add junk posts

junk/faulhaber/faulhaber.js

@@ -0,0 +1,111 @@
+/*
+ * Copyright (C) 2026 filifa
+ *
+ * License: 0BSD (https://spdx.org/licenses/0BSD.html)
+ */
+let exp = null;
+let s = null;
+
+function stirling2(p) {
+	if (p === 0) {
+		return [1n];
+	}
+
+	let s = [0n];
+	for (let i = 1; i < p + 1; i++) {
+		s.push(1n);
+		for (let j = i - 1; j > 0; j--) {
+			s[j] = BigInt(j) * s[j] + s[j-1];
+		}
+	}
+
+	return s;
+}
+
+function faulhaber(n, s) {
+	const limit = BigInt(s.length);
+	if (limit === 1n) {
+		return n;
+	}
+
+	let q = n + 1n;
+	let total = 0n;
+	for (let k = 1n; k < limit; k++) {
+		q *= n + 1n - k;
+		total += s[k] * q / (k + 1n);
+	}
+
+	return total;
+}
+
+function calculate() {
+	const limit = document.querySelector("#limit");
+	const exponent = document.querySelector("#exponent");
+
+	const e = parseInt(exponent.value)
+	if (exp === null || exp !== e) {
+		exp = e;
+		s = stirling2(exp);
+	}
+
+	const n = BigInt(limit.value);
+	const r = faulhaber(n, s);
+	const result = document.querySelector("#result");
+	result.value = r;
+}
+
+function calculateStirling() {
+	const limit = document.querySelector("#stirling-limit");
+	const p = parseInt(limit.value)
+	s = stirling2(p);
+
+	const table = buildTable(s);
+	const result = document.querySelector("#stirling-result");
+	while (result.firstChild) {
+		result.removeChild(result.firstChild);
+	}
+	result.appendChild(table);
+}
+
+function buildTable(values) {
+	const table = document.createElement("table");
+	const caption = document.createElement("caption");
+	caption.textContent = "Stirling numbers S(p,k) from k=0 to k=p";
+	table.appendChild(caption);
+
+	const tbody = document.createElement("tbody");
+	table.appendChild(tbody);
+
+	const n = values.length;
+	const ks = Array(n);
+	for (let i = 0; i < n; i++) {
+		ks[i] = i;
+	}
+
+	const nrow = buildRow("k", ks);
+	tbody.appendChild(nrow);
+
+	const vrow = buildRow("S(p,k)", values);
+	tbody.appendChild(vrow);
+
+	return table;
+}
+
+function buildRow(htext, values) {
+	const row = document.createElement("tr");
+	const head = document.createElement("th");
+	head.textContent = htext;
+	row.appendChild(head);
+
+	const n = values.length;
+	for (let i = 0; i < n; i++) {
+		const elem = document.createElement("td");
+		elem.textContent = values[i];
+		row.appendChild(elem);
+	}
+
+	return row;
+}
+
+document.querySelector("#enter").addEventListener("click", () => calculate())
+document.querySelector("#stirling-enter").addEventListener("click", () => calculateStirling())