116 lines
2.2 KiB
JavaScript
116 lines
2.2 KiB
JavaScript
function xgcd(a, b) {
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let [old_r, r] = [a, b];
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let [old_s, s] = [1n, 0n];
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let [old_t, t] = [0n, 1n];
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while (r !== 0n) {
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const quotient = old_r / r;
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[old_r, r] = [r, old_r - quotient * r];
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[old_s, s] = [s, old_s - quotient * s];
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[old_t, t] = [t, old_t - quotient * t];
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}
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return [old_r, old_s, old_t];
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}
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function modinv(x, modulus) {
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let [r, s, t] = xgcd(x, modulus);
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if (r !== 1n) {
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throw new Error(`no inverse exists - ${x} and ${modulus} are not coprime`);
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}
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if (s < 0n) {
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s += modulus;
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}
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return s;
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}
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function modpow(base, exponent, modulus) {
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if (exponent < 0n) {
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const p = modpow(base, -exponent, modulus);
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return modinv(p, modulus);
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}
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if (modulus === 1n) {
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return 0n;
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}
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let result = 1n;
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base %= modulus;
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while (exponent > 0) {
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if (exponent % 2n === 1n) {
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result *= base;
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result %= modulus;
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}
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exponent >>= 1n;
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base *= base;
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base %= modulus;
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}
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return result;
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}
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function binaryOpPop(stack) {
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const b = stack.pop();
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const a = stack.pop();
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if (a === undefined || b === undefined) {
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throw new Error("invalid expression");
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}
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return [a, b];
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}
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function compute(queue, modulus) {
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const stack = [];
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for (const token of queue) {
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if (typeof token === "bigint") {
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stack.push(token);
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} else if (token === "+") {
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let [a, b] = binaryOpPop(stack);
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a %= modulus;
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b %= modulus;
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const c = (a + b) % modulus;
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stack.push(c);
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} else if (token === "-") {
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let [a, b] = binaryOpPop(stack);
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a %= modulus;
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b %= modulus;
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const c = (a - b) % modulus;
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stack.push(c);
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} else if (token === "*") {
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let [a, b] = binaryOpPop(stack);
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a %= modulus;
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b %= modulus;
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const c = (a * b) % modulus;
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stack.push(c);
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} else if (token === "/") {
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let [a, b] = binaryOpPop(stack);
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a %= modulus;
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b %= modulus;
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const binv = modinv(b, modulus);
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const c = (a * binv) % modulus;
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stack.push(c);
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} else if (token === "^") {
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const [a, b] = binaryOpPop(stack);
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const c = modpow(a, b, modulus);
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stack.push(c);
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}
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}
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if (stack.length !== 1) {
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throw new Error("error evaluating expression");
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}
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let result = stack[0] % modulus;
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if (result < 0n) {
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result += modulus;
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}
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return result;
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}
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export { compute };
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