C#: Implement `Mathf.SinCos`

Implement `Mathf.SinCos` that wraps a call to `System.Math.SinCos`,
this allows us to use the `SinCos` method more conveniently with
`real_t`.

Using `Math.SinCos` is often cheaper than separate calls to `Math.Sin`
and `Math.Cos`, and they are often used together.

6 files changed, 73 insertions, 48 deletions

diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Basis.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Basis.cs
index 19f7c54847..b57317e1d0 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Basis.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Basis.cs
@@ -816,26 +816,26 @@ namespace Godot
         public Basis(Vector3 axis, real_t angle)
         {
             Vector3 axisSq = new Vector3(axis.x * axis.x, axis.y * axis.y, axis.z * axis.z);
-            real_t cosine = Mathf.Cos(angle);
-            Row0.x = axisSq.x + cosine * (1.0f - axisSq.x);
-            Row1.y = axisSq.y + cosine * (1.0f - axisSq.y);
-            Row2.z = axisSq.z + cosine * (1.0f - axisSq.z);
+            (real_t sin, real_t cos) = Mathf.SinCos(angle);
 
-            real_t sine = Mathf.Sin(angle);
-            real_t t = 1.0f - cosine;
+            Row0.x = axisSq.x + cos * (1.0f - axisSq.x);
+            Row1.y = axisSq.y + cos * (1.0f - axisSq.y);
+            Row2.z = axisSq.z + cos * (1.0f - axisSq.z);
+
+            real_t t = 1.0f - cos;
 
             real_t xyzt = axis.x * axis.y * t;
-            real_t zyxs = axis.z * sine;
+            real_t zyxs = axis.z * sin;
             Row0.y = xyzt - zyxs;
             Row1.x = xyzt + zyxs;
 
             xyzt = axis.x * axis.z * t;
-            zyxs = axis.y * sine;
+            zyxs = axis.y * sin;
             Row0.z = xyzt + zyxs;
             Row2.x = xyzt - zyxs;
 
             xyzt = axis.y * axis.z * t;
-            zyxs = axis.x * sine;
+            zyxs = axis.x * sin;
             Row1.z = xyzt - zyxs;
             Row2.y = xyzt + zyxs;
         }
@@ -885,19 +885,29 @@ namespace Godot
         /// <param name="order">The order to compose the Euler angles.</param>
         public static Basis FromEuler(Vector3 euler, EulerOrder order = EulerOrder.Yxz)
         {
-            real_t c, s;
-
-            c = Mathf.Cos(euler.x);
-            s = Mathf.Sin(euler.x);
-            Basis xmat = new Basis(new Vector3(1, 0, 0), new Vector3(0, c, s), new Vector3(0, -s, c));
+            (real_t sin, real_t cos) = Mathf.SinCos(euler.x);
+            Basis xmat = new Basis
+            (
+                new Vector3(1, 0, 0),
+                new Vector3(0, cos, sin),
+                new Vector3(0, -sin, cos)
+            );
 
-            c = Mathf.Cos(euler.y);
-            s = Mathf.Sin(euler.y);
-            Basis ymat = new Basis(new Vector3(c, 0, -s), new Vector3(0, 1, 0), new Vector3(s, 0, c));
+            (sin, cos) = Mathf.SinCos(euler.y);
+            Basis ymat = new Basis
+            (
+                new Vector3(cos, 0, -sin),
+                new Vector3(0, 1, 0),
+                new Vector3(sin, 0, cos)
+            );
 
-            c = Mathf.Cos(euler.z);
-            s = Mathf.Sin(euler.z);
-            Basis zmat = new Basis(new Vector3(c, s, 0), new Vector3(-s, c, 0), new Vector3(0, 0, 1));
+            (sin, cos) = Mathf.SinCos(euler.z);
+            Basis zmat = new Basis
+            (
+                new Vector3(cos, sin, 0),
+                new Vector3(-sin, cos, 0),
+                new Vector3(0, 0, 1)
+            );
 
             switch (order)
             {
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs
index ea05c1547c..72a1868964 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/MathfEx.cs
@@ -83,6 +83,17 @@ namespace Godot
         }
 
         /// <summary>
+        /// Returns the sine and cosine of angle <paramref name="s"/> in radians.
+        /// </summary>
+        /// <param name="s">The angle in radians.</param>
+        /// <returns>The sine and cosine of that angle.</returns>
+        public static (real_t Sin, real_t Cos) SinCos(real_t s)
+        {
+            (double sin, double cos) = Math.SinCos(s);
+            return ((real_t)sin, (real_t)cos);
+        }
+
+        /// <summary>
         /// Returns <see langword="true"/> if <paramref name="a"/> and <paramref name="b"/> are approximately
         /// equal to each other.
         /// The comparison is done using the provided tolerance value.
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Projection.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Projection.cs
index fd37f8d9e8..f11b3c553a 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Projection.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Projection.cs
@@ -381,14 +381,14 @@ namespace Godot
             }
             real_t radians = Mathf.DegToRad(fovyDegrees / (real_t)2.0);
             real_t deltaZ = zFar - zNear;
-            real_t sine = Mathf.Sin(radians);
+            (real_t sin, real_t cos) = Mathf.SinCos(radians);
 
-            if ((deltaZ == 0) || (sine == 0) || (aspect == 0))
+            if ((deltaZ == 0) || (sin == 0) || (aspect == 0))
             {
                 return Zero;
             }
 
-            real_t cotangent = Mathf.Cos(radians) / sine;
+            real_t cotangent = cos / sin;
 
             Projection proj = Projection.Identity;
 
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs
index 47106bb402..8e4f9178f7 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Quaternion.cs
@@ -542,14 +542,13 @@ namespace Godot
             }
             else
             {
-                real_t sinAngle = Mathf.Sin(angle * 0.5f);
-                real_t cosAngle = Mathf.Cos(angle * 0.5f);
-                real_t s = sinAngle / d;
+                (real_t sin, real_t cos) = Mathf.SinCos(angle * 0.5f);
+                real_t s = sin / d;
 
                 x = axis.x * s;
                 y = axis.y * s;
                 z = axis.z * s;
-                w = cosAngle;
+                w = cos;
             }
         }
 
@@ -593,12 +592,9 @@ namespace Godot
             // Conversion to quaternion as listed in https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf (page A-6)
             // a3 is the angle of the first rotation, following the notation in this reference.
 
-            real_t cosA1 = Mathf.Cos(halfA1);
-            real_t sinA1 = Mathf.Sin(halfA1);
-            real_t cosA2 = Mathf.Cos(halfA2);
-            real_t sinA2 = Mathf.Sin(halfA2);
-            real_t cosA3 = Mathf.Cos(halfA3);
-            real_t sinA3 = Mathf.Sin(halfA3);
+            (real_t sinA1, real_t cosA1) = Mathf.SinCos(halfA1);
+            (real_t sinA2, real_t cosA2) = Mathf.SinCos(halfA2);
+            (real_t sinA3, real_t cosA3) = Mathf.SinCos(halfA3);
 
             return new Quaternion(
                 (sinA1 * cosA2 * sinA3) + (cosA1 * sinA2 * cosA3),
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Transform2D.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Transform2D.cs
index 6dda150c2b..fa060e3a53 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Transform2D.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Transform2D.cs
@@ -195,8 +195,10 @@ namespace Godot
             Vector2 s2 = transform.GetScale();
 
             // Slerp rotation
-            var v1 = new Vector2(Mathf.Cos(r1), Mathf.Sin(r1));
-            var v2 = new Vector2(Mathf.Cos(r2), Mathf.Sin(r2));
+            (real_t sin1, real_t cos1) = Mathf.SinCos(r1);
+            (real_t sin2, real_t cos2) = Mathf.SinCos(r2);
+            var v1 = new Vector2(cos1, sin1);
+            var v2 = new Vector2(cos2, sin2);
 
             real_t dot = v1.Dot(v2);
 
@@ -213,7 +215,8 @@ namespace Godot
             {
                 real_t angle = weight * Mathf.Acos(dot);
                 Vector2 v3 = (v2 - (v1 * dot)).Normalized();
-                v = (v1 * Mathf.Cos(angle)) + (v3 * Mathf.Sin(angle));
+                (real_t sine, real_t cos) = Mathf.SinCos(angle);
+                v = (v1 * sine) + (v3 * cos);
             }
 
             // Extract parameters
@@ -434,8 +437,9 @@ namespace Godot
         /// <param name="origin">The origin vector, or column index 2.</param>
         public Transform2D(real_t rotation, Vector2 origin)
         {
-            x.x = y.y = Mathf.Cos(rotation);
-            x.y = y.x = Mathf.Sin(rotation);
+            (real_t sin, real_t cos) = Mathf.SinCos(rotation);
+            x.x = y.y = cos;
+            x.y = y.x = sin;
             y.x *= -1;
             this.origin = origin;
         }
@@ -451,10 +455,12 @@ namespace Godot
         /// <param name="origin">The origin vector, or column index 2.</param>
         public Transform2D(real_t rotation, Vector2 scale, real_t skew, Vector2 origin)
         {
-            x.x = Mathf.Cos(rotation) * scale.x;
-            y.y = Mathf.Cos(rotation + skew) * scale.y;
-            y.x = -Mathf.Sin(rotation + skew) * scale.y;
-            x.y = Mathf.Sin(rotation) * scale.x;
+            (real_t rotationSin, real_t rotationCos) = Mathf.SinCos(rotation);
+            (real_t rotationSkewSin, real_t rotationSkewCos) = Mathf.SinCos(rotation + skew);
+            x.x = rotationCos * scale.x;
+            y.y = rotationSkewCos * scale.y;
+            y.x = -rotationSkewSin * scale.y;
+            x.y = rotationSin * scale.x;
             this.origin = origin;
         }
 
diff --git a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
index 57cbef1c5c..1e88e18b3d 100644
--- a/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
+++ b/modules/mono/glue/GodotSharp/GodotSharp/Core/Vector2.cs
@@ -539,11 +539,12 @@ namespace Godot
         /// <returns>The rotated vector.</returns>
         public readonly Vector2 Rotated(real_t angle)
         {
-            real_t sine = Mathf.Sin(angle);
-            real_t cosi = Mathf.Cos(angle);
-            return new Vector2(
-                x * cosi - y * sine,
-                x * sine + y * cosi);
+            (real_t sin, real_t cos) = Mathf.SinCos(angle);
+            return new Vector2
+            (
+                x * cos - y * sin,
+                x * sin + y * cos
+            );
         }
 
         /// <summary>
@@ -693,7 +694,8 @@ namespace Godot
         /// <returns>The resulting vector.</returns>
         public static Vector2 FromAngle(real_t angle)
         {
-            return new Vector2(Mathf.Cos(angle), Mathf.Sin(angle));
+            (real_t sin, real_t cos) = Mathf.SinCos(angle);
+            return new Vector2(cos, sin);
         }
 
         /// <summary>