feat: First iteration, multi themes, I18N

public/js/engine/formulas.js

@@ -0,0 +1,37 @@
+// Pure math helpers. No state, no DOM.
+
+export function clamp(value, min, max) {
+  return Math.min(max, Math.max(min, value));
+}
+
+/** Price of the next item when `owned` items are already owned. */
+export function unitCost(base, growth, owned) {
+  return base * growth ** owned;
+}
+
+/** Total price of buying `count` more items (geometric series, rounded up). */
+export function bulkCost(base, growth, owned, count) {
+  if (count <= 0) return 0;
+  return Math.ceil((unitCost(base, growth, owned) * (growth ** count - 1)) / (growth - 1));
+}
+
+/** How many items `budget` can pay for, robust against float error. */
+export function maxAffordable(base, growth, owned, budget) {
+  const first = unitCost(base, growth, owned);
+  if (Number.isNaN(budget) || budget < first) return 0;
+  let n = Math.floor(Math.log((budget * (growth - 1)) / first + 1) / Math.log(growth));
+  while (n > 0 && bulkCost(base, growth, owned, n) > budget) n--;
+  while (bulkCost(base, growth, owned, n + 1) <= budget) n++;
+  return Math.max(n, 0);
+}
+
+/**
+ * Units customers want to buy per second at `price`.
+ * Demand is maxed at or below the fair price and drops steeply above it, so
+ * extra production is only worth selling at a higher price while supply is
+ * short; to sell more at the fair price, the player needs more demand.
+ */
+export function demandPerSecond(market, price, multiplier) {
+  const overpriced = Math.max(1, price / market.fairPrice);
+  return (market.baseDemand * multiplier) / overpriced ** market.elasticity;
+}