bigfraction.js

/**
 * @license Fraction.js v4.0.12 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:
 *
 * let f = new Fraction("9.4'31'");
 * f.mul([-4, 3]).div(4.9);
 *
 */

(function(root) {

  "use strict";
  
  // Set Identity function to downgrade BigInt to Number if needed
  if (!BigInt) BigInt = function(n) {return n;};
  
  const C_ONE = BigInt(1);
  const C_ZERO = BigInt(0);
  const C_TEN = BigInt(10);
  const C_TWO = BigInt(2);
  const C_FIVE = BigInt(5);

  // 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
  //const MAX_CYCLE_LEN = BigInt(2000);

  // Parsed data to avoid calling "new" all the time
  const P = {
    "s": C_ONE,
    "n": C_ZERO,
    "d": C_ONE
  };

  function createError(name) {

    function errorConstructor() {
      const temp = Error.apply(this, arguments);
      temp['name'] = this['name'] = name;
      this['stack'] = temp['stack'];
      this['message'] = temp['message'];
    }

    /**
     * Error constructor
     *
     * @constructor
     */
    function IntermediateInheritor() {}
    IntermediateInheritor.prototype = Error.prototype;
    errorConstructor.prototype = new IntermediateInheritor();

    return errorConstructor;
  }

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

  function assign(n, s) {
    
    try {
      n = BigInt(n);
    } catch (e) {
      throw new InvalidParameter();
    }

    return n * s;
  }

  const parse = function(p1, p2) {

    let n = C_ZERO, d = C_ONE, s = C_ONE;

    if (p1 === undefined || p1 === null) {
      /* void */
    } else if (p2 !== undefined) {
      n = BigInt(p1);
      d = BigInt(p2);
      s = n * d;
    } else if (typeof p1 === "object") {
      if ("d" in p1 && "n" in p1) {
        n = BigInt(p1["n"]);
        d = BigInt(p1["d"]);
        if ("s" in p1)
          n *= BigInt(p1["s"]);
      } else if (0 in p1) {
        n = BigInt(p1[0]);
        if (1 in p1)
          d = BigInt(p1[1]);
      } else if (p1 instanceof BigInt) {
        n = BigInt(p1);
      } else {
        throw new InvalidParameter();
      }
      s = n * d;
    } else if (typeof p1 === "number") {
      
      if (isNaN(p1)) {
        throw new InvalidParameter();
      }

      if (p1 < 0) {
        s = -C_ONE;
        p1 = -p1;
      }

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

        let z = 1;

        let A = 0, B = 1;
        let C = 1, D = 1;

        let N = 10000000;

        if (p1 >= 1) {
          z = 10 ** Math.floor(1 + Math.log10(p1));
          p1 /= z;
        }


        // Using Farey Sequences
        
        while (B <= N && D <= N) {
          let 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 = BigInt(n) * BigInt(z);
        d = BigInt(d);

      } else if (isNaN(p1)) {
        d = n = NaN;
      }
      
    } else if (typeof p1 === "string") {
      
      let ndx = 0;

      let v = C_ZERO, w = C_ZERO, x = C_ZERO, y = C_ONE, z = C_ONE;

      let match = p1.match(/\d+|./g);

      if (match === null)
       throw new InvalidParameter()

      if (match[ndx] === '-') {// Check for minus sign at the beginning
        s = -C_ONE;
        ndx++;
      } else if (match[ndx] === '+') {// Check for plus sign at the beginning
        ndx++;
      }

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

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

        // Check for decimal places
        if (ndx + 1 === match.length || match[ndx + 1] === '(' && match[ndx + 3] === ')' || match[ndx + 1] === "'" && match[ndx + 3] === "'") {
          w = assign(match[ndx], s);
          y = C_TEN ** BigInt(match[ndx].length);
          ndx++;
        }

        // Check for repeating places
        if (match[ndx] === '(' && match[ndx + 2] === ')' || match[ndx] === "'" && match[ndx + 2] === "'") {
          x = assign(match[ndx + 1], s);
          z = C_TEN ** BigInt(match[ndx + 1].length) - C_ONE;
          ndx += 3;
        }

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

      if (match.length <= ndx) { // Check for more tokens on the stack
        d = y * z;
        s = /* void */
        n = x + d * v + z * w;
      } else {
        throw new InvalidParameter();
      }

    } else {
      throw new InvalidParameter();
    }

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

    P["s"] = s < C_ZERO ? -C_ONE : C_ONE;
    P["n"] = n < C_ZERO ? -n : n;
    P["d"] = d < C_ZERO ? -d : d;

  };

  function modpow(b, e, m) {

    let r = C_ONE;
    for (; e > C_ZERO; b = (b * b) % m, e >>= C_ONE) {

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

  function cycleLen(n, d) {

    for (; d % C_TWO === C_ZERO;
            d /= C_TWO) {
    }

    for (; d % C_FIVE === C_ZERO;
            d /= C_FIVE) {
    }

    if (d === C_ONE) // Catch non-cyclic numbers
      return C_ZERO;

    // 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.

    let rem = C_TEN % d;
    let t = C_ONE;

    for (; rem !== C_ONE; t++) {
      rem = rem * C_TEN % d;

      //if (t > MAX_CYCLE_LEN)
       // return C_ZERO; // 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;
  }
  
  function cycleStart(n, d, len) {

    let rem1 = C_ONE;
    let rem2 = modpow(C_TEN, len, d);

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

      if (rem1 === rem2)
        return BigInt(t);

      rem1 = rem1 * C_TEN % d;
      rem2 = rem2 * C_TEN % 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;
    }
  }

  /**
   * 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);

    a = gcd(P["d"], P["n"]); // Abuse a

    this["s"] = P["s"];
    this["n"] = P["n"] / a | C_ZERO;
    this["d"] = P["d"] / a | C_ZERO;
  }
  
  Fraction.prototype = {

    "s": C_ONE,
    "n": C_ZERO,
    "d": C_ONE,

    /**
     * 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 (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"]) * gcd(P["d"], this["d"]), 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"] === C_ZERO && this["n"] === C_ZERO) {
        return new Fraction;
      }
      return new Fraction(P["n"] * this["n"], gcd(P["n"], this["n"]) * gcd(P["d"], this["d"]));
    },
  
    /**
     * 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((this['s'] * this["d"]) ** BigInt(-m), this["n"] ** BigInt(-m));
      } else {
        return new Fraction((this['s'] * this["n"]) ** BigInt(+m), this["d"] ** BigInt(+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);
      let t = (this["s"] * this["n"] * P["d"] - P["s"] * P["n"] * this["d"]);
      
      return (C_ZERO < t) - (t < C_ZERO);
    },

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

      places = 10 ** Number(places || 0);

      return new Fraction(Math.ceil(places * Number(this["s"] * this["n"]) / Number(this["d"])), places);
    },

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

      places = 10 ** Number(places || 0);

      return new Fraction(Math.floor(places * Number(this["s"] * this["n"]) / Number(this["d"])), places);
    },

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

      places = 10 ** Number(places || 0);

      return new Fraction(Math.round(places * Number(this["s"] * this["n"]) / Number(this["d"])), places);
    },

    /**
     * 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() {
      // Best we can do so far
      return Number(this["s"] * this["n"]) / Number(this["d"]);
    },

    /**
     * Creates a string representation of a fraction with all digits
     *
     * Ex: new Fraction("100.'91823'").toString() => "100.(91823)"
     **/
    'toString': function(dec = false) {

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

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

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

      let str = this['s'] < C_ZERO ? "-" : "";

      // Append integer part
      str += N / D | C_ZERO;

      N %= D;
      N *= C_TEN;

      if (N)
        str += ".";

      if (cycLen && !dec) {

        for (let i = cycOff; i--; ) {
          str += N / D | C_ZERO;
          N %= D;
          N *= C_TEN;
        }
        str += "(";
        for (let i = cycLen; i--; ) {
          str += N / D | C_ZERO;
          N %= D;
          N *= C_TEN;
        }
        str += ")";
      } else {
        while (N) {
	  if (dec && str.length > dec) return
          str += N / D | C_ZERO;
          N %= D;
          N *= C_TEN;
        }
      }
      return str;
    },
    
    /**
     * Returns a string-fraction representation of a Fraction object
     *
     * Ex: new Fraction("1.'3'").toFraction() => "4 1/3"
     **/
    'toFraction': function(excludeWhole) {

      let n = this["n"];
      let d = this["d"];
      let str = this['s'] < C_ZERO ? "-" : "";

      if (d === C_ONE) {
        str += n;
      } else {
        let whole = n / d | C_ZERO;
        if (excludeWhole && whole > C_ZERO) {
          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) {

      let n = this["n"];
      let d = this["d"];
      let str = this['s'] < C_ZERO ? "-" : "";

      if (d === C_ONE) {
        str += n;
      } else {
        let whole = n / d | C_ZERO;
        if (excludeWhole && whole > C_ZERO) {
          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() {

      let a = this['n'];
      let b = this['d'];
      let res = [];

      do {
        res.push(a / b | C_ZERO);
        let t = a % b;
        a = b;
        b = t;
      } while (a !== C_ONE);

      return res;
    },
    
    "simplify": function(eps) {

      // First naive implementation, needs improvement

      let cont = this['abs']()['toContinued']();

      eps = eps || 0.001;

      function rec(a) {
        if (a.length === 1)
          return new Fraction(a[0]);
        return rec(a.slice(1))['inverse']()['add'](a[0]);
      }

      for (let i = 0; i < cont.length; i++) {
        let tmp = rec(cont.slice(0, i + 1));
        if (tmp['sub'](this['abs']())['abs']().valueOf() < eps) {
          return tmp['mul'](this['s']);
        }
      }
      return this;
    }
  };
  
  if (typeof define === "function" && define["amd"]) {
    define([], function() {
      return Fraction;
    });
  } else if (typeof exports === "object") {
    Object.defineProperty(exports, "__esModule", {'value': true});
    Fraction['default'] = Fraction;
    Fraction['Fraction'] = Fraction;
    module['exports'] = Fraction;
  } else {
    root['Fraction'] = Fraction;
  }

})(this);