```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 without causing overflow by checking if 2**i would exceed cap/base
        # If base == 0, then base * 2**i == 0, so min(cap, 0) = 0
        if base == 0:
            result.append(0.0)
            continue
        
        # Check if 2**i * base > cap, in which case we use cap
        # To avoid overflow, we can check if 2**i > cap / base
        # But cap / base might be problematic if base is very small.
        # Alternative: compute 2**i as an integer, then multiply by base.
        # If 2**i is too large to convert to float, we know the result exceeds cap (since cap is finite).
        # So we can check: if 2**i > cap / base, use cap.
        # However, cap / base could be large. Let's handle it carefully.
        
        # We need to compute min(cap, base * 2**i)
        # If base * 2**i > cap, return cap.
        # To avoid overflow, check if 2**i > cap / base.
        # But cap / base might not be an integer. Let's use a different approach.
        
        # Compute power = 2**i as an integer.
        power = 2 ** i
        # If base * power > cap, use cap.
        # To avoid overflow when converting power to float, check if power > cap / base.
        # But cap / base could be a float. Let's compute threshold = cap / base.
        # If base == 0, handled above.
        # If power > cap / base, then base * power > cap, so use cap.
        # Otherwise, compute base * power as float.
        
        # Check if power is too large to convert to float safely.
        # If power > cap / base, use cap.
        # Compute cap / base as a float.
        threshold = cap / base
        if power > threshold:
            result.append(cap)
        else:
            result.append(base * power)
    
    return result
```