alt Hacker NewsFixed point arithmetic isn't truly associative unless they have infinite precision. The second you hit a limit or saturate/clamp a value the result very much depends on order of operations.
Fixed point arithmetic isn't truly associative unless they have infinite precision. The second you hit a limit or saturate/clamp a value the result very much depends on order of operations.
Ah yes, I forgot about saturating arithmetic. But even for that, you wouldn't need infinite precision for all values, you'd only need "enough" precision for the intermediate values, right? E.g. for an inner product of two N-element vectors containing M-bit integers, an accumulator with at least ceil(log2(N))+2*M bits would guarantee no overflow.