```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 converting huge int to float
        # If base is 0, delay is 0
        if base == 0:
            delay = 0
        else:
            # Check if base * 2**i exceeds cap
            # We need to compare base * 2**i with cap
            # Since cap is a float, we need to handle carefully
            # If 2**i is too large, base * 2**i will definitely exceed cap (if cap is finite)
            # But we need to avoid OverflowError when converting int to float
            
            # Approach: if base * 2**i > cap, use cap
            # To check this without overflow:
            # If base == 0, handled above
            # If cap == 0, delay is 0
            if cap == 0:
                delay = 0
            else:
                # Check if base * 2**i > cap
                # We can compute 2**i as int, then multiply by base
                # But base might be float, so base * 2**i could overflow when converting 2**i to float
                
                # Alternative: check if 2**i > cap / base (if base > 0)
                # But cap / base might be problematic if base is very small
                
                # Safer approach: if 2**i is large enough that base * 2**i > cap, use cap
                # We can check: if base * 2**i > cap
                # To avoid overflow, first check if 2**i alone is so large that even the smallest positive base would exceed cap
                # Actually, let's think differently:
                # If base > 0 and cap > 0:
                #   We want min(cap, base * 2**i)
                #   If base * 2**i > cap, return cap
                #   Otherwise, return base * 2**i
                
                # To check base * 2**i > cap without overflow:
                # If 2**i > cap / base, then base * 2**i > cap
                # But cap / base could be inf or have precision issues
                
                # Let's use a different approach:
                # If base is an int, base * 2**i is an int, and we can compare with cap (float)
                # If base is a float, we need to be careful
                
                # Actually, the issue is when 2**i is a huge int and we try to convert it to float for multiplication with base (float)
                
                # Let's check if 2**i is too large to convert to float
                # Python floats can represent up to about 1.8e308
                # 2**i > 1.8e308 means i > ~1024
                
                # If i > 1024, 2**i as float would overflow
                # In that case, base * 2**i (as float) would be inf, which is > cap (assuming cap is finite)
                # So we can just use cap
                
                # But we need to handle the case where base * 2**i as int is compared to cap as float
                # If base is int, base * 2**i is int, and int > float comparison works fine in Python
                # If base is float, base * 2**i requires converting 2**i to float, which can overflow
                
                # So: if base is int, we can compute base * 2**i as int and compare with cap
                # If base is float, we need to check if 2**i can be converted to float without overflow
                
                if isinstance(base, int):
                    val = base * (2 ** i)
                    if val > cap:
                        delay = cap
                    else:
                        delay = val
                else:
                    # base is float
                    # Check if 2**i can be converted to float
                    # Max float is about 1.8e308, so 2**i > 1.8e