```
export function maskFromPrefix(prefix: number): string {
  if (!Number.isInteger(prefix) || prefix < 0 || prefix > 32) {
    throw new Error("prefix must be an integer from 0 to 32");
  }
  const octets: number[] = [];
  for (let slot = 0; slot < 4; slot += 1) {
    const ones = Math.min(8, Math.max(0, prefix - slot * 8));
    octets.push(256 - 2 ** (8 - ones));
  }
  return octets.join(".");
}

export function prefixFromMask(mask: string): number {
  if (typeof mask !== "string") {
    throw new Error("mask must be a string");
  }
  const parts = mask.split(".");
  if (parts.length !== 4) {
    throw new Error("mask must have exactly four dot-separated fields");
  }

  let totalOnes = 0;
  for (const part of parts) {
    if (!/^\d+$/.test(part)) {
      throw new Error(`invalid octet: ${part}`);
    }
    const value = parseInt(part, 10);
    if (value < 0 || value > 255) {
      throw new Error(`octet out of range: ${part}`);
    }

    // Check for leading zero in non-zero octets
    if (value !== 0 && part.startsWith("0")) {
      throw new Error(`invalid octet: ${part}`);
    }

    totalOnes += value === 255 ? 8 : Math.floor(Math.log2(256 - value));
  }

  return totalOnes;
}
```