GEN-1: add vitest + exact Fraction utility

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

gerbil-manager-web/src/genetics/fraction.ts

@@ -0,0 +1,70 @@
+/**
+ * Exact rational arithmetic for genetics probabilities.
+ *
+ * Punnett distributions are unions of dyadic/rational fractions (1/4, 3/16, …).
+ * Using exact fractions instead of floats keeps probabilities precise and lets
+ * us assert e.g. "exactly 1/4 of young are lost" after renormalisation.
+ */
+export interface Fraction {
+  readonly num: number
+  readonly den: number
+}
+
+function gcd(a: number, b: number): number {
+  a = Math.abs(a)
+  b = Math.abs(b)
+  while (b !== 0) {
+    ;[a, b] = [b, a % b]
+  }
+  return a
+}
+
+/** Create a normalised (reduced, positive-denominator) fraction. */
+export function frac(num: number, den: number): Fraction {
+  if (den === 0) throw new Error('Fraction denominator must not be zero')
+  if (den < 0) {
+    num = -num
+    den = -den
+  }
+  if (num === 0) return { num: 0, den: 1 }
+  const g = gcd(num, den)
+  return { num: num / g, den: den / g }
+}
+
+export const ZERO: Fraction = { num: 0, den: 1 }
+export const ONE: Fraction = { num: 1, den: 1 }
+
+export function add(a: Fraction, b: Fraction): Fraction {
+  return frac(a.num * b.den + b.num * a.den, a.den * b.den)
+}
+
+export function multiply(a: Fraction, b: Fraction): Fraction {
+  return frac(a.num * b.num, a.den * b.den)
+}
+
+export function divide(a: Fraction, b: Fraction): Fraction {
+  if (b.num === 0) throw new Error('Cannot divide by zero fraction')
+  return frac(a.num * b.den, a.den * b.num)
+}
+
+export function equals(a: Fraction, b: Fraction): boolean {
+  return a.num * b.den === b.num * a.den
+}
+
+export function toNumber(f: Fraction): number {
+  return f.num / f.den
+}
+
+/** Human-readable "3/16" (or "0" / "1"). */
+export function toString(f: Fraction): string {
+  if (f.num === 0) return '0'
+  if (f.den === 1) return String(f.num)
+  return `${f.num}/${f.den}`
+}
+
+/** "18.75 %" style label for display (rounded to `digits` decimals). */
+export function toPercentString(f: Fraction, digits = 2): string {
+  const pct = (f.num / f.den) * 100
+  const rounded = Number(pct.toFixed(digits))
+  return `${rounded} %`
+}