```ts
/** Fixed-point money helpers: parse, format, and allocate integer cents. */

export function parseAmount(text: string): number {
  if (typeof text !== "string") {
    throw new Error("amount must be a string");
  }
  const match = /^(\d+)(?:\.(\d{2}))?$/.exec(text);
  if (match === null) {
    throw new Error(`malformed amount: ${text}`);
  }
  const whole = Number(match[1]);
  const cents = match[2] === undefined ? 0 : Number(match[2]);
  return whole * 100 + cents;
}

export function formatAmount(cents: number): string {
  if (!Number.isInteger(cents) || cents < 0) {
    throw new Error("cents must be a non-negative integer");
  }
  const whole = Math.floor(cents / 100);
  const rest = String(cents % 100).padStart(2, "0");
  return `${whole}.${rest}`;
}

export function allocateCents(totalCents: number, weights: number[]): number[] {
  if (!Array.isArray(weights) || weights.length === 0) {
    throw new Error("weights must be a non-empty array");
  }
  if (weights.some(weight => typeof weight !== "number" || weight < 0)) {
    throw new Error("all weights must be non-negative integers");
  }
  if (!Number.isInteger(totalCents) || totalCents < 0) {
    throw new Error("totalCents must be a non-negative integer");
  }
  const sum = weights.reduce((acc, weight) => acc + weight, 0);
  if (sum === 0) {
    throw new Error("weights must sum to a non-zero value");
  }

  let result = weights.map(() => Math.floor(totalCents * 100 / sum));
  let remainder = totalCents - result.reduce((acc, val) => acc + val, 0);

  const indices = Array.from({ length: weights.length }, (_, i) => i);
  indices.sort((a, b) => (totalCents * weights[b] / sum) % 1 - (totalCents * weights[a] / sum) % 1);

  for (const index of indices) {
    if (remainder > 0) {
      result[index]++;
      remainder--;
    } else {
      break;
    }
  }

  return result.map(val => Math.floor(val / 100));
}
```