Convert IEEE754 double precision into mpmath arbitrary precision

ieee754_to_arb.py

import mpmath as mp

# default number of digits of precision for calculations
mp.mp.dps = 300

# frequently-used constants with arbitrary precision
zero      = mp.mpf("0")
one       = mp.mpf("1")
two       = mp.mpf("2")

# constants used in the definition of IEEE754 double precision variables
exponentBias  = mp.mpf("1023")
mantissaScale = mp.power(two, mp.mpf("52"))

def ieee754_to_arb(s, E, M):
    '''
    Given three integers, compute an arbitrary-precision equivalent
    of the 64-bit double precision variable F
    represented by s, E and M according to:
    
    F = (-1)^s * 2^(E - 1023) * (1 + M/2^52)
    
    Only one of the IEEE754 special cases is handled here,
    which is an exact zero (s ignored, E=0, M=0).
    
    Parameters:
        s (unsigned int): 0 or 1; sign bit
        E (unsigned int): 0, 1, ..., 2047; exponent (11 bit)
        M (unsigned int): 0, 1, ... (2^52-1); mantissa (52-bit)
    '''
    
    # capture exact zero
    if E == 0 and M == 0:
        return zero

    # parse sign bit
    # 0 means positive, 1 means negative, as in (-1)^s
    sign = None
    if s == 0:
        sign = one
    else:
        sign = -one

    # compute exact representation of double precision variable
    return sign * mp.power(two, E - exponentBias) * (one + M/mantissaScale)