```python
def retry_delays(attempts, base, cap):
    if isinstance(attempts, bool) or not isinstance(attempts, int):
        raise TypeError("attempts must be a non-negative integer")
    if attempts < 0:
        raise ValueError("attempts must be non-negative")
    if base < 0:
        raise ValueError("base must be non-negative")
    if cap < 0:
        raise ValueError("cap must be non-negative")
    
    result = []
    for i in range(attempts):
        # Compute base * 2**i carefully to avoid overflow
        # If base is 0, delay is 0
        if base == 0:
            delay = 0
        else:
            # Check if base * 2**i would exceed cap
            # We can compare using logarithms or iterative multiplication
            # To avoid overflow, we can check if 2**i * base > cap
            # Since cap is non-negative, if base * 2**i >= cap, use cap
            # We need to avoid computing 2**i as a huge int then converting to float
            
            # Approach: compute 2**i as int, but if it's too large, we know the result will be >= cap
            # We can check: if base * (2**i) >= cap, then delay = cap
            # But base * (2**i) could overflow when converting to float
            
            # Better approach: use logarithms to check if base * 2**i > cap
            # log2(base * 2**i) = log2(base) + i
            # If log2(base) + i > log2(cap), then base * 2**i > cap
            
            import math
            if base == 0:
                delay = 0
            elif cap == 0:
                delay = 0
            else:
                # Check if base * 2**i > cap
                # Use log comparison to avoid overflow
                if base > 0 and cap > 0:
                    log_base = math.log2(base)
                    log_cap = math.log2(cap)
                    if log_base + i > log_cap:
                        delay = cap
                    else:
                        delay = base * (2 ** i)
                else:
                    delay = base * (2 ** i)
        result.append(delay)
    return result
```