```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, i.e., 2**i > cap / base
        # To avoid computing huge 2**i, we can check if i is large enough that 2**i * base > cap
        # Since cap and base are non-negative, if cap == 0, then min(cap, ...) = 0
        if cap == 0:
            result.append(0.0)
            continue
        
        # We need min(cap, base * 2**i)
        # If base * 2**i >= cap, then result is cap
        # Otherwise, result is base * 2**i
        
        # To avoid overflow, check if 2**i * base > cap
        # This is equivalent to 2**i > cap / base
        # We can compute this safely by checking if i is large enough
        
        # If i is large, 2**i can be huge. We need to check if base * 2**i > cap
        # Let's compute 2**i only when it's safe, or use logarithms
        
        # Alternative: if base * 2**i > cap, return cap
        # We can check: if 2**i > cap / base, then result = cap
        # cap / base is a float, and 2**i as int can be huge
        
        # Use logarithm to check: i * log(2) > log(cap / base)
        # But we can't import math. So we need another approach.
        
        # Actually, we can compute 2**i as int, but if it's too large to convert to float, we know base * 2**i > cap (since cap is finite)
        # So we can try to compute base * 2**i, and if OverflowError occurs, then base * 2**i > cap, so result = cap
        
        try:
            power = 2 ** i
            value = base * power
            if value > cap:
                result.append(cap)
            else:
                result.append(value)
        except OverflowError:
            result.append(cap)
    
    return result
```