forked from github/cordova-android
84cb08b23e
This reverts commit 5a5f544a4890ff65519329303e75a649e482df23. Rationale: base64-js update in 5a5f544 causes extra base64-js version to be installed under plist (node_modules/plist/node_modules/base64-js), which would need to be committed to satisfy the needs of the deprecated Node.js 4 version. The extra base64-js version in node_modules/plist/node_modules/base64-js was missed at the time 5a5f544 was committed. The base64-js update in 5a5f544 is now deemed as not wanted due to the extra base64-js version that would need to be committed. The other dependencies updates in 5a5f544 may be nice to have but not considered necessary for the patch release. Reverting now to unblock the upcoming 7.1.4 patch release. Note that neither 5a5f544 nor this revert will show up in the master branch.
1309 lines
44 KiB
JavaScript
1309 lines
44 KiB
JavaScript
var bigInt = (function (undefined) {
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"use strict";
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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);
|
|
}
|
|
result.reverse();
|
|
return [arrayToSmall(result), arrayToSmall(part)];
|
|
}
|
|
|
|
function divModSmall(value, lambda) {
|
|
var length = value.length,
|
|
quotient = createArray(length),
|
|
base = BASE,
|
|
i, q, remainder, divisor;
|
|
remainder = 0;
|
|
for (i = length - 1; i >= 0; --i) {
|
|
divisor = remainder * base + value[i];
|
|
q = truncate(divisor / lambda);
|
|
remainder = divisor - q * lambda;
|
|
quotient[i] = q | 0;
|
|
}
|
|
return [quotient, remainder | 0];
|
|
}
|
|
|
|
function divModAny(self, v) {
|
|
var value, n = parseValue(v);
|
|
var a = self.value, b = n.value;
|
|
var quotient;
|
|
if (b === 0) throw new Error("Cannot divide by zero");
|
|
if (self.isSmall) {
|
|
if (n.isSmall) {
|
|
return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)];
|
|
}
|
|
return [Integer[0], self];
|
|
}
|
|
if (n.isSmall) {
|
|
if (b === 1) return [self, Integer[0]];
|
|
if (b == -1) return [self.negate(), Integer[0]];
|
|
var abs = Math.abs(b);
|
|
if (abs < BASE) {
|
|
value = divModSmall(a, abs);
|
|
quotient = arrayToSmall(value[0]);
|
|
var remainder = value[1];
|
|
if (self.sign) remainder = -remainder;
|
|
if (typeof quotient === "number") {
|
|
if (self.sign !== n.sign) quotient = -quotient;
|
|
return [new SmallInteger(quotient), new SmallInteger(remainder)];
|
|
}
|
|
return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)];
|
|
}
|
|
b = smallToArray(abs);
|
|
}
|
|
var comparison = compareAbs(a, b);
|
|
if (comparison === -1) return [Integer[0], self];
|
|
if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]];
|
|
|
|
// divMod1 is faster on smaller input sizes
|
|
if (a.length + b.length <= 200)
|
|
value = divMod1(a, b);
|
|
else value = divMod2(a, b);
|
|
|
|
quotient = value[0];
|
|
var qSign = self.sign !== n.sign,
|
|
mod = value[1],
|
|
mSign = self.sign;
|
|
if (typeof quotient === "number") {
|
|
if (qSign) quotient = -quotient;
|
|
quotient = new SmallInteger(quotient);
|
|
} else quotient = new BigInteger(quotient, qSign);
|
|
if (typeof mod === "number") {
|
|
if (mSign) mod = -mod;
|
|
mod = new SmallInteger(mod);
|
|
} 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;
|
|
});
|
|
}
|