add multiplicative order button

index.html

@@ -23,6 +23,7 @@
 			<output id="result" for="expr modulus"></output>
 
 			<div id="extra-buttons">
+				<button id="ord" type="button">ord</button>
 				<button id="sqrt" type="button">√</button>
 				<button id="inv" type="button">x<sup>-1</sup></button>
 				<button id="pow" type="button">^</button>

main.js

@@ -130,6 +130,7 @@ document.querySelector("#rparen").addEventListener("click", () => keyPress(")"))
 document.querySelector("#pow").addEventListener("click", () => keyPress("^"));
 document.querySelector("#inv").addEventListener("click", () => keyPress("^-1"));
 document.querySelector("#sqrt").addEventListener("click", () => keyPress("sqrt("));
+document.querySelector("#ord").addEventListener("click", () => keyPress("ord("));
 
 document.querySelector("#clear").addEventListener("click", clear);
 document.querySelector("#enter").addEventListener("click", evaluate);

modules/compute.js

@@ -1,4 +1,4 @@
-import { modinv, modpow, modsqrt } from "./math.js";
+import { modinv, modpow, modsqrt, ord } from "./math.js";
 
 function binaryOpPop(stack) {
 	const b = stack.pop();
@@ -56,6 +56,10 @@ function compute(queue, modulus) {
 			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);
 		}
 	}
 

modules/lexer.js

@@ -1,7 +1,11 @@
 function tokenize(expr) {
 	// NOTE: not handling whitespace
 	// NOTE: currently ends early if string doesn't match token
-	const regexp = /[0-9]+|[-+*/^]|\(|\)|sqrt/gy;
+
+	// TODO: it would probably be beneficial to create some sort of
+	// function token instead of updating strings in several different
+	// places
+	const regexp = /[0-9]+|[-+*/^]|\(|\)|sqrt|ord/gy;
 	const matches = expr.matchAll(regexp);
 	
 	const tokens = [];
@@ -10,12 +14,14 @@ function tokenize(expr) {
 			tokens.push(BigInt(match[0]));
 		} else if (/[-+*^/]/.test(match[0])) {
 			tokens.push(match[0])
-		} else if (match[0] == "(") {
+		} else if (match[0] === "(") {
 			tokens.push("(");
-		} else if (match[0] == ")") {
+		} else if (match[0] === ")") {
 			tokens.push(")");
-		} else if (match[0] == "sqrt") {
+		} else if (match[0] === "sqrt") {
 			tokens.push("sqrt")
+		} else if (match[0] === "ord") {
+			tokens.push("ord")
 		}
 	}
 

modules/math.js

@@ -181,4 +181,28 @@ function modsqrt(n, modulus) {
 	return tonelliShanks(n, modulus);
 }
 
-export { modsqrt, modinv, modpow };
+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;
+}
+
+export { modsqrt, modinv, modpow, ord };

modules/parser.js

@@ -27,6 +27,8 @@ function popOps(opstack, queue, op, powInStack) {
 	// rather than complicate things by evaluating exponent expressions
 	// normally instead of modularly (and consequently needing to deal with
 	// fractions) we simply require exponents to be integers
+	// NOTE: as written this allows for the exponent to be a function, not
+	// sure if that should change or not
 	if (powInStack && op !== "u") {
 		throw new Error("exponent must be an integer, not an expression");
 	}
@@ -48,7 +50,8 @@ function popBetweenParens(opstack, queue, powInStack) {
 	}
 
 	opstack.pop();
-	if (opstack.at(-1) === "sqrt") {
+	const t = opstack.at(-1);
+	if (t === "sqrt" || t === "ord") {
 		const func = opstack.pop();
 		queue.push(func);
 	}
@@ -95,6 +98,8 @@ function shunt(tokens) {
 			powInStack = popBetweenParens(opstack, queue, powInStack);
 		} else if (token === "sqrt") {
 			opstack.push(token);
+		} else if (token === "ord") {
+			opstack.push(token);
 		}
 
 		lastToken = token;