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:
- https://en.wikipedia.org/wiki/Computer_number_format#Representing_fractions_in_binary
- https://www.electronics-tutorials.ws/binary/binary-fractions.html
- https://ryanstutorials.net/binary-tutorial/binary-floating-point.php
- https://planetcalc.com/862/
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
pippackages (uses built-inmathandfractionsmodules)
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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