Make acos and asin safe

A common bug with using acos and asin is that input outside -1 to 1 range will result in Nan output. This can occur due to floating point error in the input.

The standard solution is to provide safe_acos function with clamped input. For Godot it may make more sense to make the standard functions safe.

core/math/basis.cpp

@@ -925,6 +925,7 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
 	// as we have reached here there are no singularities so we can handle normally
 	real_t s = Math::sqrt((elements[1][2] - elements[2][1]) * (elements[1][2] - elements[2][1]) + (elements[2][0] - elements[0][2]) * (elements[2][0] - elements[0][2]) + (elements[0][1] - elements[1][0]) * (elements[0][1] - elements[1][0])); // s=|axis||sin(angle)|, used to normalise
 
+	// acos does clamping.
 	angle = Math::acos((elements[0][0] + elements[1][1] + elements[2][2] - 1) / 2);
 	if (angle < 0) {
 		s = -s;

core/math/math_funcs.h

@@ -74,11 +74,13 @@ public:
 	static _ALWAYS_INLINE_ double tanh(double p_x) { return ::tanh(p_x); }
 	static _ALWAYS_INLINE_ float tanh(float p_x) { return ::tanhf(p_x); }
 
-	static _ALWAYS_INLINE_ double asin(double p_x) { return ::asin(p_x); }
+	// Always does clamping so always safe to use.
-	static _ALWAYS_INLINE_ float asin(float p_x) { return ::asinf(p_x); }
+	static _ALWAYS_INLINE_ double asin(double p_x) { return p_x < -1 ? (-Math_PI / 2) : (p_x > 1 ? (Math_PI / 2) : ::asin(p_x)); }
+	static _ALWAYS_INLINE_ float asin(float p_x) { return p_x < -1 ? (-Math_PI / 2) : (p_x > 1 ? (Math_PI / 2) : ::asinf(p_x)); }
 
-	static _ALWAYS_INLINE_ double acos(double p_x) { return ::acos(p_x); }
+	// Always does clamping so always safe to use.
-	static _ALWAYS_INLINE_ float acos(float p_x) { return ::acosf(p_x); }
+	static _ALWAYS_INLINE_ double acos(double p_x) { return p_x < -1 ? Math_PI : (p_x > 1 ? 0 : ::acos(p_x)); }
+	static _ALWAYS_INLINE_ float acos(float p_x) { return p_x < -1 ? Math_PI : (p_x > 1 ? 0 : ::acosf(p_x)); }
 
 	static _ALWAYS_INLINE_ double atan(double p_x) { return ::atan(p_x); }
 	static _ALWAYS_INLINE_ float atan(float p_x) { return ::atanf(p_x); }

core/math/quat.cpp

@@ -35,7 +35,9 @@
 
 real_t Quat::angle_to(const Quat &p_to) const {
 	real_t d = dot(p_to);
-	return Math::acos(CLAMP(d * d * 2 - 1, -1, 1));
+
+	// acos does clamping.
+	return Math::acos(d * d * 2 - 1);
 }
 
 // set_euler_xyz expects a vector containing the Euler angles in the format

modules/gdscript/doc_classes/@GDScript.xml

@@ -52,7 +52,7 @@
 			<return type="float" />
 			<argument index="0" name="s" type="float" />
 			<description>
-				Returns the arc cosine of [code]s[/code] in radians. Use to get the angle of cosine [code]s[/code]. [code]s[/code] must be between [code]-1.0[/code] and [code]1.0[/code] (inclusive), otherwise, [method acos] will return [constant NAN].
+				Returns the arc cosine of [code]s[/code] in radians. Use to get the angle of cosine [code]s[/code]. [code]s[/code] will be clamped between [code]-1.0[/code] and [code]1.0[/code] (inclusive), in order to prevent [method acos] from returning [constant NAN].
 				[codeblock]
 				# c is 0.523599 or 30 degrees if converted with rad2deg(s)
 				c = acos(0.866025)
@@ -63,7 +63,7 @@
 			<return type="float" />
 			<argument index="0" name="s" type="float" />
 			<description>
-				Returns the arc sine of [code]s[/code] in radians. Use to get the angle of sine [code]s[/code]. [code]s[/code] must be between [code]-1.0[/code] and [code]1.0[/code] (inclusive), otherwise, [method asin] will return [constant NAN].
+				Returns the arc sine of [code]s[/code] in radians. Use to get the angle of sine [code]s[/code]. [code]s[/code] will be clamped between [code]-1.0[/code] and [code]1.0[/code] (inclusive), in order to prevent [method asin] from returning [constant NAN].
 				[codeblock]
 				# s is 0.523599 or 30 degrees if converted with rad2deg(s)
 				s = asin(0.5)

scene/3d/path.cpp

@@ -175,7 +175,9 @@ void PathFollow::_update_transform(bool p_update_xyz_rot) {
 
 			Vector3 axis = t_prev.cross(t_cur);
 			float dot = t_prev.dot(t_cur);
-			float angle = Math::acos(CLAMP(dot, -1, 1));
+
+			// acos does clamping.
+			float angle = Math::acos(dot);
 
 			if (likely(!Math::is_zero_approx(angle))) {
 				if (rotation_mode == ROTATION_Y) {

scene/animation/skeleton_ik.cpp

@@ -296,7 +296,8 @@ void FabrikInverseKinematic::solve(Task *p_task, real_t blending_delta, bool ove
 			const Vector3 rot_axis(initial_ori.cross(ci->current_ori).normalized());
 
 			if (rot_axis[0] != 0 && rot_axis[1] != 0 && rot_axis[2] != 0) {
-				const real_t rot_angle(Math::acos(CLAMP(initial_ori.dot(ci->current_ori), -1, 1)));
+				// acos does clamping.
+				const real_t rot_angle(Math::acos(initial_ori.dot(ci->current_ori)));
 				new_bone_pose.basis.rotate(rot_axis, rot_angle);
 			}
 

scene/resources/sky.cpp

@@ -173,7 +173,8 @@ Ref<Image> ProceduralSky::_generate_sky() {
 
 				normal.normalize();
 
-				float v_angle = Math::acos(CLAMP(normal.y, -1.0, 1.0));
+				// acos does clamping.
+				float v_angle = Math::acos(normal.y);
 
 				Color color;
 
@@ -192,7 +193,8 @@ Ref<Image> ProceduralSky::_generate_sky() {
 					color.g *= sky_energy;
 					color.b *= sky_energy;
 
-					float sun_angle = Math::rad2deg(Math::acos(CLAMP(sun.dot(normal), -1.0, 1.0)));
+					// acos does clamping.
+					float sun_angle = Math::rad2deg(Math::acos(sun.dot(normal)));
 
 					if (sun_angle < sun_angle_min) {
 						color = color.blend(sun_linear);