NumericAnnex

NumericAnnex supplements the numeric facilities provided in the Swift standard
library.

Features

• The exponentiation operator ** and the compound assignment operator **=.
• Extension methods for BinaryInteger exponentiation, square root, cube root,
  greatest common divisor, and least common multiple.
• Math, a protocol for signed numeric types that support elementary functions.
• Real, a protocol for floating-point types that support elementary functions
  and a selection of special functions.
• PRNG, a protocol for pseudo-random number generators.
• Rational, a value type to represent rational values which supports division
  by zero.
• Complex, a value type to represent complex values in Cartesian form.
• Random and Random.Xoroshiro, two reference types implementing efficient
  pseudo-random number generators.

Note: This project is in the early stages of development and is not
production-ready at this time.

Requirements

NumericAnnex requires Swift 4.1 (swift-4.1-branch) or Swift 4.2 (master). On
Apple platforms, it also requires the Security framework for cryptographically
secure random bytes.

Installation

After NumericAnnex has been cloned or downloaded locally, build the library
using the command swift build (macOS) or swift build -Xcc -D_GNU_SOURCE
(Linux). Run tests with the command swift test (macOS) or
swift test -Xcc -D_GNU_SOURCE (Linux). An Xcode project can be generated with
the command swift package generate-xcodeproj.

To add the package as a dependency using CocoaPods,
insert the following line in your Podfile:

pod 'NumericAnnex', '~> 0.1.19'

Swift Package Manager can also be used to
add the package as a dependency. See Swift documentation for details.

Basic Usage

import NumericAnnex

print(2 ** 3)
// Prints "8".

print(4.0 ** 5.0)
// Prints "1024.0".

print(Int.cbrt(8))
// Prints "2".

print(Double.cbrt(27.0))
// Prints "3.0".

var x: Ratio = 1 / 4
// Ratio is a type alias for Rational<Int>.

print(x.reciprocal())
// Prints "4".

x *= 8
print(x + x)
// Prints "4".

x = Ratio(Float.phi) // Golden ratio.
print(x)
// Prints "13573053/8388608".

var z: Complex64 = 42 * .i
// Complex64 is a type alias for Complex<Float>.

print(Complex.sqrt(z))
// Prints "4.58258 + 4.58258i".

z = .pi + .i * .log(2 - .sqrt(3))
print(Complex.cos(z).real)
// Prints "-2.0".

Documentation

All public protocols, types, and functions have been carefully documented in the
code. See the formatted reference for
details.

The project adheres to many design patterns found in the Swift standard library.
For example, Math types provide methods such as cubeRoot() and tangent()
just as FloatingPoint types provide methods such as squareRoot().

No free functions are declared in this library unless they overload existing
ones in the Swift standard library. Instead, functions such as cbrt(_:) and
tan(_:) are provided as static members. This avoids collisions with C standard
library functions that you may wish to use. It also promotes clarity at the call
site when the result of a complex operation differs from that of its real
counterpart (e.g., Complex128.cbrt(-8) != -2).

Future Directions

• Add more tests, including performance tests
• Design and implement additional methods on PRNG

License

All original work is released under the MIT license. See
LICENSE for details.

Portions of the complex square root and elementary transcendental functions use
checks for special values adapted from libc++. Code in libc++ is dual-licensed
under the MIT and UIUC/NCSA licenses.