为什么转换（无符号长长）DBL_MAX（或 FLT_MAX）也会导致 FE_INEXACT 升高？

Question

代码（t1.c）：

#include <stdio.h>
#include <float.h>
#include <fenv.h>

#if _MSC_VER
#pragma fenv_access (on)
#else
#pragma STDC FENV_ACCESS ON
#endif


void print_fpe()
{
    int fpe = fetestexcept(FE_ALL_EXCEPT);
    printf("current exceptions raised:");
    if (fpe & FE_DIVBYZERO)       printf(" FE_DIVBYZERO");
    if (fpe & FE_INEXACT)         printf(" FE_INEXACT");
    if (fpe & FE_INVALID)         printf(" FE_INVALID");
    if (fpe & FE_OVERFLOW)        printf(" FE_OVERFLOW");
    if (fpe & FE_UNDERFLOW)       printf(" FE_UNDERFLOW");
    if ((fpe & FE_ALL_EXCEPT)==0) printf(" none");
}

volatile double d = DBL_MAX;
volatile float f = FLT_MAX;
volatile signed long long ll;
volatile signed long l;
volatile signed int i;
volatile signed short s;
volatile signed char c;
volatile unsigned long long ull;
volatile unsigned long ul;
volatile unsigned int ui;
volatile unsigned short us;
volatile unsigned char uc;

#define TEST(dst, type, src)         \
    feclearexcept(FE_ALL_EXCEPT);    \
    dst = (type)(src);               \
    print_fpe();                     \
    printf(" line %u\n", __LINE__);

int main(void)
{
    TEST(ll, signed long long, d);
    TEST(l, signed long, d);
    TEST(i, signed int, d);
    TEST(s, signed short, d);
    TEST(c, signed char, d);
    TEST(ll, signed long long, f);
    TEST(l, signed long, f);
    TEST(i, signed int, f);
    TEST(s, signed short, f);
    TEST(c, signed char, f);
    TEST(ull, unsigned long long, d); // line 55
    TEST(ul, unsigned long, d);
    TEST(ui, unsigned int, d);
    TEST(us, unsigned short, d);
    TEST(uc, unsigned char, d);
    TEST(ull, unsigned long long, f); // line 60
    TEST(ul, unsigned long, f);
    TEST(ui, unsigned int, f);
    TEST(us, unsigned short, f);
    TEST(uc, unsigned char, f);
    return 0;
}

调用和结果：

$ cl t1.c && t1
current exceptions raised: FE_INVALID line 45
current exceptions raised: FE_INVALID line 46
current exceptions raised: FE_INVALID line 47
current exceptions raised: FE_INVALID line 48
current exceptions raised: FE_INVALID line 49
current exceptions raised: FE_INVALID line 50
current exceptions raised: FE_INVALID line 51
current exceptions raised: FE_INVALID line 52
current exceptions raised: FE_INVALID line 53
current exceptions raised: FE_INVALID line 54
current exceptions raised: FE_INEXACT FE_INVALID line 55
current exceptions raised: FE_INVALID line 56
current exceptions raised: FE_INVALID line 57
current exceptions raised: FE_INVALID line 58
current exceptions raised: FE_INVALID line 59
current exceptions raised: FE_INEXACT FE_INVALID line 60
current exceptions raised: FE_INVALID line 61
current exceptions raised: FE_INVALID line 62
current exceptions raised: FE_INVALID line 63
current exceptions raised: FE_INVALID line 64

$ clang t1.c && ./a.exe
t1.c:8:14: warning: pragma STDC FENV_ACCESS ON is not supported, ignoring pragma [-Wunknown-pragmas]
#pragma STDC FENV_ACCESS ON
             ^
1 warning generated.
current exceptions raised: FE_INVALID line 45
current exceptions raised: FE_INVALID line 46
current exceptions raised: FE_INVALID line 47
current exceptions raised: FE_INVALID line 48
current exceptions raised: FE_INVALID line 49
current exceptions raised: FE_INVALID line 50
current exceptions raised: FE_INVALID line 51
current exceptions raised: FE_INVALID line 52
current exceptions raised: FE_INVALID line 53
current exceptions raised: FE_INVALID line 54
current exceptions raised: FE_INEXACT FE_INVALID line 55
current exceptions raised: FE_INEXACT FE_INVALID line 56
current exceptions raised: FE_INVALID line 57
current exceptions raised: FE_INVALID line 58
current exceptions raised: FE_INVALID line 59
current exceptions raised: FE_INEXACT FE_INVALID line 60
current exceptions raised: FE_INEXACT FE_INVALID line 61
current exceptions raised: FE_INVALID line 62
current exceptions raised: FE_INVALID line 63
current exceptions raised: FE_INVALID line 64

$ gcc t1.c && ./a.exe
current exceptions raised: FE_INVALID line 45
current exceptions raised: FE_INVALID line 46
current exceptions raised: FE_INVALID line 47
current exceptions raised: FE_INVALID line 48
current exceptions raised: FE_INVALID line 49
current exceptions raised: FE_INVALID line 50
current exceptions raised: FE_INVALID line 51
current exceptions raised: FE_INVALID line 52
current exceptions raised: FE_INVALID line 53
current exceptions raised: FE_INVALID line 54
current exceptions raised: FE_INEXACT FE_INVALID line 55
current exceptions raised: FE_INEXACT FE_INVALID line 56
current exceptions raised: FE_INVALID line 57
current exceptions raised: FE_INVALID line 58
current exceptions raised: FE_INVALID line 59
current exceptions raised: FE_INEXACT FE_INVALID line 60
current exceptions raised: FE_INEXACT FE_INVALID line 61
current exceptions raised: FE_INVALID line 62
current exceptions raised: FE_INVALID line 63
current exceptions raised: FE_INVALID line 64

问题：为什么转换(unsigned long long)DBL_MAX（或FLT_MAX）也会引起FE_INEXACT的提升？

Answer 1

我想您正在 x86 上对此进行测试，因为这就是我看到您描述的行为的地方。 Example。这是底层的解释。

在 x86-64 上，gcc 至少使用cvttsd2si 指令将大多数浮点数转换为整数，该指令将双精度浮点数转换为 32 位或 64 位 有符号 整数，如果结果超出范围，则引发“无效”异常。该指令可用于转换为任何有符号整数类型，也可用于转换为 32 位或更低的无符号整数类型 - 例如，可以通过转换为有符号 64 位并丢弃高位来转换为无符号 32 位。

但这不适用于转换为无符号 64 位，因为输入可能是一个不适合有符号 64 位但适合无符号 64 位的数字，而 x86 没有指令可以做到这一点直接转换。因此，需要一些额外的算术，正是这些额外的指令产生了“不精确”的异常。 （具体来说，它会使用subsd 从输入中减去(double)LLONG_MAX，这确实会在输入为DBL_MAX 时导致精度损失。）

请参阅Unsigned 64-bit to double conversion: why this algorithm from g++，了解 gcc 为尽可能高效地执行此操作而采取的各种体操示例。

请注意，在 x86-64 上，您实际上也会看到 FP_INEXACT 转换为 unsigned long，因为它与 unsigned long long 相同。我得到了您在 x86-32 上观察到的确切行为，其中 unsigned long long 是唯一适用的 64 位类型。这种情况下的代码有点复杂，如果您真的感兴趣，我会留给您通读程序集。

相比之下，当我在 AArch64 上运行此代码时，所有行都简单地给出FE_INVALID。这是因为 AArch64 确实有一条专用指令将浮点数转换为无符号 64 位 (fcvtzu)，因此没有可能涉及不精确结果的进一步算法。

Answer 2

根据 C11 6.3.1.4，代码 (unsigned long long)DBL_MAX 具有未定义的行为：

当实浮点类型的有限值转换为_Bool以外的整数类型时，小数部分被丢弃（即，该值被截断为零）。如果整数部分的值不能用整数类型表示，则行为未定义

由于行为未定义，“任何事情都可能发生”，即标准未涵盖该行为。