Add AsinPi, AcosPi, AtanPi and Atan2Pi

src/libraries/System.Private.CoreLib/src/System/Math.cs

@@ -1620,5 +1620,68 @@ public static double TanPi(double x)
             double tan = Tan(rem * PI);
             return invert ? -tan : tan;
         }
+
+        // We don't need to special case inverse-trigs as long as getting precise PI/2 and PI.
+        // Guarded in unit test.
+
+        /// <summary>
+        /// Returns the angle measured in half-turns whose sine is the specified number.
+        /// </summary>
+        /// <param name="x">A number representing a sine, where <paramref name="x"/> must be greater than or equal to -1, but
+        /// less than or equal to 1.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -0.5 ≤ θ ≤ 0.5.
+        /// -or-
+        /// <see cref="double.NaN"/> if <paramref name="x"/> &lt; -1 or <paramref name="x"/> &gt; 1
+        /// or <paramref name="x"/> equals <see cref="double.NaN"/>.</returns>
+        public static double AsinPi(double x) => Asin(x) / PI;
+
+        /// <summary>
+        /// Returns the angle measured in half-turns whose cosine is the specified number.
+        /// </summary>
+        /// <param name="x">A number representing a cosine, where <paramref name="x"/> must be greater than or equal to -1, but
+        /// less than or equal to 1.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -0.5 ≤ θ ≤ 0.5.
+        /// -or-
+        /// <see cref="double.NaN"/> if <paramref name="x"/> &lt; -1 or <paramref name="x"/> &gt; 1
+        /// or <paramref name="x"/> equals <see cref="double.NaN"/>.</returns>
+        public static double AcosPi(double x) => Acos(x) / PI;
+
+        /// <summary>
+        /// Returns the angle measured in half-turns whose tangent is the specified number.
+        /// </summary>
+        /// <param name="x">A number representing a tangent.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -0.5 ≤ θ ≤ 0.5.
+        /// -or-
+        /// <see cref="double.NaN"/> if <paramref name="x"/> equals <see cref="double.NaN"/>,
+        /// -0.5 if <paramref name="x"/> equals <see cref="double.NegativeInfinity"/>,
+        /// or 0.5 if <paramref name="x"/> equals <see cref="double.PositiveInfinity"/>.</returns>
+        public static double AtanPi(double x) => Atan(x) / PI;
+
+        /// <summary>
+        /// Returns the angle whose measured in half-turns tangent is the quotient of two specified numbers.
+        /// </summary>
+        /// <param name="y">The y coordinate of a point.</param>
+        /// <param name="x">The x coordinate of a point.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -1 ≤ θ ≤ 1, and tan(θ) = y / x,
+        /// where (x, y) is a point in the Cartesian plane. Observe the following:
+        /// <list type="bullet">
+        /// <item>For (x, y) in quadrant 1, 0 &lt; θ &lt; 0.5. </item>
+        /// <item>For (x, y) in quadrant 2, 0.5 &lt; θ ≤ 1. </item>
+        /// <item>For (x, y) in quadrant 3, -1 &lt; θ &lt; -0.5. </item>
+        /// <item>For (x, y) in quadrant 4, -0.5 &lt; θ &lt; 0. </item>
+        /// </list>
+        /// For points on the boundaries of the quadrants, the return value is the following:
+        /// <list type="bullet">
+        /// <item>If y is 0 and x is not negative, θ = 0.</item>
+        /// <item>If y is 0 and x is negative, θ = 1.</item>
+        /// <item>If y is positive and x is 0, θ = 0.5.</item>
+        /// <item>If y is negative and x is 0, θ = -0.5.</item>
+        /// <item>If y is 0 and x is 0, θ = 0.</item>
+        /// <item>If y is 0 and x is 0, θ = 0.</item>
+        /// </list>
+        /// If x or y is <see cref="double.NaN"/>, or if x and y are either
+        /// <see cref="double.PositiveInfinity"/> or <see cref="double.NegativeInfinity"/>,
+        /// the method returns <see cref="double.NaN"/>.</returns>
+        public static double Atan2Pi(double y, double x) => Atan2(y, x) / PI;
     }
 }

src/libraries/System.Private.CoreLib/src/System/MathF.cs

@@ -691,5 +691,68 @@ public static float TanPi(float x)
             float tan = Tan(rem * PI);
             return invert ? -tan : tan;
         }
+
+        // We don't need to special case inverse-trigs as long as getting precise PI/2 and PI.
+        // Guarded in unit test.
+
+        /// <summary>
+        /// Returns the angle measured in half-turns whose sine is the specified number.
+        /// </summary>
+        /// <param name="x">A number representing a sine, where <paramref name="x"/> must be greater than or equal to -1, but
+        /// less than or equal to 1.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -0.5 ≤ θ ≤ 0.5.
+        /// -or-
+        /// <see cref="float.NaN"/> if <paramref name="x"/> &lt; -1 or <paramref name="x"/> &gt; 1
+        /// or <paramref name="x"/> equals <see cref="float.NaN"/>.</returns>
+        public static float AsinPi(float x) => Asin(x) / PI;
+
+        /// <summary>
+        /// Returns the angle measured in half-turns whose cosine is the specified number.
+        /// </summary>
+        /// <param name="x">A number representing a cosine, where <paramref name="x"/> must be greater than or equal to -1, but
+        /// less than or equal to 1.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -0.5 ≤ θ ≤ 0.5.
+        /// -or-
+        /// <see cref="float.NaN"/> if <paramref name="x"/> &lt; -1 or <paramref name="x"/> &gt; 1
+        /// or <paramref name="x"/> equals <see cref="float.NaN"/>.</returns>
+        public static float AcosPi(float x) => Acos(x) / PI;
+
+        /// <summary>
+        /// Returns the angle measured in half-turns whose tangent is the specified number.
+        /// </summary>
+        /// <param name="x">A number representing a tangent.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -0.5 ≤ θ ≤ 0.5.
+        /// -or-
+        /// <see cref="float.NaN"/> if <paramref name="x"/> equals <see cref="float.NaN"/>,
+        /// -0.5 if <paramref name="x"/> equals <see cref="float.NegativeInfinity"/>,
+        /// or 0.5 if <paramref name="x"/> equals <see cref="float.PositiveInfinity"/>.</returns>
+        public static float AtanPi(float x) => Atan(x) / PI;
+
+        /// <summary>
+        /// Returns the angle whose measured in half-turns tangent is the quotient of two specified numbers.
+        /// </summary>
+        /// <param name="y">The y coordinate of a point.</param>
+        /// <param name="x">The x coordinate of a point.</param>
+        /// <returns>An angle, θ, measured in half-turns, such that -1 ≤ θ ≤ 1, and tan(θ) = y / x,
+        /// where (x, y) is a point in the Cartesian plane. Observe the following:
+        /// <list type="bullet">
+        /// <item>For (x, y) in quadrant 1, 0 &lt; θ &lt; 0.5. </item>
+        /// <item>For (x, y) in quadrant 2, 0.5 &lt; θ ≤ 1. </item>
+        /// <item>For (x, y) in quadrant 3, -1 &lt; θ &lt; -0.5. </item>
+        /// <item>For (x, y) in quadrant 4, -0.5 &lt; θ &lt; 0. </item>
+        /// </list>
+        /// For points on the boundaries of the quadrants, the return value is the following:
+        /// <list type="bullet">
+        /// <item>If y is 0 and x is not negative, θ = 0.</item>
+        /// <item>If y is 0 and x is negative, θ = 1.</item>
+        /// <item>If y is positive and x is 0, θ = 0.5.</item>
+        /// <item>If y is negative and x is 0, θ = -0.5.</item>
+        /// <item>If y is 0 and x is 0, θ = 0.</item>
+        /// <item>If y is 0 and x is 0, θ = 0.</item>
+        /// </list>
+        /// If x or y is <see cref="float.NaN"/>, or if x and y are either
+        /// <see cref="float.PositiveInfinity"/> or <see cref="float.NegativeInfinity"/>,
+        /// the method returns <see cref="float.NaN"/>.</returns>
+        public static float Atan2Pi(float y, float x) => Atan2(y, x) / PI;
     }
 }

src/libraries/System.Runtime/ref/System.Runtime.cs

@@ -2751,11 +2751,15 @@ public static partial class Math
         public static float Abs(float value) { throw null; }
         public static double Acos(double d) { throw null; }
         public static double Acosh(double d) { throw null; }
+        public static double AcosPi(double x) { throw null; }
         public static double Asin(double d) { throw null; }
         public static double Asinh(double d) { throw null; }
+        public static double AsinPi(double x) { throw null; }
         public static double Atan(double d) { throw null; }
         public static double Atan2(double y, double x) { throw null; }
+        public static double Atan2Pi(double y, double x) { throw null; }
         public static double Atanh(double d) { throw null; }
+        public static double AtanPi(double x) { throw null; }
         public static long BigMul(int a, int b) { throw null; }
         public static long BigMul(long a, long b, out long low) { throw null; }
         [System.CLSCompliantAttribute(false)]
@@ -2892,11 +2896,15 @@ public static partial class MathF
         public static float Abs(float x) { throw null; }
         public static float Acos(float x) { throw null; }
         public static float Acosh(float x) { throw null; }
+        public static float AcosPi(float x) { throw null; }
         public static float Asin(float x) { throw null; }
         public static float Asinh(float x) { throw null; }
+        public static float AsinPi(float x) { throw null; }
         public static float Atan(float x) { throw null; }
         public static float Atan2(float y, float x) { throw null; }
+        public static float Atan2Pi(float y, float x) { throw null; }
         public static float Atanh(float x) { throw null; }
+        public static float AtanPi(float x) { throw null; }
         public static float BitDecrement(float x) { throw null; }
         public static float BitIncrement(float x) { throw null; }
         public static float Cbrt(float x) { throw null; }