# ---
# jupyter:
#   jupytext:
#     text_representation:
#       extension: .py
#       format_name: light
#       format_version: '1.5'
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# # Picking apart a floating point number
#
# Copyright (C) 2020 <NAME>
#
# <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
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
# </details>

# + jupyter={"outputs_hidden": false}
# 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)))


# + jupyter={"outputs_hidden": false}
pretty_print_fp(3)
# -

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

# + jupyter={"outputs_hidden": true}


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