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https://github.com/formulae-org/package-arithmetic-js

Arithmetic package for Fōrmulæ, in JavaScript
https://github.com/formulae-org/package-arithmetic-js

arbitrary-precision arithmetic educational-software extensible-project formulae integer-division math mathematical-expressions mathematics maths pretty-printing programming-language rational-arithmetic rational-numbers rounding trigonometry visualization-tools

Last synced: 20 days ago
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Arithmetic package for Fōrmulæ, in JavaScript

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README 

        
# package-arithmetic-js



Arithmetic package for the [Fōrmulæ](https://formulae.org) programming language.



Fōrmulæ is also a software framework for visualization, edition and manipulation of complex expressions, from many fields. The code for an specific field —i.e. arithmetics— is encapsulated in a single unit called a Fōrmulæ **package**.



This repository contains the source code for the **arithmetic package**. It is intended to the computation of many arithmetical and mathematical operations.



The GitHub organization [formulae-org](https://github.com/formulae-org) encompasses the source code for the rest of packages, as well as the [web application](https://github.com/formulae-org/formulae-js).



Take a look at this [tutorial](https://formulae.org/?script=tutorials/Arithmetic) to know the capabilities of the Fōrmulæ arithmetic package.



### Capabilities ###



* Types of numbers

    * [Integer numbers](https://en.wikipedia.org/wiki/Integer) of arbitrary size

    * [Decimal numbers](https://en.wikipedia.org/wiki/Real_number), of arbitrary precision

    * [Rational numbers](https://en.wikipedia.org/wiki/Rational_number), of arbitrary size for numerator / denominator

* Precision management

    * Based on [significant digits](https://en.wikipedia.org/wiki/Significant_digit)

    * It can be set globally or by specific operation

* [Rounding](https://en.wikipedia.org/wiki/Rounding)

  * Rounding operation

    * Rounding to precision. This mode is used by most operations

  * Rounding modes. They can be set globally or by specific operation

    * Direct, away from zero

    * Direct, towards zero

    * Direct, towards infinity

    * Direct, towards minus infinity

    * To nearest, half away from zero

    * To nearest, half towards zero

    * To nearest, half towards infinity

    * To nearest, half towards minus infinity

    * To nearest, half to even

* "Numeric" operation, forces the operation to be performed with decimal arithmetic. Precision can be specified

* Basic arithmetic operations: addition, multiplication, division and exponentiation

   * Integer, decimal and rational numbers, even mixing them

   * With any precision and rounding mode

   * Division is visualized as fraction $\frac{a}{b}$

   * Exponentiation is visualized as $a^b$

* Comparison between integer, decimal and rational numbers, even mixing them

  * [Relational operators](https://en.wikipedia.org/wiki/Relational_operator) $a = b$, $a \ne b$, $a > b$, $a < b$, $a \leq b$, $a \geq b$

  * [Three-way comparison](https://en.wikipedia.org/wiki/Three-way_comparison) operator

* Rationalization of decimal values. Rationalization specifying number of repeating digits

* [Absolute value](https://en.wikipedia.org/wiki/Absolute_value), visualized as $|a|$

* [Sign function](https://en.wikipedia.org/wiki/Sign_function)

* [Square root](https://en.wikipedia.org/wiki/Square_root), visualized as $\sqrt a$

* [Factorial](https://en.wikipedia.org/wiki/Factorial), visualized as $n!$

* Rounding decimal and rational numbers to integers

     * Truncation

     * Floor, visualized as $\lfloor x \rfloor$

     * Ceiling, visualized as $\lceil x \rceil$

     * Any other rounding mode

* Rounding decimal and rational numbers to decimal with decimal places

* Rounding decimal and rational numbers to multiple values

* Separation of integer and decimal parts, retrieving the number of decimal places

* List of digits of a integer positive number

     * In base 10 by default, but any integer positive number can be specified as the base

     * A size (of list) can be specified. For numbers with less digits, zero values are padded

* [Pseudorandom number](https://en.wikipedia.org/wiki/Pseudorandom_number_generator) generation with uniform distribution

   * In the real interval $\[ 0, 1 \rangle$

   * In a range of integer values

* Testing operation

     * Expression being a real number (integer or decimal)

     * Expression being a rational number

     * Expression being numeric (a integer, decimal or rational number)

     * Expression beig an integer number (an integer, or decimal number with no fractional part)

     * Expression being an integer number

     * Expression being a decimal number

     * Expression beign a positive number, either integer, decimal or rational

     * Expression beign a negative number, either integer, decimal or rational

     * Expression being a zero number, either integer or decimal

     * Expression being an even number (either integer or decimal with no fractional part)

     * Expression being an odd number (either integer or decimal with no fractional part)

     * Whether an integer number [divides](https://en.wikipedia.org/wiki/Divisor#Definition) other, visualization as $a \mid b$

     * Whether an integer number does not [divide](https://en.wikipedia.org/wiki/Divisor#Definition) other, visualization as $a \nmid b$

* Conversion from/to other data types

   * From string to integer or decimal values, in decimal or bases between 2 and 36

   * From integer or decimal number to a string representation

* Div, Mod and DivMod operations

   * Between integer, decimal and rational number, even mixing them

   * Using any precision

   * Using any of the 9 roundig modes, or the [euclidean division](https://en.wikipedia.org/wiki/Euclidean_division) mode

* Related to [number theory](https://en.wikipedia.org/wiki/Number_theory)

   * [Primality test](https://en.wikipedia.org/wiki/Primality_test) of a positive integer number

   * List of [prime factors](https://en.wikipedia.org/wiki/Integer_factorization) of a integer number

   * [Greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of a list of integer numbers

   * [Least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of a list of integer numbers

   * [Modular exponentiation](https://en.wikipedia.org/wiki/Modular_exponentiation)

   * [Modular multiplicative inverse](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse)

* [Piecewise-defined functions](https://en.wikipedia.org/wiki/Piecewise)

* [Summation of a sequence](https://en.wikipedia.org/wiki/Summation) of a finite number of terms, visually using the [Capital-sigma notation](https://en.wikipedia.org/wiki/Iterated_binary_operation#Notation) $\sum$

* [Product of a sequence](https://en.wikipedia.org/wiki/Multiplication#Product_of_a_sequence) of a finite number of terms, visually using the [Capital-pi notation](https://en.wikipedia.org/wiki/Iterated_binary_operation#Notation) $\prod$

* Numerical calculation of the following [transcendental functions](https://en.wikipedia.org/wiki/Transcendental_function), for a decimal number, with any precision and rounding mode

  * [Common (base 10) logarithm](https://en.wikipedia.org/wiki/Common_logarithm)

  * [Natural logarithm](https://en.wikipedia.org/wiki/Natural_logarithm)

  * [Binary logarithm](https://en.wikipedia.org/wiki/Binary_logarithm)

  * [Logarithm in specific base](https://en.wikipedia.org/wiki/Logarithm)

* Numerical calculation of the following [trigonometric functions](https://en.wikipedia.org/wiki/Trigonometric_functions), for a decimal number, with any precision and rounding mode

  * Sine, cosine, tangent, cotangent, secant, cosecant

  * Arc sine, arc cosine, arc tangent, arc cotangent, arc secant, arc cosecant

  * [2-argument arctangent](https://en.wikipedia.org/wiki/Atan2) (atan2)

* Numerical calculation of the following [hyperbolic functions](https://en.wikipedia.org/wiki/Hyperbolic_functions), for a decimal number, with any precision and rounding mode

  * Sine, cosine, tangent, cotangent, secant, cosecant

  * Arc sine, arc cosine, arc tangent, arc cotangent, arc secant, arc cosecant

* Symbolic representation of π and e constants. Numeric conversion with any precision and roundig mode.