This app provides monitoring and information features for the common freifunk user and the technical stuff of a freifunk community.
Code base is taken from a TUM Practical Course project and added here to see if Freifunk Altdorf can use it.
https://www.freifunk-altdorf.de
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1308 lines
44 KiB
1308 lines
44 KiB
var bigInt = (function (undefined) { |
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"use strict"; |
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|
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var BASE = 1e7, |
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LOG_BASE = 7, |
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MAX_INT = 9007199254740992, |
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MAX_INT_ARR = smallToArray(MAX_INT), |
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LOG_MAX_INT = Math.log(MAX_INT); |
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|
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function Integer(v, radix) { |
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if (typeof v === "undefined") return Integer[0]; |
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if (typeof radix !== "undefined") return +radix === 10 ? parseValue(v) : parseBase(v, radix); |
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return parseValue(v); |
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} |
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|
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function BigInteger(value, sign) { |
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this.value = value; |
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this.sign = sign; |
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this.isSmall = false; |
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} |
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BigInteger.prototype = Object.create(Integer.prototype); |
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|
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function SmallInteger(value) { |
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this.value = value; |
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this.sign = value < 0; |
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this.isSmall = true; |
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} |
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SmallInteger.prototype = Object.create(Integer.prototype); |
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|
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function isPrecise(n) { |
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return -MAX_INT < n && n < MAX_INT; |
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} |
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function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes |
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if (n < 1e7) |
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return [n]; |
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if (n < 1e14) |
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return [n % 1e7, Math.floor(n / 1e7)]; |
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return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)]; |
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} |
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function arrayToSmall(arr) { // If BASE changes this function may need to change |
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trim(arr); |
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var length = arr.length; |
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if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) { |
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switch (length) { |
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case 0: return 0; |
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case 1: return arr[0]; |
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case 2: return arr[0] + arr[1] * BASE; |
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default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE; |
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} |
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} |
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return arr; |
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} |
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|
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function trim(v) { |
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var i = v.length; |
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while (v[--i] === 0); |
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v.length = i + 1; |
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} |
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|
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function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger |
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var x = new Array(length); |
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var i = -1; |
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while (++i < length) { |
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x[i] = 0; |
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} |
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return x; |
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} |
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function truncate(n) { |
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if (n > 0) return Math.floor(n); |
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return Math.ceil(n); |
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} |
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|
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function add(a, b) { // assumes a and b are arrays with a.length >= b.length |
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var l_a = a.length, |
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l_b = b.length, |
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r = new Array(l_a), |
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carry = 0, |
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base = BASE, |
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sum, i; |
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for (i = 0; i < l_b; i++) { |
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sum = a[i] + b[i] + carry; |
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carry = sum >= base ? 1 : 0; |
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r[i] = sum - carry * base; |
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} |
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while (i < l_a) { |
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sum = a[i] + carry; |
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carry = sum === base ? 1 : 0; |
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r[i++] = sum - carry * base; |
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} |
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if (carry > 0) r.push(carry); |
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return r; |
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} |
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|
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function addAny(a, b) { |
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if (a.length >= b.length) return add(a, b); |
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return add(b, a); |
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} |
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|
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function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT |
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var l = a.length, |
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r = new Array(l), |
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base = BASE, |
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sum, i; |
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for (i = 0; i < l; i++) { |
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sum = a[i] - base + carry; |
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carry = Math.floor(sum / base); |
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r[i] = sum - carry * base; |
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carry += 1; |
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} |
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while (carry > 0) { |
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r[i++] = carry % base; |
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carry = Math.floor(carry / base); |
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} |
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return r; |
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} |
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|
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BigInteger.prototype.add = function (v) { |
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var n = parseValue(v); |
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if (this.sign !== n.sign) { |
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return this.subtract(n.negate()); |
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} |
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var a = this.value, b = n.value; |
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if (n.isSmall) { |
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return new BigInteger(addSmall(a, Math.abs(b)), this.sign); |
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} |
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return new BigInteger(addAny(a, b), this.sign); |
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}; |
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BigInteger.prototype.plus = BigInteger.prototype.add; |
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|
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SmallInteger.prototype.add = function (v) { |
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var n = parseValue(v); |
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var a = this.value; |
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if (a < 0 !== n.sign) { |
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return this.subtract(n.negate()); |
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} |
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var b = n.value; |
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if (n.isSmall) { |
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if (isPrecise(a + b)) return new SmallInteger(a + b); |
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b = smallToArray(Math.abs(b)); |
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} |
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return new BigInteger(addSmall(b, Math.abs(a)), a < 0); |
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}; |
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SmallInteger.prototype.plus = SmallInteger.prototype.add; |
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|
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function subtract(a, b) { // assumes a and b are arrays with a >= b |
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var a_l = a.length, |
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b_l = b.length, |
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r = new Array(a_l), |
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borrow = 0, |
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base = BASE, |
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i, difference; |
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for (i = 0; i < b_l; i++) { |
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difference = a[i] - borrow - b[i]; |
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if (difference < 0) { |
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difference += base; |
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borrow = 1; |
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} else borrow = 0; |
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r[i] = difference; |
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} |
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for (i = b_l; i < a_l; i++) { |
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difference = a[i] - borrow; |
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if (difference < 0) difference += base; |
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else { |
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r[i++] = difference; |
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break; |
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} |
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r[i] = difference; |
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} |
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for (; i < a_l; i++) { |
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r[i] = a[i]; |
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} |
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trim(r); |
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return r; |
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} |
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function subtractAny(a, b, sign) { |
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var value; |
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if (compareAbs(a, b) >= 0) { |
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value = subtract(a, b); |
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} else { |
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value = subtract(b, a); |
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sign = !sign; |
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} |
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value = arrayToSmall(value); |
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if (typeof value === "number") { |
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if (sign) value = -value; |
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return new SmallInteger(value); |
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} |
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return new BigInteger(value, sign); |
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} |
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function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT |
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var l = a.length, |
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r = new Array(l), |
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carry = -b, |
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base = BASE, |
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i, difference; |
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for (i = 0; i < l; i++) { |
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difference = a[i] + carry; |
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carry = Math.floor(difference / base); |
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difference %= base; |
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r[i] = difference < 0 ? difference + base : difference; |
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} |
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r = arrayToSmall(r); |
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if (typeof r === "number") { |
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if (sign) r = -r; |
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return new SmallInteger(r); |
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} return new BigInteger(r, sign); |
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} |
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BigInteger.prototype.subtract = function (v) { |
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var n = parseValue(v); |
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if (this.sign !== n.sign) { |
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return this.add(n.negate()); |
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} |
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var a = this.value, b = n.value; |
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if (n.isSmall) |
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return subtractSmall(a, Math.abs(b), this.sign); |
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return subtractAny(a, b, this.sign); |
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}; |
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BigInteger.prototype.minus = BigInteger.prototype.subtract; |
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SmallInteger.prototype.subtract = function (v) { |
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var n = parseValue(v); |
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var a = this.value; |
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if (a < 0 !== n.sign) { |
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return this.add(n.negate()); |
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} |
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var b = n.value; |
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if (n.isSmall) { |
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return new SmallInteger(a - b); |
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} |
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return subtractSmall(b, Math.abs(a), a >= 0); |
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}; |
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SmallInteger.prototype.minus = SmallInteger.prototype.subtract; |
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BigInteger.prototype.negate = function () { |
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return new BigInteger(this.value, !this.sign); |
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}; |
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SmallInteger.prototype.negate = function () { |
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var sign = this.sign; |
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var small = new SmallInteger(-this.value); |
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small.sign = !sign; |
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return small; |
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}; |
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BigInteger.prototype.abs = function () { |
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return new BigInteger(this.value, false); |
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}; |
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SmallInteger.prototype.abs = function () { |
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return new SmallInteger(Math.abs(this.value)); |
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}; |
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function multiplyLong(a, b) { |
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var a_l = a.length, |
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b_l = b.length, |
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l = a_l + b_l, |
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r = createArray(l), |
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base = BASE, |
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product, carry, i, a_i, b_j; |
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for (i = 0; i < a_l; ++i) { |
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a_i = a[i]; |
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for (var j = 0; j < b_l; ++j) { |
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b_j = b[j]; |
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product = a_i * b_j + r[i + j]; |
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carry = Math.floor(product / base); |
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r[i + j] = product - carry * base; |
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r[i + j + 1] += carry; |
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} |
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} |
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trim(r); |
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return r; |
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} |
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function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE |
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var l = a.length, |
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r = new Array(l), |
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base = BASE, |
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carry = 0, |
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product, i; |
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for (i = 0; i < l; i++) { |
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product = a[i] * b + carry; |
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carry = Math.floor(product / base); |
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r[i] = product - carry * base; |
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} |
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while (carry > 0) { |
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r[i++] = carry % base; |
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carry = Math.floor(carry / base); |
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} |
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return r; |
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} |
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function shiftLeft(x, n) { |
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var r = []; |
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while (n-- > 0) r.push(0); |
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return r.concat(x); |
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} |
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function multiplyKaratsuba(x, y) { |
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var n = Math.max(x.length, y.length); |
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if (n <= 30) return multiplyLong(x, y); |
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n = Math.ceil(n / 2); |
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var b = x.slice(n), |
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a = x.slice(0, n), |
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d = y.slice(n), |
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c = y.slice(0, n); |
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var ac = multiplyKaratsuba(a, c), |
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bd = multiplyKaratsuba(b, d), |
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abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d)); |
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var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n)); |
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trim(product); |
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return product; |
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} |
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// The following function is derived from a surface fit of a graph plotting the performance difference |
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// between long multiplication and karatsuba multiplication versus the lengths of the two arrays. |
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function useKaratsuba(l1, l2) { |
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return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0; |
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} |
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BigInteger.prototype.multiply = function (v) { |
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var n = parseValue(v), |
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a = this.value, b = n.value, |
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sign = this.sign !== n.sign, |
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abs; |
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if (n.isSmall) { |
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if (b === 0) return Integer[0]; |
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if (b === 1) return this; |
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if (b === -1) return this.negate(); |
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abs = Math.abs(b); |
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if (abs < BASE) { |
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return new BigInteger(multiplySmall(a, abs), sign); |
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} |
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b = smallToArray(abs); |
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} |
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if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes |
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return new BigInteger(multiplyKaratsuba(a, b), sign); |
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return new BigInteger(multiplyLong(a, b), sign); |
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}; |
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BigInteger.prototype.times = BigInteger.prototype.multiply; |
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function multiplySmallAndArray(a, b, sign) { // a >= 0 |
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if (a < BASE) { |
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return new BigInteger(multiplySmall(b, a), sign); |
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} |
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return new BigInteger(multiplyLong(b, smallToArray(a)), sign); |
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} |
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SmallInteger.prototype._multiplyBySmall = function (a) { |
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if (isPrecise(a.value * this.value)) { |
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return new SmallInteger(a.value * this.value); |
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} |
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return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign); |
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}; |
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BigInteger.prototype._multiplyBySmall = function (a) { |
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if (a.value === 0) return Integer[0]; |
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if (a.value === 1) return this; |
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if (a.value === -1) return this.negate(); |
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return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign); |
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}; |
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SmallInteger.prototype.multiply = function (v) { |
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return parseValue(v)._multiplyBySmall(this); |
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}; |
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SmallInteger.prototype.times = SmallInteger.prototype.multiply; |
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function square(a) { |
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//console.assert(2 * BASE * BASE < MAX_INT); |
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var l = a.length, |
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r = createArray(l + l), |
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base = BASE, |
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product, carry, i, a_i, a_j; |
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for (i = 0; i < l; i++) { |
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a_i = a[i]; |
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carry = 0 - a_i * a_i; |
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for (var j = i; j < l; j++) { |
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a_j = a[j]; |
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product = 2 * (a_i * a_j) + r[i + j] + carry; |
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carry = Math.floor(product / base); |
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r[i + j] = product - carry * base; |
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} |
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r[i + l] = carry; |
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} |
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trim(r); |
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return r; |
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} |
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BigInteger.prototype.square = function () { |
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return new BigInteger(square(this.value), false); |
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}; |
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SmallInteger.prototype.square = function () { |
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var value = this.value * this.value; |
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if (isPrecise(value)) return new SmallInteger(value); |
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return new BigInteger(square(smallToArray(Math.abs(this.value))), false); |
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}; |
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|
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function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes. |
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var a_l = a.length, |
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b_l = b.length, |
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base = BASE, |
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result = createArray(b.length), |
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divisorMostSignificantDigit = b[b_l - 1], |
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// normalization |
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lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)), |
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remainder = multiplySmall(a, lambda), |
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divisor = multiplySmall(b, lambda), |
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quotientDigit, shift, carry, borrow, i, l, q; |
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if (remainder.length <= a_l) remainder.push(0); |
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divisor.push(0); |
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divisorMostSignificantDigit = divisor[b_l - 1]; |
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for (shift = a_l - b_l; shift >= 0; shift--) { |
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quotientDigit = base - 1; |
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if (remainder[shift + b_l] !== divisorMostSignificantDigit) { |
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quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit); |
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} |
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// quotientDigit <= base - 1 |
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carry = 0; |
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borrow = 0; |
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l = divisor.length; |
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for (i = 0; i < l; i++) { |
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carry += quotientDigit * divisor[i]; |
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q = Math.floor(carry / base); |
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borrow += remainder[shift + i] - (carry - q * base); |
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carry = q; |
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if (borrow < 0) { |
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remainder[shift + i] = borrow + base; |
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borrow = -1; |
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} else { |
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remainder[shift + i] = borrow; |
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borrow = 0; |
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} |
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} |
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while (borrow !== 0) { |
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quotientDigit -= 1; |
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carry = 0; |
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for (i = 0; i < l; i++) { |
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carry += remainder[shift + i] - base + divisor[i]; |
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if (carry < 0) { |
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remainder[shift + i] = carry + base; |
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carry = 0; |
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} else { |
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remainder[shift + i] = carry; |
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carry = 1; |
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} |
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} |
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borrow += carry; |
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} |
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result[shift] = quotientDigit; |
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} |
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// denormalization |
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remainder = divModSmall(remainder, lambda)[0]; |
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return [arrayToSmall(result), arrayToSmall(remainder)]; |
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} |
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|
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function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/ |
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// Performs faster than divMod1 on larger input sizes. |
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var a_l = a.length, |
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b_l = b.length, |
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result = [], |
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part = [], |
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base = BASE, |
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guess, xlen, highx, highy, check; |
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while (a_l) { |
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part.unshift(a[--a_l]); |
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trim(part); |
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if (compareAbs(part, b) < 0) { |
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result.push(0); |
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continue; |
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} |
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xlen = part.length; |
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highx = part[xlen - 1] * base + part[xlen - 2]; |
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highy = b[b_l - 1] * base + b[b_l - 2]; |
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if (xlen > b_l) { |
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highx = (highx + 1) * base; |
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} |
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guess = Math.ceil(highx / highy); |
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do { |
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check = multiplySmall(b, guess); |
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if (compareAbs(check, part) <= 0) break; |
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guess--; |
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} while (guess); |
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result.push(guess); |
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part = subtract(part, check); |
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} |
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result.reverse(); |
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return [arrayToSmall(result), arrayToSmall(part)]; |
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} |
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|
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function divModSmall(value, lambda) { |
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var length = value.length, |
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quotient = createArray(length), |
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base = BASE, |
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i, q, remainder, divisor; |
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remainder = 0; |
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for (i = length - 1; i >= 0; --i) { |
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divisor = remainder * base + value[i]; |
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q = truncate(divisor / lambda); |
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remainder = divisor - q * lambda; |
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quotient[i] = q | 0; |
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} |
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return [quotient, remainder | 0]; |
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} |
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|
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function divModAny(self, v) { |
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var value, n = parseValue(v); |
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var a = self.value, b = n.value; |
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var quotient; |
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if (b === 0) throw new Error("Cannot divide by zero"); |
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if (self.isSmall) { |
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if (n.isSmall) { |
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return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)]; |
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} |
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return [Integer[0], self]; |
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} |
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if (n.isSmall) { |
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if (b === 1) return [self, Integer[0]]; |
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if (b == -1) return [self.negate(), Integer[0]]; |
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var abs = Math.abs(b); |
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if (abs < BASE) { |
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value = divModSmall(a, abs); |
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quotient = arrayToSmall(value[0]); |
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var remainder = value[1]; |
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if (self.sign) remainder = -remainder; |
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if (typeof quotient === "number") { |
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if (self.sign !== n.sign) quotient = -quotient; |
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return [new SmallInteger(quotient), new SmallInteger(remainder)]; |
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} |
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return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)]; |
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} |
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b = smallToArray(abs); |
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} |
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var comparison = compareAbs(a, b); |
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if (comparison === -1) return [Integer[0], self]; |
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if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]]; |
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|
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// divMod1 is faster on smaller input sizes |
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if (a.length + b.length <= 200) |
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value = divMod1(a, b); |
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else value = divMod2(a, b); |
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|
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quotient = value[0]; |
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var qSign = self.sign !== n.sign, |
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mod = value[1], |
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mSign = self.sign; |
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if (typeof quotient === "number") { |
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if (qSign) quotient = -quotient; |
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quotient = new SmallInteger(quotient); |
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} else quotient = new BigInteger(quotient, qSign); |
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if (typeof mod === "number") { |
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if (mSign) mod = -mod; |
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mod = new SmallInteger(mod); |
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} else mod = new BigInteger(mod, mSign); |
|
return [quotient, mod]; |
|
} |
|
|
|
BigInteger.prototype.divmod = function (v) { |
|
var result = divModAny(this, v); |
|
return { |
|
quotient: result[0], |
|
remainder: result[1] |
|
}; |
|
}; |
|
SmallInteger.prototype.divmod = BigInteger.prototype.divmod; |
|
|
|
BigInteger.prototype.divide = function (v) { |
|
return divModAny(this, v)[0]; |
|
}; |
|
SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide; |
|
|
|
BigInteger.prototype.mod = function (v) { |
|
return divModAny(this, v)[1]; |
|
}; |
|
SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod; |
|
|
|
BigInteger.prototype.pow = function (v) { |
|
var n = parseValue(v), |
|
a = this.value, |
|
b = n.value, |
|
value, x, y; |
|
if (b === 0) return Integer[1]; |
|
if (a === 0) return Integer[0]; |
|
if (a === 1) return Integer[1]; |
|
if (a === -1) return n.isEven() ? Integer[1] : Integer[-1]; |
|
if (n.sign) { |
|
return Integer[0]; |
|
} |
|
if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large."); |
|
if (this.isSmall) { |
|
if (isPrecise(value = Math.pow(a, b))) |
|
return new SmallInteger(truncate(value)); |
|
} |
|
x = this; |
|
y = Integer[1]; |
|
while (true) { |
|
if (b & 1 === 1) { |
|
y = y.times(x); |
|
--b; |
|
} |
|
if (b === 0) break; |
|
b /= 2; |
|
x = x.square(); |
|
} |
|
return y; |
|
}; |
|
SmallInteger.prototype.pow = BigInteger.prototype.pow; |
|
|
|
BigInteger.prototype.modPow = function (exp, mod) { |
|
exp = parseValue(exp); |
|
mod = parseValue(mod); |
|
if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0"); |
|
var r = Integer[1], |
|
base = this.mod(mod); |
|
while (exp.isPositive()) { |
|
if (base.isZero()) return Integer[0]; |
|
if (exp.isOdd()) r = r.multiply(base).mod(mod); |
|
exp = exp.divide(2); |
|
base = base.square().mod(mod); |
|
} |
|
return r; |
|
}; |
|
SmallInteger.prototype.modPow = BigInteger.prototype.modPow; |
|
|
|
function compareAbs(a, b) { |
|
if (a.length !== b.length) { |
|
return a.length > b.length ? 1 : -1; |
|
} |
|
for (var i = a.length - 1; i >= 0; i--) { |
|
if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1; |
|
} |
|
return 0; |
|
} |
|
|
|
BigInteger.prototype.compareAbs = function (v) { |
|
var n = parseValue(v), |
|
a = this.value, |
|
b = n.value; |
|
if (n.isSmall) return 1; |
|
return compareAbs(a, b); |
|
}; |
|
SmallInteger.prototype.compareAbs = function (v) { |
|
var n = parseValue(v), |
|
a = Math.abs(this.value), |
|
b = n.value; |
|
if (n.isSmall) { |
|
b = Math.abs(b); |
|
return a === b ? 0 : a > b ? 1 : -1; |
|
} |
|
return -1; |
|
}; |
|
|
|
BigInteger.prototype.compare = function (v) { |
|
// See discussion about comparison with Infinity: |
|
// https://github.com/peterolson/BigInteger.js/issues/61 |
|
if (v === Infinity) { |
|
return -1; |
|
} |
|
if (v === -Infinity) { |
|
return 1; |
|
} |
|
|
|
var n = parseValue(v), |
|
a = this.value, |
|
b = n.value; |
|
if (this.sign !== n.sign) { |
|
return n.sign ? 1 : -1; |
|
} |
|
if (n.isSmall) { |
|
return this.sign ? -1 : 1; |
|
} |
|
return compareAbs(a, b) * (this.sign ? -1 : 1); |
|
}; |
|
BigInteger.prototype.compareTo = BigInteger.prototype.compare; |
|
|
|
SmallInteger.prototype.compare = function (v) { |
|
if (v === Infinity) { |
|
return -1; |
|
} |
|
if (v === -Infinity) { |
|
return 1; |
|
} |
|
|
|
var n = parseValue(v), |
|
a = this.value, |
|
b = n.value; |
|
if (n.isSmall) { |
|
return a == b ? 0 : a > b ? 1 : -1; |
|
} |
|
if (a < 0 !== n.sign) { |
|
return a < 0 ? -1 : 1; |
|
} |
|
return a < 0 ? 1 : -1; |
|
}; |
|
SmallInteger.prototype.compareTo = SmallInteger.prototype.compare; |
|
|
|
BigInteger.prototype.equals = function (v) { |
|
return this.compare(v) === 0; |
|
}; |
|
SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals; |
|
|
|
BigInteger.prototype.notEquals = function (v) { |
|
return this.compare(v) !== 0; |
|
}; |
|
SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals; |
|
|
|
BigInteger.prototype.greater = function (v) { |
|
return this.compare(v) > 0; |
|
}; |
|
SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater; |
|
|
|
BigInteger.prototype.lesser = function (v) { |
|
return this.compare(v) < 0; |
|
}; |
|
SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser; |
|
|
|
BigInteger.prototype.greaterOrEquals = function (v) { |
|
return this.compare(v) >= 0; |
|
}; |
|
SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals; |
|
|
|
BigInteger.prototype.lesserOrEquals = function (v) { |
|
return this.compare(v) <= 0; |
|
}; |
|
SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals; |
|
|
|
BigInteger.prototype.isEven = function () { |
|
return (this.value[0] & 1) === 0; |
|
}; |
|
SmallInteger.prototype.isEven = function () { |
|
return (this.value & 1) === 0; |
|
}; |
|
|
|
BigInteger.prototype.isOdd = function () { |
|
return (this.value[0] & 1) === 1; |
|
}; |
|
SmallInteger.prototype.isOdd = function () { |
|
return (this.value & 1) === 1; |
|
}; |
|
|
|
BigInteger.prototype.isPositive = function () { |
|
return !this.sign; |
|
}; |
|
SmallInteger.prototype.isPositive = function () { |
|
return this.value > 0; |
|
}; |
|
|
|
BigInteger.prototype.isNegative = function () { |
|
return this.sign; |
|
}; |
|
SmallInteger.prototype.isNegative = function () { |
|
return this.value < 0; |
|
}; |
|
|
|
BigInteger.prototype.isUnit = function () { |
|
return false; |
|
}; |
|
SmallInteger.prototype.isUnit = function () { |
|
return Math.abs(this.value) === 1; |
|
}; |
|
|
|
BigInteger.prototype.isZero = function () { |
|
return false; |
|
}; |
|
SmallInteger.prototype.isZero = function () { |
|
return this.value === 0; |
|
}; |
|
BigInteger.prototype.isDivisibleBy = function (v) { |
|
var n = parseValue(v); |
|
var value = n.value; |
|
if (value === 0) return false; |
|
if (value === 1) return true; |
|
if (value === 2) return this.isEven(); |
|
return this.mod(n).equals(Integer[0]); |
|
}; |
|
SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy; |
|
|
|
function isBasicPrime(v) { |
|
var n = v.abs(); |
|
if (n.isUnit()) return false; |
|
if (n.equals(2) || n.equals(3) || n.equals(5)) return true; |
|
if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false; |
|
if (n.lesser(25)) return true; |
|
// we don't know if it's prime: let the other functions figure it out |
|
} |
|
|
|
BigInteger.prototype.isPrime = function () { |
|
var isPrime = isBasicPrime(this); |
|
if (isPrime !== undefined) return isPrime; |
|
var n = this.abs(), |
|
nPrev = n.prev(); |
|
var a = [2, 3, 5, 7, 11, 13, 17, 19], |
|
b = nPrev, |
|
d, t, i, x; |
|
while (b.isEven()) b = b.divide(2); |
|
for (i = 0; i < a.length; i++) { |
|
x = bigInt(a[i]).modPow(b, n); |
|
if (x.equals(Integer[1]) || x.equals(nPrev)) continue; |
|
for (t = true, d = b; t && d.lesser(nPrev); d = d.multiply(2)) { |
|
x = x.square().mod(n); |
|
if (x.equals(nPrev)) t = false; |
|
} |
|
if (t) return false; |
|
} |
|
return true; |
|
}; |
|
SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime; |
|
|
|
BigInteger.prototype.isProbablePrime = function (iterations) { |
|
var isPrime = isBasicPrime(this); |
|
if (isPrime !== undefined) return isPrime; |
|
var n = this.abs(); |
|
var t = iterations === undefined ? 5 : iterations; |
|
// use the Fermat primality test |
|
for (var i = 0; i < t; i++) { |
|
var a = bigInt.randBetween(2, n.minus(2)); |
|
if (!a.modPow(n.prev(), n).isUnit()) return false; // definitely composite |
|
} |
|
return true; // large chance of being prime |
|
}; |
|
SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime; |
|
|
|
BigInteger.prototype.modInv = function (n) { |
|
var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR; |
|
while (!newR.equals(bigInt.zero)) { |
|
q = r.divide(newR); |
|
lastT = t; |
|
lastR = r; |
|
t = newT; |
|
r = newR; |
|
newT = lastT.subtract(q.multiply(newT)); |
|
newR = lastR.subtract(q.multiply(newR)); |
|
} |
|
if (!r.equals(1)) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime"); |
|
if (t.compare(0) === -1) { |
|
t = t.add(n); |
|
} |
|
if (this.isNegative()) { |
|
return t.negate(); |
|
} |
|
return t; |
|
}; |
|
|
|
SmallInteger.prototype.modInv = BigInteger.prototype.modInv; |
|
|
|
BigInteger.prototype.next = function () { |
|
var value = this.value; |
|
if (this.sign) { |
|
return subtractSmall(value, 1, this.sign); |
|
} |
|
return new BigInteger(addSmall(value, 1), this.sign); |
|
}; |
|
SmallInteger.prototype.next = function () { |
|
var value = this.value; |
|
if (value + 1 < MAX_INT) return new SmallInteger(value + 1); |
|
return new BigInteger(MAX_INT_ARR, false); |
|
}; |
|
|
|
BigInteger.prototype.prev = function () { |
|
var value = this.value; |
|
if (this.sign) { |
|
return new BigInteger(addSmall(value, 1), true); |
|
} |
|
return subtractSmall(value, 1, this.sign); |
|
}; |
|
SmallInteger.prototype.prev = function () { |
|
var value = this.value; |
|
if (value - 1 > -MAX_INT) return new SmallInteger(value - 1); |
|
return new BigInteger(MAX_INT_ARR, true); |
|
}; |
|
|
|
var powersOfTwo = [1]; |
|
while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]); |
|
var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1]; |
|
|
|
function shift_isSmall(n) { |
|
return ((typeof n === "number" || typeof n === "string") && +Math.abs(n) <= BASE) || |
|
(n instanceof BigInteger && n.value.length <= 1); |
|
} |
|
|
|
BigInteger.prototype.shiftLeft = function (n) { |
|
if (!shift_isSmall(n)) { |
|
throw new Error(String(n) + " is too large for shifting."); |
|
} |
|
n = +n; |
|
if (n < 0) return this.shiftRight(-n); |
|
var result = this; |
|
if (result.isZero()) return result; |
|
while (n >= powers2Length) { |
|
result = result.multiply(highestPower2); |
|
n -= powers2Length - 1; |
|
} |
|
return result.multiply(powersOfTwo[n]); |
|
}; |
|
SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft; |
|
|
|
BigInteger.prototype.shiftRight = function (n) { |
|
var remQuo; |
|
if (!shift_isSmall(n)) { |
|
throw new Error(String(n) + " is too large for shifting."); |
|
} |
|
n = +n; |
|
if (n < 0) return this.shiftLeft(-n); |
|
var result = this; |
|
while (n >= powers2Length) { |
|
if (result.isZero() || (result.isNegative() && result.isUnit())) return result; |
|
remQuo = divModAny(result, highestPower2); |
|
result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; |
|
n -= powers2Length - 1; |
|
} |
|
remQuo = divModAny(result, powersOfTwo[n]); |
|
return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0]; |
|
}; |
|
SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight; |
|
|
|
function bitwise(x, y, fn) { |
|
y = parseValue(y); |
|
var xSign = x.isNegative(), ySign = y.isNegative(); |
|
var xRem = xSign ? x.not() : x, |
|
yRem = ySign ? y.not() : y; |
|
var xDigit = 0, yDigit = 0; |
|
var xDivMod = null, yDivMod = null; |
|
var result = []; |
|
while (!xRem.isZero() || !yRem.isZero()) { |
|
xDivMod = divModAny(xRem, highestPower2); |
|
xDigit = xDivMod[1].toJSNumber(); |
|
if (xSign) { |
|
xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers |
|
} |
|
|
|
yDivMod = divModAny(yRem, highestPower2); |
|
yDigit = yDivMod[1].toJSNumber(); |
|
if (ySign) { |
|
yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers |
|
} |
|
|
|
xRem = xDivMod[0]; |
|
yRem = yDivMod[0]; |
|
result.push(fn(xDigit, yDigit)); |
|
} |
|
var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0); |
|
for (var i = result.length - 1; i >= 0; i -= 1) { |
|
sum = sum.multiply(highestPower2).add(bigInt(result[i])); |
|
} |
|
return sum; |
|
} |
|
|
|
BigInteger.prototype.not = function () { |
|
return this.negate().prev(); |
|
}; |
|
SmallInteger.prototype.not = BigInteger.prototype.not; |
|
|
|
BigInteger.prototype.and = function (n) { |
|
return bitwise(this, n, function (a, b) { return a & b; }); |
|
}; |
|
SmallInteger.prototype.and = BigInteger.prototype.and; |
|
|
|
BigInteger.prototype.or = function (n) { |
|
return bitwise(this, n, function (a, b) { return a | b; }); |
|
}; |
|
SmallInteger.prototype.or = BigInteger.prototype.or; |
|
|
|
BigInteger.prototype.xor = function (n) { |
|
return bitwise(this, n, function (a, b) { return a ^ b; }); |
|
}; |
|
SmallInteger.prototype.xor = BigInteger.prototype.xor; |
|
|
|
var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I; |
|
function roughLOB(n) { // get lowestOneBit (rough) |
|
// SmallInteger: return Min(lowestOneBit(n), 1 << 30) |
|
// BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7] |
|
var v = n.value, x = typeof v === "number" ? v | LOBMASK_I : v[0] + v[1] * BASE | LOBMASK_BI; |
|
return x & -x; |
|
} |
|
|
|
function integerLogarithm(value, base) { |
|
if (base.compareTo(value) <= 0) { |
|
var tmp = integerLogarithm(value, base.square(base)); |
|
var p = tmp.p; |
|
var e = tmp.e; |
|
var t = p.multiply(base); |
|
return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 }; |
|
} |
|
return { p: bigInt(1), e: 0 }; |
|
} |
|
|
|
BigInteger.prototype.bitLength = function () { |
|
var n = this; |
|
if (n.compareTo(bigInt(0)) < 0) { |
|
n = n.negate().subtract(bigInt(1)); |
|
} |
|
if (n.compareTo(bigInt(0)) === 0) { |
|
return bigInt(0); |
|
} |
|
return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1)); |
|
} |
|
SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength; |
|
|
|
function max(a, b) { |
|
a = parseValue(a); |
|
b = parseValue(b); |
|
return a.greater(b) ? a : b; |
|
} |
|
function min(a, b) { |
|
a = parseValue(a); |
|
b = parseValue(b); |
|
return a.lesser(b) ? a : b; |
|
} |
|
function gcd(a, b) { |
|
a = parseValue(a).abs(); |
|
b = parseValue(b).abs(); |
|
if (a.equals(b)) return a; |
|
if (a.isZero()) return b; |
|
if (b.isZero()) return a; |
|
var c = Integer[1], d, t; |
|
while (a.isEven() && b.isEven()) { |
|
d = Math.min(roughLOB(a), roughLOB(b)); |
|
a = a.divide(d); |
|
b = b.divide(d); |
|
c = c.multiply(d); |
|
} |
|
while (a.isEven()) { |
|
a = a.divide(roughLOB(a)); |
|
} |
|
do { |
|
while (b.isEven()) { |
|
b = b.divide(roughLOB(b)); |
|
} |
|
if (a.greater(b)) { |
|
t = b; b = a; a = t; |
|
} |
|
b = b.subtract(a); |
|
} while (!b.isZero()); |
|
return c.isUnit() ? a : a.multiply(c); |
|
} |
|
function lcm(a, b) { |
|
a = parseValue(a).abs(); |
|
b = parseValue(b).abs(); |
|
return a.divide(gcd(a, b)).multiply(b); |
|
} |
|
function randBetween(a, b) { |
|
a = parseValue(a); |
|
b = parseValue(b); |
|
var low = min(a, b), high = max(a, b); |
|
var range = high.subtract(low).add(1); |
|
if (range.isSmall) return low.add(Math.floor(Math.random() * range)); |
|
var length = range.value.length - 1; |
|
var result = [], restricted = true; |
|
for (var i = length; i >= 0; i--) { |
|
var top = restricted ? range.value[i] : BASE; |
|
var digit = truncate(Math.random() * top); |
|
result.unshift(digit); |
|
if (digit < top) restricted = false; |
|
} |
|
result = arrayToSmall(result); |
|
return low.add(typeof result === "number" ? new SmallInteger(result) : new BigInteger(result, false)); |
|
} |
|
var parseBase = function (text, base) { |
|
var length = text.length; |
|
var i; |
|
var absBase = Math.abs(base); |
|
for (var i = 0; i < length; i++) { |
|
var c = text[i].toLowerCase(); |
|
if (c === "-") continue; |
|
if (/[a-z0-9]/.test(c)) { |
|
if (/[0-9]/.test(c) && +c >= absBase) { |
|
if (c === "1" && absBase === 1) continue; |
|
throw new Error(c + " is not a valid digit in base " + base + "."); |
|
} else if (c.charCodeAt(0) - 87 >= absBase) { |
|
throw new Error(c + " is not a valid digit in base " + base + "."); |
|
} |
|
} |
|
} |
|
if (2 <= base && base <= 36) { |
|
if (length <= LOG_MAX_INT / Math.log(base)) { |
|
var result = parseInt(text, base); |
|
if (isNaN(result)) { |
|
throw new Error(c + " is not a valid digit in base " + base + "."); |
|
} |
|
return new SmallInteger(parseInt(text, base)); |
|
} |
|
} |
|
base = parseValue(base); |
|
var digits = []; |
|
var isNegative = text[0] === "-"; |
|
for (i = isNegative ? 1 : 0; i < text.length; i++) { |
|
var c = text[i].toLowerCase(), |
|
charCode = c.charCodeAt(0); |
|
if (48 <= charCode && charCode <= 57) digits.push(parseValue(c)); |
|
else if (97 <= charCode && charCode <= 122) digits.push(parseValue(c.charCodeAt(0) - 87)); |
|
else if (c === "<") { |
|
var start = i; |
|
do { i++; } while (text[i] !== ">"); |
|
digits.push(parseValue(text.slice(start + 1, i))); |
|
} |
|
else throw new Error(c + " is not a valid character"); |
|
} |
|
return parseBaseFromArray(digits, base, isNegative); |
|
}; |
|
|
|
function parseBaseFromArray(digits, base, isNegative) { |
|
var val = Integer[0], pow = Integer[1], i; |
|
for (i = digits.length - 1; i >= 0; i--) { |
|
val = val.add(digits[i].times(pow)); |
|
pow = pow.times(base); |
|
} |
|
return isNegative ? val.negate() : val; |
|
} |
|
|
|
function stringify(digit) { |
|
if (digit <= 35) { |
|
return "0123456789abcdefghijklmnopqrstuvwxyz".charAt(digit); |
|
} |
|
return "<" + digit + ">"; |
|
} |
|
|
|
function toBase(n, base) { |
|
base = bigInt(base); |
|
if (base.isZero()) { |
|
if (n.isZero()) return { value: [0], isNegative: false }; |
|
throw new Error("Cannot convert nonzero numbers to base 0."); |
|
} |
|
if (base.equals(-1)) { |
|
if (n.isZero()) return { value: [0], isNegative: false }; |
|
if (n.isNegative()) |
|
return { |
|
value: [].concat.apply([], Array.apply(null, Array(-n)) |
|
.map(Array.prototype.valueOf, [1, 0]) |
|
), |
|
isNegative: false |
|
}; |
|
|
|
var arr = Array.apply(null, Array(+n - 1)) |
|
.map(Array.prototype.valueOf, [0, 1]); |
|
arr.unshift([1]); |
|
return { |
|
value: [].concat.apply([], arr), |
|
isNegative: false |
|
}; |
|
} |
|
|
|
var neg = false; |
|
if (n.isNegative() && base.isPositive()) { |
|
neg = true; |
|
n = n.abs(); |
|
} |
|
if (base.equals(1)) { |
|
if (n.isZero()) return { value: [0], isNegative: false }; |
|
|
|
return { |
|
value: Array.apply(null, Array(+n)) |
|
.map(Number.prototype.valueOf, 1), |
|
isNegative: neg |
|
}; |
|
} |
|
var out = []; |
|
var left = n, divmod; |
|
while (left.isNegative() || left.compareAbs(base) >= 0) { |
|
divmod = left.divmod(base); |
|
left = divmod.quotient; |
|
var digit = divmod.remainder; |
|
if (digit.isNegative()) { |
|
digit = base.minus(digit).abs(); |
|
left = left.next(); |
|
} |
|
out.push(digit.toJSNumber()); |
|
} |
|
out.push(left.toJSNumber()); |
|
return { value: out.reverse(), isNegative: neg }; |
|
} |
|
|
|
function toBaseString(n, base) { |
|
var arr = toBase(n, base); |
|
return (arr.isNegative ? "-" : "") + arr.value.map(stringify).join(''); |
|
} |
|
|
|
BigInteger.prototype.toArray = function (radix) { |
|
return toBase(this, radix); |
|
}; |
|
|
|
SmallInteger.prototype.toArray = function (radix) { |
|
return toBase(this, radix); |
|
}; |
|
|
|
BigInteger.prototype.toString = function (radix) { |
|
if (radix === undefined) radix = 10; |
|
if (radix !== 10) return toBaseString(this, radix); |
|
var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit; |
|
while (--l >= 0) { |
|
digit = String(v[l]); |
|
str += zeros.slice(digit.length) + digit; |
|
} |
|
var sign = this.sign ? "-" : ""; |
|
return sign + str; |
|
}; |
|
|
|
SmallInteger.prototype.toString = function (radix) { |
|
if (radix === undefined) radix = 10; |
|
if (radix != 10) return toBaseString(this, radix); |
|
return String(this.value); |
|
}; |
|
BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString(); } |
|
|
|
BigInteger.prototype.valueOf = function () { |
|
return parseInt(this.toString(), 10); |
|
}; |
|
BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf; |
|
|
|
SmallInteger.prototype.valueOf = function () { |
|
return this.value; |
|
}; |
|
SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf; |
|
|
|
function parseStringValue(v) { |
|
if (isPrecise(+v)) { |
|
var x = +v; |
|
if (x === truncate(x)) |
|
return new SmallInteger(x); |
|
throw new Error("Invalid integer: " + v); |
|
} |
|
var sign = v[0] === "-"; |
|
if (sign) v = v.slice(1); |
|
var split = v.split(/e/i); |
|
if (split.length > 2) throw new Error("Invalid integer: " + split.join("e")); |
|
if (split.length === 2) { |
|
var exp = split[1]; |
|
if (exp[0] === "+") exp = exp.slice(1); |
|
exp = +exp; |
|
if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent."); |
|
var text = split[0]; |
|
var decimalPlace = text.indexOf("."); |
|
if (decimalPlace >= 0) { |
|
exp -= text.length - decimalPlace - 1; |
|
text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1); |
|
} |
|
if (exp < 0) throw new Error("Cannot include negative exponent part for integers"); |
|
text += (new Array(exp + 1)).join("0"); |
|
v = text; |
|
} |
|
var isValid = /^([0-9][0-9]*)$/.test(v); |
|
if (!isValid) throw new Error("Invalid integer: " + v); |
|
var r = [], max = v.length, l = LOG_BASE, min = max - l; |
|
while (max > 0) { |
|
r.push(+v.slice(min, max)); |
|
min -= l; |
|
if (min < 0) min = 0; |
|
max -= l; |
|
} |
|
trim(r); |
|
return new BigInteger(r, sign); |
|
} |
|
|
|
function parseNumberValue(v) { |
|
if (isPrecise(v)) { |
|
if (v !== truncate(v)) throw new Error(v + " is not an integer."); |
|
return new SmallInteger(v); |
|
} |
|
return parseStringValue(v.toString()); |
|
} |
|
|
|
function parseValue(v) { |
|
if (typeof v === "number") { |
|
return parseNumberValue(v); |
|
} |
|
if (typeof v === "string") { |
|
return parseStringValue(v); |
|
} |
|
return v; |
|
} |
|
// Pre-define numbers in range [-999,999] |
|
for (var i = 0; i < 1000; i++) { |
|
Integer[i] = new SmallInteger(i); |
|
if (i > 0) Integer[-i] = new SmallInteger(-i); |
|
} |
|
// Backwards compatibility |
|
Integer.one = Integer[1]; |
|
Integer.zero = Integer[0]; |
|
Integer.minusOne = Integer[-1]; |
|
Integer.max = max; |
|
Integer.min = min; |
|
Integer.gcd = gcd; |
|
Integer.lcm = lcm; |
|
Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger; }; |
|
Integer.randBetween = randBetween; |
|
|
|
Integer.fromArray = function (digits, base, isNegative) { |
|
return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative); |
|
}; |
|
|
|
return Integer; |
|
})(); |
|
|
|
// Node.js check |
|
if (typeof module !== "undefined" && module.hasOwnProperty("exports")) { |
|
module.exports = bigInt; |
|
} |
|
|
|
//amd check |
|
if (typeof define === "function" && define.amd) { |
|
define("big-integer", [], function () { |
|
return bigInt; |
|
}); |
|
}
|
|
|