2 ms·
The question of stability of the algorithm is interesting, the paper does not seem to discuss it though. You are correct that we should expect the algorithms to
by constantcrying 1y ago
The question of stability of the algorithm is interesting, the paper does not seem to discuss it though. You are correct that we should expect the algorithms to deliver different results.
>This and others optimizations are trading less multiplication for more additions, but from the little I know, on floating point additions and subtractions are risky precision wise, while multiplications are harmless.
Certainly not true. In general different orders of magnitude are a problem. With multiplication and division these are more serve problems, as they lead to greater changes in magnitude, although even that is a generalization.
- wizzwizz4 1y agoDifferent orders of magnitude aren't a problem when multiplying floats, because the order-of-magnitude portion gets translated into addition of exponents. They're a problem with fixed point: might you have been thinking of that?
- Dylan16807 1y agoWe're not looking at instructions in a vacuum. No matter what you have both multiplications and additions happening. So they're making a point that if you apply more multiplications before the inevitable addition, you are likely increasing the danger levels of that addition.
- wizzwizz4 1y agoOh, if one of the multiplications yields a positive number, and another yields a negative number of similar magnitude? That makes sense; I forgot linear spaces were over fields.