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dtoa.c
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/****************************************************************
*
* The author of this software is David M. Gay.
*
* Copyright (c) 1991, 2000, 2001 by Lucent Technologies.
*
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
* is included in all copies of any software which is or includes a copy
* or modification of this software and in all copies of the supporting
* documentation for such software.
*
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR LUCENT MAKES ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*
***************************************************************/
/* Please send bug reports to David M. Gay (dmg at acm dot org,
* with " at " changed at "@" and " dot " changed to "."). */
/* On a machine with IEEE extended-precision registers, it is
* necessary to specify double-precision (53-bit) rounding precision
* before invoking strtod or dtoa. If the machine uses (the equivalent
* of) Intel 80x87 arithmetic, the call
* _control87(PC_53, MCW_PC);
* does this with many compilers. Whether this or another call is
* appropriate depends on the compiler; for this to work, it may be
* necessary to #include "float.h" or another system-dependent header
* file.
*/
/* strtod for IEEE-, VAX-, and IBM-arithmetic machines.
*
* This strtod returns a nearest machine number to the input decimal
* string (or sets errno to ERANGE). With IEEE arithmetic, ties are
* broken by the IEEE round-even rule. Otherwise ties are broken by
* biased rounding (add half and chop).
*
* Inspired loosely by William D. Clinger's paper "How to Read Floating
* Point Numbers Accurately" [Proc. ACM SIGPLAN '90, pp. 92-101].
*
* Modifications:
*
* 1. We only require IEEE, IBM, or VAX double-precision
* arithmetic (not IEEE double-extended).
* 2. We get by with floating-point arithmetic in a case that
* Clinger missed -- when we're computing d * 10^n
* for a small integer d and the integer n is not too
* much larger than 22 (the maximum integer k for which
* we can represent 10^k exactly), we may be able to
* compute (d*10^k) * 10^(e-k) with just one roundoff.
* 3. Rather than a bit-at-a-time adjustment of the binary
* result in the hard case, we use floating-point
* arithmetic to determine the adjustment to within
* one bit; only in really hard cases do we need to
* compute a second residual.
* 4. Because of 3., we don't need a large table of powers of 10
* for ten-to-e (just some small tables, e.g. of 10^k
* for 0 <= k <= 22).
*/
/*
* #define IEEE_LITTLE_ENDIAN for IEEE-arithmetic machines where the least
* significant byte has the lowest address.
* #define IEEE_BIG_ENDIAN for IEEE-arithmetic machines where the most
* significant byte has the lowest address.
* #define Long int on machines with 32-bit ints and 64-bit longs.
* #define IBM for IBM mainframe-style floating-point arithmetic.
* #define VAX for VAX-style floating-point arithmetic (D_floating).
* #define No_leftright to omit left-right logic in fast floating-point
* computation of dtoa.
* #define Honor_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
* and strtod and dtoa should round accordingly.
* #define Check_FLT_ROUNDS if FLT_ROUNDS can assume the values 2 or 3
* and Honor_FLT_ROUNDS is not #defined.
* #define RND_PRODQUOT to use rnd_prod and rnd_quot (assembly routines
* that use extended-precision instructions to compute rounded
* products and quotients) with IBM.
* #define ROUND_BIASED for IEEE-format with biased rounding.
* #define Inaccurate_Divide for IEEE-format with correctly rounded
* products but inaccurate quotients, e.g., for Intel i860.
* #define NO_LONG_LONG on machines that do not have a "long long"
* integer type (of >= 64 bits). On such machines, you can
* #define Just_16 to store 16 bits per 32-bit Long when doing
* high-precision integer arithmetic. Whether this speeds things
* up or slows things down depends on the machine and the number
* being converted. If long long is available and the name is
* something other than "long long", #define Llong to be the name,
* and if "unsigned Llong" does not work as an unsigned version of
* Llong, #define #ULLong to be the corresponding unsigned type.
* #define KR_headers for old-style C function headers.
* #define Bad_float_h if your system lacks a float.h or if it does not
* define some or all of DBL_DIG, DBL_MAX_10_EXP, DBL_MAX_EXP,
* FLT_RADIX, FLT_ROUNDS, and DBL_MAX.
* #define MALLOC your_malloc, where your_malloc(n) acts like malloc(n)
* if memory is available and otherwise does something you deem
* appropriate. If MALLOC is undefined, malloc will be invoked
* directly -- and assumed always to succeed.
* #define Omit_Private_Memory to omit logic (added Jan. 1998) for making
* memory allocations from a private pool of memory when possible.
* When used, the private pool is PRIVATE_MEM bytes long: 2304 bytes,
* unless #defined to be a different length. This default length
* suffices to get rid of MALLOC calls except for unusual cases,
* such as decimal-to-binary conversion of a very long string of
* digits. The longest string dtoa can return is about 751 bytes
* long. For conversions by strtod of strings of 800 digits and
* all dtoa conversions in single-threaded executions with 8-byte
* pointers, PRIVATE_MEM >= 7400 appears to suffice; with 4-byte
* pointers, PRIVATE_MEM >= 7112 appears adequate.
* #define INFNAN_CHECK on IEEE systems to cause strtod to check for
* Infinity and NaN (case insensitively). On some systems (e.g.,
* some HP systems), it may be necessary to #define NAN_WORD0
* appropriately -- to the most significant word of a quiet NaN.
* (On HP Series 700/800 machines, -DNAN_WORD0=0x7ff40000 works.)
* When INFNAN_CHECK is #defined and No_Hex_NaN is not #defined,
* strtod also accepts (case insensitively) strings of the form
* NaN(x), where x is a string of hexadecimal digits and spaces;
* if there is only one string of hexadecimal digits, it is taken
* for the 52 fraction bits of the resulting NaN; if there are two
* or more strings of hex digits, the first is for the high 20 bits,
* the second and subsequent for the low 32 bits, with intervening
* white space ignored; but if this results in none of the 52
* fraction bits being on (an IEEE Infinity symbol), then NAN_WORD0
* and NAN_WORD1 are used instead.
* #define MULTIPLE_THREADS if the system offers preemptively scheduled
* multiple threads. In this case, you must provide (or suitably
* #define) two locks, acquired by ACQUIRE_DTOA_LOCK(n) and freed
* by FREE_DTOA_LOCK(n) for n = 0 or 1. (The second lock, accessed
* in pow5mult, ensures lazy evaluation of only one copy of high
* powers of 5; omitting this lock would introduce a small
* probability of wasting memory, but would otherwise be harmless.)
* You must also invoke freedtoa(s) to free the value s returned by
* dtoa. You may do so whether or not MULTIPLE_THREADS is #defined.
* #define NO_IEEE_Scale to disable new (Feb. 1997) logic in strtod that
* avoids underflows on inputs whose result does not underflow.
* If you #define NO_IEEE_Scale on a machine that uses IEEE-format
* floating-point numbers and flushes underflows to zero rather
* than implementing gradual underflow, then you must also #define
* Sudden_Underflow.
* #define YES_ALIAS to permit aliasing certain double values with
* arrays of ULongs. This leads to slightly better code with
* some compilers and was always used prior to 19990916, but it
* is not strictly legal and can cause trouble with aggressively
* optimizing compilers (e.g., gcc 2.95.1 under -O2).
* #define USE_LOCALE to use the current locale's decimal_point value.
* #define SET_INEXACT if IEEE arithmetic is being used and extra
* computation should be done to set the inexact flag when the
* result is inexact and avoid setting inexact when the result
* is exact. In this case, dtoa.c must be compiled in
* an environment, perhaps provided by #include "dtoa.c" in a
* suitable wrapper, that defines two functions,
* int get_inexact(void);
* void clear_inexact(void);
* such that get_inexact() returns a nonzero value if the
* inexact bit is already set, and clear_inexact() sets the
* inexact bit to 0. When SET_INEXACT is #defined, strtod
* also does extra computations to set the underflow and overflow
* flags when appropriate (i.e., when the result is tiny and
* inexact or when it is a numeric value rounded to +-infinity).
* #define NO_ERRNO if strtod should not assign errno = ERANGE when
* the result overflows to +-Infinity or underflows to 0.
*/
#ifdef WORDS_BIGENDIAN
#define IEEE_BIG_ENDIAN
#else
#define IEEE_LITTLE_ENDIAN
#endif
#ifdef __vax__
#define VAX
#undef IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif
#if defined(__arm__) && !defined(__VFP_FP__)
#define IEEE_BIG_ENDIAN
#undef IEEE_LITTLE_ENDIAN
#endif
#undef Long
#undef ULong
#include <assert.h>
#include <limits.h>
#include <stddef.h>
#include <stdint.h>
#if (INT_MAX >> 30) && !(INT_MAX >> 31)
#define Long int
#define ULong unsigned int
#elif (LONG_MAX >> 30) && !(LONG_MAX >> 31)
#define Long long int
#define ULong unsigned long int
#else
#error No 32bit integer
#endif
#if defined(HAVE_LONG_LONG) && (HAVE_LONG_LONG)
#define Llong LONG_LONG
#else
#define NO_LONG_LONG
#endif
#ifdef DEBUG
#include <stdio.h>
#define Bug(x) {fprintf(stderr, "%s\n", (x)); exit(EXIT_FAILURE);}
#endif
#ifndef ISDIGIT
#include <ctype.h>
#define ISDIGIT(c) isdigit(c)
#endif
#include <errno.h>
#include <stdlib.h>
#include <string.h>
#ifdef USE_LOCALE
#include <locale.h>
#endif
#ifdef MALLOC
extern void *MALLOC(size_t);
#else
#define MALLOC malloc
#endif
#ifdef FREE
extern void FREE(void*);
#else
#define FREE free
#endif
#ifndef NO_SANITIZE
#define NO_SANITIZE(x, y) y
#endif
#ifndef Omit_Private_Memory
#ifndef PRIVATE_MEM
#define PRIVATE_MEM 2304
#endif
#define PRIVATE_mem ((PRIVATE_MEM+sizeof(double)-1)/sizeof(double))
static double private_mem[PRIVATE_mem], *pmem_next = private_mem;
#endif
#undef IEEE_Arith
#undef Avoid_Underflow
#ifdef IEEE_BIG_ENDIAN
#define IEEE_Arith
#endif
#ifdef IEEE_LITTLE_ENDIAN
#define IEEE_Arith
#endif
#ifdef Bad_float_h
#ifdef IEEE_Arith
#define DBL_DIG 15
#define DBL_MAX_10_EXP 308
#define DBL_MAX_EXP 1024
#define FLT_RADIX 2
#endif /*IEEE_Arith*/
#ifdef IBM
#define DBL_DIG 16
#define DBL_MAX_10_EXP 75
#define DBL_MAX_EXP 63
#define FLT_RADIX 16
#define DBL_MAX 7.2370055773322621e+75
#endif
#ifdef VAX
#define DBL_DIG 16
#define DBL_MAX_10_EXP 38
#define DBL_MAX_EXP 127
#define FLT_RADIX 2
#define DBL_MAX 1.7014118346046923e+38
#endif
#ifndef LONG_MAX
#define LONG_MAX 2147483647
#endif
#else /* ifndef Bad_float_h */
#include <float.h>
#endif /* Bad_float_h */
#include <math.h>
#ifdef __cplusplus
extern "C" {
#if 0
} /* satisfy cc-mode */
#endif
#endif
#ifndef hexdigit
static const char hexdigit[] = "0123456789abcdef0123456789ABCDEF";
#endif
#if defined(IEEE_LITTLE_ENDIAN) + defined(IEEE_BIG_ENDIAN) + defined(VAX) + defined(IBM) != 1
Exactly one of IEEE_LITTLE_ENDIAN, IEEE_BIG_ENDIAN, VAX, or IBM should be defined.
#endif
typedef union { double d; ULong L[2]; } U;
#ifdef YES_ALIAS
typedef double double_u;
# define dval(x) (x)
# ifdef IEEE_LITTLE_ENDIAN
# define word0(x) (((ULong *)&(x))[1])
# define word1(x) (((ULong *)&(x))[0])
# else
# define word0(x) (((ULong *)&(x))[0])
# define word1(x) (((ULong *)&(x))[1])
# endif
#else
typedef U double_u;
# ifdef IEEE_LITTLE_ENDIAN
# define word0(x) ((x).L[1])
# define word1(x) ((x).L[0])
# else
# define word0(x) ((x).L[0])
# define word1(x) ((x).L[1])
# endif
# define dval(x) ((x).d)
#endif
/* The following definition of Storeinc is appropriate for MIPS processors.
* An alternative that might be better on some machines is
* #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)
*/
#if defined(IEEE_LITTLE_ENDIAN) + defined(VAX) + defined(__arm__)
#define Storeinc(a,b,c) (((unsigned short *)(a))[1] = (unsigned short)(b), \
((unsigned short *)(a))[0] = (unsigned short)(c), (a)++)
#else
#define Storeinc(a,b,c) (((unsigned short *)(a))[0] = (unsigned short)(b), \
((unsigned short *)(a))[1] = (unsigned short)(c), (a)++)
#endif
/* #define P DBL_MANT_DIG */
/* Ten_pmax = floor(P*log(2)/log(5)) */
/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */
/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */
/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */
#ifdef IEEE_Arith
#define Exp_shift 20
#define Exp_shift1 20
#define Exp_msk1 0x100000
#define Exp_msk11 0x100000
#define Exp_mask 0x7ff00000
#define P 53
#define Bias 1023
#define Emin (-1022)
#define Exp_1 0x3ff00000
#define Exp_11 0x3ff00000
#define Ebits 11
#define Frac_mask 0xfffff
#define Frac_mask1 0xfffff
#define Ten_pmax 22
#define Bletch 0x10
#define Bndry_mask 0xfffff
#define Bndry_mask1 0xfffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 1
#define Tiny0 0
#define Tiny1 1
#define Quick_max 14
#define Int_max 14
#ifndef NO_IEEE_Scale
#define Avoid_Underflow
#ifdef Flush_Denorm /* debugging option */
#undef Sudden_Underflow
#endif
#endif
#ifndef Flt_Rounds
#ifdef FLT_ROUNDS
#define Flt_Rounds FLT_ROUNDS
#else
#define Flt_Rounds 1
#endif
#endif /*Flt_Rounds*/
#ifdef Honor_FLT_ROUNDS
#define Rounding rounding
#undef Check_FLT_ROUNDS
#define Check_FLT_ROUNDS
#else
#define Rounding Flt_Rounds
#endif
#else /* ifndef IEEE_Arith */
#undef Check_FLT_ROUNDS
#undef Honor_FLT_ROUNDS
#undef SET_INEXACT
#undef Sudden_Underflow
#define Sudden_Underflow
#ifdef IBM
#undef Flt_Rounds
#define Flt_Rounds 0
#define Exp_shift 24
#define Exp_shift1 24
#define Exp_msk1 0x1000000
#define Exp_msk11 0x1000000
#define Exp_mask 0x7f000000
#define P 14
#define Bias 65
#define Exp_1 0x41000000
#define Exp_11 0x41000000
#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */
#define Frac_mask 0xffffff
#define Frac_mask1 0xffffff
#define Bletch 4
#define Ten_pmax 22
#define Bndry_mask 0xefffff
#define Bndry_mask1 0xffffff
#define LSB 1
#define Sign_bit 0x80000000
#define Log2P 4
#define Tiny0 0x100000
#define Tiny1 0
#define Quick_max 14
#define Int_max 15
#else /* VAX */
#undef Flt_Rounds
#define Flt_Rounds 1
#define Exp_shift 23
#define Exp_shift1 7
#define Exp_msk1 0x80
#define Exp_msk11 0x800000
#define Exp_mask 0x7f80
#define P 56
#define Bias 129
#define Exp_1 0x40800000
#define Exp_11 0x4080
#define Ebits 8
#define Frac_mask 0x7fffff
#define Frac_mask1 0xffff007f
#define Ten_pmax 24
#define Bletch 2
#define Bndry_mask 0xffff007f
#define Bndry_mask1 0xffff007f
#define LSB 0x10000
#define Sign_bit 0x8000
#define Log2P 1
#define Tiny0 0x80
#define Tiny1 0
#define Quick_max 15
#define Int_max 15
#endif /* IBM, VAX */
#endif /* IEEE_Arith */
#ifndef IEEE_Arith
#define ROUND_BIASED
#endif
#ifdef RND_PRODQUOT
#define rounded_product(a,b) ((a) = rnd_prod((a), (b)))
#define rounded_quotient(a,b) ((a) = rnd_quot((a), (b)))
extern double rnd_prod(double, double), rnd_quot(double, double);
#else
#define rounded_product(a,b) ((a) *= (b))
#define rounded_quotient(a,b) ((a) /= (b))
#endif
#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))
#define Big1 0xffffffff
#ifndef Pack_32
#define Pack_32
#endif
#define FFFFFFFF 0xffffffffUL
#ifdef NO_LONG_LONG
#undef ULLong
#ifdef Just_16
#undef Pack_32
/* When Pack_32 is not defined, we store 16 bits per 32-bit Long.
* This makes some inner loops simpler and sometimes saves work
* during multiplications, but it often seems to make things slightly
* slower. Hence the default is now to store 32 bits per Long.
*/
#endif
#else /* long long available */
#ifndef Llong
#define Llong long long
#endif
#ifndef ULLong
#define ULLong unsigned Llong
#endif
#endif /* NO_LONG_LONG */
#define MULTIPLE_THREADS 1
#ifndef MULTIPLE_THREADS
#define ACQUIRE_DTOA_LOCK(n) /*nothing*/
#define FREE_DTOA_LOCK(n) /*nothing*/
#else
#define ACQUIRE_DTOA_LOCK(n) /*unused right now*/
#define FREE_DTOA_LOCK(n) /*unused right now*/
#endif
#ifndef ATOMIC_PTR_CAS
#define ATOMIC_PTR_CAS(var, old, new) ((var) = (new), (void *)(old))
#endif
#ifndef LIKELY
#define LIKELY(x) (x)
#endif
#ifndef UNLIKELY
#define UNLIKELY(x) (x)
#endif
#ifndef ASSUME
#define ASSUME(x) (void)(x)
#endif
#define Kmax 15
struct Bigint {
struct Bigint *next;
int k, maxwds, sign, wds;
ULong x[1];
};
typedef struct Bigint Bigint;
static Bigint *freelist[Kmax+1];
#define BLOCKING_BIGINT ((Bigint *)(-1))
static Bigint *
Balloc(int k)
{
int x;
Bigint *rv;
#ifndef Omit_Private_Memory
size_t len;
#endif
rv = 0;
ACQUIRE_DTOA_LOCK(0);
if (k <= Kmax) {
rv = freelist[k];
while (rv) {
Bigint *rvn = rv;
rv = ATOMIC_PTR_CAS(freelist[k], rv, BLOCKING_BIGINT);
if (LIKELY(rv != BLOCKING_BIGINT && rvn == rv)) {
rvn = ATOMIC_PTR_CAS(freelist[k], BLOCKING_BIGINT, rv->next);
assert(rvn == BLOCKING_BIGINT);
ASSUME(rv);
break;
}
}
}
if (!rv) {
x = 1 << k;
#ifdef Omit_Private_Memory
rv = (Bigint *)MALLOC(sizeof(Bigint) + (x-1)*sizeof(ULong));
#else
len = (sizeof(Bigint) + (x-1)*sizeof(ULong) + sizeof(double) - 1)
/sizeof(double);
if (k <= Kmax) {
double *pnext = pmem_next;
while (pnext - private_mem + len <= PRIVATE_mem) {
double *p = pnext;
pnext = ATOMIC_PTR_CAS(pmem_next, pnext, pnext + len);
if (LIKELY(p == pnext)) {
rv = (Bigint*)pnext;
ASSUME(rv);
break;
}
}
}
if (!rv)
rv = (Bigint*)MALLOC(len*sizeof(double));
#endif
rv->k = k;
rv->maxwds = x;
}
FREE_DTOA_LOCK(0);
rv->sign = rv->wds = 0;
return rv;
}
static void
Bfree(Bigint *v)
{
Bigint *vn;
if (v) {
if (v->k > Kmax) {
FREE(v);
return;
}
ACQUIRE_DTOA_LOCK(0);
do {
do {
vn = ATOMIC_PTR_CAS(freelist[v->k], 0, 0);
} while (UNLIKELY(vn == BLOCKING_BIGINT));
v->next = vn;
} while (UNLIKELY(ATOMIC_PTR_CAS(freelist[v->k], vn, v) != vn));
FREE_DTOA_LOCK(0);
}
}
#define Bcopy(x,y) memcpy((char *)&(x)->sign, (char *)&(y)->sign, \
(y)->wds*sizeof(Long) + 2*sizeof(int))
static Bigint *
multadd(Bigint *b, int m, int a) /* multiply by m and add a */
{
int i, wds;
ULong *x;
#ifdef ULLong
ULLong carry, y;
#else
ULong carry, y;
#ifdef Pack_32
ULong xi, z;
#endif
#endif
Bigint *b1;
wds = b->wds;
x = b->x;
i = 0;
carry = a;
do {
#ifdef ULLong
y = *x * (ULLong)m + carry;
carry = y >> 32;
*x++ = (ULong)(y & FFFFFFFF);
#else
#ifdef Pack_32
xi = *x;
y = (xi & 0xffff) * m + carry;
z = (xi >> 16) * m + (y >> 16);
carry = z >> 16;
*x++ = (z << 16) + (y & 0xffff);
#else
y = *x * m + carry;
carry = y >> 16;
*x++ = y & 0xffff;
#endif
#endif
} while (++i < wds);
if (carry) {
if (wds >= b->maxwds) {
b1 = Balloc(b->k+1);
Bcopy(b1, b);
Bfree(b);
b = b1;
}
b->x[wds++] = (ULong)carry;
b->wds = wds;
}
return b;
}
static Bigint *
s2b(const char *s, int nd0, int nd, ULong y9)
{
Bigint *b;
int i, k;
Long x, y;
x = (nd + 8) / 9;
for (k = 0, y = 1; x > y; y <<= 1, k++) ;
#ifdef Pack_32
b = Balloc(k);
b->x[0] = y9;
b->wds = 1;
#else
b = Balloc(k+1);
b->x[0] = y9 & 0xffff;
b->wds = (b->x[1] = y9 >> 16) ? 2 : 1;
#endif
i = 9;
if (9 < nd0) {
s += 9;
do {
b = multadd(b, 10, *s++ - '0');
} while (++i < nd0);
s++;
}
else
s += 10;
for (; i < nd; i++)
b = multadd(b, 10, *s++ - '0');
return b;
}
static int
hi0bits(register ULong x)
{
register int k = 0;
if (!(x & 0xffff0000)) {
k = 16;
x <<= 16;
}
if (!(x & 0xff000000)) {
k += 8;
x <<= 8;
}
if (!(x & 0xf0000000)) {
k += 4;
x <<= 4;
}
if (!(x & 0xc0000000)) {
k += 2;
x <<= 2;
}
if (!(x & 0x80000000)) {
k++;
if (!(x & 0x40000000))
return 32;
}
return k;
}
static int
lo0bits(ULong *y)
{
register int k;
register ULong x = *y;
if (x & 7) {
if (x & 1)
return 0;
if (x & 2) {
*y = x >> 1;
return 1;
}
*y = x >> 2;
return 2;
}
k = 0;
if (!(x & 0xffff)) {
k = 16;
x >>= 16;
}
if (!(x & 0xff)) {
k += 8;
x >>= 8;
}
if (!(x & 0xf)) {
k += 4;
x >>= 4;
}
if (!(x & 0x3)) {
k += 2;
x >>= 2;
}
if (!(x & 1)) {
k++;
x >>= 1;
if (!x)
return 32;
}
*y = x;
return k;
}
static Bigint *
i2b(int i)
{
Bigint *b;
b = Balloc(1);
b->x[0] = i;
b->wds = 1;
return b;
}
static Bigint *
mult(Bigint *a, Bigint *b)
{
Bigint *c;
int k, wa, wb, wc;
ULong *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
ULong y;
#ifdef ULLong
ULLong carry, z;
#else
ULong carry, z;
#ifdef Pack_32
ULong z2;
#endif
#endif
if (a->wds < b->wds) {
c = a;
a = b;
b = c;
}
k = a->k;
wa = a->wds;
wb = b->wds;
wc = wa + wb;
if (wc > a->maxwds)
k++;
c = Balloc(k);
for (x = c->x, xa = x + wc; x < xa; x++)
*x = 0;
xa = a->x;
xae = xa + wa;
xb = b->x;
xbe = xb + wb;
xc0 = c->x;
#ifdef ULLong
for (; xb < xbe; xc0++) {
if ((y = *xb++) != 0) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * (ULLong)y + *xc + carry;
carry = z >> 32;
*xc++ = (ULong)(z & FFFFFFFF);
} while (x < xae);
*xc = (ULong)carry;
}
}
#else
#ifdef Pack_32
for (; xb < xbe; xb++, xc0++) {
if ((y = *xb & 0xffff) != 0) {
x = xa;
xc = xc0;
carry = 0;
do {
z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
carry = z >> 16;
z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
carry = z2 >> 16;
Storeinc(xc, z2, z);
} while (x < xae);
*xc = (ULong)carry;
}
if ((y = *xb >> 16) != 0) {
x = xa;
xc = xc0;
carry = 0;
z2 = *xc;
do {
z = (*x & 0xffff) * y + (*xc >> 16) + carry;
carry = z >> 16;
Storeinc(xc, z, z2);
z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
carry = z2 >> 16;
} while (x < xae);
*xc = z2;
}
}
#else
for (; xb < xbe; xc0++) {
if (y = *xb++) {
x = xa;
xc = xc0;
carry = 0;
do {
z = *x++ * y + *xc + carry;
carry = z >> 16;
*xc++ = z & 0xffff;
} while (x < xae);
*xc = (ULong)carry;
}
}
#endif
#endif
for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc) ;
c->wds = wc;
return c;
}
static Bigint *p5s;
static Bigint *
pow5mult(Bigint *b, int k)
{
Bigint *b1, *p5, *p51;
Bigint *p5tmp;
int i;
static const int p05[3] = { 5, 25, 125 };
if ((i = k & 3) != 0)
b = multadd(b, p05[i-1], 0);
if (!(k >>= 2))
return b;
if (!(p5 = p5s)) {
/* first time */
ACQUIRE_DTOA_LOCK(1);
if (!(p5 = p5s)) {
p5 = i2b(625);
p5->next = 0;
p5tmp = ATOMIC_PTR_CAS(p5s, NULL, p5);
if (UNLIKELY(p5tmp)) {
Bfree(p5);
p5 = p5tmp;
}
}
FREE_DTOA_LOCK(1);
}
for (;;) {
if (k & 1) {
b1 = mult(b, p5);
Bfree(b);
b = b1;
}
if (!(k >>= 1))
break;
if (!(p51 = p5->next)) {
ACQUIRE_DTOA_LOCK(1);
if (!(p51 = p5->next)) {
p51 = mult(p5,p5);
p51->next = 0;
p5tmp = ATOMIC_PTR_CAS(p5->next, NULL, p51);
if (UNLIKELY(p5tmp)) {
Bfree(p51);
p51 = p5tmp;
}
}
FREE_DTOA_LOCK(1);
}
p5 = p51;
}
return b;
}
static Bigint *
lshift(Bigint *b, int k)
{
int i, k1, n, n1;
Bigint *b1;
ULong *x, *x1, *xe, z;
#ifdef Pack_32
n = k >> 5;
#else
n = k >> 4;
#endif
k1 = b->k;
n1 = n + b->wds + 1;
for (i = b->maxwds; n1 > i; i <<= 1)
k1++;
b1 = Balloc(k1);
x1 = b1->x;
for (i = 0; i < n; i++)
*x1++ = 0;
x = b->x;
xe = x + b->wds;
#ifdef Pack_32
if (k &= 0x1f) {
k1 = 32 - k;
z = 0;
do {
*x1++ = *x << k | z;
z = *x++ >> k1;
} while (x < xe);
if ((*x1 = z) != 0)
++n1;
}
#else
if (k &= 0xf) {
k1 = 16 - k;
z = 0;
do {
*x1++ = *x << k & 0xffff | z;
z = *x++ >> k1;
} while (x < xe);
if (*x1 = z)
++n1;
}
#endif
else
do {
*x1++ = *x++;
} while (x < xe);
b1->wds = n1 - 1;
Bfree(b);
return b1;
}
static int
cmp(Bigint *a, Bigint *b)
{
ULong *xa, *xa0, *xb, *xb0;
int i, j;
i = a->wds;
j = b->wds;
#ifdef DEBUG
if (i > 1 && !a->x[i-1])
Bug("cmp called with a->x[a->wds-1] == 0");
if (j > 1 && !b->x[j-1])