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https://github.com/xwu/NumericAnnex

Numeric facilities for Swift
https://github.com/xwu/NumericAnnex

math numerics swift

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Numeric facilities for Swift

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# NumericAnnex
NumericAnnex



NumericAnnex supplements the numeric facilities provided in the Swift standard

library.



[![Build Status](https://travis-ci.org/xwu/NumericAnnex.svg?branch=master)](https://travis-ci.org/xwu/NumericAnnex)

[![codecov](https://codecov.io/gh/xwu/NumericAnnex/branch/master/graph/badge.svg)](https://codecov.io/gh/xwu/NumericAnnex)



## 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](https://cocoapods.org),

insert the following line in your `Podfile`:



```ruby

pod 'NumericAnnex', '~> 0.1.19'

```



[Swift Package Manager](https://swift.org/package-manager/) can also be used to

add the package as a dependency. See Swift documentation for details.



## Basic Usage



```swift

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.



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.



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](https://xwu.github.io/NumericAnnex/) 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](https://github.com/xwu/NumericAnnex/blob/master/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.