mcalc/modules/compute.js

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 > 0) {
		if (exponent % 2n === 1n) {
			result *= base;
			result %= modulus;
		}

		exponent >>= 1n;
		base *= base;
		base %= modulus;
	}

	return result;
}

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 === "^") {
			// FIXME: not always valid - consider 2^3^4 mod 7
			// also 2^(3+4)
			// solution might be to change parser
			// might also be better to just mod once at the end
			// instead of with every op
			const [a, b] = binaryOpPop(stack);
			const c = modpow(a, b, modulus);
			stack.push(c);
		}
	}

	if (stack.length !== 1) {
		throw new Error("error evaluating expression");
	}

	let result = stack[0] % modulus;
	if (result < 0n) {
		result += modulus;
	}

	return result;
}

export { compute };