β¨ An arithmagick overhaul in Swift.
Package | Swift | iOS | Mac Catalyst | macOS | tvOS | watchOS |
---|---|---|---|---|---|---|
0.17.0 | 5.7 | 14.0 | 14.0 | 11.0 | 14.0 | 7.0 |
Important
The development of this project has moved over to Ultimathnum.
It turns out that I need ~(~(x)) to equal x for all x.
This is not possible with arbitrary unsigned integers at the moment.
So I'm working on a novel abstraction that permits this.
It unifies all sizes and brings recovery mechanisms to generic code.
Also, I'm open to work.
NBKCoreKit (Sources, Tests, Benchmarks)
A new protocol hierarchy that refines Swift's standard library.
- NBKBinaryInteger
- NBKBitPatternConvertible
- NBKCoreInteger
- NBKFixedWidthInteger
- NBKSignedInteger
- NBKUnsignedInteger
A composable, large, fixed-width, two's complement, binary integer.
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>
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.
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.
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:
βββββββββββββββββββββββββββββ βββββββββββββββββββββββββββββ
β Int256 β β UInt256 β
βββββββββββββββ¬ββββββββββββββ€ βββββββββββββββ¬ββββββββββββββ€
β Int128 β UInt128 β β UInt128 β UInt128 β
ββββββββ¬βββββββΌβββββββ¬βββββββ€ ββββββββ¬βββββββΌβββββββ¬βββββββ€
β Int β UInt β UInt β UInt β β UInt β UInt β UInt β UInt β
ββββββββ΄βββββββ΄βββββββ΄βββββββ ββββββββ΄βββββββ΄βββββββ΄βββββββ
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.
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)
Important
It's a work in progress. I may rework it at any time.
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
Numberick contains several modules. Import some or all of them.
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"
This project is inspired by Int128 and DoubleWidth by Apple.