[image] Functional programming is not capable of achieving absolute top performance Obviously, sum(x), std(x) is the cleanest but it isn’t the fastest, as I assume that approach needs to scan through the vector x twice. MOST likely you call sum, then std, i.e. separate loops and scan twice, BU…

[image] Palli: The compiler is allowed the reverse order or even more advanced (because these are pure functions): No it’s not. x + y is pure, but (x + y) + z \ne x + (y + z) for floating-point numbers (in general), so the compiler isn’t allowed to re-associate without some explicit annotati…

The compiler is allowed to reorder when pure, as you say in practice always including for this, and see below for Postis float-like (and well also allowed for the standard integers… not though all types, e.g. not for saturated). [image] stevengj: A single-pass algorithm looks fundamentally diff…

[image] Functional programming is not capable of achieving absolute top performance [image] stevengj: A single-pass algorithm looks fundamentally different than the two-pass algorithm […] Why is that exactly? There are plenty of articles on single-pass numerically stable algorithms for …

[image] stevengj: If it fits in the cache then you don’t need to reverse the order either. The oldest data is most likely to no longer be in cache, why reverse seems better, when scanning backwards in the second, svd phase. I was wrong writing then it needs all to fit in cache (that would be …

[image] Palli: The oldest data is most likely to no longer be in cache, why reverse seems better, when scanning backwards in the second, svd phase. I was wrong writing then it needs all to fit in cache (that would be ideal, yes) but would degrade gracefully if the data isn’t no longer all in cac…

Compilers, purity, and variance computation

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Compilers, purity, and variance computation

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