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.

(cherry picked from commit 50c5ed4876250f785be54b8f6124e7663afa38dc)

5 files changed, 16 insertions, 13 deletions

diff --git a/core/math/basis.cpp b/core/math/basis.cpp
index 95a4187062..bfd902c7e2 100644
--- a/core/math/basis.cpp
+++ b/core/math/basis.cpp
@@ -807,8 +807,8 @@ void Basis::get_axis_angle(Vector3 &r_axis, real_t &r_angle) const {
 	z = (rows[1][0] - rows[0][1]) / s;
 
 	r_axis = Vector3(x, y, z);
-	// CLAMP to avoid NaN if the value passed to acos is not in [0,1].
-	r_angle = Math::acos(CLAMP((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2, (real_t)0.0, (real_t)1.0));
+	// acos does clamping.
+	r_angle = Math::acos((rows[0][0] + rows[1][1] + rows[2][2] - 1) / 2);
 }
 
 void Basis::set_quaternion(const Quaternion &p_quaternion) {
diff --git a/core/math/math_funcs.h b/core/math/math_funcs.h
index 078320d620..f96d3a909f 100644
--- a/core/math/math_funcs.h
+++ b/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); }
-	static _ALWAYS_INLINE_ float asin(float p_x) { return ::asinf(p_x); }
+	// Always does clamping so always safe to use.
+	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); }
-	static _ALWAYS_INLINE_ float acos(float p_x) { return ::acosf(p_x); }
+	// Always does clamping so always safe to use.
+	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); }
diff --git a/core/math/quaternion.cpp b/core/math/quaternion.cpp
index 34e212a5b6..e4ad17c8ef 100644
--- a/core/math/quaternion.cpp
+++ b/core/math/quaternion.cpp
@@ -35,7 +35,8 @@
 
 real_t Quaternion::angle_to(const Quaternion &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);
 }
 
 Vector3 Quaternion::get_euler(EulerOrder p_order) const {
diff --git a/doc/classes/@GlobalScope.xml b/doc/classes/@GlobalScope.xml
index 73f1fe9ad6..8c84a55ba0 100644
--- a/doc/classes/@GlobalScope.xml
+++ b/doc/classes/@GlobalScope.xml
@@ -65,7 +65,7 @@
 			<return type="float" />
 			<param index="0" name="x" type="float" />
 			<description>
-				Returns the arc cosine of [param x] in radians. Use to get the angle of cosine [param x]. [param x] must be between [code]-1.0[/code] and [code]1.0[/code] (inclusive), otherwise, [method acos] will return [constant @GDScript.NAN].
+				Returns the arc cosine of [param x] in radians. Use to get the angle of cosine [param x]. [param x] will be clamped between [code]-1.0[/code] and [code]1.0[/code] (inclusive), in order to prevent [method acos] from returning [constant @GDScript.NAN].
 				[codeblock]
 				# c is 0.523599 or 30 degrees if converted with rad_to_deg(c)
 				var c = acos(0.866025)
@@ -76,7 +76,7 @@
 			<return type="float" />
 			<param index="0" name="x" type="float" />
 			<description>
-				Returns the arc sine of [param x] in radians. Use to get the angle of sine [param x]. [param x] must be between [code]-1.0[/code] and [code]1.0[/code] (inclusive), otherwise, [method asin] will return [constant @GDScript.NAN].
+				Returns the arc sine of [param x] in radians. Use to get the angle of sine [param x]. [param x] will be clamped between [code]-1.0[/code] and [code]1.0[/code] (inclusive), in order to prevent [method asin] from returning [constant @GDScript.NAN].
 				[codeblock]
 				# s is 0.523599 or 30 degrees if converted with rad_to_deg(s)
 				var s = asin(0.5)
diff --git a/tests/core/math/test_math_funcs.h b/tests/core/math/test_math_funcs.h
index c01cdd78b0..b6cb9620f1 100644
--- a/tests/core/math/test_math_funcs.h
+++ b/tests/core/math/test_math_funcs.h
@@ -157,15 +157,15 @@ TEST_CASE_TEMPLATE("[Math] asin/acos/atan", T, float, double) {
 	CHECK(Math::asin((T)0.1) == doctest::Approx((T)0.1001674212));
 	CHECK(Math::asin((T)0.5) == doctest::Approx((T)0.5235987756));
 	CHECK(Math::asin((T)1.0) == doctest::Approx((T)1.5707963268));
-	CHECK(Math::is_nan(Math::asin((T)1.5)));
-	CHECK(Math::is_nan(Math::asin((T)450.0)));
+	CHECK(Math::asin((T)2.0) == doctest::Approx((T)1.5707963268));
+	CHECK(Math::asin((T)-2.0) == doctest::Approx((T)-1.5707963268));
 
 	CHECK(Math::acos((T)-0.1) == doctest::Approx((T)1.670963748));
 	CHECK(Math::acos((T)0.1) == doctest::Approx((T)1.4706289056));
 	CHECK(Math::acos((T)0.5) == doctest::Approx((T)1.0471975512));
 	CHECK(Math::acos((T)1.0) == doctest::Approx((T)0.0));
-	CHECK(Math::is_nan(Math::acos((T)1.5)));
-	CHECK(Math::is_nan(Math::acos((T)450.0)));
+	CHECK(Math::acos((T)2.0) == doctest::Approx((T)0.0));
+	CHECK(Math::acos((T)-2.0) == doctest::Approx((T)Math_PI));
 
 	CHECK(Math::atan((T)-0.1) == doctest::Approx((T)-0.0996686525));
 	CHECK(Math::atan((T)0.1) == doctest::Approx((T)0.0996686525));