add ability to sieve custom function

junk/sieves/sieves.html

@@ -20,6 +20,7 @@
 				<hgroup>
 					<h1>Sieving Multiplicative Functions</h1>
 					<p>Posted <time datetime="2026-04-15">April 15, 2026</time></p>
+					<p>Updated <time datetime="2026-05-04">May 4, 2026</time></p>
 				</hgroup>
 
 				<p>The
@@ -29,7 +30,7 @@
 				particular, a segmented version can be implemented to limit memory
 				usage.</p>
 
-				Furthermore, a similar approach can be used to "sieve" the values of
+				<p>Furthermore, a similar approach can be used to "sieve" the values of
 				<a href="https://en.wikipedia.org/wiki/Multiplicative_function">multiplicative functions</a>.
 				For instance,
 				<a href="https://cp-algorithms.com/algebra/phi-function.html">this page</a>
@@ -76,8 +77,15 @@
 							<option value="mobius">Mobius</option>
 							<option value="big-omega">Prime omega (with multiplicity)</option>
 							<option value="little-omega">Prime omega (without multiplicity)</option>
+							<option value="custom">Custom</option>
 						</select>
 
+						<label hidden id="custom-function-label" for="custom-function">Custom function definition</label>
+						<textarea hidden spellcheck=false placeholder="return Math.pow(p, k-1) * (p-1);" id="custom-function"></textarea>
+
+						<label hidden id="custom-function-additive-label" for="custom-function-additive">Function is additive</label>
+						<input hidden type="checkbox" id="custom-function-additive" />
+
 						<input type="button" id="enter" value="Enter" />
 					</div>
 
@@ -1125,7 +1133,8 @@ function mobius(p, k) {
 
 					<p>Many multiplicative and additive functions have simple formulas
 					for prime powers, which makes adding a new function to sieve very
-					easy with this approach.</p>
+					easy with this approach. The demo even lets you write your own custom
+					function to sieve - try it out!</p>
 				</section>
 
 				<section>

junk/sieves/sieves.js

@@ -133,6 +133,14 @@ function sieveMultiples(p, q, l, r, y, sieve, quo, additive) {
 	}
 }
 
+function setCustomFunctionVisibility(e) {
+	const isHidden = e.target.value !== "custom";
+	document.querySelector("#custom-function-label").hidden = isHidden;
+	document.querySelector("#custom-function").hidden = isHidden;
+	document.querySelector("#custom-function-additive-label").hidden = isHidden;
+	document.querySelector("#custom-function-additive").hidden = isHidden;
+}
+
 function getFunc(func) {
 	switch (func.value) {
 		case "num-divisors":
@@ -149,6 +157,11 @@ function getFunc(func) {
 			return [littleOmega, true];
 		case "big-omega":
 			return [bigOmega, true];
+		case "custom":
+			const def = document.querySelector("#custom-function");
+			const isAdditive = document.querySelector("#custom-function-additive");
+			const f = new Function("p", "k", def.value);
+			return [f, isAdditive.checked];
 		default:
 			throw new Error("function not implemented!");
 	}
@@ -219,4 +232,5 @@ function calculate() {
 	result.appendChild(table);
 }
 
+document.querySelector("#function").addEventListener("change", (e) => setCustomFunctionVisibility(e))
 document.querySelector("#enter").addEventListener("click", () => calculate())

styles/junk.css

@@ -3,6 +3,10 @@
 	overflow-y: hidden;
 }
 
+figure {
+	margin: 1vw;
+}
+
 pre {
 	overflow: auto;
 	background-color: black;