Print bits of float number does not work, can you explain me why?

Question

I want to print the bits of a float number.

My plan was to:

• Discover how many bits there are at all
• Create and int array and insert into it the bits of the number using simple right bits shifting.
• Because the bits were inserted in a reversed order to what I need, lets run another loop to go over the array one again but this time, from the last element to the first one.

Why ?

Lets take for example the number 4.2: I believe the bits were entered in the following way:

4 - 1000

2 - 0010

So together it's 10000010.

Enters FILO - First in -> Last out. So 0 will be the first element but as you cans see here, we need it in the end.

Here is my code:

float FloatAnalysis(float number)
{
    int arr[32] = {0};
    float num_cpy = number;
    size_t num_of_bits = 0, i = 0;
    
    while (0 != number)
    {
        num_cpy >>= 1;
        ++num_of_bits;
    }
    
    num_cpy = number;
    
    for(i = 0; i < num_of_bits; ++i)
    {
    
        arr[i] = (num_cpy & 1);
        num_cpy >>= 1;
    
    }
    
    
    for(i = num_of_bits-1; i => 0; --i)
    {
    
        printf("%d", arr[i]);
    
    }
    
}

And here the output:

bitwise.c:359:11: error: invalid operands to binary >> (have ‘float’ and ‘int’)
  359 |   num_cpy >>= 1;
      |           ^~~
bitwise.c:368:21: error: invalid operands to binary & (have ‘float’ and ‘int’)
  368 |   arr[i] = (num_cpy & 1);
      |                     ^
bitwise.c:369:11: error: invalid operands to binary >> (have ‘float’ and ‘int’)
  369 |   num_cpy >>= 1;
      |           ^~~

Can you expl

ain me what is going on here?

Answer 1

Use memcpy

You cannot perform bitwise operations on a float.

You can use memcpy to copy your float to an unsigned int and preserves its bits:

float num_cpy = number;

becomes

unsigned int num_cpy;
memcpy(&num_cpy, &number, sizeof(unsigned)); 

Note that if you try to cast the result, by taking your float address in memory and cast it as unsigned, with:

num_cpy = *(float *)&number; 

You will strip the floating point part away, you will preserve the value (or what can be preserved) but loose the accuracy of its binary representation.

---

Example

In the below example,

float number = 42.42;
unsigned int num_cpy;
memcpy(&num_cpy, &number, sizeof(unsigned)); 
unsigned int num_cpy2 = *(float *)&number;
printf("Bits in num_cpy: %d    bits in num_cpy2: %d\n", __builtin_popcount(num_cpy), __builtin_popcount(num_cpy2));
printf("%d\n", num_cpy);
printf("%d\n", num_cpy2);

will output

Bits in num_cpy: 12    bits in num_cpy2: 3
1110027796 // memcpy
42 // cast

---

More reading

I recommend that you especially take a look at floating point internal representation that sums up very well what is going at the bits level.

Internal Representation: sign: 1 bit, exponent: 8 bits, fraction: 23 bits
(for a single precision, 32 bits floating point, that we call float in C)

Answer 2

OP's code has various problems aside from compiler error.

i => 0 is not proprer code. Perhaps OP wanted i >= 0 ?. Even that has trouble.

size_t num_of_bits = 0, i = 0;
...
//  Bug: i => 0 is always true as `i` is an unsigned type.
for(i = num_of_bits-1; i >= 0; --i)  {
    printf("%d", arr[i]);
}

OP's repaired code.

float FloatAnalysis(float number) {
  assert(sizeof(float) == sizeof(unsigned));
  int arr[32] = {0};

  //float num_cpy = number;
  unsigned num_cpy;
  memcpy(&num_cpy, &number, sizeof num_cpy);  // copy the bit pattern to an unsigned

  // size_t num_of_bits = 0, i = 0;
  size_t num_of_bits = 32, i = 0;  // Always print 32 bits

  //while (0 != number) {
  //  num_cpy >>= 1;
  //  ++num_of_bits;
  //}
  //num_cpy = number;

  for (i = 0; i < num_of_bits; ++i) {
    arr[i] = (num_cpy & 1);
    num_cpy >>= 1;
  }

  // for(i = num_of_bits-1; i => 0; --i)
  for (i = num_of_bits; i-- > 0; ) { // Change test condition
    printf("%d", arr[i]);
  }
  printf("\n");

  // Some more output
  //      12345678901234567890123456789012
  printf("sEeeeeeeeMmmmmmmmmmmmmmmmmmmmmmm\n");
  printf("%a\n", number);
  return number;
}

int main() {
  FloatAnalysis(4.2f);
}

Output

01000000100001100110011001100110
sEeeeeeeeMmmmmmmmmmmmmmmmmmmmmmm
0x1.0cccccp+2