# 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("Stored exponent: %d" % exponent)
print("Exponent (with offset): %d" % (exponent - 1023))
fraction = get_bits(0, 52)
if exponent != 0:
significand = fraction + 2**52
else:
significand = fraction
print("Significand (binary):", bin(significand)[2:])
print("Shifted significand:", repr(significand / (2**52)))
In [27]:
pretty_print_fp(3)
---------------------------------------------
Floating point structure for 3
---------------------------------------------
Sign bit (1:negative): 0
Stored exponent: 1024
Exponent (with offset): 1
Significand (binary): 11000000000000000000000000000000000000000000000000000
Shifted significand: 1.5

Things to try:

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