from math import frexp, ldexp, copysign, isnan, isinf
import re, sys

_parser = re.compile(r"""
  \A\s*                      # leading whitespace
  (?P<sign>[-+]?)            # optional sign
  (
    0x                       # hex indicator
    (?=[0-9a-f]|\.[0-9a-f])  # lookahead guaranteeing at least one hex digit
    (?P<int>[0-9a-f]*)       # integer part (possibly empty)
    (\.(?P<frac>[0-9a-f]*))? # followed by optional fractional part
    p(?P<exp>[-+]?\d+)       # exponent
  |
    (?P<special>Inf(inity)?|NaN)
  )
  \s*\Z                      # trailing whitespace
""", re.VERBOSE | re.IGNORECASE).match

nbits_correction = {'0': 4, '1': 3, '2': 2, '3': 2,
                    '4': 1, '5': 1, '6': 1, '7': 1,
                    '8': 0, '9': 0, 'a': 0, 'b': 0,
                    'c': 0, 'd': 0, 'e': 0, 'f': 0}

mant_dig = sys.float_info.mant_dig
min_exp = sys.float_info.min_exp
# dap = max no. of hex digits after the point, assuming 1 bit before
dap = (mant_dig+2) // 4

def fromHex(s):
    """Convert a hex floating-point string to a float."""
    m = _parser(s)
    if m is None:
        raise ValueError("Invalid hex float literal: %s" % s)
    if m.group('special'):
        return float(s)

    # express in the form sign * c * 2**e, with c and e integral
    fracpart = m.group('frac') or ''
    intpart = (m.group('int') + fracpart).lstrip('0') or '0'
    c = int('0x' + intpart, 16)
    e = int(m.group('exp')) - 4*len(fracpart)

    # round if there are more bits than fit in a float
    nbits = 4*len(intpart) - nbits_correction[intpart[0]]
    shift = max(nbits - mant_dig, min_exp - mant_dig - e)
    if shift > 0:
        e += shift
        if shift > nbits:
            c = 0
        else:
            half = 1 << (shift-1)
            c = (c >> shift) + bool(c & half and c & (3*half-1))
    return ldexp(c, e)*(-1.0 if m.group('sign') == '-' else 1.0)

def toHex(x):
    """Express a float as a hex floating-point string."""
    if isnan(x) or isinf(x):
        return str(x)
    sign = '-' if copysign(1., x) < 0 else ''
    if not x:
        return sign + '0x0p+0'
    m, e = frexp(abs(x))
    shift = mant_dig + min(e - min_exp, 0)
    c = '%x' % int(m*2**shift)
    c = '0'*(dap+1-len(c)) + c
    return '%s0x%s.%sp%+d' % (sign, c[0], c[1:], e-shift+4*dap)