A Python package for floating-point binary fractions. Do math in base 2!

Last update: Oct 29, 2022

Overview

Floating-point Binary Fractions: Do math in base 2!

An implementation of a floating-point binary fractions class and module in Python. Work with binary fractions and binary floats with ease!

This module allows one to represent integers, floats and fractions as binary strings.

e.g. the integer 3 will be represented as string '0b11'.
e.g. the float -3.75 will be represented as string '-0b11.11'.
e.g. the fraction 1/2 will be represented as string '0b0.1'
Exponential representation is also possible: '-0b0.01111e3', '-0b11.1e1' or '-0b1110e-2' all represent float -3.75.

Many operations and transformations are offered. You can sum, subtract, multiply, divide, compute power of, etc. of long floating-point binary fractions.

Basic representation of binary fractions and binary floats: A binary fraction is a subset of binary floats. Basically, a binary fraction is a binary float without an exponent (e.g. '-0b101.0101'). Let's have a look at an example binary float value to see how it is represented.

     prefix '0b' to indicate "binary" or "base 2"
     ||
     ||   decimal point
     ||   |
     ||   |    exponent separator
     ||   |    |
     ||   |    | exponent in base 10 (not base 2!)
     ||   |    | ||
    -0b101.0101e-34  <-- example floating-point binary fraction
    |  ||| |||| |
 sign  ||| |||| exponent sign
       ||| ||||
       ||| fraction bits in base 2
       |||
       integer bits in base 2

If you are curious about floating point binary fractions, have a look at:

License:

GPL v3 or later

Features:

Python 3
constructors for various types: int, float, Fraction, Binary, str
supports many operators: +, -, *, /, //, %, **, not, ...
supports many methods: lshift, rshift, <<, >>, round, floor, ceil, ...
very high precision
many operations are lossless, i.e. with no rounding errors or loss of precision
supports very long binary fractions
supports exponential representations
well documented. Please read the documentation inside the source code (binary.py). Or look at the pydoc-generated documentation in README.md.

Sample usage, Example calls:

$ python # sample usage, examples
>>> from binary import Binary
>>> Binary()
Binary(0, 0, False)
>>> Binary(1)
Binary(1, 0, False)
>>> Binary(2)
Binary(10, 0, False)
>>> Binary('11')
Binary(11, 0, False)
>>> Binary('11.11')
Binary(11.11, 0, False)
>>> Binary('11.11e-2')
Binary(1111e-4, 0, False)
>>> Binary('-11.11e-2')
Binary(-1111e-4, 1, False)
>>> Binary('NaN')
Binary(NaN, 0, True)
>>> Binary('-Infinity')
Binary(-Infinity, 1, True)
>>> Binary(-8.5)
Warning: mixing floats and Binary
Binary(-1000.1, 1, False)
>>> Binary('-0b111001.0001001e-12')
Binary(-1110010001001e-19, 1, False)
>>> Binary('-111001.0001001e-12')
Binary(-1110010001001e-19, 1, False)
>>> Binary('111001.0001001e-12')
Binary(1110010001001e-19, 0, False)
>>> Binary(3/4)
Binary(0.11, 0, False)
>>> Binary(17/19)
Binary(0.11100101000011010111100101000011, 0, False)
>>> Binary(128+32+8+2+17/19)
Binary(10101010.11100101000011010111100101000011, 0, False)
Binary(2**20+128+32+8+2+17/19)
Binary(100000000000010101010.11100101000011010111100101000011, 0, False)
>>> Binary((1, (1,0,0,1,1,0,0,0,1), -3))
Binary(-100110001e-3, 1, False)

>>> b=Binary(2**20+128+32+8+2+17/19)
>>> b.float()
1048746.894736842
>>> b.to_not_exponential()
Binary(100000000000010101010.11100101000011010111100101000011, 0, False)
>>> b.round(2)
Binary(100000000000010101011, 0, False)
>>> b.round(3)
Binary(100000000000010101010.111, 0, False)
>>> b.round(4)
Binary(100000000000010101010.111, 0, False)
>>> b.fill(10)
'100000000000010101010.11100101000011010111100101000011'
>>> b.fill(10,True)
'100000000000010101010.1110010100'
>>> b.fill(64)
'100000000000010101010.1110010100001101011110010100001100000000000000000000000000000000'
>>> b.fill(64,True)
'100000000000010101010.1110010100001101011110010100001100000000000000000000000000000000'
>>> b.to_simple_exponential() # no comma
Binary(10000000000001010101011100101000011010111100101000011e-32, 0, False)
>>> b.to_sci_exponential() # 1 digit before comma
Binary(1.0000000000001010101011100101000011010111100101000011e20, 0, False)
>>> b2=Binary(7)
>>> b2.to_sci_exponential()
Binary(1.11e2, 0, False)
>>> b2=Binary('111')
>>> b2.to_sci_exponential()
Binary(1.11e2, 0, False)
>>> b2.components()
(0, '111', '', 0)
>>> b3=b2.to_sci_exponential()
>>> b3.components()
(0, '1', '11', 2)
>>> b3.isinfinity()
False
>>> b2.compare(b3) # same value, returns equal
Binary(0, 0, False)
>>> b2 == b3  # same value, returns equal
True
>>> b2._cmp(b3) # same value, returns equal
0
>>> b2.compare_representation(b3) # different representation, returns unequal
False
>>> b2
Binary(111, 0, False)
>>> str(b2)
'0b111'
>>> b4=Binary(7.125)
>>> str(b4)
'0b111.001'
>>> b4.np() # no prefix, '0b' prefix removed
'111.001'
>>> # simple math
>>> Binary('111') + Binary(3)
Binary(1010, 0, False)
>>> Binary('111.1') - Binary(3)
Binary(100.1, 0, False)
>>> Binary('111.1') * Binary(2.0)
Binary(1111, 0, False)
>>> Binary('111.1') / Binary(4.0)
Binary(1.111, 0, False)
>>> Binary('111.1') // Binary(4.0)
Binary(1, 0, False)
>>> float(Binary('111.1'))
7.5
>>> int(Binary('111.1'))
7
>>> # works with large numbers
>>> Binary('11100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111111111111111.100000000000000000000000000000000000000010101010101010101010101010101010101010101010101010101') * Binary('11111111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111100000000000000000000000000000000000000111111111111.0111111111111111111111111111111111111111111111111111111111100000000000000000000000000011111111111111111111e-12')
Binary(1101111111111111111111111111111111111111111111111111111111111111100100000000000000000000000000000000000000000000000000000000000000000000000100000000000000000000000000000000001101111111111111111111111111100111111111111111111111110010000000000001010101010101010101011001010101010011100101010101010011111111111101011001010101010101010101001110010101010101010101011000110011111111101111110010000000000000000001000000000000110101010101100101010101010101010101010101010101001.1101010001011001010101010101010101110101111111111111100101010101010101100101010101010101010100101000101010111110101011001010101, 0, False)
>>> # and so much more

Requirements:

Python 3
requires no pip packages (uses built-in math and fractions modules)

Installation:

see https://pypi.org/project/binary-fractions/
pip install binary-fractions

Contributions:

PRs are welcome and very much appreciated! Please run selftest() before issuing a PR to be sure all test cases pass.
File Format: linted/beautified with black

Enjoy ❤️ !

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A Python package for floating-point binary fractions. Do math in base 2!

Related tags

Overview

Floating-point Binary Fractions: Do math in base 2!

License:

Features:

Sample usage, Example calls:

Requirements:

Installation:

Contributions:

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