How are float and doubles represented in C++ (gcc)?

Question

How are floating points represented and interpreted by a compiler. I am trying to understand that so I can easily interpret what byte array would mean for floats and doubles.

Thanks

Answer 1

Try this link: http://en.wikipedia.org/wiki/IEEE_754

I just found that this might be a little more helpful: http://en.wikipedia.org/wiki/IEEE_754-1985

This is the IEEE-Standard for floating point numbers. There is one from 1985 and a revised edition from 2008. Float is 32bit, double is 64bit (explained in the second link).

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Edit: Thx to the comment by Don, here's the link to Intels 80bit floating point description: http://en.wikipedia.org/wiki/Extended_precision

Answer 2

It might also be worth noting that there is a static bool const member of std::numeric_limits, is_iec559, which is naturally only available for floating point types. The name is pretty self explanatory...

Answer 3

To actually interpret it you would probably not want to treat it as bytes anyway because mantisa boundries don't align to an 8bit boundry.

Something along the lines of:

mantisa =  (*(unsigned int *)&floatVal) | MANTISA_MASK;
exp     = ((*(unsigned int *)&floatVal) | EXP_MASK    ) >> EXP_SHIFT;
sign    = ((*(unsigned int *)&floatVal) | SIGN_MASK   ) >> SIGN_SHIFT;

Would let you pull it apart to play with the juice center.

EDIT:

    #include <stdio.h>

    void main()
    {
    float a = 4;
    unsigned int exp,sign,mantisa;
    int i;

        for(i = 0;i<4;i++)
        {
         exp      = (*((unsigned int *)&a) >>23) & 0xFF;
         sign     = (*((unsigned int *)&a) >>31) & 0x01;
         mantisa  = (*((unsigned int *)&a)) & 0x7FFFFF | 0x800000;

         printf("a       = %04x\r\n",*((unsigned int *)&a));
         printf("a       = %f\r\n",a);
         printf("exp     = %i, %02x\r\n",exp,exp);
         printf("sign    = %i, %02x\r\n",sign,sign);
         printf("mantisa = %i, %02x\r\n\r\n",mantisa,mantisa);
         a = -a / 2;

      }
    }

Produces:

    a       = 40800000
    a       = 4.000000
    exp     = 129, 81
    sign    = 0, 00
    mantisa = 8388608, 800000

    a       = c0000000
    a       = -2.000000
    exp     = 128, 80
    sign    = 1, 01
    mantisa = 8388608, 800000

    a       = 3f800000
    a       = 1.000000
    exp     = 127, 7f
    sign    = 0, 00
    mantisa = 8388608, 800000

    a       = bf000000
    a       = -0.500000
    exp     = 126, 7e
    sign    = 1, 01
    mantisa = 8388608, 800000

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