Swift simd matrix init bench Raw

matrix.swift

import simd
import Foundation
import Darwin

public enum Random {
    public static func unit() -> Float32 {
        return Float32(arc4random()) / Float32(UInt32.max)
    }
}

public extension float3x3 {
    var inverse2: float3x3 {
        var inverse = float3x3(0)
        inverse[0, 0] = self[1, 1] * self[2, 2] - self[2, 1] * self[1, 2]
        inverse[0, 1] = self[2, 1] * self[0, 2] - self[0, 1] * self[2, 2]
        inverse[0, 2] = self[0, 1] * self[1, 2] - self[1, 1] * self[0, 2]

        inverse[1, 0] = self[2, 0] * self[1, 2] - self[1, 0] * self[2, 2]
        inverse[1, 1] = self[0, 0] * self[2, 2] - self[2, 0] * self[0, 2]
        inverse[1, 2] = self[1, 0] * self[0, 2] - self[0, 0] * self[1, 2]

        inverse[2, 0] = self[1, 0] * self[2, 1] - self[2, 0] * self[1, 1]
        inverse[2, 1] = self[2, 0] * self[0, 1] - self[0, 0] * self[2, 1]
        inverse[2, 2] = self[0, 0] * self[1, 1] - self[1, 0] * self[0, 1]

        let determinant = self[0, 0] * inverse[0, 0] +
                          self[1, 0] * inverse[0, 1] +
                          self[2, 0] * inverse[0, 2]

        if abs(determinant) <= 1E-6 {
            return inverse // false
        }

        let invDeterminant = 1 / determinant

        return inverse * invDeterminant // true
    }

    var inverse3: float3x3 {
        let m00 = self[1, 1] * self[2, 2] - self[2, 1] * self[1, 2]
        let m01 = self[2, 1] * self[0, 2] - self[0, 1] * self[2, 2]
        let m02 = self[0, 1] * self[1, 2] - self[1, 1] * self[0, 2]

        let m10 = self[2, 0] * self[1, 2] - self[1, 0] * self[2, 2]
        let m11 = self[0, 0] * self[2, 2] - self[2, 0] * self[0, 2]
        let m12 = self[1, 0] * self[0, 2] - self[0, 0] * self[1, 2]

        let m20 = self[1, 0] * self[2, 1] - self[2, 0] * self[1, 1]
        let m21 = self[2, 0] * self[0, 1] - self[0, 0] * self[2, 1]
        let m22 = self[0, 0] * self[1, 1] - self[1, 0] * self[0, 1]

        var inverse = float3x3([
            float3(m00, m01, m02),
            float3(m10, m11, m12),
            float3(m20, m21, m22)
        ])

        let determinant = self[0, 0] * inverse[0, 0] +
            self[1, 0] * inverse[0, 1] +
            self[2, 0] * inverse[0, 2]

        if abs(determinant) <= 1E-6 {
            return inverse // false
        }

        let invDeterminant = 1 / determinant

        return inverse * invDeterminant // true
    }

    var inverse4: float3x3 {
        let m00 = self[1, 1] * self[2, 2] - self[2, 1] * self[1, 2]
        let m01 = self[2, 1] * self[0, 2] - self[0, 1] * self[2, 2]
        let m02 = self[0, 1] * self[1, 2] - self[1, 1] * self[0, 2]

        let m10 = self[2, 0] * self[1, 2] - self[1, 0] * self[2, 2]
        let m11 = self[0, 0] * self[2, 2] - self[2, 0] * self[0, 2]
        let m12 = self[1, 0] * self[0, 2] - self[0, 0] * self[1, 2]

        let m20 = self[1, 0] * self[2, 1] - self[2, 0] * self[1, 1]
        let m21 = self[2, 0] * self[0, 1] - self[0, 0] * self[2, 1]
        let m22 = self[0, 0] * self[1, 1] - self[1, 0] * self[0, 1]

        var inverse = float3x3(columns: (
            float3(m00, m01, m02),
            float3(m10, m11, m12),
            float3(m20, m21, m22)
        ))

        let determinant = self[0, 0] * inverse[0, 0] +
            self[1, 0] * inverse[0, 1] +
            self[2, 0] * inverse[0, 2]

        if abs(determinant) <= 1E-6 {
            return inverse // false
        }

        let invDeterminant = 1 / determinant

        return inverse * invDeterminant // true
    }

    var inverse5: float3x3 {
        let m00 = self[1, 1] * self[2, 2] - self[2, 1] * self[1, 2]
        let m01 = self[2, 0] * self[1, 2] - self[1, 0] * self[2, 2]
        let m02 = self[1, 0] * self[2, 1] - self[2, 0] * self[1, 1]
        let m10 = self[2, 1] * self[0, 2] - self[0, 1] * self[2, 2]
        let m11 = self[0, 0] * self[2, 2] - self[2, 0] * self[0, 2]
        let m12 = self[2, 0] * self[0, 1] - self[0, 0] * self[2, 1]
        let m20 = self[0, 1] * self[1, 2] - self[1, 1] * self[0, 2]
        let m21 = self[1, 0] * self[0, 2] - self[0, 0] * self[1, 2]
        let m22 = self[0, 0] * self[1, 1] - self[1, 0] * self[0, 1]

        var inverse = float3x3(rows: [
            float3(m00, m01, m02),
            float3(m10, m11, m12),
            float3(m20, m21, m22)
        ])

        let determinant = self[0, 0] * inverse[0, 0] +
            self[1, 0] * inverse[0, 1] +
            self[2, 0] * inverse[0, 2]

        if abs(determinant) <= 1E-6 {
            return inverse // false
        }

        let invDeterminant = 1 / determinant

        return inverse * invDeterminant // true
    }

    var inverse6: float3x3 {
        let m00 = self[1, 1] * self[2, 2] - self[2, 1] * self[1, 2]
        let m01 = self[2, 1] * self[0, 2] - self[0, 1] * self[2, 2]
        let m02 = self[0, 1] * self[1, 2] - self[1, 1] * self[0, 2]

        let m10 = self[2, 0] * self[1, 2] - self[1, 0] * self[2, 2]
        let m11 = self[0, 0] * self[2, 2] - self[2, 0] * self[0, 2]
        let m12 = self[1, 0] * self[0, 2] - self[0, 0] * self[1, 2]

        let m20 = self[1, 0] * self[2, 1] - self[2, 0] * self[1, 1]
        let m21 = self[2, 0] * self[0, 1] - self[0, 0] * self[2, 1]
        let m22 = self[0, 0] * self[1, 1] - self[1, 0] * self[0, 1]

        var inverse = float3x3(
            float3(m00, m01, m02),
            float3(m10, m11, m12),
            float3(m20, m21, m22)
        )

        let determinant = self[0, 0] * inverse[0, 0] +
            self[1, 0] * inverse[0, 1] +
            self[2, 0] * inverse[0, 2]

        if abs(determinant) <= 1E-6 {
            return inverse // false
        }

        let invDeterminant = 1 / determinant

        return inverse * invDeterminant // true
    }
    
    /// https://forums.swift.org/t/creating-a-simd-floatnxn-from-array-is-very-slow/8796/6?u=qroc
    init(fromArray array: [float3]) {
        precondition(array.count == 3, "float3x3 requires an array with 3 elements.")
        self.init(columns: (array[0], array[1], array[2]))
    }
    
    var inverse7: float3x3 {
        let m00 = self[1, 1] * self[2, 2] - self[2, 1] * self[1, 2]
        let m01 = self[2, 1] * self[0, 2] - self[0, 1] * self[2, 2]
        let m02 = self[0, 1] * self[1, 2] - self[1, 1] * self[0, 2]

        let m10 = self[2, 0] * self[1, 2] - self[1, 0] * self[2, 2]
        let m11 = self[0, 0] * self[2, 2] - self[2, 0] * self[0, 2]
        let m12 = self[1, 0] * self[0, 2] - self[0, 0] * self[1, 2]

        let m20 = self[1, 0] * self[2, 1] - self[2, 0] * self[1, 1]
        let m21 = self[2, 0] * self[0, 1] - self[0, 0] * self[2, 1]
        let m22 = self[0, 0] * self[1, 1] - self[1, 0] * self[0, 1]

        var inverse = float3x3(fromArray: [
            float3(m00, m01, m02),
            float3(m10, m11, m12),
            float3(m20, m21, m22)
            ])

        let determinant = self[0, 0] * inverse[0, 0] +
            self[1, 0] * inverse[0, 1] +
            self[2, 0] * inverse[0, 2]

        if abs(determinant) <= 1E-6 {
            return inverse // false
        }

        let invDeterminant = 1 / determinant

        return inverse * invDeterminant // true
    }
}

let matrix = float3x3(
    float3(Random.unit(), Random.unit(), Random.unit()),
    float3(Random.unit(), Random.unit(), Random.unit()),
    float3(Random.unit(), Random.unit(), Random.unit())
)

func printTimeElapsedWhenRunningCode(title: String, operation: () -> ()) {
    let startTime = CFAbsoluteTimeGetCurrent()
    operation()
    let timeElapsed = CFAbsoluteTimeGetCurrent() - startTime
    print("Time elapsed for \(title): \(timeElapsed) s.")
}

let maxIterations = Int(Random.range(from: 50000000.01, to: 50000000.1))

// ============
// Warming up
var res1 = matrix
for _ in 0...maxIterations {
    res1 += res1.inverse
}

var res2 = matrix
for _ in 0...maxIterations {
    res2 += res2.inverse2
}

var res3 = matrix
for _ in 0...maxIterations {
    res3 += res3.inverse3
}

var res4 = matrix
for _ in 0...maxIterations {
    res4 += res4.inverse4
}

var res5 = matrix
for _ in 0...maxIterations {
    res5 += res5.inverse5
}


var res6 = matrix
for _ in 0...maxIterations {
    res6 += res6.inverse6
}


var res7 = matrix
for _ in 0...maxIterations {
    res7 += res7.inverse7
}

// ============
// Bench
printTimeElapsedWhenRunningCode(title: "inverse") {
    for _ in 0...maxIterations {
        res1 += res1.inverse
    }
}

printTimeElapsedWhenRunningCode(title: "inverse2") {
    for _ in 0...maxIterations {
        res2 += res2.inverse2
    }
}

printTimeElapsedWhenRunningCode(title: "inverse3") {
    for _ in 0...maxIterations {
        res3 += res3.inverse3
    }
}

printTimeElapsedWhenRunningCode(title: "inverse4") {
    for _ in 0...maxIterations {
        res4 += res4.inverse4
    }
}

printTimeElapsedWhenRunningCode(title: "inverse5") {
    for _ in 0...maxIterations {
        res5 += res5.inverse5
    }
}

printTimeElapsedWhenRunningCode(title: "inverse6") {
    for _ in 0...maxIterations {
        res6 += res6.inverse6
    }
}

printTimeElapsedWhenRunningCode(title: "inverse7") {
    for _ in 0...maxIterations {
        res7 += res7.inverse7
    }
}

if res2 != res1 {
    print("res2 fail")
}

if res3 != res1 {
    print("res3 fail")
}

if res4 != res1 {
    print("res4 fail")
}

if res5 != res1 {
    print("res5 fail")
}

if res6 != res1 {
    print("res6 fail")
}


if res7 != res1 {
    print("res7 fail")
}

Results

Build flags: --configuration release
swiftc: -Ounchecked -gnone -whole-module-optimization -static-stdlib

Time elapsed for inverse: 2.64717900753021 s.
Time elapsed for inverse2: 1.35483705997467 s.
Time elapsed for inverse3: 11.727156996727 s.
Time elapsed for inverse4: 1.38384604454041 s.
Time elapsed for inverse5: 11.8544869422913 s.
Time elapsed for inverse6: 1.38975405693054 s.
Time elapsed for inverse7: 1.37177407939121 s.