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Written by Markus Redeker on 2024-08-09 at 08:34

@sstadnicki No, it is more interesting:

Assume that we want to interpolate between two n-dimensional vectors of reals and the costs of a multiplication and an addition are m and a respectively. Then the cost of the first method is

(2m + a)n + a

and that of the second method is

(m + 2a)n.

This means that on very old hardware on which multiplication is an expensive operation, the second method is better. With modern floating-point processing, we have m = a and the methods are equivalent.

Here I have taken “costs” as something like the required time for the operation. If we take costs as energy consumption, then I think multiplication is still more expensive an the second method is still better.

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