```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 (!Number.isInteger(totalCents) || totalCents < 0) {
    throw new Error("total cents must be a non-negative integer");
  }
  if (weights.length === 0) {
    throw new Error("weights list cannot be empty");
  }
  if (weights.some(weight => !Number.isInteger(weight) || weight < 0)) {
    throw new Error("all weights must be non-negative integers");
  }
  const sum = weights.reduce((acc, weight) => acc + weight, 0);
  if (sum === 0) {
    throw new Error("weights cannot sum to zero");
  }

  let remainingCents = totalCents;
  const shares = weights.map(weight => Math.floor((totalCents * weight) / sum));

  for (let i = 0; i < remainingCents; ++i) {
    const maxRemainderIndex = shares.findIndex((share, index) => 
      share % weights[index] === Math.max(...shares.map((s, idx) => s % weights[idx]))
    );
    shares[maxRemainderIndex]++;
  }

  return shares;
}
```