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 ❤️ !

Fcpy: A Python package for high performance, fast convergence and high precision numerical fractional calculus computing.

1 Mar 23, 2022

python package for generating typescript grpc-web stubs from protobuf files.

grpc-web-proto-compile NOTE: This package has been superseded by romnn/proto-compile, which provides the same functionality but offers a lot more flex

0 Sep 5, 2021

DUQ is a python package for working with physical Dimensions, Units, and Quantities.

2 Nov 2, 2022

Casefy (/keɪsfaɪ/) is a lightweight Python package to convert the casing of strings

Casefy (/keɪsfaɪ/) is a lightweight Python package to convert the casing of strings. It has no third-party dependencies and supports Unicode.

12 Jan 8, 2023

Personal Toolbox Package

Jammy (Jam) A personal toolbox by Qsh.zh. Usage setup For core package, run pip install jammy To access functions in bin git clone https://gitlab.com/

5 Sep 16, 2022

Package that allows for validate and sanitize of string values.

py.validator A library of string validators and sanitizers Insipired by validator.js Strings only This library validates and sanitizes strings only. P

22 Nov 8, 2022

This is a package that allows you to create a key-value vault for storing variables in a global context

This is a package that allows you to create a key-value vault for storing variables in a global context. It allows you to set up a keyring with pre-defined constants which act as keys for the vault. These constants are then what is stored inside the vault. A key is just a string, but the value that the key is mapped to can be assigned to any type of object in Python. If the object is serializable (like a list or a dict), it can also be writen to a JSON file You can then use a decorator to annotate functions that you want to have use this vault to either store return variables in or to extract variables to be used as input for the function.

2 Dec 14, 2022

Dill_tils is a package that has my commonly used functions inside it for ease of use.

DilllonB07 Utilities Dill_tils is a package that has my commonly used functions inside it for ease of use. Installation Anyone can use this package by

2 Dec 5, 2021

An extremely simple package with a single utillity class used for gracefully handling POSIX shutdown signals.

graceful-killer An extremely simple package with a single utillity class used for gracefully handling POSIX shutdown signals. Installation Use pip to

1 Dec 9, 2021

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:

You might also like...

Fcpy: A Python package for high performance, fast convergence and high precision numerical fractional calculus computing.

python package for generating typescript grpc-web stubs from protobuf files.

DUQ is a python package for working with physical Dimensions, Units, and Quantities.

Casefy (/keɪsfaɪ/) is a lightweight Python package to convert the casing of strings

Personal Toolbox Package

Package that allows for validate and sanitize of string values.

This is a package that allows you to create a key-value vault for storing variables in a global context

Dill_tils is a package that has my commonly used functions inside it for ease of use.

An extremely simple package with a single utillity class used for gracefully handling POSIX shutdown signals.

Releases(PyPi)

PyPi(Jul 16, 2021)

Owner

Blender 2.93 addon for loading Quake II MD2 files

Find version automatically based on git tags and commit messages.

NFT-Generator is the best way to generate thousands of NFTs quick and easily with Python.

This is discord nitro code generator and checker made with python. This will generate nitro codes and checks if the code is valid or not. If code is valid then it will print the code leaving 2 lines and if not then it will print '*'.

Factoral Methods using two different method

This tool lets you perform some quick tasks for CTFs and Pentesting.

Build capture utility for Linux

This is Cool Utility tools that you can use in python.

Python code to remove empty folders from Windows/Android.

This repository contains scripts that help you validate QR codes.

Extract the download URL from OneDrive or SharePoint share link and push it to aria2

Skywater 130nm Klayout Device Generators PDK

Application for easy configuration of swap file and swappiness priority in slackware and others linux distributions.

🍰 ConnectMP - An easy and efficient way to share data between Processes in Python.

A simple tool to extract python code from a Jupyter notebook, and then run pylint on it for static analysis.

Protect your eyes from eye strain using this simple and beautiful, yet extensible break reminder

Greenery - tools for parsing and manipulating regular expressions

ColorController is a Pythonic interface for managing colors by english-language name and various color values.

✨ Un bot Twitter totalement fait en Python par moi, et en français.

Set of scripts for some automation during Magic Lantern development