```ts
/** a divided by b */
export function safeDivide(a: number, b: number): number {
  if (typeof a !== 'number' || typeof b !== 'number') {
    throw new Error("Both arguments must be numbers.");
  }
  if (a === Infinity || b === Infinity || a === -Infinity || b === -Infinity) {
    if (Number.isNaN(a) || Number.isNaN(b)) {
      throw new Error("Both arguments must be finite numbers.");
    } else if (
      a > 0 && b < 0 ||
      b > 0 && a < 0
    ) {
      return Infinity; // For negative infinity, divide both by -1 to keep the sign.
    }
  }
  if (b === 0 || Number.isNaN(b)) {
    throw new Error("Divisor cannot be zero.");
  }
  
  return a / b;
}
```