BaseMath

Basic math functions for float and double arrays in Swift for Mac or Linux, with no dependencies, via the BaseVector protocol. They are generally around 3-5x faster than standard swift loops or maps, since they use pointers, which avoids the overhead of Swift’s copy-on-write checking. The following functions are provided (all also have a version suffixed with _ and a version prefixed with sum - see below of details):

• Binary functions,: sqr, abs, min, max, pow, atan2, copysign, fdim, fmax, fmin, hypot, nextafter, add, sub, mul, div, subRev, divRev
• Unary functions,: acos, acosh, asin, asinh, atan, atanh, cbrt, cos, cosh, erf, erfc, exp, exp2, expm1, log, log10, log1p, log2, logb, nearbyint, rint, sin, sinh, tan, tanh, tgamma

Use it with Swift Package Manager by adding to your Package.swift:

dependencies: [
    .package(url:"https://github.com/jph00/BaseMath.git", from: "1.0.0"),
]

For reasonable performance, compile with make (which is also required if you make changes to the gyb templates) or use:

swift build -Xswiftc -Ounchecked -Xcc -ffast-math -Xcc -O2 -Xcc -march=native

This library is used by SwiftyMKL, which adds more optimized versions of the functions from Intel’s Performance Libraries, along with various linear algebra and statistical functions.

Math functions from Foundation (which in turn provides the functions available in math.h) are used, except for sum() (and sum${f}(), where ${f} is a function name from math.h), which are written in C, since reductions in Swift are currently not vectorized. The standard math operators are also provided, including optimized assignment versions. Functions with _ suffix are in-place. In addition the sqr function is provided. Note that abs is called fabs in C versions since that’s what it’s called in math.h.

Because the library uses pointers, Swift’s copy-on-write and let immutability are bypassed. Use the provided copy() method to get a real copy of an Array.

To avoid surprises, you might prefer to use the provided AlignedStorage struct, which supports much of the same functionality as Array, but doesn’t use copy-on-write, and aligns memory for (sometimes) better performance. In addition, UnsafeMutableBufferPointer is extended to conform to BaseVector so it also gets the same functionality.

After import BaseVector you’ll find that all the standard unary and binary math functions have been added to Array for floats and doubles, along with reduction versions of each which start with sum (e.g sumabs, sumcos, etc).

See the test suite for examples of use (note that tests won’t run on Mac due to objective-c xctest issues). For more information on background and implementation details, see [this article] (TBA).