VexFlow - Copyright (c) Mohit Muthanna 2010.
Fraction class that represents a rational number
@author zz85 @author incompleteopus (modifications)
/* eslint-disable no-underscore-dangle */
import { Vex } from './vex';
export class Fraction {
/**
* GCD: Find greatest common divisor using Euclidean algorithm
*/
static GCD(a, b) {
if (typeof a !== 'number' || typeof b !== 'number') {
throw new Vex.RERR('BadArgument', `Invalid numbers: ${a}, ${b}`);
}
let t;
while (b !== 0) {
t = b;
b = a % b;
a = t;
}
return a;
}
/**
* LCM: Lowest common multiple
*/
static LCM(a, b) {
return ((a * b) / Fraction.GCD(a, b));
}
/**
* LCMM: Lowest common multiple for more than two numbers
*/
static LCMM(args) {
if (args.length === 0) {
return 0;
} else if (args.length === 1) {
return args[0];
} else if (args.length === 2) {
return Fraction.LCM(args[0], args[1]);
} else {
const arg0 = args[0];
args.shift();
return Fraction.LCM(arg0, Fraction.LCMM(args));
}
}
constructor(numerator, denominator) {
this.set(numerator, denominator);
}
set(numerator, denominator) {
this.numerator = numerator === undefined ? 1 : numerator;
this.denominator = denominator === undefined ? 1 : denominator;
return this;
}
value() {
return this.numerator / this.denominator;
}
simplify() {
let u = this.numerator;
let d = this.denominator;
const gcd = Fraction.GCD(u, d);
u /= gcd;
d /= gcd;
if (d < 0) {
d = -d;
u = -u;
}
return this.set(u, d);
}
add(param1, param2) {
let otherNumerator;
let otherDenominator;
if (param1 instanceof Fraction) {
otherNumerator = param1.numerator;
otherDenominator = param1.denominator;
} else {
if (param1 !== undefined) {
otherNumerator = param1;
} else {
otherNumerator = 0;
}
if (param2 !== undefined) {
otherDenominator = param2;
} else {
otherDenominator = 1;
}
}
const lcm = Fraction.LCM(this.denominator, otherDenominator);
const a = lcm / this.denominator;
const b = lcm / otherDenominator;
const u = this.numerator * a + otherNumerator * b;
return this.set(u, lcm);
}
subtract(param1, param2) {
let otherNumerator;
let otherDenominator;
if (param1 instanceof Fraction) {
otherNumerator = param1.numerator;
otherDenominator = param1.denominator;
} else {
if (param1 !== undefined) {
otherNumerator = param1;
} else {
otherNumerator = 0;
}
if (param2 !== undefined) {
otherDenominator = param2;
} else {
otherDenominator = 1;
}
}
const lcm = Fraction.LCM(this.denominator, otherDenominator);
const a = lcm / this.denominator;
const b = lcm / otherDenominator;
const u = this.numerator * a - otherNumerator * b;
return this.set(u, lcm);
}
multiply(param1, param2) {
let otherNumerator;
let otherDenominator;
if (param1 instanceof Fraction) {
otherNumerator = param1.numerator;
otherDenominator = param1.denominator;
} else {
if (param1 !== undefined) {
otherNumerator = param1;
} else {
otherNumerator = 1;
}
if (param2 !== undefined) {
otherDenominator = param2;
} else {
otherDenominator = 1;
}
}
return this.set(this.numerator * otherNumerator, this.denominator * otherDenominator);
}
divide(param1, param2) {
let otherNumerator;
let otherDenominator;
if (param1 instanceof Fraction) {
otherNumerator = param1.numerator;
otherDenominator = param1.denominator;
} else {
if (param1 !== undefined) {
otherNumerator = param1;
} else {
otherNumerator = 1;
}
if (param2 !== undefined) {
otherDenominator = param2;
} else {
otherDenominator = 1;
}
}
return this.set(this.numerator * otherDenominator, this.denominator * otherNumerator);
}Simplifies both sides and checks if they are equal.
equals(compare) {
const a = Fraction.__compareA.copy(compare).simplify();
const b = Fraction.__compareB.copy(this).simplify();
return (a.numerator === b.numerator) && (a.denominator === b.denominator);
}Greater than operator.
greaterThan(compare) {
const a = Fraction.__compareB.copy(this);
a.subtract(compare);
return (a.numerator > 0);
}Greater than or equals operator.
greaterThanEquals(compare) {
const a = Fraction.__compareB.copy(this);
a.subtract(compare);
return (a.numerator >= 0);
}Less than operator.
lessThan(compare) {
return !(this.greaterThanEquals(compare));
}Less than or equals operator.
lessThanEquals(compare) {
return !(this.greaterThan(compare));
}Creates a new copy with this current values.
clone() {
return new Fraction(this.numerator, this.denominator);
}Copies value of another Fraction into itself.
copy(copy) {
return this.set(copy.numerator, copy.denominator);
}Returns the integer component eg. (4/2) == 2
quotient() {
return Math.floor(this.numerator / this.denominator);
}Returns the fraction component when reduced to a mixed number
fraction() {
return this.numerator % this.denominator;
}Returns the absolute value
abs() {
this.denominator = Math.abs(this.denominator);
this.numerator = Math.abs(this.numerator);
return this;
}Returns a raw string representation
toString() {
return this.numerator + '/' + this.denominator;
}Returns a simplified string respresentation
toSimplifiedString() {
return Fraction.__tmp.copy(this).simplify().toString();
}Returns string representation in mixed form
toMixedString() {
let s = '';
const q = this.quotient();
const f = Fraction.__tmp.copy(this);
if (q < 0) {
f.abs().fraction();
} else {
f.fraction();
}
if (q !== 0) {
s += q;
if (f.numerator !== 0) {
s += ' ' + f.toSimplifiedString();
}
} else {
if (f.numerator === 0) {
s = '0';
} else {
s = f.toSimplifiedString();
}
}
return s;
}Parses a fraction string
parse(str) {
const i = str.split('/');
const n = parseInt(i[0], 10);
const d = (i[1]) ? parseInt(i[1], 10) : 1;
return this.set(n, d);
}
}Temporary cached objects
Fraction.__compareA = new Fraction();
Fraction.__compareB = new Fraction();
Fraction.__tmp = new Fraction();