```typescript
export function safeDivide(a: number, b: number): number {
  if (!isFinite(a) || !isFinite(b)) {
    throw new Error("Both a and b must be finite numbers.");
  }
  if (b === 0 && !isNaN(b)) {
    throw new Error("Division by zero is not allowed.");
  }
  return a / b;
}

function isFinite(num: number): boolean {
  return Number.isFinite(num);
}
```