[2023-03-13] How many values are nan? (IEEE-754 float64)

README.md

How many nan values exist?

It turns out a lot (2**52). Anything where the 12 exponent bits are all 1, independent of the values of the other 52 bits).

$ python main.py
binary(1.0)  = 0011111111110000000000000000000000000000000000000000000000000000
binary(2.0)  = 0100000000000000000000000000000000000000000000000000000000000000
binary(-1.0) = 1011111111110000000000000000000000000000000000000000000000000000
binary(1.5)  = 0011111111111000000000000000000000000000000000000000000000000000
binary(1.75) = 0011111111111100000000000000000000000000000000000000000000000000
binary(nan)  = 0111111111111000000000000000000000000000000000000000000000000000
================================================================================
float(0011111111110000000000000000000000000000000000000000000000000000) = 1.0
float(0111111111111000000000000000000000000000000000000000000000000000) = nan
float(0111111111111100000000000000000000000000000000000000000000000000) = nan
float(0111111111111110000000000000000000000000000000000000000000000000) = nan
float(1111111111111110000000000000000000000000000000000000000000000000) = nan

main.py

import struct


# NOTE: We use big-endian because it reads left-to-right, even though most
#       systems use little-endian.
FLOAT_FORMAT = ">d"


def as_bits(value):
    as_bytes = struct.pack(FLOAT_FORMAT, value)
    return "".join([f"{byte_:08b}" for byte_ in as_bytes])


def from_bits(bits64):
    as_bytes = bytes([int(bits64[i : i + 8], 2) for i in range(0, 64, 8)])
    (value,) = struct.unpack(FLOAT_FORMAT, as_bytes)
    return value


def main():
    print(f"binary(1.0)  = {as_bits(1.0)}")
    print(f"binary(2.0)  = {as_bits(2.0)}")
    print(f"binary(-1.0) = {as_bits(-1.0)}")
    print(f"binary(1.5)  = {as_bits(1.5)}")
    print(f"binary(1.75) = {as_bits(1.75)}")
    print(f"binary(nan)  = {as_bits(float('nan'))}")
    print("=" * 80)
    binary1_0 = "0011111111110000000000000000000000000000000000000000000000000000"
    print(f"float({binary1_0}) = {from_bits(binary1_0)}")
    binary_nan1 = "0111111111111000000000000000000000000000000000000000000000000000"
    print(f"float({binary_nan1}) = {from_bits(binary_nan1)}")
    binary_nan2 = "0111111111111100000000000000000000000000000000000000000000000000"
    print(f"float({binary_nan2}) = {from_bits(binary_nan2)}")
    binary_nan3 = "0111111111111110000000000000000000000000000000000000000000000000"
    print(f"float({binary_nan3}) = {from_bits(binary_nan3)}")
    binary_nan4 = "1111111111111110000000000000000000000000000000000000000000000000"
    print(f"float({binary_nan4}) = {from_bits(binary_nan4)}")


if __name__ == "__main__":
    main()