3448 lines
84 KiB
JavaScript
3448 lines
84 KiB
JavaScript
(function (module, exports) {
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'use strict'; // Utils
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function assert(val, msg) {
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if (!val) throw new Error(msg || 'Assertion failed');
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} // Could use `inherits` module, but don't want to move from single file
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// architecture yet.
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function inherits(ctor, superCtor) {
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ctor.super_ = superCtor;
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var TempCtor = function () {};
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TempCtor.prototype = superCtor.prototype;
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ctor.prototype = new TempCtor();
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ctor.prototype.constructor = ctor;
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} // BN
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function BN(number, base, endian) {
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if (BN.isBN(number)) {
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return number;
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}
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this.negative = 0;
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this.words = null;
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this.length = 0; // Reduction context
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this.red = null;
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if (number !== null) {
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if (base === 'le' || base === 'be') {
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endian = base;
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base = 10;
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}
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this._init(number || 0, base || 10, endian || 'be');
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}
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}
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if (typeof module === 'object') {
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module.exports = BN;
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} else {
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exports.BN = BN;
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}
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BN.BN = BN;
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BN.wordSize = 26;
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var Buffer;
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try {
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Buffer = require("./buffer.js").Buffer;
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} catch (e) {}
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BN.isBN = function isBN(num) {
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if (num instanceof BN) {
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return true;
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}
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return num !== null && typeof num === 'object' && num.constructor.wordSize === BN.wordSize && Array.isArray(num.words);
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};
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BN.max = function max(left, right) {
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if (left.cmp(right) > 0) return left;
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return right;
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};
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BN.min = function min(left, right) {
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if (left.cmp(right) < 0) return left;
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return right;
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};
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BN.prototype._init = function init(number, base, endian) {
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if (typeof number === 'number') {
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return this._initNumber(number, base, endian);
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}
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if (typeof number === 'object') {
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return this._initArray(number, base, endian);
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}
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if (base === 'hex') {
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base = 16;
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}
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assert(base === (base | 0) && base >= 2 && base <= 36);
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number = number.toString().replace(/\s+/g, '');
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var start = 0;
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if (number[0] === '-') {
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start++;
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}
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if (base === 16) {
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this._parseHex(number, start);
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} else {
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this._parseBase(number, base, start);
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}
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if (number[0] === '-') {
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this.negative = 1;
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}
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this.strip();
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if (endian !== 'le') return;
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this._initArray(this.toArray(), base, endian);
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};
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BN.prototype._initNumber = function _initNumber(number, base, endian) {
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if (number < 0) {
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this.negative = 1;
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number = -number;
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}
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if (number < 0x4000000) {
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this.words = [number & 0x3ffffff];
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this.length = 1;
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} else if (number < 0x10000000000000) {
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this.words = [number & 0x3ffffff, number / 0x4000000 & 0x3ffffff];
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this.length = 2;
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} else {
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assert(number < 0x20000000000000); // 2 ^ 53 (unsafe)
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this.words = [number & 0x3ffffff, number / 0x4000000 & 0x3ffffff, 1];
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this.length = 3;
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}
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if (endian !== 'le') return; // Reverse the bytes
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this._initArray(this.toArray(), base, endian);
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};
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BN.prototype._initArray = function _initArray(number, base, endian) {
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// Perhaps a Uint8Array
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assert(typeof number.length === 'number');
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if (number.length <= 0) {
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this.words = [0];
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this.length = 1;
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return this;
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}
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this.length = Math.ceil(number.length / 3);
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this.words = new Array(this.length);
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for (var i = 0; i < this.length; i++) {
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this.words[i] = 0;
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}
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var j, w;
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var off = 0;
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if (endian === 'be') {
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for (i = number.length - 1, j = 0; i >= 0; i -= 3) {
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w = number[i] | number[i - 1] << 8 | number[i - 2] << 16;
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this.words[j] |= w << off & 0x3ffffff;
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this.words[j + 1] = w >>> 26 - off & 0x3ffffff;
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off += 24;
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if (off >= 26) {
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off -= 26;
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j++;
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}
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}
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} else if (endian === 'le') {
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for (i = 0, j = 0; i < number.length; i += 3) {
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w = number[i] | number[i + 1] << 8 | number[i + 2] << 16;
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this.words[j] |= w << off & 0x3ffffff;
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this.words[j + 1] = w >>> 26 - off & 0x3ffffff;
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off += 24;
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if (off >= 26) {
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off -= 26;
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j++;
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}
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}
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}
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return this.strip();
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};
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function parseHex(str, start, end) {
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var r = 0;
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var len = Math.min(str.length, end);
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for (var i = start; i < len; i++) {
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var c = str.charCodeAt(i) - 48;
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r <<= 4; // 'a' - 'f'
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if (c >= 49 && c <= 54) {
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r |= c - 49 + 0xa; // 'A' - 'F'
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} else if (c >= 17 && c <= 22) {
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r |= c - 17 + 0xa; // '0' - '9'
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} else {
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r |= c & 0xf;
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}
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}
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return r;
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}
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BN.prototype._parseHex = function _parseHex(number, start) {
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// Create possibly bigger array to ensure that it fits the number
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this.length = Math.ceil((number.length - start) / 6);
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this.words = new Array(this.length);
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for (var i = 0; i < this.length; i++) {
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this.words[i] = 0;
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}
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var j, w; // Scan 24-bit chunks and add them to the number
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var off = 0;
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for (i = number.length - 6, j = 0; i >= start; i -= 6) {
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w = parseHex(number, i, i + 6);
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this.words[j] |= w << off & 0x3ffffff; // NOTE: `0x3fffff` is intentional here, 26bits max shift + 24bit hex limb
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this.words[j + 1] |= w >>> 26 - off & 0x3fffff;
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off += 24;
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if (off >= 26) {
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off -= 26;
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j++;
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}
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}
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if (i + 6 !== start) {
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w = parseHex(number, start, i + 6);
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this.words[j] |= w << off & 0x3ffffff;
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this.words[j + 1] |= w >>> 26 - off & 0x3fffff;
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}
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this.strip();
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};
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function parseBase(str, start, end, mul) {
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var r = 0;
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var len = Math.min(str.length, end);
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for (var i = start; i < len; i++) {
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var c = str.charCodeAt(i) - 48;
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r *= mul; // 'a'
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if (c >= 49) {
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r += c - 49 + 0xa; // 'A'
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} else if (c >= 17) {
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r += c - 17 + 0xa; // '0' - '9'
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} else {
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r += c;
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}
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}
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return r;
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}
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BN.prototype._parseBase = function _parseBase(number, base, start) {
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// Initialize as zero
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this.words = [0];
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this.length = 1; // Find length of limb in base
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for (var limbLen = 0, limbPow = 1; limbPow <= 0x3ffffff; limbPow *= base) {
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limbLen++;
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}
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limbLen--;
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limbPow = limbPow / base | 0;
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var total = number.length - start;
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var mod = total % limbLen;
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var end = Math.min(total, total - mod) + start;
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var word = 0;
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for (var i = start; i < end; i += limbLen) {
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word = parseBase(number, i, i + limbLen, base);
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this.imuln(limbPow);
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if (this.words[0] + word < 0x4000000) {
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this.words[0] += word;
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} else {
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this._iaddn(word);
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}
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}
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if (mod !== 0) {
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var pow = 1;
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word = parseBase(number, i, number.length, base);
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for (i = 0; i < mod; i++) {
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pow *= base;
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}
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this.imuln(pow);
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if (this.words[0] + word < 0x4000000) {
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this.words[0] += word;
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} else {
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this._iaddn(word);
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}
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}
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};
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BN.prototype.copy = function copy(dest) {
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dest.words = new Array(this.length);
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for (var i = 0; i < this.length; i++) {
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dest.words[i] = this.words[i];
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}
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dest.length = this.length;
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dest.negative = this.negative;
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dest.red = this.red;
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};
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BN.prototype.clone = function clone() {
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var r = new BN(null);
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this.copy(r);
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return r;
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};
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BN.prototype._expand = function _expand(size) {
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while (this.length < size) {
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this.words[this.length++] = 0;
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}
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return this;
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}; // Remove leading `0` from `this`
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BN.prototype.strip = function strip() {
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while (this.length > 1 && this.words[this.length - 1] === 0) {
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this.length--;
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}
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return this._normSign();
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};
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BN.prototype._normSign = function _normSign() {
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// -0 = 0
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if (this.length === 1 && this.words[0] === 0) {
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this.negative = 0;
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}
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return this;
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};
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BN.prototype.inspect = function inspect() {
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return (this.red ? '<BN-R: ' : '<BN: ') + this.toString(16) + '>';
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};
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/*
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var zeros = [];
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var groupSizes = [];
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var groupBases = [];
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var s = '';
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var i = -1;
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while (++i < BN.wordSize) {
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zeros[i] = s;
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s += '0';
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}
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groupSizes[0] = 0;
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groupSizes[1] = 0;
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groupBases[0] = 0;
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groupBases[1] = 0;
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var base = 2 - 1;
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while (++base < 36 + 1) {
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var groupSize = 0;
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var groupBase = 1;
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while (groupBase < (1 << BN.wordSize) / base) {
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groupBase *= base;
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groupSize += 1;
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}
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groupSizes[base] = groupSize;
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groupBases[base] = groupBase;
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}
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*/
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var zeros = ['', '0', '00', '000', '0000', '00000', '000000', '0000000', '00000000', '000000000', '0000000000', '00000000000', '000000000000', '0000000000000', '00000000000000', '000000000000000', '0000000000000000', '00000000000000000', '000000000000000000', '0000000000000000000', '00000000000000000000', '000000000000000000000', '0000000000000000000000', '00000000000000000000000', '000000000000000000000000', '0000000000000000000000000'];
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var groupSizes = [0, 0, 25, 16, 12, 11, 10, 9, 8, 8, 7, 7, 7, 7, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5];
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var groupBases = [0, 0, 33554432, 43046721, 16777216, 48828125, 60466176, 40353607, 16777216, 43046721, 10000000, 19487171, 35831808, 62748517, 7529536, 11390625, 16777216, 24137569, 34012224, 47045881, 64000000, 4084101, 5153632, 6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149, 24300000, 28629151, 33554432, 39135393, 45435424, 52521875, 60466176];
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BN.prototype.toString = function toString(base, padding) {
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base = base || 10;
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padding = padding | 0 || 1;
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var out;
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if (base === 16 || base === 'hex') {
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out = '';
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var off = 0;
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var carry = 0;
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for (var i = 0; i < this.length; i++) {
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var w = this.words[i];
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var word = ((w << off | carry) & 0xffffff).toString(16);
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carry = w >>> 24 - off & 0xffffff;
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if (carry !== 0 || i !== this.length - 1) {
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out = zeros[6 - word.length] + word + out;
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} else {
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out = word + out;
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}
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off += 2;
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if (off >= 26) {
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off -= 26;
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i--;
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}
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}
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if (carry !== 0) {
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out = carry.toString(16) + out;
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}
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while (out.length % padding !== 0) {
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out = '0' + out;
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}
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if (this.negative !== 0) {
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out = '-' + out;
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}
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return out;
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}
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if (base === (base | 0) && base >= 2 && base <= 36) {
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// var groupSize = Math.floor(BN.wordSize * Math.LN2 / Math.log(base));
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var groupSize = groupSizes[base]; // var groupBase = Math.pow(base, groupSize);
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var groupBase = groupBases[base];
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out = '';
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var c = this.clone();
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c.negative = 0;
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while (!c.isZero()) {
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var r = c.modn(groupBase).toString(base);
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c = c.idivn(groupBase);
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if (!c.isZero()) {
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out = zeros[groupSize - r.length] + r + out;
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} else {
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out = r + out;
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}
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}
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if (this.isZero()) {
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out = '0' + out;
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}
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while (out.length % padding !== 0) {
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out = '0' + out;
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}
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if (this.negative !== 0) {
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out = '-' + out;
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}
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return out;
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}
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assert(false, 'Base should be between 2 and 36');
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};
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BN.prototype.toNumber = function toNumber() {
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var ret = this.words[0];
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if (this.length === 2) {
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ret += this.words[1] * 0x4000000;
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} else if (this.length === 3 && this.words[2] === 0x01) {
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// NOTE: at this stage it is known that the top bit is set
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ret += 0x10000000000000 + this.words[1] * 0x4000000;
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} else if (this.length > 2) {
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assert(false, 'Number can only safely store up to 53 bits');
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}
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return this.negative !== 0 ? -ret : ret;
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};
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BN.prototype.toJSON = function toJSON() {
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return this.toString(16);
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};
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BN.prototype.toBuffer = function toBuffer(endian, length) {
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assert(typeof Buffer !== 'undefined');
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return this.toArrayLike(Buffer, endian, length);
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};
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BN.prototype.toArray = function toArray(endian, length) {
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return this.toArrayLike(Array, endian, length);
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};
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BN.prototype.toArrayLike = function toArrayLike(ArrayType, endian, length) {
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var byteLength = this.byteLength();
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var reqLength = length || Math.max(1, byteLength);
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assert(byteLength <= reqLength, 'byte array longer than desired length');
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assert(reqLength > 0, 'Requested array length <= 0');
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this.strip();
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var littleEndian = endian === 'le';
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var res = new ArrayType(reqLength);
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var b, i;
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var q = this.clone();
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if (!littleEndian) {
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// Assume big-endian
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for (i = 0; i < reqLength - byteLength; i++) {
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res[i] = 0;
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}
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for (i = 0; !q.isZero(); i++) {
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b = q.andln(0xff);
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q.iushrn(8);
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res[reqLength - i - 1] = b;
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}
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} else {
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for (i = 0; !q.isZero(); i++) {
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b = q.andln(0xff);
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q.iushrn(8);
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res[i] = b;
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}
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for (; i < reqLength; i++) {
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res[i] = 0;
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}
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}
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return res;
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};
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if (Math.clz32) {
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BN.prototype._countBits = function _countBits(w) {
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return 32 - Math.clz32(w);
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};
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} else {
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BN.prototype._countBits = function _countBits(w) {
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var t = w;
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var r = 0;
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if (t >= 0x1000) {
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r += 13;
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t >>>= 13;
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}
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if (t >= 0x40) {
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r += 7;
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t >>>= 7;
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}
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if (t >= 0x8) {
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r += 4;
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t >>>= 4;
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}
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if (t >= 0x02) {
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r += 2;
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t >>>= 2;
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}
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return r + t;
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};
|
|
}
|
|
|
|
BN.prototype._zeroBits = function _zeroBits(w) {
|
|
// Short-cut
|
|
if (w === 0) return 26;
|
|
var t = w;
|
|
var r = 0;
|
|
|
|
if ((t & 0x1fff) === 0) {
|
|
r += 13;
|
|
t >>>= 13;
|
|
}
|
|
|
|
if ((t & 0x7f) === 0) {
|
|
r += 7;
|
|
t >>>= 7;
|
|
}
|
|
|
|
if ((t & 0xf) === 0) {
|
|
r += 4;
|
|
t >>>= 4;
|
|
}
|
|
|
|
if ((t & 0x3) === 0) {
|
|
r += 2;
|
|
t >>>= 2;
|
|
}
|
|
|
|
if ((t & 0x1) === 0) {
|
|
r++;
|
|
}
|
|
|
|
return r;
|
|
}; // Return number of used bits in a BN
|
|
|
|
|
|
BN.prototype.bitLength = function bitLength() {
|
|
var w = this.words[this.length - 1];
|
|
|
|
var hi = this._countBits(w);
|
|
|
|
return (this.length - 1) * 26 + hi;
|
|
};
|
|
|
|
function toBitArray(num) {
|
|
var w = new Array(num.bitLength());
|
|
|
|
for (var bit = 0; bit < w.length; bit++) {
|
|
var off = bit / 26 | 0;
|
|
var wbit = bit % 26;
|
|
w[bit] = (num.words[off] & 1 << wbit) >>> wbit;
|
|
}
|
|
|
|
return w;
|
|
} // Number of trailing zero bits
|
|
|
|
|
|
BN.prototype.zeroBits = function zeroBits() {
|
|
if (this.isZero()) return 0;
|
|
var r = 0;
|
|
|
|
for (var i = 0; i < this.length; i++) {
|
|
var b = this._zeroBits(this.words[i]);
|
|
|
|
r += b;
|
|
if (b !== 26) break;
|
|
}
|
|
|
|
return r;
|
|
};
|
|
|
|
BN.prototype.byteLength = function byteLength() {
|
|
return Math.ceil(this.bitLength() / 8);
|
|
};
|
|
|
|
BN.prototype.toTwos = function toTwos(width) {
|
|
if (this.negative !== 0) {
|
|
return this.abs().inotn(width).iaddn(1);
|
|
}
|
|
|
|
return this.clone();
|
|
};
|
|
|
|
BN.prototype.fromTwos = function fromTwos(width) {
|
|
if (this.testn(width - 1)) {
|
|
return this.notn(width).iaddn(1).ineg();
|
|
}
|
|
|
|
return this.clone();
|
|
};
|
|
|
|
BN.prototype.isNeg = function isNeg() {
|
|
return this.negative !== 0;
|
|
}; // Return negative clone of `this`
|
|
|
|
|
|
BN.prototype.neg = function neg() {
|
|
return this.clone().ineg();
|
|
};
|
|
|
|
BN.prototype.ineg = function ineg() {
|
|
if (!this.isZero()) {
|
|
this.negative ^= 1;
|
|
}
|
|
|
|
return this;
|
|
}; // Or `num` with `this` in-place
|
|
|
|
|
|
BN.prototype.iuor = function iuor(num) {
|
|
while (this.length < num.length) {
|
|
this.words[this.length++] = 0;
|
|
}
|
|
|
|
for (var i = 0; i < num.length; i++) {
|
|
this.words[i] = this.words[i] | num.words[i];
|
|
}
|
|
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.ior = function ior(num) {
|
|
assert((this.negative | num.negative) === 0);
|
|
return this.iuor(num);
|
|
}; // Or `num` with `this`
|
|
|
|
|
|
BN.prototype.or = function or(num) {
|
|
if (this.length > num.length) return this.clone().ior(num);
|
|
return num.clone().ior(this);
|
|
};
|
|
|
|
BN.prototype.uor = function uor(num) {
|
|
if (this.length > num.length) return this.clone().iuor(num);
|
|
return num.clone().iuor(this);
|
|
}; // And `num` with `this` in-place
|
|
|
|
|
|
BN.prototype.iuand = function iuand(num) {
|
|
// b = min-length(num, this)
|
|
var b;
|
|
|
|
if (this.length > num.length) {
|
|
b = num;
|
|
} else {
|
|
b = this;
|
|
}
|
|
|
|
for (var i = 0; i < b.length; i++) {
|
|
this.words[i] = this.words[i] & num.words[i];
|
|
}
|
|
|
|
this.length = b.length;
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.iand = function iand(num) {
|
|
assert((this.negative | num.negative) === 0);
|
|
return this.iuand(num);
|
|
}; // And `num` with `this`
|
|
|
|
|
|
BN.prototype.and = function and(num) {
|
|
if (this.length > num.length) return this.clone().iand(num);
|
|
return num.clone().iand(this);
|
|
};
|
|
|
|
BN.prototype.uand = function uand(num) {
|
|
if (this.length > num.length) return this.clone().iuand(num);
|
|
return num.clone().iuand(this);
|
|
}; // Xor `num` with `this` in-place
|
|
|
|
|
|
BN.prototype.iuxor = function iuxor(num) {
|
|
// a.length > b.length
|
|
var a;
|
|
var b;
|
|
|
|
if (this.length > num.length) {
|
|
a = this;
|
|
b = num;
|
|
} else {
|
|
a = num;
|
|
b = this;
|
|
}
|
|
|
|
for (var i = 0; i < b.length; i++) {
|
|
this.words[i] = a.words[i] ^ b.words[i];
|
|
}
|
|
|
|
if (this !== a) {
|
|
for (; i < a.length; i++) {
|
|
this.words[i] = a.words[i];
|
|
}
|
|
}
|
|
|
|
this.length = a.length;
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.ixor = function ixor(num) {
|
|
assert((this.negative | num.negative) === 0);
|
|
return this.iuxor(num);
|
|
}; // Xor `num` with `this`
|
|
|
|
|
|
BN.prototype.xor = function xor(num) {
|
|
if (this.length > num.length) return this.clone().ixor(num);
|
|
return num.clone().ixor(this);
|
|
};
|
|
|
|
BN.prototype.uxor = function uxor(num) {
|
|
if (this.length > num.length) return this.clone().iuxor(num);
|
|
return num.clone().iuxor(this);
|
|
}; // Not ``this`` with ``width`` bitwidth
|
|
|
|
|
|
BN.prototype.inotn = function inotn(width) {
|
|
assert(typeof width === 'number' && width >= 0);
|
|
var bytesNeeded = Math.ceil(width / 26) | 0;
|
|
var bitsLeft = width % 26; // Extend the buffer with leading zeroes
|
|
|
|
this._expand(bytesNeeded);
|
|
|
|
if (bitsLeft > 0) {
|
|
bytesNeeded--;
|
|
} // Handle complete words
|
|
|
|
|
|
for (var i = 0; i < bytesNeeded; i++) {
|
|
this.words[i] = ~this.words[i] & 0x3ffffff;
|
|
} // Handle the residue
|
|
|
|
|
|
if (bitsLeft > 0) {
|
|
this.words[i] = ~this.words[i] & 0x3ffffff >> 26 - bitsLeft;
|
|
} // And remove leading zeroes
|
|
|
|
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.notn = function notn(width) {
|
|
return this.clone().inotn(width);
|
|
}; // Set `bit` of `this`
|
|
|
|
|
|
BN.prototype.setn = function setn(bit, val) {
|
|
assert(typeof bit === 'number' && bit >= 0);
|
|
var off = bit / 26 | 0;
|
|
var wbit = bit % 26;
|
|
|
|
this._expand(off + 1);
|
|
|
|
if (val) {
|
|
this.words[off] = this.words[off] | 1 << wbit;
|
|
} else {
|
|
this.words[off] = this.words[off] & ~(1 << wbit);
|
|
}
|
|
|
|
return this.strip();
|
|
}; // Add `num` to `this` in-place
|
|
|
|
|
|
BN.prototype.iadd = function iadd(num) {
|
|
var r; // negative + positive
|
|
|
|
if (this.negative !== 0 && num.negative === 0) {
|
|
this.negative = 0;
|
|
r = this.isub(num);
|
|
this.negative ^= 1;
|
|
return this._normSign(); // positive + negative
|
|
} else if (this.negative === 0 && num.negative !== 0) {
|
|
num.negative = 0;
|
|
r = this.isub(num);
|
|
num.negative = 1;
|
|
return r._normSign();
|
|
} // a.length > b.length
|
|
|
|
|
|
var a, b;
|
|
|
|
if (this.length > num.length) {
|
|
a = this;
|
|
b = num;
|
|
} else {
|
|
a = num;
|
|
b = this;
|
|
}
|
|
|
|
var carry = 0;
|
|
|
|
for (var i = 0; i < b.length; i++) {
|
|
r = (a.words[i] | 0) + (b.words[i] | 0) + carry;
|
|
this.words[i] = r & 0x3ffffff;
|
|
carry = r >>> 26;
|
|
}
|
|
|
|
for (; carry !== 0 && i < a.length; i++) {
|
|
r = (a.words[i] | 0) + carry;
|
|
this.words[i] = r & 0x3ffffff;
|
|
carry = r >>> 26;
|
|
}
|
|
|
|
this.length = a.length;
|
|
|
|
if (carry !== 0) {
|
|
this.words[this.length] = carry;
|
|
this.length++; // Copy the rest of the words
|
|
} else if (a !== this) {
|
|
for (; i < a.length; i++) {
|
|
this.words[i] = a.words[i];
|
|
}
|
|
}
|
|
|
|
return this;
|
|
}; // Add `num` to `this`
|
|
|
|
|
|
BN.prototype.add = function add(num) {
|
|
var res;
|
|
|
|
if (num.negative !== 0 && this.negative === 0) {
|
|
num.negative = 0;
|
|
res = this.sub(num);
|
|
num.negative ^= 1;
|
|
return res;
|
|
} else if (num.negative === 0 && this.negative !== 0) {
|
|
this.negative = 0;
|
|
res = num.sub(this);
|
|
this.negative = 1;
|
|
return res;
|
|
}
|
|
|
|
if (this.length > num.length) return this.clone().iadd(num);
|
|
return num.clone().iadd(this);
|
|
}; // Subtract `num` from `this` in-place
|
|
|
|
|
|
BN.prototype.isub = function isub(num) {
|
|
// this - (-num) = this + num
|
|
if (num.negative !== 0) {
|
|
num.negative = 0;
|
|
var r = this.iadd(num);
|
|
num.negative = 1;
|
|
return r._normSign(); // -this - num = -(this + num)
|
|
} else if (this.negative !== 0) {
|
|
this.negative = 0;
|
|
this.iadd(num);
|
|
this.negative = 1;
|
|
return this._normSign();
|
|
} // At this point both numbers are positive
|
|
|
|
|
|
var cmp = this.cmp(num); // Optimization - zeroify
|
|
|
|
if (cmp === 0) {
|
|
this.negative = 0;
|
|
this.length = 1;
|
|
this.words[0] = 0;
|
|
return this;
|
|
} // a > b
|
|
|
|
|
|
var a, b;
|
|
|
|
if (cmp > 0) {
|
|
a = this;
|
|
b = num;
|
|
} else {
|
|
a = num;
|
|
b = this;
|
|
}
|
|
|
|
var carry = 0;
|
|
|
|
for (var i = 0; i < b.length; i++) {
|
|
r = (a.words[i] | 0) - (b.words[i] | 0) + carry;
|
|
carry = r >> 26;
|
|
this.words[i] = r & 0x3ffffff;
|
|
}
|
|
|
|
for (; carry !== 0 && i < a.length; i++) {
|
|
r = (a.words[i] | 0) + carry;
|
|
carry = r >> 26;
|
|
this.words[i] = r & 0x3ffffff;
|
|
} // Copy rest of the words
|
|
|
|
|
|
if (carry === 0 && i < a.length && a !== this) {
|
|
for (; i < a.length; i++) {
|
|
this.words[i] = a.words[i];
|
|
}
|
|
}
|
|
|
|
this.length = Math.max(this.length, i);
|
|
|
|
if (a !== this) {
|
|
this.negative = 1;
|
|
}
|
|
|
|
return this.strip();
|
|
}; // Subtract `num` from `this`
|
|
|
|
|
|
BN.prototype.sub = function sub(num) {
|
|
return this.clone().isub(num);
|
|
};
|
|
|
|
function smallMulTo(self, num, out) {
|
|
out.negative = num.negative ^ self.negative;
|
|
var len = self.length + num.length | 0;
|
|
out.length = len;
|
|
len = len - 1 | 0; // Peel one iteration (compiler can't do it, because of code complexity)
|
|
|
|
var a = self.words[0] | 0;
|
|
var b = num.words[0] | 0;
|
|
var r = a * b;
|
|
var lo = r & 0x3ffffff;
|
|
var carry = r / 0x4000000 | 0;
|
|
out.words[0] = lo;
|
|
|
|
for (var k = 1; k < len; k++) {
|
|
// Sum all words with the same `i + j = k` and accumulate `ncarry`,
|
|
// note that ncarry could be >= 0x3ffffff
|
|
var ncarry = carry >>> 26;
|
|
var rword = carry & 0x3ffffff;
|
|
var maxJ = Math.min(k, num.length - 1);
|
|
|
|
for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) {
|
|
var i = k - j | 0;
|
|
a = self.words[i] | 0;
|
|
b = num.words[j] | 0;
|
|
r = a * b + rword;
|
|
ncarry += r / 0x4000000 | 0;
|
|
rword = r & 0x3ffffff;
|
|
}
|
|
|
|
out.words[k] = rword | 0;
|
|
carry = ncarry | 0;
|
|
}
|
|
|
|
if (carry !== 0) {
|
|
out.words[k] = carry | 0;
|
|
} else {
|
|
out.length--;
|
|
}
|
|
|
|
return out.strip();
|
|
} // TODO(indutny): it may be reasonable to omit it for users who don't need
|
|
// to work with 256-bit numbers, otherwise it gives 20% improvement for 256-bit
|
|
// multiplication (like elliptic secp256k1).
|
|
|
|
|
|
var comb10MulTo = function comb10MulTo(self, num, out) {
|
|
var a = self.words;
|
|
var b = num.words;
|
|
var o = out.words;
|
|
var c = 0;
|
|
var lo;
|
|
var mid;
|
|
var hi;
|
|
var a0 = a[0] | 0;
|
|
var al0 = a0 & 0x1fff;
|
|
var ah0 = a0 >>> 13;
|
|
var a1 = a[1] | 0;
|
|
var al1 = a1 & 0x1fff;
|
|
var ah1 = a1 >>> 13;
|
|
var a2 = a[2] | 0;
|
|
var al2 = a2 & 0x1fff;
|
|
var ah2 = a2 >>> 13;
|
|
var a3 = a[3] | 0;
|
|
var al3 = a3 & 0x1fff;
|
|
var ah3 = a3 >>> 13;
|
|
var a4 = a[4] | 0;
|
|
var al4 = a4 & 0x1fff;
|
|
var ah4 = a4 >>> 13;
|
|
var a5 = a[5] | 0;
|
|
var al5 = a5 & 0x1fff;
|
|
var ah5 = a5 >>> 13;
|
|
var a6 = a[6] | 0;
|
|
var al6 = a6 & 0x1fff;
|
|
var ah6 = a6 >>> 13;
|
|
var a7 = a[7] | 0;
|
|
var al7 = a7 & 0x1fff;
|
|
var ah7 = a7 >>> 13;
|
|
var a8 = a[8] | 0;
|
|
var al8 = a8 & 0x1fff;
|
|
var ah8 = a8 >>> 13;
|
|
var a9 = a[9] | 0;
|
|
var al9 = a9 & 0x1fff;
|
|
var ah9 = a9 >>> 13;
|
|
var b0 = b[0] | 0;
|
|
var bl0 = b0 & 0x1fff;
|
|
var bh0 = b0 >>> 13;
|
|
var b1 = b[1] | 0;
|
|
var bl1 = b1 & 0x1fff;
|
|
var bh1 = b1 >>> 13;
|
|
var b2 = b[2] | 0;
|
|
var bl2 = b2 & 0x1fff;
|
|
var bh2 = b2 >>> 13;
|
|
var b3 = b[3] | 0;
|
|
var bl3 = b3 & 0x1fff;
|
|
var bh3 = b3 >>> 13;
|
|
var b4 = b[4] | 0;
|
|
var bl4 = b4 & 0x1fff;
|
|
var bh4 = b4 >>> 13;
|
|
var b5 = b[5] | 0;
|
|
var bl5 = b5 & 0x1fff;
|
|
var bh5 = b5 >>> 13;
|
|
var b6 = b[6] | 0;
|
|
var bl6 = b6 & 0x1fff;
|
|
var bh6 = b6 >>> 13;
|
|
var b7 = b[7] | 0;
|
|
var bl7 = b7 & 0x1fff;
|
|
var bh7 = b7 >>> 13;
|
|
var b8 = b[8] | 0;
|
|
var bl8 = b8 & 0x1fff;
|
|
var bh8 = b8 >>> 13;
|
|
var b9 = b[9] | 0;
|
|
var bl9 = b9 & 0x1fff;
|
|
var bh9 = b9 >>> 13;
|
|
out.negative = self.negative ^ num.negative;
|
|
out.length = 19;
|
|
/* k = 0 */
|
|
|
|
lo = Math.imul(al0, bl0);
|
|
mid = Math.imul(al0, bh0);
|
|
mid = mid + Math.imul(ah0, bl0) | 0;
|
|
hi = Math.imul(ah0, bh0);
|
|
var w0 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w0 >>> 26) | 0;
|
|
w0 &= 0x3ffffff;
|
|
/* k = 1 */
|
|
|
|
lo = Math.imul(al1, bl0);
|
|
mid = Math.imul(al1, bh0);
|
|
mid = mid + Math.imul(ah1, bl0) | 0;
|
|
hi = Math.imul(ah1, bh0);
|
|
lo = lo + Math.imul(al0, bl1) | 0;
|
|
mid = mid + Math.imul(al0, bh1) | 0;
|
|
mid = mid + Math.imul(ah0, bl1) | 0;
|
|
hi = hi + Math.imul(ah0, bh1) | 0;
|
|
var w1 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w1 >>> 26) | 0;
|
|
w1 &= 0x3ffffff;
|
|
/* k = 2 */
|
|
|
|
lo = Math.imul(al2, bl0);
|
|
mid = Math.imul(al2, bh0);
|
|
mid = mid + Math.imul(ah2, bl0) | 0;
|
|
hi = Math.imul(ah2, bh0);
|
|
lo = lo + Math.imul(al1, bl1) | 0;
|
|
mid = mid + Math.imul(al1, bh1) | 0;
|
|
mid = mid + Math.imul(ah1, bl1) | 0;
|
|
hi = hi + Math.imul(ah1, bh1) | 0;
|
|
lo = lo + Math.imul(al0, bl2) | 0;
|
|
mid = mid + Math.imul(al0, bh2) | 0;
|
|
mid = mid + Math.imul(ah0, bl2) | 0;
|
|
hi = hi + Math.imul(ah0, bh2) | 0;
|
|
var w2 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w2 >>> 26) | 0;
|
|
w2 &= 0x3ffffff;
|
|
/* k = 3 */
|
|
|
|
lo = Math.imul(al3, bl0);
|
|
mid = Math.imul(al3, bh0);
|
|
mid = mid + Math.imul(ah3, bl0) | 0;
|
|
hi = Math.imul(ah3, bh0);
|
|
lo = lo + Math.imul(al2, bl1) | 0;
|
|
mid = mid + Math.imul(al2, bh1) | 0;
|
|
mid = mid + Math.imul(ah2, bl1) | 0;
|
|
hi = hi + Math.imul(ah2, bh1) | 0;
|
|
lo = lo + Math.imul(al1, bl2) | 0;
|
|
mid = mid + Math.imul(al1, bh2) | 0;
|
|
mid = mid + Math.imul(ah1, bl2) | 0;
|
|
hi = hi + Math.imul(ah1, bh2) | 0;
|
|
lo = lo + Math.imul(al0, bl3) | 0;
|
|
mid = mid + Math.imul(al0, bh3) | 0;
|
|
mid = mid + Math.imul(ah0, bl3) | 0;
|
|
hi = hi + Math.imul(ah0, bh3) | 0;
|
|
var w3 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w3 >>> 26) | 0;
|
|
w3 &= 0x3ffffff;
|
|
/* k = 4 */
|
|
|
|
lo = Math.imul(al4, bl0);
|
|
mid = Math.imul(al4, bh0);
|
|
mid = mid + Math.imul(ah4, bl0) | 0;
|
|
hi = Math.imul(ah4, bh0);
|
|
lo = lo + Math.imul(al3, bl1) | 0;
|
|
mid = mid + Math.imul(al3, bh1) | 0;
|
|
mid = mid + Math.imul(ah3, bl1) | 0;
|
|
hi = hi + Math.imul(ah3, bh1) | 0;
|
|
lo = lo + Math.imul(al2, bl2) | 0;
|
|
mid = mid + Math.imul(al2, bh2) | 0;
|
|
mid = mid + Math.imul(ah2, bl2) | 0;
|
|
hi = hi + Math.imul(ah2, bh2) | 0;
|
|
lo = lo + Math.imul(al1, bl3) | 0;
|
|
mid = mid + Math.imul(al1, bh3) | 0;
|
|
mid = mid + Math.imul(ah1, bl3) | 0;
|
|
hi = hi + Math.imul(ah1, bh3) | 0;
|
|
lo = lo + Math.imul(al0, bl4) | 0;
|
|
mid = mid + Math.imul(al0, bh4) | 0;
|
|
mid = mid + Math.imul(ah0, bl4) | 0;
|
|
hi = hi + Math.imul(ah0, bh4) | 0;
|
|
var w4 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w4 >>> 26) | 0;
|
|
w4 &= 0x3ffffff;
|
|
/* k = 5 */
|
|
|
|
lo = Math.imul(al5, bl0);
|
|
mid = Math.imul(al5, bh0);
|
|
mid = mid + Math.imul(ah5, bl0) | 0;
|
|
hi = Math.imul(ah5, bh0);
|
|
lo = lo + Math.imul(al4, bl1) | 0;
|
|
mid = mid + Math.imul(al4, bh1) | 0;
|
|
mid = mid + Math.imul(ah4, bl1) | 0;
|
|
hi = hi + Math.imul(ah4, bh1) | 0;
|
|
lo = lo + Math.imul(al3, bl2) | 0;
|
|
mid = mid + Math.imul(al3, bh2) | 0;
|
|
mid = mid + Math.imul(ah3, bl2) | 0;
|
|
hi = hi + Math.imul(ah3, bh2) | 0;
|
|
lo = lo + Math.imul(al2, bl3) | 0;
|
|
mid = mid + Math.imul(al2, bh3) | 0;
|
|
mid = mid + Math.imul(ah2, bl3) | 0;
|
|
hi = hi + Math.imul(ah2, bh3) | 0;
|
|
lo = lo + Math.imul(al1, bl4) | 0;
|
|
mid = mid + Math.imul(al1, bh4) | 0;
|
|
mid = mid + Math.imul(ah1, bl4) | 0;
|
|
hi = hi + Math.imul(ah1, bh4) | 0;
|
|
lo = lo + Math.imul(al0, bl5) | 0;
|
|
mid = mid + Math.imul(al0, bh5) | 0;
|
|
mid = mid + Math.imul(ah0, bl5) | 0;
|
|
hi = hi + Math.imul(ah0, bh5) | 0;
|
|
var w5 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w5 >>> 26) | 0;
|
|
w5 &= 0x3ffffff;
|
|
/* k = 6 */
|
|
|
|
lo = Math.imul(al6, bl0);
|
|
mid = Math.imul(al6, bh0);
|
|
mid = mid + Math.imul(ah6, bl0) | 0;
|
|
hi = Math.imul(ah6, bh0);
|
|
lo = lo + Math.imul(al5, bl1) | 0;
|
|
mid = mid + Math.imul(al5, bh1) | 0;
|
|
mid = mid + Math.imul(ah5, bl1) | 0;
|
|
hi = hi + Math.imul(ah5, bh1) | 0;
|
|
lo = lo + Math.imul(al4, bl2) | 0;
|
|
mid = mid + Math.imul(al4, bh2) | 0;
|
|
mid = mid + Math.imul(ah4, bl2) | 0;
|
|
hi = hi + Math.imul(ah4, bh2) | 0;
|
|
lo = lo + Math.imul(al3, bl3) | 0;
|
|
mid = mid + Math.imul(al3, bh3) | 0;
|
|
mid = mid + Math.imul(ah3, bl3) | 0;
|
|
hi = hi + Math.imul(ah3, bh3) | 0;
|
|
lo = lo + Math.imul(al2, bl4) | 0;
|
|
mid = mid + Math.imul(al2, bh4) | 0;
|
|
mid = mid + Math.imul(ah2, bl4) | 0;
|
|
hi = hi + Math.imul(ah2, bh4) | 0;
|
|
lo = lo + Math.imul(al1, bl5) | 0;
|
|
mid = mid + Math.imul(al1, bh5) | 0;
|
|
mid = mid + Math.imul(ah1, bl5) | 0;
|
|
hi = hi + Math.imul(ah1, bh5) | 0;
|
|
lo = lo + Math.imul(al0, bl6) | 0;
|
|
mid = mid + Math.imul(al0, bh6) | 0;
|
|
mid = mid + Math.imul(ah0, bl6) | 0;
|
|
hi = hi + Math.imul(ah0, bh6) | 0;
|
|
var w6 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w6 >>> 26) | 0;
|
|
w6 &= 0x3ffffff;
|
|
/* k = 7 */
|
|
|
|
lo = Math.imul(al7, bl0);
|
|
mid = Math.imul(al7, bh0);
|
|
mid = mid + Math.imul(ah7, bl0) | 0;
|
|
hi = Math.imul(ah7, bh0);
|
|
lo = lo + Math.imul(al6, bl1) | 0;
|
|
mid = mid + Math.imul(al6, bh1) | 0;
|
|
mid = mid + Math.imul(ah6, bl1) | 0;
|
|
hi = hi + Math.imul(ah6, bh1) | 0;
|
|
lo = lo + Math.imul(al5, bl2) | 0;
|
|
mid = mid + Math.imul(al5, bh2) | 0;
|
|
mid = mid + Math.imul(ah5, bl2) | 0;
|
|
hi = hi + Math.imul(ah5, bh2) | 0;
|
|
lo = lo + Math.imul(al4, bl3) | 0;
|
|
mid = mid + Math.imul(al4, bh3) | 0;
|
|
mid = mid + Math.imul(ah4, bl3) | 0;
|
|
hi = hi + Math.imul(ah4, bh3) | 0;
|
|
lo = lo + Math.imul(al3, bl4) | 0;
|
|
mid = mid + Math.imul(al3, bh4) | 0;
|
|
mid = mid + Math.imul(ah3, bl4) | 0;
|
|
hi = hi + Math.imul(ah3, bh4) | 0;
|
|
lo = lo + Math.imul(al2, bl5) | 0;
|
|
mid = mid + Math.imul(al2, bh5) | 0;
|
|
mid = mid + Math.imul(ah2, bl5) | 0;
|
|
hi = hi + Math.imul(ah2, bh5) | 0;
|
|
lo = lo + Math.imul(al1, bl6) | 0;
|
|
mid = mid + Math.imul(al1, bh6) | 0;
|
|
mid = mid + Math.imul(ah1, bl6) | 0;
|
|
hi = hi + Math.imul(ah1, bh6) | 0;
|
|
lo = lo + Math.imul(al0, bl7) | 0;
|
|
mid = mid + Math.imul(al0, bh7) | 0;
|
|
mid = mid + Math.imul(ah0, bl7) | 0;
|
|
hi = hi + Math.imul(ah0, bh7) | 0;
|
|
var w7 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w7 >>> 26) | 0;
|
|
w7 &= 0x3ffffff;
|
|
/* k = 8 */
|
|
|
|
lo = Math.imul(al8, bl0);
|
|
mid = Math.imul(al8, bh0);
|
|
mid = mid + Math.imul(ah8, bl0) | 0;
|
|
hi = Math.imul(ah8, bh0);
|
|
lo = lo + Math.imul(al7, bl1) | 0;
|
|
mid = mid + Math.imul(al7, bh1) | 0;
|
|
mid = mid + Math.imul(ah7, bl1) | 0;
|
|
hi = hi + Math.imul(ah7, bh1) | 0;
|
|
lo = lo + Math.imul(al6, bl2) | 0;
|
|
mid = mid + Math.imul(al6, bh2) | 0;
|
|
mid = mid + Math.imul(ah6, bl2) | 0;
|
|
hi = hi + Math.imul(ah6, bh2) | 0;
|
|
lo = lo + Math.imul(al5, bl3) | 0;
|
|
mid = mid + Math.imul(al5, bh3) | 0;
|
|
mid = mid + Math.imul(ah5, bl3) | 0;
|
|
hi = hi + Math.imul(ah5, bh3) | 0;
|
|
lo = lo + Math.imul(al4, bl4) | 0;
|
|
mid = mid + Math.imul(al4, bh4) | 0;
|
|
mid = mid + Math.imul(ah4, bl4) | 0;
|
|
hi = hi + Math.imul(ah4, bh4) | 0;
|
|
lo = lo + Math.imul(al3, bl5) | 0;
|
|
mid = mid + Math.imul(al3, bh5) | 0;
|
|
mid = mid + Math.imul(ah3, bl5) | 0;
|
|
hi = hi + Math.imul(ah3, bh5) | 0;
|
|
lo = lo + Math.imul(al2, bl6) | 0;
|
|
mid = mid + Math.imul(al2, bh6) | 0;
|
|
mid = mid + Math.imul(ah2, bl6) | 0;
|
|
hi = hi + Math.imul(ah2, bh6) | 0;
|
|
lo = lo + Math.imul(al1, bl7) | 0;
|
|
mid = mid + Math.imul(al1, bh7) | 0;
|
|
mid = mid + Math.imul(ah1, bl7) | 0;
|
|
hi = hi + Math.imul(ah1, bh7) | 0;
|
|
lo = lo + Math.imul(al0, bl8) | 0;
|
|
mid = mid + Math.imul(al0, bh8) | 0;
|
|
mid = mid + Math.imul(ah0, bl8) | 0;
|
|
hi = hi + Math.imul(ah0, bh8) | 0;
|
|
var w8 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w8 >>> 26) | 0;
|
|
w8 &= 0x3ffffff;
|
|
/* k = 9 */
|
|
|
|
lo = Math.imul(al9, bl0);
|
|
mid = Math.imul(al9, bh0);
|
|
mid = mid + Math.imul(ah9, bl0) | 0;
|
|
hi = Math.imul(ah9, bh0);
|
|
lo = lo + Math.imul(al8, bl1) | 0;
|
|
mid = mid + Math.imul(al8, bh1) | 0;
|
|
mid = mid + Math.imul(ah8, bl1) | 0;
|
|
hi = hi + Math.imul(ah8, bh1) | 0;
|
|
lo = lo + Math.imul(al7, bl2) | 0;
|
|
mid = mid + Math.imul(al7, bh2) | 0;
|
|
mid = mid + Math.imul(ah7, bl2) | 0;
|
|
hi = hi + Math.imul(ah7, bh2) | 0;
|
|
lo = lo + Math.imul(al6, bl3) | 0;
|
|
mid = mid + Math.imul(al6, bh3) | 0;
|
|
mid = mid + Math.imul(ah6, bl3) | 0;
|
|
hi = hi + Math.imul(ah6, bh3) | 0;
|
|
lo = lo + Math.imul(al5, bl4) | 0;
|
|
mid = mid + Math.imul(al5, bh4) | 0;
|
|
mid = mid + Math.imul(ah5, bl4) | 0;
|
|
hi = hi + Math.imul(ah5, bh4) | 0;
|
|
lo = lo + Math.imul(al4, bl5) | 0;
|
|
mid = mid + Math.imul(al4, bh5) | 0;
|
|
mid = mid + Math.imul(ah4, bl5) | 0;
|
|
hi = hi + Math.imul(ah4, bh5) | 0;
|
|
lo = lo + Math.imul(al3, bl6) | 0;
|
|
mid = mid + Math.imul(al3, bh6) | 0;
|
|
mid = mid + Math.imul(ah3, bl6) | 0;
|
|
hi = hi + Math.imul(ah3, bh6) | 0;
|
|
lo = lo + Math.imul(al2, bl7) | 0;
|
|
mid = mid + Math.imul(al2, bh7) | 0;
|
|
mid = mid + Math.imul(ah2, bl7) | 0;
|
|
hi = hi + Math.imul(ah2, bh7) | 0;
|
|
lo = lo + Math.imul(al1, bl8) | 0;
|
|
mid = mid + Math.imul(al1, bh8) | 0;
|
|
mid = mid + Math.imul(ah1, bl8) | 0;
|
|
hi = hi + Math.imul(ah1, bh8) | 0;
|
|
lo = lo + Math.imul(al0, bl9) | 0;
|
|
mid = mid + Math.imul(al0, bh9) | 0;
|
|
mid = mid + Math.imul(ah0, bl9) | 0;
|
|
hi = hi + Math.imul(ah0, bh9) | 0;
|
|
var w9 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w9 >>> 26) | 0;
|
|
w9 &= 0x3ffffff;
|
|
/* k = 10 */
|
|
|
|
lo = Math.imul(al9, bl1);
|
|
mid = Math.imul(al9, bh1);
|
|
mid = mid + Math.imul(ah9, bl1) | 0;
|
|
hi = Math.imul(ah9, bh1);
|
|
lo = lo + Math.imul(al8, bl2) | 0;
|
|
mid = mid + Math.imul(al8, bh2) | 0;
|
|
mid = mid + Math.imul(ah8, bl2) | 0;
|
|
hi = hi + Math.imul(ah8, bh2) | 0;
|
|
lo = lo + Math.imul(al7, bl3) | 0;
|
|
mid = mid + Math.imul(al7, bh3) | 0;
|
|
mid = mid + Math.imul(ah7, bl3) | 0;
|
|
hi = hi + Math.imul(ah7, bh3) | 0;
|
|
lo = lo + Math.imul(al6, bl4) | 0;
|
|
mid = mid + Math.imul(al6, bh4) | 0;
|
|
mid = mid + Math.imul(ah6, bl4) | 0;
|
|
hi = hi + Math.imul(ah6, bh4) | 0;
|
|
lo = lo + Math.imul(al5, bl5) | 0;
|
|
mid = mid + Math.imul(al5, bh5) | 0;
|
|
mid = mid + Math.imul(ah5, bl5) | 0;
|
|
hi = hi + Math.imul(ah5, bh5) | 0;
|
|
lo = lo + Math.imul(al4, bl6) | 0;
|
|
mid = mid + Math.imul(al4, bh6) | 0;
|
|
mid = mid + Math.imul(ah4, bl6) | 0;
|
|
hi = hi + Math.imul(ah4, bh6) | 0;
|
|
lo = lo + Math.imul(al3, bl7) | 0;
|
|
mid = mid + Math.imul(al3, bh7) | 0;
|
|
mid = mid + Math.imul(ah3, bl7) | 0;
|
|
hi = hi + Math.imul(ah3, bh7) | 0;
|
|
lo = lo + Math.imul(al2, bl8) | 0;
|
|
mid = mid + Math.imul(al2, bh8) | 0;
|
|
mid = mid + Math.imul(ah2, bl8) | 0;
|
|
hi = hi + Math.imul(ah2, bh8) | 0;
|
|
lo = lo + Math.imul(al1, bl9) | 0;
|
|
mid = mid + Math.imul(al1, bh9) | 0;
|
|
mid = mid + Math.imul(ah1, bl9) | 0;
|
|
hi = hi + Math.imul(ah1, bh9) | 0;
|
|
var w10 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w10 >>> 26) | 0;
|
|
w10 &= 0x3ffffff;
|
|
/* k = 11 */
|
|
|
|
lo = Math.imul(al9, bl2);
|
|
mid = Math.imul(al9, bh2);
|
|
mid = mid + Math.imul(ah9, bl2) | 0;
|
|
hi = Math.imul(ah9, bh2);
|
|
lo = lo + Math.imul(al8, bl3) | 0;
|
|
mid = mid + Math.imul(al8, bh3) | 0;
|
|
mid = mid + Math.imul(ah8, bl3) | 0;
|
|
hi = hi + Math.imul(ah8, bh3) | 0;
|
|
lo = lo + Math.imul(al7, bl4) | 0;
|
|
mid = mid + Math.imul(al7, bh4) | 0;
|
|
mid = mid + Math.imul(ah7, bl4) | 0;
|
|
hi = hi + Math.imul(ah7, bh4) | 0;
|
|
lo = lo + Math.imul(al6, bl5) | 0;
|
|
mid = mid + Math.imul(al6, bh5) | 0;
|
|
mid = mid + Math.imul(ah6, bl5) | 0;
|
|
hi = hi + Math.imul(ah6, bh5) | 0;
|
|
lo = lo + Math.imul(al5, bl6) | 0;
|
|
mid = mid + Math.imul(al5, bh6) | 0;
|
|
mid = mid + Math.imul(ah5, bl6) | 0;
|
|
hi = hi + Math.imul(ah5, bh6) | 0;
|
|
lo = lo + Math.imul(al4, bl7) | 0;
|
|
mid = mid + Math.imul(al4, bh7) | 0;
|
|
mid = mid + Math.imul(ah4, bl7) | 0;
|
|
hi = hi + Math.imul(ah4, bh7) | 0;
|
|
lo = lo + Math.imul(al3, bl8) | 0;
|
|
mid = mid + Math.imul(al3, bh8) | 0;
|
|
mid = mid + Math.imul(ah3, bl8) | 0;
|
|
hi = hi + Math.imul(ah3, bh8) | 0;
|
|
lo = lo + Math.imul(al2, bl9) | 0;
|
|
mid = mid + Math.imul(al2, bh9) | 0;
|
|
mid = mid + Math.imul(ah2, bl9) | 0;
|
|
hi = hi + Math.imul(ah2, bh9) | 0;
|
|
var w11 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w11 >>> 26) | 0;
|
|
w11 &= 0x3ffffff;
|
|
/* k = 12 */
|
|
|
|
lo = Math.imul(al9, bl3);
|
|
mid = Math.imul(al9, bh3);
|
|
mid = mid + Math.imul(ah9, bl3) | 0;
|
|
hi = Math.imul(ah9, bh3);
|
|
lo = lo + Math.imul(al8, bl4) | 0;
|
|
mid = mid + Math.imul(al8, bh4) | 0;
|
|
mid = mid + Math.imul(ah8, bl4) | 0;
|
|
hi = hi + Math.imul(ah8, bh4) | 0;
|
|
lo = lo + Math.imul(al7, bl5) | 0;
|
|
mid = mid + Math.imul(al7, bh5) | 0;
|
|
mid = mid + Math.imul(ah7, bl5) | 0;
|
|
hi = hi + Math.imul(ah7, bh5) | 0;
|
|
lo = lo + Math.imul(al6, bl6) | 0;
|
|
mid = mid + Math.imul(al6, bh6) | 0;
|
|
mid = mid + Math.imul(ah6, bl6) | 0;
|
|
hi = hi + Math.imul(ah6, bh6) | 0;
|
|
lo = lo + Math.imul(al5, bl7) | 0;
|
|
mid = mid + Math.imul(al5, bh7) | 0;
|
|
mid = mid + Math.imul(ah5, bl7) | 0;
|
|
hi = hi + Math.imul(ah5, bh7) | 0;
|
|
lo = lo + Math.imul(al4, bl8) | 0;
|
|
mid = mid + Math.imul(al4, bh8) | 0;
|
|
mid = mid + Math.imul(ah4, bl8) | 0;
|
|
hi = hi + Math.imul(ah4, bh8) | 0;
|
|
lo = lo + Math.imul(al3, bl9) | 0;
|
|
mid = mid + Math.imul(al3, bh9) | 0;
|
|
mid = mid + Math.imul(ah3, bl9) | 0;
|
|
hi = hi + Math.imul(ah3, bh9) | 0;
|
|
var w12 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w12 >>> 26) | 0;
|
|
w12 &= 0x3ffffff;
|
|
/* k = 13 */
|
|
|
|
lo = Math.imul(al9, bl4);
|
|
mid = Math.imul(al9, bh4);
|
|
mid = mid + Math.imul(ah9, bl4) | 0;
|
|
hi = Math.imul(ah9, bh4);
|
|
lo = lo + Math.imul(al8, bl5) | 0;
|
|
mid = mid + Math.imul(al8, bh5) | 0;
|
|
mid = mid + Math.imul(ah8, bl5) | 0;
|
|
hi = hi + Math.imul(ah8, bh5) | 0;
|
|
lo = lo + Math.imul(al7, bl6) | 0;
|
|
mid = mid + Math.imul(al7, bh6) | 0;
|
|
mid = mid + Math.imul(ah7, bl6) | 0;
|
|
hi = hi + Math.imul(ah7, bh6) | 0;
|
|
lo = lo + Math.imul(al6, bl7) | 0;
|
|
mid = mid + Math.imul(al6, bh7) | 0;
|
|
mid = mid + Math.imul(ah6, bl7) | 0;
|
|
hi = hi + Math.imul(ah6, bh7) | 0;
|
|
lo = lo + Math.imul(al5, bl8) | 0;
|
|
mid = mid + Math.imul(al5, bh8) | 0;
|
|
mid = mid + Math.imul(ah5, bl8) | 0;
|
|
hi = hi + Math.imul(ah5, bh8) | 0;
|
|
lo = lo + Math.imul(al4, bl9) | 0;
|
|
mid = mid + Math.imul(al4, bh9) | 0;
|
|
mid = mid + Math.imul(ah4, bl9) | 0;
|
|
hi = hi + Math.imul(ah4, bh9) | 0;
|
|
var w13 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w13 >>> 26) | 0;
|
|
w13 &= 0x3ffffff;
|
|
/* k = 14 */
|
|
|
|
lo = Math.imul(al9, bl5);
|
|
mid = Math.imul(al9, bh5);
|
|
mid = mid + Math.imul(ah9, bl5) | 0;
|
|
hi = Math.imul(ah9, bh5);
|
|
lo = lo + Math.imul(al8, bl6) | 0;
|
|
mid = mid + Math.imul(al8, bh6) | 0;
|
|
mid = mid + Math.imul(ah8, bl6) | 0;
|
|
hi = hi + Math.imul(ah8, bh6) | 0;
|
|
lo = lo + Math.imul(al7, bl7) | 0;
|
|
mid = mid + Math.imul(al7, bh7) | 0;
|
|
mid = mid + Math.imul(ah7, bl7) | 0;
|
|
hi = hi + Math.imul(ah7, bh7) | 0;
|
|
lo = lo + Math.imul(al6, bl8) | 0;
|
|
mid = mid + Math.imul(al6, bh8) | 0;
|
|
mid = mid + Math.imul(ah6, bl8) | 0;
|
|
hi = hi + Math.imul(ah6, bh8) | 0;
|
|
lo = lo + Math.imul(al5, bl9) | 0;
|
|
mid = mid + Math.imul(al5, bh9) | 0;
|
|
mid = mid + Math.imul(ah5, bl9) | 0;
|
|
hi = hi + Math.imul(ah5, bh9) | 0;
|
|
var w14 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w14 >>> 26) | 0;
|
|
w14 &= 0x3ffffff;
|
|
/* k = 15 */
|
|
|
|
lo = Math.imul(al9, bl6);
|
|
mid = Math.imul(al9, bh6);
|
|
mid = mid + Math.imul(ah9, bl6) | 0;
|
|
hi = Math.imul(ah9, bh6);
|
|
lo = lo + Math.imul(al8, bl7) | 0;
|
|
mid = mid + Math.imul(al8, bh7) | 0;
|
|
mid = mid + Math.imul(ah8, bl7) | 0;
|
|
hi = hi + Math.imul(ah8, bh7) | 0;
|
|
lo = lo + Math.imul(al7, bl8) | 0;
|
|
mid = mid + Math.imul(al7, bh8) | 0;
|
|
mid = mid + Math.imul(ah7, bl8) | 0;
|
|
hi = hi + Math.imul(ah7, bh8) | 0;
|
|
lo = lo + Math.imul(al6, bl9) | 0;
|
|
mid = mid + Math.imul(al6, bh9) | 0;
|
|
mid = mid + Math.imul(ah6, bl9) | 0;
|
|
hi = hi + Math.imul(ah6, bh9) | 0;
|
|
var w15 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w15 >>> 26) | 0;
|
|
w15 &= 0x3ffffff;
|
|
/* k = 16 */
|
|
|
|
lo = Math.imul(al9, bl7);
|
|
mid = Math.imul(al9, bh7);
|
|
mid = mid + Math.imul(ah9, bl7) | 0;
|
|
hi = Math.imul(ah9, bh7);
|
|
lo = lo + Math.imul(al8, bl8) | 0;
|
|
mid = mid + Math.imul(al8, bh8) | 0;
|
|
mid = mid + Math.imul(ah8, bl8) | 0;
|
|
hi = hi + Math.imul(ah8, bh8) | 0;
|
|
lo = lo + Math.imul(al7, bl9) | 0;
|
|
mid = mid + Math.imul(al7, bh9) | 0;
|
|
mid = mid + Math.imul(ah7, bl9) | 0;
|
|
hi = hi + Math.imul(ah7, bh9) | 0;
|
|
var w16 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w16 >>> 26) | 0;
|
|
w16 &= 0x3ffffff;
|
|
/* k = 17 */
|
|
|
|
lo = Math.imul(al9, bl8);
|
|
mid = Math.imul(al9, bh8);
|
|
mid = mid + Math.imul(ah9, bl8) | 0;
|
|
hi = Math.imul(ah9, bh8);
|
|
lo = lo + Math.imul(al8, bl9) | 0;
|
|
mid = mid + Math.imul(al8, bh9) | 0;
|
|
mid = mid + Math.imul(ah8, bl9) | 0;
|
|
hi = hi + Math.imul(ah8, bh9) | 0;
|
|
var w17 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w17 >>> 26) | 0;
|
|
w17 &= 0x3ffffff;
|
|
/* k = 18 */
|
|
|
|
lo = Math.imul(al9, bl9);
|
|
mid = Math.imul(al9, bh9);
|
|
mid = mid + Math.imul(ah9, bl9) | 0;
|
|
hi = Math.imul(ah9, bh9);
|
|
var w18 = (c + lo | 0) + ((mid & 0x1fff) << 13) | 0;
|
|
c = (hi + (mid >>> 13) | 0) + (w18 >>> 26) | 0;
|
|
w18 &= 0x3ffffff;
|
|
o[0] = w0;
|
|
o[1] = w1;
|
|
o[2] = w2;
|
|
o[3] = w3;
|
|
o[4] = w4;
|
|
o[5] = w5;
|
|
o[6] = w6;
|
|
o[7] = w7;
|
|
o[8] = w8;
|
|
o[9] = w9;
|
|
o[10] = w10;
|
|
o[11] = w11;
|
|
o[12] = w12;
|
|
o[13] = w13;
|
|
o[14] = w14;
|
|
o[15] = w15;
|
|
o[16] = w16;
|
|
o[17] = w17;
|
|
o[18] = w18;
|
|
|
|
if (c !== 0) {
|
|
o[19] = c;
|
|
out.length++;
|
|
}
|
|
|
|
return out;
|
|
}; // Polyfill comb
|
|
|
|
|
|
if (!Math.imul) {
|
|
comb10MulTo = smallMulTo;
|
|
}
|
|
|
|
function bigMulTo(self, num, out) {
|
|
out.negative = num.negative ^ self.negative;
|
|
out.length = self.length + num.length;
|
|
var carry = 0;
|
|
var hncarry = 0;
|
|
|
|
for (var k = 0; k < out.length - 1; k++) {
|
|
// Sum all words with the same `i + j = k` and accumulate `ncarry`,
|
|
// note that ncarry could be >= 0x3ffffff
|
|
var ncarry = hncarry;
|
|
hncarry = 0;
|
|
var rword = carry & 0x3ffffff;
|
|
var maxJ = Math.min(k, num.length - 1);
|
|
|
|
for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) {
|
|
var i = k - j;
|
|
var a = self.words[i] | 0;
|
|
var b = num.words[j] | 0;
|
|
var r = a * b;
|
|
var lo = r & 0x3ffffff;
|
|
ncarry = ncarry + (r / 0x4000000 | 0) | 0;
|
|
lo = lo + rword | 0;
|
|
rword = lo & 0x3ffffff;
|
|
ncarry = ncarry + (lo >>> 26) | 0;
|
|
hncarry += ncarry >>> 26;
|
|
ncarry &= 0x3ffffff;
|
|
}
|
|
|
|
out.words[k] = rword;
|
|
carry = ncarry;
|
|
ncarry = hncarry;
|
|
}
|
|
|
|
if (carry !== 0) {
|
|
out.words[k] = carry;
|
|
} else {
|
|
out.length--;
|
|
}
|
|
|
|
return out.strip();
|
|
}
|
|
|
|
function jumboMulTo(self, num, out) {
|
|
var fftm = new FFTM();
|
|
return fftm.mulp(self, num, out);
|
|
}
|
|
|
|
BN.prototype.mulTo = function mulTo(num, out) {
|
|
var res;
|
|
var len = this.length + num.length;
|
|
|
|
if (this.length === 10 && num.length === 10) {
|
|
res = comb10MulTo(this, num, out);
|
|
} else if (len < 63) {
|
|
res = smallMulTo(this, num, out);
|
|
} else if (len < 1024) {
|
|
res = bigMulTo(this, num, out);
|
|
} else {
|
|
res = jumboMulTo(this, num, out);
|
|
}
|
|
|
|
return res;
|
|
}; // Cooley-Tukey algorithm for FFT
|
|
// slightly revisited to rely on looping instead of recursion
|
|
|
|
|
|
function FFTM(x, y) {
|
|
this.x = x;
|
|
this.y = y;
|
|
}
|
|
|
|
FFTM.prototype.makeRBT = function makeRBT(N) {
|
|
var t = new Array(N);
|
|
var l = BN.prototype._countBits(N) - 1;
|
|
|
|
for (var i = 0; i < N; i++) {
|
|
t[i] = this.revBin(i, l, N);
|
|
}
|
|
|
|
return t;
|
|
}; // Returns binary-reversed representation of `x`
|
|
|
|
|
|
FFTM.prototype.revBin = function revBin(x, l, N) {
|
|
if (x === 0 || x === N - 1) return x;
|
|
var rb = 0;
|
|
|
|
for (var i = 0; i < l; i++) {
|
|
rb |= (x & 1) << l - i - 1;
|
|
x >>= 1;
|
|
}
|
|
|
|
return rb;
|
|
}; // Performs "tweedling" phase, therefore 'emulating'
|
|
// behaviour of the recursive algorithm
|
|
|
|
|
|
FFTM.prototype.permute = function permute(rbt, rws, iws, rtws, itws, N) {
|
|
for (var i = 0; i < N; i++) {
|
|
rtws[i] = rws[rbt[i]];
|
|
itws[i] = iws[rbt[i]];
|
|
}
|
|
};
|
|
|
|
FFTM.prototype.transform = function transform(rws, iws, rtws, itws, N, rbt) {
|
|
this.permute(rbt, rws, iws, rtws, itws, N);
|
|
|
|
for (var s = 1; s < N; s <<= 1) {
|
|
var l = s << 1;
|
|
var rtwdf = Math.cos(2 * Math.PI / l);
|
|
var itwdf = Math.sin(2 * Math.PI / l);
|
|
|
|
for (var p = 0; p < N; p += l) {
|
|
var rtwdf_ = rtwdf;
|
|
var itwdf_ = itwdf;
|
|
|
|
for (var j = 0; j < s; j++) {
|
|
var re = rtws[p + j];
|
|
var ie = itws[p + j];
|
|
var ro = rtws[p + j + s];
|
|
var io = itws[p + j + s];
|
|
var rx = rtwdf_ * ro - itwdf_ * io;
|
|
io = rtwdf_ * io + itwdf_ * ro;
|
|
ro = rx;
|
|
rtws[p + j] = re + ro;
|
|
itws[p + j] = ie + io;
|
|
rtws[p + j + s] = re - ro;
|
|
itws[p + j + s] = ie - io;
|
|
/* jshint maxdepth : false */
|
|
|
|
if (j !== l) {
|
|
rx = rtwdf * rtwdf_ - itwdf * itwdf_;
|
|
itwdf_ = rtwdf * itwdf_ + itwdf * rtwdf_;
|
|
rtwdf_ = rx;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
};
|
|
|
|
FFTM.prototype.guessLen13b = function guessLen13b(n, m) {
|
|
var N = Math.max(m, n) | 1;
|
|
var odd = N & 1;
|
|
var i = 0;
|
|
|
|
for (N = N / 2 | 0; N; N = N >>> 1) {
|
|
i++;
|
|
}
|
|
|
|
return 1 << i + 1 + odd;
|
|
};
|
|
|
|
FFTM.prototype.conjugate = function conjugate(rws, iws, N) {
|
|
if (N <= 1) return;
|
|
|
|
for (var i = 0; i < N / 2; i++) {
|
|
var t = rws[i];
|
|
rws[i] = rws[N - i - 1];
|
|
rws[N - i - 1] = t;
|
|
t = iws[i];
|
|
iws[i] = -iws[N - i - 1];
|
|
iws[N - i - 1] = -t;
|
|
}
|
|
};
|
|
|
|
FFTM.prototype.normalize13b = function normalize13b(ws, N) {
|
|
var carry = 0;
|
|
|
|
for (var i = 0; i < N / 2; i++) {
|
|
var w = Math.round(ws[2 * i + 1] / N) * 0x2000 + Math.round(ws[2 * i] / N) + carry;
|
|
ws[i] = w & 0x3ffffff;
|
|
|
|
if (w < 0x4000000) {
|
|
carry = 0;
|
|
} else {
|
|
carry = w / 0x4000000 | 0;
|
|
}
|
|
}
|
|
|
|
return ws;
|
|
};
|
|
|
|
FFTM.prototype.convert13b = function convert13b(ws, len, rws, N) {
|
|
var carry = 0;
|
|
|
|
for (var i = 0; i < len; i++) {
|
|
carry = carry + (ws[i] | 0);
|
|
rws[2 * i] = carry & 0x1fff;
|
|
carry = carry >>> 13;
|
|
rws[2 * i + 1] = carry & 0x1fff;
|
|
carry = carry >>> 13;
|
|
} // Pad with zeroes
|
|
|
|
|
|
for (i = 2 * len; i < N; ++i) {
|
|
rws[i] = 0;
|
|
}
|
|
|
|
assert(carry === 0);
|
|
assert((carry & ~0x1fff) === 0);
|
|
};
|
|
|
|
FFTM.prototype.stub = function stub(N) {
|
|
var ph = new Array(N);
|
|
|
|
for (var i = 0; i < N; i++) {
|
|
ph[i] = 0;
|
|
}
|
|
|
|
return ph;
|
|
};
|
|
|
|
FFTM.prototype.mulp = function mulp(x, y, out) {
|
|
var N = 2 * this.guessLen13b(x.length, y.length);
|
|
var rbt = this.makeRBT(N);
|
|
|
|
var _ = this.stub(N);
|
|
|
|
var rws = new Array(N);
|
|
var rwst = new Array(N);
|
|
var iwst = new Array(N);
|
|
var nrws = new Array(N);
|
|
var nrwst = new Array(N);
|
|
var niwst = new Array(N);
|
|
var rmws = out.words;
|
|
rmws.length = N;
|
|
this.convert13b(x.words, x.length, rws, N);
|
|
this.convert13b(y.words, y.length, nrws, N);
|
|
this.transform(rws, _, rwst, iwst, N, rbt);
|
|
this.transform(nrws, _, nrwst, niwst, N, rbt);
|
|
|
|
for (var i = 0; i < N; i++) {
|
|
var rx = rwst[i] * nrwst[i] - iwst[i] * niwst[i];
|
|
iwst[i] = rwst[i] * niwst[i] + iwst[i] * nrwst[i];
|
|
rwst[i] = rx;
|
|
}
|
|
|
|
this.conjugate(rwst, iwst, N);
|
|
this.transform(rwst, iwst, rmws, _, N, rbt);
|
|
this.conjugate(rmws, _, N);
|
|
this.normalize13b(rmws, N);
|
|
out.negative = x.negative ^ y.negative;
|
|
out.length = x.length + y.length;
|
|
return out.strip();
|
|
}; // Multiply `this` by `num`
|
|
|
|
|
|
BN.prototype.mul = function mul(num) {
|
|
var out = new BN(null);
|
|
out.words = new Array(this.length + num.length);
|
|
return this.mulTo(num, out);
|
|
}; // Multiply employing FFT
|
|
|
|
|
|
BN.prototype.mulf = function mulf(num) {
|
|
var out = new BN(null);
|
|
out.words = new Array(this.length + num.length);
|
|
return jumboMulTo(this, num, out);
|
|
}; // In-place Multiplication
|
|
|
|
|
|
BN.prototype.imul = function imul(num) {
|
|
return this.clone().mulTo(num, this);
|
|
};
|
|
|
|
BN.prototype.imuln = function imuln(num) {
|
|
assert(typeof num === 'number');
|
|
assert(num < 0x4000000); // Carry
|
|
|
|
var carry = 0;
|
|
|
|
for (var i = 0; i < this.length; i++) {
|
|
var w = (this.words[i] | 0) * num;
|
|
var lo = (w & 0x3ffffff) + (carry & 0x3ffffff);
|
|
carry >>= 26;
|
|
carry += w / 0x4000000 | 0; // NOTE: lo is 27bit maximum
|
|
|
|
carry += lo >>> 26;
|
|
this.words[i] = lo & 0x3ffffff;
|
|
}
|
|
|
|
if (carry !== 0) {
|
|
this.words[i] = carry;
|
|
this.length++;
|
|
}
|
|
|
|
return this;
|
|
};
|
|
|
|
BN.prototype.muln = function muln(num) {
|
|
return this.clone().imuln(num);
|
|
}; // `this` * `this`
|
|
|
|
|
|
BN.prototype.sqr = function sqr() {
|
|
return this.mul(this);
|
|
}; // `this` * `this` in-place
|
|
|
|
|
|
BN.prototype.isqr = function isqr() {
|
|
return this.imul(this.clone());
|
|
}; // Math.pow(`this`, `num`)
|
|
|
|
|
|
BN.prototype.pow = function pow(num) {
|
|
var w = toBitArray(num);
|
|
if (w.length === 0) return new BN(1); // Skip leading zeroes
|
|
|
|
var res = this;
|
|
|
|
for (var i = 0; i < w.length; i++, res = res.sqr()) {
|
|
if (w[i] !== 0) break;
|
|
}
|
|
|
|
if (++i < w.length) {
|
|
for (var q = res.sqr(); i < w.length; i++, q = q.sqr()) {
|
|
if (w[i] === 0) continue;
|
|
res = res.mul(q);
|
|
}
|
|
}
|
|
|
|
return res;
|
|
}; // Shift-left in-place
|
|
|
|
|
|
BN.prototype.iushln = function iushln(bits) {
|
|
assert(typeof bits === 'number' && bits >= 0);
|
|
var r = bits % 26;
|
|
var s = (bits - r) / 26;
|
|
var carryMask = 0x3ffffff >>> 26 - r << 26 - r;
|
|
var i;
|
|
|
|
if (r !== 0) {
|
|
var carry = 0;
|
|
|
|
for (i = 0; i < this.length; i++) {
|
|
var newCarry = this.words[i] & carryMask;
|
|
var c = (this.words[i] | 0) - newCarry << r;
|
|
this.words[i] = c | carry;
|
|
carry = newCarry >>> 26 - r;
|
|
}
|
|
|
|
if (carry) {
|
|
this.words[i] = carry;
|
|
this.length++;
|
|
}
|
|
}
|
|
|
|
if (s !== 0) {
|
|
for (i = this.length - 1; i >= 0; i--) {
|
|
this.words[i + s] = this.words[i];
|
|
}
|
|
|
|
for (i = 0; i < s; i++) {
|
|
this.words[i] = 0;
|
|
}
|
|
|
|
this.length += s;
|
|
}
|
|
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.ishln = function ishln(bits) {
|
|
// TODO(indutny): implement me
|
|
assert(this.negative === 0);
|
|
return this.iushln(bits);
|
|
}; // Shift-right in-place
|
|
// NOTE: `hint` is a lowest bit before trailing zeroes
|
|
// NOTE: if `extended` is present - it will be filled with destroyed bits
|
|
|
|
|
|
BN.prototype.iushrn = function iushrn(bits, hint, extended) {
|
|
assert(typeof bits === 'number' && bits >= 0);
|
|
var h;
|
|
|
|
if (hint) {
|
|
h = (hint - hint % 26) / 26;
|
|
} else {
|
|
h = 0;
|
|
}
|
|
|
|
var r = bits % 26;
|
|
var s = Math.min((bits - r) / 26, this.length);
|
|
var mask = 0x3ffffff ^ 0x3ffffff >>> r << r;
|
|
var maskedWords = extended;
|
|
h -= s;
|
|
h = Math.max(0, h); // Extended mode, copy masked part
|
|
|
|
if (maskedWords) {
|
|
for (var i = 0; i < s; i++) {
|
|
maskedWords.words[i] = this.words[i];
|
|
}
|
|
|
|
maskedWords.length = s;
|
|
}
|
|
|
|
if (s === 0) {// No-op, we should not move anything at all
|
|
} else if (this.length > s) {
|
|
this.length -= s;
|
|
|
|
for (i = 0; i < this.length; i++) {
|
|
this.words[i] = this.words[i + s];
|
|
}
|
|
} else {
|
|
this.words[0] = 0;
|
|
this.length = 1;
|
|
}
|
|
|
|
var carry = 0;
|
|
|
|
for (i = this.length - 1; i >= 0 && (carry !== 0 || i >= h); i--) {
|
|
var word = this.words[i] | 0;
|
|
this.words[i] = carry << 26 - r | word >>> r;
|
|
carry = word & mask;
|
|
} // Push carried bits as a mask
|
|
|
|
|
|
if (maskedWords && carry !== 0) {
|
|
maskedWords.words[maskedWords.length++] = carry;
|
|
}
|
|
|
|
if (this.length === 0) {
|
|
this.words[0] = 0;
|
|
this.length = 1;
|
|
}
|
|
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.ishrn = function ishrn(bits, hint, extended) {
|
|
// TODO(indutny): implement me
|
|
assert(this.negative === 0);
|
|
return this.iushrn(bits, hint, extended);
|
|
}; // Shift-left
|
|
|
|
|
|
BN.prototype.shln = function shln(bits) {
|
|
return this.clone().ishln(bits);
|
|
};
|
|
|
|
BN.prototype.ushln = function ushln(bits) {
|
|
return this.clone().iushln(bits);
|
|
}; // Shift-right
|
|
|
|
|
|
BN.prototype.shrn = function shrn(bits) {
|
|
return this.clone().ishrn(bits);
|
|
};
|
|
|
|
BN.prototype.ushrn = function ushrn(bits) {
|
|
return this.clone().iushrn(bits);
|
|
}; // Test if n bit is set
|
|
|
|
|
|
BN.prototype.testn = function testn(bit) {
|
|
assert(typeof bit === 'number' && bit >= 0);
|
|
var r = bit % 26;
|
|
var s = (bit - r) / 26;
|
|
var q = 1 << r; // Fast case: bit is much higher than all existing words
|
|
|
|
if (this.length <= s) return false; // Check bit and return
|
|
|
|
var w = this.words[s];
|
|
return !!(w & q);
|
|
}; // Return only lowers bits of number (in-place)
|
|
|
|
|
|
BN.prototype.imaskn = function imaskn(bits) {
|
|
assert(typeof bits === 'number' && bits >= 0);
|
|
var r = bits % 26;
|
|
var s = (bits - r) / 26;
|
|
assert(this.negative === 0, 'imaskn works only with positive numbers');
|
|
|
|
if (this.length <= s) {
|
|
return this;
|
|
}
|
|
|
|
if (r !== 0) {
|
|
s++;
|
|
}
|
|
|
|
this.length = Math.min(s, this.length);
|
|
|
|
if (r !== 0) {
|
|
var mask = 0x3ffffff ^ 0x3ffffff >>> r << r;
|
|
this.words[this.length - 1] &= mask;
|
|
}
|
|
|
|
return this.strip();
|
|
}; // Return only lowers bits of number
|
|
|
|
|
|
BN.prototype.maskn = function maskn(bits) {
|
|
return this.clone().imaskn(bits);
|
|
}; // Add plain number `num` to `this`
|
|
|
|
|
|
BN.prototype.iaddn = function iaddn(num) {
|
|
assert(typeof num === 'number');
|
|
assert(num < 0x4000000);
|
|
if (num < 0) return this.isubn(-num); // Possible sign change
|
|
|
|
if (this.negative !== 0) {
|
|
if (this.length === 1 && (this.words[0] | 0) < num) {
|
|
this.words[0] = num - (this.words[0] | 0);
|
|
this.negative = 0;
|
|
return this;
|
|
}
|
|
|
|
this.negative = 0;
|
|
this.isubn(num);
|
|
this.negative = 1;
|
|
return this;
|
|
} // Add without checks
|
|
|
|
|
|
return this._iaddn(num);
|
|
};
|
|
|
|
BN.prototype._iaddn = function _iaddn(num) {
|
|
this.words[0] += num; // Carry
|
|
|
|
for (var i = 0; i < this.length && this.words[i] >= 0x4000000; i++) {
|
|
this.words[i] -= 0x4000000;
|
|
|
|
if (i === this.length - 1) {
|
|
this.words[i + 1] = 1;
|
|
} else {
|
|
this.words[i + 1]++;
|
|
}
|
|
}
|
|
|
|
this.length = Math.max(this.length, i + 1);
|
|
return this;
|
|
}; // Subtract plain number `num` from `this`
|
|
|
|
|
|
BN.prototype.isubn = function isubn(num) {
|
|
assert(typeof num === 'number');
|
|
assert(num < 0x4000000);
|
|
if (num < 0) return this.iaddn(-num);
|
|
|
|
if (this.negative !== 0) {
|
|
this.negative = 0;
|
|
this.iaddn(num);
|
|
this.negative = 1;
|
|
return this;
|
|
}
|
|
|
|
this.words[0] -= num;
|
|
|
|
if (this.length === 1 && this.words[0] < 0) {
|
|
this.words[0] = -this.words[0];
|
|
this.negative = 1;
|
|
} else {
|
|
// Carry
|
|
for (var i = 0; i < this.length && this.words[i] < 0; i++) {
|
|
this.words[i] += 0x4000000;
|
|
this.words[i + 1] -= 1;
|
|
}
|
|
}
|
|
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.addn = function addn(num) {
|
|
return this.clone().iaddn(num);
|
|
};
|
|
|
|
BN.prototype.subn = function subn(num) {
|
|
return this.clone().isubn(num);
|
|
};
|
|
|
|
BN.prototype.iabs = function iabs() {
|
|
this.negative = 0;
|
|
return this;
|
|
};
|
|
|
|
BN.prototype.abs = function abs() {
|
|
return this.clone().iabs();
|
|
};
|
|
|
|
BN.prototype._ishlnsubmul = function _ishlnsubmul(num, mul, shift) {
|
|
var len = num.length + shift;
|
|
var i;
|
|
|
|
this._expand(len);
|
|
|
|
var w;
|
|
var carry = 0;
|
|
|
|
for (i = 0; i < num.length; i++) {
|
|
w = (this.words[i + shift] | 0) + carry;
|
|
var right = (num.words[i] | 0) * mul;
|
|
w -= right & 0x3ffffff;
|
|
carry = (w >> 26) - (right / 0x4000000 | 0);
|
|
this.words[i + shift] = w & 0x3ffffff;
|
|
}
|
|
|
|
for (; i < this.length - shift; i++) {
|
|
w = (this.words[i + shift] | 0) + carry;
|
|
carry = w >> 26;
|
|
this.words[i + shift] = w & 0x3ffffff;
|
|
}
|
|
|
|
if (carry === 0) return this.strip(); // Subtraction overflow
|
|
|
|
assert(carry === -1);
|
|
carry = 0;
|
|
|
|
for (i = 0; i < this.length; i++) {
|
|
w = -(this.words[i] | 0) + carry;
|
|
carry = w >> 26;
|
|
this.words[i] = w & 0x3ffffff;
|
|
}
|
|
|
|
this.negative = 1;
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype._wordDiv = function _wordDiv(num, mode) {
|
|
var shift = this.length - num.length;
|
|
var a = this.clone();
|
|
var b = num; // Normalize
|
|
|
|
var bhi = b.words[b.length - 1] | 0;
|
|
|
|
var bhiBits = this._countBits(bhi);
|
|
|
|
shift = 26 - bhiBits;
|
|
|
|
if (shift !== 0) {
|
|
b = b.ushln(shift);
|
|
a.iushln(shift);
|
|
bhi = b.words[b.length - 1] | 0;
|
|
} // Initialize quotient
|
|
|
|
|
|
var m = a.length - b.length;
|
|
var q;
|
|
|
|
if (mode !== 'mod') {
|
|
q = new BN(null);
|
|
q.length = m + 1;
|
|
q.words = new Array(q.length);
|
|
|
|
for (var i = 0; i < q.length; i++) {
|
|
q.words[i] = 0;
|
|
}
|
|
}
|
|
|
|
var diff = a.clone()._ishlnsubmul(b, 1, m);
|
|
|
|
if (diff.negative === 0) {
|
|
a = diff;
|
|
|
|
if (q) {
|
|
q.words[m] = 1;
|
|
}
|
|
}
|
|
|
|
for (var j = m - 1; j >= 0; j--) {
|
|
var qj = (a.words[b.length + j] | 0) * 0x4000000 + (a.words[b.length + j - 1] | 0); // NOTE: (qj / bhi) is (0x3ffffff * 0x4000000 + 0x3ffffff) / 0x2000000 max
|
|
// (0x7ffffff)
|
|
|
|
qj = Math.min(qj / bhi | 0, 0x3ffffff);
|
|
|
|
a._ishlnsubmul(b, qj, j);
|
|
|
|
while (a.negative !== 0) {
|
|
qj--;
|
|
a.negative = 0;
|
|
|
|
a._ishlnsubmul(b, 1, j);
|
|
|
|
if (!a.isZero()) {
|
|
a.negative ^= 1;
|
|
}
|
|
}
|
|
|
|
if (q) {
|
|
q.words[j] = qj;
|
|
}
|
|
}
|
|
|
|
if (q) {
|
|
q.strip();
|
|
}
|
|
|
|
a.strip(); // Denormalize
|
|
|
|
if (mode !== 'div' && shift !== 0) {
|
|
a.iushrn(shift);
|
|
}
|
|
|
|
return {
|
|
div: q || null,
|
|
mod: a
|
|
};
|
|
}; // NOTE: 1) `mode` can be set to `mod` to request mod only,
|
|
// to `div` to request div only, or be absent to
|
|
// request both div & mod
|
|
// 2) `positive` is true if unsigned mod is requested
|
|
|
|
|
|
BN.prototype.divmod = function divmod(num, mode, positive) {
|
|
assert(!num.isZero());
|
|
|
|
if (this.isZero()) {
|
|
return {
|
|
div: new BN(0),
|
|
mod: new BN(0)
|
|
};
|
|
}
|
|
|
|
var div, mod, res;
|
|
|
|
if (this.negative !== 0 && num.negative === 0) {
|
|
res = this.neg().divmod(num, mode);
|
|
|
|
if (mode !== 'mod') {
|
|
div = res.div.neg();
|
|
}
|
|
|
|
if (mode !== 'div') {
|
|
mod = res.mod.neg();
|
|
|
|
if (positive && mod.negative !== 0) {
|
|
mod.iadd(num);
|
|
}
|
|
}
|
|
|
|
return {
|
|
div: div,
|
|
mod: mod
|
|
};
|
|
}
|
|
|
|
if (this.negative === 0 && num.negative !== 0) {
|
|
res = this.divmod(num.neg(), mode);
|
|
|
|
if (mode !== 'mod') {
|
|
div = res.div.neg();
|
|
}
|
|
|
|
return {
|
|
div: div,
|
|
mod: res.mod
|
|
};
|
|
}
|
|
|
|
if ((this.negative & num.negative) !== 0) {
|
|
res = this.neg().divmod(num.neg(), mode);
|
|
|
|
if (mode !== 'div') {
|
|
mod = res.mod.neg();
|
|
|
|
if (positive && mod.negative !== 0) {
|
|
mod.isub(num);
|
|
}
|
|
}
|
|
|
|
return {
|
|
div: res.div,
|
|
mod: mod
|
|
};
|
|
} // Both numbers are positive at this point
|
|
// Strip both numbers to approximate shift value
|
|
|
|
|
|
if (num.length > this.length || this.cmp(num) < 0) {
|
|
return {
|
|
div: new BN(0),
|
|
mod: this
|
|
};
|
|
} // Very short reduction
|
|
|
|
|
|
if (num.length === 1) {
|
|
if (mode === 'div') {
|
|
return {
|
|
div: this.divn(num.words[0]),
|
|
mod: null
|
|
};
|
|
}
|
|
|
|
if (mode === 'mod') {
|
|
return {
|
|
div: null,
|
|
mod: new BN(this.modn(num.words[0]))
|
|
};
|
|
}
|
|
|
|
return {
|
|
div: this.divn(num.words[0]),
|
|
mod: new BN(this.modn(num.words[0]))
|
|
};
|
|
}
|
|
|
|
return this._wordDiv(num, mode);
|
|
}; // Find `this` / `num`
|
|
|
|
|
|
BN.prototype.div = function div(num) {
|
|
return this.divmod(num, 'div', false).div;
|
|
}; // Find `this` % `num`
|
|
|
|
|
|
BN.prototype.mod = function mod(num) {
|
|
return this.divmod(num, 'mod', false).mod;
|
|
};
|
|
|
|
BN.prototype.umod = function umod(num) {
|
|
return this.divmod(num, 'mod', true).mod;
|
|
}; // Find Round(`this` / `num`)
|
|
|
|
|
|
BN.prototype.divRound = function divRound(num) {
|
|
var dm = this.divmod(num); // Fast case - exact division
|
|
|
|
if (dm.mod.isZero()) return dm.div;
|
|
var mod = dm.div.negative !== 0 ? dm.mod.isub(num) : dm.mod;
|
|
var half = num.ushrn(1);
|
|
var r2 = num.andln(1);
|
|
var cmp = mod.cmp(half); // Round down
|
|
|
|
if (cmp < 0 || r2 === 1 && cmp === 0) return dm.div; // Round up
|
|
|
|
return dm.div.negative !== 0 ? dm.div.isubn(1) : dm.div.iaddn(1);
|
|
};
|
|
|
|
BN.prototype.modn = function modn(num) {
|
|
assert(num <= 0x3ffffff);
|
|
var p = (1 << 26) % num;
|
|
var acc = 0;
|
|
|
|
for (var i = this.length - 1; i >= 0; i--) {
|
|
acc = (p * acc + (this.words[i] | 0)) % num;
|
|
}
|
|
|
|
return acc;
|
|
}; // In-place division by number
|
|
|
|
|
|
BN.prototype.idivn = function idivn(num) {
|
|
assert(num <= 0x3ffffff);
|
|
var carry = 0;
|
|
|
|
for (var i = this.length - 1; i >= 0; i--) {
|
|
var w = (this.words[i] | 0) + carry * 0x4000000;
|
|
this.words[i] = w / num | 0;
|
|
carry = w % num;
|
|
}
|
|
|
|
return this.strip();
|
|
};
|
|
|
|
BN.prototype.divn = function divn(num) {
|
|
return this.clone().idivn(num);
|
|
};
|
|
|
|
BN.prototype.egcd = function egcd(p) {
|
|
assert(p.negative === 0);
|
|
assert(!p.isZero());
|
|
var x = this;
|
|
var y = p.clone();
|
|
|
|
if (x.negative !== 0) {
|
|
x = x.umod(p);
|
|
} else {
|
|
x = x.clone();
|
|
} // A * x + B * y = x
|
|
|
|
|
|
var A = new BN(1);
|
|
var B = new BN(0); // C * x + D * y = y
|
|
|
|
var C = new BN(0);
|
|
var D = new BN(1);
|
|
var g = 0;
|
|
|
|
while (x.isEven() && y.isEven()) {
|
|
x.iushrn(1);
|
|
y.iushrn(1);
|
|
++g;
|
|
}
|
|
|
|
var yp = y.clone();
|
|
var xp = x.clone();
|
|
|
|
while (!x.isZero()) {
|
|
for (var i = 0, im = 1; (x.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
|
|
|
|
if (i > 0) {
|
|
x.iushrn(i);
|
|
|
|
while (i-- > 0) {
|
|
if (A.isOdd() || B.isOdd()) {
|
|
A.iadd(yp);
|
|
B.isub(xp);
|
|
}
|
|
|
|
A.iushrn(1);
|
|
B.iushrn(1);
|
|
}
|
|
}
|
|
|
|
for (var j = 0, jm = 1; (y.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
|
|
|
|
if (j > 0) {
|
|
y.iushrn(j);
|
|
|
|
while (j-- > 0) {
|
|
if (C.isOdd() || D.isOdd()) {
|
|
C.iadd(yp);
|
|
D.isub(xp);
|
|
}
|
|
|
|
C.iushrn(1);
|
|
D.iushrn(1);
|
|
}
|
|
}
|
|
|
|
if (x.cmp(y) >= 0) {
|
|
x.isub(y);
|
|
A.isub(C);
|
|
B.isub(D);
|
|
} else {
|
|
y.isub(x);
|
|
C.isub(A);
|
|
D.isub(B);
|
|
}
|
|
}
|
|
|
|
return {
|
|
a: C,
|
|
b: D,
|
|
gcd: y.iushln(g)
|
|
};
|
|
}; // This is reduced incarnation of the binary EEA
|
|
// above, designated to invert members of the
|
|
// _prime_ fields F(p) at a maximal speed
|
|
|
|
|
|
BN.prototype._invmp = function _invmp(p) {
|
|
assert(p.negative === 0);
|
|
assert(!p.isZero());
|
|
var a = this;
|
|
var b = p.clone();
|
|
|
|
if (a.negative !== 0) {
|
|
a = a.umod(p);
|
|
} else {
|
|
a = a.clone();
|
|
}
|
|
|
|
var x1 = new BN(1);
|
|
var x2 = new BN(0);
|
|
var delta = b.clone();
|
|
|
|
while (a.cmpn(1) > 0 && b.cmpn(1) > 0) {
|
|
for (var i = 0, im = 1; (a.words[0] & im) === 0 && i < 26; ++i, im <<= 1);
|
|
|
|
if (i > 0) {
|
|
a.iushrn(i);
|
|
|
|
while (i-- > 0) {
|
|
if (x1.isOdd()) {
|
|
x1.iadd(delta);
|
|
}
|
|
|
|
x1.iushrn(1);
|
|
}
|
|
}
|
|
|
|
for (var j = 0, jm = 1; (b.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1);
|
|
|
|
if (j > 0) {
|
|
b.iushrn(j);
|
|
|
|
while (j-- > 0) {
|
|
if (x2.isOdd()) {
|
|
x2.iadd(delta);
|
|
}
|
|
|
|
x2.iushrn(1);
|
|
}
|
|
}
|
|
|
|
if (a.cmp(b) >= 0) {
|
|
a.isub(b);
|
|
x1.isub(x2);
|
|
} else {
|
|
b.isub(a);
|
|
x2.isub(x1);
|
|
}
|
|
}
|
|
|
|
var res;
|
|
|
|
if (a.cmpn(1) === 0) {
|
|
res = x1;
|
|
} else {
|
|
res = x2;
|
|
}
|
|
|
|
if (res.cmpn(0) < 0) {
|
|
res.iadd(p);
|
|
}
|
|
|
|
return res;
|
|
};
|
|
|
|
BN.prototype.gcd = function gcd(num) {
|
|
if (this.isZero()) return num.abs();
|
|
if (num.isZero()) return this.abs();
|
|
var a = this.clone();
|
|
var b = num.clone();
|
|
a.negative = 0;
|
|
b.negative = 0; // Remove common factor of two
|
|
|
|
for (var shift = 0; a.isEven() && b.isEven(); shift++) {
|
|
a.iushrn(1);
|
|
b.iushrn(1);
|
|
}
|
|
|
|
do {
|
|
while (a.isEven()) {
|
|
a.iushrn(1);
|
|
}
|
|
|
|
while (b.isEven()) {
|
|
b.iushrn(1);
|
|
}
|
|
|
|
var r = a.cmp(b);
|
|
|
|
if (r < 0) {
|
|
// Swap `a` and `b` to make `a` always bigger than `b`
|
|
var t = a;
|
|
a = b;
|
|
b = t;
|
|
} else if (r === 0 || b.cmpn(1) === 0) {
|
|
break;
|
|
}
|
|
|
|
a.isub(b);
|
|
} while (true);
|
|
|
|
return b.iushln(shift);
|
|
}; // Invert number in the field F(num)
|
|
|
|
|
|
BN.prototype.invm = function invm(num) {
|
|
return this.egcd(num).a.umod(num);
|
|
};
|
|
|
|
BN.prototype.isEven = function isEven() {
|
|
return (this.words[0] & 1) === 0;
|
|
};
|
|
|
|
BN.prototype.isOdd = function isOdd() {
|
|
return (this.words[0] & 1) === 1;
|
|
}; // And first word and num
|
|
|
|
|
|
BN.prototype.andln = function andln(num) {
|
|
return this.words[0] & num;
|
|
}; // Increment at the bit position in-line
|
|
|
|
|
|
BN.prototype.bincn = function bincn(bit) {
|
|
assert(typeof bit === 'number');
|
|
var r = bit % 26;
|
|
var s = (bit - r) / 26;
|
|
var q = 1 << r; // Fast case: bit is much higher than all existing words
|
|
|
|
if (this.length <= s) {
|
|
this._expand(s + 1);
|
|
|
|
this.words[s] |= q;
|
|
return this;
|
|
} // Add bit and propagate, if needed
|
|
|
|
|
|
var carry = q;
|
|
|
|
for (var i = s; carry !== 0 && i < this.length; i++) {
|
|
var w = this.words[i] | 0;
|
|
w += carry;
|
|
carry = w >>> 26;
|
|
w &= 0x3ffffff;
|
|
this.words[i] = w;
|
|
}
|
|
|
|
if (carry !== 0) {
|
|
this.words[i] = carry;
|
|
this.length++;
|
|
}
|
|
|
|
return this;
|
|
};
|
|
|
|
BN.prototype.isZero = function isZero() {
|
|
return this.length === 1 && this.words[0] === 0;
|
|
};
|
|
|
|
BN.prototype.cmpn = function cmpn(num) {
|
|
var negative = num < 0;
|
|
if (this.negative !== 0 && !negative) return -1;
|
|
if (this.negative === 0 && negative) return 1;
|
|
this.strip();
|
|
var res;
|
|
|
|
if (this.length > 1) {
|
|
res = 1;
|
|
} else {
|
|
if (negative) {
|
|
num = -num;
|
|
}
|
|
|
|
assert(num <= 0x3ffffff, 'Number is too big');
|
|
var w = this.words[0] | 0;
|
|
res = w === num ? 0 : w < num ? -1 : 1;
|
|
}
|
|
|
|
if (this.negative !== 0) return -res | 0;
|
|
return res;
|
|
}; // Compare two numbers and return:
|
|
// 1 - if `this` > `num`
|
|
// 0 - if `this` == `num`
|
|
// -1 - if `this` < `num`
|
|
|
|
|
|
BN.prototype.cmp = function cmp(num) {
|
|
if (this.negative !== 0 && num.negative === 0) return -1;
|
|
if (this.negative === 0 && num.negative !== 0) return 1;
|
|
var res = this.ucmp(num);
|
|
if (this.negative !== 0) return -res | 0;
|
|
return res;
|
|
}; // Unsigned comparison
|
|
|
|
|
|
BN.prototype.ucmp = function ucmp(num) {
|
|
// At this point both numbers have the same sign
|
|
if (this.length > num.length) return 1;
|
|
if (this.length < num.length) return -1;
|
|
var res = 0;
|
|
|
|
for (var i = this.length - 1; i >= 0; i--) {
|
|
var a = this.words[i] | 0;
|
|
var b = num.words[i] | 0;
|
|
if (a === b) continue;
|
|
|
|
if (a < b) {
|
|
res = -1;
|
|
} else if (a > b) {
|
|
res = 1;
|
|
}
|
|
|
|
break;
|
|
}
|
|
|
|
return res;
|
|
};
|
|
|
|
BN.prototype.gtn = function gtn(num) {
|
|
return this.cmpn(num) === 1;
|
|
};
|
|
|
|
BN.prototype.gt = function gt(num) {
|
|
return this.cmp(num) === 1;
|
|
};
|
|
|
|
BN.prototype.gten = function gten(num) {
|
|
return this.cmpn(num) >= 0;
|
|
};
|
|
|
|
BN.prototype.gte = function gte(num) {
|
|
return this.cmp(num) >= 0;
|
|
};
|
|
|
|
BN.prototype.ltn = function ltn(num) {
|
|
return this.cmpn(num) === -1;
|
|
};
|
|
|
|
BN.prototype.lt = function lt(num) {
|
|
return this.cmp(num) === -1;
|
|
};
|
|
|
|
BN.prototype.lten = function lten(num) {
|
|
return this.cmpn(num) <= 0;
|
|
};
|
|
|
|
BN.prototype.lte = function lte(num) {
|
|
return this.cmp(num) <= 0;
|
|
};
|
|
|
|
BN.prototype.eqn = function eqn(num) {
|
|
return this.cmpn(num) === 0;
|
|
};
|
|
|
|
BN.prototype.eq = function eq(num) {
|
|
return this.cmp(num) === 0;
|
|
}; //
|
|
// A reduce context, could be using montgomery or something better, depending
|
|
// on the `m` itself.
|
|
//
|
|
|
|
|
|
BN.red = function red(num) {
|
|
return new Red(num);
|
|
};
|
|
|
|
BN.prototype.toRed = function toRed(ctx) {
|
|
assert(!this.red, 'Already a number in reduction context');
|
|
assert(this.negative === 0, 'red works only with positives');
|
|
return ctx.convertTo(this)._forceRed(ctx);
|
|
};
|
|
|
|
BN.prototype.fromRed = function fromRed() {
|
|
assert(this.red, 'fromRed works only with numbers in reduction context');
|
|
return this.red.convertFrom(this);
|
|
};
|
|
|
|
BN.prototype._forceRed = function _forceRed(ctx) {
|
|
this.red = ctx;
|
|
return this;
|
|
};
|
|
|
|
BN.prototype.forceRed = function forceRed(ctx) {
|
|
assert(!this.red, 'Already a number in reduction context');
|
|
return this._forceRed(ctx);
|
|
};
|
|
|
|
BN.prototype.redAdd = function redAdd(num) {
|
|
assert(this.red, 'redAdd works only with red numbers');
|
|
return this.red.add(this, num);
|
|
};
|
|
|
|
BN.prototype.redIAdd = function redIAdd(num) {
|
|
assert(this.red, 'redIAdd works only with red numbers');
|
|
return this.red.iadd(this, num);
|
|
};
|
|
|
|
BN.prototype.redSub = function redSub(num) {
|
|
assert(this.red, 'redSub works only with red numbers');
|
|
return this.red.sub(this, num);
|
|
};
|
|
|
|
BN.prototype.redISub = function redISub(num) {
|
|
assert(this.red, 'redISub works only with red numbers');
|
|
return this.red.isub(this, num);
|
|
};
|
|
|
|
BN.prototype.redShl = function redShl(num) {
|
|
assert(this.red, 'redShl works only with red numbers');
|
|
return this.red.shl(this, num);
|
|
};
|
|
|
|
BN.prototype.redMul = function redMul(num) {
|
|
assert(this.red, 'redMul works only with red numbers');
|
|
|
|
this.red._verify2(this, num);
|
|
|
|
return this.red.mul(this, num);
|
|
};
|
|
|
|
BN.prototype.redIMul = function redIMul(num) {
|
|
assert(this.red, 'redMul works only with red numbers');
|
|
|
|
this.red._verify2(this, num);
|
|
|
|
return this.red.imul(this, num);
|
|
};
|
|
|
|
BN.prototype.redSqr = function redSqr() {
|
|
assert(this.red, 'redSqr works only with red numbers');
|
|
|
|
this.red._verify1(this);
|
|
|
|
return this.red.sqr(this);
|
|
};
|
|
|
|
BN.prototype.redISqr = function redISqr() {
|
|
assert(this.red, 'redISqr works only with red numbers');
|
|
|
|
this.red._verify1(this);
|
|
|
|
return this.red.isqr(this);
|
|
}; // Square root over p
|
|
|
|
|
|
BN.prototype.redSqrt = function redSqrt() {
|
|
assert(this.red, 'redSqrt works only with red numbers');
|
|
|
|
this.red._verify1(this);
|
|
|
|
return this.red.sqrt(this);
|
|
};
|
|
|
|
BN.prototype.redInvm = function redInvm() {
|
|
assert(this.red, 'redInvm works only with red numbers');
|
|
|
|
this.red._verify1(this);
|
|
|
|
return this.red.invm(this);
|
|
}; // Return negative clone of `this` % `red modulo`
|
|
|
|
|
|
BN.prototype.redNeg = function redNeg() {
|
|
assert(this.red, 'redNeg works only with red numbers');
|
|
|
|
this.red._verify1(this);
|
|
|
|
return this.red.neg(this);
|
|
};
|
|
|
|
BN.prototype.redPow = function redPow(num) {
|
|
assert(this.red && !num.red, 'redPow(normalNum)');
|
|
|
|
this.red._verify1(this);
|
|
|
|
return this.red.pow(this, num);
|
|
}; // Prime numbers with efficient reduction
|
|
|
|
|
|
var primes = {
|
|
k256: null,
|
|
p224: null,
|
|
p192: null,
|
|
p25519: null
|
|
}; // Pseudo-Mersenne prime
|
|
|
|
function MPrime(name, p) {
|
|
// P = 2 ^ N - K
|
|
this.name = name;
|
|
this.p = new BN(p, 16);
|
|
this.n = this.p.bitLength();
|
|
this.k = new BN(1).iushln(this.n).isub(this.p);
|
|
this.tmp = this._tmp();
|
|
}
|
|
|
|
MPrime.prototype._tmp = function _tmp() {
|
|
var tmp = new BN(null);
|
|
tmp.words = new Array(Math.ceil(this.n / 13));
|
|
return tmp;
|
|
};
|
|
|
|
MPrime.prototype.ireduce = function ireduce(num) {
|
|
// Assumes that `num` is less than `P^2`
|
|
// num = HI * (2 ^ N - K) + HI * K + LO = HI * K + LO (mod P)
|
|
var r = num;
|
|
var rlen;
|
|
|
|
do {
|
|
this.split(r, this.tmp);
|
|
r = this.imulK(r);
|
|
r = r.iadd(this.tmp);
|
|
rlen = r.bitLength();
|
|
} while (rlen > this.n);
|
|
|
|
var cmp = rlen < this.n ? -1 : r.ucmp(this.p);
|
|
|
|
if (cmp === 0) {
|
|
r.words[0] = 0;
|
|
r.length = 1;
|
|
} else if (cmp > 0) {
|
|
r.isub(this.p);
|
|
} else {
|
|
r.strip();
|
|
}
|
|
|
|
return r;
|
|
};
|
|
|
|
MPrime.prototype.split = function split(input, out) {
|
|
input.iushrn(this.n, 0, out);
|
|
};
|
|
|
|
MPrime.prototype.imulK = function imulK(num) {
|
|
return num.imul(this.k);
|
|
};
|
|
|
|
function K256() {
|
|
MPrime.call(this, 'k256', 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f');
|
|
}
|
|
|
|
inherits(K256, MPrime);
|
|
|
|
K256.prototype.split = function split(input, output) {
|
|
// 256 = 9 * 26 + 22
|
|
var mask = 0x3fffff;
|
|
var outLen = Math.min(input.length, 9);
|
|
|
|
for (var i = 0; i < outLen; i++) {
|
|
output.words[i] = input.words[i];
|
|
}
|
|
|
|
output.length = outLen;
|
|
|
|
if (input.length <= 9) {
|
|
input.words[0] = 0;
|
|
input.length = 1;
|
|
return;
|
|
} // Shift by 9 limbs
|
|
|
|
|
|
var prev = input.words[9];
|
|
output.words[output.length++] = prev & mask;
|
|
|
|
for (i = 10; i < input.length; i++) {
|
|
var next = input.words[i] | 0;
|
|
input.words[i - 10] = (next & mask) << 4 | prev >>> 22;
|
|
prev = next;
|
|
}
|
|
|
|
prev >>>= 22;
|
|
input.words[i - 10] = prev;
|
|
|
|
if (prev === 0 && input.length > 10) {
|
|
input.length -= 10;
|
|
} else {
|
|
input.length -= 9;
|
|
}
|
|
};
|
|
|
|
K256.prototype.imulK = function imulK(num) {
|
|
// K = 0x1000003d1 = [ 0x40, 0x3d1 ]
|
|
num.words[num.length] = 0;
|
|
num.words[num.length + 1] = 0;
|
|
num.length += 2; // bounded at: 0x40 * 0x3ffffff + 0x3d0 = 0x100000390
|
|
|
|
var lo = 0;
|
|
|
|
for (var i = 0; i < num.length; i++) {
|
|
var w = num.words[i] | 0;
|
|
lo += w * 0x3d1;
|
|
num.words[i] = lo & 0x3ffffff;
|
|
lo = w * 0x40 + (lo / 0x4000000 | 0);
|
|
} // Fast length reduction
|
|
|
|
|
|
if (num.words[num.length - 1] === 0) {
|
|
num.length--;
|
|
|
|
if (num.words[num.length - 1] === 0) {
|
|
num.length--;
|
|
}
|
|
}
|
|
|
|
return num;
|
|
};
|
|
|
|
function P224() {
|
|
MPrime.call(this, 'p224', 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001');
|
|
}
|
|
|
|
inherits(P224, MPrime);
|
|
|
|
function P192() {
|
|
MPrime.call(this, 'p192', 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff');
|
|
}
|
|
|
|
inherits(P192, MPrime);
|
|
|
|
function P25519() {
|
|
// 2 ^ 255 - 19
|
|
MPrime.call(this, '25519', '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed');
|
|
}
|
|
|
|
inherits(P25519, MPrime);
|
|
|
|
P25519.prototype.imulK = function imulK(num) {
|
|
// K = 0x13
|
|
var carry = 0;
|
|
|
|
for (var i = 0; i < num.length; i++) {
|
|
var hi = (num.words[i] | 0) * 0x13 + carry;
|
|
var lo = hi & 0x3ffffff;
|
|
hi >>>= 26;
|
|
num.words[i] = lo;
|
|
carry = hi;
|
|
}
|
|
|
|
if (carry !== 0) {
|
|
num.words[num.length++] = carry;
|
|
}
|
|
|
|
return num;
|
|
}; // Exported mostly for testing purposes, use plain name instead
|
|
|
|
|
|
BN._prime = function prime(name) {
|
|
// Cached version of prime
|
|
if (primes[name]) return primes[name];
|
|
var prime;
|
|
|
|
if (name === 'k256') {
|
|
prime = new K256();
|
|
} else if (name === 'p224') {
|
|
prime = new P224();
|
|
} else if (name === 'p192') {
|
|
prime = new P192();
|
|
} else if (name === 'p25519') {
|
|
prime = new P25519();
|
|
} else {
|
|
throw new Error('Unknown prime ' + name);
|
|
}
|
|
|
|
primes[name] = prime;
|
|
return prime;
|
|
}; //
|
|
// Base reduction engine
|
|
//
|
|
|
|
|
|
function Red(m) {
|
|
if (typeof m === 'string') {
|
|
var prime = BN._prime(m);
|
|
|
|
this.m = prime.p;
|
|
this.prime = prime;
|
|
} else {
|
|
assert(m.gtn(1), 'modulus must be greater than 1');
|
|
this.m = m;
|
|
this.prime = null;
|
|
}
|
|
}
|
|
|
|
Red.prototype._verify1 = function _verify1(a) {
|
|
assert(a.negative === 0, 'red works only with positives');
|
|
assert(a.red, 'red works only with red numbers');
|
|
};
|
|
|
|
Red.prototype._verify2 = function _verify2(a, b) {
|
|
assert((a.negative | b.negative) === 0, 'red works only with positives');
|
|
assert(a.red && a.red === b.red, 'red works only with red numbers');
|
|
};
|
|
|
|
Red.prototype.imod = function imod(a) {
|
|
if (this.prime) return this.prime.ireduce(a)._forceRed(this);
|
|
return a.umod(this.m)._forceRed(this);
|
|
};
|
|
|
|
Red.prototype.neg = function neg(a) {
|
|
if (a.isZero()) {
|
|
return a.clone();
|
|
}
|
|
|
|
return this.m.sub(a)._forceRed(this);
|
|
};
|
|
|
|
Red.prototype.add = function add(a, b) {
|
|
this._verify2(a, b);
|
|
|
|
var res = a.add(b);
|
|
|
|
if (res.cmp(this.m) >= 0) {
|
|
res.isub(this.m);
|
|
}
|
|
|
|
return res._forceRed(this);
|
|
};
|
|
|
|
Red.prototype.iadd = function iadd(a, b) {
|
|
this._verify2(a, b);
|
|
|
|
var res = a.iadd(b);
|
|
|
|
if (res.cmp(this.m) >= 0) {
|
|
res.isub(this.m);
|
|
}
|
|
|
|
return res;
|
|
};
|
|
|
|
Red.prototype.sub = function sub(a, b) {
|
|
this._verify2(a, b);
|
|
|
|
var res = a.sub(b);
|
|
|
|
if (res.cmpn(0) < 0) {
|
|
res.iadd(this.m);
|
|
}
|
|
|
|
return res._forceRed(this);
|
|
};
|
|
|
|
Red.prototype.isub = function isub(a, b) {
|
|
this._verify2(a, b);
|
|
|
|
var res = a.isub(b);
|
|
|
|
if (res.cmpn(0) < 0) {
|
|
res.iadd(this.m);
|
|
}
|
|
|
|
return res;
|
|
};
|
|
|
|
Red.prototype.shl = function shl(a, num) {
|
|
this._verify1(a);
|
|
|
|
return this.imod(a.ushln(num));
|
|
};
|
|
|
|
Red.prototype.imul = function imul(a, b) {
|
|
this._verify2(a, b);
|
|
|
|
return this.imod(a.imul(b));
|
|
};
|
|
|
|
Red.prototype.mul = function mul(a, b) {
|
|
this._verify2(a, b);
|
|
|
|
return this.imod(a.mul(b));
|
|
};
|
|
|
|
Red.prototype.isqr = function isqr(a) {
|
|
return this.imul(a, a.clone());
|
|
};
|
|
|
|
Red.prototype.sqr = function sqr(a) {
|
|
return this.mul(a, a);
|
|
};
|
|
|
|
Red.prototype.sqrt = function sqrt(a) {
|
|
if (a.isZero()) return a.clone();
|
|
var mod3 = this.m.andln(3);
|
|
assert(mod3 % 2 === 1); // Fast case
|
|
|
|
if (mod3 === 3) {
|
|
var pow = this.m.add(new BN(1)).iushrn(2);
|
|
return this.pow(a, pow);
|
|
} // Tonelli-Shanks algorithm (Totally unoptimized and slow)
|
|
//
|
|
// Find Q and S, that Q * 2 ^ S = (P - 1)
|
|
|
|
|
|
var q = this.m.subn(1);
|
|
var s = 0;
|
|
|
|
while (!q.isZero() && q.andln(1) === 0) {
|
|
s++;
|
|
q.iushrn(1);
|
|
}
|
|
|
|
assert(!q.isZero());
|
|
var one = new BN(1).toRed(this);
|
|
var nOne = one.redNeg(); // Find quadratic non-residue
|
|
// NOTE: Max is such because of generalized Riemann hypothesis.
|
|
|
|
var lpow = this.m.subn(1).iushrn(1);
|
|
var z = this.m.bitLength();
|
|
z = new BN(2 * z * z).toRed(this);
|
|
|
|
while (this.pow(z, lpow).cmp(nOne) !== 0) {
|
|
z.redIAdd(nOne);
|
|
}
|
|
|
|
var c = this.pow(z, q);
|
|
var r = this.pow(a, q.addn(1).iushrn(1));
|
|
var t = this.pow(a, q);
|
|
var m = s;
|
|
|
|
while (t.cmp(one) !== 0) {
|
|
var tmp = t;
|
|
|
|
for (var i = 0; tmp.cmp(one) !== 0; i++) {
|
|
tmp = tmp.redSqr();
|
|
}
|
|
|
|
assert(i < m);
|
|
var b = this.pow(c, new BN(1).iushln(m - i - 1));
|
|
r = r.redMul(b);
|
|
c = b.redSqr();
|
|
t = t.redMul(c);
|
|
m = i;
|
|
}
|
|
|
|
return r;
|
|
};
|
|
|
|
Red.prototype.invm = function invm(a) {
|
|
var inv = a._invmp(this.m);
|
|
|
|
if (inv.negative !== 0) {
|
|
inv.negative = 0;
|
|
return this.imod(inv).redNeg();
|
|
} else {
|
|
return this.imod(inv);
|
|
}
|
|
};
|
|
|
|
Red.prototype.pow = function pow(a, num) {
|
|
if (num.isZero()) return new BN(1).toRed(this);
|
|
if (num.cmpn(1) === 0) return a.clone();
|
|
var windowSize = 4;
|
|
var wnd = new Array(1 << windowSize);
|
|
wnd[0] = new BN(1).toRed(this);
|
|
wnd[1] = a;
|
|
|
|
for (var i = 2; i < wnd.length; i++) {
|
|
wnd[i] = this.mul(wnd[i - 1], a);
|
|
}
|
|
|
|
var res = wnd[0];
|
|
var current = 0;
|
|
var currentLen = 0;
|
|
var start = num.bitLength() % 26;
|
|
|
|
if (start === 0) {
|
|
start = 26;
|
|
}
|
|
|
|
for (i = num.length - 1; i >= 0; i--) {
|
|
var word = num.words[i];
|
|
|
|
for (var j = start - 1; j >= 0; j--) {
|
|
var bit = word >> j & 1;
|
|
|
|
if (res !== wnd[0]) {
|
|
res = this.sqr(res);
|
|
}
|
|
|
|
if (bit === 0 && current === 0) {
|
|
currentLen = 0;
|
|
continue;
|
|
}
|
|
|
|
current <<= 1;
|
|
current |= bit;
|
|
currentLen++;
|
|
if (currentLen !== windowSize && (i !== 0 || j !== 0)) continue;
|
|
res = this.mul(res, wnd[current]);
|
|
currentLen = 0;
|
|
current = 0;
|
|
}
|
|
|
|
start = 26;
|
|
}
|
|
|
|
return res;
|
|
};
|
|
|
|
Red.prototype.convertTo = function convertTo(num) {
|
|
var r = num.umod(this.m);
|
|
return r === num ? r.clone() : r;
|
|
};
|
|
|
|
Red.prototype.convertFrom = function convertFrom(num) {
|
|
var res = num.clone();
|
|
res.red = null;
|
|
return res;
|
|
}; //
|
|
// Montgomery method engine
|
|
//
|
|
|
|
|
|
BN.mont = function mont(num) {
|
|
return new Mont(num);
|
|
};
|
|
|
|
function Mont(m) {
|
|
Red.call(this, m);
|
|
this.shift = this.m.bitLength();
|
|
|
|
if (this.shift % 26 !== 0) {
|
|
this.shift += 26 - this.shift % 26;
|
|
}
|
|
|
|
this.r = new BN(1).iushln(this.shift);
|
|
this.r2 = this.imod(this.r.sqr());
|
|
this.rinv = this.r._invmp(this.m);
|
|
this.minv = this.rinv.mul(this.r).isubn(1).div(this.m);
|
|
this.minv = this.minv.umod(this.r);
|
|
this.minv = this.r.sub(this.minv);
|
|
}
|
|
|
|
inherits(Mont, Red);
|
|
|
|
Mont.prototype.convertTo = function convertTo(num) {
|
|
return this.imod(num.ushln(this.shift));
|
|
};
|
|
|
|
Mont.prototype.convertFrom = function convertFrom(num) {
|
|
var r = this.imod(num.mul(this.rinv));
|
|
r.red = null;
|
|
return r;
|
|
};
|
|
|
|
Mont.prototype.imul = function imul(a, b) {
|
|
if (a.isZero() || b.isZero()) {
|
|
a.words[0] = 0;
|
|
a.length = 1;
|
|
return a;
|
|
}
|
|
|
|
var t = a.imul(b);
|
|
var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
|
|
var u = t.isub(c).iushrn(this.shift);
|
|
var res = u;
|
|
|
|
if (u.cmp(this.m) >= 0) {
|
|
res = u.isub(this.m);
|
|
} else if (u.cmpn(0) < 0) {
|
|
res = u.iadd(this.m);
|
|
}
|
|
|
|
return res._forceRed(this);
|
|
};
|
|
|
|
Mont.prototype.mul = function mul(a, b) {
|
|
if (a.isZero() || b.isZero()) return new BN(0)._forceRed(this);
|
|
var t = a.mul(b);
|
|
var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m);
|
|
var u = t.isub(c).iushrn(this.shift);
|
|
var res = u;
|
|
|
|
if (u.cmp(this.m) >= 0) {
|
|
res = u.isub(this.m);
|
|
} else if (u.cmpn(0) < 0) {
|
|
res = u.iadd(this.m);
|
|
}
|
|
|
|
return res._forceRed(this);
|
|
};
|
|
|
|
Mont.prototype.invm = function invm(a) {
|
|
// (AR)^-1 * R^2 = (A^-1 * R^-1) * R^2 = A^-1 * R
|
|
var res = this.imod(a._invmp(this.m).mul(this.r2));
|
|
return res._forceRed(this);
|
|
};
|
|
})(typeof module === 'undefined' || module, this); |