Contents

oscbyspro/numberick

✨ An arithmagick overhaul in Swift.

Table of Contents

<a name="nbkcorekit"/>

NBKCoreKit ([Sources][COR/S], [Tests][COR/T], [Benchmarks][COR/B])

A new protocol hierarchy that refines Swift's standard library.

Protocols

Models

<a name="nbkdoublewidthkit"/>

[NBKDoubleWidthKit][DBL/D] ([Sources][DBL/S], [Tests][DBL/T], [Benchmarks][DBL/B])

A composable, large, fixed-width, two's complement, binary integer.

🧩 Composable

`NBKDoubleWidth is a generic software model for working with fixed-width integers larger than one machine word. Its bit width is double the bit width of its High` component. In this way, you may construct new integer types:

typealias  Int256 = NBKDoubleWidth< Int128>
typealias UInt256 = NBKDoubleWidth<UInt128>

💕 Two's Complement

Like other binary integers, `NBKDoubleWidth` has two's complement semantics. 

The two's complement representation of  0 is an infinite sequence of 0s.
The two's complement representation of -1 is an infinite sequence of 1s.

🏰 Fixed-Width Integer

Each `NBKDoubleWidth` has a fixed bit width, and so do its halves. This design comes with a suite of overflow and bit-casting operations. The even split also lends itself to divide-and-conquer strategies.

📖 Trivial UInt Collection

`NBKDoubleWidth models a trivial UInt collection, where UInt is an unsigned machine word. It contains at least two words, but the exact count depends on the platform's architecture. You should, therefore, use properties like startIndex and endIndex` instead of hard-coded indices.

// Int256 and UInt256, as constructed on a 64-bit platform:
┌───────────────────────────┐ ┌───────────────────────────┐
│           Int256          │ │          UInt256          │
├─────────────┬─────────────┤ ├─────────────┬─────────────┤
│    Int128   │   UInt128   │ │   UInt128   │   UInt128   │
├──────┬──────┼──────┬──────┤ ├──────┬──────┼──────┬──────┤
│  Int │ UInt │ UInt │ UInt │ │ UInt │ UInt │ UInt │ UInt │
└──────┴──────┴──────┴──────┘ └──────┴──────┴──────┴──────┘

Swift's type system enforces proper layout insofar as Int and UInt are the only types in the standard library that meet its type requirements. Specifically, only Int and UInt have NBKCoreInteger<UInt> Digit types.

🚀 Single Digit Arithmagick

Alongside its ordinary arithmagick operations, `NBKDoubleWidth` provides single-digit operations, where a digit is an un/signed machine word. These operations are more efficient for small calculations. Here are some examples:

Int256(1) + Int(1), UInt256(1) + UInt(1)
Int256(2) - Int(2), UInt256(2) - UInt(2)
Int256(3) * Int(3), UInt256(3) * UInt(3)
Int256(4) / Int(4), UInt256(4) / UInt(4)
Int256(5) % Int(5), UInt256(5) % UInt(5)

<a name="nbkflexiblewidthkit"/>

[NBKFlexibleWidthKit][FLX/D] ([Sources][FLX/S], [Tests][FLX/T], [Benchmarks][FLX/B])

[!IMPORTANT] It's a work in progress. I may rework it at any time.

Models

Fibonacci

NBKFibonacciXL(0) // (index: 0, element: 0, next: 1)
NBKFibonacciXL(1) // (index: 1, element: 1, next: 1)
NBKFibonacciXL(2) // (index: 2, element: 1, next: 2)
NBKFibonacciXL(3) // (index: 3, element: 2, next: 3)
NBKFibonacciXL(4) // (index: 4, element: 3, next: 5)
NBKFibonacciXL(5) // (index: 5, element: 5, next: 8)

It uses a fast double-and-add algorithm:

NBKFibonacciXL(10_000_000) // 2.3s on MacBook Pro, 13-inch, M1, 2020

But you can also step through it manually:

mutating func increment() { ... } // index + 1
mutating func decrement() { ... } // index - 1
mutating func    double() { ... } // index * 2

<a name="installation"/>

Installation

Numberick contains several modules. Import some or all of them.

SemVer 2.0.0

Major version zero (0.y.z) is for initial development.

Anything MAY change at any time.

The public API SHOULD NOT be considered stable.

Using SwiftPM

Add this package to your list of package dependencies.

.package(url: "https://github.com/oscbyspro/Numberick.git", .upToNextMinor(from: "0.17.0")),

Choose target dependencies from the products in Package.swift.

.product(name: "Numberick",           package: "Numberick"),
.product(name: "NBKCoreKit",          package: "Numberick"),
.product(name: "NBKDoubleWidthKit",   package: "Numberick"),
.product(name: "NBKFlexibleWidthKit", package: "Numberick"),

Using CocoaPods

Choose target dependencies from the pods listed in the root directory.

pod "Numberick",                   "~> 0.17.0"
pod "Numberick-NBKCoreKit",        "~> 0.17.0"
pod "Numberick-NBKDoubleWidthKit", "~> 0.17.0"

<a name="acknowledgements"/>

Acknowledgements

This project is inspired by [Int128][Apple/Int128] and [DoubleWidth][Apple/DoubleWidth] by Apple.

[NBK/D]: https://oscbyspro.github.io/Numberick/documentation/numberick [DBL/D]: https://oscbyspro.github.io/Numberick/documentation/numberick/nbkdoublewidth [FLX/D]: https://oscbyspro.github.io/Numberick/documentation/numberick/nbkflexiblewidth [SIG/D]: https://oscbyspro.github.io/Numberick/documentation/numberick/nbksigned

[COR/S]: Sources/NBKCoreKit [DBL/S]: Sources/NBKDoubleWidthKit [FLX/S]: Sources/NBKFlexibleWidthKit

[COR/T]: Tests/NBKCoreKitTests [DBL/T]: Tests/NBKDoubleWidthKitTests [FLX/T]: Tests/NBKFlexibleWidthKitTests

[COR/B]: Tests/NBKCoreKitBenchmarks [DBL/B]: Tests/NBKDoubleWidthKitBenchmarks [FLX/B]: Tests/NBKFlexibleWidthKitBenchmarks

[Apple/Int128]: https://github.com/apple/swift/blob/main/stdlib/public/core/Int128.swift.gyb [Apple/DoubleWidth]: https://github.com/apple/swift/blob/main/test/Prototypes/DoubleWidth.swift.gyb

Package Metadata

Repository: oscbyspro/numberick

Default branch: main

README: README.md