How is 1 encoded in C/C++ as a float (assuming IEEE 754 single precision representation)?

问题

My impression is that C float has 8 bits of exponent and 23 bits of mantissa.

So one is 0011 1111 1000 0000 0000 0000 0000 0000 = 0x3F800000.

However, the following code produced 1.06535e+09 instead of 1. Can anyone help me understand why?

#include <iostream>
#include <math.h>  

using namespace std;

int main()
{
    float i = 0x3F800000;
    cout<<i << endl;
    return 0;
}

回答1:

How is 1 coded in C as a float?

Can anyone help me understand why (code fails)?

float i = 0x3F800000;

is the same as i = 1065353216;

In C, to overlay the bit pattern use a union or use memcpy().

In C++, suggest memcpy().

Using a cast risks failure due to anti-aliasing. @Eric Postpischil

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

_Static_assert(sizeof(float) == sizeof(uint32_t), "Unexpected types");

int main(void) {
  union {
    uint32_t u; 
    float f;
  } x = {.u = 0x3f800000};
  float f = x.f;
  printf("%e\n", f);
  return 0;
}

On less common systems, this can fail due to

float is not binary32.
Endian differs between float/uint32

回答2:

Using IEEE-754, the floating point number 1 is written as:

0 01111111 00000000000000000000000 (base-2) = 3f80 0000 (base-16)

So, your assumption is correct. Unfortunately, the bit-pattern represented by 0x3f800000 cannot be assigned to a float by just doing:

float a = 0x3f800000

The hexadecimal number will first be converted to an unsigned integer which has the value 1065353216 in base-10. This number will then implicitly be converted to the nearest floating-point number.

So in short, while your bit-pattern for an IEEE-754 floating point number is correct, your assumption how to assign this pattern is incorrect. Have a look at Convert a hexadecimal to a float and viceversa in C how this can be achieved or the other answers in this question.

来源：https://stackoverflow.com/questions/56710780/how-is-1-encoded-in-c-c-as-a-float-assuming-ieee-754-single-precision-represe

标签

floating-point

ieee-754