# Fraction.js **Repository Path**: mirrors_josdejong/Fraction.js ## Basic Information - **Project Name**: Fraction.js - **Description**: A rational number library - **Primary Language**: Unknown - **License**: Not specified - **Default Branch**: master - **Homepage**: None - **GVP Project**: No ## Statistics - **Stars**: 0 - **Forks**: 0 - **Created**: 2020-08-09 - **Last Updated**: 2026-02-14 ## Categories & Tags **Categories**: Uncategorized **Tags**: None ## README # Fraction.js - ℚ in JavaSript Tired of inprecise numbers represented by doubles, which have to store ratios and irrational numbers like PI or sqrt(2) the same way? If you need more precision or just want a fraction as a result, have a look at *Fraction.js*! Internally, numbers are represented as *numerator / denominator*, which adds just a little overhead. The library is written with performance in mind. Examples === A simple example might be ```javascript var Fraction = require('fraction.js'); var f = new Fraction("9.4'31'"); // 9.4313131313131... f.mul([-4, 3]).mod("4.'8'"); // 4.88888888888888... ``` The result is ```javascript console.log(f.getFraction()); // -4154 / 1485 ``` You could of course also access the sign (s), numerator (n) and denominator (d) on your own: ```javascript f.s * f.n / f.d = -1 * 4154 / 1485 = -2.797306... ``` If you would try to calculate it yourself, you would come up with something like: ```javascript (9.4313131 * (-4 / 3)) % 4.888888 = -2.797308133... ``` Quite okay, but yea - not as accurate as it could be. Another example might be to calculate degrees/minutes/seconds into precise decimal representations: 57+45/60+17/3600 ```javascript var deg = 57; // 57° var min = 45; // 45 Minutes var sec = 17; // 17 Seconds new Fraction(57).add(45, 60).add(17, 3600).toString() // -> 57.7547(2) ``` Now it's getting messy ;d To approximate a number like *sqrt(5) - 2 as n / d*, you can reformat the equation as follows: *pow(n / d + 2, 2) equals 5*. (It's not the best idea to approximate an irrational number as a rational one. That's not for what Fraction.js was invented for!) Then the following algorithm will generate the binary representation and the actual result. ```javascript var x = "/", s = ""; var a = new Fraction(0), b = new Fraction(1); for (var n = 0; n <= 10; n++) { var c = new Fraction(a).add(b).div(2); console.log(n + "\t" + a.n + "/" + a.d + "\t" + b.n + "/" + b.d + "\t" + c.n + "/" + c.d + "\t" + x); if (Math.pow(c.n / c.d + 2, 2) < 5) { a = c; x = "1"; } else { b = c; x = "0"; } s+= x; } console.log(s) ``` The result is ``` n a[n] b[n] c[n] x[n] 0 0/1 1/1 1/2 / 1 0/1 1/2 1/4 0 2 0/1 1/4 1/8 0 3 1/8 1/4 3/16 1 4 3/16 1/4 7/32 1 5 7/32 1/4 15/64 1 6 15/64 1/4 31/128 1 7 15/64 31/128 61/256 0 8 15/64 61/256 121/512 0 9 15/64 121/512 241/1024 0 10 241/1024 121/512 483/2048 1 ``` Thus the approximation after 11 iterations of the bisection method is *483 / 2048* and the binary representation is 0.00111100011 (see [WolframAlpha](http://www.wolframalpha.com/input/?i=sqrt%285%29-2+binary)) I published another example on how to approximate PI with fraction.js on my [blog](http://www.xarg.org/2014/03/precise-calculations-in-javascript/) (Still not the best idea to approximate irrational numbers, but it illustrates the capabilities of Fraction.js perfectly). Get the exact fractional part of a number --- ```javascript var f = new Fraction("-6.(3416)"); console.log("" + f.mod(1).abs()); // Same as: Math.abs(f - parseInt(f), 10); ``` Mathematical correct modulo --- The behaviour on negative congruences is different to most modulo implementations in computer science. Even the *mod()* function of Fraction.js behaves in the typical way. To solve the problem of having the mathematical correct modulo with Fraction.js you could come up with this: ```javascript var a = -1; var b = 10.99; console.log(new Fraction(a) .mod(b) // Not correct, normal implementation .valueOf()); console.log(new Fraction(a) .mod(b).add(b).mod(b) // Correct! Mathematical Modulo .valueOf()); ``` fmod() impreciseness circumvented --- It turns out that Fraction.js outperforms almost any fmod() implementation, including JavaScript itself, [php.js](http://phpjs.org/functions/fmod/), C++, Python, Java and even Wolframalpha due to the fact that numbers like 0.05, 0.1, ... are infinite decimal in base 2. The equation *fmod(4.55, 0.05)* gives *0.04999999999999957*, wolframalpha says *1/20*. The correct answer should be **zero**, as 0.05 divides 4.55 without any remainder. Parser === Any function (see below) as well as the constructor of the *Fraction* class parses it's input and reduce it to the smallest term. You can pass either Arrays, Objects, Integers, Doubles or Strings. Arrays / Objects --- ```javascript new Fraction(numerator, denumerator); new Fraction([numerator, denumerator]); new Fraction({n: numerator, d: denumerator}); ``` Integers --- ```javascript new Fraction(123); ``` Doubles --- ```javascript new Fraction(55.4); ``` **Note:** If you pass a double as it is, Fraction.js will perform a number analysis based on Farey Sequences. If you concern performance, cache Fraction.js objects and pass arrays/objects. The method is really precise, but too large exact numbers, like 1234567.9991829 will result in a wrong approximation. If you want to keep the number as it is, convert it to a string, as the string parser will not perform any further approximation. Strings --- ```javascript new Fraction("123.45"); new Fraction("123/45"); // A fraction represented as two decimals, separated by a slash new Fraction("123.'456'"); // Note the quotes, see below! new Fraction("123.(456)"); // Note the brackets, see below! new Fraction("123.45'6'"); // Note the quotes, see below! new Fraction("123.45(6)"); // Note the brackets, see below! ``` Repeating decimal places --- *Fraction.js* can easily handle repeating decimal places. For example *1/3* is *0.3333...*. There is only one repeating digit. As you can see in the examples above, you can pass a number like *1/3* as "0.'3'" or "0.(3)", which are synonym. There are no tests to parse something like 0.166666666 to 1/6! If you really want to handle this number, wrap around brackets on your own with the function below for example: 0.1(66666666) Assume you want to divide 123.32 / 33.6(567). [WolframAlpha](http://www.wolframalpha.com/input/?i=123.32+%2F+%2812453%2F370%29) states that you'll get a period of 1776 digits. *Fraction.js* comes to the same result. Give it a try: ```javascript var f = new Fraction("123.32"); console.log("Bam: " + f.div("33.6(567)")); ``` To automatically make a number like "0.123123123" to something more Fraction.js friendly like "0.(123)", I hacked this little brute force algorithm in a 10 minutes. Improvements are welcome... ```javascript function formatDecimal(str) { var comma, pre, offset, pad, times, repeat; if (-1 === (comma = str.indexOf("."))) return str; pre = str.substr(0, comma + 1); str = str.substr(comma + 1); for (var i = 0; i < str.length; i++) { offset = str.substr(0, i); for (var j = 0; j < 5; j++) { pad = str.substr(i, j + 1); times = Math.ceil((str.length - offset.length) / pad.length); repeat = new Array(times + 1).join(pad); // Silly String.repeat hack if (0 === (offset + repeat).indexOf(str)) { return pre + offset + "(" + pad + ")"; } } } return null; } var f, x = formatDecimal("13.0123123123"); // = 13.0(123) if (x !== null) { f = new Fraction(x); } ``` Functions === Fraction abs() --- Returns the actual number without any sign information Fraction add(n) --- Returns the sum of the actual number and the parameter n Fraction sub(n) --- Returns the difference of the actual number and the parameter n Fraction mul(n) --- Returns the product of the actual number and the parameter n Fraction div(n) --- Returns the quotient of the actual number and the parameter n Fraction set(n) --- Set a number n to the actual object Fraction mod(n) --- Returns the modulus (rest of the division) of the actual object and n (this % n). It's a much more precise [fmod()](#fmod-impreciseness-circumvented) if you will. Please note that *mod()* is just like the modulo operator of most programming languages. If you want a mathematical correct modulo, see [here](#mathematical-correct-modulo). Fraction gcd(n) --- Returns the fractional greatest common divisor Fraction ceil() --- Returns the ceiling of a rational number (rounded up) Fraction floor() --- Returns the floor of a rational number (rounded down) Fraction round() --- Returns the rational number rounded (normal round) Fraction reciprocal() --- Returns the reciprocal of the actual number (n / d becomes d / n) boolean equals(n) --- Check if two numbers are equal boolean compare(n) --- Compare two numbers. ``` result < 0: n is greater than actual number result > 0: n is smaller than actual number result = 0: n is equal to the actual number ``` boolean divisible(n) --- Check if two numbers are divisible (n divides this) double valueOf() --- Returns a decimal representation of the fraction String toString() --- Generates an exact string representation of the actual object, including repeating decimal places of any length. String toLatex() --- Generates an exact LaTeX representation of the actual object. Fraction clone() --- Creates a copy of the actual Fraction object Exceptions === If a really hard error occurs (parsing error, division by zero), *fraction.js* throws exceptions! Please make sure you handle them correctly. Installation === Installing fraction.js is as easy as cloning this repo or use one of the following commands: ``` bower install fraction.js ``` or ``` npm install fraction.js ``` Coding Style === As every library I publish, fraction.js is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library. Testing === If you plan to enhance the library, make sure you add test cases and all the previous tests are passing. You can test the library with ``` npm test ``` Copyright and licensing === Copyright (c) 2014, Robert Eisele (robert@xarg.org) Dual licensed under the MIT or GPL Version 2 licenses.