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

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Jonny-exe/binary-fractions

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PyPiPyPI - DownloadsBlackChecked with mypyDocs

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

This module allows one to represent integers, floats and fractions asbinary 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.
  • two's complement representation is possible too:'11.11' for -1.25 in decimal, or '-0b1.01' in binary fraction.

Many operations and transformations are offered.You can sum, subtract, multiply, and divide long floating-point binaryfractions. You can compute power of them, shift them left, shift them right,etc.

Basic representation of binary fractions and binary floats:A binary fraction is a subset of binary floats. Basically, a binary fractionis 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 in 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:

If you are curious about Two's complement:

License:

  • GPL v3 or later

Features:

  • Python 3
  • constructors for various types: int, float, Fraction, str, TwosComplement, Binary
  • supports many operators: +, -, *, /, //, %, **, <<, >>, ~, &, ...
  • supports many methods: not, abs, round, floor, ceil, ...
  • internally the value is kept as a Fraction and most operations are donein Fractions. This results in better performance and infinite precision.Only a few limited operations such as 'and', 'or', 'xor', and 'invert'are done on strings.
  • 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 inREADME.md.
  • well tested
    • over 1600 test cases

Sample usage, Example calls:

Please have a look at the short example program that uses theBinary class and module. See filebinary_sample.py.

The sample source code looks like this:

#!/usr/bin/python3# Sample program using the Binary class and module.# Install with: pip3 install --upgrade binary-fractionsif __name__ == "__main__":    from binary_fractions import TwosComplement, Binary    from math import ceil, floor    bf1str: str = "-1.01"  # -1.25    bf2str: str = "10.1"  # 2.5    bf3str: str = "10.1e-3"  # 2.5/8    tcstr1: str = "10.1"  # -1.5 in two's complement, '-0b1.1' as binary fraction    tcstr2: str = "100001001000.1"  # -1975.5 in two's complement, '-0b11110111000.1'    fl1: float = 2.3    fl2: float = -1975.5    bf1: Binary = Binary(bf1str)    bf2: Binary = Binary(bf2str)    bf3: Binary = Binary(bf3str)    tc1: TwosComplement = TwosComplement(tcstr1)    tc2: TwosComplement = TwosComplement(tcstr2)    tc3: TwosComplement = TwosComplement(fl2)    print("Sample program demonstrating binary fractions class and module:")    print(f"Binary({fl1}) = {Binary(fl1)}")    print(f"Binary({fl2}) = {Binary(fl2)}")    print(f"Binary({bf3str}) = {Binary(bf3str)}")    print(f"{bf1} = {bf1}")    print(f"{bf1} + {bf2} = {bf1+bf2}")    print(f"{bf1} - {bf2} = {bf1-bf2}")    print(f"{bf1} * {bf2} = {bf1*bf2}")    print(f"{bf1} / {bf2} = {bf1/bf2}")    print(f"{bf1} // {bf2} = {bf1//bf2}")    print(f"{bf1} % {bf2} = {bf1%bf2}")    print(f"{bf2} ** {bf1} = {bf2**bf1}")    print(f"{bf1} >> {1} = {bf1>>1}")    print(f"{bf1} << {1} = {bf1<<1}")    print(f"abs({bf1}) = {abs(bf1)}")    print(f"round({bf1}) = {round(bf1)}")    print(f"ceil({bf1}) = {ceil(bf1)} (int)")    print(f"Binary('{bf1}').ceil() = {bf1.ceil()} (Binary)")    print(f"floor({bf1}) = {floor(bf1)} (int)")    print(f"Binary('{bf1}').floor() = {bf1.floor()} (Binary)")    print(f"int({bf1}) = {int(bf1)}")    print(f"float({bf1}) = {float(bf1)}")    print(f"str({bf1}) = {str(bf1)}")    print(f"str({bf3}) = {str(bf3)}")    print(f"Fraction({bf1}) = {bf1.fraction}")    print(f"Binary({bf1}).fraction = {bf1.fraction}")    print(f"Binary({fl2}).string = {Binary(fl2).string}")    print(f"{bf1} & {bf2} = {bf1&bf2}")    print(f"{bf1} | {bf2} = {bf1|bf2}")    print(f"{bf1} ^ {bf2} = {bf1^bf2}")    print(f"~(floor({bf2})) = {~(floor(bf2))}")    print(f"type({bf1}) = {type(bf1)}")    print(f"type({tc1}) = {type(tc1)}")    print(f"Binary('{bf3}').to_no_exponent() = {bf3.to_no_exponent()}")    print(f"Binary('{bf3}').to_no_mantissa() = {bf3.to_no_mantissa()}")    # scientific notation    print(f"Binary('{bf3}').to_sci_exponent() = {bf3.to_sci_exponent()}")    # engineering notation    print(f"Binary('{bf3}').to_eng_exponent() = {bf3.to_eng_exponent()}")    print(f"Binary('{bf1}').to_twos_complement() = {bf1.to_twoscomplement()}")    print(f"Binary(TwosComplement('{tcstr1}')) = {Binary.from_twoscomplement(tc1)}")    print(f"Binary(TwosComplement('{tcstr2}')) = {Binary.from_twoscomplement(tc2)}")    print(f"Binary(TwosComplement({fl2})) = {Binary.from_twoscomplement(tc3)}")    print(f"TwosComplement({fl2}) = {TwosComplement(fl2)}")    print("And there are more operands, more methods, more functions, ...")    print("For more information read the documentation at:")    print("https://raw.githubusercontent.com/Jonny-exe/binary-fractions")

When executed with the commandpython3 binary_sample.py, it returns theseresults:

Sample program demonstrating binary fractions class and module:Binary(2.3) = 0b10.01001100110011001100110011001100110011001100110011Binary(-1975.5) = -0b11110110111.1Binary(10.1e-3) = 0b10.1e-3-0b1.01 = -0b1.01-0b1.01 + 0b10.1 = 0b1.01-0b1.01 - 0b10.1 = -0b11.11-0b1.01 * 0b10.1 = -0b11.001-0b1.01 / 0b10.1 = -0b0.1-0b1.01 // 0b10.1 = -0b1-0b1.01 % 0b10.1 = 0b1.010b10.1 ** -0b1.01 = 0b0.010100010110111110001011100001001001101110110100110011-0b1.01 >> 1 = -0b0.101-0b1.01 << 1 = -0b10.1abs(-0b1.01) = 0b1.01round(-0b1.01) = -0b1ceil(-0b1.01) = -1 (int)Binary('-0b1.01').ceil() = -0b1 (Binary)floor(-0b1.01) = -2 (int)Binary('-0b1.01').floor() = -0b10 (Binary)int(-0b1.01) = -1float(-0b1.01) = -1.25str(-0b1.01) = -0b1.01str(0b10.1e-3) = 0b10.1e-3Fraction(-0b1.01) = -5/4-0b1.01 & 0b10.1 = 0b10.1-0b1.01 | 0b10.1 = -0b1.01-0b1.01 ^ 0b10.1 = -0b11.11~(floor(0b10.1)) = -3type(-0b1.01) = <class 'binary.Binary'>type(10.1) = <class 'binary.TwosComplement'>Binary('0b10.1e-3').to_no_exponent() = 0b0.0101Binary('0b10.1e-3').to_no_mantissa() = 0b101e-4Binary('0b10.1e-3').to_sci_exponent() = 0b1.01e-2Binary('0b10.1e-3').to_eng_exponent() = 0b101000000e-10Binary('-0b1.01').to_twos_complement() = 10.11Binary(TwosComplement('10.1')) = -1.1Binary(TwosComplement('100001001000.1')) = -11110110111.1Binary(TwosComplement(-1975.5)) = -11110110111.1TwosComplement(-1975.5) = 100001001000.1

Requirements:

  • Python 3
  • requires nopip packages (uses built-inmath andfractions modules formath operations, usesunittest for unit testing)

Installation:

Testing, Maturity

  • runpython3 binary_sample.py to execute a simple sample program
  • runpython3 binary_test.py to execute all unit tests
  • Binary is relatively mature, more than 1600 test cases have been written and allpassed.

Contributions:

  • PRs are welcome and very much appreciated! 👍
  • Please run and pass all existing 1600+ test cases inbinary_test.pybefore issuing a PR.
  • File Format: linted/beautified withblack
  • This project uses static typing.mypyis used for type checking.
  • Test case format:unittest
  • Documentation format:pydoc

Enjoy ❤️ !

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