3 ms·
Sollya is probably the best modern tool for doing this. Under the hood, it does a Remez approximation followed by LLL to quantize to floating point. No use of
by pclmulqdq 2y ago
Sollya is probably the best modern tool for doing this. Under the hood, it does a Remez approximation followed by LLL to quantize to floating point. No use of Chebyshev directly.
- janwas 2y agohm, why not Chebfun? Result is a rational polynomial so we have to divide, but that seems fine/fast on servers.
- pclmulqdq 2y agoSollya can also do rational approximants, which are only faster in some circumstances, and Chebfun does not (as far as I know) account for floating point quantization, which is a big deal if you are trying to be accurate.
- janwas 2y agoPossible misunderstanding: I mean a rational function in the sense of Padé approximation or CF [1], not just representing individual numbers as p/q. I did not find anything related to this in Sollya [2]. [1]: https://www.jstor.org/stable/2157229 https://www.jstor.org/stable/2157229 [2]: https://www.sollya.org/releases/sollya-8.0/sollya-8.0.pdf https://www.sollya.org/releases/sollya-8.0/sollya-8.0.pdf
- pclmulqdq 2y agohttps://hal.science/hal-04093020/document https://hal.science/hal-04093020/document May not have been merged yet. Pade approximants are also less useful than you might think - it's very hard to get to truly correctly rounded functions with the division.
- janwas 2y agoThanks! Yes, that (rminimax/ratapprox) looks very interesting. I got the impression that this was separate from Sollya. Fair point about the correct rounding. We'd be fine with several ULPs.