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- (function(root) {
- "use strict";
-
-
-
- var MAX_CYCLE_LEN = 2000;
-
- var P = {
- "s": 1,
- "n": 0,
- "d": 1
- };
- function assign(n, s) {
- if (isNaN(n = parseInt(n, 10))) {
- throw InvalidParameter();
- }
- return n * s;
- }
-
- function newFraction(n, d) {
- if (d === 0) {
- throw DivisionByZero();
- }
- var f = Object.create(Fraction.prototype);
- f["s"] = n < 0 ? -1 : 1;
- n = n < 0 ? -n : n;
- var a = gcd(n, d);
- f["n"] = n / a;
- f["d"] = d / a;
- return f;
- }
- function factorize(num) {
- var factors = {};
- var n = num;
- var i = 2;
- var s = 4;
- while (s <= n) {
- while (n % i === 0) {
- n/= i;
- factors[i] = (factors[i] || 0) + 1;
- }
- s+= 1 + 2 * i++;
- }
- if (n !== num) {
- if (n > 1)
- factors[n] = (factors[n] || 0) + 1;
- } else {
- factors[num] = (factors[num] || 0) + 1;
- }
- return factors;
- }
- var parse = function(p1, p2) {
- var n = 0, d = 1, s = 1;
- var v = 0, w = 0, x = 0, y = 1, z = 1;
- var A = 0, B = 1;
- var C = 1, D = 1;
- var N = 10000000;
- var M;
- if (p1 === undefined || p1 === null) {
-
- } else if (p2 !== undefined) {
- n = p1;
- d = p2;
- s = n * d;
- if (n % 1 !== 0 || d % 1 !== 0) {
- throw NonIntegerParameter();
- }
- } else
- switch (typeof p1) {
- case "object":
- {
- if ("d" in p1 && "n" in p1) {
- n = p1["n"];
- d = p1["d"];
- if ("s" in p1)
- n*= p1["s"];
- } else if (0 in p1) {
- n = p1[0];
- if (1 in p1)
- d = p1[1];
- } else {
- throw InvalidParameter();
- }
- s = n * d;
- break;
- }
- case "number":
- {
- if (p1 < 0) {
- s = p1;
- p1 = -p1;
- }
- if (p1 % 1 === 0) {
- n = p1;
- } else if (p1 > 0) {
- if (p1 >= 1) {
- z = Math.pow(10, Math.floor(1 + Math.log(p1) / Math.LN10));
- p1/= z;
- }
-
-
- while (B <= N && D <= N) {
- M = (A + C) / (B + D);
- if (p1 === M) {
- if (B + D <= N) {
- n = A + C;
- d = B + D;
- } else if (D > B) {
- n = C;
- d = D;
- } else {
- n = A;
- d = B;
- }
- break;
- } else {
- if (p1 > M) {
- A+= C;
- B+= D;
- } else {
- C+= A;
- D+= B;
- }
- if (B > N) {
- n = C;
- d = D;
- } else {
- n = A;
- d = B;
- }
- }
- }
- n*= z;
- } else if (isNaN(p1) || isNaN(p2)) {
- d = n = NaN;
- }
- break;
- }
- case "string":
- {
- B = p1.match(/\d+|./g);
- if (B === null)
- throw InvalidParameter();
- if (B[A] === '-') {
- s = -1;
- A++;
- } else if (B[A] === '+') {
- A++;
- }
- if (B.length === A + 1) {
- w = assign(B[A++], s);
- } else if (B[A + 1] === '.' || B[A] === '.') {
- if (B[A] !== '.') {
- v = assign(B[A++], s);
- }
- A++;
-
- if (A + 1 === B.length || B[A + 1] === '(' && B[A + 3] === ')' || B[A + 1] === "'" && B[A + 3] === "'") {
- w = assign(B[A], s);
- y = Math.pow(10, B[A].length);
- A++;
- }
-
- if (B[A] === '(' && B[A + 2] === ')' || B[A] === "'" && B[A + 2] === "'") {
- x = assign(B[A + 1], s);
- z = Math.pow(10, B[A + 1].length) - 1;
- A+= 3;
- }
- } else if (B[A + 1] === '/' || B[A + 1] === ':') {
- w = assign(B[A], s);
- y = assign(B[A + 2], 1);
- A+= 3;
- } else if (B[A + 3] === '/' && B[A + 1] === ' ') {
- v = assign(B[A], s);
- w = assign(B[A + 2], s);
- y = assign(B[A + 4], 1);
- A+= 5;
- }
- if (B.length <= A) {
- d = y * z;
- s =
- n = x + d * v + z * w;
- break;
- }
-
- }
- default:
- throw InvalidParameter();
- }
- if (d === 0) {
- throw DivisionByZero();
- }
- P["s"] = s < 0 ? -1 : 1;
- P["n"] = Math.abs(n);
- P["d"] = Math.abs(d);
- };
- function modpow(b, e, m) {
- var r = 1;
- for (; e > 0; b = (b * b) % m, e >>= 1) {
- if (e & 1) {
- r = (r * b) % m;
- }
- }
- return r;
- }
- function cycleLen(n, d) {
- for (; d % 2 === 0;
- d/= 2) {
- }
- for (; d % 5 === 0;
- d/= 5) {
- }
- if (d === 1)
- return 0;
-
-
-
-
- var rem = 10 % d;
- var t = 1;
- for (; rem !== 1; t++) {
- rem = rem * 10 % d;
- if (t > MAX_CYCLE_LEN)
- return 0;
- }
- return t;
- }
- function cycleStart(n, d, len) {
- var rem1 = 1;
- var rem2 = modpow(10, len, d);
- for (var t = 0; t < 300; t++) {
-
- if (rem1 === rem2)
- return t;
- rem1 = rem1 * 10 % d;
- rem2 = rem2 * 10 % d;
- }
- return 0;
- }
- function gcd(a, b) {
- if (!a)
- return b;
- if (!b)
- return a;
- while (1) {
- a%= b;
- if (!a)
- return b;
- b%= a;
- if (!b)
- return a;
- }
- };
-
- function Fraction(a, b) {
- parse(a, b);
- if (this instanceof Fraction) {
- a = gcd(P["d"], P["n"]);
- this["s"] = P["s"];
- this["n"] = P["n"] / a;
- this["d"] = P["d"] / a;
- } else {
- return newFraction(P['s'] * P['n'], P['d']);
- }
- }
- var DivisionByZero = function() { return new Error("Division by Zero"); };
- var InvalidParameter = function() { return new Error("Invalid argument"); };
- var NonIntegerParameter = function() { return new Error("Parameters must be integer"); };
- Fraction.prototype = {
- "s": 1,
- "n": 0,
- "d": 1,
-
- "abs": function() {
- return newFraction(this["n"], this["d"]);
- },
-
- "neg": function() {
- return newFraction(-this["s"] * this["n"], this["d"]);
- },
-
- "add": function(a, b) {
- parse(a, b);
- return newFraction(
- this["s"] * this["n"] * P["d"] + P["s"] * this["d"] * P["n"],
- this["d"] * P["d"]
- );
- },
-
- "sub": function(a, b) {
- parse(a, b);
- return newFraction(
- this["s"] * this["n"] * P["d"] - P["s"] * this["d"] * P["n"],
- this["d"] * P["d"]
- );
- },
-
- "mul": function(a, b) {
- parse(a, b);
- return newFraction(
- this["s"] * P["s"] * this["n"] * P["n"],
- this["d"] * P["d"]
- );
- },
-
- "div": function(a, b) {
- parse(a, b);
- return newFraction(
- this["s"] * P["s"] * this["n"] * P["d"],
- this["d"] * P["n"]
- );
- },
-
- "clone": function() {
- return newFraction(this['s'] * this['n'], this['d']);
- },
-
- "mod": function(a, b) {
- if (isNaN(this['n']) || isNaN(this['d'])) {
- return new Fraction(NaN);
- }
- if (a === undefined) {
- return newFraction(this["s"] * this["n"] % this["d"], 1);
- }
- parse(a, b);
- if (0 === P["n"] && 0 === this["d"]) {
- throw DivisionByZero();
- }
-
-
- return newFraction(
- this["s"] * (P["d"] * this["n"]) % (P["n"] * this["d"]),
- P["d"] * this["d"]
- );
- },
-
- "gcd": function(a, b) {
- parse(a, b);
-
- return newFraction(gcd(P["n"], this["n"]) * gcd(P["d"], this["d"]), P["d"] * this["d"]);
- },
-
- "lcm": function(a, b) {
- parse(a, b);
-
- if (P["n"] === 0 && this["n"] === 0) {
- return newFraction(0, 1);
- }
- return newFraction(P["n"] * this["n"], gcd(P["n"], this["n"]) * gcd(P["d"], this["d"]));
- },
-
- "ceil": function(places) {
- places = Math.pow(10, places || 0);
- if (isNaN(this["n"]) || isNaN(this["d"])) {
- return new Fraction(NaN);
- }
- return newFraction(Math.ceil(places * this["s"] * this["n"] / this["d"]), places);
- },
-
- "floor": function(places) {
- places = Math.pow(10, places || 0);
- if (isNaN(this["n"]) || isNaN(this["d"])) {
- return new Fraction(NaN);
- }
- return newFraction(Math.floor(places * this["s"] * this["n"] / this["d"]), places);
- },
-
- "round": function(places) {
- places = Math.pow(10, places || 0);
- if (isNaN(this["n"]) || isNaN(this["d"])) {
- return new Fraction(NaN);
- }
- return newFraction(Math.round(places * this["s"] * this["n"] / this["d"]), places);
- },
-
- "roundTo": function(a, b) {
-
- parse(a, b);
- return newFraction(this['s'] * Math.round(this['n'] * P['d'] / (this['d'] * P['n'])) * P['n'], P['d']);
- },
-
- "inverse": function() {
- return newFraction(this["s"] * this["d"], this["n"]);
- },
-
- "pow": function(a, b) {
- parse(a, b);
-
- if (P['d'] === 1) {
- if (P['s'] < 0) {
- return newFraction(Math.pow(this['s'] * this["d"], P['n']), Math.pow(this["n"], P['n']));
- } else {
- return newFraction(Math.pow(this['s'] * this["n"], P['n']), Math.pow(this["d"], P['n']));
- }
- }
-
-
-
-
-
-
- if (this['s'] < 0) return null;
-
- var N = factorize(this['n']);
- var D = factorize(this['d']);
-
- 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);
- },
-
- "equals": function(a, b) {
- parse(a, b);
- return this["s"] * this["n"] * P["d"] === P["s"] * P["n"] * this["d"];
- },
-
- "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 (Math.abs(s['sub'](thisABS).valueOf()) < eps) {
- return s['mul'](this['s']);
- }
- }
- return this;
- },
-
- "divisible": function(a, b) {
- parse(a, b);
- return !(!(P["n"] * this["d"]) || ((this["n"] * P["d"]) % (P["n"] * this["d"])));
- },
-
- 'valueOf': function() {
- return this["s"] * this["n"] / this["d"];
- },
-
- '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;
- },
-
- '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;
- },
-
- '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;
- },
-
- 'toString': function(dec) {
- var N = this["n"];
- var D = this["d"];
- if (isNaN(N) || isNaN(D)) {
- return "NaN";
- }
- dec = dec || 15;
- var cycLen = cycleLen(N, D);
- var cycOff = cycleStart(N, D, cycLen);
- 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 exports === "object") {
- Object.defineProperty(exports, "__esModule", { 'value': true });
- exports['default'] = Fraction;
- module['exports'] = Fraction;
- } else {
- root['Fraction'] = Fraction;
- }
- })(this);
|