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.
A simple example might be
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
console.log(f.getFraction()); // -4154 / 1485You could of course also access the sign (s), numerator (n) and denominator (d) on your own:
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:
(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
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.
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)
I published another example on how to approximate PI with fraction.js on my blog (Still not the best idea to approximate irrational numbers, but it illustrates the capabilities of Fraction.js perfectly).
var f = new Fraction("-6.(3416)");
console.log("" + f.mod(1).abs()); // Same as: Math.abs(f - parseInt(f), 10);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:
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());It turns out that Fraction.js outperforms almost any fmod() implementation, including JavaScript itself, php.js, 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.
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.
new Fraction(numerator, denumerator);
new Fraction([numerator, denumerator]);
new Fraction({n: numerator, d: denumerator});new Fraction(123);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.
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!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 states that you'll get a period of 1776 digits. Fraction.js comes to the same result. Give it a try:
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...
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);
}Returns the actual number without any sign information
Returns the sum of the actual number and the parameter n
Returns the difference of the actual number and the parameter n
Returns the product of the actual number and the parameter n
Returns the quotient of the actual number and the parameter n
Set a number n to the actual object
Returns the modulus (rest of the division) of the actual object and n (this % n). It's a much more precise fmod() 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.
Returns the fractional greatest common divisor
Returns the ceiling of a rational number (rounded up)
Returns the floor of a rational number (rounded down)
Returns the rational number rounded (normal round)
Returns the reciprocal of the actual number (n / d becomes d / n)
Check if two numbers are equal
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
Check if two numbers are divisible (n divides this)
Returns a decimal representation of the fraction
Generates an exact string representation of the actual object, including repeating decimal places of any length.
Generates an exact LaTeX representation of the actual object.
Creates a copy of the actual Fraction object
If a really hard error occurs (parsing error, division by zero), fraction.js throws exceptions! Please make sure you handle them correctly.
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
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.
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 (c) 2014, Robert Eisele (robert@xarg.org) Dual licensed under the MIT or GPL Version 2 licenses.