为什么通过一个字符串来回转换不安全的双？ [英] Why is a round-trip conversion via a string not safe for a double?

问题描述

最近，我不得不序列化出双入文本，然后拿回来。价值似乎不等同的：

Recently I have had to serialize a double into text, and then get it back. The value seems to not be equivalent:

double d1 = 0.84551240822557006;
string s = d1.ToString("R");
double d2 = double.Parse(s);
bool s1 = d1 == d2;
// -> s1 is False

但根据 MSDN：标准数字格式字符串中的R的选项应该保证往返的安全。

But according to MSDN: Standard Numeric Format Strings, the "R" option is supposed to guarantee round-trip safety.

往返（R）格式说明用于确保被转换成字符串的数值将被解析回相同的数值

The round-trip ("R") format specifier is used to ensure that a numeric value that is converted to a string will be parsed back into the same numeric value

为什么会出现这种情况？

Why did this happen?

推荐答案

我发现的bug。

.NET确实在 <$以下C $ C> CLR \\ SRC \\虚拟机\\ comnumber.cpp ：

.NET does the following in 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 是pretty简单 - 它只是调用 _ecvt ，这是在C运行时：

DoubleToNumber is pretty simple -- it just calls _ecvt, which is in the C runtime:

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;
    }
}

原来， _ecvt 返回字符串 845512408225570 。

注意尾随零？的原来，使所有的差异！结果
当零为present，结果居然解析回 0.84551240822557006 ，这是你的原始的数量 - 所以它比较平等的，因此，只有15位被返回。

Notice the trailing zero? It turns out that makes all the difference!
When the zero is present, the result actually parses back to 0.84551240822557006, which is your original number -- so it compares equal, and hence only 15 digits are returned.

不过，如果我削去在零的字符串 84551240822557 ，然后我回去 0.84551240822556994 ，这是的不的你原来的号码，因此它会返回17位。

However, if I truncate the string at that zero to 84551240822557, then I get back 0.84551240822556994, which is not your original number, and hence it would return 17 digits.

证明：运行下面的64位code在调试器（其中大部分是我从微软共享源代码CLI 2.0中提取），并检查 v 在结束主：

Proof: run the following 64-bit code (most of which I extracted from the Microsoft Shared Source CLI 2.0) in your debugger and examine v at the end of 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;
}

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