# coding: utf-8 # # 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) # Things to try: # # * Twiddle the sign bit # * 1,2,4,8 # * 0.5,0.25 # * \$2^{1023}\$, \$2^{1024}\$ # * `float("nan")`