Parity Primitives

Parity — the two-element even/odd classification of integers, modelling the Z₂ group under addition and the parity of products, with zero platform dependencies.

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Quick Start

Parity is the equivalence class of an integer under modulo 2: .even or .odd. Rather than recomputing value % 2 at every site and threading a bare Bool whose meaning is ambiguous, you capture the classification once in a named type that knows its own algebra — addition (even + even = even, odd + odd = even) and multiplication (odd × odd = odd, else even) — so parity-tracking algorithms read in the vocabulary of the mathematics.

import Parity_Primitives

// Classify integers.
let a = Parity(42)   // even
let b = Parity(7)    // odd

// The Z₂ group: parity of a sum, without touching the operands' values.
print(a.adding(b))        // odd   (even + odd = odd)
print(b.adding(b))        // even  (odd + odd = even)

// Parity of a product.
print(b.multiplying(b))   // odd   (odd × odd = odd)
print(a.multiplying(b))   // even  (even × anything = even)

// The opposite parity, by method or prefix operator.
print(a.opposite)         // odd
print(!b)                 // even

Parity is Hashable, Sendable, CaseIterable, and Codable (outside Embedded). Because it is a closed two-case enum, a switch over it is exhaustive without a default.

To carry a payload alongside its parity, Parity.Value pairs the two:

import Pair_Primitives
import Parity_Primitives

// Parity.Value<Payload> is Pair<Parity, Payload>.
let tagged: Parity.Value<Int> = Pair(.even, 4)
print(tagged.first)    // even
print(tagged.second)   // 4

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Installation

dependencies: [
    .package(url: "https://github.com/swift-primitives/swift-parity-primitives.git", branch: "main")
]

.target(
    name: "App",
    dependencies: [
        .product(name: "Parity Primitives", package: "swift-parity-primitives"),
    ]
)

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Architecture

Two library products. Depends only on the Pair primitive, which it re-exports.

Product	Target	Purpose
Parity Primitives	Sources/Parity Primitives/	The Parity enum (.even / .odd), its BinaryInteger classification init, the Z₂ adding / multiplying / opposite algebra and prefix !, and the Parity.Value<Payload> pairing typealias. Re-exports Pair Primitives.
Parity Primitives Test Support	Tests/Support/	Re-exports the main target for test consumers.

Foundation-free.

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Platform Support

Platform	Status
macOS 26	Full support
Linux	Full support
Windows	Full support
iOS / tvOS / watchOS / visionOS	Supported

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Community

License

Apache 2.0. See LICENSE.md.