```ts
/**
 * Divides `a` by `b`. Throws an Error if `b` is zero (including -0), or either `a` or `b` is not a finite number.
 * @param a The dividend.
 * @param b The divisor.
 * @returns The result of dividing `a` by `b`.
 */
export function safeDivide(a: number, b: number): number {
  if (!Number.isFinite(a) || !Number.isFinite(b)) {
    throw new Error('Both arguments must be finite numbers.');
  }
  if (b === 0 || b === -0) {
    throw new Error('Divisor cannot be zero.');
  }
  return a / b;
}
```