rithm 14.7.1

Arbitrary precision arithmetic.

rithm

In what follows python is an alias for python3.10 or pypy3.10 or any later version (python3.11, pypy3.11 and so on).

Installation

Prerequisites

Install the latest pip & setuptools packages versions

python -m pip install --upgrade pip setuptools

User

Download and install the latest stable version from PyPI repository

python -m pip install --upgrade rithm

Developer

Download the latest version from GitHub repository

git clone https://github.com/lycantropos/rithm.git
cd rithm

Install

python -m pip install -e '.'

Usage

Python

Arbitrary precision integer

With setup

>>> from rithm.integer import Int

we can:

• construct

  >>> Int()
  Int(0)
  >>> Int(9)
  Int(9)
  >>> Int('9')
  Int(9)
  >>> Int('0b1001', 2)
  Int(9)
  >>> Int('0o11', 8)
  Int(9)
  >>> Int('0x9', 16)
  Int(9)
  >>> Int('1001', 2)
  Int(9)
  >>> Int('11', 8)
  Int(9)
  >>> Int('9', 16)
  Int(9)
  >>> Int(9.99)
  Int(9)
  

• compare

  >>> Int(9) == Int(9)
  True
  >>> Int(9) >= Int(9)
  True
  >>> Int(9) > Int(8)
  True
  >>> Int(9) <= Int(9)
  True
  >>> Int(9) < Int(10)
  True
  

• calculate

  >>> abs(Int(-9))
  Int(9)
  >>> Int(4) + Int(5)
  Int(9)
  >>> Int(9) & Int(11)
  Int(9)
  >>> Int(19) // Int(2)
  Int(9)
  >>> ~Int(-10)
  Int(9)
  >>> Int(19) % Int(10)
  Int(9)
  >>> Int(3) * Int(3)
  Int(9)
  >>> -Int(-9)
  Int(9)
  >>> Int(1) | Int(8)
  Int(9)
  >>> Int(3) ** Int(2)
  Int(9)
  >>> Int(5) << Int(1)
  Int(10)
  >>> Int(5) >> Int(1)
  Int(2)
  >>> Int(25) - Int(16)
  Int(9)
  >>> Int(18) / Int(2)
  Fraction(Int(9), Int(1))
  >>> Int(2) ^ Int(11)
  Int(9)
  

Exact fraction

With setup

>>> from rithm.fraction import Fraction

we can:

• construct

  >>> Fraction()
  Fraction(Int(0), Int(1))
  >>> Fraction(1)
  Fraction(Int(1), Int(1))
  >>> Fraction(1, 2)
  Fraction(Int(1), Int(2))
  >>> Fraction(50, 100)
  Fraction(Int(1), Int(2))
  >>> Fraction(0.5)
  Fraction(Int(1), Int(2))
  

• compare

  >>> Fraction(1, 2) == Fraction(1, 2)
  True
  >>> Fraction(1, 2) >= Fraction(1, 2)
  True
  >>> Fraction(1, 2) > Fraction(1, 3)
  True
  >>> Fraction(1, 2) < Fraction(2, 3)
  True
  >>> Fraction(1, 2) != Fraction(1, 3)
  True
  

• calculate

  >>> abs(Fraction(-1, 2))
  Fraction(Int(1), Int(2))
  >>> Fraction(1, 3) + Fraction(1, 6)
  Fraction(Int(1), Int(2))
  >>> Fraction(3, 2) // Fraction(1)
  Int(1)
  >>> Fraction(3, 2) % Fraction(1)
  Fraction(Int(1), Int(2))
  >>> Fraction(1, 3) * Fraction(3, 2)
  Fraction(Int(1), Int(2))
  >>> -Fraction(-1, 2)
  Fraction(Int(1), Int(2))
  >>> Fraction(1, 2) ** 2
  Fraction(Int(1), Int(4))
  >>> Fraction(3, 2) - Fraction(1)
  Fraction(Int(1), Int(2))
  >>> Fraction(1, 3) / Fraction(2, 3)
  Fraction(Int(1), Int(2))
  

Rust

Arbitrary precision integer

/// With setup
use std::convert::TryFrom;
use traiter::numbers::{
    Abs, DivEuclid, FromStrRadix, Pow, RemEuclid, Zero
};
use rithm::big_int;

#[cfg(target_arch = "x86")]
type Digit = u16;
#[cfg(not(target_arch = "x86"))]
type Digit = u32;
const DIGIT_BITNESS: usize = (Digit::BITS - 1) as usize;
const _: () = assert!(big_int::is_valid_digit_bitness::<Digit, DIGIT_BITNESS>());
type BigInt = big_int::BigInt<Digit, DIGIT_BITNESS>;
/// we can:
/// - construct
assert_eq!(BigInt::zero(), 0);
assert_eq!(BigInt::from(9), 9);
assert_eq!(BigInt::try_from("9").unwrap(), 9);
assert_eq!(BigInt::try_from("0b1001").unwrap(), 9);
assert_eq!(BigInt::try_from("0o11").unwrap(), 9);
assert_eq!(BigInt::try_from("0x9").unwrap(), 9);
assert_eq!(BigInt::from_str_radix("1001", 2).unwrap(), 9);
assert_eq!(BigInt::from_str_radix("11", 8).unwrap(), 9);
assert_eq!(BigInt::from_str_radix("9", 16).unwrap(), 9);
assert_eq!(BigInt::try_from(9.99).unwrap(), 9);
/// - compare
assert!(BigInt::from(9) == BigInt::from(9));
assert!(BigInt::from(9) >= BigInt::from(9));
assert!(BigInt::from(9) > BigInt::from(8));
assert!(BigInt::from(9) <= BigInt::from(9));
assert!(BigInt::from(9) < BigInt::from(10));
/// - calculate
assert_eq!(BigInt::from(-9).abs(), 9);
assert_eq!(BigInt::from(4) + BigInt::from(5), 9);
assert_eq!(BigInt::from(9) & BigInt::from(11), 9);
assert_eq!(BigInt::from(1) | BigInt::from(8), 9);
assert_eq!(BigInt::from(2) ^ BigInt::from(11), 9);
assert_eq!(BigInt::from(19) / BigInt::from(2), 9);
assert_eq!(BigInt::from(19).div_euclid(BigInt::from(2)), 9);
assert_eq!(BigInt::from(3) * BigInt::from(3), 9);
assert_eq!(-BigInt::from(-9), 9);
assert_eq!(!BigInt::from(-10), 9);
assert_eq!(BigInt::from(3).pow(BigInt::from(2)), 9);
assert_eq!(BigInt::from(19) % BigInt::from(10), 9);
assert_eq!(BigInt::from(19).rem_euclid(BigInt::from(10)), 9);
assert_eq!(BigInt::from(5) << 1, 10);
assert_eq!(BigInt::from(5) >> 1, 2);
assert_eq!(BigInt::from(25) - BigInt::from(16), 9);

Exact fraction

/// With setup
use std::convert::TryFrom;
use traiter::numbers::{Abs, DivEuclid, One, Pow, RemEuclid, Zero};
use rithm::fraction;

type Fraction = fraction::Fraction<i8>;
/// we can:
/// - construct
assert_eq!(Fraction::zero(), 0);
assert_eq!(Fraction::one(), 1);
assert_eq!(Fraction::new(1, 2), Some(Fraction::from(1) / 2));
assert_eq!(Fraction::new(50, 100), Fraction::new(1, 2));
assert_eq!(Fraction::try_from(0.5).unwrap(), Fraction::new(1, 2).unwrap());
/// - compare
assert!(Fraction::new(1, 2).unwrap() == Fraction::new(1, 2).unwrap());
assert!(Fraction::new(1, 2).unwrap() >= Fraction::new(1, 2).unwrap());
assert!(Fraction::new(1, 2).unwrap() > Fraction::new(1, 3).unwrap());
assert!(Fraction::new(1, 2).unwrap() <= Fraction::new(1, 2).unwrap());
assert!(Fraction::new(1, 2).unwrap() < Fraction::new(2, 3).unwrap());
assert!(Fraction::new(1, 2).unwrap() != Fraction::new(1, 3).unwrap());
/// - calculate
assert_eq!(Fraction::new(-1, 2).unwrap().abs(), Fraction::new(1, 2).unwrap());
assert_eq!(Fraction::new(1, 3).unwrap() + Fraction::new(1, 6).unwrap(),
           Fraction::new(1, 2).unwrap());
assert_eq!(Fraction::new(1, 3).unwrap() / Fraction::new(2, 3).unwrap(),
           Fraction::new(1, 2).unwrap());
assert_eq!(Fraction::new(3, 2).unwrap().div_euclid(Fraction::from(1)), 1);
assert_eq!(Fraction::new(1, 3).unwrap() * Fraction::new(3, 2).unwrap(),
           Fraction::new(1, 2).unwrap());
assert_eq!(-Fraction::new(-1, 2).unwrap(), Fraction::new(1, 2).unwrap());
assert_eq!(Fraction::new(1, 2).unwrap().pow(2), Fraction::new(1, 4).unwrap());
assert_eq!(Fraction::new(3, 2).unwrap() % Fraction::from(1),
           Fraction::new(1, 2).unwrap());
assert_eq!(Fraction::new(3, 2).unwrap().rem_euclid(Fraction::from(1)),
           Fraction::new(1, 2).unwrap());
assert_eq!(Fraction::new(3, 2).unwrap() - Fraction::from(1),
           Fraction::new(1, 2).unwrap());

Development

Bumping version

Prerequisites

Install bump-my-version.

Release

Choose which version number category to bump following semver specification.

Test bumping version

bump-my-version bump --dry-run --verbose $CATEGORY

where $CATEGORY is the target version number category name, possible values are patch/minor/major.

Bump version

bump-my-version bump --verbose $CATEGORY

This will set version to major.minor.patch.

Running tests

Plain

Install with dependencies

python -m pip install -e '.[tests]'

Run

pytest

Docker container

Run

• with CPython

  docker-compose --file docker-compose.cpython.yml up
  

• with PyPy

  docker-compose --file docker-compose.pypy.yml up
  

Bash script

Run

• with CPython

  ./run-tests.sh
  

  or

  ./run-tests.sh cpython
  

• with PyPy

  ./run-tests.sh pypy
  

PowerShell script

Run

• with CPython

  .\run-tests.ps1
  

  or

  .\run-tests.ps1 cpython
  

• with PyPy

  .\run-tests.ps1 pypy