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Introducing Angle type [Issue #88] #169

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Introducing Angle type [Issue #88] #169

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b313290
Introduced Angle type [Issue #88]
jkalias Dec 8, 2020
c924790
Removed hyperbolic functions
jkalias Dec 8, 2020
437b280
cos(Angle) changed, 270deg stil not giving 0
jkalias Dec 9, 2020
bb19809
cos works for all cases
jkalias Dec 9, 2020
d4a4c3c
sin(Angle) also works as expected
jkalias Dec 9, 2020
f676bc1
removed newline
jkalias Dec 9, 2020
bb474f5
more tests for cos and sin
jkalias Dec 9, 2020
2fad678
cos and sin tests along the whole (-π,π) interval
jkalias Dec 9, 2020
4844b2a
tests and implementation for tan
jkalias Dec 9, 2020
c5828b8
Strict equality in tests, not approximate
jkalias Dec 9, 2020
2fba7c7
Removed conformance to BinaryFloatingPoint
jkalias Dec 13, 2020
79f5f7a
Added conformance to AdditiveArithmetic and other utilities
jkalias Dec 13, 2020
5f57416
Added AdditiveArithmetic tests
jkalias Dec 13, 2020
e09ef7a
Fixed conformance to Equatable, and added range containment functions…
jkalias Dec 14, 2020
131774a
Updated public access modifier style
jkalias Dec 14, 2020
949c9a2
Refactored AngleTests
jkalias Dec 16, 2020
63bdaaf
cos and sin for exact degrees
jkalias Dec 18, 2020
acd67fb
exact tan implemented
jkalias Dec 18, 2020
14c520b
inverse trigonometric functions fixed
jkalias Dec 19, 2020
9e7fb84
range containment and distance checks
jkalias Dec 20, 2020
1743914
documentation
jkalias Dec 20, 2020
56c5ffc
Angle type with trig-pi branch (#85)
jkalias Mar 21, 2021
83ba41b
Merge branch 'main' into angle-type
jkalias Mar 18, 2022
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86 changes: 78 additions & 8 deletions Sources/RealModule/Angle.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -14,32 +14,87 @@
///
/// All trigonometric functions expect the argument to be passed as radians (Real), but this is not enforced by the type system.
/// This type serves exactly this purpose, and can be seen as an alternative to the underlying Real implementation.
public struct Angle<T: Real> {
public struct Angle<T: Real & BinaryFloatingPoint> {
public var radians: T
public init(radians: T) { self.radians = radians }
public static func radians(_ val: T) -> Angle<T> { .init(radians: val) }

public var degrees: T { radians * 180 / .pi }
public init(degrees: T) { self.init(radians: degrees * .pi / 180) }
public init(degrees: T) {
let normalized = normalize(degrees, limit: 180)
self.init(radians: normalized * .pi / 180)
}
public static func degrees(_ val: T) -> Angle<T> { .init(degrees: val) }
}

public extension Angle {
public extension ElementaryFunctions
where Self: Real & BinaryFloatingPoint {
/// See also:
/// -
/// `ElementaryFunctions.cos()`
var cos: T { T.cos(radians) }
static func cos(_ angle: Angle<Self>) -> Self {
let normalizedRadians = normalize(angle.radians, limit: .pi)

if -.pi/4 < normalizedRadians && normalizedRadians < .pi/4 {
return Self.cos(normalizedRadians)
}

if normalizedRadians > 3 * .pi / 4 || normalizedRadians < -3 * .pi / 4 {
return -Self.cos(.pi - normalizedRadians)
}

if normalizedRadians >= 0 {
return Self.sin(.pi/2 - normalizedRadians)
}

return Self.sin(normalizedRadians + .pi / 2)
}

/// See also:
/// -
/// `ElementaryFunctions.sin()`
var sin: T { T.sin(radians) }
static func sin(_ angle: Angle<Self>) -> Self {
let normalizedRadians = normalize(angle.radians, limit: .pi)

if .pi / 4 < normalizedRadians && normalizedRadians < 3 * .pi / 4 {
return Self.sin(normalizedRadians)
}

if -3 * .pi / 4 < normalizedRadians && normalizedRadians < -.pi / 4 {
return -Self.sin(-normalizedRadians)
}

if normalizedRadians > 3 * .pi / 4 {
return Self.sin(.pi - normalizedRadians)
}

if normalizedRadians < -3 * .pi / 4 {
return -Self.sin(.pi + normalizedRadians)
}

return Self.sin(normalizedRadians)
}

/// See also:
/// -
/// `ElementaryFunctions.tan()`
var tan: T { T.tan(radians) }

static func tan(_ angle: Angle<Self>) -> Self {
let sine = sin(angle)
let cosine = cos(angle)

guard cosine != 0 else {
var result = Self.infinity
if sine.sign == .minus {
result.negate()
}
return result
}

return sine / cosine
}
}

public extension Angle {
/// See also:
/// -
/// `ElementaryFunctions.acos()`
Expand All @@ -60,3 +115,18 @@ public extension Angle {
/// `RealFunctions.atan2()`
static func atan2(y: T, x: T) -> Self { Angle.radians(T.atan2(y: y, x: x)) }
}

private func normalize<T>(_ input: T, limit: T) -> T
where T: Real & BinaryFloatingPoint {
var normalized = input

while normalized > limit {
normalized -= 2 * limit
}

while normalized < -limit {
normalized += 2 * limit
}

return normalized
}
79 changes: 76 additions & 3 deletions Tests/RealTests/AngleTests.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -31,10 +31,79 @@ where Self: BinaryFloatingPoint {
assertClose(0.3843967744956390830381948729670469737, Angle<Self>.asin(0.375).radians)
assertClose(0.3587706702705722203959200639264604997, Angle<Self>.atan(0.375).radians)
assertClose(0.54041950027058415544357836460859991, Angle<Self>.atan2(y: 0.375, x: 0.625).radians)

assertClose(0.9305076219123142911494767922295555080, cos(Angle<Self>(radians: 0.375)))
assertClose(0.3662725290860475613729093517162641571, sin(Angle<Self>(radians: 0.375)))
assertClose(0.3936265759256327582294137871012180981, tan(Angle<Self>(radians: 0.375)))
}

static func specialDegreesTrigonometricFunctionChecks() {
assertClose(1, cos(Angle<Self>(degrees: -360)))
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The tests with exact results should test exact equality, not assertClose.

assertClose(0, cos(Angle<Self>(degrees: -270)))
assertClose(-1, cos(Angle<Self>(degrees: -180)))
assertClose(-0.86602540378443864676372317075293618347, cos(Angle<Self>(degrees: -150)))
assertClose(-0.70710678118654752440084436210484903929, cos(Angle<Self>(degrees: -135)))
assertClose(-0.5, cos(Angle<Self>(degrees: -120)))
assertClose(0, cos(Angle<Self>(degrees: -90)))
assertClose(0.5, cos(Angle<Self>(degrees: -60)))
assertClose(0.70710678118654752440084436210484903929, cos(Angle<Self>(degrees: -45)))
assertClose(0.86602540378443864676372317075293618347, cos(Angle<Self>(degrees: -30)))
assertClose(1, cos(Angle<Self>(degrees: 0)))
assertClose(0.86602540378443864676372317075293618347, cos(Angle<Self>(degrees: 30)))
assertClose(0.70710678118654752440084436210484903929, cos(Angle<Self>(degrees: 45)))
assertClose(0.5, cos(Angle<Self>(degrees: 60)))
assertClose(0, cos(Angle<Self>(degrees: 90)))
assertClose(-0.5, cos(Angle<Self>(degrees: 120)))
assertClose(-0.70710678118654752440084436210484903929, cos(Angle<Self>(degrees: 135)))
assertClose(-0.86602540378443864676372317075293618347, cos(Angle<Self>(degrees: 150)))
assertClose(-1, cos(Angle<Self>(degrees: 180)))
assertClose(0, cos(Angle<Self>(degrees: 270)))
assertClose(1, cos(Angle<Self>(degrees: 360)))

assertClose(0, sin(Angle<Self>(degrees: -360)))
assertClose(1, sin(Angle<Self>(degrees: -270)))
assertClose(0, sin(Angle<Self>(degrees: -180)))
assertClose(-0.5, sin(Angle<Self>(degrees: -150)))
assertClose(-0.70710678118654752440084436210484903929, sin(Angle<Self>(degrees: -135)))
assertClose(-0.86602540378443864676372317075293618347, sin(Angle<Self>(degrees: -120)))
assertClose(-1, sin(Angle<Self>(degrees: -90)))
assertClose(-0.86602540378443864676372317075293618347, sin(Angle<Self>(degrees: -60)))
assertClose(-0.70710678118654752440084436210484903929, sin(Angle<Self>(degrees: -45)))
assertClose(-0.5, sin(Angle<Self>(degrees: -30)))
assertClose(0, sin(Angle<Self>(degrees: 0)))
assertClose(0.5, sin(Angle<Self>(degrees: 30)))
assertClose(0.70710678118654752440084436210484903929, sin(Angle<Self>(degrees: 45)))
assertClose(0.86602540378443864676372317075293618347, sin(Angle<Self>(degrees: 60)))
assertClose(1, sin(Angle<Self>(degrees: 90)))
assertClose(0.86602540378443864676372317075293618347, sin(Angle<Self>(degrees: 120)))
assertClose(0.70710678118654752440084436210484903929, sin(Angle<Self>(degrees: 135)))
assertClose(0.5, sin(Angle<Self>(degrees: 150)))
assertClose(0, sin(Angle<Self>(degrees: 180)))
assertClose(-1, sin(Angle<Self>(degrees: 270)))
assertClose(0, sin(Angle<Self>(degrees: 360)))

assertClose(0, tan(Angle<Self>(degrees: -360)))
assertClose(Double.infinity, tan(Angle<Self>(degrees: -270)))
assertClose(0, tan(Angle<Self>(degrees: -180)))
assertClose(0.57735026918962576450914878050195745565, tan(Angle<Self>(degrees: -150)))
assertClose(1, tan(Angle<Self>(degrees: -135)))
assertClose(1.7320508075688772935274463415058723669, tan(Angle<Self>(degrees: -120)))
assertClose(-Double.infinity, tan(Angle<Self>(degrees: -90)))
assertClose(-1.7320508075688772935274463415058723669, tan(Angle<Self>(degrees: -60)))
assertClose(-1, tan(Angle<Self>(degrees: -45)))
assertClose(-0.57735026918962576450914878050195745565, tan(Angle<Self>(degrees: -30)))
assertClose(0, tan(Angle<Self>(degrees: 0)))
assertClose(0.57735026918962576450914878050195745565, tan(Angle<Self>(degrees: 30)))
assertClose(1, tan(Angle<Self>(degrees: 45)))
assertClose(1.7320508075688772935274463415058723669, tan(Angle<Self>(degrees: 60)))
assertClose(Double.infinity, tan(Angle<Self>(degrees: 90)))
assertClose(-1.7320508075688772935274463415058723669, tan(Angle<Self>(degrees: 120)))
assertClose(-1, tan(Angle<Self>(degrees: 135)))
assertClose(-0.57735026918962576450914878050195745565, tan(Angle<Self>(degrees: 150)))
assertClose(0, tan(Angle<Self>(degrees: 180)))
assertClose(-Double.infinity, tan(Angle<Self>(degrees: 270)))
assertClose(0, tan(Angle<Self>(degrees: 360)))

assertClose(0.9305076219123142911494767922295555080, Angle<Self>(radians: 0.375).cos)
assertClose(0.3662725290860475613729093517162641571, Angle<Self>(radians: 0.375).sin)
assertClose(0.3936265759256327582294137871012180981, Angle<Self>(radians: 0.375).tan)
}
}

Expand All @@ -44,24 +113,28 @@ final class AngleTests: XCTestCase {
if #available(iOS 14.0, watchOS 14.0, tvOS 7.0, *) {
Float16.conversionBetweenRadiansAndDegreesChecks()
Float16.trigonometricFunctionChecks()
Float16.specialDegreesTrigonometricFunctionChecks()
}
}
#endif

func testFloat() {
Float.conversionBetweenRadiansAndDegreesChecks()
Float.trigonometricFunctionChecks()
Float.specialDegreesTrigonometricFunctionChecks()
}

func testDouble() {
Double.conversionBetweenRadiansAndDegreesChecks()
Double.trigonometricFunctionChecks()
Double.specialDegreesTrigonometricFunctionChecks()
}

#if (arch(i386) || arch(x86_64)) && !os(Windows) && !os(Android)
func testFloat80() {
Float80.conversionBetweenRadiansAndDegreesChecks()
Float80.trigonometricFunctionChecks()
Float80.specialDegreesTrigonometricFunctionChecks()
}
#endif
}
8 changes: 6 additions & 2 deletions Tests/RealTests/ElementaryFunctionChecks.swift
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Original file line number Diff line number Diff line change
Expand Up @@ -27,6 +27,11 @@ internal func assertClose<T>(
file: StaticString = #file,
line: UInt = #line
) -> T where T: BinaryFloatingPoint {
// we need to first check if the values are zero before we check the signs
// otherwise, "0" and "-0" compare as unequal (eg. sin(-180) == 0)
let expectedT = T(expected)
if observed.isZero && expectedT.isZero { return 0 }

// Shortcut relative-error check if we got the sign wrong; it's OK to
// underflow to zero, but we do not want to allow going right through
// zero and getting the sign wrong.
Expand All @@ -38,8 +43,7 @@ internal func assertClose<T>(
if observed.isNaN && expected.isNaN { return 0 }
// If T(expected) is zero or infinite, and matches observed, the error
// is zero.
let expectedT = T(expected)
if observed.isZero && expectedT.isZero { return 0 }

if observed.isInfinite && expectedT.isInfinite { return 0 }
// Special-case where only one of expectedT or observed is infinity.
// Artificially knock everything down a binade, treat actual infinity as
Expand Down