Picking apart a floating point number

In [33]:
# Never mind the details of this function...

def pretty_print_fp(x):
    print("---------------------------------------------")
    print("Floating point structure for %r" % x)
    print("---------------------------------------------")
    import struct
    s = struct.pack("d", x)

    def get_bit(i):
        byte_nr, bit_nr = divmod(i, 8)
        return int(bool(
            s[byte_nr] & (1 << bit_nr)
            ))

    def get_bits(lsb, count):
        return sum(get_bit(i+lsb)*2**i for i in range(count))

    # https://en.wikipedia.org/wiki/Double_precision_floating-point_format

    print("Sign bit (1:negative):", get_bit(63))
    
    stored_exponent = get_bits(52, 11)
    fraction = get_bits(0, 52)
    
    if stored_exponent == 0:
        exponent = -1022
        significand = fraction
    else:
        exponent = stored_exponent - 1023
        significand = fraction + 2**52
        
    print("Stored exponent value: %d" % stored_exponent)
    print("Mathematical exponent: %d" % exponent)

    print("Fraction (bin): {0:052b}".format(fraction))
    print("Signif. (bin): {0:053b}".format(significand))
    print("Significand (decimal, scaled to <=2):", repr(significand / (2**52)))
In [41]:
pretty_print_fp(1)
---------------------------------------------
Floating point structure for 1
---------------------------------------------
Sign bit (1:negative): 0
Stored exponent value: 1023
Mathematical exponent: 0
Fraction (bin): 0000000000000000000000000000000000000000000000000000
Signif. (bin): 10000000000000000000000000000000000000000000000000000
Significand (decimal, scaled to <=2): 1.0

Things to try:

  • Twiddle the sign bit
  • 1,2,4,8
  • 0.5,0.25
  • $2^{\pm 1023}$, $2^{\pm 1024}$
  • float("nan")
In [ ]: