#!/usr/bin/env python3
import math
import re
import sys
from string import hexdigits
from types import SimpleNamespace
 
 
def float_to_bin_hex(f,
                     hex2bin={ord(h): '{:04b}'.format(int(h, 16)) for h in hexdigits}):
    if math.isinf(f) or math.isnan(f):
        return repr(f)  # inf nan
    # abuse .hex()
    h = f.hex()
    prefix, suffix = h.find('.'), h.rfind('p')
    return (h[:prefix].replace('x', 'b')
            + h[prefix:suffix].translate(hex2bin)
            + h[suffix:])
 
 
def float_to_bin(f):
    # NOTE: the implementation closely follows float.hex()
    if not math.isfinite(f):
        return repr(f)  # inf nan
 
    sign = '-' * (math.copysign(1.0, f) < 0)
    if f == 0:  # zero
        return sign + '0b0.0p+0'
 
    # f = m * 2**e
    m, e = math.frexp(math.fabs(f))
    shift = 1 - max(sys.float_info.min_exp - e, 0)
    m = math.ldexp(m, shift)  # m * (2**shift) -- make *im* 0 or 1
    e -= shift
 
    fm, im = math.modf(m)
    assert im == 1.0 or im == 0.0
    n, d = fm.as_integer_ratio()
    assert d & (d - 1) == 0  # power of two
    return '{sign}0b{i}.{frac:0{width}b}p{e:+}'.format(
        sign=sign, i=int(im), frac=n, width=d.bit_length() - 1, e=e)
 
 
def bin_to_float(bin_float):
    if bin_float in ['nan', 'inf', '-inf']:  # special
        return float(bin_float)
 
    d = SimpleNamespace(**re.fullmatch(
        r'(?P<sign>-?)0b(?P<integer>[01])\.(?P<frac>[01]+)p(?P<esign>[-+]?)(?P<exp>\d+)',
        bin_float).groupdict())
    m = d.integer + d.frac  # mantissa
    n = math.ldexp(int(m, 2), (-1 if d.esign else 1) * int(d.exp) - len(m))
    return math.copysign(n, (-1 if d.sign else 1))
 
 
for f in [-123.45, -0.0, 0.0, math.nan, math.inf, -math.inf, 0.5, 2**-1074,
          0.1, 0.01, 0.001, 10.1, 100.1, 1000.1]:
    print(f, float_to_bin(f), sep='\t')
    got = bin_to_float(float_to_bin(f))
    expected = bin_to_float(float_to_bin_hex(f))
    assert got == expected or (math.isnan(got) and math.isnan(expected)), (f, got, expected,
                                                                           float_to_bin(f), float_to_bin_hex(f))
 

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