Picking apart a floating point number

In [25]: 
# 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))
    exponent = get_bits(52, 11)
    print("Exponent: %d" % (exponent - 1023))
    fraction = get_bits(0, 52)
    significand = fraction + 2**52
    print("Significand (binary):", bin(significand)[2:])
    print("Shifted significand:", repr(significand / (2**52)))
In [24]: 
pretty_print_fp(1)

---------------------------------------------
Floating point structure for 1
---------------------------------------------
Sign bit (1:negative): 0
Exponent: 0
Significand (binary): 10000000000000000000000000000000000000000000000000000
Shifted significand: 1.0

Things to try:

  • Twiddle the sign bit
  • 1,2,4,8
  • 0.5,0.25
  • \(2^{1023}\), \(2^{1024}\)
  • float("nan")