如果结果不正常，可以设置浮点状态标志FE_UNDERFLOW吗? [英] Can the floating-point status flag FE_UNDERFLOW set when the result is not sub-normal?

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问题描述

在研究浮点异常状态标志时，我遇到了一个奇怪的情况:状态标志FE_UNDERFLOW在不期望的时候置位.

While investigating floating-point exception status flags, I came across the curious case of a status flag FE_UNDERFLOW set when not expected.

这类似于何时发生下溢?却陷入了可能是C规范问题或FP硬件缺陷.

This is similar to When does underflow occur? yet goes into a corner case that may be a C specification issue or FP hardware defect.

// pseudo code
//                       s bias_expo implied "mantissa"
w = smallest_normal;  // 0 000...001 (1)     000...000
x = w * 2;            // 0 000...010 (1)     000...000
y = next_smaller(x);  // 0 000...001 (1)     111...111
round_mode(FE_TONEAREST);
clear_status_flags();
z = y/2;              // 0 000...001 (1)     000...000

FE_UNDERFLOW is set!?

我没想到将FE_UNDERFLOW设置为上面的z是正常的，而不是次要的.
我希望早期的浮点运算的结果不合标准且精度下降时会出现FE_UNDERFLOW.在这种情况下，会损失精度.

I did not expect FE_UNDERFLOW to be set as z above is normal, not a sub-normal.
I expect FE_UNDERFLOW when the result of an earlier floating-point operation was subnormal with a loss of precision. In this case there is a loss of precision.

我用float和long double进行了尝试，并得到了相同的结果.

I tried this with my float and long double and had the same result.

经过大量调查，我注意到__STDC_IEC_559__未定义 .

After much investigation, I noted that __STDC_IEC_559__ is not defined.

问题

如果定义了__STDC_IEC_559__，在这种情况下下溢的正确状态是什么?

If __STDC_IEC_559__ is defined, what is the correct state of underflow in this case?

在缺少定义的__STDC_IEC_559__的情况下，我是否坚持未定义__STDC_IEC_559__的实现不需要符合这些要求" 规范." C11或是否有一些C规范表明此结果不正确?

With lack of a defined __STDC_IEC_559__ am I stuck with "Implementations that do not define __STDC_IEC_559__ are not required to conform to these specifications." C11 or is there some C specification that indicates this result is incorrect?

由于这肯定是我的硬件(处理器)导致的，因此您的结果可能会有所不同，这很有趣.

Since this is certainly a result of my hardware (processor), your result may differ and that would be interesting to know.

以下是一些演示此问题的测试代码.起初我怀疑是因为FLT_EVAL_METHOD = 2在我的计算机上，但是后来我尝试使用long double进行类似的代码并得到相同的结果.

Follows is some test code that demos this. At first I suspected it is because FLT_EVAL_METHOD = 2 on my machine, yet then I tried similar code with long double and the same result.

// These 2 includes missing in original post, yet in my true test code
#include <float.h>
#include <math.h>

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

#define N (sizeof excepts/sizeof excepts[0])
void Report_IEC_FP_exception_status_flags(const char *s) {
  printf("%s", s);
  int excepts[] = { //
      FE_DIVBYZERO, FE_INEXACT, FE_INVALID, FE_OVERFLOW, FE_UNDERFLOW, };
  const char *excepts_str[N] = { //
      "FE_DIVBYZERO", "FE_INEXACT", "FE_INVALID", "FE_OVERFLOW", "FE_UNDERFLOW", };
  int excepts_val[N];

  for (unsigned i = 0; i < N; i++) {
    excepts_val[i] = fetestexcept(excepts[i]);
  }
  for (unsigned i = 0; i < N; i++) {
    if (excepts_val[i]) printf(" %s", excepts_str[i]);
  }
  printf("\n");
  fflush(stdout);
}
#undef N

void test2(float f, int round_mode, const char *name) {
  union {
    float f;
    uint32_t u32;
    } x = { .f = f};

  printf("x:%+17a %08lX normal:%c round_mode:%d %s\n", //
  f, (unsigned long) x.u32, isnormal(f) ? 'Y' : 'n', round_mode, name);
  if (feclearexcept(FE_ALL_EXCEPT)) puts("Clear Fail");
  Report_IEC_FP_exception_status_flags("Before:");

  f /= 2;

  Report_IEC_FP_exception_status_flags("After :");
  printf("y:%+17a %08lX normal:%c\n\n", 
      f,(unsigned long) x.u32, isnormal(f) ? 'Y' : 'n');
}

驱动程序

// In same file as above
int main(void) {
  #ifdef __STDC_IEC_559__
    printf("__STDC_IEC_559__ = %d\n", __STDC_IEC_559__);
  #else
    printf("__STDC_IEC_559__ = not define\n");
  #endif

  float f = FLT_MIN;
  printf("FLT_EVAL_METHOD = %d\n", FLT_EVAL_METHOD);
  printf("FLT_MIN:%+17a\n", f);
  f *= 2.0f;
  test2(f, FE_TONEAREST, "FE_TONEAREST");
  f = nextafterf(f, 0);
  test2(f, FE_TONEAREST, "FE_TONEAREST");   // *** problem? ***
  f = nextafterf(f, 0);
  test2(f, FE_TONEAREST, "FE_TONEAREST");
}

输出

__STDC_IEC_559__ = not define
FLT_EVAL_METHOD = 2
FLT_MIN:        +0x1p-126
x:        +0x1p-125 01000000 normal:Y round_mode:0 FE_TONEAREST
Before:
After :
y:        +0x1p-126 01000000 normal:Y

x: +0x1.fffffep-126 00FFFFFF normal:Y round_mode:0 FE_TONEAREST
Before:
After : FE_INEXACT FE_UNDERFLOW                *** Why FE_UNDERFLOW? ***
y:        +0x1p-126 00FFFFFF normal:Y          *** Result is normal  ***

x: +0x1.fffffcp-126 00FFFFFE normal:Y round_mode:0 FE_TONEAREST
Before:
After :
y: +0x1.fffffcp-127 00FFFFFE normal:n

参考

IEEE_754

实施说明:

GNU C11(GCC)版本6.4.0(i686-pc-cygwin) 由GNU C版本6.4.0，GMP版本6.1.2，MPFR版本3.1.5-p10，MPC版本1.0.3，isl版本0.14或0.13编译

GNU C11 (GCC) version 6.4.0 (i686-pc-cygwin) compiled by GNU C version 6.4.0, GMP version 6.1.2, MPFR version 3.1.5-p10, MPC version 1.0.3, isl version 0.14 or 0.13

glibc 2.26发布了.

glibc 2.26 released.

Intel Xeon W3530，64位操作系统(Windows 7)

Intel Xeon W3530, 64-bit OS (Windows 7)

[次要更新]作为32位十六进制数字的商的说明性打印应使用y.u32.这不会更改被测功能

[Minor Update] The illustrative print of the quotient as an 32-bit hex number should have used y.u32. This does not change the function under test

// printf("y:%+17a %08lX normal:%c\n\n", 
//    f,(unsigned long) x.u32, isnormal(f) ? 'Y' : 'n');
union {
  float f;
  uint32_t u32;
} y = { .f = f};
printf("y:%+17a %08lX normal:%c\n\n", 
    f,(unsigned long) y.u32, isnormal(f) ? 'Y' : 'n');
//                    ^^^^^

如果结果不正常，可以设置浮点状态标志FE_UNDERFLOW吗? [英] Can the floating-point status flag FE_UNDERFLOW set when the result is not sub-normal?

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如果结果不正常，可以设置浮点状态标志FE_UNDERFLOW吗? [英] Can the floating-point status flag FE_UNDERFLOW set when the result is not sub-normal?

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