mirror of
https://github.com/zkitter/ffjavascript.git
synced 2026-01-14 17:37:57 -05:00
7923 lines
485 KiB
JavaScript
7923 lines
485 KiB
JavaScript
'use strict';
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Object.defineProperty(exports, '__esModule', { value: true });
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function _interopDefault (ex) { return (ex && (typeof ex === 'object') && 'default' in ex) ? ex['default'] : ex; }
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var crypto = _interopDefault(require('crypto'));
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var os = _interopDefault(require('os'));
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var NodeWorker_mod = _interopDefault(require('worker_threads'));
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/* global BigInt */
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const hexLen = [ 0, 1, 2, 2, 3, 3, 3, 3, 4 ,4 ,4 ,4 ,4 ,4 ,4 ,4];
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function fromString(s, radix) {
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if ((!radix)||(radix==10)) {
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return BigInt(s);
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} else if (radix==16) {
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if (s.slice(0,2) == "0x") {
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return BigInt(s);
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} else {
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return BigInt("0x"+s);
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}
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}
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}
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const e = fromString;
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function fromArray(a, radix) {
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let acc =0n;
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radix = BigInt(radix);
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for (let i=0; i<a.length; i++) {
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acc = acc*radix + BigInt(a[i]);
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}
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return acc;
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}
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function bitLength(a) {
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const aS =a.toString(16);
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return (aS.length-1)*4 +hexLen[parseInt(aS[0], 16)];
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}
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function isNegative(a) {
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return BigInt(a) < 0n;
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}
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function isZero(a) {
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return !a;
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}
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function shiftLeft(a, n) {
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return BigInt(a) << BigInt(n);
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}
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function shiftRight(a, n) {
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return BigInt(a) >> BigInt(n);
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}
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const shl = shiftLeft;
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const shr = shiftRight;
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function isOdd(a) {
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return (BigInt(a) & 1n) == 1n;
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}
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function naf(n) {
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let E = BigInt(n);
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const res = [];
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while (E) {
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if (E & 1n) {
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const z = 2 - Number(E % 4n);
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res.push( z );
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E = E - BigInt(z);
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} else {
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res.push( 0 );
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}
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E = E >> 1n;
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}
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return res;
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}
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function bits(n) {
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let E = BigInt(n);
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const res = [];
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while (E) {
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if (E & 1n) {
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res.push(1);
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} else {
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res.push( 0 );
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}
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E = E >> 1n;
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}
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return res;
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}
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function toNumber(s) {
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if (s>BigInt(Number.MAX_SAFE_INTEGER )) {
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throw new Error("Number too big");
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}
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return Number(s);
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}
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function toArray(s, radix) {
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const res = [];
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let rem = BigInt(s);
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radix = BigInt(radix);
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while (rem) {
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res.unshift( Number(rem % radix));
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rem = rem / radix;
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}
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return res;
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}
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function add(a, b) {
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return BigInt(a) + BigInt(b);
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}
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function sub(a, b) {
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return BigInt(a) - BigInt(b);
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}
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function neg(a) {
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return -BigInt(a);
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}
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function mul(a, b) {
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return BigInt(a) * BigInt(b);
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}
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function square(a) {
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return BigInt(a) * BigInt(a);
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}
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function pow(a, b) {
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return BigInt(a) ** BigInt(b);
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}
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function exp(a, b) {
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return BigInt(a) ** BigInt(b);
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}
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function abs(a) {
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return BigInt(a) >= 0 ? BigInt(a) : -BigInt(a);
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}
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function div(a, b) {
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return BigInt(a) / BigInt(b);
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}
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function mod(a, b) {
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return BigInt(a) % BigInt(b);
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}
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function eq(a, b) {
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return BigInt(a) == BigInt(b);
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}
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function neq(a, b) {
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return BigInt(a) != BigInt(b);
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}
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function lt(a, b) {
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return BigInt(a) < BigInt(b);
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}
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function gt(a, b) {
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return BigInt(a) > BigInt(b);
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}
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function leq(a, b) {
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return BigInt(a) <= BigInt(b);
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}
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function geq(a, b) {
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return BigInt(a) >= BigInt(b);
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}
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function band(a, b) {
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return BigInt(a) & BigInt(b);
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}
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function bor(a, b) {
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return BigInt(a) | BigInt(b);
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}
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function bxor(a, b) {
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return BigInt(a) ^ BigInt(b);
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}
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function land(a, b) {
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return BigInt(a) && BigInt(b);
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}
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function lor(a, b) {
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return BigInt(a) || BigInt(b);
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}
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function lnot(a) {
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return !BigInt(a);
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}
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var Scalar_native = /*#__PURE__*/Object.freeze({
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__proto__: null,
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fromString: fromString,
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e: e,
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fromArray: fromArray,
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bitLength: bitLength,
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isNegative: isNegative,
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isZero: isZero,
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shiftLeft: shiftLeft,
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shiftRight: shiftRight,
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shl: shl,
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shr: shr,
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isOdd: isOdd,
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naf: naf,
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bits: bits,
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toNumber: toNumber,
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toArray: toArray,
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add: add,
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sub: sub,
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neg: neg,
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mul: mul,
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square: square,
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pow: pow,
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exp: exp,
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abs: abs,
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div: div,
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mod: mod,
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eq: eq,
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neq: neq,
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lt: lt,
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gt: gt,
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leq: leq,
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geq: geq,
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band: band,
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bor: bor,
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bxor: bxor,
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land: land,
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lor: lor,
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lnot: lnot
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});
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function createCommonjsModule(fn, module) {
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return module = { exports: {} }, fn(module, module.exports), module.exports;
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}
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var BigInteger = createCommonjsModule(function (module) {
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var bigInt = (function (undefined$1) {
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var BASE = 1e7,
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LOG_BASE = 7,
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MAX_INT = 9007199254740992,
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MAX_INT_ARR = smallToArray(MAX_INT),
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DEFAULT_ALPHABET = "0123456789abcdefghijklmnopqrstuvwxyz";
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var supportsNativeBigInt = typeof BigInt === "function";
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function Integer(v, radix, alphabet, caseSensitive) {
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if (typeof v === "undefined") return Integer[0];
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if (typeof radix !== "undefined") return +radix === 10 && !alphabet ? parseValue(v) : parseBase(v, radix, alphabet, caseSensitive);
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return parseValue(v);
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}
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function BigInteger(value, sign) {
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this.value = value;
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this.sign = sign;
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this.isSmall = false;
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}
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BigInteger.prototype = Object.create(Integer.prototype);
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function SmallInteger(value) {
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this.value = value;
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this.sign = value < 0;
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this.isSmall = true;
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}
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SmallInteger.prototype = Object.create(Integer.prototype);
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function NativeBigInt(value) {
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this.value = value;
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}
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NativeBigInt.prototype = Object.create(Integer.prototype);
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function isPrecise(n) {
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return -MAX_INT < n && n < MAX_INT;
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}
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function smallToArray(n) { // For performance reasons doesn't reference BASE, need to change this function if BASE changes
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if (n < 1e7)
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return [n];
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if (n < 1e14)
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return [n % 1e7, Math.floor(n / 1e7)];
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return [n % 1e7, Math.floor(n / 1e7) % 1e7, Math.floor(n / 1e14)];
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}
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function arrayToSmall(arr) { // If BASE changes this function may need to change
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trim(arr);
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var length = arr.length;
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if (length < 4 && compareAbs(arr, MAX_INT_ARR) < 0) {
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switch (length) {
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case 0: return 0;
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case 1: return arr[0];
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case 2: return arr[0] + arr[1] * BASE;
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default: return arr[0] + (arr[1] + arr[2] * BASE) * BASE;
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}
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}
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return arr;
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}
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function trim(v) {
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var i = v.length;
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while (v[--i] === 0);
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v.length = i + 1;
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}
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function createArray(length) { // function shamelessly stolen from Yaffle's library https://github.com/Yaffle/BigInteger
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var x = new Array(length);
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var i = -1;
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while (++i < length) {
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x[i] = 0;
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}
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return x;
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}
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function truncate(n) {
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if (n > 0) return Math.floor(n);
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return Math.ceil(n);
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}
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function add(a, b) { // assumes a and b are arrays with a.length >= b.length
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var l_a = a.length,
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l_b = b.length,
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r = new Array(l_a),
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carry = 0,
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base = BASE,
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sum, i;
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for (i = 0; i < l_b; i++) {
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sum = a[i] + b[i] + carry;
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carry = sum >= base ? 1 : 0;
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r[i] = sum - carry * base;
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}
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while (i < l_a) {
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sum = a[i] + carry;
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carry = sum === base ? 1 : 0;
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r[i++] = sum - carry * base;
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}
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if (carry > 0) r.push(carry);
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return r;
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}
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function addAny(a, b) {
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if (a.length >= b.length) return add(a, b);
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return add(b, a);
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}
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function addSmall(a, carry) { // assumes a is array, carry is number with 0 <= carry < MAX_INT
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var l = a.length,
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r = new Array(l),
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base = BASE,
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sum, i;
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for (i = 0; i < l; i++) {
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sum = a[i] - base + carry;
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carry = Math.floor(sum / base);
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r[i] = sum - carry * base;
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carry += 1;
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}
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while (carry > 0) {
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r[i++] = carry % base;
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carry = Math.floor(carry / base);
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}
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return r;
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}
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BigInteger.prototype.add = function (v) {
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var n = parseValue(v);
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if (this.sign !== n.sign) {
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return this.subtract(n.negate());
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}
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var a = this.value, b = n.value;
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if (n.isSmall) {
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return new BigInteger(addSmall(a, Math.abs(b)), this.sign);
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}
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return new BigInteger(addAny(a, b), this.sign);
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};
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BigInteger.prototype.plus = BigInteger.prototype.add;
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SmallInteger.prototype.add = function (v) {
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var n = parseValue(v);
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var a = this.value;
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if (a < 0 !== n.sign) {
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return this.subtract(n.negate());
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}
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var b = n.value;
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if (n.isSmall) {
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if (isPrecise(a + b)) return new SmallInteger(a + b);
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b = smallToArray(Math.abs(b));
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}
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return new BigInteger(addSmall(b, Math.abs(a)), a < 0);
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};
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SmallInteger.prototype.plus = SmallInteger.prototype.add;
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NativeBigInt.prototype.add = function (v) {
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return new NativeBigInt(this.value + parseValue(v).value);
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};
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NativeBigInt.prototype.plus = NativeBigInt.prototype.add;
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function subtract(a, b) { // assumes a and b are arrays with a >= b
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var a_l = a.length,
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b_l = b.length,
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r = new Array(a_l),
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borrow = 0,
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base = BASE,
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i, difference;
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for (i = 0; i < b_l; i++) {
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difference = a[i] - borrow - b[i];
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if (difference < 0) {
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difference += base;
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borrow = 1;
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} else borrow = 0;
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r[i] = difference;
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}
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for (i = b_l; i < a_l; i++) {
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difference = a[i] - borrow;
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if (difference < 0) difference += base;
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else {
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r[i++] = difference;
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break;
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}
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r[i] = difference;
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}
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for (; i < a_l; i++) {
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r[i] = a[i];
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}
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trim(r);
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return r;
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}
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function subtractAny(a, b, sign) {
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var value;
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if (compareAbs(a, b) >= 0) {
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value = subtract(a, b);
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} else {
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value = subtract(b, a);
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sign = !sign;
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}
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value = arrayToSmall(value);
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if (typeof value === "number") {
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if (sign) value = -value;
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return new SmallInteger(value);
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}
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return new BigInteger(value, sign);
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}
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function subtractSmall(a, b, sign) { // assumes a is array, b is number with 0 <= b < MAX_INT
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var l = a.length,
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r = new Array(l),
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carry = -b,
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base = BASE,
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i, difference;
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for (i = 0; i < l; i++) {
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difference = a[i] + carry;
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carry = Math.floor(difference / base);
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difference %= base;
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r[i] = difference < 0 ? difference + base : difference;
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}
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r = arrayToSmall(r);
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if (typeof r === "number") {
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if (sign) r = -r;
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return new SmallInteger(r);
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} return new BigInteger(r, sign);
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}
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BigInteger.prototype.subtract = function (v) {
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var n = parseValue(v);
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if (this.sign !== n.sign) {
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return this.add(n.negate());
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}
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var a = this.value, b = n.value;
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if (n.isSmall)
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return subtractSmall(a, Math.abs(b), this.sign);
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return subtractAny(a, b, this.sign);
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};
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BigInteger.prototype.minus = BigInteger.prototype.subtract;
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SmallInteger.prototype.subtract = function (v) {
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var n = parseValue(v);
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var a = this.value;
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if (a < 0 !== n.sign) {
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return this.add(n.negate());
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}
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var b = n.value;
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if (n.isSmall) {
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return new SmallInteger(a - b);
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}
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return subtractSmall(b, Math.abs(a), a >= 0);
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};
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SmallInteger.prototype.minus = SmallInteger.prototype.subtract;
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NativeBigInt.prototype.subtract = function (v) {
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return new NativeBigInt(this.value - parseValue(v).value);
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};
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NativeBigInt.prototype.minus = NativeBigInt.prototype.subtract;
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BigInteger.prototype.negate = function () {
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return new BigInteger(this.value, !this.sign);
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};
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SmallInteger.prototype.negate = function () {
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var sign = this.sign;
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var small = new SmallInteger(-this.value);
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small.sign = !sign;
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return small;
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};
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NativeBigInt.prototype.negate = function () {
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return new NativeBigInt(-this.value);
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};
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BigInteger.prototype.abs = function () {
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return new BigInteger(this.value, false);
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};
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SmallInteger.prototype.abs = function () {
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return new SmallInteger(Math.abs(this.value));
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};
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NativeBigInt.prototype.abs = function () {
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return new NativeBigInt(this.value >= 0 ? this.value : -this.value);
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};
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function multiplyLong(a, b) {
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var a_l = a.length,
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b_l = b.length,
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l = a_l + b_l,
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r = createArray(l),
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base = BASE,
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product, carry, i, a_i, b_j;
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for (i = 0; i < a_l; ++i) {
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a_i = a[i];
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for (var j = 0; j < b_l; ++j) {
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b_j = b[j];
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product = a_i * b_j + r[i + j];
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carry = Math.floor(product / base);
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r[i + j] = product - carry * base;
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r[i + j + 1] += carry;
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}
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}
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trim(r);
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return r;
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}
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function multiplySmall(a, b) { // assumes a is array, b is number with |b| < BASE
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var l = a.length,
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r = new Array(l),
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base = BASE,
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carry = 0,
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product, i;
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for (i = 0; i < l; i++) {
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product = a[i] * b + carry;
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carry = Math.floor(product / base);
|
|
r[i] = product - carry * base;
|
|
}
|
|
while (carry > 0) {
|
|
r[i++] = carry % base;
|
|
carry = Math.floor(carry / base);
|
|
}
|
|
return r;
|
|
}
|
|
|
|
function shiftLeft(x, n) {
|
|
var r = [];
|
|
while (n-- > 0) r.push(0);
|
|
return r.concat(x);
|
|
}
|
|
|
|
function multiplyKaratsuba(x, y) {
|
|
var n = Math.max(x.length, y.length);
|
|
|
|
if (n <= 30) return multiplyLong(x, y);
|
|
n = Math.ceil(n / 2);
|
|
|
|
var b = x.slice(n),
|
|
a = x.slice(0, n),
|
|
d = y.slice(n),
|
|
c = y.slice(0, n);
|
|
|
|
var ac = multiplyKaratsuba(a, c),
|
|
bd = multiplyKaratsuba(b, d),
|
|
abcd = multiplyKaratsuba(addAny(a, b), addAny(c, d));
|
|
|
|
var product = addAny(addAny(ac, shiftLeft(subtract(subtract(abcd, ac), bd), n)), shiftLeft(bd, 2 * n));
|
|
trim(product);
|
|
return product;
|
|
}
|
|
|
|
// The following function is derived from a surface fit of a graph plotting the performance difference
|
|
// between long multiplication and karatsuba multiplication versus the lengths of the two arrays.
|
|
function useKaratsuba(l1, l2) {
|
|
return -0.012 * l1 - 0.012 * l2 + 0.000015 * l1 * l2 > 0;
|
|
}
|
|
|
|
BigInteger.prototype.multiply = function (v) {
|
|
var n = parseValue(v),
|
|
a = this.value, b = n.value,
|
|
sign = this.sign !== n.sign,
|
|
abs;
|
|
if (n.isSmall) {
|
|
if (b === 0) return Integer[0];
|
|
if (b === 1) return this;
|
|
if (b === -1) return this.negate();
|
|
abs = Math.abs(b);
|
|
if (abs < BASE) {
|
|
return new BigInteger(multiplySmall(a, abs), sign);
|
|
}
|
|
b = smallToArray(abs);
|
|
}
|
|
if (useKaratsuba(a.length, b.length)) // Karatsuba is only faster for certain array sizes
|
|
return new BigInteger(multiplyKaratsuba(a, b), sign);
|
|
return new BigInteger(multiplyLong(a, b), sign);
|
|
};
|
|
|
|
BigInteger.prototype.times = BigInteger.prototype.multiply;
|
|
|
|
function multiplySmallAndArray(a, b, sign) { // a >= 0
|
|
if (a < BASE) {
|
|
return new BigInteger(multiplySmall(b, a), sign);
|
|
}
|
|
return new BigInteger(multiplyLong(b, smallToArray(a)), sign);
|
|
}
|
|
SmallInteger.prototype._multiplyBySmall = function (a) {
|
|
if (isPrecise(a.value * this.value)) {
|
|
return new SmallInteger(a.value * this.value);
|
|
}
|
|
return multiplySmallAndArray(Math.abs(a.value), smallToArray(Math.abs(this.value)), this.sign !== a.sign);
|
|
};
|
|
BigInteger.prototype._multiplyBySmall = function (a) {
|
|
if (a.value === 0) return Integer[0];
|
|
if (a.value === 1) return this;
|
|
if (a.value === -1) return this.negate();
|
|
return multiplySmallAndArray(Math.abs(a.value), this.value, this.sign !== a.sign);
|
|
};
|
|
SmallInteger.prototype.multiply = function (v) {
|
|
return parseValue(v)._multiplyBySmall(this);
|
|
};
|
|
SmallInteger.prototype.times = SmallInteger.prototype.multiply;
|
|
|
|
NativeBigInt.prototype.multiply = function (v) {
|
|
return new NativeBigInt(this.value * parseValue(v).value);
|
|
};
|
|
NativeBigInt.prototype.times = NativeBigInt.prototype.multiply;
|
|
|
|
function square(a) {
|
|
//console.assert(2 * BASE * BASE < MAX_INT);
|
|
var l = a.length,
|
|
r = createArray(l + l),
|
|
base = BASE,
|
|
product, carry, i, a_i, a_j;
|
|
for (i = 0; i < l; i++) {
|
|
a_i = a[i];
|
|
carry = 0 - a_i * a_i;
|
|
for (var j = i; j < l; j++) {
|
|
a_j = a[j];
|
|
product = 2 * (a_i * a_j) + r[i + j] + carry;
|
|
carry = Math.floor(product / base);
|
|
r[i + j] = product - carry * base;
|
|
}
|
|
r[i + l] = carry;
|
|
}
|
|
trim(r);
|
|
return r;
|
|
}
|
|
|
|
BigInteger.prototype.square = function () {
|
|
return new BigInteger(square(this.value), false);
|
|
};
|
|
|
|
SmallInteger.prototype.square = function () {
|
|
var value = this.value * this.value;
|
|
if (isPrecise(value)) return new SmallInteger(value);
|
|
return new BigInteger(square(smallToArray(Math.abs(this.value))), false);
|
|
};
|
|
|
|
NativeBigInt.prototype.square = function (v) {
|
|
return new NativeBigInt(this.value * this.value);
|
|
};
|
|
|
|
function divMod1(a, b) { // Left over from previous version. Performs faster than divMod2 on smaller input sizes.
|
|
var a_l = a.length,
|
|
b_l = b.length,
|
|
base = BASE,
|
|
result = createArray(b.length),
|
|
divisorMostSignificantDigit = b[b_l - 1],
|
|
// normalization
|
|
lambda = Math.ceil(base / (2 * divisorMostSignificantDigit)),
|
|
remainder = multiplySmall(a, lambda),
|
|
divisor = multiplySmall(b, lambda),
|
|
quotientDigit, shift, carry, borrow, i, l, q;
|
|
if (remainder.length <= a_l) remainder.push(0);
|
|
divisor.push(0);
|
|
divisorMostSignificantDigit = divisor[b_l - 1];
|
|
for (shift = a_l - b_l; shift >= 0; shift--) {
|
|
quotientDigit = base - 1;
|
|
if (remainder[shift + b_l] !== divisorMostSignificantDigit) {
|
|
quotientDigit = Math.floor((remainder[shift + b_l] * base + remainder[shift + b_l - 1]) / divisorMostSignificantDigit);
|
|
}
|
|
// quotientDigit <= base - 1
|
|
carry = 0;
|
|
borrow = 0;
|
|
l = divisor.length;
|
|
for (i = 0; i < l; i++) {
|
|
carry += quotientDigit * divisor[i];
|
|
q = Math.floor(carry / base);
|
|
borrow += remainder[shift + i] - (carry - q * base);
|
|
carry = q;
|
|
if (borrow < 0) {
|
|
remainder[shift + i] = borrow + base;
|
|
borrow = -1;
|
|
} else {
|
|
remainder[shift + i] = borrow;
|
|
borrow = 0;
|
|
}
|
|
}
|
|
while (borrow !== 0) {
|
|
quotientDigit -= 1;
|
|
carry = 0;
|
|
for (i = 0; i < l; i++) {
|
|
carry += remainder[shift + i] - base + divisor[i];
|
|
if (carry < 0) {
|
|
remainder[shift + i] = carry + base;
|
|
carry = 0;
|
|
} else {
|
|
remainder[shift + i] = carry;
|
|
carry = 1;
|
|
}
|
|
}
|
|
borrow += carry;
|
|
}
|
|
result[shift] = quotientDigit;
|
|
}
|
|
// denormalization
|
|
remainder = divModSmall(remainder, lambda)[0];
|
|
return [arrayToSmall(result), arrayToSmall(remainder)];
|
|
}
|
|
|
|
function divMod2(a, b) { // Implementation idea shamelessly stolen from Silent Matt's library http://silentmatt.com/biginteger/
|
|
// Performs faster than divMod1 on larger input sizes.
|
|
var a_l = a.length,
|
|
b_l = b.length,
|
|
result = [],
|
|
part = [],
|
|
base = BASE,
|
|
guess, xlen, highx, highy, check;
|
|
while (a_l) {
|
|
part.unshift(a[--a_l]);
|
|
trim(part);
|
|
if (compareAbs(part, b) < 0) {
|
|
result.push(0);
|
|
continue;
|
|
}
|
|
xlen = part.length;
|
|
highx = part[xlen - 1] * base + part[xlen - 2];
|
|
highy = b[b_l - 1] * base + b[b_l - 2];
|
|
if (xlen > b_l) {
|
|
highx = (highx + 1) * base;
|
|
}
|
|
guess = Math.ceil(highx / highy);
|
|
do {
|
|
check = multiplySmall(b, guess);
|
|
if (compareAbs(check, part) <= 0) break;
|
|
guess--;
|
|
} while (guess);
|
|
result.push(guess);
|
|
part = subtract(part, check);
|
|
}
|
|
result.reverse();
|
|
return [arrayToSmall(result), arrayToSmall(part)];
|
|
}
|
|
|
|
function divModSmall(value, lambda) {
|
|
var length = value.length,
|
|
quotient = createArray(length),
|
|
base = BASE,
|
|
i, q, remainder, divisor;
|
|
remainder = 0;
|
|
for (i = length - 1; i >= 0; --i) {
|
|
divisor = remainder * base + value[i];
|
|
q = truncate(divisor / lambda);
|
|
remainder = divisor - q * lambda;
|
|
quotient[i] = q | 0;
|
|
}
|
|
return [quotient, remainder | 0];
|
|
}
|
|
|
|
function divModAny(self, v) {
|
|
var value, n = parseValue(v);
|
|
if (supportsNativeBigInt) {
|
|
return [new NativeBigInt(self.value / n.value), new NativeBigInt(self.value % n.value)];
|
|
}
|
|
var a = self.value, b = n.value;
|
|
var quotient;
|
|
if (b === 0) throw new Error("Cannot divide by zero");
|
|
if (self.isSmall) {
|
|
if (n.isSmall) {
|
|
return [new SmallInteger(truncate(a / b)), new SmallInteger(a % b)];
|
|
}
|
|
return [Integer[0], self];
|
|
}
|
|
if (n.isSmall) {
|
|
if (b === 1) return [self, Integer[0]];
|
|
if (b == -1) return [self.negate(), Integer[0]];
|
|
var abs = Math.abs(b);
|
|
if (abs < BASE) {
|
|
value = divModSmall(a, abs);
|
|
quotient = arrayToSmall(value[0]);
|
|
var remainder = value[1];
|
|
if (self.sign) remainder = -remainder;
|
|
if (typeof quotient === "number") {
|
|
if (self.sign !== n.sign) quotient = -quotient;
|
|
return [new SmallInteger(quotient), new SmallInteger(remainder)];
|
|
}
|
|
return [new BigInteger(quotient, self.sign !== n.sign), new SmallInteger(remainder)];
|
|
}
|
|
b = smallToArray(abs);
|
|
}
|
|
var comparison = compareAbs(a, b);
|
|
if (comparison === -1) return [Integer[0], self];
|
|
if (comparison === 0) return [Integer[self.sign === n.sign ? 1 : -1], Integer[0]];
|
|
|
|
// divMod1 is faster on smaller input sizes
|
|
if (a.length + b.length <= 200)
|
|
value = divMod1(a, b);
|
|
else value = divMod2(a, b);
|
|
|
|
quotient = value[0];
|
|
var qSign = self.sign !== n.sign,
|
|
mod = value[1],
|
|
mSign = self.sign;
|
|
if (typeof quotient === "number") {
|
|
if (qSign) quotient = -quotient;
|
|
quotient = new SmallInteger(quotient);
|
|
} else quotient = new BigInteger(quotient, qSign);
|
|
if (typeof mod === "number") {
|
|
if (mSign) mod = -mod;
|
|
mod = new SmallInteger(mod);
|
|
} else mod = new BigInteger(mod, mSign);
|
|
return [quotient, mod];
|
|
}
|
|
|
|
BigInteger.prototype.divmod = function (v) {
|
|
var result = divModAny(this, v);
|
|
return {
|
|
quotient: result[0],
|
|
remainder: result[1]
|
|
};
|
|
};
|
|
NativeBigInt.prototype.divmod = SmallInteger.prototype.divmod = BigInteger.prototype.divmod;
|
|
|
|
|
|
BigInteger.prototype.divide = function (v) {
|
|
return divModAny(this, v)[0];
|
|
};
|
|
NativeBigInt.prototype.over = NativeBigInt.prototype.divide = function (v) {
|
|
return new NativeBigInt(this.value / parseValue(v).value);
|
|
};
|
|
SmallInteger.prototype.over = SmallInteger.prototype.divide = BigInteger.prototype.over = BigInteger.prototype.divide;
|
|
|
|
BigInteger.prototype.mod = function (v) {
|
|
return divModAny(this, v)[1];
|
|
};
|
|
NativeBigInt.prototype.mod = NativeBigInt.prototype.remainder = function (v) {
|
|
return new NativeBigInt(this.value % parseValue(v).value);
|
|
};
|
|
SmallInteger.prototype.remainder = SmallInteger.prototype.mod = BigInteger.prototype.remainder = BigInteger.prototype.mod;
|
|
|
|
BigInteger.prototype.pow = function (v) {
|
|
var n = parseValue(v),
|
|
a = this.value,
|
|
b = n.value,
|
|
value, x, y;
|
|
if (b === 0) return Integer[1];
|
|
if (a === 0) return Integer[0];
|
|
if (a === 1) return Integer[1];
|
|
if (a === -1) return n.isEven() ? Integer[1] : Integer[-1];
|
|
if (n.sign) {
|
|
return Integer[0];
|
|
}
|
|
if (!n.isSmall) throw new Error("The exponent " + n.toString() + " is too large.");
|
|
if (this.isSmall) {
|
|
if (isPrecise(value = Math.pow(a, b)))
|
|
return new SmallInteger(truncate(value));
|
|
}
|
|
x = this;
|
|
y = Integer[1];
|
|
while (true) {
|
|
if (b & 1 === 1) {
|
|
y = y.times(x);
|
|
--b;
|
|
}
|
|
if (b === 0) break;
|
|
b /= 2;
|
|
x = x.square();
|
|
}
|
|
return y;
|
|
};
|
|
SmallInteger.prototype.pow = BigInteger.prototype.pow;
|
|
|
|
NativeBigInt.prototype.pow = function (v) {
|
|
var n = parseValue(v);
|
|
var a = this.value, b = n.value;
|
|
var _0 = BigInt(0), _1 = BigInt(1), _2 = BigInt(2);
|
|
if (b === _0) return Integer[1];
|
|
if (a === _0) return Integer[0];
|
|
if (a === _1) return Integer[1];
|
|
if (a === BigInt(-1)) return n.isEven() ? Integer[1] : Integer[-1];
|
|
if (n.isNegative()) return new NativeBigInt(_0);
|
|
var x = this;
|
|
var y = Integer[1];
|
|
while (true) {
|
|
if ((b & _1) === _1) {
|
|
y = y.times(x);
|
|
--b;
|
|
}
|
|
if (b === _0) break;
|
|
b /= _2;
|
|
x = x.square();
|
|
}
|
|
return y;
|
|
};
|
|
|
|
BigInteger.prototype.modPow = function (exp, mod) {
|
|
exp = parseValue(exp);
|
|
mod = parseValue(mod);
|
|
if (mod.isZero()) throw new Error("Cannot take modPow with modulus 0");
|
|
var r = Integer[1],
|
|
base = this.mod(mod);
|
|
if (exp.isNegative()) {
|
|
exp = exp.multiply(Integer[-1]);
|
|
base = base.modInv(mod);
|
|
}
|
|
while (exp.isPositive()) {
|
|
if (base.isZero()) return Integer[0];
|
|
if (exp.isOdd()) r = r.multiply(base).mod(mod);
|
|
exp = exp.divide(2);
|
|
base = base.square().mod(mod);
|
|
}
|
|
return r;
|
|
};
|
|
NativeBigInt.prototype.modPow = SmallInteger.prototype.modPow = BigInteger.prototype.modPow;
|
|
|
|
function compareAbs(a, b) {
|
|
if (a.length !== b.length) {
|
|
return a.length > b.length ? 1 : -1;
|
|
}
|
|
for (var i = a.length - 1; i >= 0; i--) {
|
|
if (a[i] !== b[i]) return a[i] > b[i] ? 1 : -1;
|
|
}
|
|
return 0;
|
|
}
|
|
|
|
BigInteger.prototype.compareAbs = function (v) {
|
|
var n = parseValue(v),
|
|
a = this.value,
|
|
b = n.value;
|
|
if (n.isSmall) return 1;
|
|
return compareAbs(a, b);
|
|
};
|
|
SmallInteger.prototype.compareAbs = function (v) {
|
|
var n = parseValue(v),
|
|
a = Math.abs(this.value),
|
|
b = n.value;
|
|
if (n.isSmall) {
|
|
b = Math.abs(b);
|
|
return a === b ? 0 : a > b ? 1 : -1;
|
|
}
|
|
return -1;
|
|
};
|
|
NativeBigInt.prototype.compareAbs = function (v) {
|
|
var a = this.value;
|
|
var b = parseValue(v).value;
|
|
a = a >= 0 ? a : -a;
|
|
b = b >= 0 ? b : -b;
|
|
return a === b ? 0 : a > b ? 1 : -1;
|
|
};
|
|
|
|
BigInteger.prototype.compare = function (v) {
|
|
// See discussion about comparison with Infinity:
|
|
// https://github.com/peterolson/BigInteger.js/issues/61
|
|
if (v === Infinity) {
|
|
return -1;
|
|
}
|
|
if (v === -Infinity) {
|
|
return 1;
|
|
}
|
|
|
|
var n = parseValue(v),
|
|
a = this.value,
|
|
b = n.value;
|
|
if (this.sign !== n.sign) {
|
|
return n.sign ? 1 : -1;
|
|
}
|
|
if (n.isSmall) {
|
|
return this.sign ? -1 : 1;
|
|
}
|
|
return compareAbs(a, b) * (this.sign ? -1 : 1);
|
|
};
|
|
BigInteger.prototype.compareTo = BigInteger.prototype.compare;
|
|
|
|
SmallInteger.prototype.compare = function (v) {
|
|
if (v === Infinity) {
|
|
return -1;
|
|
}
|
|
if (v === -Infinity) {
|
|
return 1;
|
|
}
|
|
|
|
var n = parseValue(v),
|
|
a = this.value,
|
|
b = n.value;
|
|
if (n.isSmall) {
|
|
return a == b ? 0 : a > b ? 1 : -1;
|
|
}
|
|
if (a < 0 !== n.sign) {
|
|
return a < 0 ? -1 : 1;
|
|
}
|
|
return a < 0 ? 1 : -1;
|
|
};
|
|
SmallInteger.prototype.compareTo = SmallInteger.prototype.compare;
|
|
|
|
NativeBigInt.prototype.compare = function (v) {
|
|
if (v === Infinity) {
|
|
return -1;
|
|
}
|
|
if (v === -Infinity) {
|
|
return 1;
|
|
}
|
|
var a = this.value;
|
|
var b = parseValue(v).value;
|
|
return a === b ? 0 : a > b ? 1 : -1;
|
|
};
|
|
NativeBigInt.prototype.compareTo = NativeBigInt.prototype.compare;
|
|
|
|
BigInteger.prototype.equals = function (v) {
|
|
return this.compare(v) === 0;
|
|
};
|
|
NativeBigInt.prototype.eq = NativeBigInt.prototype.equals = SmallInteger.prototype.eq = SmallInteger.prototype.equals = BigInteger.prototype.eq = BigInteger.prototype.equals;
|
|
|
|
BigInteger.prototype.notEquals = function (v) {
|
|
return this.compare(v) !== 0;
|
|
};
|
|
NativeBigInt.prototype.neq = NativeBigInt.prototype.notEquals = SmallInteger.prototype.neq = SmallInteger.prototype.notEquals = BigInteger.prototype.neq = BigInteger.prototype.notEquals;
|
|
|
|
BigInteger.prototype.greater = function (v) {
|
|
return this.compare(v) > 0;
|
|
};
|
|
NativeBigInt.prototype.gt = NativeBigInt.prototype.greater = SmallInteger.prototype.gt = SmallInteger.prototype.greater = BigInteger.prototype.gt = BigInteger.prototype.greater;
|
|
|
|
BigInteger.prototype.lesser = function (v) {
|
|
return this.compare(v) < 0;
|
|
};
|
|
NativeBigInt.prototype.lt = NativeBigInt.prototype.lesser = SmallInteger.prototype.lt = SmallInteger.prototype.lesser = BigInteger.prototype.lt = BigInteger.prototype.lesser;
|
|
|
|
BigInteger.prototype.greaterOrEquals = function (v) {
|
|
return this.compare(v) >= 0;
|
|
};
|
|
NativeBigInt.prototype.geq = NativeBigInt.prototype.greaterOrEquals = SmallInteger.prototype.geq = SmallInteger.prototype.greaterOrEquals = BigInteger.prototype.geq = BigInteger.prototype.greaterOrEquals;
|
|
|
|
BigInteger.prototype.lesserOrEquals = function (v) {
|
|
return this.compare(v) <= 0;
|
|
};
|
|
NativeBigInt.prototype.leq = NativeBigInt.prototype.lesserOrEquals = SmallInteger.prototype.leq = SmallInteger.prototype.lesserOrEquals = BigInteger.prototype.leq = BigInteger.prototype.lesserOrEquals;
|
|
|
|
BigInteger.prototype.isEven = function () {
|
|
return (this.value[0] & 1) === 0;
|
|
};
|
|
SmallInteger.prototype.isEven = function () {
|
|
return (this.value & 1) === 0;
|
|
};
|
|
NativeBigInt.prototype.isEven = function () {
|
|
return (this.value & BigInt(1)) === BigInt(0);
|
|
};
|
|
|
|
BigInteger.prototype.isOdd = function () {
|
|
return (this.value[0] & 1) === 1;
|
|
};
|
|
SmallInteger.prototype.isOdd = function () {
|
|
return (this.value & 1) === 1;
|
|
};
|
|
NativeBigInt.prototype.isOdd = function () {
|
|
return (this.value & BigInt(1)) === BigInt(1);
|
|
};
|
|
|
|
BigInteger.prototype.isPositive = function () {
|
|
return !this.sign;
|
|
};
|
|
SmallInteger.prototype.isPositive = function () {
|
|
return this.value > 0;
|
|
};
|
|
NativeBigInt.prototype.isPositive = SmallInteger.prototype.isPositive;
|
|
|
|
BigInteger.prototype.isNegative = function () {
|
|
return this.sign;
|
|
};
|
|
SmallInteger.prototype.isNegative = function () {
|
|
return this.value < 0;
|
|
};
|
|
NativeBigInt.prototype.isNegative = SmallInteger.prototype.isNegative;
|
|
|
|
BigInteger.prototype.isUnit = function () {
|
|
return false;
|
|
};
|
|
SmallInteger.prototype.isUnit = function () {
|
|
return Math.abs(this.value) === 1;
|
|
};
|
|
NativeBigInt.prototype.isUnit = function () {
|
|
return this.abs().value === BigInt(1);
|
|
};
|
|
|
|
BigInteger.prototype.isZero = function () {
|
|
return false;
|
|
};
|
|
SmallInteger.prototype.isZero = function () {
|
|
return this.value === 0;
|
|
};
|
|
NativeBigInt.prototype.isZero = function () {
|
|
return this.value === BigInt(0);
|
|
};
|
|
|
|
BigInteger.prototype.isDivisibleBy = function (v) {
|
|
var n = parseValue(v);
|
|
if (n.isZero()) return false;
|
|
if (n.isUnit()) return true;
|
|
if (n.compareAbs(2) === 0) return this.isEven();
|
|
return this.mod(n).isZero();
|
|
};
|
|
NativeBigInt.prototype.isDivisibleBy = SmallInteger.prototype.isDivisibleBy = BigInteger.prototype.isDivisibleBy;
|
|
|
|
function isBasicPrime(v) {
|
|
var n = v.abs();
|
|
if (n.isUnit()) return false;
|
|
if (n.equals(2) || n.equals(3) || n.equals(5)) return true;
|
|
if (n.isEven() || n.isDivisibleBy(3) || n.isDivisibleBy(5)) return false;
|
|
if (n.lesser(49)) return true;
|
|
// we don't know if it's prime: let the other functions figure it out
|
|
}
|
|
|
|
function millerRabinTest(n, a) {
|
|
var nPrev = n.prev(),
|
|
b = nPrev,
|
|
r = 0,
|
|
d, i, x;
|
|
while (b.isEven()) b = b.divide(2), r++;
|
|
next: for (i = 0; i < a.length; i++) {
|
|
if (n.lesser(a[i])) continue;
|
|
x = bigInt(a[i]).modPow(b, n);
|
|
if (x.isUnit() || x.equals(nPrev)) continue;
|
|
for (d = r - 1; d != 0; d--) {
|
|
x = x.square().mod(n);
|
|
if (x.isUnit()) return false;
|
|
if (x.equals(nPrev)) continue next;
|
|
}
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// Set "strict" to true to force GRH-supported lower bound of 2*log(N)^2
|
|
BigInteger.prototype.isPrime = function (strict) {
|
|
var isPrime = isBasicPrime(this);
|
|
if (isPrime !== undefined$1) return isPrime;
|
|
var n = this.abs();
|
|
var bits = n.bitLength();
|
|
if (bits <= 64)
|
|
return millerRabinTest(n, [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]);
|
|
var logN = Math.log(2) * bits.toJSNumber();
|
|
var t = Math.ceil((strict === true) ? (2 * Math.pow(logN, 2)) : logN);
|
|
for (var a = [], i = 0; i < t; i++) {
|
|
a.push(bigInt(i + 2));
|
|
}
|
|
return millerRabinTest(n, a);
|
|
};
|
|
NativeBigInt.prototype.isPrime = SmallInteger.prototype.isPrime = BigInteger.prototype.isPrime;
|
|
|
|
BigInteger.prototype.isProbablePrime = function (iterations, rng) {
|
|
var isPrime = isBasicPrime(this);
|
|
if (isPrime !== undefined$1) return isPrime;
|
|
var n = this.abs();
|
|
var t = iterations === undefined$1 ? 5 : iterations;
|
|
for (var a = [], i = 0; i < t; i++) {
|
|
a.push(bigInt.randBetween(2, n.minus(2), rng));
|
|
}
|
|
return millerRabinTest(n, a);
|
|
};
|
|
NativeBigInt.prototype.isProbablePrime = SmallInteger.prototype.isProbablePrime = BigInteger.prototype.isProbablePrime;
|
|
|
|
BigInteger.prototype.modInv = function (n) {
|
|
var t = bigInt.zero, newT = bigInt.one, r = parseValue(n), newR = this.abs(), q, lastT, lastR;
|
|
while (!newR.isZero()) {
|
|
q = r.divide(newR);
|
|
lastT = t;
|
|
lastR = r;
|
|
t = newT;
|
|
r = newR;
|
|
newT = lastT.subtract(q.multiply(newT));
|
|
newR = lastR.subtract(q.multiply(newR));
|
|
}
|
|
if (!r.isUnit()) throw new Error(this.toString() + " and " + n.toString() + " are not co-prime");
|
|
if (t.compare(0) === -1) {
|
|
t = t.add(n);
|
|
}
|
|
if (this.isNegative()) {
|
|
return t.negate();
|
|
}
|
|
return t;
|
|
};
|
|
|
|
NativeBigInt.prototype.modInv = SmallInteger.prototype.modInv = BigInteger.prototype.modInv;
|
|
|
|
BigInteger.prototype.next = function () {
|
|
var value = this.value;
|
|
if (this.sign) {
|
|
return subtractSmall(value, 1, this.sign);
|
|
}
|
|
return new BigInteger(addSmall(value, 1), this.sign);
|
|
};
|
|
SmallInteger.prototype.next = function () {
|
|
var value = this.value;
|
|
if (value + 1 < MAX_INT) return new SmallInteger(value + 1);
|
|
return new BigInteger(MAX_INT_ARR, false);
|
|
};
|
|
NativeBigInt.prototype.next = function () {
|
|
return new NativeBigInt(this.value + BigInt(1));
|
|
};
|
|
|
|
BigInteger.prototype.prev = function () {
|
|
var value = this.value;
|
|
if (this.sign) {
|
|
return new BigInteger(addSmall(value, 1), true);
|
|
}
|
|
return subtractSmall(value, 1, this.sign);
|
|
};
|
|
SmallInteger.prototype.prev = function () {
|
|
var value = this.value;
|
|
if (value - 1 > -MAX_INT) return new SmallInteger(value - 1);
|
|
return new BigInteger(MAX_INT_ARR, true);
|
|
};
|
|
NativeBigInt.prototype.prev = function () {
|
|
return new NativeBigInt(this.value - BigInt(1));
|
|
};
|
|
|
|
var powersOfTwo = [1];
|
|
while (2 * powersOfTwo[powersOfTwo.length - 1] <= BASE) powersOfTwo.push(2 * powersOfTwo[powersOfTwo.length - 1]);
|
|
var powers2Length = powersOfTwo.length, highestPower2 = powersOfTwo[powers2Length - 1];
|
|
|
|
function shift_isSmall(n) {
|
|
return Math.abs(n) <= BASE;
|
|
}
|
|
|
|
BigInteger.prototype.shiftLeft = function (v) {
|
|
var n = parseValue(v).toJSNumber();
|
|
if (!shift_isSmall(n)) {
|
|
throw new Error(String(n) + " is too large for shifting.");
|
|
}
|
|
if (n < 0) return this.shiftRight(-n);
|
|
var result = this;
|
|
if (result.isZero()) return result;
|
|
while (n >= powers2Length) {
|
|
result = result.multiply(highestPower2);
|
|
n -= powers2Length - 1;
|
|
}
|
|
return result.multiply(powersOfTwo[n]);
|
|
};
|
|
NativeBigInt.prototype.shiftLeft = SmallInteger.prototype.shiftLeft = BigInteger.prototype.shiftLeft;
|
|
|
|
BigInteger.prototype.shiftRight = function (v) {
|
|
var remQuo;
|
|
var n = parseValue(v).toJSNumber();
|
|
if (!shift_isSmall(n)) {
|
|
throw new Error(String(n) + " is too large for shifting.");
|
|
}
|
|
if (n < 0) return this.shiftLeft(-n);
|
|
var result = this;
|
|
while (n >= powers2Length) {
|
|
if (result.isZero() || (result.isNegative() && result.isUnit())) return result;
|
|
remQuo = divModAny(result, highestPower2);
|
|
result = remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
|
|
n -= powers2Length - 1;
|
|
}
|
|
remQuo = divModAny(result, powersOfTwo[n]);
|
|
return remQuo[1].isNegative() ? remQuo[0].prev() : remQuo[0];
|
|
};
|
|
NativeBigInt.prototype.shiftRight = SmallInteger.prototype.shiftRight = BigInteger.prototype.shiftRight;
|
|
|
|
function bitwise(x, y, fn) {
|
|
y = parseValue(y);
|
|
var xSign = x.isNegative(), ySign = y.isNegative();
|
|
var xRem = xSign ? x.not() : x,
|
|
yRem = ySign ? y.not() : y;
|
|
var xDigit = 0, yDigit = 0;
|
|
var xDivMod = null, yDivMod = null;
|
|
var result = [];
|
|
while (!xRem.isZero() || !yRem.isZero()) {
|
|
xDivMod = divModAny(xRem, highestPower2);
|
|
xDigit = xDivMod[1].toJSNumber();
|
|
if (xSign) {
|
|
xDigit = highestPower2 - 1 - xDigit; // two's complement for negative numbers
|
|
}
|
|
|
|
yDivMod = divModAny(yRem, highestPower2);
|
|
yDigit = yDivMod[1].toJSNumber();
|
|
if (ySign) {
|
|
yDigit = highestPower2 - 1 - yDigit; // two's complement for negative numbers
|
|
}
|
|
|
|
xRem = xDivMod[0];
|
|
yRem = yDivMod[0];
|
|
result.push(fn(xDigit, yDigit));
|
|
}
|
|
var sum = fn(xSign ? 1 : 0, ySign ? 1 : 0) !== 0 ? bigInt(-1) : bigInt(0);
|
|
for (var i = result.length - 1; i >= 0; i -= 1) {
|
|
sum = sum.multiply(highestPower2).add(bigInt(result[i]));
|
|
}
|
|
return sum;
|
|
}
|
|
|
|
BigInteger.prototype.not = function () {
|
|
return this.negate().prev();
|
|
};
|
|
NativeBigInt.prototype.not = SmallInteger.prototype.not = BigInteger.prototype.not;
|
|
|
|
BigInteger.prototype.and = function (n) {
|
|
return bitwise(this, n, function (a, b) { return a & b; });
|
|
};
|
|
NativeBigInt.prototype.and = SmallInteger.prototype.and = BigInteger.prototype.and;
|
|
|
|
BigInteger.prototype.or = function (n) {
|
|
return bitwise(this, n, function (a, b) { return a | b; });
|
|
};
|
|
NativeBigInt.prototype.or = SmallInteger.prototype.or = BigInteger.prototype.or;
|
|
|
|
BigInteger.prototype.xor = function (n) {
|
|
return bitwise(this, n, function (a, b) { return a ^ b; });
|
|
};
|
|
NativeBigInt.prototype.xor = SmallInteger.prototype.xor = BigInteger.prototype.xor;
|
|
|
|
var LOBMASK_I = 1 << 30, LOBMASK_BI = (BASE & -BASE) * (BASE & -BASE) | LOBMASK_I;
|
|
function roughLOB(n) { // get lowestOneBit (rough)
|
|
// SmallInteger: return Min(lowestOneBit(n), 1 << 30)
|
|
// BigInteger: return Min(lowestOneBit(n), 1 << 14) [BASE=1e7]
|
|
var v = n.value,
|
|
x = typeof v === "number" ? v | LOBMASK_I :
|
|
typeof v === "bigint" ? v | BigInt(LOBMASK_I) :
|
|
v[0] + v[1] * BASE | LOBMASK_BI;
|
|
return x & -x;
|
|
}
|
|
|
|
function integerLogarithm(value, base) {
|
|
if (base.compareTo(value) <= 0) {
|
|
var tmp = integerLogarithm(value, base.square(base));
|
|
var p = tmp.p;
|
|
var e = tmp.e;
|
|
var t = p.multiply(base);
|
|
return t.compareTo(value) <= 0 ? { p: t, e: e * 2 + 1 } : { p: p, e: e * 2 };
|
|
}
|
|
return { p: bigInt(1), e: 0 };
|
|
}
|
|
|
|
BigInteger.prototype.bitLength = function () {
|
|
var n = this;
|
|
if (n.compareTo(bigInt(0)) < 0) {
|
|
n = n.negate().subtract(bigInt(1));
|
|
}
|
|
if (n.compareTo(bigInt(0)) === 0) {
|
|
return bigInt(0);
|
|
}
|
|
return bigInt(integerLogarithm(n, bigInt(2)).e).add(bigInt(1));
|
|
};
|
|
NativeBigInt.prototype.bitLength = SmallInteger.prototype.bitLength = BigInteger.prototype.bitLength;
|
|
|
|
function max(a, b) {
|
|
a = parseValue(a);
|
|
b = parseValue(b);
|
|
return a.greater(b) ? a : b;
|
|
}
|
|
function min(a, b) {
|
|
a = parseValue(a);
|
|
b = parseValue(b);
|
|
return a.lesser(b) ? a : b;
|
|
}
|
|
function gcd(a, b) {
|
|
a = parseValue(a).abs();
|
|
b = parseValue(b).abs();
|
|
if (a.equals(b)) return a;
|
|
if (a.isZero()) return b;
|
|
if (b.isZero()) return a;
|
|
var c = Integer[1], d, t;
|
|
while (a.isEven() && b.isEven()) {
|
|
d = min(roughLOB(a), roughLOB(b));
|
|
a = a.divide(d);
|
|
b = b.divide(d);
|
|
c = c.multiply(d);
|
|
}
|
|
while (a.isEven()) {
|
|
a = a.divide(roughLOB(a));
|
|
}
|
|
do {
|
|
while (b.isEven()) {
|
|
b = b.divide(roughLOB(b));
|
|
}
|
|
if (a.greater(b)) {
|
|
t = b; b = a; a = t;
|
|
}
|
|
b = b.subtract(a);
|
|
} while (!b.isZero());
|
|
return c.isUnit() ? a : a.multiply(c);
|
|
}
|
|
function lcm(a, b) {
|
|
a = parseValue(a).abs();
|
|
b = parseValue(b).abs();
|
|
return a.divide(gcd(a, b)).multiply(b);
|
|
}
|
|
function randBetween(a, b, rng) {
|
|
a = parseValue(a);
|
|
b = parseValue(b);
|
|
var usedRNG = rng || Math.random;
|
|
var low = min(a, b), high = max(a, b);
|
|
var range = high.subtract(low).add(1);
|
|
if (range.isSmall) return low.add(Math.floor(usedRNG() * range));
|
|
var digits = toBase(range, BASE).value;
|
|
var result = [], restricted = true;
|
|
for (var i = 0; i < digits.length; i++) {
|
|
var top = restricted ? digits[i] : BASE;
|
|
var digit = truncate(usedRNG() * top);
|
|
result.push(digit);
|
|
if (digit < top) restricted = false;
|
|
}
|
|
return low.add(Integer.fromArray(result, BASE, false));
|
|
}
|
|
|
|
var parseBase = function (text, base, alphabet, caseSensitive) {
|
|
alphabet = alphabet || DEFAULT_ALPHABET;
|
|
text = String(text);
|
|
if (!caseSensitive) {
|
|
text = text.toLowerCase();
|
|
alphabet = alphabet.toLowerCase();
|
|
}
|
|
var length = text.length;
|
|
var i;
|
|
var absBase = Math.abs(base);
|
|
var alphabetValues = {};
|
|
for (i = 0; i < alphabet.length; i++) {
|
|
alphabetValues[alphabet[i]] = i;
|
|
}
|
|
for (i = 0; i < length; i++) {
|
|
var c = text[i];
|
|
if (c === "-") continue;
|
|
if (c in alphabetValues) {
|
|
if (alphabetValues[c] >= absBase) {
|
|
if (c === "1" && absBase === 1) continue;
|
|
throw new Error(c + " is not a valid digit in base " + base + ".");
|
|
}
|
|
}
|
|
}
|
|
base = parseValue(base);
|
|
var digits = [];
|
|
var isNegative = text[0] === "-";
|
|
for (i = isNegative ? 1 : 0; i < text.length; i++) {
|
|
var c = text[i];
|
|
if (c in alphabetValues) digits.push(parseValue(alphabetValues[c]));
|
|
else if (c === "<") {
|
|
var start = i;
|
|
do { i++; } while (text[i] !== ">" && i < text.length);
|
|
digits.push(parseValue(text.slice(start + 1, i)));
|
|
}
|
|
else throw new Error(c + " is not a valid character");
|
|
}
|
|
return parseBaseFromArray(digits, base, isNegative);
|
|
};
|
|
|
|
function parseBaseFromArray(digits, base, isNegative) {
|
|
var val = Integer[0], pow = Integer[1], i;
|
|
for (i = digits.length - 1; i >= 0; i--) {
|
|
val = val.add(digits[i].times(pow));
|
|
pow = pow.times(base);
|
|
}
|
|
return isNegative ? val.negate() : val;
|
|
}
|
|
|
|
function stringify(digit, alphabet) {
|
|
alphabet = alphabet || DEFAULT_ALPHABET;
|
|
if (digit < alphabet.length) {
|
|
return alphabet[digit];
|
|
}
|
|
return "<" + digit + ">";
|
|
}
|
|
|
|
function toBase(n, base) {
|
|
base = bigInt(base);
|
|
if (base.isZero()) {
|
|
if (n.isZero()) return { value: [0], isNegative: false };
|
|
throw new Error("Cannot convert nonzero numbers to base 0.");
|
|
}
|
|
if (base.equals(-1)) {
|
|
if (n.isZero()) return { value: [0], isNegative: false };
|
|
if (n.isNegative())
|
|
return {
|
|
value: [].concat.apply([], Array.apply(null, Array(-n.toJSNumber()))
|
|
.map(Array.prototype.valueOf, [1, 0])
|
|
),
|
|
isNegative: false
|
|
};
|
|
|
|
var arr = Array.apply(null, Array(n.toJSNumber() - 1))
|
|
.map(Array.prototype.valueOf, [0, 1]);
|
|
arr.unshift([1]);
|
|
return {
|
|
value: [].concat.apply([], arr),
|
|
isNegative: false
|
|
};
|
|
}
|
|
|
|
var neg = false;
|
|
if (n.isNegative() && base.isPositive()) {
|
|
neg = true;
|
|
n = n.abs();
|
|
}
|
|
if (base.isUnit()) {
|
|
if (n.isZero()) return { value: [0], isNegative: false };
|
|
|
|
return {
|
|
value: Array.apply(null, Array(n.toJSNumber()))
|
|
.map(Number.prototype.valueOf, 1),
|
|
isNegative: neg
|
|
};
|
|
}
|
|
var out = [];
|
|
var left = n, divmod;
|
|
while (left.isNegative() || left.compareAbs(base) >= 0) {
|
|
divmod = left.divmod(base);
|
|
left = divmod.quotient;
|
|
var digit = divmod.remainder;
|
|
if (digit.isNegative()) {
|
|
digit = base.minus(digit).abs();
|
|
left = left.next();
|
|
}
|
|
out.push(digit.toJSNumber());
|
|
}
|
|
out.push(left.toJSNumber());
|
|
return { value: out.reverse(), isNegative: neg };
|
|
}
|
|
|
|
function toBaseString(n, base, alphabet) {
|
|
var arr = toBase(n, base);
|
|
return (arr.isNegative ? "-" : "") + arr.value.map(function (x) {
|
|
return stringify(x, alphabet);
|
|
}).join('');
|
|
}
|
|
|
|
BigInteger.prototype.toArray = function (radix) {
|
|
return toBase(this, radix);
|
|
};
|
|
|
|
SmallInteger.prototype.toArray = function (radix) {
|
|
return toBase(this, radix);
|
|
};
|
|
|
|
NativeBigInt.prototype.toArray = function (radix) {
|
|
return toBase(this, radix);
|
|
};
|
|
|
|
BigInteger.prototype.toString = function (radix, alphabet) {
|
|
if (radix === undefined$1) radix = 10;
|
|
if (radix !== 10) return toBaseString(this, radix, alphabet);
|
|
var v = this.value, l = v.length, str = String(v[--l]), zeros = "0000000", digit;
|
|
while (--l >= 0) {
|
|
digit = String(v[l]);
|
|
str += zeros.slice(digit.length) + digit;
|
|
}
|
|
var sign = this.sign ? "-" : "";
|
|
return sign + str;
|
|
};
|
|
|
|
SmallInteger.prototype.toString = function (radix, alphabet) {
|
|
if (radix === undefined$1) radix = 10;
|
|
if (radix != 10) return toBaseString(this, radix, alphabet);
|
|
return String(this.value);
|
|
};
|
|
|
|
NativeBigInt.prototype.toString = SmallInteger.prototype.toString;
|
|
|
|
NativeBigInt.prototype.toJSON = BigInteger.prototype.toJSON = SmallInteger.prototype.toJSON = function () { return this.toString(); };
|
|
|
|
BigInteger.prototype.valueOf = function () {
|
|
return parseInt(this.toString(), 10);
|
|
};
|
|
BigInteger.prototype.toJSNumber = BigInteger.prototype.valueOf;
|
|
|
|
SmallInteger.prototype.valueOf = function () {
|
|
return this.value;
|
|
};
|
|
SmallInteger.prototype.toJSNumber = SmallInteger.prototype.valueOf;
|
|
NativeBigInt.prototype.valueOf = NativeBigInt.prototype.toJSNumber = function () {
|
|
return parseInt(this.toString(), 10);
|
|
};
|
|
|
|
function parseStringValue(v) {
|
|
if (isPrecise(+v)) {
|
|
var x = +v;
|
|
if (x === truncate(x))
|
|
return supportsNativeBigInt ? new NativeBigInt(BigInt(x)) : new SmallInteger(x);
|
|
throw new Error("Invalid integer: " + v);
|
|
}
|
|
var sign = v[0] === "-";
|
|
if (sign) v = v.slice(1);
|
|
var split = v.split(/e/i);
|
|
if (split.length > 2) throw new Error("Invalid integer: " + split.join("e"));
|
|
if (split.length === 2) {
|
|
var exp = split[1];
|
|
if (exp[0] === "+") exp = exp.slice(1);
|
|
exp = +exp;
|
|
if (exp !== truncate(exp) || !isPrecise(exp)) throw new Error("Invalid integer: " + exp + " is not a valid exponent.");
|
|
var text = split[0];
|
|
var decimalPlace = text.indexOf(".");
|
|
if (decimalPlace >= 0) {
|
|
exp -= text.length - decimalPlace - 1;
|
|
text = text.slice(0, decimalPlace) + text.slice(decimalPlace + 1);
|
|
}
|
|
if (exp < 0) throw new Error("Cannot include negative exponent part for integers");
|
|
text += (new Array(exp + 1)).join("0");
|
|
v = text;
|
|
}
|
|
var isValid = /^([0-9][0-9]*)$/.test(v);
|
|
if (!isValid) throw new Error("Invalid integer: " + v);
|
|
if (supportsNativeBigInt) {
|
|
return new NativeBigInt(BigInt(sign ? "-" + v : v));
|
|
}
|
|
var r = [], max = v.length, l = LOG_BASE, min = max - l;
|
|
while (max > 0) {
|
|
r.push(+v.slice(min, max));
|
|
min -= l;
|
|
if (min < 0) min = 0;
|
|
max -= l;
|
|
}
|
|
trim(r);
|
|
return new BigInteger(r, sign);
|
|
}
|
|
|
|
function parseNumberValue(v) {
|
|
if (supportsNativeBigInt) {
|
|
return new NativeBigInt(BigInt(v));
|
|
}
|
|
if (isPrecise(v)) {
|
|
if (v !== truncate(v)) throw new Error(v + " is not an integer.");
|
|
return new SmallInteger(v);
|
|
}
|
|
return parseStringValue(v.toString());
|
|
}
|
|
|
|
function parseValue(v) {
|
|
if (typeof v === "number") {
|
|
return parseNumberValue(v);
|
|
}
|
|
if (typeof v === "string") {
|
|
return parseStringValue(v);
|
|
}
|
|
if (typeof v === "bigint") {
|
|
return new NativeBigInt(v);
|
|
}
|
|
return v;
|
|
}
|
|
// Pre-define numbers in range [-999,999]
|
|
for (var i = 0; i < 1000; i++) {
|
|
Integer[i] = parseValue(i);
|
|
if (i > 0) Integer[-i] = parseValue(-i);
|
|
}
|
|
// Backwards compatibility
|
|
Integer.one = Integer[1];
|
|
Integer.zero = Integer[0];
|
|
Integer.minusOne = Integer[-1];
|
|
Integer.max = max;
|
|
Integer.min = min;
|
|
Integer.gcd = gcd;
|
|
Integer.lcm = lcm;
|
|
Integer.isInstance = function (x) { return x instanceof BigInteger || x instanceof SmallInteger || x instanceof NativeBigInt; };
|
|
Integer.randBetween = randBetween;
|
|
|
|
Integer.fromArray = function (digits, base, isNegative) {
|
|
return parseBaseFromArray(digits.map(parseValue), parseValue(base || 10), isNegative);
|
|
};
|
|
|
|
return Integer;
|
|
})();
|
|
|
|
// Node.js check
|
|
if ( module.hasOwnProperty("exports")) {
|
|
module.exports = bigInt;
|
|
}
|
|
});
|
|
|
|
function fromString$1(s, radix) {
|
|
if (typeof s == "string") {
|
|
if (s.slice(0,2) == "0x") {
|
|
return BigInteger(s.slice(2), 16);
|
|
} else {
|
|
return BigInteger(s,radix);
|
|
}
|
|
} else {
|
|
return BigInteger(s, radix);
|
|
}
|
|
}
|
|
|
|
const e$1 = fromString$1;
|
|
|
|
function fromArray$1(a, radix) {
|
|
return BigInteger.fromArray(a, radix);
|
|
}
|
|
|
|
function bitLength$1(a) {
|
|
return BigInteger(a).bitLength();
|
|
}
|
|
|
|
function isNegative$1(a) {
|
|
return BigInteger(a).isNegative();
|
|
}
|
|
|
|
function isZero$1(a) {
|
|
return BigInteger(a).isZero();
|
|
}
|
|
|
|
function shiftLeft$1(a, n) {
|
|
return BigInteger(a).shiftLeft(n);
|
|
}
|
|
|
|
function shiftRight$1(a, n) {
|
|
return BigInteger(a).shiftRight(n);
|
|
}
|
|
|
|
const shl$1 = shiftLeft$1;
|
|
const shr$1 = shiftRight$1;
|
|
|
|
function isOdd$1(a) {
|
|
return BigInteger(a).isOdd();
|
|
}
|
|
|
|
|
|
function naf$1(n) {
|
|
let E = BigInteger(n);
|
|
const res = [];
|
|
while (E.gt(BigInteger.zero)) {
|
|
if (E.isOdd()) {
|
|
const z = 2 - E.mod(4).toJSNumber();
|
|
res.push( z );
|
|
E = E.minus(z);
|
|
} else {
|
|
res.push( 0 );
|
|
}
|
|
E = E.shiftRight(1);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function bits$1(n) {
|
|
let E = BigInteger(n);
|
|
const res = [];
|
|
while (E.gt(BigInteger.zero)) {
|
|
if (E.isOdd()) {
|
|
res.push(1);
|
|
} else {
|
|
res.push( 0 );
|
|
}
|
|
E = E.shiftRight(1);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function toNumber$1(s) {
|
|
if (!s.lt(BigInteger("9007199254740992", 10))) {
|
|
throw new Error("Number too big");
|
|
}
|
|
return s.toJSNumber();
|
|
}
|
|
|
|
function toArray$1(s, radix) {
|
|
return BigInteger(s).toArray(radix);
|
|
}
|
|
|
|
function add$1(a, b) {
|
|
return BigInteger(a).add(BigInteger(b));
|
|
}
|
|
|
|
function sub$1(a, b) {
|
|
return BigInteger(a).minus(BigInteger(b));
|
|
}
|
|
|
|
function neg$1(a) {
|
|
return BigInteger.zero.minus(BigInteger(a));
|
|
}
|
|
|
|
function mul$1(a, b) {
|
|
return BigInteger(a).times(BigInteger(b));
|
|
}
|
|
|
|
function square$1(a) {
|
|
return BigInteger(a).square();
|
|
}
|
|
|
|
function pow$1(a, b) {
|
|
return BigInteger(a).pow(BigInteger(b));
|
|
}
|
|
|
|
function exp$1(a, b) {
|
|
return BigInteger(a).pow(BigInteger(b));
|
|
}
|
|
|
|
function abs$1(a) {
|
|
return BigInteger(a).abs();
|
|
}
|
|
|
|
function div$1(a, b) {
|
|
return BigInteger(a).divide(BigInteger(b));
|
|
}
|
|
|
|
function mod$1(a, b) {
|
|
return BigInteger(a).mod(BigInteger(b));
|
|
}
|
|
|
|
function eq$1(a, b) {
|
|
return BigInteger(a).eq(BigInteger(b));
|
|
}
|
|
|
|
function neq$1(a, b) {
|
|
return BigInteger(a).neq(BigInteger(b));
|
|
}
|
|
|
|
function lt$1(a, b) {
|
|
return BigInteger(a).lt(BigInteger(b));
|
|
}
|
|
|
|
function gt$1(a, b) {
|
|
return BigInteger(a).gt(BigInteger(b));
|
|
}
|
|
|
|
function leq$1(a, b) {
|
|
return BigInteger(a).leq(BigInteger(b));
|
|
}
|
|
|
|
function geq$1(a, b) {
|
|
return BigInteger(a).geq(BigInteger(b));
|
|
}
|
|
|
|
function band$1(a, b) {
|
|
return BigInteger(a).and(BigInteger(b));
|
|
}
|
|
|
|
function bor$1(a, b) {
|
|
return BigInteger(a).or(BigInteger(b));
|
|
}
|
|
|
|
function bxor$1(a, b) {
|
|
return BigInteger(a).xor(BigInteger(b));
|
|
}
|
|
|
|
function land$1(a, b) {
|
|
return (!BigInteger(a).isZero()) && (!BigInteger(b).isZero());
|
|
}
|
|
|
|
function lor$1(a, b) {
|
|
return (!BigInteger(a).isZero()) || (!BigInteger(b).isZero());
|
|
}
|
|
|
|
function lnot$1(a) {
|
|
return BigInteger(a).isZero();
|
|
}
|
|
|
|
var Scalar_bigint = /*#__PURE__*/Object.freeze({
|
|
__proto__: null,
|
|
fromString: fromString$1,
|
|
e: e$1,
|
|
fromArray: fromArray$1,
|
|
bitLength: bitLength$1,
|
|
isNegative: isNegative$1,
|
|
isZero: isZero$1,
|
|
shiftLeft: shiftLeft$1,
|
|
shiftRight: shiftRight$1,
|
|
shl: shl$1,
|
|
shr: shr$1,
|
|
isOdd: isOdd$1,
|
|
naf: naf$1,
|
|
bits: bits$1,
|
|
toNumber: toNumber$1,
|
|
toArray: toArray$1,
|
|
add: add$1,
|
|
sub: sub$1,
|
|
neg: neg$1,
|
|
mul: mul$1,
|
|
square: square$1,
|
|
pow: pow$1,
|
|
exp: exp$1,
|
|
abs: abs$1,
|
|
div: div$1,
|
|
mod: mod$1,
|
|
eq: eq$1,
|
|
neq: neq$1,
|
|
lt: lt$1,
|
|
gt: gt$1,
|
|
leq: leq$1,
|
|
geq: geq$1,
|
|
band: band$1,
|
|
bor: bor$1,
|
|
bxor: bxor$1,
|
|
land: land$1,
|
|
lor: lor$1,
|
|
lnot: lnot$1
|
|
});
|
|
|
|
const supportsNativeBigInt = typeof BigInt === "function";
|
|
|
|
let Scalar = {};
|
|
if (supportsNativeBigInt) {
|
|
Object.assign(Scalar, Scalar_native);
|
|
} else {
|
|
Object.assign(Scalar, Scalar_bigint);
|
|
}
|
|
|
|
|
|
// Returns a buffer with Little Endian Representation
|
|
Scalar.toRprLE = function rprBE(buff, o, e, n8) {
|
|
const s = "0000000" + e.toString(16);
|
|
const v = new Uint32Array(buff.buffer, o, n8/4);
|
|
const l = (((s.length-7)*4 - 1) >> 5)+1; // Number of 32bit words;
|
|
for (let i=0; i<l; i++) v[i] = parseInt(s.substring(s.length-8*i-8, s.length-8*i), 16);
|
|
for (let i=l; i<v.length; i++) v[i] = 0;
|
|
for (let i=v.length*4; i<n8; i++) buff[i] = Scalar.toNumber(Scalar.band(Scalar.shiftRight(e, i*8), 0xFF));
|
|
};
|
|
|
|
// Returns a buffer with Big Endian Representation
|
|
Scalar.toRprBE = function rprLEM(buff, o, e, n8) {
|
|
const s = "0000000" + e.toString(16);
|
|
const v = new DataView(buff.buffer, buff.byteOffset + o, n8);
|
|
const l = (((s.length-7)*4 - 1) >> 5)+1; // Number of 32bit words;
|
|
for (let i=0; i<l; i++) v.setUint32(n8-i*4 -4, parseInt(s.substring(s.length-8*i-8, s.length-8*i), 16), false);
|
|
for (let i=0; i<n8/4-l; i++) v[i] = 0;
|
|
};
|
|
|
|
// Pases a buffer with Little Endian Representation
|
|
Scalar.fromRprLE = function rprLEM(buff, o, n8) {
|
|
n8 = n8 || buff.byteLength;
|
|
const v = new Uint32Array(buff.buffer, o, n8/4);
|
|
const a = new Array(n8/4);
|
|
v.forEach( (ch,i) => a[a.length-i-1] = ch.toString(16).padStart(8,"0") );
|
|
return Scalar.fromString(a.join(""), 16);
|
|
};
|
|
|
|
// Pases a buffer with Big Endian Representation
|
|
Scalar.fromRprBE = function rprLEM(buff, o, n8) {
|
|
n8 = n8 || buff.byteLength;
|
|
const v = new DataView(buff.buffer, buff.byteOffset + o, n8);
|
|
const a = new Array(n8/4);
|
|
for (let i=0; i<n8/4; i++) {
|
|
a[i] = v.getUint32(i*4, false).toString(16).padStart(8, "0");
|
|
}
|
|
return Scalar.fromString(a.join(""), 16);
|
|
};
|
|
|
|
Scalar.toString = function toString(a, radix) {
|
|
return a.toString(radix);
|
|
};
|
|
|
|
Scalar.toLEBuff = function toLEBuff(a) {
|
|
const buff = new Uint8Array(Math.floor((Scalar.bitLength(a) - 1) / 8) +1);
|
|
Scalar.toRprLE(buff, 0, a, buff.byteLength);
|
|
return buff;
|
|
};
|
|
|
|
|
|
Scalar.zero = Scalar.e(0);
|
|
Scalar.one = Scalar.e(1);
|
|
|
|
let {
|
|
toRprLE,
|
|
toRprBE,
|
|
fromRprLE,
|
|
fromRprBE,
|
|
toString,
|
|
toLEBuff,
|
|
zero,
|
|
one,
|
|
fromString: fromString$2,
|
|
e: e$2,
|
|
fromArray: fromArray$2,
|
|
bitLength: bitLength$2,
|
|
isNegative: isNegative$2,
|
|
isZero: isZero$2,
|
|
shiftLeft: shiftLeft$2,
|
|
shiftRight: shiftRight$2,
|
|
shl: shl$2,
|
|
shr: shr$2,
|
|
isOdd: isOdd$2,
|
|
naf: naf$2,
|
|
bits: bits$2,
|
|
toNumber: toNumber$2,
|
|
toArray: toArray$2,
|
|
add: add$2,
|
|
sub: sub$2,
|
|
neg: neg$2,
|
|
mul: mul$2,
|
|
square: square$2,
|
|
pow: pow$2,
|
|
exp: exp$2,
|
|
abs: abs$2,
|
|
div: div$2,
|
|
mod: mod$2,
|
|
eq: eq$2,
|
|
neq: neq$2,
|
|
lt: lt$2,
|
|
gt: gt$2,
|
|
leq: leq$2,
|
|
geq: geq$2,
|
|
band: band$2,
|
|
bor: bor$2,
|
|
bxor: bxor$2,
|
|
land: land$2,
|
|
lor: lor$2,
|
|
lnot: lnot$2,
|
|
} = Scalar;
|
|
|
|
var _Scalar = /*#__PURE__*/Object.freeze({
|
|
__proto__: null,
|
|
toRprLE: toRprLE,
|
|
toRprBE: toRprBE,
|
|
fromRprLE: fromRprLE,
|
|
fromRprBE: fromRprBE,
|
|
toString: toString,
|
|
toLEBuff: toLEBuff,
|
|
zero: zero,
|
|
one: one,
|
|
fromString: fromString$2,
|
|
e: e$2,
|
|
fromArray: fromArray$2,
|
|
bitLength: bitLength$2,
|
|
isNegative: isNegative$2,
|
|
isZero: isZero$2,
|
|
shiftLeft: shiftLeft$2,
|
|
shiftRight: shiftRight$2,
|
|
shl: shl$2,
|
|
shr: shr$2,
|
|
isOdd: isOdd$2,
|
|
naf: naf$2,
|
|
bits: bits$2,
|
|
toNumber: toNumber$2,
|
|
toArray: toArray$2,
|
|
add: add$2,
|
|
sub: sub$2,
|
|
neg: neg$2,
|
|
mul: mul$2,
|
|
square: square$2,
|
|
pow: pow$2,
|
|
exp: exp$2,
|
|
abs: abs$2,
|
|
div: div$2,
|
|
mod: mod$2,
|
|
eq: eq$2,
|
|
neq: neq$2,
|
|
lt: lt$2,
|
|
gt: gt$2,
|
|
leq: leq$2,
|
|
geq: geq$2,
|
|
band: band$2,
|
|
bor: bor$2,
|
|
bxor: bxor$2,
|
|
land: land$2,
|
|
lor: lor$2,
|
|
lnot: lnot$2
|
|
});
|
|
|
|
/*
|
|
Copyright 2018 0kims association.
|
|
|
|
This file is part of snarkjs.
|
|
|
|
snarkjs is a free software: you can redistribute it and/or
|
|
modify it under the terms of the GNU General Public License as published by the
|
|
Free Software Foundation, either version 3 of the License, or (at your option)
|
|
any later version.
|
|
|
|
snarkjs is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
|
|
more details.
|
|
|
|
You should have received a copy of the GNU General Public License along with
|
|
snarkjs. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
/*
|
|
This library does operations on polynomials with coefficients in a field F.
|
|
|
|
A polynomial P(x) = p0 + p1 * x + p2 * x^2 + ... + pn * x^n is represented
|
|
by the array [ p0, p1, p2, ... , pn ].
|
|
*/
|
|
|
|
class PolField {
|
|
constructor (F) {
|
|
this.F = F;
|
|
|
|
let rem = F.sqrt_t;
|
|
let s = F.sqrt_s;
|
|
|
|
const five = this.F.add(this.F.add(this.F.two, this.F.two), this.F.one);
|
|
|
|
this.w = new Array(s+1);
|
|
this.wi = new Array(s+1);
|
|
this.w[s] = this.F.pow(five, rem);
|
|
this.wi[s] = this.F.inv(this.w[s]);
|
|
|
|
let n=s-1;
|
|
while (n>=0) {
|
|
this.w[n] = this.F.square(this.w[n+1]);
|
|
this.wi[n] = this.F.square(this.wi[n+1]);
|
|
n--;
|
|
}
|
|
|
|
|
|
this.roots = [];
|
|
/* for (let i=0; i<16; i++) {
|
|
let r = this.F.one;
|
|
n = 1 << i;
|
|
const rootsi = new Array(n);
|
|
for (let j=0; j<n; j++) {
|
|
rootsi[j] = r;
|
|
r = this.F.mul(r, this.w[i]);
|
|
}
|
|
|
|
this.roots.push(rootsi);
|
|
}
|
|
*/
|
|
this._setRoots(15);
|
|
}
|
|
|
|
_setRoots(n) {
|
|
if (n > this.F.sqrt_s) n = this.s;
|
|
for (let i=n; (i>=0) && (!this.roots[i]); i--) {
|
|
let r = this.F.one;
|
|
const nroots = 1 << i;
|
|
const rootsi = new Array(nroots);
|
|
for (let j=0; j<nroots; j++) {
|
|
rootsi[j] = r;
|
|
r = this.F.mul(r, this.w[i]);
|
|
}
|
|
this.roots[i] = rootsi;
|
|
}
|
|
}
|
|
|
|
add(a, b) {
|
|
const m = Math.max(a.length, b.length);
|
|
const res = new Array(m);
|
|
for (let i=0; i<m; i++) {
|
|
res[i] = this.F.add(a[i] || this.F.zero, b[i] || this.F.zero);
|
|
}
|
|
return this.reduce(res);
|
|
}
|
|
|
|
double(a) {
|
|
return this.add(a,a);
|
|
}
|
|
|
|
sub(a, b) {
|
|
const m = Math.max(a.length, b.length);
|
|
const res = new Array(m);
|
|
for (let i=0; i<m; i++) {
|
|
res[i] = this.F.sub(a[i] || this.F.zero, b[i] || this.F.zero);
|
|
}
|
|
return this.reduce(res);
|
|
}
|
|
|
|
mulScalar(p, b) {
|
|
if (this.F.eq(b, this.F.zero)) return [];
|
|
if (this.F.eq(b, this.F.one)) return p;
|
|
const res = new Array(p.length);
|
|
for (let i=0; i<p.length; i++) {
|
|
res[i] = this.F.mul(p[i], b);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
|
|
|
|
mul(a, b) {
|
|
if (a.length == 0) return [];
|
|
if (b.length == 0) return [];
|
|
if (a.length == 1) return this.mulScalar(b, a[0]);
|
|
if (b.length == 1) return this.mulScalar(a, b[0]);
|
|
|
|
if (b.length > a.length) {
|
|
[b, a] = [a, b];
|
|
}
|
|
|
|
if ((b.length <= 2) || (b.length < log2(a.length))) {
|
|
return this.mulNormal(a,b);
|
|
} else {
|
|
return this.mulFFT(a,b);
|
|
}
|
|
}
|
|
|
|
mulNormal(a, b) {
|
|
let res = [];
|
|
for (let i=0; i<b.length; i++) {
|
|
res = this.add(res, this.scaleX(this.mulScalar(a, b[i]), i) );
|
|
}
|
|
return res;
|
|
}
|
|
|
|
mulFFT(a,b) {
|
|
const longestN = Math.max(a.length, b.length);
|
|
const bitsResult = log2(longestN-1)+2;
|
|
this._setRoots(bitsResult);
|
|
|
|
const m = 1 << bitsResult;
|
|
const ea = this.extend(a,m);
|
|
const eb = this.extend(b,m);
|
|
|
|
const ta = __fft(this, ea, bitsResult, 0, 1);
|
|
const tb = __fft(this, eb, bitsResult, 0, 1);
|
|
|
|
const tres = new Array(m);
|
|
|
|
for (let i=0; i<m; i++) {
|
|
tres[i] = this.F.mul(ta[i], tb[i]);
|
|
}
|
|
|
|
const res = __fft(this, tres, bitsResult, 0, 1);
|
|
|
|
const twoinvm = this.F.inv( this.F.mulScalar(this.F.one, m) );
|
|
const resn = new Array(m);
|
|
for (let i=0; i<m; i++) {
|
|
resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
|
|
}
|
|
|
|
return this.reduce(resn);
|
|
}
|
|
|
|
|
|
|
|
square(a) {
|
|
return this.mul(a,a);
|
|
}
|
|
|
|
scaleX(p, n) {
|
|
if (n==0) {
|
|
return p;
|
|
} else if (n>0) {
|
|
const z = new Array(n).fill(this.F.zero);
|
|
return z.concat(p);
|
|
} else {
|
|
if (-n >= p.length) return [];
|
|
return p.slice(-n);
|
|
}
|
|
}
|
|
|
|
eval2(p, x) {
|
|
let v = this.F.zero;
|
|
let ix = this.F.one;
|
|
for (let i=0; i<p.length; i++) {
|
|
v = this.F.add(v, this.F.mul(p[i], ix));
|
|
ix = this.F.mul(ix, x);
|
|
}
|
|
return v;
|
|
}
|
|
|
|
eval(p,x) {
|
|
const F = this.F;
|
|
if (p.length == 0) return F.zero;
|
|
const m = this._next2Power(p.length);
|
|
const ep = this.extend(p, m);
|
|
|
|
return _eval(ep, x, 0, 1, m);
|
|
|
|
function _eval(p, x, offset, step, n) {
|
|
if (n==1) return p[offset];
|
|
const newX = F.square(x);
|
|
const res= F.add(
|
|
_eval(p, newX, offset, step << 1, n >> 1),
|
|
F.mul(
|
|
x,
|
|
_eval(p, newX, offset+step , step << 1, n >> 1)));
|
|
return res;
|
|
}
|
|
}
|
|
|
|
lagrange(points) {
|
|
let roots = [this.F.one];
|
|
for (let i=0; i<points.length; i++) {
|
|
roots = this.mul(roots, [this.F.neg(points[i][0]), this.F.one]);
|
|
}
|
|
|
|
let sum = [];
|
|
for (let i=0; i<points.length; i++) {
|
|
let mpol = this.ruffini(roots, points[i][0]);
|
|
const factor =
|
|
this.F.mul(
|
|
this.F.inv(this.eval(mpol, points[i][0])),
|
|
points[i][1]);
|
|
mpol = this.mulScalar(mpol, factor);
|
|
sum = this.add(sum, mpol);
|
|
}
|
|
return sum;
|
|
}
|
|
|
|
|
|
fft(p) {
|
|
if (p.length <= 1) return p;
|
|
const bits = log2(p.length-1)+1;
|
|
this._setRoots(bits);
|
|
|
|
const m = 1 << bits;
|
|
const ep = this.extend(p, m);
|
|
const res = __fft(this, ep, bits, 0, 1);
|
|
return res;
|
|
}
|
|
|
|
fft2(p) {
|
|
if (p.length <= 1) return p;
|
|
const bits = log2(p.length-1)+1;
|
|
this._setRoots(bits);
|
|
|
|
const m = 1 << bits;
|
|
const ep = this.extend(p, m);
|
|
__bitReverse(ep, bits);
|
|
const res = __fft2(this, ep, bits);
|
|
return res;
|
|
}
|
|
|
|
|
|
ifft(p) {
|
|
|
|
if (p.length <= 1) return p;
|
|
const bits = log2(p.length-1)+1;
|
|
this._setRoots(bits);
|
|
const m = 1 << bits;
|
|
const ep = this.extend(p, m);
|
|
const res = __fft(this, ep, bits, 0, 1);
|
|
|
|
const twoinvm = this.F.inv( this.F.mulScalar(this.F.one, m) );
|
|
const resn = new Array(m);
|
|
for (let i=0; i<m; i++) {
|
|
resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
|
|
}
|
|
|
|
return resn;
|
|
|
|
}
|
|
|
|
|
|
ifft2(p) {
|
|
|
|
if (p.length <= 1) return p;
|
|
const bits = log2(p.length-1)+1;
|
|
this._setRoots(bits);
|
|
const m = 1 << bits;
|
|
const ep = this.extend(p, m);
|
|
__bitReverse(ep, bits);
|
|
const res = __fft2(this, ep, bits);
|
|
|
|
const twoinvm = this.F.inv( this.F.mulScalar(this.F.one, m) );
|
|
const resn = new Array(m);
|
|
for (let i=0; i<m; i++) {
|
|
resn[i] = this.F.mul(res[(m-i)%m], twoinvm);
|
|
}
|
|
|
|
return resn;
|
|
|
|
}
|
|
|
|
_fft(pall, bits, offset, step) {
|
|
|
|
const n = 1 << bits;
|
|
if (n==1) {
|
|
return [ pall[offset] ];
|
|
}
|
|
|
|
const ndiv2 = n >> 1;
|
|
const p1 = this._fft(pall, bits-1, offset, step*2);
|
|
const p2 = this._fft(pall, bits-1, offset+step, step*2);
|
|
|
|
const out = new Array(n);
|
|
|
|
let m= this.F.one;
|
|
for (let i=0; i<ndiv2; i++) {
|
|
out[i] = this.F.add(p1[i], this.F.mul(m, p2[i]));
|
|
out[i+ndiv2] = this.F.sub(p1[i], this.F.mul(m, p2[i]));
|
|
m = this.F.mul(m, this.w[bits]);
|
|
}
|
|
|
|
return out;
|
|
}
|
|
|
|
extend(p, e) {
|
|
if (e == p.length) return p;
|
|
const z = new Array(e-p.length).fill(this.F.zero);
|
|
|
|
return p.concat(z);
|
|
}
|
|
|
|
reduce(p) {
|
|
if (p.length == 0) return p;
|
|
if (! this.F.eq(p[p.length-1], this.F.zero) ) return p;
|
|
let i=p.length-1;
|
|
while( i>0 && this.F.eq(p[i], this.F.zero) ) i--;
|
|
return p.slice(0, i+1);
|
|
}
|
|
|
|
eq(a, b) {
|
|
const pa = this.reduce(a);
|
|
const pb = this.reduce(b);
|
|
|
|
if (pa.length != pb.length) return false;
|
|
for (let i=0; i<pb.length; i++) {
|
|
if (!this.F.eq(pa[i], pb[i])) return false;
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
ruffini(p, r) {
|
|
const res = new Array(p.length-1);
|
|
res[res.length-1] = p[p.length-1];
|
|
for (let i = res.length-2; i>=0; i--) {
|
|
res[i] = this.F.add(this.F.mul(res[i+1], r), p[i+1]);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
_next2Power(v) {
|
|
v--;
|
|
v |= v >> 1;
|
|
v |= v >> 2;
|
|
v |= v >> 4;
|
|
v |= v >> 8;
|
|
v |= v >> 16;
|
|
v++;
|
|
return v;
|
|
}
|
|
|
|
toString(p) {
|
|
const ap = this.normalize(p);
|
|
let S = "";
|
|
for (let i=ap.length-1; i>=0; i--) {
|
|
if (!this.F.eq(p[i], this.F.zero)) {
|
|
if (S!="") S += " + ";
|
|
S = S + p[i].toString(10);
|
|
if (i>0) {
|
|
S = S + "x";
|
|
if (i>1) {
|
|
S = S + "^" +i;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return S;
|
|
}
|
|
|
|
normalize(p) {
|
|
const res = new Array(p.length);
|
|
for (let i=0; i<p.length; i++) {
|
|
res[i] = this.F.normalize(p[i]);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
|
|
_reciprocal(p, bits) {
|
|
const k = 1 << bits;
|
|
if (k==1) {
|
|
return [ this.F.inv(p[0]) ];
|
|
}
|
|
const np = this.scaleX(p, -k/2);
|
|
const q = this._reciprocal(np, bits-1);
|
|
const a = this.scaleX(this.double(q), 3*k/2-2);
|
|
const b = this.mul( this.square(q), p);
|
|
|
|
return this.scaleX(this.sub(a,b), -(k-2));
|
|
}
|
|
|
|
// divides x^m / v
|
|
_div2(m, v) {
|
|
const kbits = log2(v.length-1)+1;
|
|
const k = 1 << kbits;
|
|
|
|
const scaleV = k - v.length;
|
|
|
|
// rec = x^(k - 2) / v* x^scaleV =>
|
|
// rec = x^(k-2-scaleV)/ v
|
|
//
|
|
// res = x^m/v = x^(m + (2*k-2 - scaleV) - (2*k-2 - scaleV)) /v =>
|
|
// res = rec * x^(m - (2*k-2 - scaleV)) =>
|
|
// res = rec * x^(m - 2*k + 2 + scaleV)
|
|
|
|
const rec = this._reciprocal(this.scaleX(v, scaleV), kbits);
|
|
const res = this.scaleX(rec, m - 2*k + 2 + scaleV);
|
|
|
|
return res;
|
|
}
|
|
|
|
div(_u, _v) {
|
|
if (_u.length < _v.length) return [];
|
|
const kbits = log2(_v.length-1)+1;
|
|
const k = 1 << kbits;
|
|
|
|
const u = this.scaleX(_u, k-_v.length);
|
|
const v = this.scaleX(_v, k-_v.length);
|
|
|
|
const n = v.length-1;
|
|
let m = u.length-1;
|
|
|
|
const s = this._reciprocal(v, kbits);
|
|
let t;
|
|
if (m>2*n) {
|
|
t = this.sub(this.scaleX([this.F.one], 2*n), this.mul(s, v));
|
|
}
|
|
|
|
let q = [];
|
|
let rem = u;
|
|
let us, ut;
|
|
let finish = false;
|
|
|
|
while (!finish) {
|
|
us = this.mul(rem, s);
|
|
q = this.add(q, this.scaleX(us, -2*n));
|
|
|
|
if ( m > 2*n ) {
|
|
ut = this.mul(rem, t);
|
|
rem = this.scaleX(ut, -2*n);
|
|
m = rem.length-1;
|
|
} else {
|
|
finish = true;
|
|
}
|
|
}
|
|
|
|
return q;
|
|
}
|
|
|
|
|
|
// returns the ith nth-root of one
|
|
oneRoot(n, i) {
|
|
let nbits = log2(n-1)+1;
|
|
let res = this.F.one;
|
|
let r = i;
|
|
|
|
if(i>=n) {
|
|
throw new Error("Given 'i' should be lower than 'n'");
|
|
}
|
|
else if (1<<nbits !== n) {
|
|
throw new Error(`Internal errlr: ${n} should equal ${1<<nbits}`);
|
|
}
|
|
|
|
while (r>0) {
|
|
if (r & 1 == 1) {
|
|
res = this.F.mul(res, this.w[nbits]);
|
|
}
|
|
r = r >> 1;
|
|
nbits --;
|
|
}
|
|
return res;
|
|
}
|
|
|
|
computeVanishingPolinomial(bits, t) {
|
|
const m = 1 << bits;
|
|
return this.F.sub(this.F.pow(t, m), this.F.one);
|
|
}
|
|
|
|
evaluateLagrangePolynomials(bits, t) {
|
|
const m= 1 << bits;
|
|
const tm = this.F.pow(t, m);
|
|
const u= new Array(m).fill(this.F.zero);
|
|
this._setRoots(bits);
|
|
const omega = this.w[bits];
|
|
|
|
if (this.F.eq(tm, this.F.one)) {
|
|
for (let i = 0; i < m; i++) {
|
|
if (this.F.eq(this.roots[bits][0],t)) { // i.e., t equals omega^i
|
|
u[i] = this.F.one;
|
|
return u;
|
|
}
|
|
}
|
|
}
|
|
|
|
const z = this.F.sub(tm, this.F.one);
|
|
// let l = this.F.mul(z, this.F.pow(this.F.twoinv, m));
|
|
let l = this.F.mul(z, this.F.inv(this.F.e(m)));
|
|
for (let i = 0; i < m; i++) {
|
|
u[i] = this.F.mul(l, this.F.inv(this.F.sub(t,this.roots[bits][i])));
|
|
l = this.F.mul(l, omega);
|
|
}
|
|
|
|
return u;
|
|
}
|
|
|
|
log2(V) {
|
|
return log2(V);
|
|
}
|
|
}
|
|
|
|
function log2( V )
|
|
{
|
|
return( ( ( V & 0xFFFF0000 ) !== 0 ? ( V &= 0xFFFF0000, 16 ) : 0 ) | ( ( V & 0xFF00FF00 ) !== 0 ? ( V &= 0xFF00FF00, 8 ) : 0 ) | ( ( V & 0xF0F0F0F0 ) !== 0 ? ( V &= 0xF0F0F0F0, 4 ) : 0 ) | ( ( V & 0xCCCCCCCC ) !== 0 ? ( V &= 0xCCCCCCCC, 2 ) : 0 ) | ( ( V & 0xAAAAAAAA ) !== 0 ) );
|
|
}
|
|
|
|
|
|
function __fft(PF, pall, bits, offset, step) {
|
|
|
|
const n = 1 << bits;
|
|
if (n==1) {
|
|
return [ pall[offset] ];
|
|
} else if (n==2) {
|
|
return [
|
|
PF.F.add(pall[offset], pall[offset + step]),
|
|
PF.F.sub(pall[offset], pall[offset + step])];
|
|
}
|
|
|
|
const ndiv2 = n >> 1;
|
|
const p1 = __fft(PF, pall, bits-1, offset, step*2);
|
|
const p2 = __fft(PF, pall, bits-1, offset+step, step*2);
|
|
|
|
const out = new Array(n);
|
|
|
|
for (let i=0; i<ndiv2; i++) {
|
|
out[i] = PF.F.add(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
|
|
out[i+ndiv2] = PF.F.sub(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
|
|
}
|
|
|
|
return out;
|
|
}
|
|
|
|
|
|
function __fft2(PF, pall, bits) {
|
|
|
|
const n = 1 << bits;
|
|
if (n==1) {
|
|
return [ pall[0] ];
|
|
}
|
|
|
|
const ndiv2 = n >> 1;
|
|
const p1 = __fft2(PF, pall.slice(0, ndiv2), bits-1);
|
|
const p2 = __fft2(PF, pall.slice(ndiv2), bits-1);
|
|
|
|
const out = new Array(n);
|
|
|
|
for (let i=0; i<ndiv2; i++) {
|
|
out[i] = PF.F.add(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
|
|
out[i+ndiv2] = PF.F.sub(p1[i], PF.F.mul(PF.roots[bits][i], p2[i]));
|
|
}
|
|
|
|
return out;
|
|
}
|
|
|
|
const _revTable = [];
|
|
for (let i=0; i<256; i++) {
|
|
_revTable[i] = _revSlow(i, 8);
|
|
}
|
|
|
|
function _revSlow(idx, bits) {
|
|
let res =0;
|
|
let a = idx;
|
|
for (let i=0; i<bits; i++) {
|
|
res <<= 1;
|
|
res = res | (a &1);
|
|
a >>=1;
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function rev(idx, bits) {
|
|
return (
|
|
_revTable[idx >>> 24] |
|
|
(_revTable[(idx >>> 16) & 0xFF] << 8) |
|
|
(_revTable[(idx >>> 8) & 0xFF] << 16) |
|
|
(_revTable[idx & 0xFF] << 24)
|
|
) >>> (32-bits);
|
|
}
|
|
|
|
function __bitReverse(p, bits) {
|
|
for (let k=0; k<p.length; k++) {
|
|
const r = rev(k, bits);
|
|
if (r>k) {
|
|
const tmp= p[k];
|
|
p[k] = p[r];
|
|
p[r] = tmp;
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
Copyright 2018 0kims association.
|
|
|
|
This file is part of snarkjs.
|
|
|
|
snarkjs is a free software: you can redistribute it and/or
|
|
modify it under the terms of the GNU General Public License as published by the
|
|
Free Software Foundation, either version 3 of the License, or (at your option)
|
|
any later version.
|
|
|
|
snarkjs is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
|
|
more details.
|
|
|
|
You should have received a copy of the GNU General Public License along with
|
|
snarkjs. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
|
|
function mulScalar(F, base, e) {
|
|
let res;
|
|
|
|
if (isZero$2(e)) return F.zero;
|
|
|
|
const n = naf$2(e);
|
|
|
|
if (n[n.length-1] == 1) {
|
|
res = base;
|
|
} else if (n[n.length-1] == -1) {
|
|
res = F.neg(base);
|
|
} else {
|
|
throw new Error("invlaud NAF");
|
|
}
|
|
|
|
for (let i=n.length-2; i>=0; i--) {
|
|
|
|
res = F.double(res);
|
|
|
|
if (n[i] == 1) {
|
|
res = F.add(res, base);
|
|
} else if (n[i] == -1) {
|
|
res = F.sub(res, base);
|
|
}
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
|
|
/*
|
|
exports.mulScalar = (F, base, e) =>{
|
|
let res = F.zero;
|
|
let rem = bigInt(e);
|
|
let exp = base;
|
|
|
|
while (! rem.eq(bigInt.zero)) {
|
|
if (rem.and(bigInt.one).eq(bigInt.one)) {
|
|
res = F.add(res, exp);
|
|
}
|
|
exp = F.double(exp);
|
|
rem = rem.shiftRight(1);
|
|
}
|
|
|
|
return res;
|
|
};
|
|
*/
|
|
|
|
|
|
function exp$3(F, base, e) {
|
|
|
|
if (isZero$2(e)) return F.one;
|
|
|
|
const n = bits$2(e);
|
|
|
|
if (n.legth==0) return F.one;
|
|
|
|
let res = base;
|
|
|
|
for (let i=n.length-2; i>=0; i--) {
|
|
|
|
res = F.square(res);
|
|
|
|
if (n[i]) {
|
|
res = F.mul(res, base);
|
|
}
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
// Check here: https://eprint.iacr.org/2012/685.pdf
|
|
|
|
function buildSqrt (F) {
|
|
if ((F.m % 2) == 1) {
|
|
if (eq$2(mod$2(F.p, 4), 1 )) {
|
|
if (eq$2(mod$2(F.p, 8), 1 )) {
|
|
if (eq$2(mod$2(F.p, 16), 1 )) {
|
|
// alg7_muller(F);
|
|
alg5_tonelliShanks(F);
|
|
} else if (eq$2(mod$2(F.p, 16), 9 )) {
|
|
alg4_kong(F);
|
|
} else {
|
|
throw new Error("Field withot sqrt");
|
|
}
|
|
} else if (eq$2(mod$2(F.p, 8), 5 )) {
|
|
alg3_atkin(F);
|
|
} else {
|
|
throw new Error("Field withot sqrt");
|
|
}
|
|
} else if (eq$2(mod$2(F.p, 4), 3 )) {
|
|
alg2_shanks(F);
|
|
}
|
|
} else {
|
|
const pm2mod4 = mod$2(pow$2(F.p, F.m/2), 4);
|
|
if (pm2mod4 == 1) {
|
|
alg10_adj(F);
|
|
} else if (pm2mod4 == 3) {
|
|
alg9_adj(F);
|
|
} else {
|
|
alg8_complex(F);
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
|
|
function alg5_tonelliShanks(F) {
|
|
F.sqrt_q = pow$2(F.p, F.m);
|
|
|
|
F.sqrt_s = 0;
|
|
F.sqrt_t = sub$2(F.sqrt_q, 1);
|
|
|
|
while (!isOdd$2(F.sqrt_t)) {
|
|
F.sqrt_s = F.sqrt_s + 1;
|
|
F.sqrt_t = div$2(F.sqrt_t, 2);
|
|
}
|
|
|
|
let c0 = F.one;
|
|
|
|
while (F.eq(c0, F.one)) {
|
|
const c = F.random();
|
|
F.sqrt_z = F.pow(c, F.sqrt_t);
|
|
c0 = F.pow(F.sqrt_z, 2 ** (F.sqrt_s-1) );
|
|
}
|
|
|
|
F.sqrt_tm1d2 = div$2(sub$2(F.sqrt_t, 1),2);
|
|
|
|
F.sqrt = function(a) {
|
|
const F=this;
|
|
if (F.isZero(a)) return F.zero;
|
|
let w = F.pow(a, F.sqrt_tm1d2);
|
|
const a0 = F.pow( F.mul(F.square(w), a), 2 ** (F.sqrt_s-1) );
|
|
if (F.eq(a0, F.negone)) return null;
|
|
|
|
let v = F.sqrt_s;
|
|
let x = F.mul(a, w);
|
|
let b = F.mul(x, w);
|
|
let z = F.sqrt_z;
|
|
while (!F.eq(b, F.one)) {
|
|
let b2k = F.square(b);
|
|
let k=1;
|
|
while (!F.eq(b2k, F.one)) {
|
|
b2k = F.square(b2k);
|
|
k++;
|
|
}
|
|
|
|
w = z;
|
|
for (let i=0; i<v-k-1; i++) {
|
|
w = F.square(w);
|
|
}
|
|
z = F.square(w);
|
|
b = F.mul(b, z);
|
|
x = F.mul(x, w);
|
|
v = k;
|
|
}
|
|
return F.geq(x, F.zero) ? x : F.neg(x);
|
|
};
|
|
}
|
|
|
|
function alg4_kong(F) {
|
|
F.sqrt = function() {
|
|
throw new Error("Sqrt alg 4 not implemented");
|
|
};
|
|
}
|
|
|
|
function alg3_atkin(F) {
|
|
F.sqrt = function() {
|
|
throw new Error("Sqrt alg 3 not implemented");
|
|
};
|
|
}
|
|
|
|
function alg2_shanks(F) {
|
|
|
|
F.sqrt_q = pow$2(F.p, F.m);
|
|
F.sqrt_e1 = div$2( sub$2(F.sqrt_q, 3) , 4);
|
|
|
|
F.sqrt = function(a) {
|
|
if (this.isZero(a)) return this.zero;
|
|
|
|
// Test that have solution
|
|
const a1 = this.pow(a, this.sqrt_e1);
|
|
|
|
const a0 = this.mul(this.square(a1), a);
|
|
|
|
if ( this.eq(a0, this.negone) ) return null;
|
|
|
|
const x = this.mul(a1, a);
|
|
|
|
return F.geq(x, F.zero) ? x : F.neg(x);
|
|
};
|
|
}
|
|
|
|
function alg10_adj(F) {
|
|
F.sqrt = function() {
|
|
throw new Error("Sqrt alg 10 not implemented");
|
|
};
|
|
}
|
|
|
|
function alg9_adj(F) {
|
|
F.sqrt_q = pow$2(F.p, F.m/2);
|
|
F.sqrt_e34 = div$2( sub$2(F.sqrt_q, 3) , 4);
|
|
F.sqrt_e12 = div$2( sub$2(F.sqrt_q, 1) , 2);
|
|
|
|
F.frobenius = function(n, x) {
|
|
if ((n%2) == 1) {
|
|
return F.conjugate(x);
|
|
} else {
|
|
return x;
|
|
}
|
|
};
|
|
|
|
F.sqrt = function(a) {
|
|
const F = this;
|
|
const a1 = F.pow(a, F.sqrt_e34);
|
|
const alfa = F.mul(F.square(a1), a);
|
|
const a0 = F.mul(F.frobenius(1, alfa), alfa);
|
|
if (F.eq(a0, F.negone)) return null;
|
|
const x0 = F.mul(a1, a);
|
|
let x;
|
|
if (F.eq(alfa, F.negone)) {
|
|
x = F.mul(x0, [F.F.zero, F.F.one]);
|
|
} else {
|
|
const b = F.pow(F.add(F.one, alfa), F.sqrt_e12);
|
|
x = F.mul(b, x0);
|
|
}
|
|
return F.geq(x, F.zero) ? x : F.neg(x);
|
|
};
|
|
}
|
|
|
|
|
|
function alg8_complex(F) {
|
|
F.sqrt = function() {
|
|
throw new Error("Sqrt alg 8 not implemented");
|
|
};
|
|
}
|
|
|
|
function quarterRound(st, a, b, c, d) {
|
|
|
|
st[a] = (st[a] + st[b]) >>> 0;
|
|
st[d] = (st[d] ^ st[a]) >>> 0;
|
|
st[d] = ((st[d] << 16) | ((st[d]>>>16) & 0xFFFF)) >>> 0;
|
|
|
|
st[c] = (st[c] + st[d]) >>> 0;
|
|
st[b] = (st[b] ^ st[c]) >>> 0;
|
|
st[b] = ((st[b] << 12) | ((st[b]>>>20) & 0xFFF)) >>> 0;
|
|
|
|
st[a] = (st[a] + st[b]) >>> 0;
|
|
st[d] = (st[d] ^ st[a]) >>> 0;
|
|
st[d] = ((st[d] << 8) | ((st[d]>>>24) & 0xFF)) >>> 0;
|
|
|
|
st[c] = (st[c] + st[d]) >>> 0;
|
|
st[b] = (st[b] ^ st[c]) >>> 0;
|
|
st[b] = ((st[b] << 7) | ((st[b]>>>25) & 0x7F)) >>> 0;
|
|
}
|
|
|
|
function doubleRound(st) {
|
|
quarterRound(st, 0, 4, 8,12);
|
|
quarterRound(st, 1, 5, 9,13);
|
|
quarterRound(st, 2, 6,10,14);
|
|
quarterRound(st, 3, 7,11,15);
|
|
|
|
quarterRound(st, 0, 5,10,15);
|
|
quarterRound(st, 1, 6,11,12);
|
|
quarterRound(st, 2, 7, 8,13);
|
|
quarterRound(st, 3, 4, 9,14);
|
|
}
|
|
|
|
class ChaCha {
|
|
|
|
constructor(seed) {
|
|
seed = seed || [0,0,0,0,0,0,0,0];
|
|
this.state = [
|
|
0x61707865,
|
|
0x3320646E,
|
|
0x79622D32,
|
|
0x6B206574,
|
|
seed[0],
|
|
seed[1],
|
|
seed[2],
|
|
seed[3],
|
|
seed[4],
|
|
seed[5],
|
|
seed[6],
|
|
seed[7],
|
|
0,
|
|
0,
|
|
0,
|
|
0
|
|
];
|
|
this.idx = 16;
|
|
this.buff = new Array(16);
|
|
}
|
|
|
|
nextU32() {
|
|
if (this.idx == 16) this.update();
|
|
return this.buff[this.idx++];
|
|
}
|
|
|
|
nextU64() {
|
|
return add$2(mul$2(this.nextU32(), 0x100000000), this.nextU32());
|
|
}
|
|
|
|
nextBool() {
|
|
return (this.nextU32() & 1) == 1;
|
|
}
|
|
|
|
update() {
|
|
// Copy the state
|
|
for (let i=0; i<16; i++) this.buff[i] = this.state[i];
|
|
|
|
// Apply the rounds
|
|
for (let i=0; i<10; i++) doubleRound(this.buff);
|
|
|
|
// Add to the initial
|
|
for (let i=0; i<16; i++) this.buff[i] = (this.buff[i] + this.state[i]) >>> 0;
|
|
|
|
this.idx = 0;
|
|
|
|
this.state[12] = (this.state[12] + 1) >>> 0;
|
|
if (this.state[12] != 0) return;
|
|
this.state[13] = (this.state[13] + 1) >>> 0;
|
|
if (this.state[13] != 0) return;
|
|
this.state[14] = (this.state[14] + 1) >>> 0;
|
|
if (this.state[14] != 0) return;
|
|
this.state[15] = (this.state[15] + 1) >>> 0;
|
|
}
|
|
}
|
|
|
|
/* global window */
|
|
|
|
function getRandomBytes(n) {
|
|
let array = new Uint8Array(n);
|
|
if (typeof window !== "undefined") { // Browser
|
|
if (typeof window.crypto !== "undefined") { // Supported
|
|
window.crypto.getRandomValues(array);
|
|
} else { // fallback
|
|
for (let i=0; i<n; i++) {
|
|
array[i] = (Math.random()*4294967296)>>>0;
|
|
}
|
|
}
|
|
}
|
|
else { // NodeJS
|
|
crypto.randomFillSync(array);
|
|
}
|
|
return array;
|
|
}
|
|
|
|
function getRandomSeed() {
|
|
const arr = getRandomBytes(32);
|
|
const arrV = new Uint32Array(arr.buffer);
|
|
const seed = [];
|
|
for (let i=0; i<8; i++) {
|
|
seed.push(arrV[i]);
|
|
}
|
|
return seed;
|
|
}
|
|
|
|
let threadRng = null;
|
|
|
|
function getThreadRng() {
|
|
if (threadRng) return threadRng;
|
|
threadRng = new ChaCha(getRandomSeed());
|
|
return threadRng;
|
|
}
|
|
|
|
/* global BigInt */
|
|
|
|
class ZqField {
|
|
constructor(p) {
|
|
this.type="F1";
|
|
this.one = 1n;
|
|
this.zero = 0n;
|
|
this.p = BigInt(p);
|
|
this.m = 1;
|
|
this.negone = this.p-1n;
|
|
this.two = 2n;
|
|
this.half = this.p >> 1n;
|
|
this.bitLength = bitLength$2(this.p);
|
|
this.mask = (1n << BigInt(this.bitLength)) - 1n;
|
|
|
|
this.n64 = Math.floor((this.bitLength - 1) / 64)+1;
|
|
this.n32 = this.n64*2;
|
|
this.n8 = this.n64*8;
|
|
this.R = this.e(1n << BigInt(this.n64*64));
|
|
this.Ri = this.inv(this.R);
|
|
|
|
const e = this.negone >> 1n;
|
|
this.nqr = this.two;
|
|
let r = this.pow(this.nqr, e);
|
|
while (!this.eq(r, this.negone)) {
|
|
this.nqr = this.nqr + 1n;
|
|
r = this.pow(this.nqr, e);
|
|
}
|
|
|
|
|
|
this.s = 0;
|
|
this.t = this.negone;
|
|
|
|
while ((this.t & 1n) == 0n) {
|
|
this.s = this.s + 1;
|
|
this.t = this.t >> 1n;
|
|
}
|
|
|
|
this.nqr_to_t = this.pow(this.nqr, this.t);
|
|
|
|
buildSqrt(this);
|
|
}
|
|
|
|
e(a,b) {
|
|
let res;
|
|
if (!b) {
|
|
res = BigInt(a);
|
|
} else if (b==16) {
|
|
res = BigInt("0x"+a);
|
|
}
|
|
if (res < 0) {
|
|
let nres = -res;
|
|
if (nres >= this.p) nres = nres % this.p;
|
|
return this.p - nres;
|
|
} else {
|
|
return (res>= this.p) ? res%this.p : res;
|
|
}
|
|
|
|
}
|
|
|
|
add(a, b) {
|
|
const res = a + b;
|
|
return res >= this.p ? res-this.p : res;
|
|
}
|
|
|
|
sub(a, b) {
|
|
return (a >= b) ? a-b : this.p-b+a;
|
|
}
|
|
|
|
neg(a) {
|
|
return a ? this.p-a : a;
|
|
}
|
|
|
|
mul(a, b) {
|
|
return (a*b)%this.p;
|
|
}
|
|
|
|
mulScalar(base, s) {
|
|
return (base * this.e(s)) % this.p;
|
|
}
|
|
|
|
square(a) {
|
|
return (a*a) % this.p;
|
|
}
|
|
|
|
eq(a, b) {
|
|
return a==b;
|
|
}
|
|
|
|
neq(a, b) {
|
|
return a!=b;
|
|
}
|
|
|
|
lt(a, b) {
|
|
const aa = (a > this.half) ? a - this.p : a;
|
|
const bb = (b > this.half) ? b - this.p : b;
|
|
return aa < bb;
|
|
}
|
|
|
|
gt(a, b) {
|
|
const aa = (a > this.half) ? a - this.p : a;
|
|
const bb = (b > this.half) ? b - this.p : b;
|
|
return aa > bb;
|
|
}
|
|
|
|
leq(a, b) {
|
|
const aa = (a > this.half) ? a - this.p : a;
|
|
const bb = (b > this.half) ? b - this.p : b;
|
|
return aa <= bb;
|
|
}
|
|
|
|
geq(a, b) {
|
|
const aa = (a > this.half) ? a - this.p : a;
|
|
const bb = (b > this.half) ? b - this.p : b;
|
|
return aa >= bb;
|
|
}
|
|
|
|
div(a, b) {
|
|
return this.mul(a, this.inv(b));
|
|
}
|
|
|
|
idiv(a, b) {
|
|
if (!b) throw new Error("Division by zero");
|
|
return a / b;
|
|
}
|
|
|
|
inv(a) {
|
|
if (!a) throw new Error("Division by zero");
|
|
|
|
let t = 0n;
|
|
let r = this.p;
|
|
let newt = 1n;
|
|
let newr = a % this.p;
|
|
while (newr) {
|
|
let q = r/newr;
|
|
[t, newt] = [newt, t-q*newt];
|
|
[r, newr] = [newr, r-q*newr];
|
|
}
|
|
if (t<0n) t += this.p;
|
|
return t;
|
|
}
|
|
|
|
mod(a, b) {
|
|
return a % b;
|
|
}
|
|
|
|
pow(b, e) {
|
|
return exp$3(this, b, e);
|
|
}
|
|
|
|
exp(b, e) {
|
|
return exp$3(this, b, e);
|
|
}
|
|
|
|
band(a, b) {
|
|
const res = ((a & b) & this.mask);
|
|
return res >= this.p ? res-this.p : res;
|
|
}
|
|
|
|
bor(a, b) {
|
|
const res = ((a | b) & this.mask);
|
|
return res >= this.p ? res-this.p : res;
|
|
}
|
|
|
|
bxor(a, b) {
|
|
const res = ((a ^ b) & this.mask);
|
|
return res >= this.p ? res-this.p : res;
|
|
}
|
|
|
|
bnot(a) {
|
|
const res = a ^ this.mask;
|
|
return res >= this.p ? res-this.p : res;
|
|
}
|
|
|
|
shl(a, b) {
|
|
if (Number(b) < this.bitLength) {
|
|
const res = (a << b) & this.mask;
|
|
return res >= this.p ? res-this.p : res;
|
|
} else {
|
|
const nb = this.p - b;
|
|
if (Number(nb) < this.bitLength) {
|
|
return a >> nb;
|
|
} else {
|
|
return 0n;
|
|
}
|
|
}
|
|
}
|
|
|
|
shr(a, b) {
|
|
if (Number(b) < this.bitLength) {
|
|
return a >> b;
|
|
} else {
|
|
const nb = this.p - b;
|
|
if (Number(nb) < this.bitLength) {
|
|
const res = (a << nb) & this.mask;
|
|
return res >= this.p ? res-this.p : res;
|
|
} else {
|
|
return 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
land(a, b) {
|
|
return (a && b) ? 1n : 0n;
|
|
}
|
|
|
|
lor(a, b) {
|
|
return (a || b) ? 1n : 0n;
|
|
}
|
|
|
|
lnot(a) {
|
|
return (a) ? 0n : 1n;
|
|
}
|
|
|
|
sqrt_old(n) {
|
|
|
|
if (n == 0n) return this.zero;
|
|
|
|
// Test that have solution
|
|
const res = this.pow(n, this.negone >> this.one);
|
|
if ( res != 1n ) return null;
|
|
|
|
let m = this.s;
|
|
let c = this.nqr_to_t;
|
|
let t = this.pow(n, this.t);
|
|
let r = this.pow(n, this.add(this.t, this.one) >> 1n );
|
|
|
|
while ( t != 1n ) {
|
|
let sq = this.square(t);
|
|
let i = 1;
|
|
while (sq != 1n ) {
|
|
i++;
|
|
sq = this.square(sq);
|
|
}
|
|
|
|
// b = c ^ m-i-1
|
|
let b = c;
|
|
for (let j=0; j< m-i-1; j ++) b = this.square(b);
|
|
|
|
m = i;
|
|
c = this.square(b);
|
|
t = this.mul(t, c);
|
|
r = this.mul(r, b);
|
|
}
|
|
|
|
if (r > (this.p >> 1n)) {
|
|
r = this.neg(r);
|
|
}
|
|
|
|
return r;
|
|
}
|
|
|
|
normalize(a, b) {
|
|
a = BigInt(a,b);
|
|
if (a < 0) {
|
|
let na = -a;
|
|
if (na >= this.p) na = na % this.p;
|
|
return this.p - na;
|
|
} else {
|
|
return (a>= this.p) ? a%this.p : a;
|
|
}
|
|
}
|
|
|
|
random() {
|
|
const nBytes = (this.bitLength*2 / 8);
|
|
let res =0n;
|
|
for (let i=0; i<nBytes; i++) {
|
|
res = (res << 8n) + BigInt(getRandomBytes(1)[0]);
|
|
}
|
|
return res % this.p;
|
|
}
|
|
|
|
toString(a, base) {
|
|
let vs;
|
|
if (a > this.half) {
|
|
const v = this.p-a;
|
|
vs = "-"+v.toString(base);
|
|
} else {
|
|
vs = a.toString(base);
|
|
}
|
|
return vs;
|
|
}
|
|
|
|
isZero(a) {
|
|
return a == 0n;
|
|
}
|
|
|
|
fromRng(rng) {
|
|
let v;
|
|
do {
|
|
v=0n;
|
|
for (let i=0; i<this.n64; i++) {
|
|
v += rng.nextU64() << BigInt(64 *i);
|
|
}
|
|
v &= this.mask;
|
|
} while (v >= this.p);
|
|
v = (v * this.Ri) % this.p; // Convert from montgomery
|
|
return v;
|
|
}
|
|
|
|
}
|
|
|
|
class ZqField$1 {
|
|
constructor(p) {
|
|
this.type="F1";
|
|
this.one = BigInteger.one;
|
|
this.zero = BigInteger.zero;
|
|
this.p = BigInteger(p);
|
|
this.m = 1;
|
|
this.negone = this.p.minus(BigInteger.one);
|
|
this.two = BigInteger(2);
|
|
this.half = this.p.shiftRight(1);
|
|
this.bitLength = this.p.bitLength();
|
|
this.mask = BigInteger.one.shiftLeft(this.bitLength).minus(BigInteger.one);
|
|
|
|
this.n64 = Math.floor((this.bitLength - 1) / 64)+1;
|
|
this.n32 = this.n64*2;
|
|
this.n8 = this.n64*8;
|
|
this.R = BigInteger.one.shiftLeft(this.n64*64);
|
|
this.Ri = this.inv(this.R);
|
|
|
|
const e = this.negone.shiftRight(this.one);
|
|
this.nqr = this.two;
|
|
let r = this.pow(this.nqr, e);
|
|
while (!r.equals(this.negone)) {
|
|
this.nqr = this.nqr.add(this.one);
|
|
r = this.pow(this.nqr, e);
|
|
}
|
|
|
|
this.s = this.zero;
|
|
this.t = this.negone;
|
|
|
|
while (!this.t.isOdd()) {
|
|
this.s = this.s.add(this.one);
|
|
this.t = this.t.shiftRight(this.one);
|
|
}
|
|
|
|
this.nqr_to_t = this.pow(this.nqr, this.t);
|
|
|
|
buildSqrt(this);
|
|
}
|
|
|
|
e(a,b) {
|
|
|
|
const res = BigInteger(a,b);
|
|
|
|
return this.normalize(res);
|
|
|
|
}
|
|
|
|
add(a, b) {
|
|
let res = a.add(b);
|
|
if (res.geq(this.p)) {
|
|
res = res.minus(this.p);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
sub(a, b) {
|
|
if (a.geq(b)) {
|
|
return a.minus(b);
|
|
} else {
|
|
return this.p.minus(b.minus(a));
|
|
}
|
|
}
|
|
|
|
neg(a) {
|
|
if (a.isZero()) return a;
|
|
return this.p.minus(a);
|
|
}
|
|
|
|
mul(a, b) {
|
|
return a.times(b).mod(this.p);
|
|
}
|
|
|
|
mulScalar(base, s) {
|
|
return base.times(BigInteger(s)).mod(this.p);
|
|
}
|
|
|
|
square(a) {
|
|
return a.square().mod(this.p);
|
|
}
|
|
|
|
eq(a, b) {
|
|
return a.eq(b);
|
|
}
|
|
|
|
neq(a, b) {
|
|
return a.neq(b);
|
|
}
|
|
|
|
lt(a, b) {
|
|
const aa = a.gt(this.half) ? a.minus(this.p) : a;
|
|
const bb = b.gt(this.half) ? b.minus(this.p) : b;
|
|
return aa.lt(bb);
|
|
}
|
|
|
|
gt(a, b) {
|
|
const aa = a.gt(this.half) ? a.minus(this.p) : a;
|
|
const bb = b.gt(this.half) ? b.minus(this.p) : b;
|
|
return aa.gt(bb);
|
|
}
|
|
|
|
leq(a, b) {
|
|
const aa = a.gt(this.half) ? a.minus(this.p) : a;
|
|
const bb = b.gt(this.half) ? b.minus(this.p) : b;
|
|
return aa.leq(bb);
|
|
}
|
|
|
|
geq(a, b) {
|
|
const aa = a.gt(this.half) ? a.minus(this.p) : a;
|
|
const bb = b.gt(this.half) ? b.minus(this.p) : b;
|
|
return aa.geq(bb);
|
|
}
|
|
|
|
div(a, b) {
|
|
if (b.isZero()) throw new Error("Division by zero");
|
|
return a.times(b.modInv(this.p)).mod(this.p);
|
|
}
|
|
|
|
idiv(a, b) {
|
|
if (b.isZero()) throw new Error("Division by zero");
|
|
return a.divide(b);
|
|
}
|
|
|
|
inv(a) {
|
|
if (a.isZero()) throw new Error("Division by zero");
|
|
return a.modInv(this.p);
|
|
}
|
|
|
|
mod(a, b) {
|
|
return a.mod(b);
|
|
}
|
|
|
|
pow(a, b) {
|
|
return a.modPow(b, this.p);
|
|
}
|
|
|
|
exp(a, b) {
|
|
return a.modPow(b, this.p);
|
|
}
|
|
|
|
band(a, b) {
|
|
return a.and(b).and(this.mask).mod(this.p);
|
|
}
|
|
|
|
bor(a, b) {
|
|
return a.or(b).and(this.mask).mod(this.p);
|
|
}
|
|
|
|
bxor(a, b) {
|
|
return a.xor(b).and(this.mask).mod(this.p);
|
|
}
|
|
|
|
bnot(a) {
|
|
return a.xor(this.mask).mod(this.p);
|
|
}
|
|
|
|
shl(a, b) {
|
|
if (b.lt(this.bitLength)) {
|
|
return a.shiftLeft(b).and(this.mask).mod(this.p);
|
|
} else {
|
|
const nb = this.p.minus(b);
|
|
if (nb.lt(this.bitLength)) {
|
|
return this.shr(a, nb);
|
|
} else {
|
|
return BigInteger.zero;
|
|
}
|
|
}
|
|
}
|
|
|
|
shr(a, b) {
|
|
if (b.lt(this.bitLength)) {
|
|
return a.shiftRight(b);
|
|
} else {
|
|
const nb = this.p.minus(b);
|
|
if (nb.lt(this.bitLength)) {
|
|
return this.shl(a, nb);
|
|
} else {
|
|
return BigInteger.zero;
|
|
}
|
|
}
|
|
}
|
|
|
|
land(a, b) {
|
|
return (a.isZero() || b.isZero()) ? BigInteger.zero : BigInteger.one;
|
|
}
|
|
|
|
lor(a, b) {
|
|
return (a.isZero() && b.isZero()) ? BigInteger.zero : BigInteger.one;
|
|
}
|
|
|
|
lnot(a) {
|
|
return a.isZero() ? BigInteger.one : BigInteger.zero;
|
|
}
|
|
|
|
sqrt_old(n) {
|
|
|
|
if (n.equals(this.zero)) return this.zero;
|
|
|
|
// Test that have solution
|
|
const res = this.pow(n, this.negone.shiftRight(this.one));
|
|
if (!res.equals(this.one)) return null;
|
|
|
|
let m = parseInt(this.s);
|
|
let c = this.nqr_to_t;
|
|
let t = this.pow(n, this.t);
|
|
let r = this.pow(n, this.add(this.t, this.one).shiftRight(this.one) );
|
|
|
|
while (!t.equals(this.one)) {
|
|
let sq = this.square(t);
|
|
let i = 1;
|
|
while (!sq.equals(this.one)) {
|
|
i++;
|
|
sq = this.square(sq);
|
|
}
|
|
|
|
// b = c ^ m-i-1
|
|
let b = c;
|
|
for (let j=0; j< m-i-1; j ++) b = this.square(b);
|
|
|
|
m = i;
|
|
c = this.square(b);
|
|
t = this.mul(t, c);
|
|
r = this.mul(r, b);
|
|
}
|
|
|
|
if (r.greater(this.p.shiftRight(this.one))) {
|
|
r = this.neg(r);
|
|
}
|
|
|
|
return r;
|
|
}
|
|
|
|
normalize(a) {
|
|
a = BigInteger(a);
|
|
if (a.isNegative()) {
|
|
return this.p.minus(a.abs().mod(this.p));
|
|
} else {
|
|
return a.mod(this.p);
|
|
}
|
|
}
|
|
|
|
random() {
|
|
let res = BigInteger(0);
|
|
let n = BigInteger(this.p.square());
|
|
while (!n.isZero()) {
|
|
res = res.shiftLeft(8).add(BigInteger(getRandomBytes(1)[0]));
|
|
n = n.shiftRight(8);
|
|
}
|
|
return res.mod(this.p);
|
|
}
|
|
|
|
toString(a, base) {
|
|
let vs;
|
|
if (!a.lesserOrEquals(this.p.shiftRight(BigInteger(1)))) {
|
|
const v = this.p.minus(a);
|
|
vs = "-"+v.toString(base);
|
|
} else {
|
|
vs = a.toString(base);
|
|
}
|
|
|
|
return vs;
|
|
}
|
|
|
|
isZero(a) {
|
|
return a.isZero();
|
|
}
|
|
|
|
fromRng(rng) {
|
|
let v;
|
|
do {
|
|
v = BigInteger(0);
|
|
for (let i=0; i<this.n64; i++) {
|
|
v = v.add(v, rng.nextU64().shiftLeft(64*i));
|
|
}
|
|
v = v.and(this.mask);
|
|
} while (v.geq(this.p));
|
|
v = v.times(this.Ri).mod(this.q);
|
|
return v;
|
|
}
|
|
|
|
|
|
}
|
|
|
|
const supportsNativeBigInt$1 = typeof BigInt === "function";
|
|
let _F1Field;
|
|
if (supportsNativeBigInt$1) {
|
|
_F1Field = ZqField;
|
|
} else {
|
|
_F1Field = ZqField$1;
|
|
}
|
|
|
|
class F1Field extends _F1Field {
|
|
|
|
// Returns a buffer with Little Endian Representation
|
|
toRprLE(buff, o, e) {
|
|
toRprLE(buff, o, e, this.n64*8);
|
|
}
|
|
|
|
// Returns a buffer with Big Endian Representation
|
|
toRprBE(buff, o, e) {
|
|
toRprBE(buff, o, e, this.n64*8);
|
|
}
|
|
|
|
// Returns a buffer with Big Endian Montgomery Representation
|
|
toRprBEM(buff, o, e) {
|
|
return this.toRprBE(buff, o, this.mul(this.R, e));
|
|
}
|
|
|
|
toRprLEM(buff, o, e) {
|
|
return this.toRprLE(buff, o, this.mul(this.R, e));
|
|
}
|
|
|
|
|
|
// Pases a buffer with Little Endian Representation
|
|
fromRprLE(buff, o) {
|
|
return fromRprLE(buff, o, this.n8);
|
|
}
|
|
|
|
// Pases a buffer with Big Endian Representation
|
|
fromRprBE(buff, o) {
|
|
return fromRprBE(buff, o, this.n8);
|
|
}
|
|
|
|
fromRprLEM(buff, o) {
|
|
return this.mul(this.fromRprLE(buff, o), this.Ri);
|
|
}
|
|
|
|
fromRprBEM(buff, o) {
|
|
return this.mul(this.fromRprBE(buff, o), this.Ri);
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
Copyright 2018 0kims association.
|
|
|
|
This file is part of snarkjs.
|
|
|
|
snarkjs is a free software: you can redistribute it and/or
|
|
modify it under the terms of the GNU General Public License as published by the
|
|
Free Software Foundation, either version 3 of the License, or (at your option)
|
|
any later version.
|
|
|
|
snarkjs is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
|
|
more details.
|
|
|
|
You should have received a copy of the GNU General Public License along with
|
|
snarkjs. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
class F2Field {
|
|
constructor(F, nonResidue) {
|
|
this.type="F2";
|
|
this.F = F;
|
|
this.zero = [this.F.zero, this.F.zero];
|
|
this.one = [this.F.one, this.F.zero];
|
|
this.negone = this.neg(this.one);
|
|
this.nonResidue = nonResidue;
|
|
this.m = F.m*2;
|
|
this.p = F.p;
|
|
this.n64 = F.n64*2;
|
|
this.n32 = this.n64*2;
|
|
this.n8 = this.n64*8;
|
|
|
|
buildSqrt(this);
|
|
}
|
|
|
|
_mulByNonResidue(a) {
|
|
return this.F.mul(this.nonResidue, a);
|
|
}
|
|
|
|
copy(a) {
|
|
return [this.F.copy(a[0]), this.F.copy(a[1])];
|
|
}
|
|
|
|
add(a, b) {
|
|
return [
|
|
this.F.add(a[0], b[0]),
|
|
this.F.add(a[1], b[1])
|
|
];
|
|
}
|
|
|
|
double(a) {
|
|
return this.add(a,a);
|
|
}
|
|
|
|
sub(a, b) {
|
|
return [
|
|
this.F.sub(a[0], b[0]),
|
|
this.F.sub(a[1], b[1])
|
|
];
|
|
}
|
|
|
|
neg(a) {
|
|
return this.sub(this.zero, a);
|
|
}
|
|
|
|
conjugate(a) {
|
|
return [
|
|
a[0],
|
|
this.F.neg(a[1])
|
|
];
|
|
}
|
|
|
|
mul(a, b) {
|
|
const aA = this.F.mul(a[0] , b[0]);
|
|
const bB = this.F.mul(a[1] , b[1]);
|
|
|
|
return [
|
|
this.F.add( aA , this._mulByNonResidue(bB)),
|
|
this.F.sub(
|
|
this.F.mul(
|
|
this.F.add(a[0], a[1]),
|
|
this.F.add(b[0], b[1])),
|
|
this.F.add(aA, bB))];
|
|
}
|
|
|
|
inv(a) {
|
|
const t0 = this.F.square(a[0]);
|
|
const t1 = this.F.square(a[1]);
|
|
const t2 = this.F.sub(t0, this._mulByNonResidue(t1));
|
|
const t3 = this.F.inv(t2);
|
|
return [
|
|
this.F.mul(a[0], t3),
|
|
this.F.neg(this.F.mul( a[1], t3)) ];
|
|
}
|
|
|
|
div(a, b) {
|
|
return this.mul(a, this.inv(b));
|
|
}
|
|
|
|
square(a) {
|
|
const ab = this.F.mul(a[0] , a[1]);
|
|
|
|
/*
|
|
[
|
|
(a + b) * (a + non_residue * b) - ab - non_residue * ab,
|
|
ab + ab
|
|
];
|
|
*/
|
|
|
|
return [
|
|
this.F.sub(
|
|
this.F.mul(
|
|
this.F.add(a[0], a[1]) ,
|
|
this.F.add(
|
|
a[0] ,
|
|
this._mulByNonResidue(a[1]))),
|
|
this.F.add(
|
|
ab,
|
|
this._mulByNonResidue(ab))),
|
|
this.F.add(ab, ab)
|
|
];
|
|
}
|
|
|
|
isZero(a) {
|
|
return this.F.isZero(a[0]) && this.F.isZero(a[1]);
|
|
}
|
|
|
|
eq(a, b) {
|
|
return this.F.eq(a[0], b[0]) && this.F.eq(a[1], b[1]);
|
|
}
|
|
|
|
mulScalar(base, e) {
|
|
return mulScalar(this, base, e);
|
|
}
|
|
|
|
pow(base, e) {
|
|
return exp$3(this, base, e);
|
|
}
|
|
|
|
exp(base, e) {
|
|
return exp$3(this, base, e);
|
|
}
|
|
|
|
toString(a) {
|
|
return `[ ${this.F.toString(a[0])} , ${this.F.toString(a[1])} ]`;
|
|
}
|
|
|
|
fromRng(rng) {
|
|
const c0 = this.F.fromRng(rng);
|
|
const c1 = this.F.fromRng(rng);
|
|
return [c0, c1];
|
|
}
|
|
|
|
gt(a, b) {
|
|
if (this.F.gt(a[0], b[0])) return true;
|
|
if (this.F.gt(b[0], a[0])) return false;
|
|
if (this.F.gt(a[1], b[1])) return true;
|
|
return false;
|
|
}
|
|
|
|
geq(a, b) {
|
|
return this.gt(a, b) || this.eq(a, b);
|
|
}
|
|
|
|
lt(a, b) {
|
|
return !this.geq(a,b);
|
|
}
|
|
|
|
leq(a, b) {
|
|
return !this.gt(a,b);
|
|
}
|
|
|
|
neq(a, b) {
|
|
return !this.eq(a,b);
|
|
}
|
|
|
|
random() {
|
|
return [this.F.random(), this.F.random()];
|
|
}
|
|
|
|
|
|
toRprLE(buff, o, e) {
|
|
this.F.toRprLE(buff, o, e[0]);
|
|
this.F.toRprLE(buff, o+this.F.n8, e[1]);
|
|
}
|
|
|
|
toRprBE(buff, o, e) {
|
|
this.F.toRprBE(buff, o, e[1]);
|
|
this.F.toRprBE(buff, o+this.F.n8, e[0]);
|
|
}
|
|
|
|
toRprLEM(buff, o, e) {
|
|
this.F.toRprLEM(buff, o, e[0]);
|
|
this.F.toRprLEM(buff, o+this.F.n8, e[1]);
|
|
}
|
|
|
|
|
|
toRprBEM(buff, o, e) {
|
|
this.F.toRprBEM(buff, o, e[1]);
|
|
this.F.toRprBEM(buff, o+this.F.n8, e[0]);
|
|
}
|
|
|
|
fromRprLE(buff, o) {
|
|
o = o || 0;
|
|
const c0 = this.F.fromRprLE(buff, o);
|
|
const c1 = this.F.fromRprLE(buff, o+this.F.n8);
|
|
return [c0, c1];
|
|
}
|
|
|
|
fromRprBE(buff, o) {
|
|
o = o || 0;
|
|
const c1 = this.F.fromRprBE(buff, o);
|
|
const c0 = this.F.fromRprBE(buff, o+this.F.n8);
|
|
return [c0, c1];
|
|
}
|
|
|
|
fromRprLEM(buff, o) {
|
|
o = o || 0;
|
|
const c0 = this.F.fromRprLEM(buff, o);
|
|
const c1 = this.F.fromRprLEM(buff, o+this.F.n8);
|
|
return [c0, c1];
|
|
}
|
|
|
|
fromRprBEM(buff, o) {
|
|
o = o || 0;
|
|
const c1 = this.F.fromRprBEM(buff, o);
|
|
const c0 = this.F.fromRprBEM(buff, o+this.F.n8);
|
|
return [c0, c1];
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
Copyright 2018 0kims association.
|
|
|
|
This file is part of snarkjs.
|
|
|
|
snarkjs is a free software: you can redistribute it and/or
|
|
modify it under the terms of the GNU General Public License as published by the
|
|
Free Software Foundation, either version 3 of the License, or (at your option)
|
|
any later version.
|
|
|
|
snarkjs is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
|
|
more details.
|
|
|
|
You should have received a copy of the GNU General Public License along with
|
|
snarkjs. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
class F3Field {
|
|
constructor(F, nonResidue) {
|
|
this.type="F3";
|
|
this.F = F;
|
|
this.zero = [this.F.zero, this.F.zero, this.F.zero];
|
|
this.one = [this.F.one, this.F.zero, this.F.zero];
|
|
this.negone = this.neg(this.one);
|
|
this.nonResidue = nonResidue;
|
|
this.m = F.m*3;
|
|
this.p = F.p;
|
|
this.n64 = F.n64*3;
|
|
this.n32 = this.n64*2;
|
|
this.n8 = this.n64*8;
|
|
}
|
|
|
|
_mulByNonResidue(a) {
|
|
return this.F.mul(this.nonResidue, a);
|
|
}
|
|
|
|
copy(a) {
|
|
return [this.F.copy(a[0]), this.F.copy(a[1]), this.F.copy(a[2])];
|
|
}
|
|
|
|
add(a, b) {
|
|
return [
|
|
this.F.add(a[0], b[0]),
|
|
this.F.add(a[1], b[1]),
|
|
this.F.add(a[2], b[2])
|
|
];
|
|
}
|
|
|
|
double(a) {
|
|
return this.add(a,a);
|
|
}
|
|
|
|
sub(a, b) {
|
|
return [
|
|
this.F.sub(a[0], b[0]),
|
|
this.F.sub(a[1], b[1]),
|
|
this.F.sub(a[2], b[2])
|
|
];
|
|
}
|
|
|
|
neg(a) {
|
|
return this.sub(this.zero, a);
|
|
}
|
|
|
|
mul(a, b) {
|
|
|
|
const aA = this.F.mul(a[0] , b[0]);
|
|
const bB = this.F.mul(a[1] , b[1]);
|
|
const cC = this.F.mul(a[2] , b[2]);
|
|
|
|
return [
|
|
this.F.add(
|
|
aA,
|
|
this._mulByNonResidue(
|
|
this.F.sub(
|
|
this.F.mul(
|
|
this.F.add(a[1], a[2]),
|
|
this.F.add(b[1], b[2])),
|
|
this.F.add(bB, cC)))), // aA + non_residue*((b+c)*(B+C)-bB-cC),
|
|
|
|
this.F.add(
|
|
this.F.sub(
|
|
this.F.mul(
|
|
this.F.add(a[0], a[1]),
|
|
this.F.add(b[0], b[1])),
|
|
this.F.add(aA, bB)),
|
|
this._mulByNonResidue( cC)), // (a+b)*(A+B)-aA-bB+non_residue*cC
|
|
|
|
this.F.add(
|
|
this.F.sub(
|
|
this.F.mul(
|
|
this.F.add(a[0], a[2]),
|
|
this.F.add(b[0], b[2])),
|
|
this.F.add(aA, cC)),
|
|
bB)]; // (a+c)*(A+C)-aA+bB-cC)
|
|
}
|
|
|
|
inv(a) {
|
|
const t0 = this.F.square(a[0]); // t0 = a^2 ;
|
|
const t1 = this.F.square(a[1]); // t1 = b^2 ;
|
|
const t2 = this.F.square(a[2]); // t2 = c^2;
|
|
const t3 = this.F.mul(a[0],a[1]); // t3 = ab
|
|
const t4 = this.F.mul(a[0],a[2]); // t4 = ac
|
|
const t5 = this.F.mul(a[1],a[2]); // t5 = bc;
|
|
// c0 = t0 - non_residue * t5;
|
|
const c0 = this.F.sub(t0, this._mulByNonResidue(t5));
|
|
// c1 = non_residue * t2 - t3;
|
|
const c1 = this.F.sub(this._mulByNonResidue(t2), t3);
|
|
const c2 = this.F.sub(t1, t4); // c2 = t1-t4
|
|
|
|
// t6 = (a * c0 + non_residue * (c * c1 + b * c2)).inv();
|
|
const t6 =
|
|
this.F.inv(
|
|
this.F.add(
|
|
this.F.mul(a[0], c0),
|
|
this._mulByNonResidue(
|
|
this.F.add(
|
|
this.F.mul(a[2], c1),
|
|
this.F.mul(a[1], c2)))));
|
|
|
|
return [
|
|
this.F.mul(t6, c0), // t6*c0
|
|
this.F.mul(t6, c1), // t6*c1
|
|
this.F.mul(t6, c2)]; // t6*c2
|
|
}
|
|
|
|
div(a, b) {
|
|
return this.mul(a, this.inv(b));
|
|
}
|
|
|
|
square(a) {
|
|
const s0 = this.F.square(a[0]); // s0 = a^2
|
|
const ab = this.F.mul(a[0], a[1]); // ab = a*b
|
|
const s1 = this.F.add(ab, ab); // s1 = 2ab;
|
|
const s2 = this.F.square(
|
|
this.F.add(this.F.sub(a[0],a[1]), a[2])); // s2 = (a - b + c)^2;
|
|
const bc = this.F.mul(a[1],a[2]); // bc = b*c
|
|
const s3 = this.F.add(bc, bc); // s3 = 2*bc
|
|
const s4 = this.F.square(a[2]); // s4 = c^2
|
|
|
|
|
|
return [
|
|
this.F.add(
|
|
s0,
|
|
this._mulByNonResidue(s3)), // s0 + non_residue * s3,
|
|
this.F.add(
|
|
s1,
|
|
this._mulByNonResidue(s4)), // s1 + non_residue * s4,
|
|
this.F.sub(
|
|
this.F.add( this.F.add(s1, s2) , s3 ),
|
|
this.F.add(s0, s4))]; // s1 + s2 + s3 - s0 - s4
|
|
}
|
|
|
|
isZero(a) {
|
|
return this.F.isZero(a[0]) && this.F.isZero(a[1]) && this.F.isZero(a[2]);
|
|
}
|
|
|
|
eq(a, b) {
|
|
return this.F.eq(a[0], b[0]) && this.F.eq(a[1], b[1]) && this.F.eq(a[2], b[2]);
|
|
}
|
|
|
|
affine(a) {
|
|
return [this.F.affine(a[0]), this.F.affine(a[1]), this.F.affine(a[2])];
|
|
}
|
|
|
|
mulScalar(base, e) {
|
|
return mulScalar(this, base, e);
|
|
}
|
|
|
|
pow(base, e) {
|
|
return exp$3(this, base, e);
|
|
}
|
|
|
|
exp(base, e) {
|
|
return exp$3(this, base, e);
|
|
}
|
|
|
|
toString(a) {
|
|
return `[ ${this.F.toString(a[0])} , ${this.F.toString(a[1])}, ${this.F.toString(a[2])} ]`;
|
|
}
|
|
|
|
fromRng(rng) {
|
|
const c0 = this.F.fromRng(rng);
|
|
const c1 = this.F.fromRng(rng);
|
|
const c2 = this.F.fromRng(rng);
|
|
return [c0, c1, c2];
|
|
}
|
|
|
|
gt(a, b) {
|
|
if (this.F.gt(a[0], b[0])) return true;
|
|
if (this.F.gt(b[0], a[0])) return false;
|
|
if (this.F.gt(a[1], b[1])) return true;
|
|
if (this.F.gt(b[1], a[1])) return false;
|
|
if (this.F.gt(a[2], b[2])) return true;
|
|
return false;
|
|
}
|
|
|
|
|
|
geq(a, b) {
|
|
return this.gt(a, b) || this.eq(a, b);
|
|
}
|
|
|
|
lt(a, b) {
|
|
return !this.geq(a,b);
|
|
}
|
|
|
|
leq(a, b) {
|
|
return !this.gt(a,b);
|
|
}
|
|
|
|
neq(a, b) {
|
|
return !this.eq(a,b);
|
|
}
|
|
|
|
random() {
|
|
return [this.F.random(), this.F.random(), this.F.random()];
|
|
}
|
|
|
|
|
|
toRprLE(buff, o, e) {
|
|
this.F.toRprLE(buff, o, e[0]);
|
|
this.F.toRprLE(buff, o+this.F.n8, e[1]);
|
|
this.F.toRprLE(buff, o+this.F.n8*2, e[2]);
|
|
}
|
|
|
|
toRprBE(buff, o, e) {
|
|
this.F.toRprBE(buff, o, e[2]);
|
|
this.F.toRprBE(buff, o+this.F.n8, e[1]);
|
|
this.F.toRprBE(buff, o+this.F.n8*2, e[0]);
|
|
}
|
|
|
|
toRprLEM(buff, o, e) {
|
|
this.F.toRprLEM(buff, o, e[0]);
|
|
this.F.toRprLEM(buff, o+this.F.n8, e[1]);
|
|
this.F.toRprLEM(buff, o+this.F.n8*2, e[2]);
|
|
}
|
|
|
|
|
|
toRprBEM(buff, o, e) {
|
|
this.F.toRprBEM(buff, o, e[2]);
|
|
this.F.toRprBEM(buff, o+this.F.n8, e[1]);
|
|
this.F.toRprBEM(buff, o+this.F.n8*2, e[0]);
|
|
}
|
|
|
|
fromRprLE(buff, o) {
|
|
o = o || 0;
|
|
const c0 = this.F.fromRprLE(buff, o);
|
|
const c1 = this.F.fromRprLE(buff, o+this.n8);
|
|
const c2 = this.F.fromRprLE(buff, o+this.n8*2);
|
|
return [c0, c1, c2];
|
|
}
|
|
|
|
fromRprBE(buff, o) {
|
|
o = o || 0;
|
|
const c2 = this.F.fromRprBE(buff, o);
|
|
const c1 = this.F.fromRprBE(buff, o+this.n8);
|
|
const c0 = this.F.fromRprBE(buff, o+this.n8*2);
|
|
return [c0, c1, c2];
|
|
}
|
|
|
|
fromRprLEM(buff, o) {
|
|
o = o || 0;
|
|
const c0 = this.F.fromRprLEM(buff, o);
|
|
const c1 = this.F.fromRprLEM(buff, o+this.n8);
|
|
const c2 = this.F.fromRprLEM(buff, o+this.n8*2);
|
|
return [c0, c1, c2];
|
|
}
|
|
|
|
fromRprBEM(buff, o) {
|
|
o = o || 0;
|
|
const c2 = this.F.fromRprBEM(buff, o);
|
|
const c1 = this.F.fromRprBEM(buff, o+this.n8);
|
|
const c0 = this.F.fromRprBEM(buff, o+this.n8*2);
|
|
return [c0, c1, c2];
|
|
}
|
|
|
|
}
|
|
|
|
/*
|
|
Copyright 2018 0kims association.
|
|
|
|
This file is part of snarkjs.
|
|
|
|
snarkjs is a free software: you can redistribute it and/or
|
|
modify it under the terms of the GNU General Public License as published by the
|
|
Free Software Foundation, either version 3 of the License, or (at your option)
|
|
any later version.
|
|
|
|
snarkjs is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
|
|
more details.
|
|
|
|
You should have received a copy of the GNU General Public License along with
|
|
snarkjs. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
|
|
function isGreatest(F, a) {
|
|
if (Array.isArray(a)) {
|
|
for (let i=a.length-1; i>=0; i--) {
|
|
if (!F.F.isZero(a[i])) {
|
|
return isGreatest(F.F, a[i]);
|
|
}
|
|
}
|
|
return 0;
|
|
} else {
|
|
const na = F.neg(a);
|
|
return gt$2(a, na);
|
|
}
|
|
}
|
|
|
|
|
|
class EC {
|
|
|
|
constructor(F, g) {
|
|
this.F = F;
|
|
this.g = g;
|
|
if (this.g.length == 2) this.g[2] = this.F.one;
|
|
this.zero = [this.F.zero, this.F.one, this.F.zero];
|
|
}
|
|
|
|
add(p1, p2) {
|
|
|
|
const F = this.F;
|
|
|
|
if (this.eq(p1, this.zero)) return p2;
|
|
if (this.eq(p2, this.zero)) return p1;
|
|
|
|
const res = new Array(3);
|
|
|
|
const Z1Z1 = F.square( p1[2] );
|
|
const Z2Z2 = F.square( p2[2] );
|
|
|
|
const U1 = F.mul( p1[0] , Z2Z2 ); // U1 = X1 * Z2Z2
|
|
const U2 = F.mul( p2[0] , Z1Z1 ); // U2 = X2 * Z1Z1
|
|
|
|
const Z1_cubed = F.mul( p1[2] , Z1Z1);
|
|
const Z2_cubed = F.mul( p2[2] , Z2Z2);
|
|
|
|
const S1 = F.mul( p1[1] , Z2_cubed); // S1 = Y1 * Z2 * Z2Z2
|
|
const S2 = F.mul( p2[1] , Z1_cubed); // S2 = Y2 * Z1 * Z1Z1
|
|
|
|
if (F.eq(U1,U2) && F.eq(S1,S2)) {
|
|
return this.double(p1);
|
|
}
|
|
|
|
const H = F.sub( U2 , U1 ); // H = U2-U1
|
|
|
|
const S2_minus_S1 = F.sub( S2 , S1 );
|
|
|
|
const I = F.square( F.add(H,H) ); // I = (2 * H)^2
|
|
const J = F.mul( H , I ); // J = H * I
|
|
|
|
const r = F.add( S2_minus_S1 , S2_minus_S1 ); // r = 2 * (S2-S1)
|
|
const V = F.mul( U1 , I ); // V = U1 * I
|
|
|
|
res[0] =
|
|
F.sub(
|
|
F.sub( F.square(r) , J ),
|
|
F.add( V , V )); // X3 = r^2 - J - 2 * V
|
|
|
|
const S1_J = F.mul( S1 , J );
|
|
|
|
res[1] =
|
|
F.sub(
|
|
F.mul( r , F.sub(V,res[0])),
|
|
F.add( S1_J,S1_J )); // Y3 = r * (V-X3)-2 S1 J
|
|
|
|
res[2] =
|
|
F.mul(
|
|
H,
|
|
F.sub(
|
|
F.square( F.add(p1[2],p2[2]) ),
|
|
F.add( Z1Z1 , Z2Z2 ))); // Z3 = ((Z1+Z2)^2-Z1Z1-Z2Z2) * H
|
|
|
|
return res;
|
|
}
|
|
|
|
neg(p) {
|
|
return [p[0], this.F.neg(p[1]), p[2]];
|
|
}
|
|
|
|
sub(a, b) {
|
|
return this.add(a, this.neg(b));
|
|
}
|
|
|
|
double(p) {
|
|
const F = this.F;
|
|
|
|
const res = new Array(3);
|
|
|
|
if (this.eq(p, this.zero)) return p;
|
|
|
|
const A = F.square( p[0] ); // A = X1^2
|
|
const B = F.square( p[1] ); // B = Y1^2
|
|
const C = F.square( B ); // C = B^2
|
|
|
|
let D =
|
|
F.sub(
|
|
F.square( F.add(p[0] , B )),
|
|
F.add( A , C));
|
|
D = F.add(D,D); // D = 2 * ((X1 + B)^2 - A - C)
|
|
|
|
const E = F.add( F.add(A,A), A); // E = 3 * A
|
|
const FF =F.square( E ); // F = E^2
|
|
|
|
res[0] = F.sub( FF , F.add(D,D) ); // X3 = F - 2 D
|
|
|
|
let eightC = F.add( C , C );
|
|
eightC = F.add( eightC , eightC );
|
|
eightC = F.add( eightC , eightC );
|
|
|
|
res[1] =
|
|
F.sub(
|
|
F.mul(
|
|
E,
|
|
F.sub( D, res[0] )),
|
|
eightC); // Y3 = E * (D - X3) - 8 * C
|
|
|
|
const Y1Z1 = F.mul( p[1] , p[2] );
|
|
res[2] = F.add( Y1Z1 , Y1Z1 ); // Z3 = 2 * Y1 * Z1
|
|
|
|
return res;
|
|
}
|
|
|
|
timesScalar(base, e) {
|
|
return mulScalar(this, base, e);
|
|
}
|
|
|
|
mulScalar(base, e) {
|
|
return mulScalar(this, base, e);
|
|
}
|
|
|
|
affine(p) {
|
|
const F = this.F;
|
|
if (this.isZero(p)) {
|
|
return this.zero;
|
|
} else if (F.eq(p[2], F.one)) {
|
|
return p;
|
|
} else {
|
|
const Z_inv = F.inv(p[2]);
|
|
const Z2_inv = F.square(Z_inv);
|
|
const Z3_inv = F.mul(Z2_inv, Z_inv);
|
|
|
|
const res = new Array(3);
|
|
res[0] = F.mul(p[0],Z2_inv);
|
|
res[1] = F.mul(p[1],Z3_inv);
|
|
res[2] = F.one;
|
|
|
|
return res;
|
|
}
|
|
}
|
|
|
|
multiAffine(arr) {
|
|
const keys = Object.keys(arr);
|
|
const F = this.F;
|
|
const accMul = new Array(keys.length+1);
|
|
accMul[0] = F.one;
|
|
for (let i = 0; i< keys.length; i++) {
|
|
if (F.eq(arr[keys[i]][2], F.zero)) {
|
|
accMul[i+1] = accMul[i];
|
|
} else {
|
|
accMul[i+1] = F.mul(accMul[i], arr[keys[i]][2]);
|
|
}
|
|
}
|
|
|
|
accMul[keys.length] = F.inv(accMul[keys.length]);
|
|
|
|
for (let i = keys.length-1; i>=0; i--) {
|
|
if (F.eq(arr[keys[i]][2], F.zero)) {
|
|
accMul[i] = accMul[i+1];
|
|
arr[keys[i]] = this.zero;
|
|
} else {
|
|
const Z_inv = F.mul(accMul[i], accMul[i+1]);
|
|
accMul[i] = F.mul(arr[keys[i]][2], accMul[i+1]);
|
|
|
|
const Z2_inv = F.square(Z_inv);
|
|
const Z3_inv = F.mul(Z2_inv, Z_inv);
|
|
|
|
arr[keys[i]][0] = F.mul(arr[keys[i]][0],Z2_inv);
|
|
arr[keys[i]][1] = F.mul(arr[keys[i]][1],Z3_inv);
|
|
arr[keys[i]][2] = F.one;
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
eq(p1, p2) {
|
|
const F = this.F;
|
|
|
|
if (this.F.eq(p1[2], this.F.zero)) return this.F.eq(p2[2], this.F.zero);
|
|
if (this.F.eq(p2[2], this.F.zero)) return false;
|
|
|
|
const Z1Z1 = F.square( p1[2] );
|
|
const Z2Z2 = F.square( p2[2] );
|
|
|
|
const U1 = F.mul( p1[0] , Z2Z2 );
|
|
const U2 = F.mul( p2[0] , Z1Z1 );
|
|
|
|
const Z1_cubed = F.mul( p1[2] , Z1Z1);
|
|
const Z2_cubed = F.mul( p2[2] , Z2Z2);
|
|
|
|
const S1 = F.mul( p1[1] , Z2_cubed);
|
|
const S2 = F.mul( p2[1] , Z1_cubed);
|
|
|
|
return (F.eq(U1,U2) && F.eq(S1,S2));
|
|
}
|
|
|
|
isZero(p) {
|
|
return this.F.isZero(p[2]);
|
|
}
|
|
|
|
toString(p) {
|
|
const cp = this.affine(p);
|
|
return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])} ]`;
|
|
}
|
|
|
|
fromRng(rng) {
|
|
const F = this.F;
|
|
let P = [];
|
|
let greatest;
|
|
do {
|
|
P[0] = F.fromRng(rng);
|
|
greatest = rng.nextBool();
|
|
const x3b = F.add(F.mul(F.square(P[0]), P[0]), this.b);
|
|
P[1] = F.sqrt(x3b);
|
|
} while ((P[1] == null)||(F.isZero[P]));
|
|
|
|
const s = isGreatest(F, P[1]);
|
|
if (greatest ^ s) P[1] = F.neg(P[1]);
|
|
P[2] = F.one;
|
|
|
|
if (this.cofactor) {
|
|
P = this.mulScalar(P, this.cofactor);
|
|
}
|
|
|
|
P = this.affine(P);
|
|
|
|
return P;
|
|
|
|
}
|
|
|
|
toRprLE(buff, o, p) {
|
|
p = this.affine(p);
|
|
if (this.isZero(p)) {
|
|
const BuffV = new Uint8Array(buff, o, this.F.n8*2);
|
|
BuffV.fill(0);
|
|
return;
|
|
}
|
|
this.F.toRprLE(buff, o, p[0]);
|
|
this.F.toRprLE(buff, o+this.F.n8, p[1]);
|
|
}
|
|
|
|
toRprBE(buff, o, p) {
|
|
p = this.affine(p);
|
|
if (this.isZero(p)) {
|
|
const BuffV = new Uint8Array(buff, o, this.F.n8*2);
|
|
BuffV.fill(0);
|
|
return;
|
|
}
|
|
this.F.toRprBE(buff, o, p[0]);
|
|
this.F.toRprBE(buff, o+this.F.n8, p[1]);
|
|
}
|
|
|
|
toRprLEM(buff, o, p) {
|
|
p = this.affine(p);
|
|
if (this.isZero(p)) {
|
|
const BuffV = new Uint8Array(buff, o, this.F.n8*2);
|
|
BuffV.fill(0);
|
|
return;
|
|
}
|
|
this.F.toRprLEM(buff, o, p[0]);
|
|
this.F.toRprLEM(buff, o+this.F.n8, p[1]);
|
|
}
|
|
|
|
toRprLEJM(buff, o, p) {
|
|
p = this.affine(p);
|
|
if (this.isZero(p)) {
|
|
const BuffV = new Uint8Array(buff, o, this.F.n8*2);
|
|
BuffV.fill(0);
|
|
return;
|
|
}
|
|
this.F.toRprLEM(buff, o, p[0]);
|
|
this.F.toRprLEM(buff, o+this.F.n8, p[1]);
|
|
this.F.toRprLEM(buff, o+2*this.F.n8, p[2]);
|
|
}
|
|
|
|
|
|
toRprBEM(buff, o, p) {
|
|
p = this.affine(p);
|
|
if (this.isZero(p)) {
|
|
const BuffV = new Uint8Array(buff, o, this.F.n8*2);
|
|
BuffV.fill(0);
|
|
return;
|
|
}
|
|
this.F.toRprBEM(buff, o, p[0]);
|
|
this.F.toRprBEM(buff, o+this.F.n8, p[1]);
|
|
}
|
|
|
|
fromRprLE(buff, o) {
|
|
o = o || 0;
|
|
const x = this.F.fromRprLE(buff, o);
|
|
const y = this.F.fromRprLE(buff, o+this.F.n8);
|
|
if (this.F.isZero(x) && this.F.isZero(y)) {
|
|
return this.zero;
|
|
}
|
|
return [x, y, this.F.one];
|
|
}
|
|
|
|
fromRprBE(buff, o) {
|
|
o = o || 0;
|
|
const x = this.F.fromRprBE(buff, o);
|
|
const y = this.F.fromRprBE(buff, o+this.F.n8);
|
|
if (this.F.isZero(x) && this.F.isZero(y)) {
|
|
return this.zero;
|
|
}
|
|
return [x, y, this.F.one];
|
|
}
|
|
|
|
fromRprLEM(buff, o) {
|
|
o = o || 0;
|
|
const x = this.F.fromRprLEM(buff, o);
|
|
const y = this.F.fromRprLEM(buff, o+this.F.n8);
|
|
if (this.F.isZero(x) && this.F.isZero(y)) {
|
|
return this.zero;
|
|
}
|
|
return [x, y, this.F.one];
|
|
}
|
|
|
|
fromRprLEJM(buff, o) {
|
|
o = o || 0;
|
|
const x = this.F.fromRprLEM(buff, o);
|
|
const y = this.F.fromRprLEM(buff, o+this.F.n8);
|
|
const z = this.F.fromRprLEM(buff, o+this.F.n8*2);
|
|
if (this.F.isZero(x) && this.F.isZero(y)) {
|
|
return this.zero;
|
|
}
|
|
return [x, y, z];
|
|
}
|
|
|
|
fromRprBEM(buff, o) {
|
|
o = o || 0;
|
|
const x = this.F.fromRprBEM(buff, o);
|
|
const y = this.F.fromRprBEM(buff, o+this.F.n8);
|
|
if (this.F.isZero(x) && this.F.isZero(y)) {
|
|
return this.zero;
|
|
}
|
|
return [x, y, this.F.one];
|
|
}
|
|
|
|
fromRprCompressed(buff, o) {
|
|
const F = this.F;
|
|
const v = new Uint8Array(buff.buffer, o, F.n8);
|
|
if (v[0] & 0x40) return this.zero;
|
|
const P = new Array(3);
|
|
|
|
const greatest = ((v[0] & 0x80) != 0);
|
|
v[0] = v[0] & 0x7F;
|
|
P[0] = F.fromRprBE(buff, o);
|
|
if (greatest) v[0] = v[0] | 0x80; // set back again the old value
|
|
|
|
const x3b = F.add(F.mul(F.square(P[0]), P[0]), this.b);
|
|
P[1] = F.sqrt(x3b);
|
|
|
|
if (P[1] === null) {
|
|
throw new Error("Invalid Point!");
|
|
}
|
|
|
|
const s = isGreatest(F, P[1]);
|
|
if (greatest ^ s) P[1] = F.neg(P[1]);
|
|
P[2] = F.one;
|
|
|
|
return P;
|
|
}
|
|
|
|
toRprCompressed(buff, o, p) {
|
|
p = this.affine(p);
|
|
const v = new Uint8Array(buff.buffer, o, this.F.n8);
|
|
if (this.isZero(p)) {
|
|
v.fill(0);
|
|
v[0] = 0x40;
|
|
return;
|
|
}
|
|
this.F.toRprBE(buff, o, p[0]);
|
|
|
|
if (isGreatest(this.F, p[1])) {
|
|
v[0] = v[0] | 0x80;
|
|
}
|
|
}
|
|
|
|
|
|
fromRprUncompressed(buff, o) {
|
|
if (buff[0] & 0x40) return this.zero;
|
|
|
|
return this.fromRprBE(buff, o);
|
|
}
|
|
|
|
toRprUncompressed(buff, o, p) {
|
|
this.toRprBE(buff, o, p);
|
|
|
|
if (this.isZero(p)) {
|
|
buff[o] = buff[o] | 0x40;
|
|
}
|
|
}
|
|
|
|
|
|
}
|
|
|
|
var code = 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|
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var pq = 520;
|
|
var pr = 1864;
|
|
var pG1gen = 31592;
|
|
var pG1zero = 31688;
|
|
var pG1b = 3240;
|
|
var pG2gen = 31784;
|
|
var pG2zero = 31976;
|
|
var pG2b = 12616;
|
|
var pOneT = 32168;
|
|
var prePSize = 192;
|
|
var preQSize = 19776;
|
|
var n8q = 32;
|
|
var n8r = 32;
|
|
var q = "21888242871839275222246405745257275088696311157297823662689037894645226208583";
|
|
var r = "21888242871839275222246405745257275088548364400416034343698204186575808495617";
|
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|
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var bn128_wasm = {
|
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code: code,
|
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pq: pq,
|
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pr: pr,
|
|
pG1gen: pG1gen,
|
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pG1zero: pG1zero,
|
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pG1b: pG1b,
|
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pG2gen: pG2gen,
|
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pG2zero: pG2zero,
|
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pG2b: pG2b,
|
|
pOneT: pOneT,
|
|
prePSize: prePSize,
|
|
preQSize: preQSize,
|
|
n8q: n8q,
|
|
n8r: n8r,
|
|
q: q,
|
|
r: r
|
|
};
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|
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var code$1 = 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";
|
|
var pq$1 = 760;
|
|
var pr$1 = 3640;
|
|
var pG1gen$1 = 42344;
|
|
var pG1zero$1 = 42488;
|
|
var pG1b$1 = 5016;
|
|
var pG2gen$1 = 42632;
|
|
var pG2zero$1 = 42920;
|
|
var pG2b$1 = 17224;
|
|
var pOneT$1 = 43208;
|
|
var prePSize$1 = 288;
|
|
var preQSize$1 = 20448;
|
|
var n8q$1 = 48;
|
|
var n8r$1 = 32;
|
|
var q$1 = "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787";
|
|
var r$1 = "52435875175126190479447740508185965837690552500527637822603658699938581184513";
|
|
|
|
var bls12381_wasm = {
|
|
code: code$1,
|
|
pq: pq$1,
|
|
pr: pr$1,
|
|
pG1gen: pG1gen$1,
|
|
pG1zero: pG1zero$1,
|
|
pG1b: pG1b$1,
|
|
pG2gen: pG2gen$1,
|
|
pG2zero: pG2zero$1,
|
|
pG2b: pG2b$1,
|
|
pOneT: pOneT$1,
|
|
prePSize: prePSize$1,
|
|
preQSize: preQSize$1,
|
|
n8q: n8q$1,
|
|
n8r: n8r$1,
|
|
q: q$1,
|
|
r: r$1
|
|
};
|
|
|
|
/*
|
|
Copyright 2019 0KIMS association.
|
|
|
|
This file is part of wasmsnark (Web Assembly zkSnark Prover).
|
|
|
|
wasmsnark is a free software: you can redistribute it and/or modify it
|
|
under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation, either version 3 of the License, or
|
|
(at your option) any later version.
|
|
|
|
wasmsnark is distributed in the hope that it will be useful, but WITHOUT
|
|
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
|
|
License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with wasmsnark. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
// module.exports.buildF1 = require("./src/f1.js");
|
|
// module.exports.buildBn128 = require("./src/bn128.js");
|
|
// module.exports.buildMnt6753 = require("./src/mnt6753.js");
|
|
|
|
var bn128_wasm$1 = bn128_wasm;
|
|
var bls12381_wasm$1 = bls12381_wasm;
|
|
// module.exports.mnt6753_wasm = require("./build/mnt6753_wasm.js");
|
|
|
|
var wasmcurves = {
|
|
bn128_wasm: bn128_wasm$1,
|
|
bls12381_wasm: bls12381_wasm$1
|
|
};
|
|
|
|
/* global BigInt */
|
|
|
|
function stringifyBigInts(o) {
|
|
if ((typeof(o) == "bigint") || o.eq !== undefined) {
|
|
return o.toString(10);
|
|
} else if (o instanceof Uint8Array) {
|
|
return fromRprLE(o, 0);
|
|
} else if (Array.isArray(o)) {
|
|
return o.map(stringifyBigInts);
|
|
} else if (typeof o == "object") {
|
|
const res = {};
|
|
const keys = Object.keys(o);
|
|
keys.forEach( (k) => {
|
|
res[k] = stringifyBigInts(o[k]);
|
|
});
|
|
return res;
|
|
} else {
|
|
return o;
|
|
}
|
|
}
|
|
|
|
function unstringifyBigInts(o) {
|
|
if ((typeof(o) == "string") && (/^[0-9]+$/.test(o) )) {
|
|
return BigInt(o);
|
|
} else if (Array.isArray(o)) {
|
|
return o.map(unstringifyBigInts);
|
|
} else if (typeof o == "object") {
|
|
if (o===null) return null;
|
|
const res = {};
|
|
const keys = Object.keys(o);
|
|
keys.forEach( (k) => {
|
|
res[k] = unstringifyBigInts(o[k]);
|
|
});
|
|
return res;
|
|
} else {
|
|
return o;
|
|
}
|
|
}
|
|
|
|
function beBuff2int(buff) {
|
|
let res = 0n;
|
|
let i = buff.length;
|
|
let offset = 0;
|
|
const buffV = new DataView(buff.buffer, buff.byteOffset, buff.byteLength);
|
|
while (i>0) {
|
|
if (i >= 4) {
|
|
i -= 4;
|
|
res += BigInt(buffV.getUint32(i)) << BigInt(offset*8);
|
|
offset += 4;
|
|
} else if (i >= 2) {
|
|
i -= 2;
|
|
res += BigInt(buffV.getUint16(i)) << BigInt(offset*8);
|
|
offset += 2;
|
|
} else {
|
|
i -= 1;
|
|
res += BigInt(buffV.getUint8(i)) << BigInt(offset*8);
|
|
offset += 1;
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function beInt2Buff(n, len) {
|
|
let r = n;
|
|
const buff = new Uint8Array(len);
|
|
const buffV = new DataView(buff.buffer);
|
|
let o = len;
|
|
while (o > 0) {
|
|
if (o-4 >= 0) {
|
|
o -= 4;
|
|
buffV.setUint32(o, Number(r & 0xFFFFFFFFn));
|
|
r = r >> 32n;
|
|
} else if (o-2 >= 0) {
|
|
o -= 2;
|
|
buffV.setUint16(o, Number(r & 0xFFFFn));
|
|
r = r >> 16n;
|
|
} else {
|
|
o -= 1;
|
|
buffV.setUint8(o, Number(r & 0xFFn));
|
|
r = r >> 8n;
|
|
}
|
|
}
|
|
if (r) {
|
|
throw new Error("Number does not fit in this length");
|
|
}
|
|
return buff;
|
|
}
|
|
|
|
|
|
function leBuff2int(buff) {
|
|
let res = 0n;
|
|
let i = 0;
|
|
const buffV = new DataView(buff.buffer, buff.byteOffset, buff.byteLength);
|
|
while (i<buff.length) {
|
|
if (i + 4 <= buff.length) {
|
|
res += BigInt(buffV.getUint32(i, true)) << BigInt( i*8);
|
|
i += 4;
|
|
} else if (i + 4 <= buff.length) {
|
|
res += BigInt(buffV.getUint16(i, true)) << BigInt( i*8);
|
|
i += 2;
|
|
} else {
|
|
res += BigInt(buffV.getUint8(i, true)) << BigInt( i*8);
|
|
i += 1;
|
|
}
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function leInt2Buff(n, len) {
|
|
let r = n;
|
|
if (typeof len === "undefined") {
|
|
len = Math.floor((bitLength$2(n) - 1) / 8) +1;
|
|
if (len==0) len = 1;
|
|
}
|
|
const buff = new Uint8Array(len);
|
|
const buffV = new DataView(buff.buffer);
|
|
let o = 0;
|
|
while (o < len) {
|
|
if (o+4 <= len) {
|
|
buffV.setUint32(o, Number(r & 0xFFFFFFFFn), true );
|
|
o += 4;
|
|
r = r >> 32n;
|
|
} else if (o+2 <= len) {
|
|
buffV.setUint16(Number(o, r & 0xFFFFn), true );
|
|
o += 2;
|
|
r = r >> 16n;
|
|
} else {
|
|
buffV.setUint8(Number(o, r & 0xFFn), true );
|
|
o += 1;
|
|
r = r >> 8n;
|
|
}
|
|
}
|
|
if (r) {
|
|
throw new Error("Number does not fit in this length");
|
|
}
|
|
return buff;
|
|
}
|
|
|
|
var utils_native = /*#__PURE__*/Object.freeze({
|
|
__proto__: null,
|
|
stringifyBigInts: stringifyBigInts,
|
|
unstringifyBigInts: unstringifyBigInts,
|
|
beBuff2int: beBuff2int,
|
|
beInt2Buff: beInt2Buff,
|
|
leBuff2int: leBuff2int,
|
|
leInt2Buff: leInt2Buff
|
|
});
|
|
|
|
function stringifyBigInts$1(o) {
|
|
if ((typeof(o) == "bigint") || o.eq !== undefined) {
|
|
return o.toString(10);
|
|
} else if (Array.isArray(o)) {
|
|
return o.map(stringifyBigInts$1);
|
|
} else if (typeof o == "object") {
|
|
const res = {};
|
|
const keys = Object.keys(o);
|
|
keys.forEach( (k) => {
|
|
res[k] = stringifyBigInts$1(o[k]);
|
|
});
|
|
return res;
|
|
} else {
|
|
return o;
|
|
}
|
|
}
|
|
|
|
function unstringifyBigInts$1(o) {
|
|
if ((typeof(o) == "string") && (/^[0-9]+$/.test(o) )) {
|
|
return BigInteger(o);
|
|
} else if (Array.isArray(o)) {
|
|
return o.map(unstringifyBigInts$1);
|
|
} else if (typeof o == "object") {
|
|
const res = {};
|
|
const keys = Object.keys(o);
|
|
keys.forEach( (k) => {
|
|
res[k] = unstringifyBigInts$1(o[k]);
|
|
});
|
|
return res;
|
|
} else {
|
|
return o;
|
|
}
|
|
}
|
|
|
|
function beBuff2int$1(buff) {
|
|
let res = BigInteger.zero;
|
|
for (let i=0; i<buff.length; i++) {
|
|
const n = BigInteger(buff[buff.length - i - 1]);
|
|
res = res.add(n.shiftLeft(i*8));
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function beInt2Buff$1(n, len) {
|
|
let r = n;
|
|
let o =len-1;
|
|
const buff = new Uint8Array(len);
|
|
while ((r.gt(BigInteger.zero))&&(o>=0)) {
|
|
let c = Number(r.and(BigInteger("255")));
|
|
buff[o] = c;
|
|
o--;
|
|
r = r.shiftRight(8);
|
|
}
|
|
if (!r.eq(BigInteger.zero)) {
|
|
throw new Error("Number does not fit in this length");
|
|
}
|
|
return buff;
|
|
}
|
|
|
|
|
|
function leBuff2int$1 (buff) {
|
|
let res = BigInteger.zero;
|
|
for (let i=0; i<buff.length; i++) {
|
|
const n = BigInteger(buff[i]);
|
|
res = res.add(n.shiftLeft(i*8));
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function leInt2Buff$1(n, len) {
|
|
let r = n;
|
|
let o =0;
|
|
const buff = new Uint8Array(len);
|
|
while ((r.gt(BigInteger.zero))&&(o<buff.length)) {
|
|
let c = Number(r.and(BigInteger(255)));
|
|
buff[o] = c;
|
|
o++;
|
|
r = r.shiftRight(8);
|
|
}
|
|
if (!r.eq(BigInteger.zero)) {
|
|
throw new Error("Number does not fit in this length");
|
|
}
|
|
return buff;
|
|
}
|
|
|
|
var utils_bigint = /*#__PURE__*/Object.freeze({
|
|
__proto__: null,
|
|
stringifyBigInts: stringifyBigInts$1,
|
|
unstringifyBigInts: unstringifyBigInts$1,
|
|
beBuff2int: beBuff2int$1,
|
|
beInt2Buff: beInt2Buff$1,
|
|
leBuff2int: leBuff2int$1,
|
|
leInt2Buff: leInt2Buff$1
|
|
});
|
|
|
|
let utils = {};
|
|
|
|
const supportsNativeBigInt$2 = typeof BigInt === "function";
|
|
if (supportsNativeBigInt$2) {
|
|
Object.assign(utils, utils_native);
|
|
} else {
|
|
Object.assign(utils, utils_bigint);
|
|
}
|
|
|
|
|
|
const _revTable$1 = [];
|
|
for (let i=0; i<256; i++) {
|
|
_revTable$1[i] = _revSlow$1(i, 8);
|
|
}
|
|
|
|
function _revSlow$1(idx, bits) {
|
|
let res =0;
|
|
let a = idx;
|
|
for (let i=0; i<bits; i++) {
|
|
res <<= 1;
|
|
res = res | (a &1);
|
|
a >>=1;
|
|
}
|
|
return res;
|
|
}
|
|
|
|
utils.bitReverse = function bitReverse(idx, bits) {
|
|
return (
|
|
_revTable$1[idx >>> 24] |
|
|
(_revTable$1[(idx >>> 16) & 0xFF] << 8) |
|
|
(_revTable$1[(idx >>> 8) & 0xFF] << 16) |
|
|
(_revTable$1[idx & 0xFF] << 24)
|
|
) >>> (32-bits);
|
|
};
|
|
|
|
|
|
utils.log2 = function log2( V )
|
|
{
|
|
return( ( ( V & 0xFFFF0000 ) !== 0 ? ( V &= 0xFFFF0000, 16 ) : 0 ) | ( ( V & 0xFF00FF00 ) !== 0 ? ( V &= 0xFF00FF00, 8 ) : 0 ) | ( ( V & 0xF0F0F0F0 ) !== 0 ? ( V &= 0xF0F0F0F0, 4 ) : 0 ) | ( ( V & 0xCCCCCCCC ) !== 0 ? ( V &= 0xCCCCCCCC, 2 ) : 0 ) | ( ( V & 0xAAAAAAAA ) !== 0 ) );
|
|
};
|
|
|
|
utils.buffReverseBits = function buffReverseBits(buff, eSize) {
|
|
const n = buff.byteLength /eSize;
|
|
const bits = utils.log2(n);
|
|
if (n != (1 << bits)) {
|
|
throw new Error("Invalid number of pointers");
|
|
}
|
|
for (let i=0; i<n; i++) {
|
|
const r = utils.bitReverse(i,bits);
|
|
if (i>r) {
|
|
const tmp = buff.slice(i*eSize, (i+1)*eSize);
|
|
buff.set( buff.slice(r*eSize, (r+1)*eSize), i*eSize);
|
|
buff.set(tmp, r*eSize);
|
|
}
|
|
}
|
|
};
|
|
|
|
let {
|
|
bitReverse,
|
|
log2: log2$1,
|
|
buffReverseBits,
|
|
stringifyBigInts: stringifyBigInts$2,
|
|
unstringifyBigInts: unstringifyBigInts$2,
|
|
beBuff2int: beBuff2int$2,
|
|
beInt2Buff: beInt2Buff$2,
|
|
leBuff2int: leBuff2int$2,
|
|
leInt2Buff: leInt2Buff$2,
|
|
} = utils;
|
|
|
|
var _utils = /*#__PURE__*/Object.freeze({
|
|
__proto__: null,
|
|
bitReverse: bitReverse,
|
|
log2: log2$1,
|
|
buffReverseBits: buffReverseBits,
|
|
stringifyBigInts: stringifyBigInts$2,
|
|
unstringifyBigInts: unstringifyBigInts$2,
|
|
beBuff2int: beBuff2int$2,
|
|
beInt2Buff: beInt2Buff$2,
|
|
leBuff2int: leBuff2int$2,
|
|
leInt2Buff: leInt2Buff$2
|
|
});
|
|
|
|
const PAGE_SIZE = 1<<30;
|
|
|
|
class BigBuffer {
|
|
|
|
constructor(size) {
|
|
this.buffers = [];
|
|
this.byteLength = size;
|
|
for (let i=0; i<size; i+= PAGE_SIZE) {
|
|
const n = Math.min(size-i, PAGE_SIZE);
|
|
this.buffers.push(new Uint8Array(n));
|
|
}
|
|
|
|
}
|
|
|
|
slice(fr, to) {
|
|
if ( to === undefined ) to = this.byteLength;
|
|
if ( fr === undefined ) fr = 0;
|
|
const len = to-fr;
|
|
|
|
const firstPage = Math.floor(fr / PAGE_SIZE);
|
|
const lastPage = Math.floor((fr+len-1) / PAGE_SIZE);
|
|
|
|
if ((firstPage == lastPage)||(len==0))
|
|
return this.buffers[firstPage].slice(fr%PAGE_SIZE, fr%PAGE_SIZE + len);
|
|
|
|
let buff;
|
|
|
|
let p = firstPage;
|
|
let o = fr % PAGE_SIZE;
|
|
// Remaining bytes to read
|
|
let r = len;
|
|
while (r>0) {
|
|
// bytes to copy from this page
|
|
const l = (o+r > PAGE_SIZE) ? (PAGE_SIZE -o) : r;
|
|
const srcView = new Uint8Array(this.buffers[p].buffer, this.buffers[p].byteOffset+o, l);
|
|
if (l == len) return srcView.slice();
|
|
if (!buff) {
|
|
if (len <= PAGE_SIZE) {
|
|
buff = new Uint8Array(len);
|
|
} else {
|
|
buff = new BigBuffer(len);
|
|
}
|
|
}
|
|
buff.set(srcView, len-r);
|
|
r = r-l;
|
|
p ++;
|
|
o = 0;
|
|
}
|
|
|
|
return buff;
|
|
}
|
|
|
|
set(buff, offset) {
|
|
if (offset === undefined) offset = 0;
|
|
|
|
const len = buff.byteLength;
|
|
|
|
if (len==0) return;
|
|
|
|
const firstPage = Math.floor(offset / PAGE_SIZE);
|
|
const lastPage = Math.floor((offset+len-1) / PAGE_SIZE);
|
|
|
|
if (firstPage == lastPage)
|
|
return this.buffers[firstPage].set(buff, offset % PAGE_SIZE);
|
|
|
|
|
|
let p = firstPage;
|
|
let o = offset % PAGE_SIZE;
|
|
let r = len;
|
|
while (r>0) {
|
|
const l = (o+r > PAGE_SIZE) ? (PAGE_SIZE -o) : r;
|
|
const srcView = buff.slice( len -r, len -r+l);
|
|
const dstView = new Uint8Array(this.buffers[p].buffer, this.buffers[p].byteOffset + o, l);
|
|
dstView.set(srcView);
|
|
r = r-l;
|
|
p ++;
|
|
o = 0;
|
|
}
|
|
|
|
}
|
|
}
|
|
|
|
function buildBatchConvert(tm, fnName, sIn, sOut) {
|
|
return async function batchConvert(buffIn) {
|
|
const nPoints = Math.floor(buffIn.byteLength / sIn);
|
|
if ( nPoints * sIn !== buffIn.byteLength) {
|
|
throw new Error("Invalid buffer size");
|
|
}
|
|
const pointsPerChunk = Math.floor(nPoints/tm.concurrency);
|
|
const opPromises = [];
|
|
for (let i=0; i<tm.concurrency; i++) {
|
|
let n;
|
|
if (i< tm.concurrency-1) {
|
|
n = pointsPerChunk;
|
|
} else {
|
|
n = nPoints - i*pointsPerChunk;
|
|
}
|
|
if (n==0) continue;
|
|
|
|
const buffChunk = buffIn.slice(i*pointsPerChunk*sIn, i*pointsPerChunk*sIn + n*sIn);
|
|
const task = [
|
|
{cmd: "ALLOCSET", var: 0, buff:buffChunk},
|
|
{cmd: "ALLOC", var: 1, len:sOut * n},
|
|
{cmd: "CALL", fnName: fnName, params: [
|
|
{var: 0},
|
|
{val: n},
|
|
{var: 1}
|
|
]},
|
|
{cmd: "GET", out: 0, var: 1, len:sOut * n},
|
|
];
|
|
opPromises.push(
|
|
tm.queueAction(task)
|
|
);
|
|
}
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
let fullBuffOut;
|
|
if (buffIn instanceof BigBuffer) {
|
|
fullBuffOut = new BigBuffer(nPoints*sOut);
|
|
} else {
|
|
fullBuffOut = new Uint8Array(nPoints*sOut);
|
|
}
|
|
|
|
let p =0;
|
|
for (let i=0; i<result.length; i++) {
|
|
fullBuffOut.set(result[i][0], p);
|
|
p+=result[i][0].byteLength;
|
|
}
|
|
|
|
return fullBuffOut;
|
|
};
|
|
}
|
|
|
|
class WasmField1 {
|
|
|
|
constructor(tm, prefix, n8, p) {
|
|
this.tm = tm;
|
|
this.prefix = prefix;
|
|
|
|
this.p = p;
|
|
this.n8 = n8;
|
|
this.type = "F1";
|
|
this.m = 1;
|
|
|
|
this.half = shiftRight$2(p, one);
|
|
this.bitLength = bitLength$2(p);
|
|
this.mask = sub$2(shiftLeft$2(one, this.bitLength), one);
|
|
|
|
this.pOp1 = tm.alloc(n8);
|
|
this.pOp2 = tm.alloc(n8);
|
|
this.pOp3 = tm.alloc(n8);
|
|
this.tm.instance.exports[prefix + "_zero"](this.pOp1);
|
|
this.zero = this.tm.getBuff(this.pOp1, this.n8);
|
|
this.tm.instance.exports[prefix + "_one"](this.pOp1);
|
|
this.one = this.tm.getBuff(this.pOp1, this.n8);
|
|
|
|
this.negone = this.neg(this.one);
|
|
this.two = this.add(this.one, this.one);
|
|
|
|
this.n64 = Math.floor(n8/8);
|
|
this.n32 = Math.floor(n8/4);
|
|
|
|
if(this.n64*8 != this.n8) {
|
|
throw new Error("n8 must be a multiple of 8");
|
|
}
|
|
|
|
this.half = shiftRight$2(this.p, one);
|
|
this.nqr = this.two;
|
|
let r = this.exp(this.nqr, this.half);
|
|
while (!this.eq(r, this.negone)) {
|
|
this.nqr = this.add(this.nqr, this.one);
|
|
r = this.exp(this.nqr, this.half);
|
|
}
|
|
|
|
this.shift = this.mul(this.nqr, this.nqr);
|
|
this.shiftInv = this.inv(this.shift);
|
|
|
|
this.s = 0;
|
|
let t = sub$2(this.p, one);
|
|
|
|
while ( !isOdd$2(t) ) {
|
|
this.s = this.s + 1;
|
|
t = shiftRight$2(t, one);
|
|
}
|
|
|
|
this.w = [];
|
|
this.w[this.s] = this.exp(this.nqr, t);
|
|
|
|
for (let i= this.s-1; i>=0; i--) {
|
|
this.w[i] = this.square(this.w[i+1]);
|
|
}
|
|
|
|
if (!this.eq(this.w[0], this.one)) {
|
|
throw new Error("Error calculating roots of unity");
|
|
}
|
|
|
|
this.batchToMontgomery = buildBatchConvert(tm, prefix + "_batchToMontgomery", this.n8, this.n8);
|
|
this.batchFromMontgomery = buildBatchConvert(tm, prefix + "_batchFromMontgomery", this.n8, this.n8);
|
|
}
|
|
|
|
|
|
op2(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
op2Bool(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2);
|
|
}
|
|
|
|
op1(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
op1Bool(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
}
|
|
|
|
add(a,b) {
|
|
return this.op2("_add", a, b);
|
|
}
|
|
|
|
|
|
eq(a,b) {
|
|
return this.op2Bool("_eq", a, b);
|
|
}
|
|
|
|
isZero(a) {
|
|
return this.op1Bool("_isZero", a);
|
|
}
|
|
|
|
sub(a,b) {
|
|
return this.op2("_sub", a, b);
|
|
}
|
|
|
|
neg(a) {
|
|
return this.op1("_neg", a);
|
|
}
|
|
|
|
inv(a) {
|
|
return this.op1("_inverse", a);
|
|
}
|
|
|
|
toMontgomery(a) {
|
|
return this.op1("_toMontgomery", a);
|
|
}
|
|
|
|
fromMontgomery(a) {
|
|
return this.op1("_fromMontgomery", a);
|
|
}
|
|
|
|
mul(a,b) {
|
|
return this.op2("_mul", a, b);
|
|
}
|
|
|
|
div(a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + "_inverse"](this.pOp2, this.pOp2);
|
|
this.tm.instance.exports[this.prefix + "_mul"](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
square(a) {
|
|
return this.op1("_square", a);
|
|
}
|
|
|
|
isSquare(a) {
|
|
return this.op1Bool("_isSquare", a);
|
|
}
|
|
|
|
sqrt(a) {
|
|
return this.op1("_sqrt", a);
|
|
}
|
|
|
|
exp(a, b) {
|
|
if (!(b instanceof Uint8Array)) {
|
|
b = toLEBuff(e$2(b));
|
|
}
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + "_exp"](this.pOp1, this.pOp2, b.byteLength, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
isNegative(a) {
|
|
return this.op1Bool("_isNegative", a);
|
|
}
|
|
|
|
e(a, b) {
|
|
if (a instanceof Uint8Array) return a;
|
|
let ra = e$2(a, b);
|
|
if (isNegative$2(ra)) {
|
|
ra = neg$2(ra);
|
|
if (gt$2(ra, this.p)) {
|
|
ra = mod$2(ra, this.p);
|
|
}
|
|
ra = sub$2(this.p, ra);
|
|
} else {
|
|
if (gt$2(ra, this.p)) {
|
|
ra = mod$2(ra, this.p);
|
|
}
|
|
}
|
|
const buff = leInt2Buff$2(ra, this.n8);
|
|
return this.toMontgomery(buff);
|
|
}
|
|
|
|
toString(a, radix) {
|
|
const an = this.fromMontgomery(a);
|
|
const s = fromRprLE(an, 0);
|
|
return toString(s, radix);
|
|
}
|
|
|
|
fromRng(rng) {
|
|
let v;
|
|
const buff = new Uint8Array(this.n8);
|
|
do {
|
|
v = zero;
|
|
for (let i=0; i<this.n64; i++) {
|
|
v = add$2(v, shiftLeft$2(rng.nextU64(), 64*i));
|
|
}
|
|
v = band$2(v, this.mask);
|
|
} while (geq$2(v, this.p));
|
|
toRprLE(buff, 0, v, this.n8);
|
|
return buff;
|
|
}
|
|
|
|
random() {
|
|
return this.fromRng(getThreadRng());
|
|
}
|
|
|
|
toObject(a) {
|
|
const an = this.fromMontgomery(a);
|
|
return fromRprLE(an, 0);
|
|
}
|
|
|
|
fromObject(a) {
|
|
const buff = new Uint8Array(this.n8);
|
|
toRprLE(buff, 0, a, this.n8);
|
|
return this.toMontgomery(buff);
|
|
}
|
|
|
|
toRprLE(buff, offset, a) {
|
|
buff.set(this.fromMontgomery(a), offset);
|
|
}
|
|
|
|
fromRprLE(buff, offset) {
|
|
offset = offset || 0;
|
|
const res = buff.slice(offset, offset + this.n8);
|
|
return this.toMontgomery(res);
|
|
}
|
|
|
|
|
|
}
|
|
|
|
class WasmField2 {
|
|
|
|
constructor(tm, prefix, F) {
|
|
this.tm = tm;
|
|
this.prefix = prefix;
|
|
|
|
this.F = F;
|
|
this.type = "F2";
|
|
this.m = F.m * 2;
|
|
this.n8 = this.F.n8*2;
|
|
this.n32 = this.F.n32*2;
|
|
this.n64 = this.F.n64*2;
|
|
|
|
this.pOp1 = tm.alloc(F.n8*2);
|
|
this.pOp2 = tm.alloc(F.n8*2);
|
|
this.pOp3 = tm.alloc(F.n8*2);
|
|
this.tm.instance.exports[prefix + "_zero"](this.pOp1);
|
|
this.zero = tm.getBuff(this.pOp1, this.n8);
|
|
this.tm.instance.exports[prefix + "_one"](this.pOp1);
|
|
this.one = tm.getBuff(this.pOp1, this.n8);
|
|
|
|
this.negone = this.neg(this.one);
|
|
this.two = this.add(this.one, this.one);
|
|
|
|
}
|
|
|
|
op2(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
op2Bool(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2);
|
|
}
|
|
|
|
op1(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
op1Bool(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
}
|
|
|
|
add(a,b) {
|
|
return this.op2("_add", a, b);
|
|
}
|
|
|
|
eq(a,b) {
|
|
return this.op2Bool("_eq", a, b);
|
|
}
|
|
|
|
isZero(a) {
|
|
return this.op1Bool("_isZero", a);
|
|
}
|
|
|
|
sub(a,b) {
|
|
return this.op2("_sub", a, b);
|
|
}
|
|
|
|
neg(a) {
|
|
return this.op1("_neg", a);
|
|
}
|
|
|
|
inv(a) {
|
|
return this.op1("_inverse", a);
|
|
}
|
|
|
|
isNegative(a) {
|
|
return this.op1Bool("_isNegative", a);
|
|
}
|
|
|
|
toMontgomery(a) {
|
|
return this.op1("_toMontgomery", a);
|
|
}
|
|
|
|
fromMontgomery(a) {
|
|
return this.op1("_fromMontgomery", a);
|
|
}
|
|
|
|
mul(a,b) {
|
|
return this.op2("_mul", a, b);
|
|
}
|
|
|
|
mul1(a,b) {
|
|
return this.op2("_mul1", a, b);
|
|
}
|
|
|
|
div(a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + "_inverse"](this.pOp2, this.pOp2);
|
|
this.tm.instance.exports[this.prefix + "_mul"](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
square(a) {
|
|
return this.op1("_square", a);
|
|
}
|
|
|
|
isSquare(a) {
|
|
return this.op1Bool("_isSquare", a);
|
|
}
|
|
|
|
sqrt(a) {
|
|
return this.op1("_sqrt", a);
|
|
}
|
|
|
|
exp(a, b) {
|
|
if (!(b instanceof Uint8Array)) {
|
|
b = toLEBuff(e$2(b));
|
|
}
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + "_exp"](this.pOp1, this.pOp2, b.byteLength, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
e(a, b) {
|
|
if (a instanceof Uint8Array) return a;
|
|
if ((Array.isArray(a)) && (a.length == 2)) {
|
|
const c1 = this.F.e(a[0], b);
|
|
const c2 = this.F.e(a[1], b);
|
|
const res = new Uint8Array(this.F.n8*2);
|
|
res.set(c1);
|
|
res.set(c2, this.F.n8*2);
|
|
return res;
|
|
} else {
|
|
throw new Error("invalid F2");
|
|
}
|
|
}
|
|
|
|
toString(a, radix) {
|
|
const s1 = this.F.toString(a.slice(0, this.F.n8), radix);
|
|
const s2 = this.F.toString(a.slice(this.F.n8), radix);
|
|
return `[${s1}, ${s2}]`;
|
|
}
|
|
|
|
fromRng(rng) {
|
|
const c1 = this.F.fromRng(rng);
|
|
const c2 = this.F.fromRng(rng);
|
|
const res = new Uint8Array(this.F.n8*2);
|
|
res.set(c1);
|
|
res.set(c2, this.F.n8);
|
|
return res;
|
|
}
|
|
|
|
random() {
|
|
return this.fromRng(getThreadRng());
|
|
}
|
|
|
|
toObject(a) {
|
|
const c1 = this.F.toObject(a.slice(0, this.F.n8));
|
|
const c2 = this.F.toObject(a.slice(this.F.n8, this.F.n8*2));
|
|
return [c1, c2];
|
|
}
|
|
|
|
fromObject(a) {
|
|
const buff = new Uint8Array(this.F.n8*2);
|
|
const b1 = this.F.fromObject(a[0]);
|
|
const b2 = this.F.fromObject(a[1]);
|
|
buff.set(b1);
|
|
buff.set(b2, this.F.n8);
|
|
return buff;
|
|
}
|
|
|
|
c1(a) {
|
|
return a.slice(0, this.F.n8);
|
|
}
|
|
|
|
c2(a) {
|
|
return a.slice(this.F.n8);
|
|
}
|
|
|
|
}
|
|
|
|
class WasmField3 {
|
|
|
|
constructor(tm, prefix, F) {
|
|
this.tm = tm;
|
|
this.prefix = prefix;
|
|
|
|
this.F = F;
|
|
this.type = "F3";
|
|
this.m = F.m * 3;
|
|
this.n8 = this.F.n8*3;
|
|
this.n32 = this.F.n32*3;
|
|
this.n64 = this.F.n64*3;
|
|
|
|
this.pOp1 = tm.alloc(F.n8*3);
|
|
this.pOp2 = tm.alloc(F.n8*3);
|
|
this.pOp3 = tm.alloc(F.n8*3);
|
|
this.tm.instance.exports[prefix + "_zero"](this.pOp1);
|
|
this.zero = tm.getBuff(this.pOp1, this.n8);
|
|
this.tm.instance.exports[prefix + "_one"](this.pOp1);
|
|
this.one = tm.getBuff(this.pOp1, this.n8);
|
|
|
|
this.negone = this.neg(this.one);
|
|
this.two = this.add(this.one, this.one);
|
|
|
|
}
|
|
|
|
op2(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
op2Bool(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2);
|
|
}
|
|
|
|
op1(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
op1Bool(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
}
|
|
|
|
|
|
eq(a,b) {
|
|
return this.op2Bool("_eq", a, b);
|
|
}
|
|
|
|
isZero(a) {
|
|
return this.op1Bool("_isZero", a);
|
|
}
|
|
|
|
add(a,b) {
|
|
return this.op2("_add", a, b);
|
|
}
|
|
|
|
sub(a,b) {
|
|
return this.op2("_sub", a, b);
|
|
}
|
|
|
|
neg(a) {
|
|
return this.op1("_neg", a);
|
|
}
|
|
|
|
inv(a) {
|
|
return this.op1("_inverse", a);
|
|
}
|
|
|
|
isNegative(a) {
|
|
return this.op1Bool("_isNegative", a);
|
|
}
|
|
|
|
toMontgomery(a) {
|
|
return this.op1("_toMontgomery", a);
|
|
}
|
|
|
|
fromMontgomery(a) {
|
|
return this.op1("_fromMontgomery", a);
|
|
}
|
|
|
|
mul(a,b) {
|
|
return this.op2("_mul", a, b);
|
|
}
|
|
|
|
div(a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + "_inverse"](this.pOp2, this.pOp2);
|
|
this.tm.instance.exports[this.prefix + "_mul"](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
square(a) {
|
|
return this.op1("_square", a);
|
|
}
|
|
|
|
isSquare(a) {
|
|
return this.op1Bool("_isSquare", a);
|
|
}
|
|
|
|
sqrt(a) {
|
|
return this.op1("_sqrt", a);
|
|
}
|
|
|
|
exp(a, b) {
|
|
if (!(b instanceof Uint8Array)) {
|
|
b = toLEBuff(e$2(b));
|
|
}
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + "_exp"](this.pOp1, this.pOp2, b.byteLength, this.pOp3);
|
|
return this.getBuff(this.pOp3, this.n8);
|
|
}
|
|
|
|
e(a, b) {
|
|
if (a instanceof Uint8Array) return a;
|
|
if ((Array.isArray(a)) && (a.length == 3)) {
|
|
const c1 = this.F.e(a[0], b);
|
|
const c2 = this.F.e(a[1], b);
|
|
const c3 = this.F.e(a[2], b);
|
|
const res = new Uint8Array(this.F.n8*3);
|
|
res.set(c1);
|
|
res.set(c2, this.F.n8);
|
|
res.set(c3, this.F.n8*2);
|
|
return res;
|
|
} else {
|
|
throw new Error("invalid F3");
|
|
}
|
|
}
|
|
|
|
toString(a, radix) {
|
|
const s1 = this.F.toString(a.slice(0, this.F.n8), radix);
|
|
const s2 = this.F.toString(a.slice(this.F.n8, this.F.n8*2), radix);
|
|
const s3 = this.F.toString(a.slice(this.F.n8*2), radix);
|
|
return `[${s1}, ${s2}, ${s3}]`;
|
|
}
|
|
|
|
fromRng(rng) {
|
|
const c1 = this.F.fromRng(rng);
|
|
const c2 = this.F.fromRng(rng);
|
|
const c3 = this.F.fromRng(rng);
|
|
const res = new Uint8Array(this.F.n8*3);
|
|
res.set(c1);
|
|
res.set(c2, this.F.n8);
|
|
res.set(c3, this.F.n8*2);
|
|
return res;
|
|
}
|
|
|
|
random() {
|
|
return this.fromRng(getThreadRng());
|
|
}
|
|
|
|
toObject(a) {
|
|
const c1 = this.F.toObject(a.slice(0, this.F.n8));
|
|
const c2 = this.F.toObject(a.slice(this.F.n8, this.F.n8*2));
|
|
const c3 = this.F.toObject(a.slice(this.F.n8*2, this.F.n8*3));
|
|
return [c1, c2, c3];
|
|
}
|
|
|
|
fromObject(a) {
|
|
const buff = new Uint8Array(this.F.n8*3);
|
|
const b1 = this.F.fromObject(a[0]);
|
|
const b2 = this.F.fromObject(a[1]);
|
|
const b3 = this.F.fromObject(a[2]);
|
|
buff.set(b1);
|
|
buff.set(b2, this.F.n8);
|
|
buff.set(b3, this.F.n8*2);
|
|
return buff;
|
|
}
|
|
|
|
c1(a) {
|
|
return a.slice(0, this.F.n8);
|
|
}
|
|
|
|
c2(a) {
|
|
return a.slice(this.F.n8, this.F.n8*2);
|
|
}
|
|
|
|
c3(a) {
|
|
return a.slice(this.F.n8*2);
|
|
}
|
|
|
|
}
|
|
|
|
class WasmCurve {
|
|
|
|
constructor(tm, prefix, F, pGen, pGb, cofactor) {
|
|
this.tm = tm;
|
|
this.prefix = prefix;
|
|
this.F = F;
|
|
|
|
this.pOp1 = tm.alloc(F.n8*3);
|
|
this.pOp2 = tm.alloc(F.n8*3);
|
|
this.pOp3 = tm.alloc(F.n8*3);
|
|
this.tm.instance.exports[prefix + "_zero"](this.pOp1);
|
|
this.zero = this.tm.getBuff(this.pOp1, F.n8*3);
|
|
this.tm.instance.exports[prefix + "_zeroAffine"](this.pOp1);
|
|
this.zeroAffine = this.tm.getBuff(this.pOp1, F.n8*2);
|
|
this.one = this.tm.getBuff(pGen, F.n8*3);
|
|
this.g = this.one;
|
|
this.oneAffine = this.tm.getBuff(pGen, F.n8*2);
|
|
this.gAffine = this.oneAffine;
|
|
this.b = this.tm.getBuff(pGb, F.n8);
|
|
|
|
if (cofactor) {
|
|
this.cofactor = toLEBuff(cofactor);
|
|
}
|
|
|
|
this.negone = this.neg(this.one);
|
|
this.two = this.add(this.one, this.one);
|
|
|
|
this.batchLEMtoC = buildBatchConvert(tm, prefix + "_batchLEMtoC", F.n8*2, F.n8);
|
|
this.batchLEMtoU = buildBatchConvert(tm, prefix + "_batchLEMtoU", F.n8*2, F.n8*2);
|
|
this.batchCtoLEM = buildBatchConvert(tm, prefix + "_batchCtoLEM", F.n8, F.n8*2);
|
|
this.batchUtoLEM = buildBatchConvert(tm, prefix + "_batchUtoLEM", F.n8*2, F.n8*2);
|
|
this.batchToJacobian = buildBatchConvert(tm, prefix + "_batchToJacobian", F.n8*2, F.n8*3);
|
|
this.batchToAffine = buildBatchConvert(tm, prefix + "_batchToAffine", F.n8*3, F.n8*2);
|
|
}
|
|
|
|
op2(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.F.n8*3);
|
|
}
|
|
|
|
op2bool(opName, a, b) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, b);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp2, this.pOp3);
|
|
}
|
|
|
|
op1(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.F.n8*3);
|
|
}
|
|
|
|
op1Affine(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.F.n8*2);
|
|
}
|
|
|
|
op1Bool(opName, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
return !!this.tm.instance.exports[this.prefix + opName](this.pOp1, this.pOp3);
|
|
}
|
|
|
|
add(a,b) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
if (b.byteLength == this.F.n8*3) {
|
|
return this.op2("_add", a, b);
|
|
} else if (b.byteLength == this.F.n8*2) {
|
|
return this.op2("_addMixed", a, b);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
if (b.byteLength == this.F.n8*3) {
|
|
return this.op2("_addMixed", b, a);
|
|
} else if (b.byteLength == this.F.n8*2) {
|
|
return this.op2("_addAffine", a, b);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
sub(a,b) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
if (b.byteLength == this.F.n8*3) {
|
|
return this.op2("_sub", a, b);
|
|
} else if (b.byteLength == this.F.n8*2) {
|
|
return this.op2("_subMixed", a, b);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
if (b.byteLength == this.F.n8*3) {
|
|
return this.op2("_subMixed", b, a);
|
|
} else if (b.byteLength == this.F.n8*2) {
|
|
return this.op2("_subAffine", a, b);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
neg(a) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
return this.op1("_neg", a);
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
return this.op1Affine("_negAffine", a);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
double(a) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
return this.op1("_double", a);
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
return this.op1("_doubleAffine", a);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
isZero(a) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
return this.op1Bool("_isZero", a);
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
return this.op1Bool("_isZeroAffine", a);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
timesScalar(a, s) {
|
|
if (!(s instanceof Uint8Array)) {
|
|
s = toLEBuff(e$2(s));
|
|
}
|
|
let fnName;
|
|
if (a.byteLength == this.F.n8*3) {
|
|
fnName = this.prefix + "_timesScalar";
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
fnName = this.prefix + "_timesScalarAffine";
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, s);
|
|
this.tm.instance.exports[fnName](this.pOp1, this.pOp2, s.byteLength, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.F.n8*3);
|
|
}
|
|
|
|
timesFr(a, s) {
|
|
let fnName;
|
|
if (a.byteLength == this.F.n8*3) {
|
|
fnName = this.prefix + "_timesFr";
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
fnName = this.prefix + "_timesFrAffine";
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.setBuff(this.pOp2, s);
|
|
this.tm.instance.exports[fnName](this.pOp1, this.pOp2, this.pOp3);
|
|
return this.tm.getBuff(this.pOp3, this.F.n8*3);
|
|
}
|
|
|
|
eq(a,b) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
if (b.byteLength == this.F.n8*3) {
|
|
return this.op2bool("_eq", a, b);
|
|
} else if (b.byteLength == this.F.n8*2) {
|
|
return this.op2bool("_eqMixed", a, b);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
if (b.byteLength == this.F.n8*3) {
|
|
return this.op2bool("_eqMixed", b, a);
|
|
} else if (b.byteLength == this.F.n8*2) {
|
|
return this.op2bool("_eqAffine", a, b);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
toAffine(a) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
return this.op1Affine("_toAffine", a);
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
return a;
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
toJacobian(a) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
return a;
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
return this.op1("_toJacobian", a);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
toRprUncompressed(arr, offset, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
if (a.byteLength == this.F.n8*3) {
|
|
this.tm.instance.exports[this.prefix + "_toAffine"](this.pOp1, this.pOp1);
|
|
} else if (a.byteLength != this.F.n8*2) {
|
|
throw new Error("invalid point size");
|
|
}
|
|
this.tm.instance.exports[this.prefix + "_LEMtoU"](this.pOp1, this.pOp1);
|
|
const res = this.tm.getBuff(this.pOp1, this.F.n8*2);
|
|
arr.set(res, offset);
|
|
}
|
|
|
|
fromRprUncompressed(arr, offset) {
|
|
const buff = arr.slice(offset, offset + this.F.n8*2);
|
|
this.tm.setBuff(this.pOp1, buff);
|
|
this.tm.instance.exports[this.prefix + "_UtoLEM"](this.pOp1, this.pOp1);
|
|
return this.tm.getBuff(this.pOp1, this.F.n8*2);
|
|
}
|
|
|
|
toRprCompressed(arr, offset, a) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
if (a.byteLength == this.F.n8*3) {
|
|
this.tm.instance.exports[this.prefix + "_toAffine"](this.pOp1, this.pOp1);
|
|
} else if (a.byteLength != this.F.n8*2) {
|
|
throw new Error("invalid point size");
|
|
}
|
|
this.tm.instance.exports[this.prefix + "_LEMtoC"](this.pOp1, this.pOp1);
|
|
const res = this.tm.getBuff(this.pOp1, this.F.n8);
|
|
arr.set(res, offset);
|
|
}
|
|
|
|
fromRprCompressed(arr, offset) {
|
|
const buff = arr.slice(offset, offset + this.F.n8);
|
|
this.tm.setBuff(this.pOp1, buff);
|
|
this.tm.instance.exports[this.prefix + "_CtoLEM"](this.pOp1, this.pOp2);
|
|
return this.tm.getBuff(this.pOp2, this.F.n8*2);
|
|
}
|
|
|
|
toUncompressed(a) {
|
|
const buff = new Uint8Array(this.F.n8*2);
|
|
this.toRprUncompressed(buff, 0, a);
|
|
return buff;
|
|
}
|
|
|
|
toRprLEM(arr, offset, a) {
|
|
if (a.byteLength == this.F.n8*2) {
|
|
arr.set(a, offset);
|
|
return;
|
|
} else if (a.byteLength == this.F.n8*3) {
|
|
this.tm.setBuff(this.pOp1, a);
|
|
this.tm.instance.exports[this.prefix + "_toAffine"](this.pOp1, this.pOp1);
|
|
const res = this.tm.getBuff(this.pOp1, this.F.n8*2);
|
|
arr.set(res, offset);
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
fromRprLEM(arr, offset) {
|
|
offset = offset || 0;
|
|
return arr.slice(offset, offset+this.F.n8*2);
|
|
}
|
|
|
|
toString(a, radix) {
|
|
if (a.byteLength == this.F.n8*3) {
|
|
const x = this.F.toString(a.slice(0, this.F.n8), radix);
|
|
const y = this.F.toString(a.slice(this.F.n8, this.F.n8*2), radix);
|
|
const z = this.F.toString(a.slice(this.F.n8*2), radix);
|
|
return `[ ${x}, ${y}, ${z} ]`;
|
|
} else if (a.byteLength == this.F.n8*2) {
|
|
const x = this.F.toString(a.slice(0, this.F.n8), radix);
|
|
const y = this.F.toString(a.slice(this.F.n8), radix);
|
|
return `[ ${x}, ${y} ]`;
|
|
} else {
|
|
throw new Error("invalid point size");
|
|
}
|
|
}
|
|
|
|
|
|
fromRng(rng) {
|
|
const F = this.F;
|
|
let P = [];
|
|
let greatest;
|
|
let x3b;
|
|
do {
|
|
P[0] = F.fromRng(rng);
|
|
greatest = rng.nextBool();
|
|
x3b = F.add(F.mul(F.square(P[0]), P[0]), this.b);
|
|
} while (!F.isSquare(x3b));
|
|
|
|
P[1] = F.sqrt(x3b);
|
|
|
|
const s = F.isNegative(P[1]);
|
|
if (greatest ^ s) P[1] = F.neg(P[1]);
|
|
|
|
let Pbuff = new Uint8Array(this.F.n8*2);
|
|
Pbuff.set(P[0]);
|
|
Pbuff.set(P[1], this.F.n8);
|
|
|
|
if (this.cofactor) {
|
|
Pbuff = this.timesScalar(Pbuff, this.cofactor);
|
|
}
|
|
|
|
return Pbuff;
|
|
}
|
|
|
|
|
|
|
|
toObject(a) {
|
|
if (this.isZero(a)) {
|
|
return [
|
|
this.F.toObject(this.F.zero),
|
|
this.F.toObject(this.F.one),
|
|
this.F.toObject(this.F.zero),
|
|
];
|
|
}
|
|
const x = this.F.toObject(a.slice(0, this.F.n8));
|
|
const y = this.F.toObject(a.slice(this.F.n8, this.F.n8*2));
|
|
let z;
|
|
if (a.byteLength == this.F.n8*3) {
|
|
z = this.F.toObject(a.slice(this.F.n8*2, this.F.n8*3));
|
|
} else {
|
|
z = this.F.toObject(this.F.one);
|
|
}
|
|
return [x, y, z];
|
|
}
|
|
|
|
fromObject(a) {
|
|
const x = this.F.fromObject(a[0]);
|
|
const y = this.F.fromObject(a[1]);
|
|
let z;
|
|
if (a.length==3) {
|
|
z = this.F.fromObject(a[2]);
|
|
} else {
|
|
z = this.F.one;
|
|
}
|
|
if (this.F.isZero(z, this.F.one)) {
|
|
return this.zeroAffine;
|
|
} else if (this.F.eq(z, this.F.one)) {
|
|
const buff = new Uint8Array(this.F.n8*2);
|
|
buff.set(x);
|
|
buff.set(y, this.F.n8);
|
|
return buff;
|
|
} else {
|
|
const buff = new Uint8Array(this.F.n8*3);
|
|
buff.set(x);
|
|
buff.set(y, this.F.n8);
|
|
buff.set(z, this.F.n8*2);
|
|
return buff;
|
|
}
|
|
}
|
|
|
|
e(a) {
|
|
if (a instanceof Uint8Array) return a;
|
|
return this.fromObject(a);
|
|
}
|
|
|
|
x(a) {
|
|
const tmp = this.toAffine(a);
|
|
return tmp.slice(0, this.F.n8);
|
|
}
|
|
|
|
y(a) {
|
|
const tmp = this.toAffine(a);
|
|
return tmp.slice(this.F.n8);
|
|
}
|
|
|
|
}
|
|
|
|
/* global WebAssembly */
|
|
|
|
function thread(self) {
|
|
const MAXMEM = 32767;
|
|
let instance;
|
|
let memory;
|
|
|
|
if (self) {
|
|
self.onmessage = function(e) {
|
|
let data;
|
|
if (e.data) {
|
|
data = e.data;
|
|
} else {
|
|
data = e;
|
|
}
|
|
|
|
if (data[0].cmd == "INIT") {
|
|
init(data[0]).then(function() {
|
|
self.postMessage(data.result);
|
|
});
|
|
} else if (data[0].cmd == "TERMINATE") {
|
|
process.exit();
|
|
} else {
|
|
const res = runTask(data);
|
|
self.postMessage(res);
|
|
}
|
|
};
|
|
}
|
|
|
|
async function init(data) {
|
|
const code = new Uint8Array(data.code);
|
|
const wasmModule = await WebAssembly.compile(code);
|
|
memory = new WebAssembly.Memory({initial:data.init, maximum: MAXMEM});
|
|
|
|
instance = await WebAssembly.instantiate(wasmModule, {
|
|
env: {
|
|
"memory": memory
|
|
}
|
|
});
|
|
}
|
|
|
|
|
|
|
|
function alloc(length) {
|
|
const u32 = new Uint32Array(memory.buffer, 0, 1);
|
|
while (u32[0] & 3) u32[0]++; // Return always aligned pointers
|
|
const res = u32[0];
|
|
u32[0] += length;
|
|
if (u32[0] + length > memory.buffer.byteLength) {
|
|
const currentPages = memory.buffer.byteLength / 0x10000;
|
|
let requiredPages = Math.floor((u32[0] + length) / 0x10000)+1;
|
|
if (requiredPages>MAXMEM) requiredPages=MAXMEM;
|
|
memory.grow(requiredPages-currentPages);
|
|
}
|
|
return res;
|
|
}
|
|
|
|
function allocBuffer(buffer) {
|
|
const p = alloc(buffer.byteLength);
|
|
setBuffer(p, buffer);
|
|
return p;
|
|
}
|
|
|
|
function getBuffer(pointer, length) {
|
|
const u8 = new Uint8Array(memory.buffer);
|
|
return new Uint8Array(u8.buffer, u8.byteOffset + pointer, length);
|
|
}
|
|
|
|
function setBuffer(pointer, buffer) {
|
|
const u8 = new Uint8Array(memory.buffer);
|
|
u8.set(new Uint8Array(buffer), pointer);
|
|
}
|
|
|
|
function runTask(task) {
|
|
if (task[0].cmd == "INIT") {
|
|
return init(task[0]);
|
|
}
|
|
const ctx = {
|
|
vars: [],
|
|
out: []
|
|
};
|
|
const u32a = new Uint32Array(memory.buffer, 0, 1);
|
|
const oldAlloc = u32a[0];
|
|
for (let i=0; i<task.length; i++) {
|
|
switch (task[i].cmd) {
|
|
case "ALLOCSET":
|
|
ctx.vars[task[i].var] = allocBuffer(task[i].buff);
|
|
break;
|
|
case "ALLOC":
|
|
ctx.vars[task[i].var] = alloc(task[i].len);
|
|
break;
|
|
case "SET":
|
|
setBuffer(ctx.vars[task[i].var], task[i].buff);
|
|
break;
|
|
case "CALL": {
|
|
const params = [];
|
|
for (let j=0; j<task[i].params.length; j++) {
|
|
const p = task[i].params[j];
|
|
if (typeof p.var !== "undefined") {
|
|
params.push(ctx.vars[p.var] + (p.offset || 0));
|
|
} else if (typeof p.val != "undefined") {
|
|
params.push(p.val);
|
|
}
|
|
}
|
|
instance.exports[task[i].fnName](...params);
|
|
break;
|
|
}
|
|
case "GET":
|
|
ctx.out[task[i].out] = getBuffer(ctx.vars[task[i].var], task[i].len).slice();
|
|
break;
|
|
default:
|
|
throw new Error("Invalid cmd");
|
|
}
|
|
}
|
|
const u32b = new Uint32Array(memory.buffer, 0, 1);
|
|
u32b[0] = oldAlloc;
|
|
return ctx.out;
|
|
}
|
|
|
|
|
|
return runTask;
|
|
}
|
|
|
|
/* global window, navigator, Blob, Worker, WebAssembly */
|
|
/*
|
|
Copyright 2019 0KIMS association.
|
|
|
|
This file is part of wasmsnark (Web Assembly zkSnark Prover).
|
|
|
|
wasmsnark is a free software: you can redistribute it and/or modify it
|
|
under the terms of the GNU General Public License as published by
|
|
the Free Software Foundation, either version 3 of the License, or
|
|
(at your option) any later version.
|
|
|
|
wasmsnark is distributed in the hope that it will be useful, but WITHOUT
|
|
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
|
|
License for more details.
|
|
|
|
You should have received a copy of the GNU General Public License
|
|
along with wasmsnark. If not, see <https://www.gnu.org/licenses/>.
|
|
*/
|
|
|
|
// const MEM_SIZE = 1000; // Memory size in 64K Pakes (512Mb)
|
|
const MEM_SIZE = 25; // Memory size in 64K Pakes (1600Kb)
|
|
const inBrowser = (typeof window !== "undefined");
|
|
let NodeWorker;
|
|
if (!inBrowser) {
|
|
NodeWorker = NodeWorker_mod.Worker;
|
|
}
|
|
|
|
class Deferred {
|
|
constructor() {
|
|
this.promise = new Promise((resolve, reject)=> {
|
|
this.reject = reject;
|
|
this.resolve = resolve;
|
|
});
|
|
}
|
|
}
|
|
|
|
function sleep(ms) {
|
|
return new Promise(resolve => setTimeout(resolve, ms));
|
|
}
|
|
|
|
function base64ToArrayBuffer(base64) {
|
|
if (process.browser) {
|
|
var binary_string = window.atob(base64);
|
|
var len = binary_string.length;
|
|
var bytes = new Uint8Array(len);
|
|
for (var i = 0; i < len; i++) {
|
|
bytes[i] = binary_string.charCodeAt(i);
|
|
}
|
|
return bytes;
|
|
} else {
|
|
return new Uint8Array(Buffer.from(base64, "base64"));
|
|
}
|
|
}
|
|
|
|
|
|
|
|
|
|
async function buildThreadManager(wasm, singleThread) {
|
|
const tm = new ThreadManager();
|
|
|
|
tm.memory = new WebAssembly.Memory({initial:MEM_SIZE});
|
|
tm.u8 = new Uint8Array(tm.memory.buffer);
|
|
tm.u32 = new Uint32Array(tm.memory.buffer);
|
|
|
|
const wasmModule = await WebAssembly.compile(base64ToArrayBuffer(wasm.code));
|
|
|
|
tm.instance = await WebAssembly.instantiate(wasmModule, {
|
|
env: {
|
|
"memory": tm.memory
|
|
}
|
|
});
|
|
|
|
tm.singleThread = singleThread;
|
|
tm.initalPFree = tm.u32[0]; // Save the Pointer to free space.
|
|
tm.pq = wasm.pq;
|
|
tm.pr = wasm.pr;
|
|
tm.pG1gen = wasm.pG1gen;
|
|
tm.pG1zero = wasm.pG1zero;
|
|
tm.pG2gen = wasm.pG2gen;
|
|
tm.pG2zero = wasm.pG2zero;
|
|
tm.pOneT = wasm.pOneT;
|
|
|
|
// tm.pTmp0 = tm.alloc(curve.G2.F.n8*3);
|
|
// tm.pTmp1 = tm.alloc(curve.G2.F.n8*3);
|
|
|
|
|
|
if (singleThread) {
|
|
tm.code = base64ToArrayBuffer(wasm.code);
|
|
tm.taskManager = thread();
|
|
await tm.taskManager([{
|
|
cmd: "INIT",
|
|
init: MEM_SIZE,
|
|
code: tm.code.slice()
|
|
}]);
|
|
tm.concurrency = 1;
|
|
} else {
|
|
tm.workers = [];
|
|
tm.pendingDeferreds = [];
|
|
tm.working = [];
|
|
|
|
let concurrency;
|
|
|
|
if ((typeof(navigator) === "object") && navigator.hardwareConcurrency) {
|
|
concurrency = navigator.hardwareConcurrency;
|
|
} else {
|
|
concurrency = os.cpus().length;
|
|
}
|
|
// Limit to 64 threads for memory reasons.
|
|
if (concurrency>64) concurrency=64;
|
|
tm.concurrency = concurrency;
|
|
|
|
for (let i = 0; i<concurrency; i++) {
|
|
|
|
if (inBrowser) {
|
|
const blob = new Blob(["(", thread.toString(), ")(self);"], { type: "text/javascript" });
|
|
const url = URL.createObjectURL(blob);
|
|
|
|
tm.workers[i] = new Worker(url);
|
|
|
|
tm.workers[i].onmessage = getOnMsg(i);
|
|
|
|
} else {
|
|
tm.workers[i] = new NodeWorker("(" + thread.toString()+ ")(require('worker_threads').parentPort);", {eval: true});
|
|
|
|
tm.workers[i].on("message", getOnMsg(i));
|
|
}
|
|
|
|
tm.working[i]=false;
|
|
}
|
|
|
|
const initPromises = [];
|
|
for (let i=0; i<tm.workers.length;i++) {
|
|
const copyCode = base64ToArrayBuffer(wasm.code).slice();
|
|
initPromises.push(tm.postAction(i, [{
|
|
cmd: "INIT",
|
|
init: MEM_SIZE,
|
|
code: copyCode
|
|
}], [copyCode.buffer]));
|
|
}
|
|
|
|
await Promise.all(initPromises);
|
|
|
|
}
|
|
return tm;
|
|
|
|
function getOnMsg(i) {
|
|
return function(e) {
|
|
let data;
|
|
if ((e)&&(e.data)) {
|
|
data = e.data;
|
|
} else {
|
|
data = e;
|
|
}
|
|
|
|
tm.working[i]=false;
|
|
tm.pendingDeferreds[i].resolve(data);
|
|
tm.processWorks();
|
|
};
|
|
}
|
|
|
|
}
|
|
|
|
class ThreadManager {
|
|
constructor() {
|
|
this.actionQueue = [];
|
|
this.oldPFree = 0;
|
|
}
|
|
|
|
startSyncOp() {
|
|
if (this.oldPFree != 0) throw new Error("Sync operation in progress");
|
|
this.oldPFree = this.u32[0];
|
|
}
|
|
|
|
endSyncOp() {
|
|
if (this.oldPFree == 0) throw new Error("No sync operation in progress");
|
|
this.u32[0] = this.oldPFree;
|
|
this.oldPFree = 0;
|
|
}
|
|
|
|
postAction(workerId, e, transfers, _deferred) {
|
|
if (this.working[workerId]) {
|
|
throw new Error("Posting a job t a working worker");
|
|
}
|
|
this.working[workerId] = true;
|
|
|
|
this.pendingDeferreds[workerId] = _deferred ? _deferred : new Deferred();
|
|
this.workers[workerId].postMessage(e, transfers);
|
|
|
|
return this.pendingDeferreds[workerId].promise;
|
|
}
|
|
|
|
processWorks() {
|
|
for (let i=0; (i<this.workers.length)&&(this.actionQueue.length > 0); i++) {
|
|
if (this.working[i] == false) {
|
|
const work = this.actionQueue.shift();
|
|
this.postAction(i, work.data, work.transfers, work.deferred);
|
|
}
|
|
}
|
|
}
|
|
|
|
queueAction(actionData, transfers) {
|
|
const d = new Deferred();
|
|
|
|
if (this.singleThread) {
|
|
const res = this.taskManager(actionData);
|
|
d.resolve(res);
|
|
} else {
|
|
this.actionQueue.push({
|
|
data: actionData,
|
|
transfers: transfers,
|
|
deferred: d
|
|
});
|
|
this.processWorks();
|
|
}
|
|
return d.promise;
|
|
}
|
|
|
|
resetMemory() {
|
|
this.u32[0] = this.initalPFree;
|
|
}
|
|
|
|
allocBuff(buff) {
|
|
const pointer = this.alloc(buff.byteLength);
|
|
this.setBuff(pointer, buff);
|
|
return pointer;
|
|
}
|
|
|
|
getBuff(pointer, length) {
|
|
return this.u8.slice(pointer, pointer+ length);
|
|
}
|
|
|
|
setBuff(pointer, buffer) {
|
|
this.u8.set(new Uint8Array(buffer), pointer);
|
|
}
|
|
|
|
alloc(length) {
|
|
while (this.u32[0] & 3) this.u32[0]++; // Return always aligned pointers
|
|
const res = this.u32[0];
|
|
this.u32[0] += length;
|
|
return res;
|
|
}
|
|
|
|
async terminate() {
|
|
for (let i=0; i<this.workers.length; i++) {
|
|
this.workers[i].postMessage([{cmd: "TERMINATE"}]);
|
|
}
|
|
await sleep(200);
|
|
}
|
|
|
|
}
|
|
|
|
function buildBatchApplyKey(curve, groupName) {
|
|
const G = curve[groupName];
|
|
const Fr = curve.Fr;
|
|
const tm = curve.tm;
|
|
|
|
curve[groupName].batchApplyKey = async function(buff, first, inc, inType, outType) {
|
|
inType = inType || "affine";
|
|
outType = outType || "affine";
|
|
let fnName, fnAffine;
|
|
let sGin, sGmid, sGout;
|
|
if (groupName == "G1") {
|
|
if (inType == "jacobian") {
|
|
sGin = G.F.n8*3;
|
|
fnName = "g1m_batchApplyKey";
|
|
} else {
|
|
sGin = G.F.n8*2;
|
|
fnName = "g1m_batchApplyKeyMixed";
|
|
}
|
|
sGmid = G.F.n8*3;
|
|
if (outType == "jacobian") {
|
|
sGout = G.F.n8*3;
|
|
} else {
|
|
fnAffine = "g1m_batchToAffine";
|
|
sGout = G.F.n8*2;
|
|
}
|
|
} else if (groupName == "G2") {
|
|
if (inType == "jacobian") {
|
|
sGin = G.F.n8*3;
|
|
fnName = "g2m_batchApplyKey";
|
|
} else {
|
|
sGin = G.F.n8*2;
|
|
fnName = "g2m_batchApplyKeyMixed";
|
|
}
|
|
sGmid = G.F.n8*3;
|
|
if (outType == "jacobian") {
|
|
sGout = G.F.n8*3;
|
|
} else {
|
|
fnAffine = "g2m_batchToAffine";
|
|
sGout = G.F.n8*2;
|
|
}
|
|
} else if (groupName == "Fr") {
|
|
fnName = "frm_batchApplyKey";
|
|
sGin = G.n8;
|
|
sGmid = G.n8;
|
|
sGout = G.n8;
|
|
} else {
|
|
throw new Error("Invalid group: " + groupName);
|
|
}
|
|
const nPoints = Math.floor(buff.byteLength / sGin);
|
|
const pointsPerChunk = Math.floor(nPoints/tm.concurrency);
|
|
const opPromises = [];
|
|
inc = Fr.e(inc);
|
|
let t = Fr.e(first);
|
|
for (let i=0; i<tm.concurrency; i++) {
|
|
let n;
|
|
if (i< tm.concurrency-1) {
|
|
n = pointsPerChunk;
|
|
} else {
|
|
n = nPoints - i*pointsPerChunk;
|
|
}
|
|
if (n==0) continue;
|
|
|
|
const task = [];
|
|
|
|
task.push({
|
|
cmd: "ALLOCSET",
|
|
var: 0,
|
|
buff: buff.slice(i*pointsPerChunk*sGin, i*pointsPerChunk*sGin + n*sGin)
|
|
});
|
|
task.push({cmd: "ALLOCSET", var: 1, buff: t});
|
|
task.push({cmd: "ALLOCSET", var: 2, buff: inc});
|
|
task.push({cmd: "ALLOC", var: 3, len: n*Math.max(sGmid, sGout)});
|
|
task.push({
|
|
cmd: "CALL",
|
|
fnName: fnName,
|
|
params: [
|
|
{var: 0},
|
|
{val: n},
|
|
{var: 1},
|
|
{var: 2},
|
|
{var:3}
|
|
]
|
|
});
|
|
if (fnAffine) {
|
|
task.push({
|
|
cmd: "CALL",
|
|
fnName: fnAffine,
|
|
params: [
|
|
{var: 3},
|
|
{val: n},
|
|
{var: 3},
|
|
]
|
|
});
|
|
}
|
|
task.push({cmd: "GET", out: 0, var: 3, len: n*sGout});
|
|
|
|
opPromises.push(tm.queueAction(task));
|
|
t = Fr.mul(t, Fr.exp(inc, n));
|
|
}
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
let outBuff;
|
|
if (buff instanceof BigBuffer) {
|
|
outBuff = new BigBuffer(nPoints*sGout);
|
|
} else {
|
|
outBuff = new Uint8Array(nPoints*sGout);
|
|
}
|
|
|
|
let p=0;
|
|
for (let i=0; i<result.length; i++) {
|
|
outBuff.set(result[i][0], p);
|
|
p += result[i][0].byteLength;
|
|
}
|
|
|
|
return outBuff;
|
|
};
|
|
}
|
|
|
|
function buildPairing(curve) {
|
|
const tm = curve.tm;
|
|
curve.pairing = function pairing(a, b) {
|
|
|
|
tm.startSyncOp();
|
|
const pA = tm.allocBuff(curve.G1.toJacobian(a));
|
|
const pB = tm.allocBuff(curve.G2.toJacobian(b));
|
|
const pRes = tm.alloc(curve.Gt.n8);
|
|
tm.instance.exports[curve.name + "_pairing"](pA, pB, pRes);
|
|
|
|
const res = tm.getBuff(pRes, curve.Gt.n8);
|
|
|
|
tm.endSyncOp();
|
|
return res;
|
|
};
|
|
|
|
curve.pairingEq = async function pairingEq() {
|
|
let buffCt;
|
|
let nEqs;
|
|
if ((arguments.length % 2) == 1) {
|
|
buffCt = arguments[arguments.length-1];
|
|
nEqs = (arguments.length -1) /2;
|
|
} else {
|
|
buffCt = curve.Gt.one;
|
|
nEqs = arguments.length /2;
|
|
}
|
|
|
|
const opPromises = [];
|
|
for (let i=0; i<nEqs; i++) {
|
|
|
|
const task = [];
|
|
|
|
const g1Buff = curve.G1.toJacobian(arguments[i*2]);
|
|
task.push({cmd: "ALLOCSET", var: 0, buff: g1Buff});
|
|
task.push({cmd: "ALLOC", var: 1, len: curve.prePSize});
|
|
|
|
const g2Buff = curve.G2.toJacobian(arguments[i*2 +1]);
|
|
task.push({cmd: "ALLOCSET", var: 2, buff: g2Buff});
|
|
task.push({cmd: "ALLOC", var: 3, len: curve.preQSize});
|
|
|
|
task.push({cmd: "ALLOC", var: 4, len: curve.Gt.n8});
|
|
|
|
task.push({cmd: "CALL", fnName: curve.name + "_prepareG1", params: [
|
|
{var: 0},
|
|
{var: 1}
|
|
]});
|
|
|
|
task.push({cmd: "CALL", fnName: curve.name + "_prepareG2", params: [
|
|
{var: 2},
|
|
{var: 3}
|
|
]});
|
|
|
|
task.push({cmd: "CALL", fnName: curve.name + "_millerLoop", params: [
|
|
{var: 1},
|
|
{var: 3},
|
|
{var: 4}
|
|
]});
|
|
|
|
task.push({cmd: "GET", out: 0, var: 4, len: curve.Gt.n8});
|
|
|
|
opPromises.push(
|
|
tm.queueAction(task)
|
|
);
|
|
}
|
|
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
tm.startSyncOp();
|
|
const pRes = tm.alloc(curve.Gt.n8);
|
|
tm.instance.exports.ftm_one(pRes);
|
|
|
|
for (let i=0; i<result.length; i++) {
|
|
const pMR = tm.allocBuff(result[i][0]);
|
|
tm.instance.exports.ftm_mul(pRes, pMR, pRes);
|
|
}
|
|
tm.instance.exports[curve.name + "_finalExponentiation"](pRes, pRes);
|
|
|
|
const pCt = tm.allocBuff(buffCt);
|
|
|
|
const r = !!tm.instance.exports.ftm_eq(pRes, pCt);
|
|
|
|
tm.endSyncOp();
|
|
|
|
return r;
|
|
};
|
|
|
|
curve.prepareG1 = function(p) {
|
|
this.tm.startSyncOp();
|
|
const pP = this.tm.allocBuff(p);
|
|
const pPrepP = this.tm.alloc(this.prePSize);
|
|
this.tm.instance.exports[this.name + "_prepareG1"](pP, pPrepP);
|
|
const res = this.tm.getBuff(pPrepP, this.prePSize);
|
|
this.tm.endSyncOp();
|
|
return res;
|
|
};
|
|
|
|
curve.prepareG2 = function(q) {
|
|
this.tm.startSyncOp();
|
|
const pQ = this.tm.allocBuff(q);
|
|
const pPrepQ = this.tm.alloc(this.preQSize);
|
|
this.tm.instance.exports[this.name + "_prepareG2"](pQ, pPrepQ);
|
|
const res = this.tm.getBuff(pPrepQ, this.preQSize);
|
|
this.tm.endSyncOp();
|
|
return res;
|
|
};
|
|
|
|
curve.millerLoop = function(preP, preQ) {
|
|
this.tm.startSyncOp();
|
|
const pPreP = this.tm.allocBuff(preP);
|
|
const pPreQ = this.tm.allocBuff(preQ);
|
|
const pRes = this.tm.alloc(this.Gt.n8);
|
|
this.tm.instance.exports[this.name + "_millerLoop"](pPreP, pPreQ, pRes);
|
|
const res = this.tm.getBuff(pRes, this.Gt.n8);
|
|
this.tm.endSyncOp();
|
|
return res;
|
|
};
|
|
|
|
curve.finalExponentiation = function(a) {
|
|
this.tm.startSyncOp();
|
|
const pA = this.tm.allocBuff(a);
|
|
const pRes = this.tm.alloc(this.Gt.n8);
|
|
this.tm.instance.exports[this.name + "_finalExponentiation"](pA, pRes);
|
|
const res = this.tm.getBuff(pRes, this.Gt.n8);
|
|
this.tm.endSyncOp();
|
|
return res;
|
|
};
|
|
|
|
}
|
|
|
|
const pTSizes = [
|
|
1 , 1, 1, 1, 2, 3, 4, 5,
|
|
6 , 7, 7, 8, 9, 10, 11, 12,
|
|
13, 13, 14, 15, 16, 16, 17, 17,
|
|
17, 17, 17, 17, 17, 17, 17, 17
|
|
];
|
|
|
|
function buildMultiexp(curve, groupName) {
|
|
const G = curve[groupName];
|
|
const tm = G.tm;
|
|
async function _multiExpChunk(buffBases, buffScalars, inType, logger, logText) {
|
|
if ( ! (buffBases instanceof Uint8Array) ) {
|
|
if (logger) logger.error(`${logText} _multiExpChunk buffBases is not Uint8Array`);
|
|
throw new Error(`${logText} _multiExpChunk buffBases is not Uint8Array`);
|
|
}
|
|
if ( ! (buffScalars instanceof Uint8Array) ) {
|
|
if (logger) logger.error(`${logText} _multiExpChunk buffScalars is not Uint8Array`);
|
|
throw new Error(`${logText} _multiExpChunk buffScalars is not Uint8Array`);
|
|
}
|
|
inType = inType || "affine";
|
|
|
|
let sGIn;
|
|
let fnName;
|
|
if (groupName == "G1") {
|
|
if (inType == "affine") {
|
|
fnName = "g1m_multiexpAffine_chunk";
|
|
sGIn = G.F.n8*2;
|
|
} else {
|
|
fnName = "g1m_multiexp_chunk";
|
|
sGIn = G.F.n8*3;
|
|
}
|
|
} else if (groupName == "G2") {
|
|
if (inType == "affine") {
|
|
fnName = "g2m_multiexpAffine_chunk";
|
|
sGIn = G.F.n8*2;
|
|
} else {
|
|
fnName = "g2m_multiexp_chunk";
|
|
sGIn = G.F.n8*3;
|
|
}
|
|
} else {
|
|
throw new Error("Invalid group");
|
|
}
|
|
const nPoints = Math.floor(buffBases.byteLength / sGIn);
|
|
|
|
if (nPoints == 0) return G.zero;
|
|
const sScalar = Math.floor(buffScalars.byteLength / nPoints);
|
|
if( sScalar * nPoints != buffScalars.byteLength) {
|
|
throw new Error("Scalar size does not match");
|
|
}
|
|
|
|
const bitChunkSize = pTSizes[log2$1(nPoints)];
|
|
const nChunks = Math.floor((sScalar*8 - 1) / bitChunkSize) +1;
|
|
|
|
const opPromises = [];
|
|
for (let i=0; i<nChunks; i++) {
|
|
const task = [
|
|
{cmd: "ALLOCSET", var: 0, buff: buffBases},
|
|
{cmd: "ALLOCSET", var: 1, buff: buffScalars},
|
|
{cmd: "ALLOC", var: 2, len: G.F.n8*3},
|
|
{cmd: "CALL", fnName: fnName, params: [
|
|
{var: 0},
|
|
{var: 1},
|
|
{val: sScalar},
|
|
{val: nPoints},
|
|
{val: i*bitChunkSize},
|
|
{val: Math.min(sScalar*8 - i*bitChunkSize, bitChunkSize)},
|
|
{var: 2}
|
|
]},
|
|
{cmd: "GET", out: 0, var: 2, len: G.F.n8*3}
|
|
];
|
|
opPromises.push(
|
|
G.tm.queueAction(task)
|
|
);
|
|
}
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
let res = G.zero;
|
|
for (let i=result.length-1; i>=0; i--) {
|
|
if (!G.isZero(res)) {
|
|
for (let j=0; j<bitChunkSize; j++) res = G.double(res);
|
|
}
|
|
res = G.add(res, result[i][0]);
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
async function _multiExp(buffBases, buffScalars, inType, logger, logText) {
|
|
const MAX_CHUNK_SIZE = 1 << 22;
|
|
const MIN_CHUNK_SIZE = 1 << 10;
|
|
let sGIn;
|
|
|
|
if (groupName == "G1") {
|
|
if (inType == "affine") {
|
|
sGIn = G.F.n8*2;
|
|
} else {
|
|
sGIn = G.F.n8*3;
|
|
}
|
|
} else if (groupName == "G2") {
|
|
if (inType == "affine") {
|
|
sGIn = G.F.n8*2;
|
|
} else {
|
|
sGIn = G.F.n8*3;
|
|
}
|
|
} else {
|
|
throw new Error("Invalid group");
|
|
}
|
|
|
|
const nPoints = Math.floor(buffBases.byteLength / sGIn);
|
|
const sScalar = Math.floor(buffScalars.byteLength / nPoints);
|
|
if( sScalar * nPoints != buffScalars.byteLength) {
|
|
throw new Error("Scalar size does not match");
|
|
}
|
|
|
|
const bitChunkSize = pTSizes[log2$1(nPoints)];
|
|
const nChunks = Math.floor((sScalar*8 - 1) / bitChunkSize) +1;
|
|
|
|
let chunkSize;
|
|
chunkSize = Math.floor(nPoints / (tm.concurrency /nChunks));
|
|
if (chunkSize>MAX_CHUNK_SIZE) chunkSize = MAX_CHUNK_SIZE;
|
|
if (chunkSize<MIN_CHUNK_SIZE) chunkSize = MIN_CHUNK_SIZE;
|
|
|
|
const opPromises = [];
|
|
for (let i=0; i<nPoints; i += chunkSize) {
|
|
if (logger) logger.debug(`Multiexp start: ${logText}: ${i}/${nPoints}`);
|
|
const n= Math.min(nPoints - i, chunkSize);
|
|
const buffBasesChunk = buffBases.slice(i*sGIn, (i+n)*sGIn);
|
|
const buffScalarsChunk = buffScalars.slice(i*sScalar, (i+n)*sScalar);
|
|
opPromises.push(_multiExpChunk(buffBasesChunk, buffScalarsChunk, inType, logger, logText).then( (r) => {
|
|
if (logger) logger.debug(`Multiexp end: ${logText}: ${i}/${nPoints}`);
|
|
return r;
|
|
}));
|
|
}
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
let res = G.zero;
|
|
for (let i=result.length-1; i>=0; i--) {
|
|
res = G.add(res, result[i]);
|
|
}
|
|
|
|
return res;
|
|
}
|
|
|
|
G.multiExp = async function multiExpAffine(buffBases, buffScalars, logger, logText) {
|
|
return await _multiExp(buffBases, buffScalars, "jacobian", logger, logText);
|
|
};
|
|
G.multiExpAffine = async function multiExpAffine(buffBases, buffScalars, logger, logText) {
|
|
return await _multiExp(buffBases, buffScalars, "affine", logger, logText);
|
|
};
|
|
}
|
|
|
|
function buildFFT(curve, groupName) {
|
|
const G = curve[groupName];
|
|
const Fr = curve.Fr;
|
|
const tm = G.tm;
|
|
async function _fft(buff, inverse, inType, outType, logger, loggerTxt) {
|
|
|
|
inType = inType || "affine";
|
|
outType = outType || "affine";
|
|
const MAX_BITS_THREAD = 14;
|
|
|
|
let sIn, sMid, sOut, fnIn2Mid, fnMid2Out, fnFFTMix, fnFFTJoin, fnFFTFinal;
|
|
if (groupName == "G1") {
|
|
if (inType == "affine") {
|
|
sIn = G.F.n8*2;
|
|
fnIn2Mid = "g1m_batchToJacobian";
|
|
} else {
|
|
sIn = G.F.n8*3;
|
|
}
|
|
sMid = G.F.n8*3;
|
|
if (inverse) {
|
|
fnFFTFinal = "g1m_fftFinal";
|
|
}
|
|
fnFFTJoin = "g1m_fftJoin";
|
|
fnFFTMix = "g1m_fftMix";
|
|
|
|
if (outType == "affine") {
|
|
sOut = G.F.n8*2;
|
|
fnMid2Out = "g1m_batchToAffine";
|
|
} else {
|
|
sOut = G.F.n8*3;
|
|
}
|
|
|
|
} else if (groupName == "G2") {
|
|
if (inType == "affine") {
|
|
sIn = G.F.n8*2;
|
|
fnIn2Mid = "g2m_batchToJacobian";
|
|
} else {
|
|
sIn = G.F.n8*3;
|
|
}
|
|
sMid = G.F.n8*3;
|
|
if (inverse) {
|
|
fnFFTFinal = "g2m_fftFinal";
|
|
}
|
|
fnFFTJoin = "g2m_fftJoin";
|
|
fnFFTMix = "g2m_fftMix";
|
|
if (outType == "affine") {
|
|
sOut = G.F.n8*2;
|
|
fnMid2Out = "g2m_batchToAffine";
|
|
} else {
|
|
sOut = G.F.n8*3;
|
|
}
|
|
} else if (groupName == "Fr") {
|
|
sIn = G.n8;
|
|
sMid = G.n8;
|
|
sOut = G.n8;
|
|
if (inverse) {
|
|
fnFFTFinal = "frm_fftFinal";
|
|
}
|
|
fnFFTMix = "frm_fftMix";
|
|
fnFFTJoin = "frm_fftJoin";
|
|
}
|
|
|
|
|
|
let returnArray = false;
|
|
if (Array.isArray(buff)) {
|
|
buff = curve.array2buffer(buff, sIn);
|
|
returnArray = true;
|
|
}
|
|
|
|
const nPoints = buff.byteLength / sIn;
|
|
const bits = log2$1(nPoints);
|
|
|
|
if ((1 << bits) != nPoints) {
|
|
throw new Error("fft must be multiple of 2" );
|
|
}
|
|
|
|
if (bits == Fr.s +1) {
|
|
let buffOut;
|
|
|
|
if (inverse) {
|
|
buffOut = await _fftExtInv(buff, inType, outType, logger, loggerTxt);
|
|
} else {
|
|
buffOut = await _fftExt(buff, inType, outType, logger, loggerTxt);
|
|
}
|
|
|
|
if (returnArray) {
|
|
return curve.buffer2array(buffOut, sOut);
|
|
} else {
|
|
return buffOut;
|
|
}
|
|
}
|
|
|
|
let inv;
|
|
if (inverse) {
|
|
inv = Fr.inv(Fr.e(nPoints));
|
|
}
|
|
|
|
let buffOut;
|
|
|
|
buffReverseBits(buff, sIn);
|
|
|
|
let chunks;
|
|
let pointsInChunk = Math.min(1 << MAX_BITS_THREAD, nPoints);
|
|
let nChunks = nPoints / pointsInChunk;
|
|
|
|
while ((nChunks < tm.concurrency)&&(pointsInChunk>=16)) {
|
|
nChunks *= 2;
|
|
pointsInChunk /= 2;
|
|
}
|
|
|
|
const l2Chunk = log2$1(pointsInChunk);
|
|
|
|
const promises = [];
|
|
for (let i = 0; i< nChunks; i++) {
|
|
if (logger) logger.debug(`${loggerTxt}: fft ${bits} mix start: ${i}/${nChunks}`);
|
|
const task = [];
|
|
task.push({cmd: "ALLOC", var: 0, len: sMid*pointsInChunk});
|
|
const buffChunk = buff.slice( (pointsInChunk * i)*sIn, (pointsInChunk * (i+1))*sIn);
|
|
task.push({cmd: "SET", var: 0, buff: buffChunk});
|
|
if (fnIn2Mid) {
|
|
task.push({cmd: "CALL", fnName:fnIn2Mid, params: [{var:0}, {val: pointsInChunk}, {var: 0}]});
|
|
}
|
|
for (let j=1; j<=l2Chunk;j++) {
|
|
task.push({cmd: "CALL", fnName:fnFFTMix, params: [{var:0}, {val: pointsInChunk}, {val: j}]});
|
|
}
|
|
|
|
if (l2Chunk==bits) {
|
|
if (fnFFTFinal) {
|
|
task.push({cmd: "ALLOCSET", var: 1, buff: inv});
|
|
task.push({cmd: "CALL", fnName: fnFFTFinal, params:[
|
|
{var: 0},
|
|
{val: pointsInChunk},
|
|
{var: 1},
|
|
]});
|
|
}
|
|
if (fnMid2Out) {
|
|
task.push({cmd: "CALL", fnName:fnMid2Out, params: [{var:0}, {val: pointsInChunk}, {var: 0}]});
|
|
}
|
|
task.push({cmd: "GET", out: 0, var: 0, len: pointsInChunk*sOut});
|
|
} else {
|
|
task.push({cmd: "GET", out:0, var: 0, len: sMid*pointsInChunk});
|
|
}
|
|
promises.push(tm.queueAction(task).then( (r) => {
|
|
if (logger) logger.debug(`${loggerTxt}: fft ${bits} mix end: ${i}/${nChunks}`);
|
|
return r;
|
|
}));
|
|
}
|
|
|
|
chunks = await Promise.all(promises);
|
|
for (let i = 0; i< nChunks; i++) chunks[i] = chunks[i][0];
|
|
|
|
for (let i = l2Chunk+1; i<=bits; i++) {
|
|
if (logger) logger.debug(`${loggerTxt}: fft ${bits} join: ${i}/${bits}`);
|
|
const nGroups = 1 << (bits - i);
|
|
const nChunksPerGroup = nChunks / nGroups;
|
|
const opPromises = [];
|
|
for (let j=0; j<nGroups; j++) {
|
|
for (let k=0; k <nChunksPerGroup/2; k++) {
|
|
const first = Fr.exp( Fr.w[i], k*pointsInChunk);
|
|
const inc = Fr.w[i];
|
|
const o1 = j*nChunksPerGroup + k;
|
|
const o2 = j*nChunksPerGroup + k + nChunksPerGroup/2;
|
|
|
|
const task = [];
|
|
task.push({cmd: "ALLOCSET", var: 0, buff: chunks[o1]});
|
|
task.push({cmd: "ALLOCSET", var: 1, buff: chunks[o2]});
|
|
task.push({cmd: "ALLOCSET", var: 2, buff: first});
|
|
task.push({cmd: "ALLOCSET", var: 3, buff: inc});
|
|
task.push({cmd: "CALL", fnName: fnFFTJoin, params:[
|
|
{var: 0},
|
|
{var: 1},
|
|
{val: pointsInChunk},
|
|
{var: 2},
|
|
{var: 3}
|
|
]});
|
|
if (i==bits) {
|
|
if (fnFFTFinal) {
|
|
task.push({cmd: "ALLOCSET", var: 4, buff: inv});
|
|
task.push({cmd: "CALL", fnName: fnFFTFinal, params:[
|
|
{var: 0},
|
|
{val: pointsInChunk},
|
|
{var: 4},
|
|
]});
|
|
task.push({cmd: "CALL", fnName: fnFFTFinal, params:[
|
|
{var: 1},
|
|
{val: pointsInChunk},
|
|
{var: 4},
|
|
]});
|
|
}
|
|
if (fnMid2Out) {
|
|
task.push({cmd: "CALL", fnName:fnMid2Out, params: [{var:0}, {val: pointsInChunk}, {var: 0}]});
|
|
task.push({cmd: "CALL", fnName:fnMid2Out, params: [{var:1}, {val: pointsInChunk}, {var: 1}]});
|
|
}
|
|
task.push({cmd: "GET", out: 0, var: 0, len: pointsInChunk*sOut});
|
|
task.push({cmd: "GET", out: 1, var: 1, len: pointsInChunk*sOut});
|
|
} else {
|
|
task.push({cmd: "GET", out: 0, var: 0, len: pointsInChunk*sMid});
|
|
task.push({cmd: "GET", out: 1, var: 1, len: pointsInChunk*sMid});
|
|
}
|
|
opPromises.push(tm.queueAction(task).then( (r) => {
|
|
if (logger) logger.debug(`${loggerTxt}: fft ${bits} join ${i}/${bits} ${j+1}/${nGroups} ${k}/${nChunksPerGroup/2}`);
|
|
return r;
|
|
}));
|
|
}
|
|
}
|
|
|
|
const res = await Promise.all(opPromises);
|
|
for (let j=0; j<nGroups; j++) {
|
|
for (let k=0; k <nChunksPerGroup/2; k++) {
|
|
const o1 = j*nChunksPerGroup + k;
|
|
const o2 = j*nChunksPerGroup + k + nChunksPerGroup/2;
|
|
const resChunk = res.shift();
|
|
chunks[o1] = resChunk[0];
|
|
chunks[o2] = resChunk[1];
|
|
}
|
|
}
|
|
}
|
|
|
|
if (buff instanceof BigBuffer) {
|
|
buffOut = new BigBuffer(nPoints*sOut);
|
|
} else {
|
|
buffOut = new Uint8Array(nPoints*sOut);
|
|
}
|
|
if (inverse) {
|
|
buffOut.set(chunks[0].slice((pointsInChunk-1)*sOut));
|
|
let p= sOut;
|
|
for (let i=nChunks-1; i>0; i--) {
|
|
buffOut.set(chunks[i], p);
|
|
p += pointsInChunk*sOut;
|
|
delete chunks[i]; // Liberate mem
|
|
}
|
|
buffOut.set(chunks[0].slice(0, (pointsInChunk-1)*sOut), p);
|
|
delete chunks[0];
|
|
} else {
|
|
for (let i=0; i<nChunks; i++) {
|
|
buffOut.set(chunks[i], pointsInChunk*sOut*i);
|
|
delete chunks[i];
|
|
}
|
|
}
|
|
|
|
if (returnArray) {
|
|
return curve.buffer2array(buffOut, sOut);
|
|
} else {
|
|
return buffOut;
|
|
}
|
|
}
|
|
|
|
async function _fftExt(buff, inType, outType, logger, loggerTxt) {
|
|
let b1, b2;
|
|
b1 = buff.slice( 0 , buff.byteLength/2);
|
|
b2 = buff.slice( buff.byteLength/2, buff.byteLength);
|
|
|
|
const promises = [];
|
|
|
|
[b1, b2] = await _fftJoinExt(b1, b2, "fftJoinExt", Fr.one, Fr.shift, inType, "jacobian", logger, loggerTxt);
|
|
|
|
promises.push( _fft(b1, false, "jacobian", outType, logger, loggerTxt));
|
|
promises.push( _fft(b2, false, "jacobian", outType, logger, loggerTxt));
|
|
|
|
const res1 = await Promise.all(promises);
|
|
|
|
let buffOut;
|
|
if (res1[0].byteLength > (1<<28)) {
|
|
buffOut = new BigBuffer(res1[0].byteLength*2);
|
|
} else {
|
|
buffOut = new Uint8Array(res1[0].byteLength*2);
|
|
}
|
|
|
|
buffOut.set(res1[0]);
|
|
buffOut.set(res1[1], res1[0].byteLength);
|
|
|
|
return buffOut;
|
|
}
|
|
|
|
async function _fftExtInv(buff, inType, outType, logger, loggerTxt) {
|
|
let b1, b2;
|
|
b1 = buff.slice( 0 , buff.byteLength/2);
|
|
b2 = buff.slice( buff.byteLength/2, buff.byteLength);
|
|
|
|
const promises = [];
|
|
|
|
promises.push( _fft(b1, true, inType, "jacobian", logger, loggerTxt));
|
|
promises.push( _fft(b2, true, inType, "jacobian", logger, loggerTxt));
|
|
|
|
[b1, b2] = await Promise.all(promises);
|
|
|
|
const res1 = await _fftJoinExt(b1, b2, "fftJoinExtInv", Fr.one, Fr.shiftInv, "jacobian", outType, logger, loggerTxt);
|
|
|
|
let buffOut;
|
|
if (res1[0].byteLength > (1<<28)) {
|
|
buffOut = new BigBuffer(res1[0].byteLength*2);
|
|
} else {
|
|
buffOut = new Uint8Array(res1[0].byteLength*2);
|
|
}
|
|
|
|
buffOut.set(res1[0]);
|
|
buffOut.set(res1[1], res1[0].byteLength);
|
|
|
|
return buffOut;
|
|
}
|
|
|
|
|
|
async function _fftJoinExt(buff1, buff2, fn, first, inc, inType, outType, logger, loggerTxt) {
|
|
const MAX_CHUNK_SIZE = 1<<16;
|
|
const MIN_CHUNK_SIZE = 1<<4;
|
|
|
|
let fnName;
|
|
let fnIn2Mid, fnMid2Out;
|
|
let sOut, sIn, sMid;
|
|
|
|
if (groupName == "G1") {
|
|
if (inType == "affine") {
|
|
sIn = G.F.n8*2;
|
|
fnIn2Mid = "g1m_batchToJacobian";
|
|
} else {
|
|
sIn = G.F.n8*3;
|
|
}
|
|
sMid = G.F.n8*3;
|
|
fnName = "g1m_"+fn;
|
|
if (outType == "affine") {
|
|
fnMid2Out = "g1m_batchToAffine";
|
|
sOut = G.F.n8*2;
|
|
} else {
|
|
sOut = G.F.n8*3;
|
|
}
|
|
} else if (groupName == "G2") {
|
|
if (inType == "affine") {
|
|
sIn = G.F.n8*2;
|
|
fnIn2Mid = "g2m_batchToJacobian";
|
|
} else {
|
|
sIn = G.F.n8*3;
|
|
}
|
|
fnName = "g2m_"+fn;
|
|
sMid = G.F.n8*3;
|
|
if (outType == "affine") {
|
|
fnMid2Out = "g2m_batchToAffine";
|
|
sOut = G.F.n8*2;
|
|
} else {
|
|
sOut = G.F.n8*3;
|
|
}
|
|
} else if (groupName == "Fr") {
|
|
sIn = Fr.n8;
|
|
sOut = Fr.n8;
|
|
sMid = Fr.n8;
|
|
fnName = "frm_" + fn;
|
|
} else {
|
|
throw new Error("Invalid group");
|
|
}
|
|
|
|
if (buff1.byteLength != buff2.byteLength) {
|
|
throw new Error("Invalid buffer size");
|
|
}
|
|
const nPoints = Math.floor(buff1.byteLength / sIn);
|
|
if (nPoints != 1 << log2$1(nPoints)) {
|
|
throw new Error("Invalid number of points");
|
|
}
|
|
|
|
let chunkSize = Math.floor(nPoints /tm.concurrency);
|
|
if (chunkSize < MIN_CHUNK_SIZE) chunkSize = MIN_CHUNK_SIZE;
|
|
if (chunkSize > MAX_CHUNK_SIZE) chunkSize = MAX_CHUNK_SIZE;
|
|
|
|
const opPromises = [];
|
|
|
|
for (let i=0; i<nPoints; i += chunkSize) {
|
|
if (logger) logger.debug(`${loggerTxt}: fftJoinExt Start: ${i}/${nPoints}`);
|
|
const n= Math.min(nPoints - i, chunkSize);
|
|
|
|
const firstChunk = Fr.mul(first, Fr.exp( inc, i));
|
|
const task = [];
|
|
|
|
const b1 = buff1.slice(i*sIn, (i+n)*sIn);
|
|
const b2 = buff2.slice(i*sIn, (i+n)*sIn);
|
|
|
|
task.push({cmd: "ALLOC", var: 0, len: sMid*n});
|
|
task.push({cmd: "SET", var: 0, buff: b1});
|
|
task.push({cmd: "ALLOC", var: 1, len: sMid*n});
|
|
task.push({cmd: "SET", var: 1, buff: b2});
|
|
task.push({cmd: "ALLOCSET", var: 2, buff: firstChunk});
|
|
task.push({cmd: "ALLOCSET", var: 3, buff: inc});
|
|
if (fnIn2Mid) {
|
|
task.push({cmd: "CALL", fnName:fnIn2Mid, params: [{var:0}, {val: n}, {var: 0}]});
|
|
task.push({cmd: "CALL", fnName:fnIn2Mid, params: [{var:1}, {val: n}, {var: 1}]});
|
|
}
|
|
task.push({cmd: "CALL", fnName: fnName, params: [
|
|
{var: 0},
|
|
{var: 1},
|
|
{val: n},
|
|
{var: 2},
|
|
{var: 3},
|
|
{val: Fr.s},
|
|
]});
|
|
if (fnMid2Out) {
|
|
task.push({cmd: "CALL", fnName:fnMid2Out, params: [{var:0}, {val: n}, {var: 0}]});
|
|
task.push({cmd: "CALL", fnName:fnMid2Out, params: [{var:1}, {val: n}, {var: 1}]});
|
|
}
|
|
task.push({cmd: "GET", out: 0, var: 0, len: n*sOut});
|
|
task.push({cmd: "GET", out: 1, var: 1, len: n*sOut});
|
|
opPromises.push(
|
|
tm.queueAction(task).then( (r) => {
|
|
if (logger) logger.debug(`${loggerTxt}: fftJoinExt End: ${i}/${nPoints}`);
|
|
return r;
|
|
})
|
|
);
|
|
}
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
let fullBuffOut1;
|
|
let fullBuffOut2;
|
|
if (nPoints * sOut > 1<<28) {
|
|
fullBuffOut1 = new BigBuffer(nPoints*sOut);
|
|
fullBuffOut2 = new BigBuffer(nPoints*sOut);
|
|
} else {
|
|
fullBuffOut1 = new Uint8Array(nPoints*sOut);
|
|
fullBuffOut2 = new Uint8Array(nPoints*sOut);
|
|
}
|
|
|
|
let p =0;
|
|
for (let i=0; i<result.length; i++) {
|
|
fullBuffOut1.set(result[i][0], p);
|
|
fullBuffOut2.set(result[i][1], p);
|
|
p+=result[i][0].byteLength;
|
|
}
|
|
|
|
return [fullBuffOut1, fullBuffOut2];
|
|
}
|
|
|
|
|
|
G.fft = async function(buff, inType, outType, logger, loggerTxt) {
|
|
return await _fft(buff, false, inType, outType, logger, loggerTxt);
|
|
};
|
|
|
|
G.ifft = async function(buff, inType, outType, logger, loggerTxt) {
|
|
return await _fft(buff, true, inType, outType, logger, loggerTxt);
|
|
};
|
|
|
|
G.lagrangeEvaluations = async function (buff, inType, outType, logger, loggerTxt) {
|
|
inType = inType || "affine";
|
|
outType = outType || "affine";
|
|
|
|
let sIn;
|
|
if (groupName == "G1") {
|
|
if (inType == "affine") {
|
|
sIn = G.F.n8*2;
|
|
} else {
|
|
sIn = G.F.n8*3;
|
|
}
|
|
} else if (groupName == "G2") {
|
|
if (inType == "affine") {
|
|
sIn = G.F.n8*2;
|
|
} else {
|
|
sIn = G.F.n8*3;
|
|
}
|
|
} else if (groupName == "Fr") {
|
|
sIn = Fr.n8;
|
|
} else {
|
|
throw new Error("Invalid group");
|
|
}
|
|
|
|
const nPoints = buff.byteLength /sIn;
|
|
const bits = log2$1(nPoints);
|
|
|
|
if ((2 ** bits)*sIn != buff.byteLength) {
|
|
if (logger) logger.error("lagrangeEvaluations iinvalid input size");
|
|
throw new Error("lagrangeEvaluations invalid Input size");
|
|
}
|
|
|
|
if (bits <= Fr.s) {
|
|
return await G.ifft(buff, inType, outType, logger, loggerTxt);
|
|
}
|
|
|
|
if (bits > Fr.s+1) {
|
|
if (logger) logger.error("lagrangeEvaluations input too big");
|
|
throw new Error("lagrangeEvaluations input too big");
|
|
}
|
|
|
|
let t0 = buff.slice(0, buff.byteLength/2);
|
|
let t1 = buff.slice(buff.byteLength/2, buff.byteLength);
|
|
|
|
|
|
const shiftToSmallM = Fr.exp(Fr.shift, nPoints/2);
|
|
const sConst = Fr.inv( Fr.sub(Fr.one, shiftToSmallM));
|
|
|
|
[t0, t1] = await _fftJoinExt(t0, t1, "prepareLagrangeEvaluation", sConst, Fr.shiftInv, inType, "jacobian", logger, loggerTxt + " prep");
|
|
|
|
const promises = [];
|
|
|
|
promises.push( _fft(t0, true, "jacobian", outType, logger, loggerTxt + " t0"));
|
|
promises.push( _fft(t1, true, "jacobian", outType, logger, loggerTxt + " t1"));
|
|
|
|
[t0, t1] = await Promise.all(promises);
|
|
|
|
let buffOut;
|
|
if (t0.byteLength > (1<<28)) {
|
|
buffOut = new BigBuffer(t0.byteLength*2);
|
|
} else {
|
|
buffOut = new Uint8Array(t0.byteLength*2);
|
|
}
|
|
|
|
buffOut.set(t0);
|
|
buffOut.set(t1, t0.byteLength);
|
|
|
|
return buffOut;
|
|
};
|
|
|
|
G.fftMix = async function fftMix(buff) {
|
|
const sG = G.F.n8*3;
|
|
let fnName, fnFFTJoin;
|
|
if (groupName == "G1") {
|
|
fnName = "g1m_fftMix";
|
|
fnFFTJoin = "g1m_fftJoin";
|
|
} else if (groupName == "G2") {
|
|
fnName = "g2m_fftMix";
|
|
fnFFTJoin = "g2m_fftJoin";
|
|
} else if (groupName == "Fr") {
|
|
fnName = "frm_fftMix";
|
|
fnFFTJoin = "frm_fftJoin";
|
|
} else {
|
|
throw new Error("Invalid group");
|
|
}
|
|
|
|
const nPoints = Math.floor(buff.byteLength / sG);
|
|
const power = log2$1(nPoints);
|
|
|
|
let nChunks = 1 << log2$1(tm.concurrency);
|
|
|
|
if (nPoints <= nChunks*2) nChunks = 1;
|
|
|
|
const pointsPerChunk = nPoints / nChunks;
|
|
|
|
const powerChunk = log2$1(pointsPerChunk);
|
|
|
|
const opPromises = [];
|
|
for (let i=0; i<nChunks; i++) {
|
|
const task = [];
|
|
const b = buff.slice((i* pointsPerChunk)*sG, ((i+1)* pointsPerChunk)*sG);
|
|
task.push({cmd: "ALLOCSET", var: 0, buff: b});
|
|
for (let j=1; j<=powerChunk; j++) {
|
|
task.push({cmd: "CALL", fnName: fnName, params: [
|
|
{var: 0},
|
|
{val: pointsPerChunk},
|
|
{val: j}
|
|
]});
|
|
}
|
|
task.push({cmd: "GET", out: 0, var: 0, len: pointsPerChunk*sG});
|
|
opPromises.push(
|
|
tm.queueAction(task)
|
|
);
|
|
}
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
const chunks = [];
|
|
for (let i=0; i<result.length; i++) chunks[i] = result[i][0];
|
|
|
|
|
|
for (let i = powerChunk+1; i<=power; i++) {
|
|
const nGroups = 1 << (power - i);
|
|
const nChunksPerGroup = nChunks / nGroups;
|
|
const opPromises = [];
|
|
for (let j=0; j<nGroups; j++) {
|
|
for (let k=0; k <nChunksPerGroup/2; k++) {
|
|
const first = Fr.exp( Fr.w[i], k*pointsPerChunk);
|
|
const inc = Fr.w[i];
|
|
const o1 = j*nChunksPerGroup + k;
|
|
const o2 = j*nChunksPerGroup + k + nChunksPerGroup/2;
|
|
|
|
const task = [];
|
|
task.push({cmd: "ALLOCSET", var: 0, buff: chunks[o1]});
|
|
task.push({cmd: "ALLOCSET", var: 1, buff: chunks[o2]});
|
|
task.push({cmd: "ALLOCSET", var: 2, buff: first});
|
|
task.push({cmd: "ALLOCSET", var: 3, buff: inc});
|
|
task.push({cmd: "CALL", fnName: fnFFTJoin, params:[
|
|
{var: 0},
|
|
{var: 1},
|
|
{val: pointsPerChunk},
|
|
{var: 2},
|
|
{var: 3}
|
|
]});
|
|
task.push({cmd: "GET", out: 0, var: 0, len: pointsPerChunk*sG});
|
|
task.push({cmd: "GET", out: 1, var: 1, len: pointsPerChunk*sG});
|
|
opPromises.push(tm.queueAction(task));
|
|
}
|
|
}
|
|
|
|
const res = await Promise.all(opPromises);
|
|
for (let j=0; j<nGroups; j++) {
|
|
for (let k=0; k <nChunksPerGroup/2; k++) {
|
|
const o1 = j*nChunksPerGroup + k;
|
|
const o2 = j*nChunksPerGroup + k + nChunksPerGroup/2;
|
|
const resChunk = res.shift();
|
|
chunks[o1] = resChunk[0];
|
|
chunks[o2] = resChunk[1];
|
|
}
|
|
}
|
|
}
|
|
|
|
let fullBuffOut;
|
|
if (buff instanceof BigBuffer) {
|
|
fullBuffOut = new BigBuffer(nPoints*sG);
|
|
} else {
|
|
fullBuffOut = new Uint8Array(nPoints*sG);
|
|
}
|
|
let p =0;
|
|
for (let i=0; i<nChunks; i++) {
|
|
fullBuffOut.set(chunks[i], p);
|
|
p+=chunks[i].byteLength;
|
|
}
|
|
|
|
return fullBuffOut;
|
|
};
|
|
|
|
G.fftJoin = async function fftJoin(buff1, buff2, first, inc) {
|
|
const sG = G.F.n8*3;
|
|
let fnName;
|
|
if (groupName == "G1") {
|
|
fnName = "g1m_fftJoin";
|
|
} else if (groupName == "G2") {
|
|
fnName = "g2m_fftJoin";
|
|
} else if (groupName == "Fr") {
|
|
fnName = "frm_fftJoin";
|
|
} else {
|
|
throw new Error("Invalid group");
|
|
}
|
|
|
|
if (buff1.byteLength != buff2.byteLength) {
|
|
throw new Error("Invalid buffer size");
|
|
}
|
|
const nPoints = Math.floor(buff1.byteLength / sG);
|
|
if (nPoints != 1 << log2$1(nPoints)) {
|
|
throw new Error("Invalid number of points");
|
|
}
|
|
|
|
let nChunks = 1 << log2$1(tm.concurrency);
|
|
if (nPoints <= nChunks*2) nChunks = 1;
|
|
|
|
const pointsPerChunk = nPoints / nChunks;
|
|
|
|
|
|
const opPromises = [];
|
|
for (let i=0; i<nChunks; i++) {
|
|
const task = [];
|
|
|
|
const firstChunk = Fr.mul(first, Fr.exp(inc, i*pointsPerChunk));
|
|
const b1 = buff1.slice((i* pointsPerChunk)*sG, ((i+1)* pointsPerChunk)*sG);
|
|
const b2 = buff2.slice((i* pointsPerChunk)*sG, ((i+1)* pointsPerChunk)*sG);
|
|
task.push({cmd: "ALLOCSET", var: 0, buff: b1});
|
|
task.push({cmd: "ALLOCSET", var: 1, buff: b2});
|
|
task.push({cmd: "ALLOCSET", var: 2, buff: firstChunk});
|
|
task.push({cmd: "ALLOCSET", var: 3, buff: inc});
|
|
task.push({cmd: "CALL", fnName: fnName, params: [
|
|
{var: 0},
|
|
{var: 1},
|
|
{val: pointsPerChunk},
|
|
{var: 2},
|
|
{var: 3}
|
|
]});
|
|
task.push({cmd: "GET", out: 0, var: 0, len: pointsPerChunk*sG});
|
|
task.push({cmd: "GET", out: 1, var: 1, len: pointsPerChunk*sG});
|
|
opPromises.push(
|
|
tm.queueAction(task)
|
|
);
|
|
|
|
}
|
|
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
let fullBuffOut1;
|
|
let fullBuffOut2;
|
|
if (buff1 instanceof BigBuffer) {
|
|
fullBuffOut1 = new BigBuffer(nPoints*sG);
|
|
fullBuffOut2 = new BigBuffer(nPoints*sG);
|
|
} else {
|
|
fullBuffOut1 = new Uint8Array(nPoints*sG);
|
|
fullBuffOut2 = new Uint8Array(nPoints*sG);
|
|
}
|
|
|
|
let p =0;
|
|
for (let i=0; i<result.length; i++) {
|
|
fullBuffOut1.set(result[i][0], p);
|
|
fullBuffOut2.set(result[i][1], p);
|
|
p+=result[i][0].byteLength;
|
|
}
|
|
|
|
return [fullBuffOut1, fullBuffOut2];
|
|
};
|
|
|
|
|
|
|
|
G.fftFinal = async function fftFinal(buff, factor) {
|
|
const sG = G.F.n8*3;
|
|
const sGout = G.F.n8*2;
|
|
let fnName, fnToAffine;
|
|
if (groupName == "G1") {
|
|
fnName = "g1m_fftFinal";
|
|
fnToAffine = "g1m_batchToAffine";
|
|
} else if (groupName == "G2") {
|
|
fnName = "g2m_fftFinal";
|
|
fnToAffine = "g2m_batchToAffine";
|
|
} else {
|
|
throw new Error("Invalid group");
|
|
}
|
|
|
|
const nPoints = Math.floor(buff.byteLength / sG);
|
|
if (nPoints != 1 << log2$1(nPoints)) {
|
|
throw new Error("Invalid number of points");
|
|
}
|
|
|
|
const pointsPerChunk = Math.floor(nPoints / tm.concurrency);
|
|
|
|
const opPromises = [];
|
|
for (let i=0; i<tm.concurrency; i++) {
|
|
let n;
|
|
if (i< tm.concurrency-1) {
|
|
n = pointsPerChunk;
|
|
} else {
|
|
n = nPoints - i*pointsPerChunk;
|
|
}
|
|
if (n==0) continue;
|
|
const task = [];
|
|
const b = buff.slice((i* pointsPerChunk)*sG, (i*pointsPerChunk+n)*sG);
|
|
task.push({cmd: "ALLOCSET", var: 0, buff: b});
|
|
task.push({cmd: "ALLOCSET", var: 1, buff: factor});
|
|
task.push({cmd: "CALL", fnName: fnName, params: [
|
|
{var: 0},
|
|
{val: n},
|
|
{var: 1},
|
|
]});
|
|
task.push({cmd: "CALL", fnName: fnToAffine, params: [
|
|
{var: 0},
|
|
{val: n},
|
|
{var: 0},
|
|
]});
|
|
task.push({cmd: "GET", out: 0, var: 0, len: n*sGout});
|
|
opPromises.push(
|
|
tm.queueAction(task)
|
|
);
|
|
|
|
}
|
|
|
|
const result = await Promise.all(opPromises);
|
|
|
|
let fullBuffOut;
|
|
if (buff instanceof BigBuffer) {
|
|
fullBuffOut = new BigBuffer(nPoints*sGout);
|
|
} else {
|
|
fullBuffOut = new Uint8Array(nPoints*sGout);
|
|
}
|
|
|
|
let p =0;
|
|
for (let i=result.length-1; i>=0; i--) {
|
|
fullBuffOut.set(result[i][0], p);
|
|
p+=result[i][0].byteLength;
|
|
}
|
|
|
|
return fullBuffOut;
|
|
};
|
|
}
|
|
|
|
async function buildEngine(params) {
|
|
|
|
const tm = await buildThreadManager(params.wasm, params.singleThread);
|
|
|
|
|
|
const curve = {};
|
|
|
|
curve.q = e$2(params.wasm.q);
|
|
curve.r = e$2(params.wasm.r);
|
|
curve.name = params.name;
|
|
curve.tm = tm;
|
|
curve.prePSize = params.wasm.prePSize;
|
|
curve.preQSize = params.wasm.preQSize;
|
|
curve.Fr = new WasmField1(tm, "frm", params.n8r, params.r);
|
|
curve.F1 = new WasmField1(tm, "f1m", params.n8q, params.q);
|
|
curve.F2 = new WasmField2(tm, "f2m", curve.F1);
|
|
curve.G1 = new WasmCurve(tm, "g1m", curve.F1, params.wasm.pG1gen, params.wasm.pG1b, params.cofactorG1);
|
|
curve.G2 = new WasmCurve(tm, "g2m", curve.F2, params.wasm.pG2gen, params.wasm.pG2b, params.cofactorG2);
|
|
curve.F6 = new WasmField3(tm, "f6m", curve.F2);
|
|
curve.F12 = new WasmField2(tm, "ftm", curve.F6);
|
|
|
|
curve.Gt = curve.F12;
|
|
|
|
buildBatchApplyKey(curve, "G1");
|
|
buildBatchApplyKey(curve, "G2");
|
|
buildBatchApplyKey(curve, "Fr");
|
|
|
|
buildMultiexp(curve, "G1");
|
|
buildMultiexp(curve, "G2");
|
|
|
|
buildFFT(curve, "G1");
|
|
buildFFT(curve, "G2");
|
|
buildFFT(curve, "Fr");
|
|
|
|
buildPairing(curve);
|
|
|
|
curve.array2buffer = function(arr, sG) {
|
|
const buff = new Uint8Array(sG*arr.length);
|
|
|
|
for (let i=0; i<arr.length; i++) {
|
|
buff.set(arr[i], i*sG);
|
|
}
|
|
|
|
return buff;
|
|
};
|
|
|
|
curve.buffer2array = function(buff , sG) {
|
|
const n= buff.byteLength / sG;
|
|
const arr = new Array(n);
|
|
for (let i=0; i<n; i++) {
|
|
arr[i] = buff.slice(i*sG, i*sG+sG);
|
|
}
|
|
return arr;
|
|
};
|
|
|
|
return curve;
|
|
}
|
|
|
|
global.curve_bn128 = null;
|
|
|
|
async function buildBn128(singleThread) {
|
|
|
|
if ((!singleThread)&&(global.curve_bn128)) return global.curve_bn128;
|
|
const params = {
|
|
name: "bn128",
|
|
wasm: wasmcurves.bn128_wasm,
|
|
q: e$2("21888242871839275222246405745257275088696311157297823662689037894645226208583"),
|
|
r: e$2("21888242871839275222246405745257275088548364400416034343698204186575808495617"),
|
|
n8q: 32,
|
|
n8r: 32,
|
|
cofactorG2: e$2("30644e72e131a029b85045b68181585e06ceecda572a2489345f2299c0f9fa8d", 16),
|
|
singleThread: singleThread ? true : false
|
|
};
|
|
|
|
const curve = await buildEngine(params);
|
|
curve.terminate = async function() {
|
|
if (!params.singleThread) {
|
|
global.curve_bn128 = null;
|
|
await this.tm.terminate();
|
|
}
|
|
};
|
|
|
|
if (!singleThread) {
|
|
global.curve_bn128 = curve;
|
|
}
|
|
|
|
return curve;
|
|
}
|
|
|
|
global.curve_bls12381 = null;
|
|
|
|
async function buildBls12381(singleThread) {
|
|
|
|
if ((!singleThread)&&(global.curve_bls12381)) return global.curve_bls12381;
|
|
const params = {
|
|
name: "bls12381",
|
|
wasm: wasmcurves.bls12381_wasm,
|
|
q: e$2("1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab", 16),
|
|
r: e$2("73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", 16),
|
|
n8q: 48,
|
|
n8r: 32,
|
|
cofactorG1: e$2("0x396c8c005555e1568c00aaab0000aaab", 16),
|
|
cofactorG2: e$2("0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5", 16),
|
|
singleThread: singleThread ? true : false
|
|
};
|
|
|
|
const curve = await buildEngine(params);
|
|
curve.terminate = async function() {
|
|
if (!params.singleThread) {
|
|
global.curve_bls12381 = null;
|
|
await this.tm.terminate();
|
|
}
|
|
};
|
|
|
|
return curve;
|
|
}
|
|
|
|
const bls12381r = e$2("73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001", 16);
|
|
const bn128r = e$2("21888242871839275222246405745257275088548364400416034343698204186575808495617");
|
|
|
|
const bls12381q = e$2("1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab", 16);
|
|
const bn128q = e$2("21888242871839275222246405745257275088696311157297823662689037894645226208583");
|
|
|
|
async function getCurveFromR(r, singleThread) {
|
|
let curve;
|
|
if (eq$2(r, bn128r)) {
|
|
curve = await buildBn128(singleThread);
|
|
} else if (eq$2(r, bls12381r)) {
|
|
curve = await buildBn128(singleThread);
|
|
} else {
|
|
throw new Error(`Curve not supported: ${toString(r)}`);
|
|
}
|
|
return curve;
|
|
}
|
|
|
|
async function getCurveFromQ(q, singleThread) {
|
|
let curve;
|
|
if (eq$2(q, bn128q)) {
|
|
curve = await buildBn128(singleThread);
|
|
} else if (eq$2(q, bls12381q)) {
|
|
curve = await buildBn128(singleThread);
|
|
} else {
|
|
throw new Error(`Curve not supported: ${toString(q)}`);
|
|
}
|
|
return curve;
|
|
}
|
|
|
|
async function getCurveFromName(name, singleThread) {
|
|
let curve;
|
|
const normName = normalizeName(name);
|
|
if (["BN128", "BN254", "ALTBN128"].indexOf(normName) >= 0) {
|
|
curve = await buildBn128(singleThread);
|
|
} else if (["BLS12381"].indexOf(normName) >= 0) {
|
|
curve = await buildBn128(singleThread);
|
|
} else {
|
|
throw new Error(`Curve not supported: ${name}`);
|
|
}
|
|
return curve;
|
|
|
|
function normalizeName(n) {
|
|
return n.toUpperCase().match(/[A-Za-z0-9]+/g).join("");
|
|
}
|
|
|
|
}
|
|
|
|
const Scalar$1=_Scalar;
|
|
const utils$1 = _utils;
|
|
|
|
exports.BigBuffer = BigBuffer;
|
|
exports.ChaCha = ChaCha;
|
|
exports.EC = EC;
|
|
exports.F1Field = F1Field;
|
|
exports.F2Field = F2Field;
|
|
exports.F3Field = F3Field;
|
|
exports.PolField = PolField;
|
|
exports.Scalar = Scalar$1;
|
|
exports.ZqField = F1Field;
|
|
exports.buildBls12381 = buildBls12381;
|
|
exports.buildBn128 = buildBn128;
|
|
exports.getCurveFromName = getCurveFromName;
|
|
exports.getCurveFromQ = getCurveFromQ;
|
|
exports.getCurveFromR = getCurveFromR;
|
|
exports.utils = utils$1;
|