```typescript
/** A safe division function that throws errors for invalid inputs. */
export function safeDivide(a: number, b: number): number {
  if (isNaN(a) || isNaN(b)) {
    throw new Error("Both arguments must be finite numbers.");
  }
  if (!Number.isFinite(a) || !Number.isFinite(b)) return NaN;

  // Handle zero division and -0
  const divisorIsZero = b === 0 || b === -0;
  if (divisorIsZero && a !== 0) {
    throw new Error("Cannot divide by zero.");
  }

  return a / b;
}
```