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Add inverse hyperbolic functions asinh(), acosh() & atanh()

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GDScript has the following built-in trigonometry functions:

- `sin()`
- `cos()`
- `tan()`
- `asin()`
- `acos()`
- `atan()`
- `atan()`
- `sinh()`
- `cosh()`
- `tanh()`

However, it lacks the hyperbolic arc (also known as inverse
hyperbolic) functions:

- `asinh()`
- `acosh()`
- `atanh()`

Implement them by just exposing the C++ Math library, but clamping
its values to the closest real defined value.
For the cosine, clamp input values lower than 1 to 1.
In the case of the tangent, where the limit value is infinite,
clamp it to -inf or +inf.

References #78377
Fixes godotengine/godot-proposals#7110
This commit is contained in:
Jcrespo 2023-06-18 14:47:01 +02:00 committed by Jaime Crespo
parent 549fcce5f8
commit 528a76486c
5 changed files with 100 additions and 0 deletions
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11
core/math/math_funcs.h
View file

@ -88,6 +88,17 @@ public:
static _ALWAYS_INLINE_ double atan2(double p_y, double p_x) { return ::atan2(p_y, p_x); }
static _ALWAYS_INLINE_ float atan2(float p_y, float p_x) { return ::atan2f(p_y, p_x); }
static _ALWAYS_INLINE_ double asinh(double p_x) { return ::asinh(p_x); }
static _ALWAYS_INLINE_ float asinh(float p_x) { return ::asinhf(p_x); }
// Always does clamping so always safe to use.
static _ALWAYS_INLINE_ double acosh(double p_x) { return p_x < 1 ? 0 : ::acosh(p_x); }
static _ALWAYS_INLINE_ float acosh(float p_x) { return p_x < 1 ? 0 : ::acoshf(p_x); }
// Always does clamping so always safe to use.
static _ALWAYS_INLINE_ double atanh(double p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanh(p_x)); }
static _ALWAYS_INLINE_ float atanh(float p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanhf(p_x)); }
static _ALWAYS_INLINE_ double sqrt(double p_x) { return ::sqrt(p_x); }
static _ALWAYS_INLINE_ float sqrt(float p_x) { return ::sqrtf(p_x); }

16
core/variant/variant_utility.cpp
View file

@ -81,6 +81,18 @@ double VariantUtilityFunctions::atan2(double y, double x) {
return Math::atan2(y, x);
}
double VariantUtilityFunctions::asinh(double arg) {
return Math::asinh(arg);
}
double VariantUtilityFunctions::acosh(double arg) {
return Math::acosh(arg);
}
double VariantUtilityFunctions::atanh(double arg) {
return Math::atanh(arg);
}
double VariantUtilityFunctions::sqrt(double x) {
return Math::sqrt(x);
}
@ -1502,6 +1514,10 @@ void Variant::_register_variant_utility_functions() {
FUNCBINDR(atan2, sarray("y", "x"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(asinh, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(acosh, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(atanh, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(sqrt, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(fmod, sarray("x", "y"), Variant::UTILITY_FUNC_TYPE_MATH);
FUNCBINDR(fposmod, sarray("x", "y"), Variant::UTILITY_FUNC_TYPE_MATH);

3
core/variant/variant_utility.h
View file

@ -45,6 +45,9 @@ struct VariantUtilityFunctions {
static double acos(double arg);
static double atan(double arg);
static double atan2(double y, double x);
static double asinh(double arg);
static double acosh(double arg);
static double atanh(double arg);
static double sqrt(double x);
static double fmod(double b, double r);
static double fposmod(double b, double r);

39
doc/classes/@GlobalScope.xml
View file

@ -72,6 +72,19 @@
[/codeblock]
</description>
</method>
<method name="acosh">
<return type="float" />
<param index="0" name="x" type="float" />
<description>
Returns the hyperbolic arc (also called inverse) cosine of [param x], returning a value in radians. Use it to get the angle from an angle's cosine in hyperbolic space if [param x] is larger or equal to 1. For values of [param x] lower than 1, it will return 0, in order to prevent [method acosh] from returning [constant @GDScript.NAN].
[codeblock]
var a = acosh(2) # Returns 1.31695789692482
cosh(a) # Returns 2
var b = acosh(-1) # Returns 0
[/codeblock]
</description>
</method>
<method name="asin">
<return type="float" />
<param index="0" name="x" type="float" />
@ -83,6 +96,17 @@
[/codeblock]
</description>
</method>
<method name="asinh">
<return type="float" />
<param index="0" name="x" type="float" />
<description>
Returns the hyperbolic arc (also called inverse) sine of [param x], returning a value in radians. Use it to get the angle from an angle's sine in hyperbolic space.
[codeblock]
var a = asinh(0.9) # Returns 0.8088669356527824
sinh(a) # Returns 0.9
[/codeblock]
</description>
</method>
<method name="atan">
<return type="float" />
<param index="0" name="x" type="float" />
@ -107,6 +131,21 @@
[/codeblock]
</description>
</method>
<method name="atanh">
<return type="float" />
<param index="0" name="x" type="float" />
<description>
Returns the hyperbolic arc (also called inverse) tangent of [param x], returning a value in radians. Use it to get the angle from an angle's tangent in hyperbolic space if [param x] is between -1 and 1 (non-inclusive).
In mathematics, the inverse hyperbolic tangent is only defined for -1 &lt; [param x] &lt; 1 in the real set, so values equal or lower to -1 for [param x] return negative [constant @GDScript.INF] and values equal or higher than 1 return positive [constant @GDScript.INF] in order to prevent [method atanh] from returning [constant @GDScript.NAN].
[codeblock]
var a = atanh(0.9) # Returns 1.47221948958322
tanh(a) # Returns 0.9
var b = atanh(-2) # Returns -inf
tanh(b) # Returns -1
[/codeblock]
</description>
</method>
<method name="bezier_derivative">
<return type="float" />
<param index="0" name="start" type="float" />

31
tests/core/math/test_math_funcs.h
View file

@ -175,6 +175,37 @@ TEST_CASE_TEMPLATE("[Math] asin/acos/atan", T, float, double) {
CHECK(Math::atan((T)450.0) == doctest::Approx((T)1.5685741082));
}
TEST_CASE_TEMPLATE("[Math] asinh/acosh/atanh", T, float, double) {
CHECK(Math::asinh((T)-2.0) == doctest::Approx((T)-1.4436354751));
CHECK(Math::asinh((T)-0.1) == doctest::Approx((T)-0.0998340788));
CHECK(Math::asinh((T)0.1) == doctest::Approx((T)0.0998340788));
CHECK(Math::asinh((T)0.5) == doctest::Approx((T)0.4812118250));
CHECK(Math::asinh((T)1.0) == doctest::Approx((T)0.8813735870));
CHECK(Math::asinh((T)2.0) == doctest::Approx((T)1.4436354751));
CHECK(Math::acosh((T)-2.0) == doctest::Approx((T)0.0));
CHECK(Math::acosh((T)-0.1) == doctest::Approx((T)0.0));
CHECK(Math::acosh((T)0.1) == doctest::Approx((T)0.0));
CHECK(Math::acosh((T)0.5) == doctest::Approx((T)0.0));
CHECK(Math::acosh((T)1.0) == doctest::Approx((T)0.0));
CHECK(Math::acosh((T)2.0) == doctest::Approx((T)1.3169578969));
CHECK(Math::acosh((T)450.0) == doctest::Approx((T)6.8023935287));
CHECK(Math::is_inf(Math::atanh((T)-2.0)));
CHECK(Math::atanh((T)-2.0) < (T)0.0);
CHECK(Math::is_inf(Math::atanh((T)-1.0)));
CHECK(Math::atanh((T)-1.0) < (T)0.0);
CHECK(Math::atanh((T)-0.1) == doctest::Approx((T)-0.1003353477));
CHECK(Math::atanh((T)0.1) == doctest::Approx((T)0.1003353477));
CHECK(Math::atanh((T)0.5) == doctest::Approx((T)0.5493061443));
CHECK(Math::is_inf(Math::atanh((T)1.0)));
CHECK(Math::atanh((T)1.0) > (T)0.0);
CHECK(Math::is_inf(Math::atanh((T)1.5)));
CHECK(Math::atanh((T)1.5) > (T)0.0);
CHECK(Math::is_inf(Math::atanh((T)450.0)));
CHECK(Math::atanh((T)450.0) > (T)0.0);
}
TEST_CASE_TEMPLATE("[Math] sinc/sincn/atan2", T, float, double) {
CHECK(Math::sinc((T)-0.1) == doctest::Approx((T)0.9983341665));
CHECK(Math::sinc((T)0.1) == doctest::Approx((T)0.9983341665));