```ts
/** a divided by b. */
export function safeDivide(a: number, b: number): number {
  if (b === Infinity || b === -Infinity) {
    throw new Error('Division by infinity not allowed.');
  }
  if (!Number.isFinite(a) || !Number.isFinite(b)) {
    throw new Error('Both arguments must be finite numbers.');
  }
  if (b === 0) {
    throw new Error('Division by zero not allowed.');
  }
  return a / b;
}
```