Я знайшов помилку.
.NET робить наступне в clr\src\vm\comnumber.cpp
:
DoubleToNumber(value, DOUBLE_PRECISION, &number);
if (number.scale == (int) SCALE_NAN) {
gc.refRetVal = gc.numfmt->sNaN;
goto lExit;
}
if (number.scale == SCALE_INF) {
gc.refRetVal = (number.sign? gc.numfmt->sNegativeInfinity: gc.numfmt->sPositiveInfinity);
goto lExit;
}
NumberToDouble(&number, &dTest);
if (dTest == value) {
gc.refRetVal = NumberToString(&number, 'G', DOUBLE_PRECISION, gc.numfmt);
goto lExit;
}
DoubleToNumber(value, 17, &number);
DoubleToNumber
досить простий - він просто дзвонить _ecvt
, що є в режимі C:
void DoubleToNumber(double value, int precision, NUMBER* number)
{
WRAPPER_CONTRACT
_ASSERTE(number != NULL);
number->precision = precision;
if (((FPDOUBLE*)&value)->exp == 0x7FF) {
number->scale = (((FPDOUBLE*)&value)->mantLo || ((FPDOUBLE*)&value)->mantHi) ? SCALE_NAN: SCALE_INF;
number->sign = ((FPDOUBLE*)&value)->sign;
number->digits[0] = 0;
}
else {
char* src = _ecvt(value, precision, &number->scale, &number->sign);
wchar* dst = number->digits;
if (*src != '0') {
while (*src) *dst++ = *src++;
}
*dst = 0;
}
}
Виявляється, _ecvt
повертає рядок 845512408225570
.
Помічаєте кінцевий нуль? Виявляється, все має значення!
Коли нуль присутній, результат насправді аналізується назад0.84551240822557006
, що є вашим початковим номером - тому він порівнює рівне, а значить, повертається лише 15 цифр.
Однак якщо я обрізаю рядок на цьому нулі до 84551240822557
, я повертаюсь назад 0.84551240822556994
, що не є вашим початковим номером, а значить, він поверне 17 цифр.
Доказ: запустіть наступний 64-розрядний код (більшу частину якого я витягнув із Microsoft Shared Source CLI 2.0) у своєму відладчику та вивчіть v
наприкінці main
:
#include <stdlib.h>
#include <string.h>
#include <math.h>
#define min(a, b) (((a) < (b)) ? (a) : (b))
struct NUMBER {
int precision;
int scale;
int sign;
wchar_t digits[20 + 1];
NUMBER() : precision(0), scale(0), sign(0) {}
};
#define I64(x) x##LL
static const unsigned long long rgval64Power10[] = {
// powers of 10
/*1*/ I64(0xa000000000000000),
/*2*/ I64(0xc800000000000000),
/*3*/ I64(0xfa00000000000000),
/*4*/ I64(0x9c40000000000000),
/*5*/ I64(0xc350000000000000),
/*6*/ I64(0xf424000000000000),
/*7*/ I64(0x9896800000000000),
/*8*/ I64(0xbebc200000000000),
/*9*/ I64(0xee6b280000000000),
/*10*/ I64(0x9502f90000000000),
/*11*/ I64(0xba43b74000000000),
/*12*/ I64(0xe8d4a51000000000),
/*13*/ I64(0x9184e72a00000000),
/*14*/ I64(0xb5e620f480000000),
/*15*/ I64(0xe35fa931a0000000),
// powers of 0.1
/*1*/ I64(0xcccccccccccccccd),
/*2*/ I64(0xa3d70a3d70a3d70b),
/*3*/ I64(0x83126e978d4fdf3c),
/*4*/ I64(0xd1b71758e219652e),
/*5*/ I64(0xa7c5ac471b478425),
/*6*/ I64(0x8637bd05af6c69b7),
/*7*/ I64(0xd6bf94d5e57a42be),
/*8*/ I64(0xabcc77118461ceff),
/*9*/ I64(0x89705f4136b4a599),
/*10*/ I64(0xdbe6fecebdedd5c2),
/*11*/ I64(0xafebff0bcb24ab02),
/*12*/ I64(0x8cbccc096f5088cf),
/*13*/ I64(0xe12e13424bb40e18),
/*14*/ I64(0xb424dc35095cd813),
/*15*/ I64(0x901d7cf73ab0acdc),
};
static const signed char rgexp64Power10[] = {
// exponents for both powers of 10 and 0.1
/*1*/ 4,
/*2*/ 7,
/*3*/ 10,
/*4*/ 14,
/*5*/ 17,
/*6*/ 20,
/*7*/ 24,
/*8*/ 27,
/*9*/ 30,
/*10*/ 34,
/*11*/ 37,
/*12*/ 40,
/*13*/ 44,
/*14*/ 47,
/*15*/ 50,
};
static const unsigned long long rgval64Power10By16[] = {
// powers of 10^16
/*1*/ I64(0x8e1bc9bf04000000),
/*2*/ I64(0x9dc5ada82b70b59e),
/*3*/ I64(0xaf298d050e4395d6),
/*4*/ I64(0xc2781f49ffcfa6d4),
/*5*/ I64(0xd7e77a8f87daf7fa),
/*6*/ I64(0xefb3ab16c59b14a0),
/*7*/ I64(0x850fadc09923329c),
/*8*/ I64(0x93ba47c980e98cde),
/*9*/ I64(0xa402b9c5a8d3a6e6),
/*10*/ I64(0xb616a12b7fe617a8),
/*11*/ I64(0xca28a291859bbf90),
/*12*/ I64(0xe070f78d39275566),
/*13*/ I64(0xf92e0c3537826140),
/*14*/ I64(0x8a5296ffe33cc92c),
/*15*/ I64(0x9991a6f3d6bf1762),
/*16*/ I64(0xaa7eebfb9df9de8a),
/*17*/ I64(0xbd49d14aa79dbc7e),
/*18*/ I64(0xd226fc195c6a2f88),
/*19*/ I64(0xe950df20247c83f8),
/*20*/ I64(0x81842f29f2cce373),
/*21*/ I64(0x8fcac257558ee4e2),
// powers of 0.1^16
/*1*/ I64(0xe69594bec44de160),
/*2*/ I64(0xcfb11ead453994c3),
/*3*/ I64(0xbb127c53b17ec165),
/*4*/ I64(0xa87fea27a539e9b3),
/*5*/ I64(0x97c560ba6b0919b5),
/*6*/ I64(0x88b402f7fd7553ab),
/*7*/ I64(0xf64335bcf065d3a0),
/*8*/ I64(0xddd0467c64bce4c4),
/*9*/ I64(0xc7caba6e7c5382ed),
/*10*/ I64(0xb3f4e093db73a0b7),
/*11*/ I64(0xa21727db38cb0053),
/*12*/ I64(0x91ff83775423cc29),
/*13*/ I64(0x8380dea93da4bc82),
/*14*/ I64(0xece53cec4a314f00),
/*15*/ I64(0xd5605fcdcf32e217),
/*16*/ I64(0xc0314325637a1978),
/*17*/ I64(0xad1c8eab5ee43ba2),
/*18*/ I64(0x9becce62836ac5b0),
/*19*/ I64(0x8c71dcd9ba0b495c),
/*20*/ I64(0xfd00b89747823938),
/*21*/ I64(0xe3e27a444d8d991a),
};
static const signed short rgexp64Power10By16[] = {
// exponents for both powers of 10^16 and 0.1^16
/*1*/ 54,
/*2*/ 107,
/*3*/ 160,
/*4*/ 213,
/*5*/ 266,
/*6*/ 319,
/*7*/ 373,
/*8*/ 426,
/*9*/ 479,
/*10*/ 532,
/*11*/ 585,
/*12*/ 638,
/*13*/ 691,
/*14*/ 745,
/*15*/ 798,
/*16*/ 851,
/*17*/ 904,
/*18*/ 957,
/*19*/ 1010,
/*20*/ 1064,
/*21*/ 1117,
};
static unsigned DigitsToInt(wchar_t* p, int count)
{
wchar_t* end = p + count;
unsigned res = *p - '0';
for ( p = p + 1; p < end; p++) {
res = 10 * res + *p - '0';
}
return res;
}
#define Mul32x32To64(a, b) ((unsigned long long)((unsigned long)(a)) * (unsigned long long)((unsigned long)(b)))
static unsigned long long Mul64Lossy(unsigned long long a, unsigned long long b, int* pexp)
{
// it's ok to losse some precision here - Mul64 will be called
// at most twice during the conversion, so the error won't propagate
// to any of the 53 significant bits of the result
unsigned long long val = Mul32x32To64(a >> 32, b >> 32) +
(Mul32x32To64(a >> 32, b) >> 32) +
(Mul32x32To64(a, b >> 32) >> 32);
// normalize
if ((val & I64(0x8000000000000000)) == 0) { val <<= 1; *pexp -= 1; }
return val;
}
void NumberToDouble(NUMBER* number, double* value)
{
unsigned long long val;
int exp;
wchar_t* src = number->digits;
int remaining;
int total;
int count;
int scale;
int absscale;
int index;
total = (int)wcslen(src);
remaining = total;
// skip the leading zeros
while (*src == '0') {
remaining--;
src++;
}
if (remaining == 0) {
*value = 0;
goto done;
}
count = min(remaining, 9);
remaining -= count;
val = DigitsToInt(src, count);
if (remaining > 0) {
count = min(remaining, 9);
remaining -= count;
// get the denormalized power of 10
unsigned long mult = (unsigned long)(rgval64Power10[count-1] >> (64 - rgexp64Power10[count-1]));
val = Mul32x32To64(val, mult) + DigitsToInt(src+9, count);
}
scale = number->scale - (total - remaining);
absscale = abs(scale);
if (absscale >= 22 * 16) {
// overflow / underflow
*(unsigned long long*)value = (scale > 0) ? I64(0x7FF0000000000000) : 0;
goto done;
}
exp = 64;
// normalize the mantisa
if ((val & I64(0xFFFFFFFF00000000)) == 0) { val <<= 32; exp -= 32; }
if ((val & I64(0xFFFF000000000000)) == 0) { val <<= 16; exp -= 16; }
if ((val & I64(0xFF00000000000000)) == 0) { val <<= 8; exp -= 8; }
if ((val & I64(0xF000000000000000)) == 0) { val <<= 4; exp -= 4; }
if ((val & I64(0xC000000000000000)) == 0) { val <<= 2; exp -= 2; }
if ((val & I64(0x8000000000000000)) == 0) { val <<= 1; exp -= 1; }
index = absscale & 15;
if (index) {
int multexp = rgexp64Power10[index-1];
// the exponents are shared between the inverted and regular table
exp += (scale < 0) ? (-multexp + 1) : multexp;
unsigned long long multval = rgval64Power10[index + ((scale < 0) ? 15 : 0) - 1];
val = Mul64Lossy(val, multval, &exp);
}
index = absscale >> 4;
if (index) {
int multexp = rgexp64Power10By16[index-1];
// the exponents are shared between the inverted and regular table
exp += (scale < 0) ? (-multexp + 1) : multexp;
unsigned long long multval = rgval64Power10By16[index + ((scale < 0) ? 21 : 0) - 1];
val = Mul64Lossy(val, multval, &exp);
}
// round & scale down
if ((unsigned long)val & (1 << 10))
{
// IEEE round to even
unsigned long long tmp = val + ((1 << 10) - 1) + (((unsigned long)val >> 11) & 1);
if (tmp < val) {
// overflow
tmp = (tmp >> 1) | I64(0x8000000000000000);
exp += 1;
}
val = tmp;
}
val >>= 11;
exp += 0x3FE;
if (exp <= 0) {
if (exp <= -52) {
// underflow
val = 0;
}
else {
// denormalized
val >>= (-exp+1);
}
}
else
if (exp >= 0x7FF) {
// overflow
val = I64(0x7FF0000000000000);
}
else {
val = ((unsigned long long)exp << 52) + (val & I64(0x000FFFFFFFFFFFFF));
}
*(unsigned long long*)value = val;
done:
if (number->sign) *(unsigned long long*)value |= I64(0x8000000000000000);
}
int main()
{
NUMBER number;
number.precision = 15;
double v = 0.84551240822557006;
char *src = _ecvt(v, number.precision, &number.scale, &number.sign);
int truncate = 0; // change to 1 if you want to truncate
if (truncate)
{
while (*src && src[strlen(src) - 1] == '0')
{
src[strlen(src) - 1] = 0;
}
}
wchar_t* dst = number.digits;
if (*src != '0') {
while (*src) *dst++ = *src++;
}
*dst++ = 0;
NumberToDouble(&number, &v);
return 0;
}