Skeleton for complex elementary functions #146
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- Renamed scaled/unscaled to multiplied/divided - Adopted new Real module name - Adopted expMinusOne, log(onePlus:) names
Rebased on master, then cleaned up exp and expm1. New algorithm for expm1 that gives good componentwise accuracy as well as normwise. I _think_ that this is fundamentally new; I can't recall seeing it anywhere before, though it's simple enough that I expect someone has thought of it before. Also beefed up testing for exp and expm1. Left sketches of log/pow/sqrt/root in place, though I'm still working on filling out the testing for those.
NevinBR
reviewed
Aug 27, 2020
| // exp((log(gfm) + log(9/8), π/4) = exp((log(gfm*9/8), π/4)) | ||
| // = gfm*9/8 * (1/sqrt(2), 1/(sqrt(2)) | ||
| let x = T.log(.greatestFiniteMagnitude) + T.log(9/8) | ||
| let huge = Complex<T>.expMinusOne(Complex(x, .pi/4)) |
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This is in the testExp method, so it should be testing exp, not expMinusOne, right?
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Ah, yeah. Cleaned it up for expMinusOne and copied it back for improvements =)
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I've created a branch in the main Swift Numerics repo for further work on this, complex-elfns. If you'd like to contribute, please raise PRs against that branch. |
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This PR sets up some basic testing, and adds implementations for the following ElementaryFunctions on Complex:
expexpMinusOnelogpowrootsqrtexpandexpMinusOneare reasonably well tested. Additional testing is needed for the latter four. I also added stubs for all the other functions (which simply fatalError), except for the functions that can be defined by trivial symmetries. I expect to work through the remaining operations fairly quickly, but contributions are welcome and encouraged.If you want to make contributions, I would prefer PRs that add only a single function (or its obvious counterparts, e.g. sin and cos could come together), plus testing, as I expect to subject all of these implementations to fairly careful scrutiny.