Introducing Angle type [Issue #88]

Sources/RealModule/Angle.swift

@@ -0,0 +1,132 @@
+//===--- Angle.swift ------------------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift Numerics open source project
+//
+// Copyright (c) 2020 Apple Inc. and the Swift Numerics project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
+//
+//===----------------------------------------------------------------------===//
+
+/// A wrapper type for angle operations and functions
+///
+/// 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 & 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) {
+        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 ElementaryFunctions
+where Self: Real & BinaryFloatingPoint {
+    /// See also:
+    /// -
+    /// `ElementaryFunctions.cos()`
+    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()`
+    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()`
+    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()`
+    static func acos(_ x: T) -> Self { Angle.radians(T.acos(x)) }
+
+    /// See also:
+    /// -
+    /// `ElementaryFunctions.asin()`
+    static func asin(_ x: T) -> Self { Angle.radians(T.asin(x)) }
+
+    /// See also:
+    /// -
+    /// `ElementaryFunctions.atan()`
+    static func atan(_ x: T) -> Self { Angle.radians(T.atan(x)) }
+
+    /// See also:
+    /// -
+    /// `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
+}

Tests/RealTests/AngleTests.swift

@@ -0,0 +1,140 @@
+//===--- AngleTests.swift -------------------------------------*- swift -*-===//
+//
+// This source file is part of the Swift Numerics open source project
+//
+// Copyright (c) 2020 Apple Inc. and the Swift Numerics project authors
+// Licensed under Apache License v2.0 with Runtime Library Exception
+//
+// See https://swift.org/LICENSE.txt for license information
+// See https://swift.org/CONTRIBUTORS.txt for the list of Swift project authors
+//
+//===----------------------------------------------------------------------===//
+
+import RealModule
+import XCTest
+import _TestSupport
+
+internal extension Real
+where Self: BinaryFloatingPoint {
+    static func conversionBetweenRadiansAndDegreesChecks() {
+        let angleFromRadians = Angle<Self>(radians: Self.pi / 3)
+        assertClose(60, angleFromRadians.degrees)
+
+        let angleFromDegrees = Angle<Self>(degrees: 120)
+        // the compiler complains with the following line
+        // assertClose(2 * Self.pi / 3, angleFromDegrees.radians)
+        assertClose(2 * Double(Self.pi) / 3, angleFromDegrees.radians)
+    }
+
+    static func trigonometricFunctionChecks() {
+        assertClose(1.1863995522992575361931268186727044683, Angle<Self>.acos(0.375).radians)
+        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)))
+        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)))
+
+    }
+}
+
+final class AngleTests: XCTestCase {
+    #if swift(>=5.3) && !(os(macOS) || os(iOS) && targetEnvironment(macCatalyst))
+    func testFloat16() {
+        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
+}

Tests/RealTests/ElementaryFunctionChecks.swift

@@ -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.
@@ -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