```typescript
/** a divided by b. */
export function safeDivide(a: number, b: number): number {
  if (typeof a !== "number" || typeof b !== "number" || !isFinite(a) || !isFinite(b)) {
    throw new Error('Both arguments must be finite numbers.');
  }
  
  if (b === 0 || b === -0){
      throw new Error('Divisor cannot be zero or -zero.');
  }
  return a / b;
}
```