Hey all, lots of updates in this release:
First, the big features:
Differentiable and Float16 support is live in Swift Numerics. These are protected behind swift version checks, so you'll only see them when you're building with a Swift 5.3 or later toolchain (because earlier toolchains don't have the necessary support). For Float16, you need to also be targeting a platform with support in the standard library (i.e. not macOS). For Differentiable, you need to be using a toolchain that was built with differentiable programming support enabled.
Approximate equality comparisons have been added for types conforming to Numeric when the associatedtype Magnitude conforms to FloatingPoint. This includes all of the Real types, but also includes Complex, and can be extended to lots of other useful types as well. The most basic use is:
which performs a comparison with default relative tolerance. You can manually specify an absolute or relative tolerance (or both), as well as a norm to use via overloads and optional arguments. Consult the doc comments for more information now, but I plan to write a more in-depth README for the feature in the coming weeks.
Two implementation details have also been added on
Real , which are useful for building out other parts of the library:
cosMinusOne(_ x: Self) -> Self
This is "just
expMinusOne(_:Self), but for cosine". It's a somewhat niche feature (and trivially implementable via the half-angle formula), but it turns out to be useful when building out ElementaryFunctions support for Complex types, so it seems to make good sense to make more broadly available.
_mulAdd(_ a: Self, _ b: Self, _ c: Self) -> Self
This is intended to use either an FMA or separate multiply and add to evaluate
a*b + cas efficiently as possible. This is a much more niche implementation detail, and the name is subject to change (hence the underscore), but it's useful enough to expose for anyone who wants to use it.
Speaking of ElementaryFunctions support for Complex types, that's something that's in progress now (#146). I'll be working through it over the next few weeks, and would love to have contributions. If you'd like to contribute, be sure to read the implementation goals. Simply borrowing from C or C++ implementations will probably not be sufficient for the goals we have and semantics defined for Complex, but you can use them as a starting point if you're willing to iterate with me a bit.