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merged 1 commit into from
Feb 21, 2020
Merged

Reduced compile time by breaking up complex statements into smaller components #5

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39 changes: 30 additions & 9 deletions Sources/Complex/Functions.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -158,17 +158,32 @@ public func sin(_ value: Complex<Float80>) -> Complex<Float80> {

@_transparent
public func asin(_ value: Complex<Float>) -> Complex<Float> {
return -.i * log(.i * value + sqrt(1.0 - value * value))
//swiftlint:disable identifier_name
let iz = .i * value
let root = sqrt(1.0 - (value * value))

return -.i * log(iz + root)
//swiftlint:enable identifier_name
}

@_transparent
public func asin(_ value: Complex<Double>) -> Complex<Double> {
return -.i * log(.i * value + sqrt(1.0 - value * value))
//swiftlint:disable identifier_name
let iz = .i * value
let root = sqrt(1.0 - (value * value))

return -.i * log(iz + root)
//swiftlint:enable identifier_name
}

@_transparent
public func asin(_ value: Complex<Float80>) -> Complex<Float80> {
return -.i * log(.i * value + sqrt(1.0 - value * value))
//swiftlint:disable identifier_name
let iz = .i * value
let root = sqrt(1.0 - (value * value))

return -.i * log(iz + root)
//swiftlint:enable identifier_name
}

//
Expand Down Expand Up @@ -212,17 +227,20 @@ public func cos(_ value: Complex<Float80>) -> Complex<Float80> {

@_transparent
public func acos(_ value: Complex<Float>) -> Complex<Float> {
return -.i * log(value + sqrt(value * value - 1.0))
let root = sqrt((value * value) - 1.0)
return -.i * log(value + root)
}

@_transparent
public func acos(_ value: Complex<Double>) -> Complex<Double> {
return -.i * log(value + sqrt(value * value - 1.0))
let root = sqrt((value * value) - 1.0)
return -.i * log(value + root)
}

@_transparent
public func acos(_ value: Complex<Float80>) -> Complex<Float80> {
return -.i * log(value + sqrt(value * value - 1.0))
let root = sqrt((value * value) - 1.0)
return -.i * log(value + root)
}

//
Expand Down Expand Up @@ -265,17 +283,20 @@ public func tan(_ value: Complex<Float80>) -> Complex<Float80> {

@_transparent
public func atan(_ value: Complex<Float>) -> Complex<Float> {
return .i * 0.5 * log((.i + value) / (.i - value))
let quotient = (.i + value) / (.i - value)
return .i * 0.5 * log(quotient)
}

@_transparent
public func atan(_ value: Complex<Double>) -> Complex<Double> {
return .i * 0.5 * log((.i + value) / (.i - value))
let quotient = (.i + value) / (.i - value)
return .i * 0.5 * log(quotient)
}

@_transparent
public func atan(_ value: Complex<Float80>) -> Complex<Float80> {
return .i * 0.5 * log((.i + value) / (.i - value))
let quotient = (.i + value) / (.i - value)
return .i * 0.5 * log(quotient)
}

//
Expand Down
13 changes: 10 additions & 3 deletions Sources/Complex/Functions.swift.gyb
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Original file line number Diff line number Diff line change
Expand Up @@ -117,7 +117,12 @@ public func sin(_ value: Complex<${type}>) -> Complex<${type}> {
% for type in ["Float", "Double", "Float80"]:
@_transparent
public func asin(_ value: Complex<${type}>) -> Complex<${type}> {
return -.i * log(.i * value + sqrt(1.0 - value * value))
//swiftlint:disable identifier_name
let iz = .i * value
let root = sqrt(1.0 - (value * value))

return -.i * log(iz + root)
//swiftlint:enable identifier_name
}

% end
Expand Down Expand Up @@ -147,7 +152,8 @@ public func cos(_ value: Complex<${type}>) -> Complex<${type}> {
% for type in ["Float", "Double", "Float80"]:
@_transparent
public func acos(_ value: Complex<${type}>) -> Complex<${type}> {
return -.i * log(value + sqrt(value * value - 1.0))
let root = sqrt((value * value) - 1.0)
return -.i * log(value + root)
}

% end
Expand Down Expand Up @@ -176,7 +182,8 @@ public func tan(_ value: Complex<${type}>) -> Complex<${type}> {
% for type in ["Float", "Double", "Float80"]:
@_transparent
public func atan(_ value: Complex<${type}>) -> Complex<${type}> {
return .i * 0.5 * log((.i + value) / (.i - value))
let quotient = (.i + value) / (.i - value)
return .i * 0.5 * log(quotient)
}

% end
Expand Down
54 changes: 45 additions & 9 deletions Tests/ComplexTests/FunctionsTests.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -156,13 +156,31 @@ class FunctionsTests: XCTestCase {

func test_asin() {
for complex in sampleComplexNumbers(ofType: Float.self) {
XCTAssertEqual(asin(complex), -.i * log(.i * complex + sqrt(1.0 - complex * complex)), accuracy: 0.0001)
//swiftlint:disable identifier_name
let iz = .i * complex
let root = sqrt(1.0 - (complex * complex))
let result = -.i * log(iz + root)
//swiftlint:enable identifier_name

XCTAssertEqual(asin(complex), result, accuracy: 0.0001)
}
for complex in sampleComplexNumbers(ofType: Double.self) {
XCTAssertEqual(asin(complex), -.i * log(.i * complex + sqrt(1.0 - complex * complex)), accuracy: 0.0001)
//swiftlint:disable identifier_name
let iz = .i * complex
let root = sqrt(1.0 - (complex * complex))
let result = -.i * log(iz + root)
//swiftlint:enable identifier_name

XCTAssertEqual(asin(complex), result, accuracy: 0.0001)
}
for complex in sampleComplexNumbers(ofType: Float80.self) {
XCTAssertEqual(asin(complex), -.i * log(.i * complex + sqrt(1.0 - complex * complex)), accuracy: 0.0001)
//swiftlint:disable identifier_name
let iz = .i * complex
let root = sqrt(1.0 - (complex * complex))
let result = -.i * log(iz + root)
//swiftlint:enable identifier_name

XCTAssertEqual(asin(complex), result, accuracy: 0.0001)
}
}

Expand Down Expand Up @@ -192,13 +210,22 @@ class FunctionsTests: XCTestCase {

func test_acos() {
for complex in sampleComplexNumbers(ofType: Float.self) {
XCTAssertEqual(acos(complex), -.i * log(complex + sqrt(complex * complex - 1.0)), accuracy: 0.0001)
let root = sqrt((complex * complex) - 1.0)
let result = -.i * log(complex + root)

XCTAssertEqual(acos(complex), result, accuracy: 0.0001)
}
for complex in sampleComplexNumbers(ofType: Double.self) {
XCTAssertEqual(acos(complex), -.i * log(complex + sqrt(complex * complex - 1.0)), accuracy: 0.0001)
let root = sqrt((complex * complex) - 1.0)
let result = -.i * log(complex + root)

XCTAssertEqual(acos(complex), result, accuracy: 0.0001)
}
for complex in sampleComplexNumbers(ofType: Float80.self) {
XCTAssertEqual(acos(complex), -.i * log(complex + sqrt(complex * complex - 1.0)), accuracy: 0.0001)
let root = sqrt((complex * complex) - 1.0)
let result = -.i * log(complex + root)

XCTAssertEqual(acos(complex), result, accuracy: 0.0001)
}
}

Expand Down Expand Up @@ -228,13 +255,22 @@ class FunctionsTests: XCTestCase {

func test_atan() {
for complex in sampleComplexNumbers(ofType: Float.self) {
XCTAssertEqual(atan(complex), .i * 0.5 * log((.i + complex) / (.i - complex)), accuracy: 0.0001)
let quotient = (.i + complex) / (.i - complex)
let result = .i * 0.5 * log(quotient)

XCTAssertEqual(atan(complex), result, accuracy: 0.0001)
}
for complex in sampleComplexNumbers(ofType: Double.self) {
XCTAssertEqual(atan(complex), .i * 0.5 * log((.i + complex) / (.i - complex)), accuracy: 0.0001)
let quotient = (.i + complex) / (.i - complex)
let result = .i * 0.5 * log(quotient)

XCTAssertEqual(atan(complex), result, accuracy: 0.0001)
}
for complex in sampleComplexNumbers(ofType: Float80.self) {
XCTAssertEqual(atan(complex), .i * 0.5 * log((.i + complex) / (.i - complex)), accuracy: 0.0001)
let quotient = (.i + complex) / (.i - complex)
let result = .i * 0.5 * log(quotient)

XCTAssertEqual(atan(complex), result, accuracy: 0.0001)
}
}

Expand Down
18 changes: 15 additions & 3 deletions Tests/ComplexTests/FunctionsTests.swift.gyb
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Original file line number Diff line number Diff line change
Expand Up @@ -135,7 +135,13 @@ class FunctionsTests: XCTestCase {
func test_asin() {
% for type in ["Float", "Double", "Float80"]:
for complex in sampleComplexNumbers(ofType: ${type}.self) {
XCTAssertEqual(asin(complex), -.i * log(.i * complex + sqrt(1.0 - complex * complex)), accuracy: 0.0001)
//swiftlint:disable identifier_name
let iz = .i * complex
let root = sqrt(1.0 - (complex * complex))
let result = -.i * log(iz + root)
//swiftlint:enable identifier_name

XCTAssertEqual(asin(complex), result, accuracy: 0.0001)
}
% end
}
Expand All @@ -159,7 +165,10 @@ class FunctionsTests: XCTestCase {
func test_acos() {
% for type in ["Float", "Double", "Float80"]:
for complex in sampleComplexNumbers(ofType: ${type}.self) {
XCTAssertEqual(acos(complex), -.i * log(complex + sqrt(complex * complex - 1.0)), accuracy: 0.0001)
let root = sqrt((complex * complex) - 1.0)
let result = -.i * log(complex + root)

XCTAssertEqual(acos(complex), result, accuracy: 0.0001)
}
% end
}
Expand All @@ -183,7 +192,10 @@ class FunctionsTests: XCTestCase {
func test_atan() {
% for type in ["Float", "Double", "Float80"]:
for complex in sampleComplexNumbers(ofType: ${type}.self) {
XCTAssertEqual(atan(complex), .i * 0.5 * log((.i + complex) / (.i - complex)), accuracy: 0.0001)
let quotient = (.i + complex) / (.i - complex)
let result = .i * 0.5 * log(quotient)

XCTAssertEqual(atan(complex), result, accuracy: 0.0001)
}
% end
}
Expand Down