fraction.js

/**
 * @license Fraction.js v4.0.3 09/09/2015
 * http://www.xarg.org/2014/03/rational-numbers-in-javascript/
 *
 * Copyright (c) 2015, Robert Eisele (robert@xarg.org)
 * Dual licensed under the MIT or GPL Version 2 licenses.
 **/


/**
 *
 * This class offers the possibility to calculate fractions.
 * You can pass a fraction in different formats. Either as array, as double, as string or as an integer.
 *
 * Array/Object form
 * [ 0 => <nominator>, 1 => <denominator> ]
 * [ n => <nominator>, d => <denominator> ]
 *
 * Integer form
 * - Single integer value
 *
 * Double form
 * - Single double value
 *
 * String form
 * 123.456 - a simple double
 * 123/456 - a string fraction
 * 123.'456' - a double with repeating decimal places
 * 123.(456) - synonym
 * 123.45'6' - a double with repeating last place
 * 123.45(6) - synonym
 *
 * Example:
 *
 * var f = new Fraction("9.4'31'");
 * f.mul([-4, 3]).div(4.9);
 *
 */

(function (root) {

  "use strict";

  // Maximum search depth for cyclic rational numbers. 2000 should be more than enough.
  // Example: 1/7 = 0.(142857) has 6 repeating decimal places.
  // If MAX_CYCLE_LEN gets reduced, long cycles will not be detected and toString() only gets the first 10 digits
  var MAX_CYCLE_LEN = 2000;

  // Parsed data to avoid calling "new" all the time
  var P = {
    "s": 1,
    "n": 0,
    "d": 1
  };

  function createError(name) {
    var errorConstructor = function () {
      var temp = Error.apply(this, arguments);
      temp.name = this.name = name;
      this.stack = temp.stack;
      this.message = temp.message;
    };

    var IntermediateInheritor = function () {};
    IntermediateInheritor.prototype = Error.prototype;
    errorConstructor.prototype = new IntermediateInheritor();

    return errorConstructor;
  }

  var DivisionByZero = Fraction['DivisionByZero'] = createError('DivisionByZero');
  var InvalidParameter = Fraction['InvalidParameter'] = createError('InvalidParameter');

  function assign(n, s) {

    if (isNaN(n = parseInt(n, 10))) {
      throwInvalidParam();
    }
    return n * s;
  }

  function throwInvalidParam() {
    throw new InvalidParameter();
  }

  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) {
      /* void */
    } else if (p2 !== undefined) {
      n = p1;
      d = p2;
      s = n * d;
    } 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 {
            throwInvalidParam();
          }
          s = n * d;
          break;
        }
        case "number":
        {
          if (p1 < 0) {
            s = p1;
            p1 = -p1;
          }

          if (p1 % 1 === 0) {
            n = p1;
          } else if (p1 > 0) { // check for != 0, scale would become NaN (log(0)), which converges really slow

            if (p1 >= 1) {
              z = Math.pow(10, Math.floor(1 + Math.log(p1) / Math.LN10));
              p1/= z;
            }

            // Using Farey Sequences
            // http://www.johndcook.com/blog/2010/10/20/best-rational-approximation/

            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)
            throwInvalidParam();

          if (B[A] === '-') {// Check for minus sign at the beginning
            s = -1;
            A++;
          } else if (B[A] === '+') {// Check for plus sign at the beginning
            A++;
          }

          if (B.length === A + 1) { // Check if it's just a simple number "1234"
            w = assign(B[A++], s);
          } else if (B[A + 1] === '.' || B[A] === '.') { // Check if it's a decimal number

            if (B[A] !== '.') { // Handle 0.5 and .5
              v = assign(B[A++], s);
            }
            A++;

            // Check for decimal places
            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++;
            }

            // Check for repeating places
            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] === ':') { // Check for a simple fraction "123/456" or "123:456"
            w = assign(B[A], s);
            y = assign(B[A + 2], 1);
            A+= 3;
          } else if (B[A + 3] === '/' && B[A + 1] === ' ') { // Check for a complex fraction "123 1/2"
            v = assign(B[A], s);
            w = assign(B[A + 2], s);
            y = assign(B[A + 4], 1);
            A+= 5;
          }

          if (B.length <= A) { // Check for more tokens on the stack
            d = y * z;
            s = /* void */
                    n = x + d * v + z * w;
            break;
          }

          /* Fall through on error */
        }
        default:
          throwInvalidParam();
      }

    if (d === 0) {
      throw new DivisionByZero();
    }

    P["s"] = s < 0 ? -1 : 1;
    P["n"] = Math.abs(n);
    P["d"] = Math.abs(d);
  };

  var modpow = function (b, e, m) {

    for (var r = 1; e > 0; b = (b * b) % m, e >>= 1) {

      if (e & 1) {
        r = (r * b) % m;
      }
    }
    return r;
  };

  var cycleLen = function (n, d) {

    for (; d % 2 === 0;
            d/= 2) {}

    for (; d % 5 === 0;
            d/= 5) {}

    if (d === 1) // Catch non-cyclic numbers
      return 0;

    // If we would like to compute really large numbers quicker, we could make use of Fermat's little theorem:
    // 10^(d-1) % d == 1
    // However, we don't need such large numbers and MAX_CYCLE_LEN should be the capstone,
    // as we want to translate the numbers to strings.

    var rem = 10 % d;

    for (var t = 1; rem !== 1; t++) {
      rem = rem * 10 % d;

      if (t > MAX_CYCLE_LEN)
        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`
    }
    return t;
  };

  var cycleStart = function (n, d, len) {

    var rem1 = 1;
    var rem2 = modpow(10, len, d);

    for (var t = 0; t < 300; t++) { // s < ~log10(Number.MAX_VALUE)
      // Solve 10^s == 10^(s+t) (mod d)

      if (rem1 === rem2)
        return t;

      rem1 = rem1 * 10 % d;
      rem2 = rem2 * 10 % d;
    }
    return 0;
  };

  var gcd = function (a, b) {

    if (!a) return b;
    if (!b) return a;

    while (1) {
      a%= b;
      if (!a) return b;
      b%= a;
      if (!b) return a;
    }
  };

  /**
   * Module constructor
   *
   * @constructor
   * @param {number|Fraction} a
   * @param {number=} b
   */
  function Fraction(a, b) {

    if (!(this instanceof Fraction)) {
      return new Fraction(a, b);
    }

    parse(a, b);

    if (Fraction['REDUCE']) {
      a = gcd(P["d"], P["n"]); // Abuse a
    } else {
      a = 1;
    }

    this["s"] = P["s"];
    this["n"] = P["n"] / a;
    this["d"] = P["d"] / a;
  }

  /**
   * Boolean global variable to be able to disable automatic reduction of the fraction
   *
   */
  Fraction['REDUCE'] = 1;

  Fraction.prototype = {

    "s": 1,
    "n": 0,
    "d": 1,

    /**
     * Calculates the absolute value
     *
     * Ex: new Fraction(-4).abs() => 4
     **/
    "abs": function () {

      return new Fraction(this["n"], this["d"]);
    },

    /**
     * Inverts the sign of the current fraction
     *
     * Ex: new Fraction(-4).neg() => 4
     **/
    "neg": function () {

      return new Fraction(-this["s"] * this["n"], this["d"]);
    },

    /**
     * Adds two rational numbers
     *
     * Ex: new Fraction({n: 2, d: 3}).add("14.9") => 467 / 30
     **/
    "add": function (a, b) {

      parse(a, b);
      return new Fraction(
              this["s"] * this["n"] * P["d"] + P["s"] * this["d"] * P["n"],
              this["d"] * P["d"]
              );
    },

    /**
     * Subtracts two rational numbers
     *
     * Ex: new Fraction({n: 2, d: 3}).add("14.9") => -427 / 30
     **/
    "sub": function (a, b) {

      parse(a, b);
      return new Fraction(
              this["s"] * this["n"] * P["d"] - P["s"] * this["d"] * P["n"],
              this["d"] * P["d"]
              );
    },

    /**
     * Multiplies two rational numbers
     *
     * Ex: new Fraction("-17.(345)").mul(3) => 5776 / 111
     **/
    "mul": function (a, b) {

      parse(a, b);
      return new Fraction(
              this["s"] * P["s"] * this["n"] * P["n"],
              this["d"] * P["d"]
              );
    },

    /**
     * Divides two rational numbers
     *
     * Ex: new Fraction("-17.(345)").inverse().div(3)
     **/
    "div": function (a, b) {

      parse(a, b);
      return new Fraction(
              this["s"] * P["s"] * this["n"] * P["d"],
              this["d"] * P["n"]
              );
    },

    /**
     * Clones the actual object
     *
     * Ex: new Fraction("-17.(345)").clone()
     **/
    "clone": function () {
      return new Fraction(this);
    },

    /**
     * Calculates the modulo of two rational numbers - a more precise fmod
     *
     * Ex: new Fraction('4.(3)').mod([7, 8]) => (13/3) % (7/8) = (5/6)
     **/
    "mod": function (a, b) {

      if (isNaN(this['n']) || isNaN(this['d'])) {
        return new Fraction(NaN);
      }

      if (a === undefined) {
        return new Fraction(this["s"] * this["n"] % this["d"], 1);
      }

      parse(a, b);
      if (0 === P["n"] && 0 === this["d"]) {
        Fraction(0, 0); // Throw DivisionByZero
      }

      /*
       * First silly attempt, kinda slow
       *
       return that["sub"]({
       "n": num["n"] * Math.floor((this.n / this.d) / (num.n / num.d)),
       "d": num["d"],
       "s": this["s"]
       });*/

      /*
       * New attempt: a1 / b1 = a2 / b2 * q + r
       * => b2 * a1 = a2 * b1 * q + b1 * b2 * r
       * => (b2 * a1 % a2 * b1) / (b1 * b2)
       */
      return new Fraction(
              (this["s"] * P["d"] * this["n"]) % (P["n"] * this["d"]),
              P["d"] * this["d"]
              );
    },

    /**
     * Calculates the fractional gcd of two rational numbers
     *
     * Ex: new Fraction(5,8).gcd(3,7) => 1/56
     */
    "gcd": function (a, b) {

      parse(a, b);

      // gcd(a / b, c / d) = gcd(a, c) / lcm(b, d)

      return new Fraction(gcd(P["n"], this["n"]), P["d"] * this["d"] / gcd(P["d"], this["d"]));
    },

    /**
     * Calculates the fractional lcm of two rational numbers
     *
     * Ex: new Fraction(5,8).lcm(3,7) => 15
     */
    "lcm": function (a, b) {

      parse(a, b);

      // lcm(a / b, c / d) = lcm(a, c) / gcd(b, d)

      if (P["n"] === 0 && this["n"] === 0) {
        return new Fraction;
      }
      return new Fraction(P["n"] * this["n"] / gcd(P["n"], this["n"]), gcd(P["d"], this["d"]));
    },

    /**
     * Calculates the ceil of a rational number
     *
     * Ex: new Fraction('4.(3)').ceil() => (5 / 1)
     **/
    "ceil": function (places) {

      places = Math.pow(10, places || 0);

      if (isNaN(this["n"]) || isNaN(this["d"])) {
        return new Fraction(NaN);
      }
      return new Fraction(Math.ceil(places * this["s"] * this["n"] / this["d"]), places);
    },

    /**
     * Calculates the floor of a rational number
     *
     * Ex: new Fraction('4.(3)').floor() => (4 / 1)
     **/
    "floor": function (places) {

      places = Math.pow(10, places || 0);

      if (isNaN(this["n"]) || isNaN(this["d"])) {
        return new Fraction(NaN);
      }
      return new Fraction(Math.floor(places * this["s"] * this["n"] / this["d"]), places);
    },

    /**
     * Rounds a rational numbers
     *
     * Ex: new Fraction('4.(3)').round() => (4 / 1)
     **/
    "round": function (places) {

      places = Math.pow(10, places || 0);

      if (isNaN(this["n"]) || isNaN(this["d"])) {
        return new Fraction(NaN);
      }
      return new Fraction(Math.round(places * this["s"] * this["n"] / this["d"]), places);
    },

    /**
     * Gets the inverse of the fraction, means numerator and denumerator are exchanged
     *
     * Ex: new Fraction([-3, 4]).inverse() => -4 / 3
     **/
    "inverse": function () {

      return new Fraction(this["s"] * this["d"], this["n"]);
    },

    /**
     * Calculates the fraction to some integer exponent
     *
     * Ex: new Fraction(-1,2).pow(-3) => -8
     */
    "pow": function (m) {

      if (m < 0) {
        return new Fraction(Math.pow(this['s'] * this["d"], -m), Math.pow(this["n"], -m));
      } else {
        return new Fraction(Math.pow(this['s'] * this["n"], m), Math.pow(this["d"], m));
      }
    },

    /**
     * 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);
    },

    /**
     * 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() => "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 = [];

      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 () {

      var g;
      var N = this["n"];
      var D = this["d"];

      if (isNaN(N) || isNaN(D)) {
        return "NaN";
      }

      if (!Fraction['REDUCE']) {
        g = gcd(N, D);
        N/= g;
        D/= g;
      }

      var dec = 15; // 15 = decimal places when no repitation

      var cycLen = cycleLen(N, D); // Cycle length
      var cycOff = cycleStart(N, D, cycLen); // Cycle start

      var str = this['s'] === -1 ? "-" : "";

      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") {
    module["exports"] = Fraction;
  } else {
    root['Fraction'] = Fraction;
  }

})(this);