5 ms·
I've had good results in the past with sollya: https://www.sollya.org/ https://www.sollya.org/. Note: results. The software itself is a bit of a pain to use.
by orlp 2y ago
I've had good results in the past with sollya: https://www.sollya.org/ https://www.sollya.org/.
Note: results. The software itself is a bit of a pain to use.
- pclmulqdq 2y agoSollya 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.