move to workers dir
This commit is contained in:
filifa
102
workers/compute.js
Normal file
102
workers/compute.js
Normal file
@@ -0,0 +1,102 @@
|
||||
/*
|
||||
Copyright (C) 2025 filifa
|
||||
|
||||
This program is 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.
|
||||
|
||||
This program 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 this program. If not, see <https://www.gnu.org/licenses/>.
|
||||
*/
|
||||
importScripts("./math.js")
|
||||
|
||||
addEventListener("message", (message) => {
|
||||
if (message.data.command === "compute") {
|
||||
try {
|
||||
compute(message.data.queue, message.data.m);
|
||||
} catch(e) {
|
||||
postMessage(e);
|
||||
}
|
||||
}
|
||||
});
|
||||
|
||||
function binaryOpPop(stack) {
|
||||
const b = stack.pop();
|
||||
const a = stack.pop();
|
||||
if (a === undefined || b === undefined) {
|
||||
throw new Error("invalid expression");
|
||||
}
|
||||
|
||||
return [a, b];
|
||||
}
|
||||
|
||||
function compute(queue, modulus) {
|
||||
const stack = [];
|
||||
for (const token of queue) {
|
||||
if (typeof token === "bigint") {
|
||||
stack.push(token);
|
||||
} else if (token === "+") {
|
||||
let [a, b] = binaryOpPop(stack);
|
||||
a %= modulus;
|
||||
b %= modulus;
|
||||
const c = (a + b) % modulus;
|
||||
stack.push(c);
|
||||
} else if (token === "-") {
|
||||
let [a, b] = binaryOpPop(stack);
|
||||
a %= modulus;
|
||||
b %= modulus;
|
||||
const c = (a - b) % modulus;
|
||||
stack.push(c);
|
||||
} else if (token === "*") {
|
||||
let [a, b] = binaryOpPop(stack);
|
||||
a %= modulus;
|
||||
b %= modulus;
|
||||
const c = (a * b) % modulus;
|
||||
stack.push(c);
|
||||
} else if (token === "/") {
|
||||
let [a, b] = binaryOpPop(stack);
|
||||
a %= modulus;
|
||||
b %= modulus;
|
||||
const binv = modinv(b, modulus);
|
||||
const c = (a * binv) % modulus;
|
||||
stack.push(c);
|
||||
} else if (token === "u") {
|
||||
let a = stack.pop();
|
||||
if (a === undefined) {
|
||||
throw new Error("invalid expression");
|
||||
}
|
||||
|
||||
a *= -1n;
|
||||
stack.push(a);
|
||||
} else if (token === "^") {
|
||||
const [a, b] = binaryOpPop(stack);
|
||||
const c = modpow(a, b, modulus);
|
||||
stack.push(c);
|
||||
} else if (token === "sqrt") {
|
||||
const a = stack.pop();
|
||||
const s = modsqrt(a, modulus);
|
||||
stack.push(s);
|
||||
} else if (token === "ord") {
|
||||
const a = stack.pop();
|
||||
const r = ord(a, modulus);
|
||||
stack.push(r);
|
||||
}
|
||||
}
|
||||
|
||||
if (stack.length !== 1) {
|
||||
throw new Error("error evaluating expression");
|
||||
}
|
||||
|
||||
let result = stack[0] % modulus;
|
||||
if (result < 0n) {
|
||||
result += modulus;
|
||||
}
|
||||
|
||||
postMessage(result);
|
||||
}
|
||||
222
workers/math.js
Normal file
222
workers/math.js
Normal file
@@ -0,0 +1,222 @@
|
||||
/*
|
||||
Copyright (C) 2025 filifa
|
||||
|
||||
This program is 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.
|
||||
|
||||
This program 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 this program. If not, see <https://www.gnu.org/licenses/>.
|
||||
*/
|
||||
function xgcd(a, b) {
|
||||
let [old_r, r] = [a, b];
|
||||
let [old_s, s] = [1n, 0n];
|
||||
let [old_t, t] = [0n, 1n];
|
||||
|
||||
while (r !== 0n) {
|
||||
const quotient = old_r / r;
|
||||
[old_r, r] = [r, old_r - quotient * r];
|
||||
[old_s, s] = [s, old_s - quotient * s];
|
||||
[old_t, t] = [t, old_t - quotient * t];
|
||||
}
|
||||
|
||||
return [old_r, old_s, old_t];
|
||||
}
|
||||
|
||||
function modinv(x, modulus) {
|
||||
let [r, s, t] = xgcd(x, modulus);
|
||||
if (r !== 1n) {
|
||||
throw new Error(`no inverse exists - ${x} and ${modulus} are not coprime`);
|
||||
}
|
||||
|
||||
if (s < 0n) {
|
||||
s += modulus;
|
||||
}
|
||||
|
||||
return s;
|
||||
}
|
||||
|
||||
function modpow(base, exponent, modulus) {
|
||||
if (exponent < 0n) {
|
||||
const p = modpow(base, -exponent, modulus);
|
||||
return modinv(p, modulus);
|
||||
}
|
||||
|
||||
if (modulus === 1n) {
|
||||
return 0n;
|
||||
}
|
||||
|
||||
let result = 1n;
|
||||
base %= modulus;
|
||||
|
||||
while (exponent > 0n) {
|
||||
if (exponent % 2n === 1n) {
|
||||
result *= base;
|
||||
result %= modulus;
|
||||
}
|
||||
|
||||
exponent >>= 1n;
|
||||
base *= base;
|
||||
base %= modulus;
|
||||
}
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
function factorTwos(n) {
|
||||
let s = 0;
|
||||
while (n % 2n === 0n) {
|
||||
n /= 2n;
|
||||
s++;
|
||||
}
|
||||
|
||||
return [n, s];
|
||||
}
|
||||
|
||||
function witness(a, n) {
|
||||
const [d, s] = factorTwos(n - 1n);
|
||||
|
||||
let x = modpow(a, d, n);
|
||||
let y = null;
|
||||
for (let i = 0; i < s; i++) {
|
||||
y = modpow(x, 2n, n);
|
||||
if (y === 1n && x !== 1n && x !== n - 1n) {
|
||||
return true;
|
||||
}
|
||||
x = y
|
||||
}
|
||||
|
||||
return y !== 1n
|
||||
}
|
||||
|
||||
function randbigint() {
|
||||
return BigInt(Math.floor(Math.random() * Number.MAX_SAFE_INTEGER))
|
||||
}
|
||||
|
||||
function isprime(n) {
|
||||
if (n === 2n) {
|
||||
return true;
|
||||
} else if (n % 2n === 0n) {
|
||||
return false;
|
||||
}
|
||||
|
||||
const trials = 10;
|
||||
for (let i = 0; i < trials; i++) {
|
||||
const a = randbigint() % (n - 1n) + 1n;
|
||||
if (witness(a, n)) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
function legendreSymbol(a, p) {
|
||||
let r = modpow(a, (p - 1n)/2n, p);
|
||||
if (r === p - 1n) {
|
||||
r = -1n;
|
||||
}
|
||||
|
||||
return r;
|
||||
}
|
||||
|
||||
function quadraticNonResidue(p) {
|
||||
// TODO: consider randomizing this
|
||||
for (let a = 2n; a < p; a++) {
|
||||
if (legendreSymbol(a, p) === -1n) {
|
||||
return a;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
function tonelliShanks(n, p) {
|
||||
const [q, s] = factorTwos(p - 1n);
|
||||
const z = quadraticNonResidue(p);
|
||||
|
||||
let m = s;
|
||||
let c = modpow(z, q, p);
|
||||
let t = modpow(n, q, p);
|
||||
let r = modpow(n, (q+1n)/2n, p);
|
||||
|
||||
while (true) {
|
||||
if (t === 0n) {
|
||||
return 0n;
|
||||
} else if (t === 1n) {
|
||||
return r;
|
||||
}
|
||||
|
||||
let k = t;
|
||||
let i = null;
|
||||
for (i = 1; i < m; i++) {
|
||||
k = modpow(k, 2n, p);
|
||||
if (k === 1n) {
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
if (i === m) {
|
||||
throw new Error("radicand is not a quadratic residue of the modulus");
|
||||
}
|
||||
|
||||
const e = BigInt(Math.pow(2, m - i - 1));
|
||||
const b = modpow(c, e, p);
|
||||
m = i;
|
||||
c = modpow(b, 2n, p);
|
||||
t = (t * c) % p;
|
||||
r = (r * b) % p;
|
||||
}
|
||||
}
|
||||
|
||||
function modsqrt(n, modulus) {
|
||||
// TODO: add support for prime power modulus (Hensel's lemma)
|
||||
if (!isprime(modulus)) {
|
||||
throw new Error("modulus must be prime to compute square root");
|
||||
}
|
||||
|
||||
n %= modulus;
|
||||
if (n < 0n) {
|
||||
n += modulus;
|
||||
}
|
||||
|
||||
if (n % modulus === 0n) {
|
||||
return 0n;
|
||||
} else if (modulus === 2n) {
|
||||
return n % 2n;
|
||||
} else if (legendreSymbol(n, modulus) !== 1n) {
|
||||
throw new Error("radicand is not a quadratic residue of the modulus");
|
||||
} else if (modulus % 4n === 3n) {
|
||||
return modpow(n, (modulus+1n)/4n, modulus);
|
||||
}
|
||||
|
||||
return tonelliShanks(n, modulus);
|
||||
}
|
||||
|
||||
function ord(n, modulus) {
|
||||
n %= modulus;
|
||||
if (n < 0n) {
|
||||
n += modulus;
|
||||
}
|
||||
|
||||
const [g, s, t] = xgcd(n, modulus);
|
||||
if (g !== 1n) {
|
||||
throw new Error(`can't compute multiplicative order - ${n} and ${modulus} are not coprime`);
|
||||
}
|
||||
|
||||
// NOTE: this is a hard problem, but there are more efficient approaches
|
||||
|
||||
let k = 1n;
|
||||
let a = n;
|
||||
while (a !== 1n) {
|
||||
a *= n;
|
||||
a %= modulus;
|
||||
k += 1n;
|
||||
}
|
||||
|
||||
return k;
|
||||
}
|
||||
Reference in New Issue
Block a user