浮動小数の比較について

XCTestのXCTAssertEqual(_:_:accuracy:_:file:line:)とSwift Numericsが提供するisApproximatelyEqual()の違いについて

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3. let center = CGPoint(x: 900, y: 900) let radius: CGFloat = 1000 let p = pointOnCircle(center: center, radius: radius, angle: .pi / 2) #expect(p.x == center.x)
6. let center = CGPoint(x: 900, y: 900) let radius: CGFloat = 1000 let p = pointOnCircle(center: center, radius: radius, angle: .pi / 2) XCTAssertEqual(p.x, center.x, accuracy: 0.000001)
7. XCTest Swift Testing XCTAssert(x), XCTAssertTrue(x) #expect(x) XCTAssertFalse(x) #expect(!x) XCTAssertNil(x) #expect(x == nil) XCTAssertNotNil(x) #expect(x != nil) XCTAssertEqual(x, y) #expect(x == y) XCTAssertNotEqual(x, y) #expect(x != y) XCTAssertIdentical(x, y) #expect(x === y) XCTAssertNotIdentical(x, y) #expect(x !== y) XCTAssertGreaterThan(x, y) #expect(x > y) XCTAssertGreaterThanOrEqual(x, y) #expect(x >= y) XCTAssertLessThanOrEqual(x, y) #expect(x <= y) XCTAssertLessThan(x, y) #expect(x < y) XCTAssertThrowsError(try f()) #expect(throws: (any Error).self) { try f() } XCTAssertThrowsError(try f()) { error in … } let error = #expect(throws: (any Error).self) { try f() } XCTAssertNoThrow(try f()) #expect(throws: Never.self) { try f() } try XCTUnwrap(x) try #require(x) XCTFail("…") Issue.record("…")
8. 9$5FTU
   
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   5FTUJOH The testing library doesn’t provide an equivalent of XCTAssertEqual(_:_:accuracy:_:file:line:). To compare two numeric values within a speci fi ed accuracy, use isApproximatelyEqual() from swift-numerics.
11. XCTAssertEqual(p.x, center.x, accuracy: 0.000001) 9$5FTU 9$5"TTFSU&RVBM @@BDDVSBDZ@ fi MFMJOF
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    /VNFSJDT JT"QQSPYJNBUFMZ&RVBM UPSFMBUJWF5PMFSBODFOPSN p.x.isApproximatelyEqual( to: center.x, absoluteTolerance: ???, relativeTolerance: ???, norm: ??? )
13. 9$"TTFSU&RVBM *NQMFNFOUBUJPO private func areEqual<T: Numeric>(_ exp1: T, _ exp2: T, accuracy: T) -> Bool { // Test with equality first to handle comparing inf/-inf with itself. if exp1 == exp2 { return true } else { // NaN values are handled implicitly, since the <= operator returns false when comparing any value to NaN. let difference = (exp1.magnitude > exp2.magnitude) ? exp1 - exp2 : exp2 - exp1 return difference.magnitude <= accuracy.magnitude } } https://github.com/swiftlang/swift-corelibs-foundation/blob/main/Sources/XCTest/Public/XCTAssert.swift
14. 9$"TTFSU&RVBM *NQMFNFOUBUJPO private func areEqual<T: Numeric>(_ exp1: T, _ exp2: T, accuracy: T) -> Bool { // Test with equality first to handle comparing inf/-inf with itself. if exp1 == exp2 { return true } else { // NaN values are handled implicitly, since the <= operator returns false when comparing any value to NaN. let difference = (exp1.magnitude > exp2.magnitude) ? exp1 - exp2 : exp2 - exp1 return difference.magnitude <= accuracy.magnitude } } https://github.com/swiftlang/swift-corelibs-foundation/blob/main/Sources/XCTest/Public/XCTAssert.swift
15. 9$"TTFSU&RVBM *NQMFNFOUBUJPO private func areEqual<T: Numeric>(_ exp1: T, _ exp2: T, accuracy: T) -> Bool { // Test with equality first to handle comparing inf/-inf with itself. if exp1 == exp2 { return true } else { // NaN values are handled implicitly, since the <= operator returns false when comparing any value to NaN. let difference = (exp1.magnitude > exp2.magnitude) ? exp1 - exp2 : exp2 - exp1 return difference.magnitude <= accuracy.magnitude } } https://github.com/swiftlang/swift-corelibs-foundation/blob/main/Sources/XCTest/Public/XCTAssert.swift
16. 9$"TTFSU&RVBM *NQMFNFOUBUJPO private func areEqual<T: Numeric>(_ exp1: T, _ exp2: T, accuracy: T) -> Bool { // Test with equality first to handle comparing inf/-inf with itself. if exp1 == exp2 { return true } else { // NaN values are handled implicitly, since the <= operator returns false when comparing any value to NaN. let difference = (exp1.magnitude > exp2.magnitude) ? exp1 - exp2 : exp2 - exp1 return difference.magnitude <= accuracy.magnitude } } https://github.com/swiftlang/swift-corelibs-foundation/blob/main/Sources/XCTest/Public/XCTAssert.swift
17. 9$"TTFSU&RVBM abs(exp1 - exp2) <= accuracy
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    5FTUJOH FYQFDU XCTAssertEqual(p.x, center.x, accuracy: 0.000001) #expect(abs(p.x - center.x) <= 0.000001)
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20. https://github.com/apple/swift-numerics/blob/main/Sources/RealModule/ApproximateEquality.swift public func isApproximatelyEqual<Magnitude>( to other: Self, absoluteTolerance: Magnitude, relativeTolerance: Magnitude = 0, norm: (Self) -> Magnitude ) -> Bool where Magnitude: FloatingPoint { assert( absoluteTolerance >= 0 && absoluteTolerance.isFinite, "absoluteTolerance should be non-negative and finite, " + "but is \(absoluteTolerance)." ) assert( relativeTolerance >= 0 && relativeTolerance <= 1, "relativeTolerance should be non-negative and <= 1, " + "but is \(relativeTolerance)." ) if self == other { return true } let delta = norm(self - other) let scale = max(norm(self), norm(other)) let bound = max(absoluteTolerance, scale*relativeTolerance) return delta.isFinite && delta <= bound }
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26. https://github.com/apple/swift-numerics/blob/main/Sources/RealModule/ApproximateEquality.swift public func isApproximatelyEqual<Magnitude>( to other: Self, absoluteTolerance: Magnitude, relativeTolerance: Magnitude = 0, norm: (Self) -> Magnitude ) -> Bool where Magnitude: FloatingPoint { assert( absoluteTolerance >= 0 && absoluteTolerance.isFinite, "absoluteTolerance should be non-negative and finite, " + "but is \(absoluteTolerance)." ) assert( relativeTolerance >= 0 && relativeTolerance <= 1, "relativeTolerance should be non-negative and <= 1, " + "but is \(relativeTolerance)." ) if self == other { return true } let delta = norm(self - other) let scale = max(norm(self), norm(other)) let bound = max(absoluteTolerance, scale*relativeTolerance) return delta.isFinite && delta <= bound }
27. https://github.com/apple/swift-numerics/blob/main/Sources/RealModule/ApproximateEquality.swift public func isApproximatelyEqual<Magnitude>( to other: Self, absoluteTolerance: Magnitude, relativeTolerance: Magnitude = 0, norm: (Self) -> Magnitude ) -> Bool where Magnitude: FloatingPoint { assert( absoluteTolerance >= 0 && absoluteTolerance.isFinite, "absoluteTolerance should be non-negative and finite, " + "but is \(absoluteTolerance)." ) assert( relativeTolerance >= 0 && relativeTolerance <= 1, "relativeTolerance should be non-negative and <= 1, " + "but is \(relativeTolerance)." ) if self == other { return true } let delta = norm(self - other) let scale = max(norm(self), norm(other)) let bound = max(absoluteTolerance, scale*relativeTolerance) return delta.isFinite && delta <= bound }
28. https://github.com/apple/swift-numerics/blob/main/Sources/RealModule/ApproximateEquality.swift public func isApproximatelyEqual<Magnitude>( to other: Self, absoluteTolerance: Magnitude, relativeTolerance: Magnitude = 0, norm: (Self) -> Magnitude ) -> Bool where Magnitude: FloatingPoint { assert( absoluteTolerance >= 0 && absoluteTolerance.isFinite, "absoluteTolerance should be non-negative and finite, " + "but is \(absoluteTolerance)." ) assert( relativeTolerance >= 0 && relativeTolerance <= 1, "relativeTolerance should be non-negative and <= 1, " + "but is \(relativeTolerance)." ) if self == other { return true } let delta = norm(self - other) let scale = max(norm(self), norm(other)) let bound = max(absoluteTolerance, scale*relativeTolerance) return delta.isFinite && delta <= bound }
29. https://github.com/apple/swift-numerics/blob/main/Sources/RealModule/ApproximateEquality.swift public func isApproximatelyEqual<Magnitude>( to other: Self, absoluteTolerance: Magnitude, relativeTolerance: Magnitude = 0, norm: (Self) -> Magnitude ) -> Bool where Magnitude: FloatingPoint { assert( absoluteTolerance >= 0 && absoluteTolerance.isFinite, "absoluteTolerance should be non-negative and finite, " + "but is \(absoluteTolerance)." ) assert( relativeTolerance >= 0 && relativeTolerance <= 1, "relativeTolerance should be non-negative and <= 1, " + "but is \(relativeTolerance)." ) if self == other { return true } let delta = norm(self - other) let scale = max(norm(self), norm(other)) let bound = max(absoluteTolerance, scale*relativeTolerance) return delta.isFinite && delta <= bound }
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