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> The rest of the human race wants approximately the right answer reasonably quickly But numerical analysts really require being able to specify the semantics

> The rest of the human race wants approximately the right answer reasonably quickly But numerical analysts really require being able to specify the semantics of calculations precisely in order to write libraries that mere mortals can use to get the approximate right answer. A quick perusal of any numerical analysis textbook should convince you that order of evaluation, order of truncation, overflow modes, and the like are very relevant for being able to write a library that has the right order of error. Something like Kahan summation will have vastly different results depend on whether intermediate calculations are done at a higher precision or whether the compiler is allowed to reorder expressions. In fact, an overly aggressive optimizing compiler will make Kahan summation simply fail [1]. If all you're doing is adding a few numbers together, by all means, you don't need or want to think about precise semantics. But if you've ever used BLAS or Numpy or any other math package, you very much depend on languages and compilers being pedantic as possible in spelling out how floating point gets evaluated. [1] https://en.wikipedia.org/wiki/Kahan_summation_algorithm https://en.wikipedia.org/wiki/Kahan_summation_algorithm

alfalfasprout 10y ago
Actually, BLAS implementations usually do guarantee error bounds, but the implementation is almost always tailored for speed over precision. That said, you can always opt for extended precision at the cost of performance.
dbcurtis 10y ago
>But numerical analysts really require being able to specify the semantics of calculations precisely in order to write libraries that mere mortals can use to get the approximate right answer. >A quick perusal of any numerical analysis textbook should convince you that order of evaluation, order of truncation, overflow modes, and the like are very relevant for being able to write a library that has the right order of error. I see your point. I've done more than peruse numerical analysis textbooks, and as an old-school CPU logic designer, I've forgotten more about implementing floating point than most programmers know to start with. But your point is not in conflict with mine. Numerical analysis requires precise operation ordering. Most people not only don't care, they don't have sufficient understanding of the issues that you could even convince them to care.

alfalfasprout 10y ago

Actually, BLAS implementations usually do guarantee error bounds, but the implementation is almost always tailored for speed over precision. That said, you can always opt for extended precision at the cost of performance.

dbcurtis 10y ago

>But numerical analysts really require being able to specify the semantics of calculations precisely in order to write libraries that mere mortals can use to get the approximate right answer. >A quick perusal of any numerical analysis textbook should convince you that order of evaluation, order of truncation, overflow modes, and the like are very relevant for being able to write a library that has the right order of error. I see your point. I've done more than peruse numerical analysis textbooks, and as an old-school CPU logic designer, I've forgotten more about implementing floating point than most programmers know to start with. But your point is not in conflict with mine. Numerical analysis requires precise operation ordering. Most people not only don't care, they don't have sufficient understanding of the issues that you could even convince them to care.