如何在C语言中直接计算float类型的取值范围？

我正在完成《C程序设计语言》（K&R）第二版的习题2.1，已经算出signed/unsigned char、short、int和long类型的取值范围——补码相关的计算还算容易，但IEEE754标准的相关计算就没这么简单了。

以下是我写的部分代码：

void short_range() {
  unsigned short next = us_max;

  for (; next != 0; next *= 2)
    us_max = next;

  signed short ss_min = -us_max;
  signed short ss_max = us_max - 1;

  us_max = us_max + (us_max - 1);
  ui_max = us_max + 1;

  printf("signed short range (%d, %d)\n", ss_min, ss_max);
  printf("unsigned short range (0, %u)\n", us_max);
}

void int_range() {
  unsigned int next = ui_max;

  for (; next != 0; next *= 2)
    ui_max = next;

  signed int si_min = -ui_max;
  signed int si_max = ui_max - 1;

  ui_max = ui_max + (ui_max - 1);
  // 我搞不懂为什么只有这里要强制转换`ui_max`，之前的函数不用
  // 但如果不转的话，`ui_max`会溢出到0，搞砸`long_range`的计算
  ul_max = (long)ui_max + 1;

  printf("signed int range (%d, %d)\n", si_min, si_max);
  printf("unsigned int range (0, %u)\n", ui_max);
}

内容的提问来源于stack exchange，提问作者Fernando Castro