(a, alength, b, blength, expunits, acc, + -(Int)powers[exprem]); + // [UnitAddSub result may have leading zeros, even on zero] + if (accunits<0) result=-1; // negative result + else { // non-negative result + // check units of the result before freeing any storage + for (u=acc; u=0 integers in Unit arrays */ +/* */ +/* This routine performs the calculation: */ +/* */ +/* C=A+(B*M) */ +/* */ +/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */ +/* */ +/* A may be shorter or longer than B. */ +/* */ +/* Leading zeros are not removed after a calculation. The result is */ +/* either the same length as the longer of A and B (adding any */ +/* shift), or one Unit longer than that (if a Unit carry occurred). */ +/* */ +/* A and B content are not altered unless C is also A or B. */ +/* C may be the same array as A or B, but only if no zero padding is */ +/* requested (that is, C may be B only if bshift==0). */ +/* C is filled from the lsu; only those units necessary to complete */ +/* the calculation are referenced. */ +/* */ +/* Arg1 is A first Unit (lsu) */ +/* Arg2 is A length in Units */ +/* Arg3 is B first Unit (lsu) */ +/* Arg4 is B length in Units */ +/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */ +/* Arg6 is C first Unit (lsu) */ +/* Arg7 is M, the multiplier */ +/* */ +/* returns the count of Units written to C, which will be non-zero */ +/* and negated if the result is negative. That is, the sign of the */ +/* returned Int is the sign of the result (positive for zero) and */ +/* the absolute value of the Int is the count of Units. */ +/* */ +/* It is the caller's responsibility to make sure that C size is */ +/* safe, allowing space if necessary for a one-Unit carry. */ +/* */ +/* This routine is severely performance-critical; *any* change here */ +/* must be measured (timed) to assure no performance degradation. */ +/* In particular, trickery here tends to be counter-productive, as */ +/* increased complexity of code hurts register optimizations on */ +/* register-poor architectures. Avoiding divisions is nearly */ +/* always a Good Idea, however. */ +/* */ +/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */ +/* (IBM Warwick, UK) for some of the ideas used in this routine. */ +/* ------------------------------------------------------------------ */ +static Int decUnitAddSub(const Unit *a, Int alength, + const Unit *b, Int blength, Int bshift, + Unit *c, Int m) { + const Unit *alsu=a; // A lsu [need to remember it] + Unit *clsu=c; // C ditto + Unit *minC; // low water mark for C + Unit *maxC; // high water mark for C + eInt carry=0; // carry integer (could be Long) + Int add; // work + #if DECDPUN<=4 // myriadal, millenary, etc. + Int est; // estimated quotient + #endif + + #if DECTRACE + if (alength<1 || blength<1) + printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m); + #endif + + maxC=c+alength; // A is usually the longer + minC=c+blength; // .. and B the shorter + if (bshift!=0) { // B is shifted; low As copy across + minC+=bshift; + // if in place [common], skip copy unless there's a gap [rare] + if (a==c && bshift<=alength) { + c+=bshift; + a+=bshift; + } + else for (; cmaxC) { // swap + Unit *hold=minC; + minC=maxC; + maxC=hold; + } + + // For speed, do the addition as two loops; the first where both A + // and B contribute, and the second (if necessary) where only one or + // other of the numbers contribute. + // Carry handling is the same (i.e., duplicated) in each case. + for (; c=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [89%] + if (*c>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [99%] + if (*c>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // quotient + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + #else + // remainder operator is undefined if negative, so must test + if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1 + *c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions] + carry=1; + continue; + } + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } // c + + // now may have one or other to complete + // [pretest to avoid loop setup/shutdown] + if (cDECDPUNMAX + #if DECDPUN==4 // use divide-by-multiply + if (carry>=0) { + est=(((ueInt)carry>>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [79.7%] + if (*c>11)*53687)>>18; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c=0) { + est=(((ueInt)carry>>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // likely quotient [99%] + if (*c>3)*16777)>>21; + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + if (*c=0) { + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder + carry=est; // quotient + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + est=QUOT10(carry, DECDPUN); + *c=(Unit)(carry-est*(DECDPUNMAX+1)); + carry=est-(DECDPUNMAX+1); // correctly negative + #else + if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1 + *c=(Unit)(carry-(DECDPUNMAX+1)); + carry=1; + continue; + } + // remainder operator is undefined if negative, so must test + if (carry>=0) { + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1); + continue; + } + // negative case + carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive + *c=(Unit)(carry%(DECDPUNMAX+1)); + carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1); + #endif + } // c + + // OK, all A and B processed; might still have carry or borrow + // return number of Units in the result, negated if a borrow + if (carry==0) return c-clsu; // no carry, so no more to do + if (carry>0) { // positive carry + *c=(Unit)carry; // place as new unit + c++; // .. + return c-clsu; + } + // -ve carry: it's a borrow; complement needed + add=1; // temporary carry... + for (c=clsu; c current Unit + + #if DECCHECK + if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn; + #endif + + *dropped=0; // assume no zeros dropped + if ((dn->bits & DECSPECIAL) // fast exit if special .. + || (*dn->lsu & 0x01)) return dn; // .. or odd + if (ISZERO(dn)) { // .. or 0 + dn->exponent=0; // (sign is preserved) + return dn; + } + + // have a finite number which is even + exp=dn->exponent; + cut=1; // digit (1-DECDPUN) in Unit + up=dn->lsu; // -> current Unit + for (d=0; ddigits-1; d++) { // [don't strip the final digit] + // slice by powers + #if DECDPUN<=4 + uInt quot=QUOT10(*up, cut); + if ((*up-quot*powers[cut])!=0) break; // found non-0 digit + #else + if (*up%powers[cut]!=0) break; // found non-0 digit + #endif + // have a trailing 0 + if (!all) { // trimming + // [if exp>0 then all trailing 0s are significant for trim] + if (exp<=0) { // if digit might be significant + if (exp==0) break; // then quit + exp++; // next digit might be significant + } + } + cut++; // next power + if (cut>DECDPUN) { // need new Unit + up++; + cut=1; + } + } // d + if (d==0) return dn; // none to drop + + // may need to limit drop if clamping + if (set->clamp && !noclamp) { + Int maxd=set->emax-set->digits+1-dn->exponent; + if (maxd<=0) return dn; // nothing possible + if (d>maxd) d=maxd; + } + + // effect the drop + decShiftToLeast(dn->lsu, D2U(dn->digits), d); + dn->exponent+=d; // maintain numerical value + dn->digits-=d; // new length + *dropped=d; // report the count + return dn; + } // decTrim + +/* ------------------------------------------------------------------ */ +/* decReverse -- reverse a Unit array in place */ +/* */ +/* ulo is the start of the array */ +/* uhi is the end of the array (highest Unit to include) */ +/* */ +/* The units ulo through uhi are reversed in place (if the number */ +/* of units is odd, the middle one is untouched). Note that the */ +/* digit(s) in each unit are unaffected. */ +/* ------------------------------------------------------------------ */ +static void decReverse(Unit *ulo, Unit *uhi) { + Unit temp; + for (; ulo=uar; source--, target--) *target=*source; + } + else { + first=uar+D2U(digits+shift)-1; // where msu of source will end up + for (; source>=uar; source--, target--) { + // split the source Unit and accumulate remainder for next + #if DECDPUN<=4 + uInt quot=QUOT10(*source, cut); + uInt rem=*source-quot*powers[cut]; + next+=quot; + #else + uInt rem=*source%powers[cut]; + next+=*source/powers[cut]; + #endif + if (target<=first) *target=(Unit)next; // write to target iff valid + next=rem*powers[DECDPUN-cut]; // save remainder for next Unit + } + } // shift-move + + // propagate any partial unit to one below and clear the rest + for (; target>=uar; target--) { + *target=(Unit)next; + next=0; + } + return digits+shift; + } // decShiftToMost + +/* ------------------------------------------------------------------ */ +/* decShiftToLeast -- shift digits in array towards least significant */ +/* */ +/* uar is the array */ +/* units is length of the array, in units */ +/* shift is the number of digits to remove from the lsu end; it */ +/* must be zero or positive and <= than units*DECDPUN. */ +/* */ +/* returns the new length of the integer in the array, in units */ +/* */ +/* Removed digits are discarded (lost). Units not required to hold */ +/* the final result are unchanged. */ +/* ------------------------------------------------------------------ */ +static Int decShiftToLeast(Unit *uar, Int units, Int shift) { + Unit *target, *up; // work + Int cut, count; // work + Int quot, rem; // for division + + if (shift==0) return units; // [fastpath] nothing to do + if (shift==units*DECDPUN) { // [fastpath] little to do + *uar=0; // all digits cleared gives zero + return 1; // leaves just the one + } + + target=uar; // both paths + cut=MSUDIGITS(shift); + if (cut==DECDPUN) { // unit-boundary case; easy + up=uar+D2U(shift); + for (; updigits is > set->digits) */ +/* set is the relevant context */ +/* status is the status accumulator */ +/* */ +/* returns an allocated decNumber with the rounded result. */ +/* */ +/* lostDigits and other status may be set by this. */ +/* */ +/* Since the input is an operand, it must not be modified. */ +/* Instead, return an allocated decNumber, rounded as required. */ +/* It is the caller's responsibility to free the allocated storage. */ +/* */ +/* If no storage is available then the result cannot be used, so NULL */ +/* is returned. */ +/* ------------------------------------------------------------------ */ +static decNumber *decRoundOperand(const decNumber *dn, decContext *set, + uInt *status) { + decNumber *res; // result structure + uInt newstatus=0; // status from round + Int residue=0; // rounding accumulator + + // Allocate storage for the returned decNumber, big enough for the + // length specified by the context + res=(decNumber *)malloc(sizeof(decNumber) + +(D2U(set->digits)-1)*sizeof(Unit)); + if (res==NULL) { + *status|=DEC_Insufficient_storage; + return NULL; + } + decCopyFit(res, dn, set, &residue, &newstatus); + decApplyRound(res, set, residue, &newstatus); + + // If that set Inexact then "lost digits" is raised... + if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits; + *status|=newstatus; + return res; + } // decRoundOperand +#endif + +/* ------------------------------------------------------------------ */ +/* decCopyFit -- copy a number, truncating the coefficient if needed */ +/* */ +/* dest is the target decNumber */ +/* src is the source decNumber */ +/* set is the context [used for length (digits) and rounding mode] */ +/* residue is the residue accumulator */ +/* status contains the current status to be updated */ +/* */ +/* (dest==src is allowed and will be a no-op if fits) */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decCopyFit(decNumber *dest, const decNumber *src, + decContext *set, Int *residue, uInt *status) { + dest->bits=src->bits; + dest->exponent=src->exponent; + decSetCoeff(dest, set, src->lsu, src->digits, residue, status); + } // decCopyFit + +/* ------------------------------------------------------------------ */ +/* decSetCoeff -- set the coefficient of a number */ +/* */ +/* dn is the number whose coefficient array is to be set. */ +/* It must have space for set->digits digits */ +/* set is the context [for size] */ +/* lsu -> lsu of the source coefficient [may be dn->lsu] */ +/* len is digits in the source coefficient [may be dn->digits] */ +/* residue is the residue accumulator. This has values as in */ +/* decApplyRound, and will be unchanged unless the */ +/* target size is less than len. In this case, the */ +/* coefficient is truncated and the residue is updated to */ +/* reflect the previous residue and the dropped digits. */ +/* status is the status accumulator, as usual */ +/* */ +/* The coefficient may already be in the number, or it can be an */ +/* external intermediate array. If it is in the number, lsu must == */ +/* dn->lsu and len must == dn->digits. */ +/* */ +/* Note that the coefficient length (len) may be < set->digits, and */ +/* in this case this merely copies the coefficient (or is a no-op */ +/* if dn->lsu==lsu). */ +/* */ +/* Note also that (only internally, from decQuantizeOp and */ +/* decSetSubnormal) the value of set->digits may be less than one, */ +/* indicating a round to left. This routine handles that case */ +/* correctly; caller ensures space. */ +/* */ +/* dn->digits, dn->lsu (and as required), and dn->exponent are */ +/* updated as necessary. dn->bits (sign) is unchanged. */ +/* */ +/* DEC_Rounded status is set if any digits are discarded. */ +/* DEC_Inexact status is set if any non-zero digits are discarded, or */ +/* incoming residue was non-0 (implies rounded) */ +/* ------------------------------------------------------------------ */ +// mapping array: maps 0-9 to canonical residues, so that a residue +// can be adjusted in the range [-1, +1] and achieve correct rounding +// 0 1 2 3 4 5 6 7 8 9 +static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7}; +static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu, + Int len, Int *residue, uInt *status) { + Int discard; // number of digits to discard + uInt cut; // cut point in Unit + const Unit *up; // work + Unit *target; // .. + Int count; // .. + #if DECDPUN<=4 + uInt temp; // .. + #endif + + discard=len-set->digits; // digits to discard + if (discard<=0) { // no digits are being discarded + if (dn->lsu!=lsu) { // copy needed + // copy the coefficient array to the result number; no shift needed + count=len; // avoids D2U + up=lsu; + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) + *target=*up; + dn->digits=len; // set the new length + } + // dn->exponent and residue are unchanged, record any inexactitude + if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded); + return; + } + + // some digits must be discarded ... + dn->exponent+=discard; // maintain numerical value + *status|=DEC_Rounded; // accumulate Rounded status + if (*residue>1) *residue=1; // previous residue now to right, so reduce + + if (discard>len) { // everything, +1, is being discarded + // guard digit is 0 + // residue is all the number [NB could be all 0s] + if (*residue<=0) { // not already positive + count=len; // avoids D2U + for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0 + *residue=1; + break; // no need to check any others + } + } + if (*residue!=0) *status|=DEC_Inexact; // record inexactitude + *dn->lsu=0; // coefficient will now be 0 + dn->digits=1; // .. + return; + } // total discard + + // partial discard [most common case] + // here, at least the first (most significant) discarded digit exists + + // spin up the number, noting residue during the spin, until get to + // the Unit with the first discarded digit. When reach it, extract + // it and remember its position + count=0; + for (up=lsu;; up++) { + count+=DECDPUN; + if (count>=discard) break; // full ones all checked + if (*up!=0) *residue=1; + } // up + + // here up -> Unit with first discarded digit + cut=discard-(count-DECDPUN)-1; + if (cut==DECDPUN-1) { // unit-boundary case (fast) + Unit half=(Unit)powers[DECDPUN]>>1; + // set residue directly + if (*up>=half) { + if (*up>half) *residue=7; + else *residue+=5; // add sticky bit + } + else { // digits<=0) { // special for Quantize/Subnormal :-( + *dn->lsu=0; // .. result is 0 + dn->digits=1; // .. + } + else { // shift to least + count=set->digits; // now digits to end up with + dn->digits=count; // set the new length + up++; // move to next + // on unit boundary, so shift-down copy loop is simple + for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN) + *target=*up; + } + } // unit-boundary case + + else { // discard digit is in low digit(s), and not top digit + uInt discard1; // first discarded digit + uInt quot, rem; // for divisions + if (cut==0) quot=*up; // is at bottom of unit + else /* cut>0 */ { // it's not at bottom of unit + #if DECDPUN<=4 + quot=QUOT10(*up, cut); + rem=*up-quot*powers[cut]; + #else + rem=*up%powers[cut]; + quot=*up/powers[cut]; + #endif + if (rem!=0) *residue=1; + } + // discard digit is now at bottom of quot + #if DECDPUN<=4 + temp=(quot*6554)>>16; // fast /10 + // Vowels algorithm here not a win (9 instructions) + discard1=quot-X10(temp); + quot=temp; + #else + discard1=quot%10; + quot=quot/10; + #endif + // here, discard1 is the guard digit, and residue is everything + // else [use mapping array to accumulate residue safely] + *residue+=resmap[discard1]; + cut++; // update cut + // here: up -> Unit of the array with bottom digit + // cut is the division point for each Unit + // quot holds the uncut high-order digits for the current unit + if (set->digits<=0) { // special for Quantize/Subnormal :-( + *dn->lsu=0; // .. result is 0 + dn->digits=1; // .. + } + else { // shift to least needed + count=set->digits; // now digits to end up with + dn->digits=count; // set the new length + // shift-copy the coefficient array to the result number + for (target=dn->lsu; ; target++) { + *target=(Unit)quot; + count-=(DECDPUN-cut); + if (count<=0) break; + up++; + quot=*up; + #if DECDPUN<=4 + quot=QUOT10(quot, cut); + rem=*up-quot*powers[cut]; + #else + rem=quot%powers[cut]; + quot=quot/powers[cut]; + #endif + *target=(Unit)(*target+rem*powers[DECDPUN-cut]); + count-=cut; + if (count<=0) break; + } // shift-copy loop + } // shift to least + } // not unit boundary + + if (*residue!=0) *status|=DEC_Inexact; // record inexactitude + return; + } // decSetCoeff + +/* ------------------------------------------------------------------ */ +/* decApplyRound -- apply pending rounding to a number */ +/* */ +/* dn is the number, with space for set->digits digits */ +/* set is the context [for size and rounding mode] */ +/* residue indicates pending rounding, being any accumulated */ +/* guard and sticky information. It may be: */ +/* 6-9: rounding digit is >5 */ +/* 5: rounding digit is exactly half-way */ +/* 1-4: rounding digit is <5 and >0 */ +/* 0: the coefficient is exact */ +/* -1: as 1, but the hidden digits are subtractive, that */ +/* is, of the opposite sign to dn. In this case the */ +/* coefficient must be non-0. This case occurs when */ +/* subtracting a small number (which can be reduced to */ +/* a sticky bit); see decAddOp. */ +/* status is the status accumulator, as usual */ +/* */ +/* This routine applies rounding while keeping the length of the */ +/* coefficient constant. The exponent and status are unchanged */ +/* except if: */ +/* */ +/* -- the coefficient was increased and is all nines (in which */ +/* case Overflow could occur, and is handled directly here so */ +/* the caller does not need to re-test for overflow) */ +/* */ +/* -- the coefficient was decreased and becomes all nines (in which */ +/* case Underflow could occur, and is also handled directly). */ +/* */ +/* All fields in dn are updated as required. */ +/* */ +/* ------------------------------------------------------------------ */ +static void decApplyRound(decNumber *dn, decContext *set, Int residue, + uInt *status) { + Int bump; // 1 if coefficient needs to be incremented + // -1 if coefficient needs to be decremented + + if (residue==0) return; // nothing to apply + + bump=0; // assume a smooth ride + + // now decide whether, and how, to round, depending on mode + switch (set->round) { + case DEC_ROUND_05UP: { // round zero or five up (for reround) + // This is the same as DEC_ROUND_DOWN unless there is a + // positive residue and the lsd of dn is 0 or 5, in which case + // it is bumped; when residue is <0, the number is therefore + // bumped down unless the final digit was 1 or 6 (in which + // case it is bumped down and then up -- a no-op) + Int lsd5=*dn->lsu%5; // get lsd and quintate + if (residue<0 && lsd5!=1) bump=-1; + else if (residue>0 && lsd5==0) bump=1; + // [bump==1 could be applied directly; use common path for clarity] + break;} // r-05 + + case DEC_ROUND_DOWN: { + // no change, except if negative residue + if (residue<0) bump=-1; + break;} // r-d + + case DEC_ROUND_HALF_DOWN: { + if (residue>5) bump=1; + break;} // r-h-d + + case DEC_ROUND_HALF_EVEN: { + if (residue>5) bump=1; // >0.5 goes up + else if (residue==5) { // exactly 0.5000... + // 0.5 goes up iff [new] lsd is odd + if (*dn->lsu & 0x01) bump=1; + } + break;} // r-h-e + + case DEC_ROUND_HALF_UP: { + if (residue>=5) bump=1; + break;} // r-h-u + + case DEC_ROUND_UP: { + if (residue>0) bump=1; + break;} // r-u + + case DEC_ROUND_CEILING: { + // same as _UP for positive numbers, and as _DOWN for negatives + // [negative residue cannot occur on 0] + if (decNumberIsNegative(dn)) { + if (residue<0) bump=-1; + } + else { + if (residue>0) bump=1; + } + break;} // r-c + + case DEC_ROUND_FLOOR: { + // same as _UP for negative numbers, and as _DOWN for positive + // [negative residue cannot occur on 0] + if (!decNumberIsNegative(dn)) { + if (residue<0) bump=-1; + } + else { + if (residue>0) bump=1; + } + break;} // r-f + + default: { // e.g., DEC_ROUND_MAX + *status|=DEC_Invalid_context; + #if DECTRACE || (DECCHECK && DECVERB) + printf("Unknown rounding mode: %d\n", set->round); + #endif + break;} + } // switch + + // now bump the number, up or down, if need be + if (bump==0) return; // no action required + + // Simply use decUnitAddSub unless bumping up and the number is + // all nines. In this special case set to 100... explicitly + // and adjust the exponent by one (as otherwise could overflow + // the array) + // Similarly handle all-nines result if bumping down. + if (bump>0) { + Unit *up; // work + uInt count=dn->digits; // digits to be checked + for (up=dn->lsu; ; up++) { + if (count<=DECDPUN) { + // this is the last Unit (the msu) + if (*up!=powers[count]-1) break; // not still 9s + // here if it, too, is all nines + *up=(Unit)powers[count-1]; // here 999 -> 100 etc. + for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0 + dn->exponent++; // and bump exponent + // [which, very rarely, could cause Overflow...] + if ((dn->exponent+dn->digits)>set->emax+1) { + decSetOverflow(dn, set, status); + } + return; // done + } + // a full unit to check, with more to come + if (*up!=DECDPUNMAX) break; // not still 9s + count-=DECDPUN; + } // up + } // bump>0 + else { // -1 + // here checking for a pre-bump of 1000... (leading 1, all + // other digits zero) + Unit *up, *sup; // work + uInt count=dn->digits; // digits to be checked + for (up=dn->lsu; ; up++) { + if (count<=DECDPUN) { + // this is the last Unit (the msu) + if (*up!=powers[count-1]) break; // not 100.. + // here if have the 1000... case + sup=up; // save msu pointer + *up=(Unit)powers[count]-1; // here 100 in msu -> 999 + // others all to all-nines, too + for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1; + dn->exponent--; // and bump exponent + + // iff the number was at the subnormal boundary (exponent=etiny) + // then the exponent is now out of range, so it will in fact get + // clamped to etiny and the final 9 dropped. + // printf(">> emin=%d exp=%d sdig=%d\n", set->emin, + // dn->exponent, set->digits); + if (dn->exponent+1==set->emin-set->digits+1) { + if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9] + else { + *sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99.. + dn->digits--; + } + dn->exponent++; + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; + } + return; // done + } + + // a full unit to check, with more to come + if (*up!=0) break; // not still 0s + count-=DECDPUN; + } // up + + } // bump<0 + + // Actual bump needed. Do it. + decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump); + } // decApplyRound + +#if DECSUBSET +/* ------------------------------------------------------------------ */ +/* decFinish -- finish processing a number */ +/* */ +/* dn is the number */ +/* set is the context */ +/* residue is the rounding accumulator (as in decApplyRound) */ +/* status is the accumulator */ +/* */ +/* This finishes off the current number by: */ +/* 1. If not extended: */ +/* a. Converting a zero result to clean '0' */ +/* b. Reducing positive exponents to 0, if would fit in digits */ +/* 2. Checking for overflow and subnormals (always) */ +/* Note this is just Finalize when no subset arithmetic. */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decFinish(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + if (!set->extended) { + if ISZERO(dn) { // value is zero + dn->exponent=0; // clean exponent .. + dn->bits=0; // .. and sign + return; // no error possible + } + if (dn->exponent>=0) { // non-negative exponent + // >0; reduce to integer if possible + if (set->digits >= (dn->exponent+dn->digits)) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent); + dn->exponent=0; + } + } + } // !extended + + decFinalize(dn, set, residue, status); + } // decFinish +#endif + +/* ------------------------------------------------------------------ */ +/* decFinalize -- final check, clamp, and round of a number */ +/* */ +/* dn is the number */ +/* set is the context */ +/* residue is the rounding accumulator (as in decApplyRound) */ +/* status is the status accumulator */ +/* */ +/* This finishes off the current number by checking for subnormal */ +/* results, applying any pending rounding, checking for overflow, */ +/* and applying any clamping. */ +/* Underflow and overflow conditions are raised as appropriate. */ +/* All fields are updated as required. */ +/* ------------------------------------------------------------------ */ +static void decFinalize(decNumber *dn, decContext *set, Int *residue, + uInt *status) { + Int shift; // shift needed if clamping + Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary + + // Must be careful, here, when checking the exponent as the + // adjusted exponent could overflow 31 bits [because it may already + // be up to twice the expected]. + + // First test for subnormal. This must be done before any final + // round as the result could be rounded to Nmin or 0. + if (dn->exponent<=tinyexp) { // prefilter + Int comp; + decNumber nmin; + // A very nasty case here is dn == Nmin and residue<0 + if (dn->exponentemin; + comp=decCompare(dn, &nmin, 1); // (signless compare) + if (comp==BADINT) { // oops + *status|=DEC_Insufficient_storage; // abandon... + return; + } + if (*residue<0 && comp==0) { // neg residue and dn==Nmin + decApplyRound(dn, set, *residue, status); // might force down + decSetSubnormal(dn, set, residue, status); + return; + } + } + + // now apply any pending round (this could raise overflow). + if (*residue!=0) decApplyRound(dn, set, *residue, status); + + // Check for overflow [redundant in the 'rare' case] or clamp + if (dn->exponent<=set->emax-set->digits+1) return; // neither needed + + + // here when might have an overflow or clamp to do + if (dn->exponent>set->emax-dn->digits+1) { // too big + decSetOverflow(dn, set, status); + return; + } + // here when the result is normal but in clamp range + if (!set->clamp) return; + + // here when need to apply the IEEE exponent clamp (fold-down) + shift=dn->exponent-(set->emax-set->digits+1); + + // shift coefficient (if non-zero) + if (!ISZERO(dn)) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, shift); + } + dn->exponent-=shift; // adjust the exponent to match + *status|=DEC_Clamped; // and record the dirty deed + return; + } // decFinalize + +/* ------------------------------------------------------------------ */ +/* decSetOverflow -- set number to proper overflow value */ +/* */ +/* dn is the number (used for sign [only] and result) */ +/* set is the context [used for the rounding mode, etc.] */ +/* status contains the current status to be updated */ +/* */ +/* This sets the sign of a number and sets its value to either */ +/* Infinity or the maximum finite value, depending on the sign of */ +/* dn and the rounding mode, following IEEE 754 rules. */ +/* ------------------------------------------------------------------ */ +static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) { + Flag needmax=0; // result is maximum finite value + uByte sign=dn->bits&DECNEG; // clean and save sign bit + + if (ISZERO(dn)) { // zero does not overflow magnitude + Int emax=set->emax; // limit value + if (set->clamp) emax-=set->digits-1; // lower if clamping + if (dn->exponent>emax) { // clamp required + dn->exponent=emax; + *status|=DEC_Clamped; + } + return; + } + + decNumberZero(dn); + switch (set->round) { + case DEC_ROUND_DOWN: { + needmax=1; // never Infinity + break;} // r-d + case DEC_ROUND_05UP: { + needmax=1; // never Infinity + break;} // r-05 + case DEC_ROUND_CEILING: { + if (sign) needmax=1; // Infinity if non-negative + break;} // r-c + case DEC_ROUND_FLOOR: { + if (!sign) needmax=1; // Infinity if negative + break;} // r-f + default: break; // Infinity in all other cases + } + if (needmax) { + decSetMaxValue(dn, set); + dn->bits=sign; // set sign + } + else dn->bits=sign|DECINF; // Value is +/-Infinity + *status|=DEC_Overflow | DEC_Inexact | DEC_Rounded; + } // decSetOverflow + +/* ------------------------------------------------------------------ */ +/* decSetMaxValue -- set number to +Nmax (maximum normal value) */ +/* */ +/* dn is the number to set */ +/* set is the context [used for digits and emax] */ +/* */ +/* This sets the number to the maximum positive value. */ +/* ------------------------------------------------------------------ */ +static void decSetMaxValue(decNumber *dn, decContext *set) { + Unit *up; // work + Int count=set->digits; // nines to add + dn->digits=count; + // fill in all nines to set maximum value + for (up=dn->lsu; ; up++) { + if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines + else { // this is the msu + *up=(Unit)(powers[count]-1); + break; + } + count-=DECDPUN; // filled those digits + } // up + dn->bits=0; // + sign + dn->exponent=set->emax-set->digits+1; + } // decSetMaxValue + +/* ------------------------------------------------------------------ */ +/* decSetSubnormal -- process value whose exponent is extended) { + decNumberZero(dn); + // always full overflow + *status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded; + return; + } + #endif + + // Full arithmetic -- allow subnormals, rounded to minimum exponent + // (Etiny) if needed + etiny=set->emin-(set->digits-1); // smallest allowed exponent + + if ISZERO(dn) { // value is zero + // residue can never be non-zero here + #if DECCHECK + if (*residue!=0) { + printf("++ Subnormal 0 residue %ld\n", (LI)*residue); + *status|=DEC_Invalid_operation; + } + #endif + if (dn->exponentexponent=etiny; + *status|=DEC_Clamped; + } + return; + } + + *status|=DEC_Subnormal; // have a non-zero subnormal + adjust=etiny-dn->exponent; // calculate digits to remove + if (adjust<=0) { // not out of range; unrounded + // residue can never be non-zero here, except in the Nmin-residue + // case (which is a subnormal result), so can take fast-path here + // it may already be inexact (from setting the coefficient) + if (*status&DEC_Inexact) *status|=DEC_Underflow; + return; + } + + // adjust>0, so need to rescale the result so exponent becomes Etiny + // [this code is similar to that in rescale] + workset=*set; // clone rounding, etc. + workset.digits=dn->digits-adjust; // set requested length + workset.emin-=adjust; // and adjust emin to match + // [note that the latter can be <1, here, similar to Rescale case] + decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status); + decApplyRound(dn, &workset, *residue, status); + + // Use 754 default rule: Underflow is set iff Inexact + // [independent of whether trapped] + if (*status&DEC_Inexact) *status|=DEC_Underflow; + + // if rounded up a 999s case, exponent will be off by one; adjust + // back if so [it will fit, because it was shortened earlier] + if (dn->exponent>etiny) { + dn->digits=decShiftToMost(dn->lsu, dn->digits, 1); + dn->exponent--; // (re)adjust the exponent. + } + + // if rounded to zero, it is by definition clamped... + if (ISZERO(dn)) *status|=DEC_Clamped; + } // decSetSubnormal + +/* ------------------------------------------------------------------ */ +/* decCheckMath - check entry conditions for a math function */ +/* */ +/* This checks the context and the operand */ +/* */ +/* rhs is the operand to check */ +/* set is the context to check */ +/* status is unchanged if both are good */ +/* */ +/* returns non-zero if status is changed, 0 otherwise */ +/* */ +/* Restrictions enforced: */ +/* */ +/* digits, emax, and -emin in the context must be less than */ +/* DEC_MAX_MATH (999999), and A must be within these bounds if */ +/* non-zero. Invalid_operation is set in the status if a */ +/* restriction is violated. */ +/* ------------------------------------------------------------------ */ +static uInt decCheckMath(const decNumber *rhs, decContext *set, + uInt *status) { + uInt save=*status; // record + if (set->digits>DEC_MAX_MATH + || set->emax>DEC_MAX_MATH + || -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context; + else if ((rhs->digits>DEC_MAX_MATH + || rhs->exponent+rhs->digits>DEC_MAX_MATH+1 + || rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH)) + && !ISZERO(rhs)) *status|=DEC_Invalid_operation; + return (*status!=save); + } // decCheckMath + +/* ------------------------------------------------------------------ */ +/* decGetInt -- get integer from a number */ +/* */ +/* dn is the number [which will not be altered] */ +/* */ +/* returns one of: */ +/* BADINT if there is a non-zero fraction */ +/* the converted integer */ +/* BIGEVEN if the integer is even and magnitude > 2*10**9 */ +/* BIGODD if the integer is odd and magnitude > 2*10**9 */ +/* */ +/* This checks and gets a whole number from the input decNumber. */ +/* The sign can be determined from dn by the caller when BIGEVEN or */ +/* BIGODD is returned. */ +/* ------------------------------------------------------------------ */ +static Int decGetInt(const decNumber *dn) { + Int theInt; // result accumulator + const Unit *up; // work + Int got; // digits (real or not) processed + Int ilength=dn->digits+dn->exponent; // integral length + Flag neg=decNumberIsNegative(dn); // 1 if -ve + + // The number must be an integer that fits in 10 digits + // Assert, here, that 10 is enough for any rescale Etiny + #if DEC_MAX_EMAX > 999999999 + #error GetInt may need updating [for Emax] + #endif + #if DEC_MIN_EMIN < -999999999 + #error GetInt may need updating [for Emin] + #endif + if (ISZERO(dn)) return 0; // zeros are OK, with any exponent + + up=dn->lsu; // ready for lsu + theInt=0; // ready to accumulate + if (dn->exponent>=0) { // relatively easy + // no fractional part [usual]; allow for positive exponent + got=dn->exponent; + } + else { // -ve exponent; some fractional part to check and discard + Int count=-dn->exponent; // digits to discard + // spin up whole units until reach the Unit with the unit digit + for (; count>=DECDPUN; up++) { + if (*up!=0) return BADINT; // non-zero Unit to discard + count-=DECDPUN; + } + if (count==0) got=0; // [a multiple of DECDPUN] + else { // [not multiple of DECDPUN] + Int rem; // work + // slice off fraction digits and check for non-zero + #if DECDPUN<=4 + theInt=QUOT10(*up, count); + rem=*up-theInt*powers[count]; + #else + rem=*up%powers[count]; // slice off discards + theInt=*up/powers[count]; + #endif + if (rem!=0) return BADINT; // non-zero fraction + // it looks good + got=DECDPUN-count; // number of digits so far + up++; // ready for next + } + } + // now it's known there's no fractional part + + // tricky code now, to accumulate up to 9.3 digits + if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there + + if (ilength<11) { + Int save=theInt; + // collect any remaining unit(s) + for (; got1999999997) ilength=11; + else if (!neg && theInt>999999999) ilength=11; + if (ilength==11) theInt=save; // restore correct low bit + } + } + + if (ilength>10) { // too big + if (theInt&1) return BIGODD; // bottom bit 1 + return BIGEVEN; // bottom bit 0 + } + + if (neg) theInt=-theInt; // apply sign + return theInt; + } // decGetInt + +/* ------------------------------------------------------------------ */ +/* decDecap -- decapitate the coefficient of a number */ +/* */ +/* dn is the number to be decapitated */ +/* drop is the number of digits to be removed from the left of dn; */ +/* this must be <= dn->digits (if equal, the coefficient is */ +/* set to 0) */ +/* */ +/* Returns dn; dn->digits will be <= the initial digits less drop */ +/* (after removing drop digits there may be leading zero digits */ +/* which will also be removed). Only dn->lsu and dn->digits change. */ +/* ------------------------------------------------------------------ */ +static decNumber *decDecap(decNumber *dn, Int drop) { + Unit *msu; // -> target cut point + Int cut; // work + if (drop>=dn->digits) { // losing the whole thing + #if DECCHECK + if (drop>dn->digits) + printf("decDecap called with drop>digits [%ld>%ld]\n", + (LI)drop, (LI)dn->digits); + #endif + dn->lsu[0]=0; + dn->digits=1; + return dn; + } + msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu + cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu + if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits + // that may have left leading zero digits, so do a proper count... + dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1); + return dn; + } // decDecap + +/* ------------------------------------------------------------------ */ +/* decBiStr -- compare string with pairwise options */ +/* */ +/* targ is the string to compare */ +/* str1 is one of the strings to compare against (length may be 0) */ +/* str2 is the other; it must be the same length as str1 */ +/* */ +/* returns 1 if strings compare equal, (that is, it is the same */ +/* length as str1 and str2, and each character of targ is in either */ +/* str1 or str2 in the corresponding position), or 0 otherwise */ +/* */ +/* This is used for generic caseless compare, including the awkward */ +/* case of the Turkish dotted and dotless Is. Use as (for example): */ +/* if (decBiStr(test, "mike", "MIKE")) ... */ +/* ------------------------------------------------------------------ */ +static Flag decBiStr(const char *targ, const char *str1, const char *str2) { + for (;;targ++, str1++, str2++) { + if (*targ!=*str1 && *targ!=*str2) return 0; + // *targ has a match in one (or both, if terminator) + if (*targ=='\0') break; + } // forever + return 1; + } // decBiStr + +/* ------------------------------------------------------------------ */ +/* decNaNs -- handle NaN operand or operands */ +/* */ +/* res is the result number */ +/* lhs is the first operand */ +/* rhs is the second operand, or NULL if none */ +/* context is used to limit payload length */ +/* status contains the current status */ +/* returns res in case convenient */ +/* */ +/* Called when one or both operands is a NaN, and propagates the */ +/* appropriate result to res. When an sNaN is found, it is changed */ +/* to a qNaN and Invalid operation is set. */ +/* ------------------------------------------------------------------ */ +static decNumber * decNaNs(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set, + uInt *status) { + // This decision tree ends up with LHS being the source pointer, + // and status updated if need be + if (lhs->bits & DECSNAN) + *status|=DEC_Invalid_operation | DEC_sNaN; + else if (rhs==NULL); + else if (rhs->bits & DECSNAN) { + lhs=rhs; + *status|=DEC_Invalid_operation | DEC_sNaN; + } + else if (lhs->bits & DECNAN); + else lhs=rhs; + + // propagate the payload + if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy + else { // too long + const Unit *ul; + Unit *ur, *uresp1; + // copy safe number of units, then decapitate + res->bits=lhs->bits; // need sign etc. + uresp1=res->lsu+D2U(set->digits); + for (ur=res->lsu, ul=lhs->lsu; urdigits=D2U(set->digits)*DECDPUN; + // maybe still too long + if (res->digits>set->digits) decDecap(res, res->digits-set->digits); + } + + res->bits&=~DECSNAN; // convert any sNaN to NaN, while + res->bits|=DECNAN; // .. preserving sign + res->exponent=0; // clean exponent + // [coefficient was copied/decapitated] + return res; + } // decNaNs + +/* ------------------------------------------------------------------ */ +/* decStatus -- apply non-zero status */ +/* */ +/* dn is the number to set if error */ +/* status contains the current status (not yet in context) */ +/* set is the context */ +/* */ +/* If the status is an error status, the number is set to a NaN, */ +/* unless the error was an overflow, divide-by-zero, or underflow, */ +/* in which case the number will have already been set. */ +/* */ +/* The context status is then updated with the new status. Note that */ +/* this may raise a signal, so control may never return from this */ +/* routine (hence resources must be recovered before it is called). */ +/* ------------------------------------------------------------------ */ +static void decStatus(decNumber *dn, uInt status, decContext *set) { + if (status & DEC_NaNs) { // error status -> NaN + // if cause was an sNaN, clear and propagate [NaN is already set up] + if (status & DEC_sNaN) status&=~DEC_sNaN; + else { + decNumberZero(dn); // other error: clean throughout + dn->bits=DECNAN; // and make a quiet NaN + } + } + decContextSetStatus(set, status); // [may not return] + return; + } // decStatus + +/* ------------------------------------------------------------------ */ +/* decGetDigits -- count digits in a Units array */ +/* */ +/* uar is the Unit array holding the number (this is often an */ +/* accumulator of some sort) */ +/* len is the length of the array in units [>=1] */ +/* */ +/* returns the number of (significant) digits in the array */ +/* */ +/* All leading zeros are excluded, except the last if the array has */ +/* only zero Units. */ +/* ------------------------------------------------------------------ */ +// This may be called twice during some operations. +static Int decGetDigits(Unit *uar, Int len) { + Unit *up=uar+(len-1); // -> msu + Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu + #if DECDPUN>4 + uInt const *pow; // work + #endif + // (at least 1 in final msu) + #if DECCHECK + if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len); + #endif + + for (; up>=uar; up--) { + if (*up==0) { // unit is all 0s + if (digits==1) break; // a zero has one digit + digits-=DECDPUN; // adjust for 0 unit + continue;} + // found the first (most significant) non-zero Unit + #if DECDPUN>1 // not done yet + if (*up<10) break; // is 1-9 + digits++; + #if DECDPUN>2 // not done yet + if (*up<100) break; // is 10-99 + digits++; + #if DECDPUN>3 // not done yet + if (*up<1000) break; // is 100-999 + digits++; + #if DECDPUN>4 // count the rest ... + for (pow=&powers[4]; *up>=*pow; pow++) digits++; + #endif + #endif + #endif + #endif + break; + } // up + return digits; + } // decGetDigits + +#if DECTRACE | DECCHECK +/* ------------------------------------------------------------------ */ +/* decNumberShow -- display a number [debug aid] */ +/* dn is the number to show */ +/* */ +/* Shows: sign, exponent, coefficient (msu first), digits */ +/* or: sign, special-value */ +/* ------------------------------------------------------------------ */ +// this is public so other modules can use it +void decNumberShow(const decNumber *dn) { + const Unit *up; // work + uInt u, d; // .. + Int cut; // .. + char isign='+'; // main sign + if (dn==NULL) { + printf("NULL\n"); + return;} + if (decNumberIsNegative(dn)) isign='-'; + printf(" >> %c ", isign); + if (dn->bits&DECSPECIAL) { // Is a special value + if (decNumberIsInfinite(dn)) printf("Infinity"); + else { // a NaN + if (dn->bits&DECSNAN) printf("sNaN"); // signalling NaN + else printf("NaN"); + } + // if coefficient and exponent are 0, no more to do + if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) { + printf("\n"); + return;} + // drop through to report other information + printf(" "); + } + + // now carefully display the coefficient + up=dn->lsu+D2U(dn->digits)-1; // msu + printf("%ld", (LI)*up); + for (up=up-1; up>=dn->lsu; up--) { + u=*up; + printf(":"); + for (cut=DECDPUN-1; cut>=0; cut--) { + d=u/powers[cut]; + u-=d*powers[cut]; + printf("%ld", (LI)d); + } // cut + } // up + if (dn->exponent!=0) { + char esign='+'; + if (dn->exponent<0) esign='-'; + printf(" E%c%ld", esign, (LI)abs(dn->exponent)); + } + printf(" [%ld]\n", (LI)dn->digits); + } // decNumberShow +#endif + +#if DECTRACE || DECCHECK +/* ------------------------------------------------------------------ */ +/* decDumpAr -- display a unit array [debug/check aid] */ +/* name is a single-character tag name */ +/* ar is the array to display */ +/* len is the length of the array in Units */ +/* ------------------------------------------------------------------ */ +static void decDumpAr(char name, const Unit *ar, Int len) { + Int i; + const char *spec; + #if DECDPUN==9 + spec="%09d "; + #elif DECDPUN==8 + spec="%08d "; + #elif DECDPUN==7 + spec="%07d "; + #elif DECDPUN==6 + spec="%06d "; + #elif DECDPUN==5 + spec="%05d "; + #elif DECDPUN==4 + spec="%04d "; + #elif DECDPUN==3 + spec="%03d "; + #elif DECDPUN==2 + spec="%02d "; + #else + spec="%d "; + #endif + printf(" :%c: ", name); + for (i=len-1; i>=0; i--) { + if (i==len-1) printf("%ld ", (LI)ar[i]); + else printf(spec, ar[i]); + } + printf("\n"); + return;} +#endif + +#if DECCHECK +/* ------------------------------------------------------------------ */ +/* decCheckOperands -- check operand(s) to a routine */ +/* res is the result structure (not checked; it will be set to */ +/* quiet NaN if error found (and it is not NULL)) */ +/* lhs is the first operand (may be DECUNRESU) */ +/* rhs is the second (may be DECUNUSED) */ +/* set is the context (may be DECUNCONT) */ +/* returns 0 if both operands, and the context are clean, or 1 */ +/* otherwise (in which case the context will show an error, */ +/* unless NULL). Note that res is not cleaned; caller should */ +/* handle this so res=NULL case is safe. */ +/* The caller is expected to abandon immediately if 1 is returned. */ +/* ------------------------------------------------------------------ */ +static Flag decCheckOperands(decNumber *res, const decNumber *lhs, + const decNumber *rhs, decContext *set) { + Flag bad=0; + if (set==NULL) { // oops; hopeless + #if DECTRACE || DECVERB + printf("Reference to context is NULL.\n"); + #endif + bad=1; + return 1;} + else if (set!=DECUNCONT + && (set->digits<1 || set->round>=DEC_ROUND_MAX)) { + bad=1; + #if DECTRACE || DECVERB + printf("Bad context [digits=%ld round=%ld].\n", + (LI)set->digits, (LI)set->round); + #endif + } + else { + if (res==NULL) { + bad=1; + #if DECTRACE + // this one not DECVERB as standard tests include NULL + printf("Reference to result is NULL.\n"); + #endif + } + if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs)); + if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs)); + } + if (bad) { + if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation); + if (res!=DECUNRESU && res!=NULL) { + decNumberZero(res); + res->bits=DECNAN; // qNaN + } + } + return bad; + } // decCheckOperands + +/* ------------------------------------------------------------------ */ +/* decCheckNumber -- check a number */ +/* dn is the number to check */ +/* returns 0 if the number is clean, or 1 otherwise */ +/* */ +/* The number is considered valid if it could be a result from some */ +/* operation in some valid context. */ +/* ------------------------------------------------------------------ */ +static Flag decCheckNumber(const decNumber *dn) { + const Unit *up; // work + uInt maxuint; // .. + Int ae, d, digits; // .. + Int emin, emax; // .. + + if (dn==NULL) { // hopeless + #if DECTRACE + // this one not DECVERB as standard tests include NULL + printf("Reference to decNumber is NULL.\n"); + #endif + return 1;} + + // check special values + if (dn->bits & DECSPECIAL) { + if (dn->exponent!=0) { + #if DECTRACE || DECVERB + printf("Exponent %ld (not 0) for a special value [%02x].\n", + (LI)dn->exponent, dn->bits); + #endif + return 1;} + + // 2003.09.08: NaNs may now have coefficients, so next tests Inf only + if (decNumberIsInfinite(dn)) { + if (dn->digits!=1) { + #if DECTRACE || DECVERB + printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits); + #endif + return 1;} + if (*dn->lsu!=0) { + #if DECTRACE || DECVERB + printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu); + #endif + decDumpAr('I', dn->lsu, D2U(dn->digits)); + return 1;} + } // Inf + // 2002.12.26: negative NaNs can now appear through proposed IEEE + // concrete formats (decimal64, etc.). + return 0; + } + + // check the coefficient + if (dn->digits<1 || dn->digits>DECNUMMAXP) { + #if DECTRACE || DECVERB + printf("Digits %ld in number.\n", (LI)dn->digits); + #endif + return 1;} + + d=dn->digits; + + for (up=dn->lsu; d>0; up++) { + if (d>DECDPUN) maxuint=DECDPUNMAX; + else { // reached the msu + maxuint=powers[d]-1; + if (dn->digits>1 && *upmaxuint) { + #if DECTRACE || DECVERB + printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n", + (LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint); + #endif + return 1;} + d-=DECDPUN; + } + + // check the exponent. Note that input operands can have exponents + // which are out of the set->emin/set->emax and set->digits range + // (just as they can have more digits than set->digits). + ae=dn->exponent+dn->digits-1; // adjusted exponent + emax=DECNUMMAXE; + emin=DECNUMMINE; + digits=DECNUMMAXP; + if (ae+emax) { + #if DECTRACE || DECVERB + printf("Adjusted exponent overflow [%ld].\n", (LI)ae); + decNumberShow(dn); + #endif + return 1;} + + return 0; // it's OK + } // decCheckNumber + +/* ------------------------------------------------------------------ */ +/* decCheckInexact -- check a normal finite inexact result has digits */ +/* dn is the number to check */ +/* set is the context (for status and precision) */ +/* sets Invalid operation, etc., if some digits are missing */ +/* [this check is not made for DECSUBSET compilation or when */ +/* subnormal is not set] */ +/* ------------------------------------------------------------------ */ +static void decCheckInexact(const decNumber *dn, decContext *set) { + #if !DECSUBSET && DECEXTFLAG + if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact + && (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) { + #if DECTRACE || DECVERB + printf("Insufficient digits [%ld] on normal Inexact result.\n", + (LI)dn->digits); + decNumberShow(dn); + #endif + decContextSetStatus(set, DEC_Invalid_operation); + } + #else + // next is a noop for quiet compiler + if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation; + #endif + return; + } // decCheckInexact +#endif + +#if DECALLOC +#undef malloc +#undef free +/* ------------------------------------------------------------------ */ +/* decMalloc -- accountable allocation routine */ +/* n is the number of bytes to allocate */ +/* */ +/* Semantics is the same as the stdlib malloc routine, but bytes */ +/* allocated are accounted for globally, and corruption fences are */ +/* added before and after the 'actual' storage. */ +/* ------------------------------------------------------------------ */ +/* This routine allocates storage with an extra twelve bytes; 8 are */ +/* at the start and hold: */ +/* 0-3 the original length requested */ +/* 4-7 buffer corruption detection fence (DECFENCE, x4) */ +/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */ +/* ------------------------------------------------------------------ */ +static void *decMalloc(size_t n) { + uInt size=n+12; // true size + void *alloc; // -> allocated storage + uByte *b, *b0; // work + uInt uiwork; // for macros + + alloc=malloc(size); // -> allocated storage + if (alloc==NULL) return NULL; // out of strorage + b0=(uByte *)alloc; // as bytes + decAllocBytes+=n; // account for storage + UBFROMUI(alloc, n); // save n + // printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n); + for (b=b0+4; b play area + } // decMalloc + +/* ------------------------------------------------------------------ */ +/* decFree -- accountable free routine */ +/* alloc is the storage to free */ +/* */ +/* Semantics is the same as the stdlib malloc routine, except that */ +/* the global storage accounting is updated and the fences are */ +/* checked to ensure that no routine has written 'out of bounds'. */ +/* ------------------------------------------------------------------ */ +/* This routine first checks that the fences have not been corrupted. */ +/* It then frees the storage using the 'truw' storage address (that */ +/* is, offset by 8). */ +/* ------------------------------------------------------------------ */ +static void decFree(void *alloc) { + uInt n; // original length + uByte *b, *b0; // work + uInt uiwork; // for macros + + if (alloc==NULL) return; // allowed; it's a nop + b0=(uByte *)alloc; // as bytes + b0-=8; // -> true start of storage + n=UBTOUI(b0); // lift length + for (b=b0+4; b0 */ - /* and <10; 3 or powers of 2 are best]. */ - - /* DECNUMDIGITS is the default number of digits that can be held in */ - /* the structure. If undefined, 1 is assumed and it is assumed */ - /* that the structure will be immediately followed by extra space, */ - /* as required. DECNUMDIGITS is always >0. */ - #if !defined(DECNUMDIGITS) - #define DECNUMDIGITS 1 - #endif - - /* The size (integer data type) of each unit is determined by the */ - /* number of digits it will hold. */ - #if DECDPUN<=2 - #define decNumberUnit uint8_t - #elif DECDPUN<=4 - #define decNumberUnit uint16_t - #else - #define decNumberUnit uint32_t - #endif - /* The number of units needed is ceil(DECNUMDIGITS/DECDPUN) */ - #define DECNUMUNITS ((DECNUMDIGITS+DECDPUN-1)/DECDPUN) - - /* The data structure... */ - typedef struct { - int32_t digits; /* Count of digits in the coefficient; >0 */ - int32_t exponent; /* Unadjusted exponent, unbiased, in */ - /* range: -1999999997 through 999999999 */ - uint8_t bits; /* Indicator bits (see above) */ - /* Coefficient, from least significant unit */ - decNumberUnit lsu[DECNUMUNITS]; - } decNumber; - - /* Notes: */ - /* 1. If digits is > DECDPUN then there will one or more */ - /* decNumberUnits immediately following the first element of lsu.*/ - /* These contain the remaining (more significant) digits of the */ - /* number, and may be in the lsu array, or may be guaranteed by */ - /* some other mechanism (such as being contained in another */ - /* structure, or being overlaid on dynamically allocated */ - /* storage). */ - /* */ - /* Each integer of the coefficient (except potentially the last) */ - /* contains DECDPUN digits (e.g., a value in the range 0 through */ - /* 99999999 if DECDPUN is 8, or 0 through 999 if DECDPUN is 3). */ - /* */ - /* 2. A decNumber converted to a string may need up to digits+14 */ - /* characters. The worst cases (non-exponential and exponential */ - /* formats) are -0.00000{9...}# and -9.{9...}E+999999999# */ - /* (where # is '\0') */ - - - /* ---------------------------------------------------------------- */ - /* decNumber public functions and macros */ - /* ---------------------------------------------------------------- */ - /* Conversions */ - decNumber * decNumberFromInt32(decNumber *, int32_t); - decNumber * decNumberFromUInt32(decNumber *, uint32_t); - decNumber * decNumberFromString(decNumber *, const char *, decContext *); - char * decNumberToString(const decNumber *, char *); - char * decNumberToEngString(const decNumber *, char *); - uint32_t decNumberToUInt32(const decNumber *, decContext *); - int32_t decNumberToInt32(const decNumber *, decContext *); - uint8_t * decNumberGetBCD(const decNumber *, uint8_t *); - decNumber * decNumberSetBCD(decNumber *, const uint8_t *, uint32_t); - - /* Operators and elementary functions */ - decNumber * decNumberAbs(decNumber *, const decNumber *, decContext *); - decNumber * decNumberAdd(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberAnd(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompare(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompareSignal(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompareTotal(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberCompareTotalMag(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberDivide(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberDivideInteger(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberExp(decNumber *, const decNumber *, decContext *); - decNumber * decNumberFMA(decNumber *, const decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberInvert(decNumber *, const decNumber *, decContext *); - decNumber * decNumberLn(decNumber *, const decNumber *, decContext *); - decNumber * decNumberLogB(decNumber *, const decNumber *, decContext *); - decNumber * decNumberLog10(decNumber *, const decNumber *, decContext *); - decNumber * decNumberMax(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMaxMag(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMin(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMinMag(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberMinus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberMultiply(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberNormalize(decNumber *, const decNumber *, decContext *); - decNumber * decNumberOr(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberPlus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberPower(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberQuantize(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberReduce(decNumber *, const decNumber *, decContext *); - decNumber * decNumberRemainder(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberRemainderNear(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberRescale(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberRotate(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberSameQuantum(decNumber *, const decNumber *, const decNumber *); - decNumber * decNumberScaleB(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberShift(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberSquareRoot(decNumber *, const decNumber *, decContext *); - decNumber * decNumberSubtract(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberToIntegralExact(decNumber *, const decNumber *, decContext *); - decNumber * decNumberToIntegralValue(decNumber *, const decNumber *, decContext *); - decNumber * decNumberXor(decNumber *, const decNumber *, const decNumber *, decContext *); - - /* Utilities */ - enum decClass decNumberClass(const decNumber *, decContext *); - const char * decNumberClassToString(enum decClass); - decNumber * decNumberCopy(decNumber *, const decNumber *); - decNumber * decNumberCopyAbs(decNumber *, const decNumber *); - decNumber * decNumberCopyNegate(decNumber *, const decNumber *); - decNumber * decNumberCopySign(decNumber *, const decNumber *, const decNumber *); - decNumber * decNumberNextMinus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberNextPlus(decNumber *, const decNumber *, decContext *); - decNumber * decNumberNextToward(decNumber *, const decNumber *, const decNumber *, decContext *); - decNumber * decNumberTrim(decNumber *); - const char * decNumberVersion(void); - decNumber * decNumberZero(decNumber *); - - /* Functions for testing decNumbers (normality depends on context) */ - int32_t decNumberIsNormal(const decNumber *, decContext *); - int32_t decNumberIsSubnormal(const decNumber *, decContext *); - - /* Macros for testing decNumber *dn */ - #define decNumberIsCanonical(dn) (1) /* All decNumbers are saintly */ - #define decNumberIsFinite(dn) (((dn)->bits&DECSPECIAL)==0) - #define decNumberIsInfinite(dn) (((dn)->bits&DECINF)!=0) - #define decNumberIsNaN(dn) (((dn)->bits&(DECNAN|DECSNAN))!=0) - #define decNumberIsNegative(dn) (((dn)->bits&DECNEG)!=0) - #define decNumberIsQNaN(dn) (((dn)->bits&(DECNAN))!=0) - #define decNumberIsSNaN(dn) (((dn)->bits&(DECSNAN))!=0) - #define decNumberIsSpecial(dn) (((dn)->bits&DECSPECIAL)!=0) - #define decNumberIsZero(dn) (*(dn)->lsu==0 \ - && (dn)->digits==1 \ - && (((dn)->bits&DECSPECIAL)==0)) - #define decNumberRadix(dn) (10) - -#endif +/* ------------------------------------------------------------------ */ +/* Decimal Number arithmetic module header */ +/* ------------------------------------------------------------------ */ +/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ +/* */ +/* This software is made available under the terms of the */ +/* ICU License -- ICU 1.8.1 and later. */ +/* */ +/* The description and User's Guide ("The decNumber C Library") for */ +/* this software is called decNumber.pdf. This document is */ +/* available, together with arithmetic and format specifications, */ +/* testcases, and Web links, on the General Decimal Arithmetic page. */ +/* */ +/* Please send comments, suggestions, and corrections to the author: */ +/* mfc@uk.ibm.com */ +/* Mike Cowlishaw, IBM Fellow */ +/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECNUMBER) + #define DECNUMBER + #define DECNAME "decNumber" /* Short name */ + #define DECFULLNAME "Decimal Number Module" /* Verbose name */ + #define DECAUTHOR "Mike Cowlishaw" /* Who to blame */ + + #if !defined(DECCONTEXT) + #include "decContext.h" + #endif + + /* Bit settings for decNumber.bits */ + #define DECNEG 0x80 /* Sign; 1=negative, 0=positive or zero */ + #define DECINF 0x40 /* 1=Infinity */ + #define DECNAN 0x20 /* 1=NaN */ + #define DECSNAN 0x10 /* 1=sNaN */ + /* The remaining bits are reserved; they must be 0 */ + #define DECSPECIAL (DECINF|DECNAN|DECSNAN) /* any special value */ + + /* Define the decNumber data structure. The size and shape of the */ + /* units array in the structure is determined by the following */ + /* constant. This must not be changed without recompiling the */ + /* decNumber library modules. */ + + #define DECDPUN 3 /* DECimal Digits Per UNit [must be >0 */ + /* and <10; 3 or powers of 2 are best]. */ + + /* DECNUMDIGITS is the default number of digits that can be held in */ + /* the structure. If undefined, 1 is assumed and it is assumed */ + /* that the structure will be immediately followed by extra space, */ + /* as required. DECNUMDIGITS is always >0. */ + #if !defined(DECNUMDIGITS) + #define DECNUMDIGITS 1 + #endif + + /* The size (integer data type) of each unit is determined by the */ + /* number of digits it will hold. */ + #if DECDPUN<=2 + #define decNumberUnit uint8_t + #elif DECDPUN<=4 + #define decNumberUnit uint16_t + #else + #define decNumberUnit uint32_t + #endif + /* The number of units needed is ceil(DECNUMDIGITS/DECDPUN) */ + #define DECNUMUNITS ((DECNUMDIGITS+DECDPUN-1)/DECDPUN) + + /* The data structure... */ + typedef struct { + int32_t digits; /* Count of digits in the coefficient; >0 */ + int32_t exponent; /* Unadjusted exponent, unbiased, in */ + /* range: -1999999997 through 999999999 */ + uint8_t bits; /* Indicator bits (see above) */ + /* Coefficient, from least significant unit */ + decNumberUnit lsu[DECNUMUNITS]; + } decNumber; + + /* Notes: */ + /* 1. If digits is > DECDPUN then there will one or more */ + /* decNumberUnits immediately following the first element of lsu.*/ + /* These contain the remaining (more significant) digits of the */ + /* number, and may be in the lsu array, or may be guaranteed by */ + /* some other mechanism (such as being contained in another */ + /* structure, or being overlaid on dynamically allocated */ + /* storage). */ + /* */ + /* Each integer of the coefficient (except potentially the last) */ + /* contains DECDPUN digits (e.g., a value in the range 0 through */ + /* 99999999 if DECDPUN is 8, or 0 through 999 if DECDPUN is 3). */ + /* */ + /* 2. A decNumber converted to a string may need up to digits+14 */ + /* characters. The worst cases (non-exponential and exponential */ + /* formats) are -0.00000{9...}# and -9.{9...}E+999999999# */ + /* (where # is '\0') */ + + + /* ---------------------------------------------------------------- */ + /* decNumber public functions and macros */ + /* ---------------------------------------------------------------- */ + /* Conversions */ + decNumber * decNumberFromInt32(decNumber *, int32_t); + decNumber * decNumberFromUInt32(decNumber *, uint32_t); + decNumber * decNumberFromString(decNumber *, const char *, decContext *); + char * decNumberToString(const decNumber *, char *); + char * decNumberToEngString(const decNumber *, char *); + uint32_t decNumberToUInt32(const decNumber *, decContext *); + int32_t decNumberToInt32(const decNumber *, decContext *); + uint8_t * decNumberGetBCD(const decNumber *, uint8_t *); + decNumber * decNumberSetBCD(decNumber *, const uint8_t *, uint32_t); + + /* Operators and elementary functions */ + decNumber * decNumberAbs(decNumber *, const decNumber *, decContext *); + decNumber * decNumberAdd(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberAnd(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompare(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompareSignal(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompareTotal(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberCompareTotalMag(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberDivide(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberDivideInteger(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberExp(decNumber *, const decNumber *, decContext *); + decNumber * decNumberFMA(decNumber *, const decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberInvert(decNumber *, const decNumber *, decContext *); + decNumber * decNumberLn(decNumber *, const decNumber *, decContext *); + decNumber * decNumberLogB(decNumber *, const decNumber *, decContext *); + decNumber * decNumberLog10(decNumber *, const decNumber *, decContext *); + decNumber * decNumberMax(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMaxMag(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMin(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMinMag(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberMinus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberMultiply(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberNormalize(decNumber *, const decNumber *, decContext *); + decNumber * decNumberOr(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberPlus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberPower(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberQuantize(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberReduce(decNumber *, const decNumber *, decContext *); + decNumber * decNumberRemainder(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberRemainderNear(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberRescale(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberRotate(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberSameQuantum(decNumber *, const decNumber *, const decNumber *); + decNumber * decNumberScaleB(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberShift(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberSquareRoot(decNumber *, const decNumber *, decContext *); + decNumber * decNumberSubtract(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberToIntegralExact(decNumber *, const decNumber *, decContext *); + decNumber * decNumberToIntegralValue(decNumber *, const decNumber *, decContext *); + decNumber * decNumberXor(decNumber *, const decNumber *, const decNumber *, decContext *); + + /* Utilities */ + enum decClass decNumberClass(const decNumber *, decContext *); + const char * decNumberClassToString(enum decClass); + decNumber * decNumberCopy(decNumber *, const decNumber *); + decNumber * decNumberCopyAbs(decNumber *, const decNumber *); + decNumber * decNumberCopyNegate(decNumber *, const decNumber *); + decNumber * decNumberCopySign(decNumber *, const decNumber *, const decNumber *); + decNumber * decNumberNextMinus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberNextPlus(decNumber *, const decNumber *, decContext *); + decNumber * decNumberNextToward(decNumber *, const decNumber *, const decNumber *, decContext *); + decNumber * decNumberTrim(decNumber *); + const char * decNumberVersion(void); + decNumber * decNumberZero(decNumber *); + + /* Functions for testing decNumbers (normality depends on context) */ + int32_t decNumberIsNormal(const decNumber *, decContext *); + int32_t decNumberIsSubnormal(const decNumber *, decContext *); + + /* Macros for testing decNumber *dn */ + #define decNumberIsCanonical(dn) (1) /* All decNumbers are saintly */ + #define decNumberIsFinite(dn) (((dn)->bits&DECSPECIAL)==0) + #define decNumberIsInfinite(dn) (((dn)->bits&DECINF)!=0) + #define decNumberIsNaN(dn) (((dn)->bits&(DECNAN|DECSNAN))!=0) + #define decNumberIsNegative(dn) (((dn)->bits&DECNEG)!=0) + #define decNumberIsQNaN(dn) (((dn)->bits&(DECNAN))!=0) + #define decNumberIsSNaN(dn) (((dn)->bits&(DECSNAN))!=0) + #define decNumberIsSpecial(dn) (((dn)->bits&DECSPECIAL)!=0) + #define decNumberIsZero(dn) (*(dn)->lsu==0 \ + && (dn)->digits==1 \ + && (((dn)->bits&DECSPECIAL)==0)) + #define decNumberRadix(dn) (10) + +#endif diff --git a/texk/web2c/mplibdir/decNumberLocal.h b/texk/web2c/mplibdir/decNumberLocal.h index 5c88a5eaaf..cfd3e74e23 100644 --- a/texk/web2c/mplibdir/decNumberLocal.h +++ b/texk/web2c/mplibdir/decNumberLocal.h @@ -1,757 +1,757 @@ -/* ------------------------------------------------------------------ */ -/* decNumber package local type, tuning, and macro definitions */ -/* ------------------------------------------------------------------ */ -/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ -/* */ -/* This software is made available under the terms of the */ -/* ICU License -- ICU 1.8.1 and later. */ -/* */ -/* The description and User's Guide ("The decNumber C Library") for */ -/* this software is called decNumber.pdf. This document is */ -/* available, together with arithmetic and format specifications, */ -/* testcases, and Web links, on the General Decimal Arithmetic page. */ -/* */ -/* Please send comments, suggestions, and corrections to the author: */ -/* mfc@uk.ibm.com */ -/* Mike Cowlishaw, IBM Fellow */ -/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ -/* ------------------------------------------------------------------ */ -/* This header file is included by all modules in the decNumber */ -/* library, and contains local type definitions, tuning parameters, */ -/* etc. It should not need to be used by application programs. */ -/* decNumber.h or one of decDouble (etc.) must be included first. */ -/* ------------------------------------------------------------------ */ - -#if !defined(DECNUMBERLOC) - #define DECNUMBERLOC - #define DECVERSION "decNumber 3.68" /* Package Version [16 max.] */ - #define DECNLAUTHOR "Mike Cowlishaw" /* Who to blame */ - - #include /* for abs */ - #include /* for memset, strcpy */ - - /* Conditional code flag -- set this to match hardware platform */ - #if !defined(DECLITEND) - #define DECLITEND 1 /* 1=little-endian, 0=big-endian */ - #endif - - /* Conditional code flag -- set this to 1 for best performance */ - #if !defined(DECUSE64) - #define DECUSE64 1 /* 1=use int64s, 0=int32 & smaller only */ - #endif - - /* Conditional code flag -- set this to 0 to exclude printf calls */ - #if !defined(DECPRINT) - #define DECPRINT 1 /* 1=allow printf calls; 0=no printf */ - #endif - - /* Conditional check flags -- set these to 0 for best performance */ - #if !defined(DECCHECK) - #define DECCHECK 0 /* 1 to enable robust checking */ - #endif - #if !defined(DECALLOC) - #define DECALLOC 0 /* 1 to enable memory accounting */ - #endif - #if !defined(DECTRACE) - #define DECTRACE 0 /* 1 to trace certain internals, etc. */ - #endif - - /* Tuning parameter for decNumber (arbitrary precision) module */ - #if !defined(DECBUFFER) - #define DECBUFFER 36 /* Size basis for local buffers. This */ - /* should be a common maximum precision */ - /* rounded up to a multiple of 4; must */ - /* be zero or positive. */ - #endif - - - /* ---------------------------------------------------------------- */ - /* Check parameter dependencies */ - /* ---------------------------------------------------------------- */ - #if DECCHECK & !DECPRINT - #error DECCHECK needs DECPRINT to be useful - #endif - #if DECALLOC & !DECPRINT - #error DECALLOC needs DECPRINT to be useful - #endif - #if DECTRACE & !DECPRINT - #error DECTRACE needs DECPRINT to be useful - #endif - - /* ---------------------------------------------------------------- */ - /* Definitions for all modules (general-purpose) */ - /* ---------------------------------------------------------------- */ - - /* Local names for common types -- for safety, decNumber modules do */ - /* not use int or long directly. */ - #define Flag uint8_t - #define Byte int8_t - #define uByte uint8_t - #define Short int16_t - #define uShort uint16_t - #define Int int32_t - #define uInt uint32_t - #define Unit decNumberUnit - #if DECUSE64 - #define Long int64_t - #define uLong uint64_t - #endif - - /* Development-use definitions */ - typedef long int LI; /* for printf arguments only */ - #define DECNOINT 0 /* 1 to check no internal use of 'int' */ - /* or stdint types */ - #if DECNOINT - /* if these interfere with your C includes, do not set DECNOINT */ - #define int ? /* enable to ensure that plain C 'int' */ - #define long ?? /* .. or 'long' types are not used */ - #endif - - /* Shared lookup tables */ - extern const uByte DECSTICKYTAB[10]; /* re-round digits if sticky */ - extern const uInt DECPOWERS[10]; /* powers of ten table */ - /* The following are included from decDPD.h */ - extern const uShort DPD2BIN[1024]; /* DPD -> 0-999 */ - extern const uShort BIN2DPD[1000]; /* 0-999 -> DPD */ - extern const uInt DPD2BINK[1024]; /* DPD -> 0-999000 */ - extern const uInt DPD2BINM[1024]; /* DPD -> 0-999000000 */ - extern const uByte DPD2BCD8[4096]; /* DPD -> ddd + len */ - extern const uByte BIN2BCD8[4000]; /* 0-999 -> ddd + len */ - extern const uShort BCD2DPD[2458]; /* 0-0x999 -> DPD (0x999=2457)*/ - - /* LONGMUL32HI -- set w=(u*v)>>32, where w, u, and v are uInts */ - /* (that is, sets w to be the high-order word of the 64-bit result; */ - /* the low-order word is simply u*v.) */ - /* This version is derived from Knuth via Hacker's Delight; */ - /* it seems to optimize better than some others tried */ - #define LONGMUL32HI(w, u, v) { \ - uInt u0, u1, v0, v1, w0, w1, w2, t; \ - u0=u & 0xffff; u1=u>>16; \ - v0=v & 0xffff; v1=v>>16; \ - w0=u0*v0; \ - t=u1*v0 + (w0>>16); \ - w1=t & 0xffff; w2=t>>16; \ - w1=u0*v1 + w1; \ - (w)=u1*v1 + w2 + (w1>>16);} - - /* ROUNDUP -- round an integer up to a multiple of n */ - #define ROUNDUP(i, n) ((((i)+(n)-1)/n)*n) - #define ROUNDUP4(i) (((i)+3)&~3) /* special for n=4 */ - - /* ROUNDDOWN -- round an integer down to a multiple of n */ - #define ROUNDDOWN(i, n) (((i)/n)*n) - #define ROUNDDOWN4(i) ((i)&~3) /* special for n=4 */ - - /* References to multi-byte sequences under different sizes; these */ - /* require locally declared variables, but do not violate strict */ - /* aliasing or alignment (as did the UINTAT simple cast to uInt). */ - /* Variables needed are uswork, uiwork, etc. [so do not use at same */ - /* level in an expression, e.g., UBTOUI(x)==UBTOUI(y) may fail]. */ - - /* Return a uInt, etc., from bytes starting at a char* or uByte* */ - #define UBTOUS(b) (memcpy((void *)&uswork, b, 2), uswork) - #define UBTOUI(b) (memcpy((void *)&uiwork, b, 4), uiwork) - - /* Store a uInt, etc., into bytes starting at a char* or uByte*. */ - /* Returns i, evaluated, for convenience; has to use uiwork because */ - /* i may be an expression. */ - #define UBFROMUS(b, i) (uswork=(i), memcpy(b, (void *)&uswork, 2), uswork) - #define UBFROMUI(b, i) (uiwork=(i), memcpy(b, (void *)&uiwork, 4), uiwork) - - /* X10 and X100 -- multiply integer i by 10 or 100 */ - /* [shifts are usually faster than multiply; could be conditional] */ - #define X10(i) (((i)<<1)+((i)<<3)) - #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6)) - - /* MAXI and MINI -- general max & min (not in ANSI) for integers */ - #define MAXI(x,y) ((x)<(y)?(y):(x)) - #define MINI(x,y) ((x)>(y)?(y):(x)) - - /* Useful constants */ - #define BILLION 1000000000 /* 10**9 */ - /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC */ - #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0') - - - /* ---------------------------------------------------------------- */ - /* Definitions for arbitary-precision modules (only valid after */ - /* decNumber.h has been included) */ - /* ---------------------------------------------------------------- */ - - /* Limits and constants */ - #define DECNUMMAXP 999999999 /* maximum precision code can handle */ - #define DECNUMMAXE 999999999 /* maximum adjusted exponent ditto */ - #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto */ - #if (DECNUMMAXP != DEC_MAX_DIGITS) - #error Maximum digits mismatch - #endif - #if (DECNUMMAXE != DEC_MAX_EMAX) - #error Maximum exponent mismatch - #endif - #if (DECNUMMINE != DEC_MIN_EMIN) - #error Minimum exponent mismatch - #endif - - /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN */ - /* digits, and D2UTABLE -- the initializer for the D2U table */ - #if DECDPUN==1 - #define DECDPUNMAX 9 - #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ - 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \ - 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \ - 48,49} - #elif DECDPUN==2 - #define DECDPUNMAX 99 - #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10, \ - 11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \ - 18,19,19,20,20,21,21,22,22,23,23,24,24,25} - #elif DECDPUN==3 - #define DECDPUNMAX 999 - #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7, \ - 8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \ - 13,14,14,14,15,15,15,16,16,16,17} - #elif DECDPUN==4 - #define DECDPUNMAX 9999 - #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6, \ - 6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \ - 11,11,11,12,12,12,12,13} - #elif DECDPUN==5 - #define DECDPUNMAX 99999 - #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5, \ - 5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9, \ - 9,9,10,10,10,10} - #elif DECDPUN==6 - #define DECDPUNMAX 999999 - #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4, \ - 4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8, \ - 8,8,8,8,8,9} - #elif DECDPUN==7 - #define DECDPUNMAX 9999999 - #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3, \ - 4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7, \ - 7,7,7,7,7,7} - #elif DECDPUN==8 - #define DECDPUNMAX 99999999 - #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3, \ - 3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6, \ - 6,6,6,6,6,7} - #elif DECDPUN==9 - #define DECDPUNMAX 999999999 - #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3, \ - 3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5, \ - 5,5,6,6,6,6} - #elif defined(DECDPUN) - #error DECDPUN must be in the range 1-9 - #endif - - /* ----- Shared data (in decNumber.c) ----- */ - /* Public lookup table used by the D2U macro (see below) */ - #define DECMAXD2U 49 - extern const uByte d2utable[DECMAXD2U+1]; - - /* ----- Macros ----- */ - /* ISZERO -- return true if decNumber dn is a zero */ - /* [performance-critical in some situations] */ - #define ISZERO(dn) decNumberIsZero(dn) /* now just a local name */ - - /* D2U -- return the number of Units needed to hold d digits */ - /* (runtime version, with table lookaside for small d) */ - #if DECDPUN==8 - #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3)) - #elif DECDPUN==4 - #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2)) - #else - #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN) - #endif - /* SD2U -- static D2U macro (for compile-time calculation) */ - #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN) - - /* MSUDIGITS -- returns digits in msu, from digits, calculated */ - /* using D2U */ - #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN) - - /* D2N -- return the number of decNumber structs that would be */ - /* needed to contain that number of digits (and the initial */ - /* decNumber struct) safely. Note that one Unit is included in the */ - /* initial structure. Used for allocating space that is aligned on */ - /* a decNumber struct boundary. */ - #define D2N(d) \ - ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber)) - - /* TODIGIT -- macro to remove the leading digit from the unsigned */ - /* integer u at column cut (counting from the right, LSD=0) and */ - /* place it as an ASCII character into the character pointed to by */ - /* c. Note that cut must be <= 9, and the maximum value for u is */ - /* 2,000,000,000 (as is needed for negative exponents of */ - /* subnormals). The unsigned integer pow is used as a temporary */ - /* variable. */ - #define TODIGIT(u, cut, c, pow) { \ - *(c)='0'; \ - pow=DECPOWERS[cut]*2; \ - if ((u)>pow) { \ - pow*=4; \ - if ((u)>=pow) {(u)-=pow; *(c)+=8;} \ - pow/=2; \ - if ((u)>=pow) {(u)-=pow; *(c)+=4;} \ - pow/=2; \ - } \ - if ((u)>=pow) {(u)-=pow; *(c)+=2;} \ - pow/=2; \ - if ((u)>=pow) {(u)-=pow; *(c)+=1;} \ - } - - /* ---------------------------------------------------------------- */ - /* Definitions for fixed-precision modules (only valid after */ - /* decSingle.h, decDouble.h, or decQuad.h has been included) */ - /* ---------------------------------------------------------------- */ - - /* bcdnum -- a structure describing a format-independent finite */ - /* number, whose coefficient is a string of bcd8 uBytes */ - typedef struct { - uByte *msd; /* -> most significant digit */ - uByte *lsd; /* -> least ditto */ - uInt sign; /* 0=positive, DECFLOAT_Sign=negative */ - Int exponent; /* Unadjusted signed exponent (q), or */ - /* DECFLOAT_NaN etc. for a special */ - } bcdnum; - - /* Test if exponent or bcdnum exponent must be a special, etc. */ - #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp) - #define EXPISINF(exp) (exp==DECFLOAT_Inf) - #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN) - #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent)) - - /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian */ - /* (array) notation (the 0 word or byte contains the sign bit), */ - /* automatically adjusting for endianness; similarly address a word */ - /* in the next-wider format (decFloatWider, or dfw) */ - #define DECWORDS (DECBYTES/4) - #define DECWWORDS (DECWBYTES/4) - #if DECLITEND - #define DFBYTE(df, off) ((df)->bytes[DECBYTES-1-(off)]) - #define DFWORD(df, off) ((df)->words[DECWORDS-1-(off)]) - #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)]) - #else - #define DFBYTE(df, off) ((df)->bytes[off]) - #define DFWORD(df, off) ((df)->words[off]) - #define DFWWORD(dfw, off) ((dfw)->words[off]) - #endif - - /* Tests for sign or specials, directly on DECFLOATs */ - #define DFISSIGNED(df) ((DFWORD(df, 0)&0x80000000)!=0) - #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000) - #define DFISINF(df) ((DFWORD(df, 0)&0x7c000000)==0x78000000) - #define DFISNAN(df) ((DFWORD(df, 0)&0x7c000000)==0x7c000000) - #define DFISQNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7c000000) - #define DFISSNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7e000000) - - /* Shared lookup tables */ - extern const uInt DECCOMBMSD[64]; /* Combination field -> MSD */ - extern const uInt DECCOMBFROM[48]; /* exp+msd -> Combination */ - - /* Private generic (utility) routine */ - #if DECCHECK || DECTRACE - extern void decShowNum(const bcdnum *, const char *); - #endif - - /* Format-dependent macros and constants */ - #if defined(DECPMAX) - - /* Useful constants */ - #define DECPMAX9 (ROUNDUP(DECPMAX, 9)/9) /* 'Pmax' in 10**9s */ - /* Top words for a zero */ - #define SINGLEZERO 0x22500000 - #define DOUBLEZERO 0x22380000 - #define QUADZERO 0x22080000 - /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */ - - /* Format-dependent common tests: */ - /* DFISZERO -- test for (any) zero */ - /* DFISCCZERO -- test for coefficient continuation being zero */ - /* DFISCC01 -- test for coefficient contains only 0s and 1s */ - /* DFISINT -- test for finite and exponent q=0 */ - /* DFISUINT01 -- test for sign=0, finite, exponent q=0, and */ - /* MSD=0 or 1 */ - /* ZEROWORD is also defined here. */ - /* */ - /* In DFISZERO the first test checks the least-significant word */ - /* (most likely to be non-zero); the penultimate tests MSD and */ - /* DPDs in the signword, and the final test excludes specials and */ - /* MSD>7. DFISINT similarly has to allow for the two forms of */ - /* MSD codes. DFISUINT01 only has to allow for one form of MSD */ - /* code. */ - #if DECPMAX==7 - #define ZEROWORD SINGLEZERO - /* [test macros not needed except for Zero] */ - #define DFISZERO(df) ((DFWORD(df, 0)&0x1c0fffff)==0 \ - && (DFWORD(df, 0)&0x60000000)!=0x60000000) - #elif DECPMAX==16 - #define ZEROWORD DOUBLEZERO - #define DFISZERO(df) ((DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x1c03ffff)==0 \ - && (DFWORD(df, 0)&0x60000000)!=0x60000000)) - #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000 \ - ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000) - #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000) - #define DFISCCZERO(df) (DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x0003ffff)==0) - #define DFISCC01(df) ((DFWORD(df, 0)&~0xfffc9124)==0 \ - && (DFWORD(df, 1)&~0x49124491)==0) - #elif DECPMAX==34 - #define ZEROWORD QUADZERO - #define DFISZERO(df) ((DFWORD(df, 3)==0 \ - && DFWORD(df, 2)==0 \ - && DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x1c003fff)==0 \ - && (DFWORD(df, 0)&0x60000000)!=0x60000000)) - #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000 \ - ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000) - #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000) - #define DFISCCZERO(df) (DFWORD(df, 3)==0 \ - && DFWORD(df, 2)==0 \ - && DFWORD(df, 1)==0 \ - && (DFWORD(df, 0)&0x00003fff)==0) - - #define DFISCC01(df) ((DFWORD(df, 0)&~0xffffc912)==0 \ - && (DFWORD(df, 1)&~0x44912449)==0 \ - && (DFWORD(df, 2)&~0x12449124)==0 \ - && (DFWORD(df, 3)&~0x49124491)==0) - #endif - - /* Macros to test if a certain 10 bits of a uInt or pair of uInts */ - /* are a canonical declet [higher or lower bits are ignored]. */ - /* declet is at offset 0 (from the right) in a uInt: */ - #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e) - /* declet is at offset k (a multiple of 2) in a uInt: */ - #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0 \ - || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) - /* declet is at offset k (a multiple of 2) in a pair of uInts: */ - /* [the top 2 bits will always be in the more-significant uInt] */ - #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0 \ - || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k))) \ - || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) - - /* Macro to test whether a full-length (length DECPMAX) BCD8 */ - /* coefficient, starting at uByte u, is all zeros */ - /* Test just the LSWord first, then the remainder as a sequence */ - /* of tests in order to avoid same-level use of UBTOUI */ - #if DECPMAX==7 - #define ISCOEFFZERO(u) ( \ - UBTOUI((u)+DECPMAX-4)==0 \ - && UBTOUS((u)+DECPMAX-6)==0 \ - && *(u)==0) - #elif DECPMAX==16 - #define ISCOEFFZERO(u) ( \ - UBTOUI((u)+DECPMAX-4)==0 \ - && UBTOUI((u)+DECPMAX-8)==0 \ - && UBTOUI((u)+DECPMAX-12)==0 \ - && UBTOUI(u)==0) - #elif DECPMAX==34 - #define ISCOEFFZERO(u) ( \ - UBTOUI((u)+DECPMAX-4)==0 \ - && UBTOUI((u)+DECPMAX-8)==0 \ - && UBTOUI((u)+DECPMAX-12)==0 \ - && UBTOUI((u)+DECPMAX-16)==0 \ - && UBTOUI((u)+DECPMAX-20)==0 \ - && UBTOUI((u)+DECPMAX-24)==0 \ - && UBTOUI((u)+DECPMAX-28)==0 \ - && UBTOUI((u)+DECPMAX-32)==0 \ - && UBTOUS(u)==0) - #endif - - /* Macros and masks for the sign, exponent continuation, and MSD */ - /* Get the sign as DECFLOAT_Sign or 0 */ - #define GETSIGN(df) (DFWORD(df, 0)&0x80000000) - /* Get the exponent continuation from a decFloat *df as an Int */ - #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL))) - /* Ditto, from the next-wider format */ - #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL))) - /* Get the biased exponent similarly */ - #define GETEXP(df) ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df))) - /* Get the unbiased exponent similarly */ - #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS) - /* Get the MSD similarly (as uInt) */ - #define GETMSD(df) (DECCOMBMSD[DFWORD((df), 0)>>26]) - - /* Compile-time computes of the exponent continuation field masks */ - /* full exponent continuation field: */ - #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) - /* same, not including its first digit (the qNaN/sNaN selector): */ - #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) - - /* Macros to decode the coefficient in a finite decFloat *df into */ - /* a BCD string (uByte *bcdin) of length DECPMAX uBytes. */ - - /* In-line sequence to convert least significant 10 bits of uInt */ - /* dpd to three BCD8 digits starting at uByte u. Note that an */ - /* extra byte is written to the right of the three digits because */ - /* four bytes are moved at a time for speed; the alternative */ - /* macro moves exactly three bytes (usually slower). */ - #define dpd2bcd8(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 4) - #define dpd2bcd83(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 3) - - /* Decode the declets. After extracting each one, it is decoded */ - /* to BCD8 using a table lookup (also used for variable-length */ - /* decode). Each DPD decode is 3 bytes BCD8 plus a one-byte */ - /* length which is not used, here). Fixed-length 4-byte moves */ - /* are fast, however, almost everywhere, and so are used except */ - /* for the final three bytes (to avoid overrun). The code below */ - /* is 36 instructions for Doubles and about 70 for Quads, even */ - /* on IA32. */ - - /* Two macros are defined for each format: */ - /* GETCOEFF extracts the coefficient of the current format */ - /* GETWCOEFF extracts the coefficient of the next-wider format. */ - /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */ - - #if DECPMAX==7 - #define GETCOEFF(df, bcd) { \ - uInt sourhi=DFWORD(df, 0); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>10); \ - dpd2bcd83(bcd+4, sourhi);} - #define GETWCOEFF(df, bcd) { \ - uInt sourhi=DFWWORD(df, 0); \ - uInt sourlo=DFWWORD(df, 1); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>8); \ - dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+7, sourlo>>20); \ - dpd2bcd8(bcd+10, sourlo>>10); \ - dpd2bcd83(bcd+13, sourlo);} - - #elif DECPMAX==16 - #define GETCOEFF(df, bcd) { \ - uInt sourhi=DFWORD(df, 0); \ - uInt sourlo=DFWORD(df, 1); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>8); \ - dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+7, sourlo>>20); \ - dpd2bcd8(bcd+10, sourlo>>10); \ - dpd2bcd83(bcd+13, sourlo);} - #define GETWCOEFF(df, bcd) { \ - uInt sourhi=DFWWORD(df, 0); \ - uInt sourmh=DFWWORD(df, 1); \ - uInt sourml=DFWWORD(df, 2); \ - uInt sourlo=DFWWORD(df, 3); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>4); \ - dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ - dpd2bcd8(bcd+7, sourmh>>16); \ - dpd2bcd8(bcd+10, sourmh>>6); \ - dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ - dpd2bcd8(bcd+16, sourml>>18); \ - dpd2bcd8(bcd+19, sourml>>8); \ - dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+25, sourlo>>20); \ - dpd2bcd8(bcd+28, sourlo>>10); \ - dpd2bcd83(bcd+31, sourlo);} - - #elif DECPMAX==34 - #define GETCOEFF(df, bcd) { \ - uInt sourhi=DFWORD(df, 0); \ - uInt sourmh=DFWORD(df, 1); \ - uInt sourml=DFWORD(df, 2); \ - uInt sourlo=DFWORD(df, 3); \ - *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ - dpd2bcd8(bcd+1, sourhi>>4); \ - dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ - dpd2bcd8(bcd+7, sourmh>>16); \ - dpd2bcd8(bcd+10, sourmh>>6); \ - dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ - dpd2bcd8(bcd+16, sourml>>18); \ - dpd2bcd8(bcd+19, sourml>>8); \ - dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ - dpd2bcd8(bcd+25, sourlo>>20); \ - dpd2bcd8(bcd+28, sourlo>>10); \ - dpd2bcd83(bcd+31, sourlo);} - - #define GETWCOEFF(df, bcd) {??} /* [should never be used] */ - #endif - - /* Macros to decode the coefficient in a finite decFloat *df into */ - /* a base-billion uInt array, with the least-significant */ - /* 0-999999999 'digit' at offset 0. */ - - /* Decode the declets. After extracting each one, it is decoded */ - /* to binary using a table lookup. Three tables are used; one */ - /* the usual DPD to binary, the other two pre-multiplied by 1000 */ - /* and 1000000 to avoid multiplication during decode. These */ - /* tables can also be used for multiplying up the MSD as the DPD */ - /* code for 0 through 9 is the identity. */ - #define DPD2BIN0 DPD2BIN /* for prettier code */ - - #if DECPMAX==7 - #define GETCOEFFBILL(df, buf) { \ - uInt sourhi=DFWORD(df, 0); \ - (buf)[0]=DPD2BIN0[sourhi&0x3ff] \ - +DPD2BINK[(sourhi>>10)&0x3ff] \ - +DPD2BINM[DECCOMBMSD[sourhi>>26]];} - - #elif DECPMAX==16 - #define GETCOEFFBILL(df, buf) { \ - uInt sourhi, sourlo; \ - sourlo=DFWORD(df, 1); \ - (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ - +DPD2BINK[(sourlo>>10)&0x3ff] \ - +DPD2BINM[(sourlo>>20)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff] \ - +DPD2BINK[(sourhi>>8)&0x3ff] \ - +DPD2BINM[DECCOMBMSD[sourhi>>26]];} - - #elif DECPMAX==34 - #define GETCOEFFBILL(df, buf) { \ - uInt sourhi, sourmh, sourml, sourlo; \ - sourlo=DFWORD(df, 3); \ - (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ - +DPD2BINK[(sourlo>>10)&0x3ff] \ - +DPD2BINM[(sourlo>>20)&0x3ff]; \ - sourml=DFWORD(df, 2); \ - (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff] \ - +DPD2BINK[(sourml>>8)&0x3ff] \ - +DPD2BINM[(sourml>>18)&0x3ff]; \ - sourmh=DFWORD(df, 1); \ - (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff] \ - +DPD2BINK[(sourmh>>6)&0x3ff] \ - +DPD2BINM[(sourmh>>16)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff] \ - +DPD2BINK[(sourhi>>4)&0x3ff] \ - +DPD2BINM[DECCOMBMSD[sourhi>>26]];} - - #endif - - /* Macros to decode the coefficient in a finite decFloat *df into */ - /* a base-thousand uInt array (of size DECLETS+1, to allow for */ - /* the MSD), with the least-significant 0-999 'digit' at offset 0.*/ - - /* Decode the declets. After extracting each one, it is decoded */ - /* to binary using a table lookup. */ - #if DECPMAX==7 - #define GETCOEFFTHOU(df, buf) { \ - uInt sourhi=DFWORD(df, 0); \ - (buf)[0]=DPD2BIN[sourhi&0x3ff]; \ - (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff]; \ - (buf)[2]=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==16 - #define GETCOEFFTHOU(df, buf) { \ - uInt sourhi, sourlo; \ - sourlo=DFWORD(df, 1); \ - (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ - (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ - (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \ - (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff]; \ - (buf)[5]=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==34 - #define GETCOEFFTHOU(df, buf) { \ - uInt sourhi, sourmh, sourml, sourlo; \ - sourlo=DFWORD(df, 3); \ - (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ - (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ - (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ - sourml=DFWORD(df, 2); \ - (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \ - (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff]; \ - (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff]; \ - sourmh=DFWORD(df, 1); \ - (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \ - (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff]; \ - (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff]; \ - sourhi=DFWORD(df, 0); \ - (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \ - (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff]; \ - (buf)[11]=DECCOMBMSD[sourhi>>26];} - #endif - - - /* Macros to decode the coefficient in a finite decFloat *df and */ - /* add to a base-thousand uInt array (as for GETCOEFFTHOU). */ - /* After the addition then most significant 'digit' in the array */ - /* might have a value larger then 10 (with a maximum of 19). */ - #if DECPMAX==7 - #define ADDCOEFFTHOU(df, buf) { \ - uInt sourhi=DFWORD(df, 0); \ - (buf)[0]+=DPD2BIN[sourhi&0x3ff]; \ - if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ - (buf)[1]+=DPD2BIN[(sourhi>>10)&0x3ff]; \ - if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ - (buf)[2]+=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==16 - #define ADDCOEFFTHOU(df, buf) { \ - uInt sourhi, sourlo; \ - sourlo=DFWORD(df, 1); \ - (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \ - if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ - (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \ - if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ - (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \ - if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \ - sourhi=DFWORD(df, 0); \ - (buf)[3]+=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \ - if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \ - (buf)[4]+=DPD2BIN[(sourhi>>8)&0x3ff]; \ - if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \ - (buf)[5]+=DECCOMBMSD[sourhi>>26];} - - #elif DECPMAX==34 - #define ADDCOEFFTHOU(df, buf) { \ - uInt sourhi, sourmh, sourml, sourlo; \ - sourlo=DFWORD(df, 3); \ - (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \ - if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ - (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \ - if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ - (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \ - if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \ - sourml=DFWORD(df, 2); \ - (buf)[3]+=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \ - if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \ - (buf)[4]+=DPD2BIN[(sourml>>8)&0x3ff]; \ - if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \ - (buf)[5]+=DPD2BIN[(sourml>>18)&0x3ff]; \ - if (buf[5]>999) {buf[5]-=1000; buf[6]++;} \ - sourmh=DFWORD(df, 1); \ - (buf)[6]+=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \ - if (buf[6]>999) {buf[6]-=1000; buf[7]++;} \ - (buf)[7]+=DPD2BIN[(sourmh>>6)&0x3ff]; \ - if (buf[7]>999) {buf[7]-=1000; buf[8]++;} \ - (buf)[8]+=DPD2BIN[(sourmh>>16)&0x3ff]; \ - if (buf[8]>999) {buf[8]-=1000; buf[9]++;} \ - sourhi=DFWORD(df, 0); \ - (buf)[9]+=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \ - if (buf[9]>999) {buf[9]-=1000; buf[10]++;} \ - (buf)[10]+=DPD2BIN[(sourhi>>4)&0x3ff]; \ - if (buf[10]>999) {buf[10]-=1000; buf[11]++;} \ - (buf)[11]+=DECCOMBMSD[sourhi>>26];} - #endif - - - /* Set a decFloat to the maximum positive finite number (Nmax) */ - #if DECPMAX==7 - #define DFSETNMAX(df) \ - {DFWORD(df, 0)=0x77f3fcff;} - #elif DECPMAX==16 - #define DFSETNMAX(df) \ - {DFWORD(df, 0)=0x77fcff3f; \ - DFWORD(df, 1)=0xcff3fcff;} - #elif DECPMAX==34 - #define DFSETNMAX(df) \ - {DFWORD(df, 0)=0x77ffcff3; \ - DFWORD(df, 1)=0xfcff3fcf; \ - DFWORD(df, 2)=0xf3fcff3f; \ - DFWORD(df, 3)=0xcff3fcff;} - #endif - - /* [end of format-dependent macros and constants] */ - #endif - -#else - #error decNumberLocal included more than once -#endif +/* ------------------------------------------------------------------ */ +/* decNumber package local type, tuning, and macro definitions */ +/* ------------------------------------------------------------------ */ +/* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ +/* */ +/* This software is made available under the terms of the */ +/* ICU License -- ICU 1.8.1 and later. */ +/* */ +/* The description and User's Guide ("The decNumber C Library") for */ +/* this software is called decNumber.pdf. This document is */ +/* available, together with arithmetic and format specifications, */ +/* testcases, and Web links, on the General Decimal Arithmetic page. */ +/* */ +/* Please send comments, suggestions, and corrections to the author: */ +/* mfc@uk.ibm.com */ +/* Mike Cowlishaw, IBM Fellow */ +/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ +/* ------------------------------------------------------------------ */ +/* This header file is included by all modules in the decNumber */ +/* library, and contains local type definitions, tuning parameters, */ +/* etc. It should not need to be used by application programs. */ +/* decNumber.h or one of decDouble (etc.) must be included first. */ +/* ------------------------------------------------------------------ */ + +#if !defined(DECNUMBERLOC) + #define DECNUMBERLOC + #define DECVERSION "decNumber 3.68" /* Package Version [16 max.] */ + #define DECNLAUTHOR "Mike Cowlishaw" /* Who to blame */ + + #include /* for abs */ + #include /* for memset, strcpy */ + + /* Conditional code flag -- set this to match hardware platform */ + #if !defined(DECLITEND) + #define DECLITEND 1 /* 1=little-endian, 0=big-endian */ + #endif + + /* Conditional code flag -- set this to 1 for best performance */ + #if !defined(DECUSE64) + #define DECUSE64 1 /* 1=use int64s, 0=int32 & smaller only */ + #endif + + /* Conditional code flag -- set this to 0 to exclude printf calls */ + #if !defined(DECPRINT) + #define DECPRINT 1 /* 1=allow printf calls; 0=no printf */ + #endif + + /* Conditional check flags -- set these to 0 for best performance */ + #if !defined(DECCHECK) + #define DECCHECK 0 /* 1 to enable robust checking */ + #endif + #if !defined(DECALLOC) + #define DECALLOC 0 /* 1 to enable memory accounting */ + #endif + #if !defined(DECTRACE) + #define DECTRACE 0 /* 1 to trace certain internals, etc. */ + #endif + + /* Tuning parameter for decNumber (arbitrary precision) module */ + #if !defined(DECBUFFER) + #define DECBUFFER 36 /* Size basis for local buffers. This */ + /* should be a common maximum precision */ + /* rounded up to a multiple of 4; must */ + /* be zero or positive. */ + #endif + + + /* ---------------------------------------------------------------- */ + /* Check parameter dependencies */ + /* ---------------------------------------------------------------- */ + #if DECCHECK & !DECPRINT + #error DECCHECK needs DECPRINT to be useful + #endif + #if DECALLOC & !DECPRINT + #error DECALLOC needs DECPRINT to be useful + #endif + #if DECTRACE & !DECPRINT + #error DECTRACE needs DECPRINT to be useful + #endif + + /* ---------------------------------------------------------------- */ + /* Definitions for all modules (general-purpose) */ + /* ---------------------------------------------------------------- */ + + /* Local names for common types -- for safety, decNumber modules do */ + /* not use int or long directly. */ + #define Flag uint8_t + #define Byte int8_t + #define uByte uint8_t + #define Short int16_t + #define uShort uint16_t + #define Int int32_t + #define uInt uint32_t + #define Unit decNumberUnit + #if DECUSE64 + #define Long int64_t + #define uLong uint64_t + #endif + + /* Development-use definitions */ + typedef long int LI; /* for printf arguments only */ + #define DECNOINT 0 /* 1 to check no internal use of 'int' */ + /* or stdint types */ + #if DECNOINT + /* if these interfere with your C includes, do not set DECNOINT */ + #define int ? /* enable to ensure that plain C 'int' */ + #define long ?? /* .. or 'long' types are not used */ + #endif + + /* Shared lookup tables */ + extern const uByte DECSTICKYTAB[10]; /* re-round digits if sticky */ + extern const uInt DECPOWERS[10]; /* powers of ten table */ + /* The following are included from decDPD.h */ + extern const uShort DPD2BIN[1024]; /* DPD -> 0-999 */ + extern const uShort BIN2DPD[1000]; /* 0-999 -> DPD */ + extern const uInt DPD2BINK[1024]; /* DPD -> 0-999000 */ + extern const uInt DPD2BINM[1024]; /* DPD -> 0-999000000 */ + extern const uByte DPD2BCD8[4096]; /* DPD -> ddd + len */ + extern const uByte BIN2BCD8[4000]; /* 0-999 -> ddd + len */ + extern const uShort BCD2DPD[2458]; /* 0-0x999 -> DPD (0x999=2457)*/ + + /* LONGMUL32HI -- set w=(u*v)>>32, where w, u, and v are uInts */ + /* (that is, sets w to be the high-order word of the 64-bit result; */ + /* the low-order word is simply u*v.) */ + /* This version is derived from Knuth via Hacker's Delight; */ + /* it seems to optimize better than some others tried */ + #define LONGMUL32HI(w, u, v) { \ + uInt u0, u1, v0, v1, w0, w1, w2, t; \ + u0=u & 0xffff; u1=u>>16; \ + v0=v & 0xffff; v1=v>>16; \ + w0=u0*v0; \ + t=u1*v0 + (w0>>16); \ + w1=t & 0xffff; w2=t>>16; \ + w1=u0*v1 + w1; \ + (w)=u1*v1 + w2 + (w1>>16);} + + /* ROUNDUP -- round an integer up to a multiple of n */ + #define ROUNDUP(i, n) ((((i)+(n)-1)/n)*n) + #define ROUNDUP4(i) (((i)+3)&~3) /* special for n=4 */ + + /* ROUNDDOWN -- round an integer down to a multiple of n */ + #define ROUNDDOWN(i, n) (((i)/n)*n) + #define ROUNDDOWN4(i) ((i)&~3) /* special for n=4 */ + + /* References to multi-byte sequences under different sizes; these */ + /* require locally declared variables, but do not violate strict */ + /* aliasing or alignment (as did the UINTAT simple cast to uInt). */ + /* Variables needed are uswork, uiwork, etc. [so do not use at same */ + /* level in an expression, e.g., UBTOUI(x)==UBTOUI(y) may fail]. */ + + /* Return a uInt, etc., from bytes starting at a char* or uByte* */ + #define UBTOUS(b) (memcpy((void *)&uswork, b, 2), uswork) + #define UBTOUI(b) (memcpy((void *)&uiwork, b, 4), uiwork) + + /* Store a uInt, etc., into bytes starting at a char* or uByte*. */ + /* Returns i, evaluated, for convenience; has to use uiwork because */ + /* i may be an expression. */ + #define UBFROMUS(b, i) (uswork=(i), memcpy(b, (void *)&uswork, 2), uswork) + #define UBFROMUI(b, i) (uiwork=(i), memcpy(b, (void *)&uiwork, 4), uiwork) + + /* X10 and X100 -- multiply integer i by 10 or 100 */ + /* [shifts are usually faster than multiply; could be conditional] */ + #define X10(i) (((i)<<1)+((i)<<3)) + #define X100(i) (((i)<<2)+((i)<<5)+((i)<<6)) + + /* MAXI and MINI -- general max & min (not in ANSI) for integers */ + #define MAXI(x,y) ((x)<(y)?(y):(x)) + #define MINI(x,y) ((x)>(y)?(y):(x)) + + /* Useful constants */ + #define BILLION 1000000000 /* 10**9 */ + /* CHARMASK: 0x30303030 for ASCII/UTF8; 0xF0F0F0F0 for EBCDIC */ + #define CHARMASK ((((((((uInt)'0')<<8)+'0')<<8)+'0')<<8)+'0') + + + /* ---------------------------------------------------------------- */ + /* Definitions for arbitary-precision modules (only valid after */ + /* decNumber.h has been included) */ + /* ---------------------------------------------------------------- */ + + /* Limits and constants */ + #define DECNUMMAXP 999999999 /* maximum precision code can handle */ + #define DECNUMMAXE 999999999 /* maximum adjusted exponent ditto */ + #define DECNUMMINE -999999999 /* minimum adjusted exponent ditto */ + #if (DECNUMMAXP != DEC_MAX_DIGITS) + #error Maximum digits mismatch + #endif + #if (DECNUMMAXE != DEC_MAX_EMAX) + #error Maximum exponent mismatch + #endif + #if (DECNUMMINE != DEC_MIN_EMIN) + #error Minimum exponent mismatch + #endif + + /* Set DECDPUNMAX -- the maximum integer that fits in DECDPUN */ + /* digits, and D2UTABLE -- the initializer for the D2U table */ + #if DECDPUN==1 + #define DECDPUNMAX 9 + #define D2UTABLE {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ + 18,19,20,21,22,23,24,25,26,27,28,29,30,31,32, \ + 33,34,35,36,37,38,39,40,41,42,43,44,45,46,47, \ + 48,49} + #elif DECDPUN==2 + #define DECDPUNMAX 99 + #define D2UTABLE {0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10, \ + 11,11,12,12,13,13,14,14,15,15,16,16,17,17,18, \ + 18,19,19,20,20,21,21,22,22,23,23,24,24,25} + #elif DECDPUN==3 + #define DECDPUNMAX 999 + #define D2UTABLE {0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7, \ + 8,8,8,9,9,9,10,10,10,11,11,11,12,12,12,13,13, \ + 13,14,14,14,15,15,15,16,16,16,17} + #elif DECDPUN==4 + #define DECDPUNMAX 9999 + #define D2UTABLE {0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6, \ + 6,6,6,7,7,7,7,8,8,8,8,9,9,9,9,10,10,10,10,11, \ + 11,11,11,12,12,12,12,13} + #elif DECDPUN==5 + #define DECDPUNMAX 99999 + #define D2UTABLE {0,1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5, \ + 5,5,5,5,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,9,9,9, \ + 9,9,10,10,10,10} + #elif DECDPUN==6 + #define DECDPUNMAX 999999 + #define D2UTABLE {0,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4, \ + 4,4,4,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,8, \ + 8,8,8,8,8,9} + #elif DECDPUN==7 + #define DECDPUNMAX 9999999 + #define D2UTABLE {0,1,1,1,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3, \ + 4,4,4,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,6,7, \ + 7,7,7,7,7,7} + #elif DECDPUN==8 + #define DECDPUNMAX 99999999 + #define D2UTABLE {0,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,3,3, \ + 3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6, \ + 6,6,6,6,6,7} + #elif DECDPUN==9 + #define DECDPUNMAX 999999999 + #define D2UTABLE {0,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,3,3,3, \ + 3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5, \ + 5,5,6,6,6,6} + #elif defined(DECDPUN) + #error DECDPUN must be in the range 1-9 + #endif + + /* ----- Shared data (in decNumber.c) ----- */ + /* Public lookup table used by the D2U macro (see below) */ + #define DECMAXD2U 49 + extern const uByte d2utable[DECMAXD2U+1]; + + /* ----- Macros ----- */ + /* ISZERO -- return true if decNumber dn is a zero */ + /* [performance-critical in some situations] */ + #define ISZERO(dn) decNumberIsZero(dn) /* now just a local name */ + + /* D2U -- return the number of Units needed to hold d digits */ + /* (runtime version, with table lookaside for small d) */ + #if DECDPUN==8 + #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+7)>>3)) + #elif DECDPUN==4 + #define D2U(d) ((unsigned)((d)<=DECMAXD2U?d2utable[d]:((d)+3)>>2)) + #else + #define D2U(d) ((d)<=DECMAXD2U?d2utable[d]:((d)+DECDPUN-1)/DECDPUN) + #endif + /* SD2U -- static D2U macro (for compile-time calculation) */ + #define SD2U(d) (((d)+DECDPUN-1)/DECDPUN) + + /* MSUDIGITS -- returns digits in msu, from digits, calculated */ + /* using D2U */ + #define MSUDIGITS(d) ((d)-(D2U(d)-1)*DECDPUN) + + /* D2N -- return the number of decNumber structs that would be */ + /* needed to contain that number of digits (and the initial */ + /* decNumber struct) safely. Note that one Unit is included in the */ + /* initial structure. Used for allocating space that is aligned on */ + /* a decNumber struct boundary. */ + #define D2N(d) \ + ((((SD2U(d)-1)*sizeof(Unit))+sizeof(decNumber)*2-1)/sizeof(decNumber)) + + /* TODIGIT -- macro to remove the leading digit from the unsigned */ + /* integer u at column cut (counting from the right, LSD=0) and */ + /* place it as an ASCII character into the character pointed to by */ + /* c. Note that cut must be <= 9, and the maximum value for u is */ + /* 2,000,000,000 (as is needed for negative exponents of */ + /* subnormals). The unsigned integer pow is used as a temporary */ + /* variable. */ + #define TODIGIT(u, cut, c, pow) { \ + *(c)='0'; \ + pow=DECPOWERS[cut]*2; \ + if ((u)>pow) { \ + pow*=4; \ + if ((u)>=pow) {(u)-=pow; *(c)+=8;} \ + pow/=2; \ + if ((u)>=pow) {(u)-=pow; *(c)+=4;} \ + pow/=2; \ + } \ + if ((u)>=pow) {(u)-=pow; *(c)+=2;} \ + pow/=2; \ + if ((u)>=pow) {(u)-=pow; *(c)+=1;} \ + } + + /* ---------------------------------------------------------------- */ + /* Definitions for fixed-precision modules (only valid after */ + /* decSingle.h, decDouble.h, or decQuad.h has been included) */ + /* ---------------------------------------------------------------- */ + + /* bcdnum -- a structure describing a format-independent finite */ + /* number, whose coefficient is a string of bcd8 uBytes */ + typedef struct { + uByte *msd; /* -> most significant digit */ + uByte *lsd; /* -> least ditto */ + uInt sign; /* 0=positive, DECFLOAT_Sign=negative */ + Int exponent; /* Unadjusted signed exponent (q), or */ + /* DECFLOAT_NaN etc. for a special */ + } bcdnum; + + /* Test if exponent or bcdnum exponent must be a special, etc. */ + #define EXPISSPECIAL(exp) ((exp)>=DECFLOAT_MinSp) + #define EXPISINF(exp) (exp==DECFLOAT_Inf) + #define EXPISNAN(exp) (exp==DECFLOAT_qNaN || exp==DECFLOAT_sNaN) + #define NUMISSPECIAL(num) (EXPISSPECIAL((num)->exponent)) + + /* Refer to a 32-bit word or byte in a decFloat (df) by big-endian */ + /* (array) notation (the 0 word or byte contains the sign bit), */ + /* automatically adjusting for endianness; similarly address a word */ + /* in the next-wider format (decFloatWider, or dfw) */ + #define DECWORDS (DECBYTES/4) + #define DECWWORDS (DECWBYTES/4) + #if DECLITEND + #define DFBYTE(df, off) ((df)->bytes[DECBYTES-1-(off)]) + #define DFWORD(df, off) ((df)->words[DECWORDS-1-(off)]) + #define DFWWORD(dfw, off) ((dfw)->words[DECWWORDS-1-(off)]) + #else + #define DFBYTE(df, off) ((df)->bytes[off]) + #define DFWORD(df, off) ((df)->words[off]) + #define DFWWORD(dfw, off) ((dfw)->words[off]) + #endif + + /* Tests for sign or specials, directly on DECFLOATs */ + #define DFISSIGNED(df) ((DFWORD(df, 0)&0x80000000)!=0) + #define DFISSPECIAL(df) ((DFWORD(df, 0)&0x78000000)==0x78000000) + #define DFISINF(df) ((DFWORD(df, 0)&0x7c000000)==0x78000000) + #define DFISNAN(df) ((DFWORD(df, 0)&0x7c000000)==0x7c000000) + #define DFISQNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7c000000) + #define DFISSNAN(df) ((DFWORD(df, 0)&0x7e000000)==0x7e000000) + + /* Shared lookup tables */ + extern const uInt DECCOMBMSD[64]; /* Combination field -> MSD */ + extern const uInt DECCOMBFROM[48]; /* exp+msd -> Combination */ + + /* Private generic (utility) routine */ + #if DECCHECK || DECTRACE + extern void decShowNum(const bcdnum *, const char *); + #endif + + /* Format-dependent macros and constants */ + #if defined(DECPMAX) + + /* Useful constants */ + #define DECPMAX9 (ROUNDUP(DECPMAX, 9)/9) /* 'Pmax' in 10**9s */ + /* Top words for a zero */ + #define SINGLEZERO 0x22500000 + #define DOUBLEZERO 0x22380000 + #define QUADZERO 0x22080000 + /* [ZEROWORD is defined to be one of these in the DFISZERO macro] */ + + /* Format-dependent common tests: */ + /* DFISZERO -- test for (any) zero */ + /* DFISCCZERO -- test for coefficient continuation being zero */ + /* DFISCC01 -- test for coefficient contains only 0s and 1s */ + /* DFISINT -- test for finite and exponent q=0 */ + /* DFISUINT01 -- test for sign=0, finite, exponent q=0, and */ + /* MSD=0 or 1 */ + /* ZEROWORD is also defined here. */ + /* */ + /* In DFISZERO the first test checks the least-significant word */ + /* (most likely to be non-zero); the penultimate tests MSD and */ + /* DPDs in the signword, and the final test excludes specials and */ + /* MSD>7. DFISINT similarly has to allow for the two forms of */ + /* MSD codes. DFISUINT01 only has to allow for one form of MSD */ + /* code. */ + #if DECPMAX==7 + #define ZEROWORD SINGLEZERO + /* [test macros not needed except for Zero] */ + #define DFISZERO(df) ((DFWORD(df, 0)&0x1c0fffff)==0 \ + && (DFWORD(df, 0)&0x60000000)!=0x60000000) + #elif DECPMAX==16 + #define ZEROWORD DOUBLEZERO + #define DFISZERO(df) ((DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x1c03ffff)==0 \ + && (DFWORD(df, 0)&0x60000000)!=0x60000000)) + #define DFISINT(df) ((DFWORD(df, 0)&0x63fc0000)==0x22380000 \ + ||(DFWORD(df, 0)&0x7bfc0000)==0x6a380000) + #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbfc0000)==0x22380000) + #define DFISCCZERO(df) (DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x0003ffff)==0) + #define DFISCC01(df) ((DFWORD(df, 0)&~0xfffc9124)==0 \ + && (DFWORD(df, 1)&~0x49124491)==0) + #elif DECPMAX==34 + #define ZEROWORD QUADZERO + #define DFISZERO(df) ((DFWORD(df, 3)==0 \ + && DFWORD(df, 2)==0 \ + && DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x1c003fff)==0 \ + && (DFWORD(df, 0)&0x60000000)!=0x60000000)) + #define DFISINT(df) ((DFWORD(df, 0)&0x63ffc000)==0x22080000 \ + ||(DFWORD(df, 0)&0x7bffc000)==0x6a080000) + #define DFISUINT01(df) ((DFWORD(df, 0)&0xfbffc000)==0x22080000) + #define DFISCCZERO(df) (DFWORD(df, 3)==0 \ + && DFWORD(df, 2)==0 \ + && DFWORD(df, 1)==0 \ + && (DFWORD(df, 0)&0x00003fff)==0) + + #define DFISCC01(df) ((DFWORD(df, 0)&~0xffffc912)==0 \ + && (DFWORD(df, 1)&~0x44912449)==0 \ + && (DFWORD(df, 2)&~0x12449124)==0 \ + && (DFWORD(df, 3)&~0x49124491)==0) + #endif + + /* Macros to test if a certain 10 bits of a uInt or pair of uInts */ + /* are a canonical declet [higher or lower bits are ignored]. */ + /* declet is at offset 0 (from the right) in a uInt: */ + #define CANONDPD(dpd) (((dpd)&0x300)==0 || ((dpd)&0x6e)!=0x6e) + /* declet is at offset k (a multiple of 2) in a uInt: */ + #define CANONDPDOFF(dpd, k) (((dpd)&(0x300<<(k)))==0 \ + || ((dpd)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) + /* declet is at offset k (a multiple of 2) in a pair of uInts: */ + /* [the top 2 bits will always be in the more-significant uInt] */ + #define CANONDPDTWO(hi, lo, k) (((hi)&(0x300>>(32-(k))))==0 \ + || ((hi)&(0x6e>>(32-(k))))!=(0x6e>>(32-(k))) \ + || ((lo)&(((uInt)0x6e)<<(k)))!=(((uInt)0x6e)<<(k))) + + /* Macro to test whether a full-length (length DECPMAX) BCD8 */ + /* coefficient, starting at uByte u, is all zeros */ + /* Test just the LSWord first, then the remainder as a sequence */ + /* of tests in order to avoid same-level use of UBTOUI */ + #if DECPMAX==7 + #define ISCOEFFZERO(u) ( \ + UBTOUI((u)+DECPMAX-4)==0 \ + && UBTOUS((u)+DECPMAX-6)==0 \ + && *(u)==0) + #elif DECPMAX==16 + #define ISCOEFFZERO(u) ( \ + UBTOUI((u)+DECPMAX-4)==0 \ + && UBTOUI((u)+DECPMAX-8)==0 \ + && UBTOUI((u)+DECPMAX-12)==0 \ + && UBTOUI(u)==0) + #elif DECPMAX==34 + #define ISCOEFFZERO(u) ( \ + UBTOUI((u)+DECPMAX-4)==0 \ + && UBTOUI((u)+DECPMAX-8)==0 \ + && UBTOUI((u)+DECPMAX-12)==0 \ + && UBTOUI((u)+DECPMAX-16)==0 \ + && UBTOUI((u)+DECPMAX-20)==0 \ + && UBTOUI((u)+DECPMAX-24)==0 \ + && UBTOUI((u)+DECPMAX-28)==0 \ + && UBTOUI((u)+DECPMAX-32)==0 \ + && UBTOUS(u)==0) + #endif + + /* Macros and masks for the sign, exponent continuation, and MSD */ + /* Get the sign as DECFLOAT_Sign or 0 */ + #define GETSIGN(df) (DFWORD(df, 0)&0x80000000) + /* Get the exponent continuation from a decFloat *df as an Int */ + #define GETECON(df) ((Int)((DFWORD((df), 0)&0x03ffffff)>>(32-6-DECECONL))) + /* Ditto, from the next-wider format */ + #define GETWECON(df) ((Int)((DFWWORD((df), 0)&0x03ffffff)>>(32-6-DECWECONL))) + /* Get the biased exponent similarly */ + #define GETEXP(df) ((Int)(DECCOMBEXP[DFWORD((df), 0)>>26]+GETECON(df))) + /* Get the unbiased exponent similarly */ + #define GETEXPUN(df) ((Int)GETEXP(df)-DECBIAS) + /* Get the MSD similarly (as uInt) */ + #define GETMSD(df) (DECCOMBMSD[DFWORD((df), 0)>>26]) + + /* Compile-time computes of the exponent continuation field masks */ + /* full exponent continuation field: */ + #define ECONMASK ((0x03ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) + /* same, not including its first digit (the qNaN/sNaN selector): */ + #define ECONNANMASK ((0x01ffffff>>(32-6-DECECONL))<<(32-6-DECECONL)) + + /* Macros to decode the coefficient in a finite decFloat *df into */ + /* a BCD string (uByte *bcdin) of length DECPMAX uBytes. */ + + /* In-line sequence to convert least significant 10 bits of uInt */ + /* dpd to three BCD8 digits starting at uByte u. Note that an */ + /* extra byte is written to the right of the three digits because */ + /* four bytes are moved at a time for speed; the alternative */ + /* macro moves exactly three bytes (usually slower). */ + #define dpd2bcd8(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 4) + #define dpd2bcd83(u, dpd) memcpy(u, &DPD2BCD8[((dpd)&0x3ff)*4], 3) + + /* Decode the declets. After extracting each one, it is decoded */ + /* to BCD8 using a table lookup (also used for variable-length */ + /* decode). Each DPD decode is 3 bytes BCD8 plus a one-byte */ + /* length which is not used, here). Fixed-length 4-byte moves */ + /* are fast, however, almost everywhere, and so are used except */ + /* for the final three bytes (to avoid overrun). The code below */ + /* is 36 instructions for Doubles and about 70 for Quads, even */ + /* on IA32. */ + + /* Two macros are defined for each format: */ + /* GETCOEFF extracts the coefficient of the current format */ + /* GETWCOEFF extracts the coefficient of the next-wider format. */ + /* The latter is a copy of the next-wider GETCOEFF using DFWWORD. */ + + #if DECPMAX==7 + #define GETCOEFF(df, bcd) { \ + uInt sourhi=DFWORD(df, 0); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>10); \ + dpd2bcd83(bcd+4, sourhi);} + #define GETWCOEFF(df, bcd) { \ + uInt sourhi=DFWWORD(df, 0); \ + uInt sourlo=DFWWORD(df, 1); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>8); \ + dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+7, sourlo>>20); \ + dpd2bcd8(bcd+10, sourlo>>10); \ + dpd2bcd83(bcd+13, sourlo);} + + #elif DECPMAX==16 + #define GETCOEFF(df, bcd) { \ + uInt sourhi=DFWORD(df, 0); \ + uInt sourlo=DFWORD(df, 1); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>8); \ + dpd2bcd8(bcd+4, (sourhi<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+7, sourlo>>20); \ + dpd2bcd8(bcd+10, sourlo>>10); \ + dpd2bcd83(bcd+13, sourlo);} + #define GETWCOEFF(df, bcd) { \ + uInt sourhi=DFWWORD(df, 0); \ + uInt sourmh=DFWWORD(df, 1); \ + uInt sourml=DFWWORD(df, 2); \ + uInt sourlo=DFWWORD(df, 3); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>4); \ + dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ + dpd2bcd8(bcd+7, sourmh>>16); \ + dpd2bcd8(bcd+10, sourmh>>6); \ + dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ + dpd2bcd8(bcd+16, sourml>>18); \ + dpd2bcd8(bcd+19, sourml>>8); \ + dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+25, sourlo>>20); \ + dpd2bcd8(bcd+28, sourlo>>10); \ + dpd2bcd83(bcd+31, sourlo);} + + #elif DECPMAX==34 + #define GETCOEFF(df, bcd) { \ + uInt sourhi=DFWORD(df, 0); \ + uInt sourmh=DFWORD(df, 1); \ + uInt sourml=DFWORD(df, 2); \ + uInt sourlo=DFWORD(df, 3); \ + *(bcd)=(uByte)DECCOMBMSD[sourhi>>26]; \ + dpd2bcd8(bcd+1, sourhi>>4); \ + dpd2bcd8(bcd+4, ((sourhi)<<6) | (sourmh>>26)); \ + dpd2bcd8(bcd+7, sourmh>>16); \ + dpd2bcd8(bcd+10, sourmh>>6); \ + dpd2bcd8(bcd+13, ((sourmh)<<4) | (sourml>>28)); \ + dpd2bcd8(bcd+16, sourml>>18); \ + dpd2bcd8(bcd+19, sourml>>8); \ + dpd2bcd8(bcd+22, ((sourml)<<2) | (sourlo>>30)); \ + dpd2bcd8(bcd+25, sourlo>>20); \ + dpd2bcd8(bcd+28, sourlo>>10); \ + dpd2bcd83(bcd+31, sourlo);} + + #define GETWCOEFF(df, bcd) {??} /* [should never be used] */ + #endif + + /* Macros to decode the coefficient in a finite decFloat *df into */ + /* a base-billion uInt array, with the least-significant */ + /* 0-999999999 'digit' at offset 0. */ + + /* Decode the declets. After extracting each one, it is decoded */ + /* to binary using a table lookup. Three tables are used; one */ + /* the usual DPD to binary, the other two pre-multiplied by 1000 */ + /* and 1000000 to avoid multiplication during decode. These */ + /* tables can also be used for multiplying up the MSD as the DPD */ + /* code for 0 through 9 is the identity. */ + #define DPD2BIN0 DPD2BIN /* for prettier code */ + + #if DECPMAX==7 + #define GETCOEFFBILL(df, buf) { \ + uInt sourhi=DFWORD(df, 0); \ + (buf)[0]=DPD2BIN0[sourhi&0x3ff] \ + +DPD2BINK[(sourhi>>10)&0x3ff] \ + +DPD2BINM[DECCOMBMSD[sourhi>>26]];} + + #elif DECPMAX==16 + #define GETCOEFFBILL(df, buf) { \ + uInt sourhi, sourlo; \ + sourlo=DFWORD(df, 1); \ + (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ + +DPD2BINK[(sourlo>>10)&0x3ff] \ + +DPD2BINM[(sourlo>>20)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[1]=DPD2BIN0[((sourhi<<2) | (sourlo>>30))&0x3ff] \ + +DPD2BINK[(sourhi>>8)&0x3ff] \ + +DPD2BINM[DECCOMBMSD[sourhi>>26]];} + + #elif DECPMAX==34 + #define GETCOEFFBILL(df, buf) { \ + uInt sourhi, sourmh, sourml, sourlo; \ + sourlo=DFWORD(df, 3); \ + (buf)[0]=DPD2BIN0[sourlo&0x3ff] \ + +DPD2BINK[(sourlo>>10)&0x3ff] \ + +DPD2BINM[(sourlo>>20)&0x3ff]; \ + sourml=DFWORD(df, 2); \ + (buf)[1]=DPD2BIN0[((sourml<<2) | (sourlo>>30))&0x3ff] \ + +DPD2BINK[(sourml>>8)&0x3ff] \ + +DPD2BINM[(sourml>>18)&0x3ff]; \ + sourmh=DFWORD(df, 1); \ + (buf)[2]=DPD2BIN0[((sourmh<<4) | (sourml>>28))&0x3ff] \ + +DPD2BINK[(sourmh>>6)&0x3ff] \ + +DPD2BINM[(sourmh>>16)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[3]=DPD2BIN0[((sourhi<<6) | (sourmh>>26))&0x3ff] \ + +DPD2BINK[(sourhi>>4)&0x3ff] \ + +DPD2BINM[DECCOMBMSD[sourhi>>26]];} + + #endif + + /* Macros to decode the coefficient in a finite decFloat *df into */ + /* a base-thousand uInt array (of size DECLETS+1, to allow for */ + /* the MSD), with the least-significant 0-999 'digit' at offset 0.*/ + + /* Decode the declets. After extracting each one, it is decoded */ + /* to binary using a table lookup. */ + #if DECPMAX==7 + #define GETCOEFFTHOU(df, buf) { \ + uInt sourhi=DFWORD(df, 0); \ + (buf)[0]=DPD2BIN[sourhi&0x3ff]; \ + (buf)[1]=DPD2BIN[(sourhi>>10)&0x3ff]; \ + (buf)[2]=DECCOMBMSD[sourhi>>26];} + + #elif DECPMAX==16 + #define GETCOEFFTHOU(df, buf) { \ + uInt sourhi, sourlo; \ + sourlo=DFWORD(df, 1); \ + (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ + (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ + (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[3]=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \ + (buf)[4]=DPD2BIN[(sourhi>>8)&0x3ff]; \ + (buf)[5]=DECCOMBMSD[sourhi>>26];} + + #elif DECPMAX==34 + #define GETCOEFFTHOU(df, buf) { \ + uInt sourhi, sourmh, sourml, sourlo; \ + sourlo=DFWORD(df, 3); \ + (buf)[0]=DPD2BIN[sourlo&0x3ff]; \ + (buf)[1]=DPD2BIN[(sourlo>>10)&0x3ff]; \ + (buf)[2]=DPD2BIN[(sourlo>>20)&0x3ff]; \ + sourml=DFWORD(df, 2); \ + (buf)[3]=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \ + (buf)[4]=DPD2BIN[(sourml>>8)&0x3ff]; \ + (buf)[5]=DPD2BIN[(sourml>>18)&0x3ff]; \ + sourmh=DFWORD(df, 1); \ + (buf)[6]=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \ + (buf)[7]=DPD2BIN[(sourmh>>6)&0x3ff]; \ + (buf)[8]=DPD2BIN[(sourmh>>16)&0x3ff]; \ + sourhi=DFWORD(df, 0); \ + (buf)[9]=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \ + (buf)[10]=DPD2BIN[(sourhi>>4)&0x3ff]; \ + (buf)[11]=DECCOMBMSD[sourhi>>26];} + #endif + + + /* Macros to decode the coefficient in a finite decFloat *df and */ + /* add to a base-thousand uInt array (as for GETCOEFFTHOU). */ + /* After the addition then most significant 'digit' in the array */ + /* might have a value larger then 10 (with a maximum of 19). */ + #if DECPMAX==7 + #define ADDCOEFFTHOU(df, buf) { \ + uInt sourhi=DFWORD(df, 0); \ + (buf)[0]+=DPD2BIN[sourhi&0x3ff]; \ + if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ + (buf)[1]+=DPD2BIN[(sourhi>>10)&0x3ff]; \ + if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ + (buf)[2]+=DECCOMBMSD[sourhi>>26];} + + #elif DECPMAX==16 + #define ADDCOEFFTHOU(df, buf) { \ + uInt sourhi, sourlo; \ + sourlo=DFWORD(df, 1); \ + (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \ + if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ + (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \ + if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ + (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \ + if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \ + sourhi=DFWORD(df, 0); \ + (buf)[3]+=DPD2BIN[((sourhi<<2) | (sourlo>>30))&0x3ff]; \ + if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \ + (buf)[4]+=DPD2BIN[(sourhi>>8)&0x3ff]; \ + if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \ + (buf)[5]+=DECCOMBMSD[sourhi>>26];} + + #elif DECPMAX==34 + #define ADDCOEFFTHOU(df, buf) { \ + uInt sourhi, sourmh, sourml, sourlo; \ + sourlo=DFWORD(df, 3); \ + (buf)[0]+=DPD2BIN[sourlo&0x3ff]; \ + if (buf[0]>999) {buf[0]-=1000; buf[1]++;} \ + (buf)[1]+=DPD2BIN[(sourlo>>10)&0x3ff]; \ + if (buf[1]>999) {buf[1]-=1000; buf[2]++;} \ + (buf)[2]+=DPD2BIN[(sourlo>>20)&0x3ff]; \ + if (buf[2]>999) {buf[2]-=1000; buf[3]++;} \ + sourml=DFWORD(df, 2); \ + (buf)[3]+=DPD2BIN[((sourml<<2) | (sourlo>>30))&0x3ff]; \ + if (buf[3]>999) {buf[3]-=1000; buf[4]++;} \ + (buf)[4]+=DPD2BIN[(sourml>>8)&0x3ff]; \ + if (buf[4]>999) {buf[4]-=1000; buf[5]++;} \ + (buf)[5]+=DPD2BIN[(sourml>>18)&0x3ff]; \ + if (buf[5]>999) {buf[5]-=1000; buf[6]++;} \ + sourmh=DFWORD(df, 1); \ + (buf)[6]+=DPD2BIN[((sourmh<<4) | (sourml>>28))&0x3ff]; \ + if (buf[6]>999) {buf[6]-=1000; buf[7]++;} \ + (buf)[7]+=DPD2BIN[(sourmh>>6)&0x3ff]; \ + if (buf[7]>999) {buf[7]-=1000; buf[8]++;} \ + (buf)[8]+=DPD2BIN[(sourmh>>16)&0x3ff]; \ + if (buf[8]>999) {buf[8]-=1000; buf[9]++;} \ + sourhi=DFWORD(df, 0); \ + (buf)[9]+=DPD2BIN[((sourhi<<6) | (sourmh>>26))&0x3ff]; \ + if (buf[9]>999) {buf[9]-=1000; buf[10]++;} \ + (buf)[10]+=DPD2BIN[(sourhi>>4)&0x3ff]; \ + if (buf[10]>999) {buf[10]-=1000; buf[11]++;} \ + (buf)[11]+=DECCOMBMSD[sourhi>>26];} + #endif + + + /* Set a decFloat to the maximum positive finite number (Nmax) */ + #if DECPMAX==7 + #define DFSETNMAX(df) \ + {DFWORD(df, 0)=0x77f3fcff;} + #elif DECPMAX==16 + #define DFSETNMAX(df) \ + {DFWORD(df, 0)=0x77fcff3f; \ + DFWORD(df, 1)=0xcff3fcff;} + #elif DECPMAX==34 + #define DFSETNMAX(df) \ + {DFWORD(df, 0)=0x77ffcff3; \ + DFWORD(df, 1)=0xfcff3fcf; \ + DFWORD(df, 2)=0xf3fcff3f; \ + DFWORD(df, 3)=0xcff3fcff;} + #endif + + /* [end of format-dependent macros and constants] */ + #endif + +#else + #error decNumberLocal included more than once +#endif