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891 lines
20 KiB
891 lines
20 KiB
/** |
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* @license Fraction.js v4.2.0 05/03/2022 |
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* https://www.xarg.org/2014/03/rational-numbers-in-javascript/ |
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* |
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* Copyright (c) 2021, Robert Eisele (robert@xarg.org) |
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* Dual licensed under the MIT or GPL Version 2 licenses. |
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**/ |
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/** |
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* |
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* This class offers the possibility to calculate fractions. |
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* You can pass a fraction in different formats. Either as array, as double, as string or as an integer. |
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* |
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* Array/Object form |
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* [ 0 => <nominator>, 1 => <denominator> ] |
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* [ n => <nominator>, d => <denominator> ] |
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* |
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* Integer form |
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* - Single integer value |
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* |
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* Double form |
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* - Single double value |
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* |
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* String form |
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* 123.456 - a simple double |
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* 123/456 - a string fraction |
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* 123.'456' - a double with repeating decimal places |
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* 123.(456) - synonym |
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* 123.45'6' - a double with repeating last place |
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* 123.45(6) - synonym |
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* |
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* Example: |
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* |
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* var f = new Fraction("9.4'31'"); |
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* f.mul([-4, 3]).div(4.9); |
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* |
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*/ |
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(function(root) { |
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"use strict"; |
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// Maximum search depth for cyclic rational numbers. 2000 should be more than enough. |
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// Example: 1/7 = 0.(142857) has 6 repeating decimal places. |
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// If MAX_CYCLE_LEN gets reduced, long cycles will not be detected and toString() only gets the first 10 digits |
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var MAX_CYCLE_LEN = 2000; |
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// Parsed data to avoid calling "new" all the time |
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var P = { |
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"s": 1, |
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"n": 0, |
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"d": 1 |
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}; |
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function assign(n, s) { |
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if (isNaN(n = parseInt(n, 10))) { |
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throw Fraction['InvalidParameter']; |
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} |
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return n * s; |
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} |
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// Creates a new Fraction internally without the need of the bulky constructor |
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function newFraction(n, d) { |
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if (d === 0) { |
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throw Fraction['DivisionByZero']; |
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} |
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var f = Object.create(Fraction.prototype); |
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f["s"] = n < 0 ? -1 : 1; |
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n = n < 0 ? -n : n; |
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var a = gcd(n, d); |
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f["n"] = n / a; |
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f["d"] = d / a; |
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return f; |
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} |
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function factorize(num) { |
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var factors = {}; |
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var n = num; |
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var i = 2; |
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var s = 4; |
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while (s <= n) { |
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while (n % i === 0) { |
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n/= i; |
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factors[i] = (factors[i] || 0) + 1; |
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} |
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s+= 1 + 2 * i++; |
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} |
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if (n !== num) { |
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if (n > 1) |
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factors[n] = (factors[n] || 0) + 1; |
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} else { |
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factors[num] = (factors[num] || 0) + 1; |
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} |
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return factors; |
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} |
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var parse = function(p1, p2) { |
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var n = 0, d = 1, s = 1; |
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var v = 0, w = 0, x = 0, y = 1, z = 1; |
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var A = 0, B = 1; |
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var C = 1, D = 1; |
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var N = 10000000; |
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var M; |
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if (p1 === undefined || p1 === null) { |
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/* void */ |
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} else if (p2 !== undefined) { |
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n = p1; |
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d = p2; |
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s = n * d; |
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if (n % 1 !== 0 || d % 1 !== 0) { |
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throw Fraction['NonIntegerParameter']; |
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} |
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} else |
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switch (typeof p1) { |
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case "object": |
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{ |
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if ("d" in p1 && "n" in p1) { |
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n = p1["n"]; |
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d = p1["d"]; |
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if ("s" in p1) |
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n*= p1["s"]; |
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} else if (0 in p1) { |
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n = p1[0]; |
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if (1 in p1) |
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d = p1[1]; |
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} else { |
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throw Fraction['InvalidParameter']; |
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} |
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s = n * d; |
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break; |
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} |
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case "number": |
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{ |
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if (p1 < 0) { |
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s = p1; |
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p1 = -p1; |
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} |
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if (p1 % 1 === 0) { |
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n = p1; |
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} else if (p1 > 0) { // check for != 0, scale would become NaN (log(0)), which converges really slow |
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if (p1 >= 1) { |
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z = Math.pow(10, Math.floor(1 + Math.log(p1) / Math.LN10)); |
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p1/= z; |
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} |
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// Using Farey Sequences |
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// http://www.johndcook.com/blog/2010/10/20/best-rational-approximation/ |
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while (B <= N && D <= N) { |
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M = (A + C) / (B + D); |
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if (p1 === M) { |
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if (B + D <= N) { |
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n = A + C; |
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d = B + D; |
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} else if (D > B) { |
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n = C; |
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d = D; |
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} else { |
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n = A; |
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d = B; |
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} |
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break; |
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} else { |
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if (p1 > M) { |
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A+= C; |
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B+= D; |
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} else { |
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C+= A; |
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D+= B; |
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} |
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if (B > N) { |
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n = C; |
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d = D; |
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} else { |
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n = A; |
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d = B; |
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} |
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} |
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} |
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n*= z; |
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} else if (isNaN(p1) || isNaN(p2)) { |
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d = n = NaN; |
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} |
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break; |
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} |
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case "string": |
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{ |
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B = p1.match(/\d+|./g); |
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if (B === null) |
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throw Fraction['InvalidParameter']; |
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if (B[A] === '-') {// Check for minus sign at the beginning |
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s = -1; |
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A++; |
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} else if (B[A] === '+') {// Check for plus sign at the beginning |
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A++; |
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} |
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if (B.length === A + 1) { // Check if it's just a simple number "1234" |
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w = assign(B[A++], s); |
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} else if (B[A + 1] === '.' || B[A] === '.') { // Check if it's a decimal number |
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if (B[A] !== '.') { // Handle 0.5 and .5 |
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v = assign(B[A++], s); |
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} |
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A++; |
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// Check for decimal places |
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if (A + 1 === B.length || B[A + 1] === '(' && B[A + 3] === ')' || B[A + 1] === "'" && B[A + 3] === "'") { |
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w = assign(B[A], s); |
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y = Math.pow(10, B[A].length); |
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A++; |
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} |
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// Check for repeating places |
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if (B[A] === '(' && B[A + 2] === ')' || B[A] === "'" && B[A + 2] === "'") { |
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x = assign(B[A + 1], s); |
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z = Math.pow(10, B[A + 1].length) - 1; |
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A+= 3; |
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} |
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} else if (B[A + 1] === '/' || B[A + 1] === ':') { // Check for a simple fraction "123/456" or "123:456" |
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w = assign(B[A], s); |
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y = assign(B[A + 2], 1); |
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A+= 3; |
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} else if (B[A + 3] === '/' && B[A + 1] === ' ') { // Check for a complex fraction "123 1/2" |
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v = assign(B[A], s); |
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w = assign(B[A + 2], s); |
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y = assign(B[A + 4], 1); |
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A+= 5; |
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} |
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if (B.length <= A) { // Check for more tokens on the stack |
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d = y * z; |
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s = /* void */ |
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n = x + d * v + z * w; |
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break; |
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} |
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/* Fall through on error */ |
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} |
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default: |
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throw Fraction['InvalidParameter']; |
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} |
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if (d === 0) { |
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throw Fraction['DivisionByZero']; |
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} |
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P["s"] = s < 0 ? -1 : 1; |
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P["n"] = Math.abs(n); |
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P["d"] = Math.abs(d); |
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}; |
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function modpow(b, e, m) { |
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var r = 1; |
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for (; e > 0; b = (b * b) % m, e >>= 1) { |
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if (e & 1) { |
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r = (r * b) % m; |
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} |
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} |
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return r; |
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} |
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function cycleLen(n, d) { |
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for (; d % 2 === 0; |
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d/= 2) { |
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} |
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for (; d % 5 === 0; |
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d/= 5) { |
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} |
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if (d === 1) // Catch non-cyclic numbers |
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return 0; |
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// If we would like to compute really large numbers quicker, we could make use of Fermat's little theorem: |
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// 10^(d-1) % d == 1 |
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// However, we don't need such large numbers and MAX_CYCLE_LEN should be the capstone, |
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// as we want to translate the numbers to strings. |
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var rem = 10 % d; |
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var t = 1; |
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for (; rem !== 1; t++) { |
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rem = rem * 10 % d; |
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if (t > MAX_CYCLE_LEN) |
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return 0; // Returning 0 here means that we don't print it as a cyclic number. It's likely that the answer is `d-1` |
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} |
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return t; |
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} |
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function cycleStart(n, d, len) { |
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var rem1 = 1; |
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var rem2 = modpow(10, len, d); |
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for (var t = 0; t < 300; t++) { // s < ~log10(Number.MAX_VALUE) |
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// Solve 10^s == 10^(s+t) (mod d) |
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if (rem1 === rem2) |
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return t; |
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rem1 = rem1 * 10 % d; |
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rem2 = rem2 * 10 % d; |
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} |
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return 0; |
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} |
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function gcd(a, b) { |
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if (!a) |
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return b; |
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if (!b) |
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return a; |
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while (1) { |
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a%= b; |
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if (!a) |
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return b; |
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b%= a; |
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if (!b) |
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return a; |
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} |
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}; |
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/** |
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* Module constructor |
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* |
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* @constructor |
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* @param {number|Fraction=} a |
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* @param {number=} b |
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*/ |
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function Fraction(a, b) { |
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parse(a, b); |
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if (this instanceof Fraction) { |
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a = gcd(P["d"], P["n"]); // Abuse variable a |
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this["s"] = P["s"]; |
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this["n"] = P["n"] / a; |
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this["d"] = P["d"] / a; |
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} else { |
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return newFraction(P['s'] * P['n'], P['d']); |
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} |
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} |
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Fraction['DivisionByZero'] = new Error("Division by Zero"); |
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Fraction['InvalidParameter'] = new Error("Invalid argument"); |
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Fraction['NonIntegerParameter'] = new Error("Parameters must be integer"); |
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Fraction.prototype = { |
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"s": 1, |
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"n": 0, |
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"d": 1, |
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/** |
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* Calculates the absolute value |
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* |
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* Ex: new Fraction(-4).abs() => 4 |
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**/ |
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"abs": function() { |
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return newFraction(this["n"], this["d"]); |
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}, |
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/** |
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* Inverts the sign of the current fraction |
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* |
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* Ex: new Fraction(-4).neg() => 4 |
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**/ |
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"neg": function() { |
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return newFraction(-this["s"] * this["n"], this["d"]); |
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}, |
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/** |
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* Adds two rational numbers |
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* |
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* Ex: new Fraction({n: 2, d: 3}).add("14.9") => 467 / 30 |
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**/ |
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"add": function(a, b) { |
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parse(a, b); |
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return newFraction( |
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this["s"] * this["n"] * P["d"] + P["s"] * this["d"] * P["n"], |
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this["d"] * P["d"] |
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); |
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}, |
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/** |
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* Subtracts two rational numbers |
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* |
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* Ex: new Fraction({n: 2, d: 3}).add("14.9") => -427 / 30 |
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**/ |
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"sub": function(a, b) { |
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parse(a, b); |
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return newFraction( |
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this["s"] * this["n"] * P["d"] - P["s"] * this["d"] * P["n"], |
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this["d"] * P["d"] |
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); |
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}, |
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/** |
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* Multiplies two rational numbers |
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* |
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* Ex: new Fraction("-17.(345)").mul(3) => 5776 / 111 |
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**/ |
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"mul": function(a, b) { |
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parse(a, b); |
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return newFraction( |
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this["s"] * P["s"] * this["n"] * P["n"], |
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this["d"] * P["d"] |
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); |
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}, |
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/** |
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* Divides two rational numbers |
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* |
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* Ex: new Fraction("-17.(345)").inverse().div(3) |
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**/ |
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"div": function(a, b) { |
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parse(a, b); |
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return newFraction( |
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this["s"] * P["s"] * this["n"] * P["d"], |
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this["d"] * P["n"] |
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); |
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}, |
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/** |
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* Clones the actual object |
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* |
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* Ex: new Fraction("-17.(345)").clone() |
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**/ |
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"clone": function() { |
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return newFraction(this['s'] * this['n'], this['d']); |
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}, |
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/** |
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* Calculates the modulo of two rational numbers - a more precise fmod |
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* |
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* Ex: new Fraction('4.(3)').mod([7, 8]) => (13/3) % (7/8) = (5/6) |
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**/ |
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"mod": function(a, b) { |
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if (isNaN(this['n']) || isNaN(this['d'])) { |
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return new Fraction(NaN); |
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} |
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if (a === undefined) { |
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return newFraction(this["s"] * this["n"] % this["d"], 1); |
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} |
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parse(a, b); |
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if (0 === P["n"] && 0 === this["d"]) { |
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throw Fraction['DivisionByZero']; |
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} |
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/* |
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* First silly attempt, kinda slow |
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* |
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return that["sub"]({ |
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"n": num["n"] * Math.floor((this.n / this.d) / (num.n / num.d)), |
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"d": num["d"], |
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"s": this["s"] |
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});*/ |
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/* |
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* New attempt: a1 / b1 = a2 / b2 * q + r |
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* => b2 * a1 = a2 * b1 * q + b1 * b2 * r |
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* => (b2 * a1 % a2 * b1) / (b1 * b2) |
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*/ |
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return newFraction( |
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this["s"] * (P["d"] * this["n"]) % (P["n"] * this["d"]), |
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P["d"] * this["d"] |
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); |
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}, |
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/** |
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* Calculates the fractional gcd of two rational numbers |
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* |
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* Ex: new Fraction(5,8).gcd(3,7) => 1/56 |
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*/ |
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"gcd": function(a, b) { |
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parse(a, b); |
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// gcd(a / b, c / d) = gcd(a, c) / lcm(b, d) |
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return newFraction(gcd(P["n"], this["n"]) * gcd(P["d"], this["d"]), P["d"] * this["d"]); |
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}, |
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/** |
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* Calculates the fractional lcm of two rational numbers |
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* |
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* Ex: new Fraction(5,8).lcm(3,7) => 15 |
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*/ |
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"lcm": function(a, b) { |
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parse(a, b); |
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// lcm(a / b, c / d) = lcm(a, c) / gcd(b, d) |
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if (P["n"] === 0 && this["n"] === 0) { |
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return newFraction(0, 1); |
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} |
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return newFraction(P["n"] * this["n"], gcd(P["n"], this["n"]) * gcd(P["d"], this["d"])); |
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}, |
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/** |
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* Calculates the ceil of a rational number |
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* |
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* Ex: new Fraction('4.(3)').ceil() => (5 / 1) |
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**/ |
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"ceil": function(places) { |
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places = Math.pow(10, places || 0); |
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if (isNaN(this["n"]) || isNaN(this["d"])) { |
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return new Fraction(NaN); |
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} |
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return newFraction(Math.ceil(places * this["s"] * this["n"] / this["d"]), places); |
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}, |
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/** |
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* Calculates the floor of a rational number |
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* |
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* Ex: new Fraction('4.(3)').floor() => (4 / 1) |
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**/ |
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"floor": function(places) { |
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places = Math.pow(10, places || 0); |
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if (isNaN(this["n"]) || isNaN(this["d"])) { |
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return new Fraction(NaN); |
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} |
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return newFraction(Math.floor(places * this["s"] * this["n"] / this["d"]), places); |
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}, |
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/** |
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* Rounds a rational numbers |
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* |
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* Ex: new Fraction('4.(3)').round() => (4 / 1) |
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**/ |
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"round": function(places) { |
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places = Math.pow(10, places || 0); |
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if (isNaN(this["n"]) || isNaN(this["d"])) { |
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return new Fraction(NaN); |
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} |
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return newFraction(Math.round(places * this["s"] * this["n"] / this["d"]), places); |
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}, |
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/** |
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* Gets the inverse of the fraction, means numerator and denominator are exchanged |
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* |
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* Ex: new Fraction([-3, 4]).inverse() => -4 / 3 |
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**/ |
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"inverse": function() { |
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return newFraction(this["s"] * this["d"], this["n"]); |
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}, |
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/** |
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* Calculates the fraction to some rational exponent, if possible |
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* |
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* Ex: new Fraction(-1,2).pow(-3) => -8 |
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*/ |
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"pow": function(a, b) { |
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parse(a, b); |
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// Trivial case when exp is an integer |
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if (P['d'] === 1) { |
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|
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if (P['s'] < 0) { |
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return newFraction(Math.pow(this['s'] * this["d"], P['n']), Math.pow(this["n"], P['n'])); |
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} else { |
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return newFraction(Math.pow(this['s'] * this["n"], P['n']), Math.pow(this["d"], P['n'])); |
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} |
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} |
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// Negative roots become complex |
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// (-a/b)^(c/d) = x |
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// <=> (-1)^(c/d) * (a/b)^(c/d) = x |
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// <=> (cos(pi) + i*sin(pi))^(c/d) * (a/b)^(c/d) = x # rotate 1 by 180° |
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// <=> (cos(c*pi/d) + i*sin(c*pi/d)) * (a/b)^(c/d) = x # DeMoivre's formula in Q ( https://proofwiki.org/wiki/De_Moivre%27s_Formula/Rational_Index ) |
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// From which follows that only for c=0 the root is non-complex. c/d is a reduced fraction, so that sin(c/dpi)=0 occurs for d=1, which is handled by our trivial case. |
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if (this['s'] < 0) return null; |
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|
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// Now prime factor n and d |
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var N = factorize(this['n']); |
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var D = factorize(this['d']); |
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|
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// Exponentiate and take root for n and d individually |
|
var n = 1; |
|
var d = 1; |
|
for (var k in N) { |
|
if (k === '1') continue; |
|
if (k === '0') { |
|
n = 0; |
|
break; |
|
} |
|
N[k]*= P['n']; |
|
|
|
if (N[k] % P['d'] === 0) { |
|
N[k]/= P['d']; |
|
} else return null; |
|
n*= Math.pow(k, N[k]); |
|
} |
|
|
|
for (var k in D) { |
|
if (k === '1') continue; |
|
D[k]*= P['n']; |
|
|
|
if (D[k] % P['d'] === 0) { |
|
D[k]/= P['d']; |
|
} else return null; |
|
d*= Math.pow(k, D[k]); |
|
} |
|
|
|
if (P['s'] < 0) { |
|
return newFraction(d, n); |
|
} |
|
return newFraction(n, d); |
|
}, |
|
|
|
/** |
|
* Check if two rational numbers are the same |
|
* |
|
* Ex: new Fraction(19.6).equals([98, 5]); |
|
**/ |
|
"equals": function(a, b) { |
|
|
|
parse(a, b); |
|
return this["s"] * this["n"] * P["d"] === P["s"] * P["n"] * this["d"]; // Same as compare() === 0 |
|
}, |
|
|
|
/** |
|
* Check if two rational numbers are the same |
|
* |
|
* Ex: new Fraction(19.6).equals([98, 5]); |
|
**/ |
|
"compare": function(a, b) { |
|
|
|
parse(a, b); |
|
var t = (this["s"] * this["n"] * P["d"] - P["s"] * P["n"] * this["d"]); |
|
return (0 < t) - (t < 0); |
|
}, |
|
|
|
"simplify": function(eps) { |
|
|
|
if (isNaN(this['n']) || isNaN(this['d'])) { |
|
return this; |
|
} |
|
|
|
eps = eps || 0.001; |
|
|
|
var thisABS = this['abs'](); |
|
var cont = thisABS['toContinued'](); |
|
|
|
for (var i = 1; i < cont.length; i++) { |
|
|
|
var s = newFraction(cont[i - 1], 1); |
|
for (var k = i - 2; k >= 0; k--) { |
|
s = s['inverse']()['add'](cont[k]); |
|
} |
|
|
|
if (s['sub'](thisABS)['abs']().valueOf() < eps) { |
|
return s['mul'](this['s']); |
|
} |
|
} |
|
return this; |
|
}, |
|
|
|
/** |
|
* Check if two rational numbers are divisible |
|
* |
|
* Ex: new Fraction(19.6).divisible(1.5); |
|
*/ |
|
"divisible": function(a, b) { |
|
|
|
parse(a, b); |
|
return !(!(P["n"] * this["d"]) || ((this["n"] * P["d"]) % (P["n"] * this["d"]))); |
|
}, |
|
|
|
/** |
|
* Returns a decimal representation of the fraction |
|
* |
|
* Ex: new Fraction("100.'91823'").valueOf() => 100.91823918239183 |
|
**/ |
|
'valueOf': function() { |
|
|
|
return this["s"] * this["n"] / this["d"]; |
|
}, |
|
|
|
/** |
|
* Returns a string-fraction representation of a Fraction object |
|
* |
|
* Ex: new Fraction("1.'3'").toFraction(true) => "4 1/3" |
|
**/ |
|
'toFraction': function(excludeWhole) { |
|
|
|
var whole, str = ""; |
|
var n = this["n"]; |
|
var d = this["d"]; |
|
if (this["s"] < 0) { |
|
str+= '-'; |
|
} |
|
|
|
if (d === 1) { |
|
str+= n; |
|
} else { |
|
|
|
if (excludeWhole && (whole = Math.floor(n / d)) > 0) { |
|
str+= whole; |
|
str+= " "; |
|
n%= d; |
|
} |
|
|
|
str+= n; |
|
str+= '/'; |
|
str+= d; |
|
} |
|
return str; |
|
}, |
|
|
|
/** |
|
* Returns a latex representation of a Fraction object |
|
* |
|
* Ex: new Fraction("1.'3'").toLatex() => "\frac{4}{3}" |
|
**/ |
|
'toLatex': function(excludeWhole) { |
|
|
|
var whole, str = ""; |
|
var n = this["n"]; |
|
var d = this["d"]; |
|
if (this["s"] < 0) { |
|
str+= '-'; |
|
} |
|
|
|
if (d === 1) { |
|
str+= n; |
|
} else { |
|
|
|
if (excludeWhole && (whole = Math.floor(n / d)) > 0) { |
|
str+= whole; |
|
n%= d; |
|
} |
|
|
|
str+= "\\frac{"; |
|
str+= n; |
|
str+= '}{'; |
|
str+= d; |
|
str+= '}'; |
|
} |
|
return str; |
|
}, |
|
|
|
/** |
|
* Returns an array of continued fraction elements |
|
* |
|
* Ex: new Fraction("7/8").toContinued() => [0,1,7] |
|
*/ |
|
'toContinued': function() { |
|
|
|
var t; |
|
var a = this['n']; |
|
var b = this['d']; |
|
var res = []; |
|
|
|
if (isNaN(a) || isNaN(b)) { |
|
return res; |
|
} |
|
|
|
do { |
|
res.push(Math.floor(a / b)); |
|
t = a % b; |
|
a = b; |
|
b = t; |
|
} while (a !== 1); |
|
|
|
return res; |
|
}, |
|
|
|
/** |
|
* Creates a string representation of a fraction with all digits |
|
* |
|
* Ex: new Fraction("100.'91823'").toString() => "100.(91823)" |
|
**/ |
|
'toString': function(dec) { |
|
|
|
var N = this["n"]; |
|
var D = this["d"]; |
|
|
|
if (isNaN(N) || isNaN(D)) { |
|
return "NaN"; |
|
} |
|
|
|
dec = dec || 15; // 15 = decimal places when no repetation |
|
|
|
var cycLen = cycleLen(N, D); // Cycle length |
|
var cycOff = cycleStart(N, D, cycLen); // Cycle start |
|
|
|
var str = this['s'] < 0 ? "-" : ""; |
|
|
|
str+= N / D | 0; |
|
|
|
N%= D; |
|
N*= 10; |
|
|
|
if (N) |
|
str+= "."; |
|
|
|
if (cycLen) { |
|
|
|
for (var i = cycOff; i--;) { |
|
str+= N / D | 0; |
|
N%= D; |
|
N*= 10; |
|
} |
|
str+= "("; |
|
for (var i = cycLen; i--;) { |
|
str+= N / D | 0; |
|
N%= D; |
|
N*= 10; |
|
} |
|
str+= ")"; |
|
} else { |
|
for (var i = dec; N && i--;) { |
|
str+= N / D | 0; |
|
N%= D; |
|
N*= 10; |
|
} |
|
} |
|
return str; |
|
} |
|
}; |
|
|
|
if (typeof define === "function" && define["amd"]) { |
|
define([], function() { |
|
return Fraction; |
|
}); |
|
} else if (typeof exports === "object") { |
|
Object.defineProperty(Fraction, "__esModule", { 'value': true }); |
|
Fraction['default'] = Fraction; |
|
Fraction['Fraction'] = Fraction; |
|
module['exports'] = Fraction; |
|
} else { |
|
root['Fraction'] = Fraction; |
|
} |
|
|
|
})(this);
|
|
|