start adding square root functionality

modules/compute.js

@@ -63,6 +63,53 @@ function binaryOpPop(stack) {
 	return [a, b];
 }
 
+function witness(a, n) {
+	let d = n - 1n;
+	let s = 0;
+	while (d % 2n === 0n) {
+		d /= 2n;
+		s++;
+	}
+
+	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 tonelliShanks(n, p) {
+	throw new Error("not implemented");
+}
+
 function compute(queue, modulus) {
 	const stack = [];
 	for (const token of queue) {
@@ -105,6 +152,14 @@ function compute(queue, modulus) {
 			const [a, b] = binaryOpPop(stack);
 			const c = modpow(a, b, modulus);
 			stack.push(c);
+		} else if (token === "sqrt") {
+			if (!isprime(modulus)) {
+				throw new Error("modulus must be prime to compute square root");
+			}
+
+			const a = stack.pop();
+			const s = tonelliShanks(a, modulus);
+			stack.push(s);
 		}
 	}
 

modules/lexer.js

@@ -1,7 +1,7 @@
 function tokenize(expr) {
 	// NOTE: not handling whitespace
 	// NOTE: currently ends early if string doesn't match token
-	const regexp = /[0-9]+|[-+*/^]|\(|\)/gy;
+	const regexp = /[0-9]+|[-+*/^]|\(|\)|sqrt/gy;
 	const matches = expr.matchAll(regexp);
 	
 	const tokens = [];
@@ -14,6 +14,8 @@ function tokenize(expr) {
 			tokens.push("(");
 		} else if (match[0] == ")") {
 			tokens.push(")");
+		} else if (match[0] == "sqrt") {
+			tokens.push("sqrt")
 		}
 	}
 

modules/parser.js

@@ -48,6 +48,10 @@ function popBetweenParens(opstack, queue, powInStack) {
 	}
 
 	opstack.pop();
+	if (opstack.at(-1) === "sqrt") {
+		const func = opstack.pop();
+		queue.push(func);
+	}
 	return powInStack;
 }
 
@@ -89,6 +93,8 @@ function shunt(tokens) {
 			opstack.push(token);
 		} else if (token === ")") {
 			powInStack = popBetweenParens(opstack, queue, powInStack);
+		} else if (token === "sqrt") {
+			opstack.push(token);
 		}
 
 		lastToken = token;