// Pure math helpers. No state, no DOM.

export function clamp(value, min, max) {
  return Math.min(max, Math.max(min, value));
}

/**
 * Demand bonus from owning chips: diminishing returns (logarithmic), so a big
 * lucky streak can never run away with the game.
 */
export function chipDemandBonus(chips, gamble) {
  return 1 + gamble.chipBonusScale * Math.log2(1 + Math.max(0, chips));
}

/** 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);
}

/**
 * Raw-material price per unit of material, before market noise. Expensive at
 * first, then cheaper relative to revenue as the operation scales
 * (economies of scale): it falls from `startUnitPrice` towards `floorUnitPrice`.
 */
export function materialUnitPrice(mm, totalProduced) {
  const scale = 1 / Math.sqrt(1 + totalProduced / mm.scale);
  return mm.floorUnitPrice + (mm.startUnitPrice - mm.floorUnitPrice) * scale;
}

/**
 * What one purchase of material looks like.
 *
 * The lot covers `batchSecondsOfProduction` of current output (in doubling
 * steps, never below `minBatch`), times `sizeMultiplier` from the "bigger
 * stacks" upgrades. The price of a lot is proportional to its size: a bigger
 * stack costs more in total, while the price PER UNIT keeps falling with scale
 * (see materialUnitPrice). `factor` is the market's current noise and
 * `discount` comes from upgrades. Cost is exact to the cent.
 */
export function materialBatch(mm, totalProduced, rate, factor, discount, sizeMultiplier = 1) {
  const basis = rate * mm.batchSecondsOfProduction;
  const doublings = Math.max(0, Math.floor(Math.log2(Math.max(1, basis / mm.minBatch))));
  const size = mm.minBatch * 2 ** doublings * sizeMultiplier;
  const cents = size * materialUnitPrice(mm, totalProduced) * factor * discount;
  return { size, cost: Math.max(0.01, Math.round(cents * 100) / 100) };
}

/**
 * Units customers want to buy per second at `price`: a smooth curve, with more
 * demand the lower the price and less the higher it is (`referencePrice` is
 * just where demand equals baseDemand x multiplier).
 */
export function demandPerSecond(market, price, multiplier) {
  return market.baseDemand * multiplier * (market.referencePrice / price) ** market.elasticity;
}

/**
 * The price at which customers buy exactly what is produced. Selling for less
 * gains no volume (everything is already sold); selling for more leaves stock
 * unsold. It moves with output and every demand bonus, and the UI deliberately
 * does not reveal it: the player finds it from the market feedback.
 */
export function balancedPrice(market, supplyPerSecond, multiplier) {
  const demandAtReference = market.baseDemand * multiplier;
  return market.referencePrice * (demandAtReference / supplyPerSecond) ** (1 / market.elasticity);
}