#!/usr/bin/env python
# coding: utf-8

# # Picking apart a floating point number
# 
# Copyright (C) 2020 Andreas Kloeckner
# 
# <details>
# <summary>MIT License</summary>
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
# 
# The above copyright notice and this permission notice shall be included in
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# 
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
# </details>

# In[1]:


import numpy as np


# In[31]:


# Never mind the details of this function...

def left_pad(s, desired_len, pad="0"):
    if len(s) < desired_len:
        s = (desired_len - len(s)) * pad + s
    return s

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 bits: %d" % exponent)
    print("Exponent (with offset): %d" % (exponent - 1023))
    if exponent == 0:
        print("  In subnormal range. Effective exponent: -1022")
    fraction = get_bits(0, 52)
    print(f"Stored fraction bits: ({left_pad(bin(fraction)[2:], 52)}_2")
    if exponent != 0:
        significand = fraction + 2**52
    else:
        significand = fraction
    sig_str = left_pad(bin(significand)[2:], 53)
    print(f"Significand: ({sig_str[0]}.{sig_str[1:]})_2")
    print("Significand:", repr(significand / (2**52)))


# In[32]:


pretty_print_fp(2**(-1025))


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

# In[ ]: