[Python-Dev] Issue 3008: Binary repr of floats

[Raymond Hettinger]

The new float.hex() is really nice.  Would like to augment it with a matching float.bin() method using the same notation and 
normalization and leaving all the rightmost bits as Guido suggested. I think this would help demystify floats and make it 
straightforward to show exactly what is happening during a floating point calculation that is losing precision.

def float_as_bin(x):
    '3.125 --> -0b1.1101000000000000000000000000000000000000000000000000p+1'
    hex2bin =  {'0' : '0000', '1' : '0001', '2' : '0010', '3' : '0011',
                '4' : '0100', '5' : '0101', '6' : '0110', '7' : '0111',
                '8' : '1000', '9' : '1001', 'a' : '1010', 'b' : '1011',
                'c' : '1100', 'd' : '1101', 'e' : '1110', 'f' : '1111'}
    hex_pattern = '(\-)?0x([0-9a-f]+)\.([0-9a-f]*)(.*)'
    sign, intpart, fracpart, exp = re.search(hex_pattern, x.hex().lower()).groups()
    return ((sign or '') + '0b' + intpart + '.' +
            ''.join(hex2bin[d] for d in fracpart)[:53] + exp)

The implementation would re-use Mark's code, substituting binary output for hex in the fractional part.

Raymond