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decimal.c
1574 lines (1321 loc) · 43.5 KB
/
decimal.c
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/*
decimal.c
conversions and numerical operations for the c# type System.Decimal
Author: Martin Weindel (martin.weindel@t-online.de)
(C) 2001 by Martin Weindel
*/
/*
* machine dependent configuration for
* CSharp value type System.Decimal
*/
#include "config.h"
#include <mono/metadata/exception.h>
#include <stdio.h>
#include <memory.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#ifndef DISABLE_DECIMAL
/* needed for building microsoft dll */
#ifdef __GNUC__
#define DECINLINE __inline
#else
#define DECINLINE
#endif
#define LIT_GUINT32(x) x
#define LIT_GUINT64(x) x##LL
/* we need a UInt64 type => guint64 */
#include <glib.h>
#include "decimal.h"
/*
* Deal with anon union support.
*/
#define ss32 u.ss32
#define signscale u.signscale
/* debugging stuff */
#ifdef _DEBUG
#include <assert.h>
#define PRECONDITION(flag) assert(flag)
#define POSTCONDITION(flag) assert(flag)
#define TEST(flag) assert(flag)
#define INVARIANT_TEST(p) assert(p->signscale.scale >= 0 && p->signscale.scale <= DECIMAL_MAX_SCALE \
&& p->signscale.reserved1 == 0 && p->signscale.reserved2 == 0);
#else
#define PRECONDITION(flag)
#define POSTCONDITION(flag)
#define TEST(flag)
#define INVARIANT_TEST(p)
#endif /*#ifdef _DEBUG*/
#define DECIMAL_MAX_SCALE 28
#define DECIMAL_MAX_INTFACTORS 9
#define DECIMAL_SUCCESS 0
#define DECIMAL_FINISHED 1
#define DECIMAL_OVERFLOW 2
#define DECIMAL_INVALID_CHARACTER 2
#define DECIMAL_INTERNAL_ERROR 3
#define DECIMAL_INVALID_BITS 4
#define DECIMAL_DIVIDE_BY_ZERO 5
#define DECIMAL_BUFFER_OVERFLOW 6
/* some MACROS */
#define DECINIT(src) memset(src, 0, sizeof(decimal_repr))
#define DECCOPY(dest, src) memcpy(dest, src, sizeof(decimal_repr))
#define DECSWAP(p1, p2, h) \
h = (p1)->ss32; (p1)->ss32 = (p2)->ss32; (p2)->ss32 = h; \
h = (p1)->hi32; (p1)->hi32 = (p2)->hi32; (p2)->hi32 = h; \
h = (p1)->mid32; (p1)->mid32 = (p2)->mid32; (p2)->mid32 = h; \
h = (p1)->lo32; (p1)->lo32 = (p2)->lo32; (p2)->lo32 = h;
#define DECNEGATE(p1) (p1)->signscale.sign = 1 - (p1)->signscale.sign
#define LIT_DEC128(hi, mid, lo) { (((guint64)mid)<<32 | lo), hi }
#define DECTO128(pd, lo, hi) \
lo = (((guint64)(pd)->mid32) << 32) | (pd)->lo32; \
hi = (pd)->hi32;
/* some constants */
#define LIT_GUINT32_HIGHBIT LIT_GUINT32(0x80000000)
#define LIT_GUINT64_HIGHBIT LIT_GUINT64(0x8000000000000000)
#define DECIMAL_LOG_NEGINF -1000
static const guint32 constantsDecadeInt32Factors[DECIMAL_MAX_INTFACTORS+1] = {
LIT_GUINT32(1), LIT_GUINT32(10), LIT_GUINT32(100), LIT_GUINT32(1000),
LIT_GUINT32(10000), LIT_GUINT32(100000), LIT_GUINT32(1000000),
LIT_GUINT32(10000000), LIT_GUINT32(100000000), LIT_GUINT32(1000000000)
};
typedef struct {
guint64 lo;
guint64 hi;
} dec128_repr;
static const dec128_repr dec128decadeFactors[DECIMAL_MAX_SCALE+1] = {
LIT_DEC128( 0, 0, 1u), /* == 1 */
LIT_DEC128( 0, 0, 10u), /* == 10 */
LIT_DEC128( 0, 0, 100u), /* == 100 */
LIT_DEC128( 0, 0, 1000u), /* == 1e3m */
LIT_DEC128( 0, 0, 10000u), /* == 1e4m */
LIT_DEC128( 0, 0, 100000u), /* == 1e5m */
LIT_DEC128( 0, 0, 1000000u), /* == 1e6m */
LIT_DEC128( 0, 0, 10000000u), /* == 1e7m */
LIT_DEC128( 0, 0, 100000000u), /* == 1e8m */
LIT_DEC128( 0, 0, 1000000000u), /* == 1e9m */
LIT_DEC128( 0, 2u, 1410065408u), /* == 1e10m */
LIT_DEC128( 0, 23u, 1215752192u), /* == 1e11m */
LIT_DEC128( 0, 232u, 3567587328u), /* == 1e12m */
LIT_DEC128( 0, 2328u, 1316134912u), /* == 1e13m */
LIT_DEC128( 0, 23283u, 276447232u), /* == 1e14m */
LIT_DEC128( 0, 232830u, 2764472320u), /* == 1e15m */
LIT_DEC128( 0, 2328306u, 1874919424u), /* == 1e16m */
LIT_DEC128( 0, 23283064u, 1569325056u), /* == 1e17m */
LIT_DEC128( 0, 232830643u, 2808348672u), /* == 1e18m */
LIT_DEC128( 0, 2328306436u, 2313682944u), /* == 1e19m */
LIT_DEC128( 5u, 1808227885u, 1661992960u), /* == 1e20m */
LIT_DEC128( 54u, 902409669u, 3735027712u), /* == 1e21m */
LIT_DEC128( 542u, 434162106u, 2990538752u), /* == 1e22m */
LIT_DEC128( 5421u, 46653770u, 4135583744u), /* == 1e23m */
LIT_DEC128( 54210u, 466537709u, 2701131776u), /* == 1e24m */
LIT_DEC128( 542101u, 370409800u, 1241513984u), /* == 1e25m */
LIT_DEC128( 5421010u, 3704098002u, 3825205248u), /* == 1e26m */
LIT_DEC128( 54210108u, 2681241660u, 3892314112u), /* == 1e27m */
LIT_DEC128( 542101086u, 1042612833u, 268435456u), /* == 1e28m */
};
/* 192 bit addition: c = a + b
addition is modulo 2**128, any carry is lost */
DECINLINE static void add128(guint64 alo, guint64 ahi,
guint64 blo, guint64 bhi,
guint64* pclo, guint64* pchi)
{
alo += blo;
if (alo < blo) ahi++; /* carry */
ahi += bhi;
*pclo = alo;
*pchi = ahi;
}
/* 128 bit subtraction: c = a - b
subtraction is modulo 2**128, any carry is lost */
DECINLINE static void sub128(guint64 alo, guint64 ahi,
guint64 blo, guint64 bhi,
guint64* pclo, guint64* pchi)
{
guint64 clo, chi;
clo = alo - blo;
chi = ahi - bhi;
if (alo < blo) chi--; /* borrow */
*pclo = clo;
*pchi = chi;
}
/* 192 bit addition: c = a + b
addition is modulo 2**192, any carry is lost */
DECINLINE static void add192(guint64 alo, guint64 ami, guint64 ahi,
guint64 blo, guint64 bmi, guint64 bhi,
guint64* pclo, guint64* pcmi, guint64* pchi)
{
alo += blo;
if (alo < blo) { /* carry low */
ami++;
if (ami == 0) ahi++; /* carry mid */
}
ami += bmi;
if (ami < bmi) ahi++; /* carry mid */
ahi += bhi;
*pclo = alo;
*pcmi = ami;
*pchi = ahi;
}
/* 192 bit subtraction: c = a - b
subtraction is modulo 2**192, any carry is lost */
DECINLINE static void sub192(guint64 alo, guint64 ami, guint64 ahi,
guint64 blo, guint64 bmi, guint64 bhi,
guint64* pclo, guint64* pcmi, guint64* pchi)
{
guint64 clo, cmi, chi;
clo = alo - blo;
cmi = ami - bmi;
chi = ahi - bhi;
if (alo < blo) {
if (cmi == 0) chi--; /* borrow mid */
cmi--; /* borrow low */
}
if (ami < bmi) chi--; /* borrow mid */
*pclo = clo;
*pcmi = cmi;
*pchi = chi;
}
/* multiplication c(192bit) = a(96bit) * b(96bit) */
DECINLINE static void mult96by96to192(guint32 alo, guint32 ami, guint32 ahi,
guint32 blo, guint32 bmi, guint32 bhi,
guint64* pclo, guint64* pcmi, guint64* pchi)
{
guint64 a, b, c, d;
guint32 h0, h1, h2, h3, h4, h5;
int carry0, carry1;
a = ((guint64)alo) * blo;
h0 = (guint32) a;
a >>= 32; carry0 = 0;
b = ((guint64)alo) * bmi;
c = ((guint64)ami) * blo;
a += b; if (a < b) carry0++;
a += c; if (a < c) carry0++;
h1 = (guint32) a;
a >>= 32; carry1 = 0;
b = ((guint64)alo) * bhi;
c = ((guint64)ami) * bmi;
d = ((guint64)ahi) * blo;
a += b; if (a < b) carry1++;
a += c; if (a < c) carry1++;
a += d; if (a < d) carry1++;
h2 = (guint32) a;
a >>= 32; a += carry0; carry0 = 0;
b = ((guint64)ami) * bhi;
c = ((guint64)ahi) * bmi;
a += b; if (a < b) carry0++;
a += c; if (a < c) carry0++;
h3 = (guint32) a;
a >>= 32; a += carry1;
b = ((guint64)ahi) * bhi;
a += b;
h4 = (guint32) a;
a >>= 32; a += carry0;
h5 = (guint32) a;
*pclo = ((guint64)h1) << 32 | h0;
*pcmi = ((guint64)h3) << 32 | h2;
*pchi = ((guint64)h5) << 32 | h4;
}
/* multiplication c(128bit) = a(96bit) * b(32bit) */
DECINLINE static void mult96by32to128(guint32 alo, guint32 ami, guint32 ahi,
guint32 factor,
guint64* pclo, guint64* pchi)
{
guint64 a;
guint32 h0, h1;
a = ((guint64)alo) * factor;
h0 = (guint32) a;
a >>= 32;
a += ((guint64)ami) * factor;
h1 = (guint32) a;
a >>= 32;
a += ((guint64)ahi) * factor;
*pclo = ((guint64)h1) << 32 | h0;
*pchi = a;
}
/* multiplication c(128bit) *= b(32bit) */
DECINLINE static int mult128by32(guint64* pclo, guint64* pchi, guint32 factor, int roundBit)
{
guint64 a;
guint32 h0, h1;
a = ((guint64)(guint32)(*pclo)) * factor;
if (roundBit) a += factor / 2;
h0 = (guint32) a;
a >>= 32;
a += (*pclo >> 32) * factor;
h1 = (guint32) a;
*pclo = ((guint64)h1) << 32 | h0;
a >>= 32;
a += ((guint64)(guint32)(*pchi)) * factor;
h0 = (guint32) a;
a >>= 32;
a += (*pchi >> 32) * factor;
h1 = (guint32) a;
*pchi = ((guint64)h1) << 32 | h0;
return ((a >> 32) == 0) ? DECIMAL_SUCCESS : DECIMAL_OVERFLOW;
}
DECINLINE static int mult128DecadeFactor(guint64* pclo, guint64* pchi, int powerOfTen)
{
int idx, rc;
while (powerOfTen > 0) {
idx = (powerOfTen >= DECIMAL_MAX_INTFACTORS) ? DECIMAL_MAX_INTFACTORS : powerOfTen;
powerOfTen -= idx;
rc = mult128by32(pclo, pchi, constantsDecadeInt32Factors[idx], 0);
if (rc != DECIMAL_SUCCESS) return rc;
}
return DECIMAL_SUCCESS;
}
/* division: x(128bit) /= factor(32bit)
returns roundBit */
DECINLINE static int div128by32(guint64* plo, guint64* phi, guint32 factor, guint32* pRest)
{
guint64 a, b, c, h;
h = *phi;
a = (guint32)(h >> 32);
b = a / factor;
a -= b * factor;
a <<= 32;
a |= (guint32) h;
c = a / factor;
a -= c * factor;
a <<= 32;
*phi = b << 32 | (guint32)c;
h = *plo;
a |= (guint32)(h >> 32);
b = a / factor;
a -= b * factor;
a <<= 32;
a |= (guint32) h;
c = a / factor;
a -= c * factor;
*plo = b << 32 | (guint32)c;
if (pRest) *pRest = (guint32) a;
a <<= 1;
return (a >= factor || (a == factor && (c & 1) == 1)) ? 1 : 0;
}
/* division: x(192bit) /= factor(32bit)
no rest and no rounding*/
DECINLINE static void div192by32(guint64* plo, guint64* pmi, guint64* phi,
guint32 factor)
{
guint64 a, b, c, h;
h = *phi;
a = (guint32)(h >> 32);
b = a / factor;
a -= b * factor;
a <<= 32;
a |= (guint32) h;
c = a / factor;
a -= c * factor;
a <<= 32;
*phi = b << 32 | (guint32)c;
h = *pmi;
a |= (guint32)(h >> 32);
b = a / factor;
a -= b * factor;
a <<= 32;
a |= (guint32) h;
c = a / factor;
a -= c * factor;
a <<= 32;
*pmi = b << 32 | (guint32)c;
h = *plo;
a |= (guint32)(h >> 32);
b = a / factor;
a -= b * factor;
a <<= 32;
a |= (guint32) h;
c = a / factor;
a -= c * factor;
a <<= 32;
*plo = b << 32 | (guint32)c;
}
/* returns upper 32bit for a(192bit) /= b(32bit)
a will contain remainder */
static guint32 div192by96to32withRest(guint64* palo, guint64* pami, guint64* pahi,
guint32 blo, guint32 bmi, guint32 bhi)
{
guint64 rlo, rmi, rhi; /* remainder */
guint64 tlo, thi; /* term */
guint32 c;
rlo = *palo; rmi = *pami; rhi = *pahi;
if (rhi >= (((guint64)bhi) << 32)) {
c = LIT_GUINT32(0xFFFFFFFF);
} else {
c = (guint32) (rhi / bhi);
}
mult96by32to128(blo, bmi, bhi, c, &tlo, &thi);
sub192(rlo, rmi, rhi, 0, tlo, thi, &rlo, &rmi, &rhi);
while (((gint64)rhi) < 0) {
c--;
add192(rlo, rmi, rhi, 0, (((guint64)bmi)<<32) | blo, bhi, &rlo, &rmi, &rhi);
}
*palo = rlo ; *pami = rmi ; *pahi = rhi;
POSTCONDITION(rhi >> 32 == 0);
return c;
}
/* c(128bit) = a(192bit) / b(96bit)
b must be >= 2^95 */
static void div192by96to128(guint64 alo, guint64 ami, guint64 ahi,
guint32 blo, guint32 bmi, guint32 bhi,
guint64* pclo, guint64* pchi)
{
guint64 rlo, rmi, rhi; /* remainder */
guint32 h, c;
PRECONDITION(ahi < (((guint64)bhi) << 32 | bmi)
|| (ahi == (((guint64)bhi) << 32 | bmi) && (ami >> 32) > blo));
/* high 32 bit*/
rlo = alo; rmi = ami; rhi = ahi;
h = div192by96to32withRest(&rlo, &rmi, &rhi, blo, bmi, bhi);
/* mid 32 bit*/
rhi = (rhi << 32) | (rmi >> 32); rmi = (rmi << 32) | (rlo >> 32); rlo <<= 32;
*pchi = (((guint64)h) << 32) | div192by96to32withRest(&rlo, &rmi, &rhi, blo, bmi, bhi);
/* low 32 bit */
rhi = (rhi << 32) | (rmi >> 32); rmi = (rmi << 32) | (rlo >> 32); rlo <<= 32;
h = div192by96to32withRest(&rlo, &rmi, &rhi, blo, bmi, bhi);
/* estimate lowest 32 bit (two last bits may be wrong) */
if (rhi >= bhi) {
c = LIT_GUINT32(0xFFFFFFFF);
} else {
rhi <<= 32;
c = (guint32) (rhi / bhi);
}
*pclo = (((guint64)h) << 32) | c;
}
DECINLINE static void roundUp128(guint64* pclo, guint64* pchi) {
if (++(*pclo) == 0) ++(*pchi);
}
static int normalize128(guint64* pclo, guint64* pchi, int* pScale,
int roundFlag, int roundBit)
{
guint32 overhang = (guint32)(*pchi >> 32);
int scale = *pScale;
int deltaScale;
while (overhang != 0) {
for (deltaScale = 1; deltaScale < DECIMAL_MAX_INTFACTORS; deltaScale++)
{
if (overhang < constantsDecadeInt32Factors[deltaScale]) break;
}
scale -= deltaScale;
if (scale < 0) return DECIMAL_OVERFLOW;
roundBit = div128by32(pclo, pchi, constantsDecadeInt32Factors[deltaScale], 0);
overhang = (guint32)(*pchi >> 32);
if (roundFlag && roundBit && *pclo == (guint64)-1 && (gint32)*pchi == (gint32)-1) {
overhang = 1;
}
}
*pScale = scale;
if (roundFlag && roundBit) {
roundUp128(pclo, pchi);
TEST((*pchi >> 32) == 0);
}
return DECIMAL_SUCCESS;
}
DECINLINE static int maxLeftShift(/*[In, Out]*/decimal_repr* pA)
{
guint64 lo64 = (((guint64)(pA->mid32)) << 32) | pA->lo32;
guint32 hi32 = pA->hi32;
int shift;
for (shift = 0; ((gint32)hi32) >= 0 && shift < 96; shift++) {
hi32 <<= 1;
if (((gint64)lo64) < 0) hi32++;
lo64 <<= 1;
}
pA->lo32 = (guint32) lo64;
pA->mid32 = (guint32)(lo64>>32);
pA->hi32 = hi32;
return shift;
}
DECINLINE static void rshift128(guint64* pclo, guint64* pchi)
{
*pclo >>= 1;
if (*pchi & 1) *pclo |= LIT_GUINT64_HIGHBIT;
*pchi >>= 1;
}
DECINLINE static void lshift96(guint32* pclo, guint32* pcmid, guint32* pchi)
{
*pchi <<= 1;
if (*pcmid & LIT_GUINT32_HIGHBIT) (*pchi)++;
*pcmid <<= 1;
if (*pclo & LIT_GUINT32_HIGHBIT) (*pcmid)++;
*pclo <<= 1;
}
DECINLINE static void lshift128(guint64* pclo, guint64* pchi)
{
*pchi <<= 1;
if (*pclo & LIT_GUINT64_HIGHBIT) (*pchi)++;
*pclo <<= 1;
}
DECINLINE static void rshift192(guint64* pclo, guint64* pcmi, guint64* pchi)
{
*pclo >>= 1;
if (*pcmi & 1) *pclo |= LIT_GUINT64_HIGHBIT;
*pcmi >>= 1;
if (*pchi & 1) *pcmi |= LIT_GUINT64_HIGHBIT;
*pchi >>= 1;
}
/* returns log2(a) or DECIMAL_LOG_NEGINF for a = 0 */
DECINLINE static int log2_32(guint32 a)
{
int tlog2 = 0;
if (a == 0) return DECIMAL_LOG_NEGINF;
if ((a >> 16) != 0) {
a >>= 16;
tlog2 += 16;
}
if ((a >> 8) != 0) {
a >>= 8;
tlog2 += 8;
}
if ((a >> 4) != 0) {
a >>= 4;
tlog2 += 4;
}
if ((a >> 2) != 0) {
a >>= 2;
tlog2 += 2;
}
if ((a >> 1) != 0) {
a >>= 1;
tlog2 += 1;
}
tlog2 += (int) a;
return tlog2;
}
/* returns log2(a) or DECIMAL_LOG_NEGINF for a = 0 */
DECINLINE static int log2_64(guint64 a)
{
int tlog2 = 0;
if (a == 0) return DECIMAL_LOG_NEGINF;
if ((a >> 32) != 0) {
a >>= 32;
tlog2 += 32;
}
if ((a >> 16) != 0) {
a >>= 16;
tlog2 += 16;
}
if ((a >> 8) != 0) {
a >>= 8;
tlog2 += 8;
}
if ((a >> 4) != 0) {
a >>= 4;
tlog2 += 4;
}
if ((a >> 2) != 0) {
a >>= 2;
tlog2 += 2;
}
if ((a >> 1) != 0) {
a >>= 1;
tlog2 += 1;
}
tlog2 += (int) a;
return tlog2;
}
/* returns log2(a) or DECIMAL_LOG_NEGINF for a = 0 */
DECINLINE static int log2_128(guint64 alo, guint64 ahi)
{
if (ahi == 0) return log2_64(alo);
else return log2_64(ahi) + 64;
}
/* returns a upper limit for log2(a) considering scale */
DECINLINE static int log2withScale_128(guint64 alo, guint64 ahi, int scale)
{
int tlog2 = log2_128(alo, ahi);
if (tlog2 < 0) tlog2 = 0;
return tlog2 - (scale * 33219) / 10000;
}
DECINLINE static int pack128toDecimal(/*[Out]*/decimal_repr* pA, guint64 alo, guint64 ahi,
int scale, int sign)
{
PRECONDITION((ahi >> 32) == 0);
PRECONDITION(sign == 0 || sign == 1);
PRECONDITION(scale >= 0 && scale <= DECIMAL_MAX_SCALE);
if (scale < 0 || scale > DECIMAL_MAX_SCALE || (ahi >> 32) != 0) {
return DECIMAL_OVERFLOW;
}
pA->lo32 = (guint32) alo;
pA->mid32 = (guint32) (alo >> 32);
pA->hi32 = (guint32) ahi;
pA->signscale.sign = sign;
pA->signscale.scale = scale;
return DECIMAL_SUCCESS;
}
DECINLINE static int adjustScale128(guint64* palo, guint64* pahi, int deltaScale)
{
int idx, rc;
if (deltaScale < 0) {
deltaScale *= -1;
if (deltaScale > DECIMAL_MAX_SCALE) return DECIMAL_INTERNAL_ERROR;
while (deltaScale > 0) {
idx = (deltaScale > DECIMAL_MAX_INTFACTORS) ? DECIMAL_MAX_INTFACTORS : deltaScale;
deltaScale -= idx;
div128by32(palo, pahi, constantsDecadeInt32Factors[idx], 0);
}
} else if (deltaScale > 0) {
if (deltaScale > DECIMAL_MAX_SCALE) return DECIMAL_INTERNAL_ERROR;
while (deltaScale > 0) {
idx = (deltaScale > DECIMAL_MAX_INTFACTORS) ? DECIMAL_MAX_INTFACTORS : deltaScale;
deltaScale -= idx;
rc = mult128by32(palo, pahi, constantsDecadeInt32Factors[idx], 0);
if (rc != DECIMAL_SUCCESS) return rc;
}
}
return DECIMAL_SUCCESS;
}
/* input: c * 10^-(*pScale) * 2^-exp
output: c * 10^-(*pScale) with
minScale <= *pScale <= maxScale and (chi >> 32) == 0 */
DECINLINE static int rescale128(guint64* pclo, guint64* pchi, int* pScale, int texp,
int minScale, int maxScale, int roundFlag)
{
guint32 factor, overhang;
int scale, i, rc, roundBit = 0;
PRECONDITION(texp >= 0);
scale = *pScale;
if (texp > 0) {
/* reduce exp */
while (texp > 0 && scale <= maxScale) {
overhang = (guint32)(*pchi >> 32);
while (texp > 0 && ((*pclo & 1) == 0 || overhang > (2<<DECIMAL_MAX_INTFACTORS))) {
if (--texp == 0) roundBit = (int)(*pclo & 1);
rshift128(pclo, pchi);
overhang = (guint32)(*pchi >> 32);
}
if (texp > DECIMAL_MAX_INTFACTORS) i = DECIMAL_MAX_INTFACTORS;
else i = texp;
if (scale + i > maxScale) i = maxScale - scale;
if (i == 0) break;
texp -= i;
scale += i;
factor = constantsDecadeInt32Factors[i] >> i; /* 10^i/2^i=5^i */
mult128by32(pclo, pchi, factor, 0);
/*printf("3: %.17e\n", (((double)chi) * pow(2,64) + clo) * pow(10, -scale) * pow(2, -texp));*/
}
while (texp > 0) {
if (--texp == 0) roundBit = (int)(*pclo & 1);
rshift128(pclo, pchi);
}
}
TEST(texp == 0);
while (scale > maxScale) {
i = scale - maxScale;
if (i > DECIMAL_MAX_INTFACTORS) i = DECIMAL_MAX_INTFACTORS;
scale -= i;
roundBit = div128by32(pclo, pchi, constantsDecadeInt32Factors[i], 0);
}
while (scale < minScale) {
if (!roundFlag) roundBit = 0;
i = minScale - scale;
if (i > DECIMAL_MAX_INTFACTORS) i = DECIMAL_MAX_INTFACTORS;
scale += i;
rc = mult128by32(pclo, pchi, constantsDecadeInt32Factors[i], roundBit);
if (rc != DECIMAL_SUCCESS) return rc;
roundBit = 0;
}
TEST(scale >= 0 && scale <= DECIMAL_MAX_SCALE);
*pScale = scale;
return normalize128(pclo, pchi, pScale, roundFlag, roundBit);
}
/* performs a += b */
gint32 mono_decimalIncr(/*[In, Out]*/decimal_repr* pA, /*[In]*/decimal_repr* pB)
{
guint64 alo, ahi, blo, bhi;
int log2A, log2B, log2Result, log10Result, rc;
int subFlag, sign, scaleA, scaleB;
MONO_ARCH_SAVE_REGS;
DECTO128(pA, alo, ahi);
DECTO128(pB, blo, bhi);
sign = pA->signscale.sign;
subFlag = sign - (int)pB->signscale.sign;
scaleA = pA->signscale.scale;
scaleB = pB->signscale.scale;
if (scaleA == scaleB) {
/* same scale, that's easy */
if (subFlag) {
sub128(alo, ahi, blo, bhi, &alo, &ahi);
if (ahi & LIT_GUINT64_HIGHBIT) {
alo--;
alo = ~alo;
if (alo == 0) ahi--;
ahi = ~ahi;
sign = !sign;
}
} else {
add128(alo, ahi, blo, bhi, &alo, &ahi);
}
rc = normalize128(&alo, &ahi, &scaleA, 1, 0);
} else {
/* scales must be adjusted */
/* Estimate log10 and scale of result for adjusting scales */
log2A = log2withScale_128(alo, ahi, scaleA);
log2B = log2withScale_128(blo, bhi, scaleB);
log2Result = (log2A >= log2B) ? log2A : log2B;
if (!subFlag) log2Result++; /* result can have one bit more */
log10Result = (log2Result * 1000) / 3322 + 1;
/* we will calculate in 128bit, so we may need to adjust scale */
if (scaleB > scaleA) scaleA = scaleB;
if (scaleA + log10Result > DECIMAL_MAX_SCALE + 7) {
/* this may not fit in 128bit, so limit it */
scaleA = DECIMAL_MAX_SCALE + 7 - log10Result;
}
rc = adjustScale128(&alo, &ahi, scaleA - (int)pA->signscale.scale);
if (rc != DECIMAL_SUCCESS) return rc;
rc = adjustScale128(&blo, &bhi, scaleA - scaleB);
if (rc != DECIMAL_SUCCESS) return rc;
if (subFlag) {
sub128(alo, ahi, blo, bhi, &alo, &ahi);
if (ahi & LIT_GUINT64_HIGHBIT) {
alo--;
alo = ~alo;
if (alo == 0) ahi--;
ahi = ~ahi;
sign = !sign;
}
} else {
add128(alo, ahi, blo, bhi, &alo, &ahi);
}
rc = rescale128(&alo, &ahi,&scaleA, 0, 0, DECIMAL_MAX_SCALE, 1);
}
if (rc != DECIMAL_SUCCESS) return rc;
return pack128toDecimal(pA, alo, ahi, scaleA, sign);
}
/* performs a += factor * constants[idx] */
static int incMultConstant128(guint64* palo, guint64* pahi, int idx, int factor)
{
guint64 blo, bhi, h;
PRECONDITION(idx >= 0 && idx <= DECIMAL_MAX_SCALE);
PRECONDITION(factor > 0 && factor <= 9);
blo = dec128decadeFactors[idx].lo;
h = bhi = dec128decadeFactors[idx].hi;
if (factor != 1) {
mult128by32(&blo, &bhi, factor, 0);
if (h > bhi) return DECIMAL_OVERFLOW;
}
h = *pahi;
add128(*palo, *pahi, blo, bhi, palo, pahi);
if (h > *pahi) return DECIMAL_OVERFLOW;
return DECIMAL_SUCCESS;
}
DECINLINE static void div128DecadeFactor(guint64* palo, guint64* pahi, int powerOfTen)
{
int idx, roundBit = 0;
while (powerOfTen > 0) {
idx = (powerOfTen > DECIMAL_MAX_INTFACTORS) ? DECIMAL_MAX_INTFACTORS : powerOfTen;
powerOfTen -= idx;
roundBit = div128by32(palo, pahi, constantsDecadeInt32Factors[idx], 0);
}
if (roundBit) roundUp128(palo, pahi);
}
/* calc significant digits of mantisse */
DECINLINE static int calcDigits(guint64 alo, guint64 ahi)
{
int tlog2 = 0;
int tlog10;
if (ahi == 0) {
if (alo == 0) {
return 0; /* zero has no signficant digits */
} else {
tlog2 = log2_64(alo);
}
} else {
tlog2 = 64 + log2_64(ahi);
}
tlog10 = (tlog2 * 1000) / 3322;
/* we need an exact floor value of log10(a) */
if (dec128decadeFactors[tlog10].hi > ahi
|| (dec128decadeFactors[tlog10].hi == ahi
&& dec128decadeFactors[tlog10].lo > alo)) {
--tlog10;
}
return tlog10+1;
}
gint32 mono_double2decimal(/*[Out]*/decimal_repr* pA, double val, gint32 digits)
{
guint64 alo, ahi;
guint64* p = (guint64*)(&val);
int sigDigits, sign, texp, rc, scale;
guint16 k;
PRECONDITION(digits <= 15);
sign = ((*p & LIT_GUINT64_HIGHBIT) != 0) ? 1 : 0;
k = ((guint16)((*p) >> 52)) & 0x7FF;
alo = (*p & LIT_GUINT64(0xFFFFFFFFFFFFF)) | LIT_GUINT64(0x10000000000000);
ahi = 0;
texp = (k & 0x7FF) - 0x3FF;
if (k == 0x7FF || texp >= 96) return DECIMAL_OVERFLOW; /* NaNs, SNaNs, Infinities or >= 2^96 */
if (k == 0 || texp <= -94) { /* Subnormals, Zeros or < 2^-94 */
DECINIT(pA); /* return zero */
return DECIMAL_SUCCESS;
}
texp -= 52;
if (texp > 0) {
for (; texp > 0; texp--) {
lshift128(&alo, &ahi);
}
}
scale = 0;
rc = rescale128(&alo, &ahi, &scale, -texp, 0, DECIMAL_MAX_SCALE, 0);
if (rc != DECIMAL_SUCCESS) return rc;
sigDigits = calcDigits(alo, ahi);
/* too much digits, then round */
if (sigDigits > digits) {
div128DecadeFactor(&alo, &ahi, sigDigits - digits);
scale -= sigDigits - digits;
/* check value, may be 10^(digits+1) caused by rounding */
if (ahi == dec128decadeFactors[digits].hi
&& alo == dec128decadeFactors[digits].lo) {
div128by32(&alo, &ahi, 10, 0);
scale--;
}
if (scale < 0) {
rc = mult128DecadeFactor(&alo, &ahi, -scale);
if (rc != DECIMAL_SUCCESS) return rc;
scale = 0;
}
}
return pack128toDecimal(pA, alo, ahi, scale, sign);
}
/**
* mono_string2decimal:
* @decimal_repr:
* @str:
* @decrDecimal:
* @sign:
*
* converts a digit string to decimal
* The significant digits must be passed as an integer in buf !
*
* 1. Example:
* if you want to convert the number 123.456789012345678901234 to decimal
* buf := "123456789012345678901234"
* decrDecimal := 3
* sign := 0
*
* 2. Example:
* you want to convert -79228162514264337593543950335 to decimal
* buf := "79228162514264337593543950335"
* decrDecimal := 29
* sign := 1
*
* 3. Example:
* you want to convert -7922816251426433759354395033.250000000000001 to decimal
* buf := "7922816251426433759354395033250000000000001"
* decrDecimal := 29
* sign := 1
* returns (decimal)-7922816251426433759354395033.3
*
* 4. Example:
* you want to convert -7922816251426433759354395033.250000000000000 to decimal
* buf := "7922816251426433759354395033250000000000000"
* decrDecimal := 29
* sign := 1
* returns (decimal)-7922816251426433759354395033.2
*
* 5. Example:
* you want to convert -7922816251426433759354395033.150000000000000 to decimal
* buf := "7922816251426433759354395033150000000000000"
* decrDecimal := 29
* sign := 1
* returns (decimal)-7922816251426433759354395033.2
*
* Uses banker's rule for rounding if there are more digits than can be
* represented by the significant
*/
gint32 mono_string2decimal(/*[Out]*/decimal_repr* pA, MonoString* str, gint32 decrDecimal, gint32 sign)
{
gushort *buf = mono_string_chars(str);
gushort *p;
guint64 alo, ahi;
int n, rc, i, len, sigLen = -1, firstNonZero;
int scale, roundBit = 0;
alo = ahi = 0;
DECINIT(pA);
for (p = buf, len = 0; *p != 0; len++, p++) { }
for (p = buf, i = 0; *p != 0; i++, p++) {
n = *p - '0';
if (n < 0 || n > 9) {
return DECIMAL_INVALID_CHARACTER;
}
if (n) {
if (sigLen < 0) {
firstNonZero = i;
sigLen = (len - firstNonZero > DECIMAL_MAX_SCALE+1)
? DECIMAL_MAX_SCALE+1+firstNonZero : len;
if (decrDecimal > sigLen+1) return DECIMAL_OVERFLOW;
}
if (i >= sigLen) break;
rc = incMultConstant128(&alo, &ahi, sigLen - 1 - i, n);