```ts
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 prefix = 0;
  for (let i = 0; i < 4; i++) {
    const octet = parseInt(parts[i], 10);
    if (isNaN(octet) || octet < 0 || octet > 255 || (octet.toString().length > 1 && parts[i].startsWith("0"))) {
      throw new Error(`invalid octet in mask: ${parts[i]}`);
    }
    const ones = octet === 0 ? 0 : 32 - Math.floor(Math.log2(256 - octet));
    if (i > 0 && ones !== 8) {
      throw new Error("mask has broken run of leading one bits");
    }
    prefix += ones;
  }
  return prefix;
}
```