/**
|
* big-number.js -> Arithmetic operations on big integers
|
* Pure javascript implementation, no external libraries needed
|
* Copyright(c) 2012-2018 Alex Bardas <alex.bardas@gmail.com>
|
* MIT Licensed
|
* It supports the following operations:
|
* addition, subtraction, multiplication, division, power, absolute value
|
* It works with both positive and negative integers
|
*/
|
|
!(function() {
|
'use strict';
|
|
// Helper function which tests if a given character is a digit
|
var testDigit = function(digit) {
|
return (/^\d$/.test(digit));
|
};
|
|
// Helper function which returns the absolute value of a given number
|
var abs = function(number) {
|
var bigNumber;
|
if (typeof number === 'undefined') {
|
return;
|
}
|
bigNumber = BigNumber(number);
|
bigNumber.sign = 1;
|
return bigNumber;
|
};
|
|
// Check if argument is valid array
|
var isArray = function(arg) {
|
return Object.prototype.toString.call(arg) === '[object Array]';
|
};
|
|
var errors = {
|
'invalid': 'Invalid Number',
|
'division by zero': 'Invalid Number - Division By Zero'
|
};
|
|
// Constructor function which creates a new BigNumber object
|
// from an integer, a string, an array or other BigNumber object
|
function BigNumber(initialNumber) {
|
var index;
|
|
if (!(this instanceof BigNumber)) {
|
return new BigNumber(initialNumber);
|
}
|
|
this.number = [];
|
this.sign = 1;
|
this.rest = 0;
|
|
if (!initialNumber) {
|
this.number = [0];
|
return;
|
}
|
|
// The initial number can be an array or object
|
// e.g. array : [3,2,1], ['+',3,2,1], ['-',3,2,1]
|
// number : 312
|
// string : '321', '+321', -321'
|
// BigNumber : BigNumber(321)
|
// Every character except the first must be a digit
|
|
if (isArray(initialNumber)) {
|
if (initialNumber.length && initialNumber[0] === '-' || initialNumber[0] === '+') {
|
this.sign = initialNumber[0] === '+' ? 1 : -1;
|
initialNumber.shift(0);
|
}
|
for (index = initialNumber.length - 1; index >= 0; index--) {
|
if (!this.addDigit(initialNumber[index]))
|
return;
|
}
|
} else {
|
initialNumber = initialNumber.toString();
|
if (initialNumber.charAt(0) === '-' || initialNumber.charAt(0) === '+') {
|
this.sign = initialNumber.charAt(0) === '+' ? 1 : -1;
|
initialNumber = initialNumber.substring(1);
|
}
|
|
for (index = initialNumber.length - 1; index >= 0; index--) {
|
if (!this.addDigit(parseInt(initialNumber.charAt(index), 10))) {
|
return;
|
}
|
}
|
}
|
}
|
|
BigNumber.prototype.addDigit = function(digit) {
|
if (testDigit(digit)) {
|
this.number.push(digit);
|
} else {
|
this.number = errors['invalid'];
|
return false;
|
}
|
|
return this;
|
};
|
|
// returns:
|
// 0 if this.number === number
|
// -1 if this.number < number
|
// 1 if this.number > number
|
BigNumber.prototype._compare = function(number) {
|
// if the function is called with no arguments then return 0
|
var bigNumber;
|
var index;
|
if (typeof number === 'undefined') {
|
return 0;
|
}
|
|
bigNumber = BigNumber(number);
|
|
// If the numbers have different signs, then the positive
|
// number is greater
|
if (this.sign !== bigNumber.sign) {
|
return this.sign;
|
}
|
|
// Else, check the length
|
if (this.number.length > bigNumber.number.length) {
|
return this.sign;
|
} else if (this.number.length < bigNumber.number.length) {
|
return this.sign * (-1);
|
}
|
|
// If they have similar length, compare the numbers
|
// digit by digit
|
for (index = this.number.length - 1; index >= 0; index--) {
|
if (this.number[index] > bigNumber.number[index]) {
|
return this.sign;
|
} else if (this.number[index] < bigNumber.number[index]) {
|
return this.sign * (-1);
|
}
|
}
|
|
return 0;
|
};
|
|
// Greater than
|
BigNumber.prototype.gt = function(number) {
|
return this._compare(number) > 0;
|
};
|
|
// Greater than or equal
|
BigNumber.prototype.gte = function(number) {
|
return this._compare(number) >= 0;
|
};
|
|
// this.number equals n
|
BigNumber.prototype.equals = function(number) {
|
return this._compare(number) === 0;
|
};
|
|
// Less than or equal
|
BigNumber.prototype.lte = function(number) {
|
return this._compare(number) <= 0;
|
};
|
|
// Less than
|
BigNumber.prototype.lt = function(number) {
|
return this._compare(number) < 0;
|
};
|
|
// Addition
|
BigNumber.prototype.add = function(number) {
|
var bigNumber;
|
if (typeof number === 'undefined') {
|
return this;
|
}
|
bigNumber = BigNumber(number);
|
|
if (this.sign !== bigNumber.sign) {
|
if (this.sign > 0) {
|
bigNumber.sign = 1;
|
return this.minus(bigNumber);
|
}
|
else {
|
this.sign = 1;
|
return bigNumber.minus(this);
|
}
|
}
|
|
this.number = BigNumber._add(this, bigNumber);
|
return this;
|
};
|
|
// Subtraction
|
BigNumber.prototype.subtract = function(number) {
|
var bigNumber;
|
if (typeof number === 'undefined') {
|
return this;
|
}
|
bigNumber = BigNumber(number);
|
|
if (this.sign !== bigNumber.sign) {
|
this.number = BigNumber._add(this, bigNumber);
|
return this;
|
}
|
|
// If current number is lesser than the given bigNumber, the result will be negative
|
this.sign = (this.lt(bigNumber)) ? -1 : 1;
|
this.number = (abs(this).lt(abs(bigNumber)))
|
? BigNumber._subtract(bigNumber, this)
|
: BigNumber._subtract(this, bigNumber);
|
|
return this;
|
};
|
|
// adds two positive BigNumbers
|
BigNumber._add = function(a, b) {
|
var index;
|
var remainder = 0;
|
var length = Math.max(a.number.length, b.number.length);
|
|
for (index = 0; index < length || remainder > 0; index++) {
|
a.number[index] = (remainder += (a.number[index] || 0) + (b.number[index] || 0)) % 10;
|
remainder = Math.floor(remainder / 10);
|
}
|
|
return a.number;
|
};
|
|
// a - b
|
// a and b are 2 positive BigNumbers and a > b
|
BigNumber._subtract = function(a, b) {
|
var index;
|
var remainder = 0;
|
var length = a.number.length;
|
|
for (index = 0; index < length; index++) {
|
a.number[index] -= (b.number[index] || 0) + remainder;
|
a.number[index] += (remainder = (a.number[index] < 0) ? 1 : 0) * 10;
|
}
|
// Count the zeroes which will be removed
|
index = 0;
|
length = a.number.length - 1;
|
while (a.number[length - index] === 0 && length - index > 0) {
|
index++;
|
}
|
if (index > 0) {
|
a.number.splice(-index);
|
}
|
return a.number;
|
};
|
|
// this.number * number
|
BigNumber.prototype.multiply = function(number) {
|
if (typeof number === 'undefined') {
|
return this;
|
}
|
var bigNumber = BigNumber(number);
|
var index;
|
var givenNumberIndex;
|
var remainder = 0;
|
var result = [];
|
|
if (this.isZero() || bigNumber.isZero()) {
|
return BigNumber(0);
|
}
|
|
this.sign *= bigNumber.sign;
|
|
// multiply the numbers
|
for (index = 0; index < this.number.length; index++) {
|
for (remainder = 0, givenNumberIndex = 0; givenNumberIndex < bigNumber.number.length || remainder > 0; givenNumberIndex++) {
|
result[index + givenNumberIndex] = (remainder += (result[index + givenNumberIndex] || 0) + this.number[index] * (bigNumber.number[givenNumberIndex] || 0)) % 10;
|
remainder = Math.floor(remainder / 10);
|
}
|
}
|
|
this.number = result;
|
return this;
|
};
|
|
// this.number / number
|
BigNumber.prototype.divide = function(number) {
|
if (typeof number === 'undefined') {
|
return this;
|
}
|
|
var bigNumber = BigNumber(number);
|
var index;
|
var length;
|
var result = [];
|
var rest = BigNumber(0);
|
|
// test if one of the numbers is zero
|
if (bigNumber.isZero()) {
|
this.number = errors['division by zero'];
|
return this;
|
} else if (this.isZero()) {
|
return BigNumber(0);
|
}
|
|
this.sign *= bigNumber.sign;
|
bigNumber.sign = 1;
|
|
// Skip division by 1
|
if (bigNumber.number.length === 1 && bigNumber.number[0] === 1) {
|
this.rest = BigNumber(0);
|
return this;
|
}
|
|
for (index = this.number.length - 1; index >= 0; index--) {
|
rest.multiply(10);
|
rest.number[0] = this.number[index];
|
result[index] = 0;
|
while (bigNumber.lte(rest)) {
|
result[index]++;
|
rest.subtract(bigNumber);
|
}
|
}
|
|
index = 0;
|
length = result.length - 1;
|
while (result[length - index] === 0 && length - index > 0) {
|
index++;
|
}
|
if (index > 0) {
|
result.splice(-index);
|
}
|
|
this.rest = rest;
|
this.number = result;
|
return this;
|
};
|
|
// this.number % number
|
BigNumber.prototype.mod = function(number) {
|
return this.divide(number).rest;
|
};
|
|
BigNumber.prototype.power = function(number) {
|
if (typeof number === 'undefined')
|
return;
|
var bigNumber;
|
// Convert the argument to a number
|
number = +number;
|
if (number === 0) {
|
return BigNumber(1);
|
}
|
if (number === 1) {
|
return this;
|
}
|
|
bigNumber = BigNumber(this);
|
|
this.number = [1];
|
while (number > 0) {
|
if (number % 2 === 1) {
|
this.multiply(bigNumber);
|
number--;
|
continue;
|
}
|
bigNumber.multiply(bigNumber);
|
number = Math.floor(number / 2);
|
}
|
|
return this;
|
};
|
|
// |this.number|
|
BigNumber.prototype.abs = function() {
|
this.sign = 1;
|
return this;
|
};
|
|
// Check if this.number is equal to 0
|
BigNumber.prototype.isZero = function() {
|
var index;
|
for (index = 0; index < this.number.length; index++) {
|
if (this.number[index] !== 0) {
|
return false;
|
}
|
}
|
|
return true;
|
};
|
|
// this.number.toString()
|
BigNumber.prototype.toString = function() {
|
var index;
|
var str = '';
|
if (typeof this.number === 'string') {
|
return this.number;
|
}
|
|
for (index = this.number.length - 1; index >= 0; index--) {
|
str += this.number[index];
|
}
|
|
return (this.sign > 0) ? str : ('-' + str);
|
};
|
|
// Use shorcuts for functions names
|
BigNumber.prototype.plus = BigNumber.prototype.add;
|
BigNumber.prototype.minus = BigNumber.prototype.subtract;
|
BigNumber.prototype.div = BigNumber.prototype.divide;
|
BigNumber.prototype.mult = BigNumber.prototype.multiply;
|
BigNumber.prototype.pow = BigNumber.prototype.power;
|
BigNumber.prototype.val = BigNumber.prototype.toString;
|
|
// CommonJS
|
if (typeof exports === 'object' && typeof module !== 'undefined') {
|
module.exports = BigNumber;
|
} else if (typeof window !== 'undefined') {
|
window.BigNumber = BigNumber;
|
}
|
})();
|
