add junk posts

junk/faulhaber/faulhaber.js

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+/*
+ * 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())

junk/sieves/sieves.js

@@ -0,0 +1,222 @@
+/*
+ * Copyright (C) 2026 filifa
+ *
+ * License: 0BSD (https://spdx.org/licenses/0BSD.html)
+ */
+function sievePrimes(n) {
+	const isPrime = Array(n);
+
+	isPrime[0] = false;
+	isPrime[1] = false;
+	for (let i = 2; i < n; i++) {
+		isPrime[i] = true;
+	}
+
+	for (let i = 2; i < Math.sqrt(n); i++) {
+		if (!isPrime[i]) {
+			continue;
+		}
+
+		for (let j = i * i; j < n; j += i) {
+			isPrime[j] = false;
+		}
+	}
+
+	return isPrime;
+}
+
+function numDivisors(p, k) {
+	return k + 1;
+}
+
+function sumDivisors(p, k) {
+	return (p**(k+1) - 1) / (p - 1)
+}
+
+function totient(p, k) {
+	return p**(k-1) * (p - 1);
+}
+
+function radical(p, k) {
+	return p;
+}
+
+function littleOmega(p, k) {
+	return 1;
+}
+
+function bigOmega(p, k) {
+	return k;
+}
+
+function mobius(p, k) {
+	if (k === 1) {
+		return -1;
+	}
+
+	return 0;
+}
+
+function initArrays(l, r, additive) {
+	const sieve = Array(r - l);
+	const quo = Array(r - l);
+	for (let i = 0; i < r-l; i++) {
+		quo[i] = l + i;
+		if (additive) {
+			sieve[i] = 0;
+		} else {
+			sieve[i] = 1;
+		}
+	}
+
+	return [sieve, quo];
+}
+
+function sieveSegment(l, r, f, primes, additive) {
+	const [sieve, quo] = initArrays(l, r, additive);
+
+	for (let i = 0; i < primes.length; i++) {
+		if (i*i > r) {
+			break;
+		}
+
+		if (!primes[i]) {
+			continue;
+		}
+
+		sievePowers(i, l, r, f, sieve, quo, additive);
+	}
+
+	unusuals(f, sieve, quo, additive);
+
+	return sieve;
+}
+
+function unusuals(f, sieve, quo, additive) {
+	for (let i = 0; i < quo.length; i++) {
+		const q = quo[i];
+		if (q === 1) {
+			continue;
+		}
+
+		if (additive) {
+			sieve[i] += f(q, 1);
+		} else {
+			sieve[i] *= f(q, 1);
+		}
+	}
+}
+
+function sievePowers(p, l, r, f, sieve, quo, additive) {
+	let i = 1;
+	for (let q = p; q < r; q *= p) {
+		const y = f(p, i);
+		sieveMultiples(p, q, l, r, y, sieve, quo, additive);
+		i++;
+	}
+}
+
+function sieveMultiples(p, q, l, r, y, sieve, quo, additive) {
+	const low = Math.ceil(l / q);
+	for (let i = low * q; i < r; i += q) {
+		if (i % (p*q) === 0) {
+			continue;
+		}
+
+		if (additive) {
+			sieve[i - l] += y;
+		} else {
+			sieve[i - l] *= y;
+		}
+
+		quo[i - l] /= q
+	}
+}
+
+function getFunc(func) {
+	switch (func.value) {
+		case "num-divisors":
+			return [numDivisors, false];
+		case "sum-divisors":
+			return [sumDivisors, false];
+		case "totient":
+			return [totient, false];
+		case "mobius":
+			return [mobius, false];
+		case "radical":
+			return [radical, false];
+		case "little-omega":
+			return [littleOmega, true];
+		case "big-omega":
+			return [bigOmega, true];
+		default:
+			throw new Error("function not implemented!");
+	}
+}
+
+function buildTable(l, r, values) {
+	const table = document.createElement("table");
+	const caption = document.createElement("caption");
+	caption.id = "result-caption";
+	caption.textContent = "Results";
+	table.appendChild(caption);
+
+	const tbody = document.createElement("tbody");
+	table.appendChild(tbody);
+
+	const ns = Array(r-l);
+	for (let i = l; i < r; i++) {
+		ns[i - l] = i;
+	}
+
+	const nrow = buildRow("n", l, r, ns);
+	tbody.appendChild(nrow);
+
+	const vrow = buildRow("f(n)", l, r, values);
+	tbody.appendChild(vrow);
+
+	return table;
+}
+
+function buildRow(htext, l, r, values) {
+	const row = document.createElement("tr");
+	const head = document.createElement("th");
+	head.textContent = htext;
+	row.appendChild(head);
+
+	for (let i = l; i < r; i++) {
+		if (i === 0) {
+			continue;
+		}
+
+		const elem = document.createElement("td");
+		elem.textContent = values[i - l];
+		row.appendChild(elem);
+	}
+
+	return row;
+}
+
+function calculate() {
+	const lower = document.querySelector("#lower");
+	const upper = document.querySelector("#upper");
+	const func = document.querySelector("#function");
+
+	const [f, additive] = getFunc(func);
+
+	const l = parseInt(lower.value);
+	const r = parseInt(upper.value);
+	const s = Math.floor(Math.sqrt(r));
+	const primes = sievePrimes(s + 1);
+
+	const sieve = sieveSegment(l, r, f, primes, additive);
+
+	const table = buildTable(l, r, sieve);
+	const result = document.querySelector("#result");
+	while (result.firstChild) {
+		result.removeChild(result.firstChild);
+	}
+	result.appendChild(table);
+}
+
+document.querySelector("#enter").addEventListener("click", () => calculate())

styles/faulhaber.css

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+#demo-inputs {
+	display: grid;
+	grid-template-columns: 1fr 1fr;
+}
+
+#limit-label,
+#exponent-label {
+	text-align: end;
+}
+
+#enter {
+	grid-column: 2;
+}
+
+#result {
+	word-break: break-all;
+	max-height: 24lh;
+	overflow: auto;
+	display: inline-block;
+}
+
+#stirling-result {
+	margin: 1vh;
+}
+
+/* table styling */
+caption {
+	text-align: left;
+}
+
+td {
+	text-align: right;
+}

styles/junk.css

@@ -0,0 +1,47 @@
+.math-block {
+	overflow-x: auto;
+	overflow-y: hidden;
+}
+
+pre {
+	overflow: auto;
+	background-color: black;
+	color: lime;
+	padding: 1ch;
+	border: 1vh solid gray;
+}
+
+hgroup p {
+	font-style: italic;
+}
+
+figcaption {
+	text-align: center;
+}
+
+#footnote-list {
+	list-style-type: none;
+}
+
+/* table styling */
+table {
+	display: block;
+	overflow: auto;
+	border-collapse: collapse;
+}
+
+caption {
+	font-weight: bold;
+}
+
+tbody {
+	border: 2px solid black;
+}
+
+th {
+	background-color: mediumturquoise;
+}
+
+th, td {
+	border: 1px solid black;
+}

styles/sieves.css

@@ -0,0 +1,26 @@
+/* demo styling */
+#demo-inputs {
+	display: grid;
+	grid-template-columns: 1fr 1fr;
+}
+
+label {
+	text-align: end;
+}
+
+#enter {
+	grid-column: 2;
+}
+
+#result {
+	margin: 1vh;
+}
+
+/* table styling */
+#result-caption {
+	text-align: left;
+}
+
+td {
+	text-align: right;
+}