feat(math): add fraction conversions, GCD, LCM

Author: postspectacular

packages/math/package.json

@@ -104,6 +104,9 @@
 		"./fit": {
 			"default": "./fit.js"
 		},
+		"./fraction": {
+			"default": "./fraction.js"
+		},
 		"./int": {
 			"default": "./int.js"
 		},

packages/math/src/fraction.ts

@@ -0,0 +1,103 @@
+import type { FnN2 } from "@thi.ng/api";
+
+/**
+ * Iteratively computes Greatest Common Divisor of given `a` and `b`.
+ *
+ * @remarks
+ * Reference:
+ *
+ * - https://en.wikipedia.org/wiki/Greatest_common_divisor
+ *
+ * @param a
+ * @param b
+ */
+export const gcd: FnN2 = (a, b) => {
+	a = Math.abs(a);
+	b = Math.abs(b);
+	while (b !== 0) {
+		const tmp = b;
+		b = a % b;
+		a = tmp;
+	}
+	return a;
+};
+
+/**
+ * Computes Least Common Multiple for given `a` and `b`. Returns zero if either
+ * input is zero.
+ *
+ * @remarks
+ * Reference:
+ *
+ * - https://en.wikipedia.org/wiki/Least_common_multiple
+ *
+ * @param a
+ * @param b
+ */
+export const lcm: FnN2 = (a, b) => {
+	if (!Number.isFinite(a) || !Number.isFinite(b))
+		throw new Error("both inputs must be finite");
+	return a && b ? Math.abs(a * b) / gcd(a, b) : 0;
+};
+
+/**
+ * Converts given `x` to a fraction with optional `maxDenom`inator, using
+ * continued fractions for best possible precision.
+ *
+ * @remarks
+ * Reference:
+ *
+ * - https://en.wikipedia.org/wiki/Continued_fraction
+ *
+ * @example
+ * ```ts tangle:../export/as-fraction.ts
+ * import { asFraction } from "@thi.ng/math";
+ *
+ * console.log(Math.PI, asFraction(Math.PI));
+ * // 3.141592653589793 [1146408, 364913]
+ *
+ * // keep denominator <= 1000
+ * console.log(Math.PI, asFraction(Math.PI, 1000));
+ * // 3.141592653589793 [ 355, 113 ]
+ * ```
+ *
+ * @param x
+ * @param maxDenom
+ */
+export const asFraction = (x: number, maxDenom = 1e6) => {
+	if (!Number.isFinite(x)) throw new Error("input must be a finite");
+	if (Number.isInteger(x)) return [x, 1];
+
+	const sign = Math.sign(x);
+	x = Math.abs(x);
+
+	let n0 = 0;
+	let n1 = 1;
+	let d0 = 1;
+	let d1 = 0;
+
+	while (true) {
+		const i = Math.floor(x);
+		const d2 = i * d1 + d0;
+		if (d2 > maxDenom) break;
+
+		const n2 = i * n1 + n0;
+		n0 = n1;
+		n1 = n2;
+		d0 = d1;
+		d1 = d2;
+
+		const rem = x - i;
+		if (rem < Number.EPSILON) break;
+		x = 1 / rem;
+	}
+
+	return [sign * n1, d1];
+};
+
+/**
+ * Reverse op of {@link asFraction}. Converts a fraction tuple to a JS number.
+ *
+ * @param fraction
+ */
+export const asFloat = ([a, b]: [number, number]) => a / b;

packages/math/src/index.ts

@@ -7,6 +7,7 @@ export * from "./eqdelta.js";
 export * from "./extrema.js";
 export * from "./easing.js";
 export * from "./fit.js";
+export * from "./fraction.js";
 export * from "./int.js";
 export * from "./interval.js";
 export * from "./libc.js";