浮点数到十进制转换有什么问题？

Question

从0 10000101 01010011000000000000001转换到十进制(也就是84.75000762939453125)很好：

FP: 0 10000101 01010011000000000000001
Fraction: (1.)01010011000000000000001
Exp 10000101: 133
Bias: 133-127=6
Moving by exp: 1010100.11000000000000001
Convert parts to decimal: 84.75000762939453125

为什么我不能将0 00000001 00000000000000000000001转换为十进制(即(1.1754945E-38)：

FP: 0 00000001 00000000000000000000001
Fraction: (1.)00000000000000000000001
Exp 00000001: 1
Bias: 1-127=-126
Moving by exp: 0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
Convert parts to decimal: 0.?!?!?!

无法使1.1754945E-38将二进制0.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001转换为十进制。

我哪里错了？

Answer 1

你没有错。工具错了。

我找到了一个页面(当我在googled上搜索"ieee 754转换器“时出现的第一个页面)，它与您的号码没有问题：https://www.h-schmidt.net/FloatConverter/IEEE754.html。

我编写了一个小的C程序，它可能包含一些不可移植的、未定义的行为和过时的编码实践，但它显示了一些相关的浮点数和ints之间的转换：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

typedef union {
  float f;
  int i;
} both;

void printbits(int k) {
  int i;
  for (i = 0; i < 32; i++) {
    if (i == 1 || i == 9)
      printf(" ");
    if (k & (1<<(31-i)))
      printf("1");
    else
      printf("0");
  }
  printf("\n");
}

int main() {

  printf("sizeof(float) = %ld\n", sizeof(float));
  printf("sizeof(int) = %ld\n", sizeof(int));

  both u;

  u.i = 0x00800001;
  printbits(u.i);
  printf("%g\n", u.f);
  printf("%d %d\n", fpclassify(u.f), isnormal(u.f));
  printf("\n");

  u.i = 0x00800000;
  printbits(u.i);
  printf("%g\n", u.f);
  printf("%d %d\n", fpclassify(u.f), isnormal(u.f));
  printf("\n");

  u.i = 0x007fffe1;
  printf("%g\n", u.f);
  printf("%d %d\n", fpclassify(u.f), isnormal(u.f));
  printf("\n");

  u.i = 0x42a98001;
  printf("%g\n", u.f);
  printf("%g\n", 84.75000762939453125);
  printf("%d %d\n", fpclassify(u.f), isnormal(u.f));
  printf("\n");

  u.f = 1.17549e-38;
  printbits(u.i);
  printf("%#010x\n", u.i);
  printf("%d %d\n", fpclassify(u.f), isnormal(u.f));

  u.f = 1.1754944e-38;
  printbits(u.i);
  printf("%#010x\n", u.i);
  printf("%d %d\n", fpclassify(u.f), isnormal(u.f));

  u.f = 1.1754945e-38;
  printbits(u.i);
  printf("%#010x\n", u.i);
  printf("%d %d\n", fpclassify(u.f), isnormal(u.f));

}

输出(在Ubuntu上，由gcc编译，处理器x86)是：

sizeof(float) = 4
sizeof(int) = 4
0 00000001 00000000000000000000001
1.17549e-38
4 1

0 00000001 00000000000000000000000
1.17549e-38
4 1

1.17549e-38
3 0

84.75
84.75
4 1

0 00000000 11111111111111111100001
0x007fffe1
3 0
0 00000001 00000000000000000000000
0x00800000
4 1