Merge pull request #78404 from jynus/arc-hyperbolic
Add inverse hyperbolic functions `asinh()`, `acosh()` & `atanh()`
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commit
d134473a03
5 changed files with 100 additions and 0 deletions
core
doc/classes
tests/core/math
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@ -88,6 +88,17 @@ public:
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static _ALWAYS_INLINE_ double atan2(double p_y, double p_x) { return ::atan2(p_y, p_x); }
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static _ALWAYS_INLINE_ double atan2(double p_y, double p_x) { return ::atan2(p_y, p_x); }
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static _ALWAYS_INLINE_ float atan2(float p_y, float p_x) { return ::atan2f(p_y, p_x); }
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static _ALWAYS_INLINE_ float atan2(float p_y, float p_x) { return ::atan2f(p_y, p_x); }
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static _ALWAYS_INLINE_ double asinh(double p_x) { return ::asinh(p_x); }
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static _ALWAYS_INLINE_ float asinh(float p_x) { return ::asinhf(p_x); }
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// Always does clamping so always safe to use.
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static _ALWAYS_INLINE_ double acosh(double p_x) { return p_x < 1 ? 0 : ::acosh(p_x); }
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static _ALWAYS_INLINE_ float acosh(float p_x) { return p_x < 1 ? 0 : ::acoshf(p_x); }
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// Always does clamping so always safe to use.
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static _ALWAYS_INLINE_ double atanh(double p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanh(p_x)); }
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static _ALWAYS_INLINE_ float atanh(float p_x) { return p_x <= -1 ? -INFINITY : (p_x >= 1 ? INFINITY : ::atanhf(p_x)); }
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static _ALWAYS_INLINE_ double sqrt(double p_x) { return ::sqrt(p_x); }
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static _ALWAYS_INLINE_ double sqrt(double p_x) { return ::sqrt(p_x); }
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static _ALWAYS_INLINE_ float sqrt(float p_x) { return ::sqrtf(p_x); }
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static _ALWAYS_INLINE_ float sqrt(float p_x) { return ::sqrtf(p_x); }
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@ -81,6 +81,18 @@ double VariantUtilityFunctions::atan2(double y, double x) {
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return Math::atan2(y, x);
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return Math::atan2(y, x);
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}
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}
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double VariantUtilityFunctions::asinh(double arg) {
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return Math::asinh(arg);
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}
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double VariantUtilityFunctions::acosh(double arg) {
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return Math::acosh(arg);
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}
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double VariantUtilityFunctions::atanh(double arg) {
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return Math::atanh(arg);
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}
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double VariantUtilityFunctions::sqrt(double x) {
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double VariantUtilityFunctions::sqrt(double x) {
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return Math::sqrt(x);
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return Math::sqrt(x);
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}
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}
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@ -1502,6 +1514,10 @@ void Variant::_register_variant_utility_functions() {
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FUNCBINDR(atan2, sarray("y", "x"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(atan2, sarray("y", "x"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(asinh, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(acosh, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(atanh, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(sqrt, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(sqrt, sarray("x"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(fmod, sarray("x", "y"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(fmod, sarray("x", "y"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(fposmod, sarray("x", "y"), Variant::UTILITY_FUNC_TYPE_MATH);
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FUNCBINDR(fposmod, sarray("x", "y"), Variant::UTILITY_FUNC_TYPE_MATH);
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@ -45,6 +45,9 @@ struct VariantUtilityFunctions {
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static double acos(double arg);
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static double acos(double arg);
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static double atan(double arg);
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static double atan(double arg);
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static double atan2(double y, double x);
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static double atan2(double y, double x);
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static double asinh(double arg);
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static double acosh(double arg);
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static double atanh(double arg);
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static double sqrt(double x);
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static double sqrt(double x);
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static double fmod(double b, double r);
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static double fmod(double b, double r);
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static double fposmod(double b, double r);
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static double fposmod(double b, double r);
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@ -72,6 +72,19 @@
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[/codeblock]
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[/codeblock]
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</description>
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</description>
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</method>
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</method>
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<method name="acosh">
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<return type="float" />
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<param index="0" name="x" type="float" />
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<description>
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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].
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[codeblock]
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var a = acosh(2) # Returns 1.31695789692482
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cosh(a) # Returns 2
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var b = acosh(-1) # Returns 0
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[/codeblock]
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</description>
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</method>
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<method name="asin">
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<method name="asin">
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<return type="float" />
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<return type="float" />
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<param index="0" name="x" type="float" />
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<param index="0" name="x" type="float" />
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@ -83,6 +96,17 @@
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[/codeblock]
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[/codeblock]
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</description>
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</description>
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</method>
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</method>
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<method name="asinh">
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<return type="float" />
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<param index="0" name="x" type="float" />
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<description>
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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.
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[codeblock]
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var a = asinh(0.9) # Returns 0.8088669356527824
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sinh(a) # Returns 0.9
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[/codeblock]
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</description>
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</method>
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<method name="atan">
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<method name="atan">
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<return type="float" />
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<return type="float" />
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<param index="0" name="x" type="float" />
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<param index="0" name="x" type="float" />
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@ -107,6 +131,21 @@
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[/codeblock]
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[/codeblock]
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</description>
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</description>
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</method>
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</method>
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<method name="atanh">
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<return type="float" />
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<param index="0" name="x" type="float" />
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<description>
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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).
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In mathematics, the inverse hyperbolic tangent is only defined for -1 < [param x] < 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].
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[codeblock]
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var a = atanh(0.9) # Returns 1.47221948958322
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tanh(a) # Returns 0.9
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var b = atanh(-2) # Returns -inf
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tanh(b) # Returns -1
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[/codeblock]
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</description>
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</method>
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<method name="bezier_derivative">
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<method name="bezier_derivative">
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<return type="float" />
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<return type="float" />
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<param index="0" name="start" type="float" />
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<param index="0" name="start" type="float" />
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@ -175,6 +175,37 @@ TEST_CASE_TEMPLATE("[Math] asin/acos/atan", T, float, double) {
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CHECK(Math::atan((T)450.0) == doctest::Approx((T)1.5685741082));
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CHECK(Math::atan((T)450.0) == doctest::Approx((T)1.5685741082));
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}
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}
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TEST_CASE_TEMPLATE("[Math] asinh/acosh/atanh", T, float, double) {
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CHECK(Math::asinh((T)-2.0) == doctest::Approx((T)-1.4436354751));
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CHECK(Math::asinh((T)-0.1) == doctest::Approx((T)-0.0998340788));
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CHECK(Math::asinh((T)0.1) == doctest::Approx((T)0.0998340788));
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CHECK(Math::asinh((T)0.5) == doctest::Approx((T)0.4812118250));
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CHECK(Math::asinh((T)1.0) == doctest::Approx((T)0.8813735870));
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CHECK(Math::asinh((T)2.0) == doctest::Approx((T)1.4436354751));
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CHECK(Math::acosh((T)-2.0) == doctest::Approx((T)0.0));
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CHECK(Math::acosh((T)-0.1) == doctest::Approx((T)0.0));
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CHECK(Math::acosh((T)0.1) == doctest::Approx((T)0.0));
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CHECK(Math::acosh((T)0.5) == doctest::Approx((T)0.0));
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CHECK(Math::acosh((T)1.0) == doctest::Approx((T)0.0));
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CHECK(Math::acosh((T)2.0) == doctest::Approx((T)1.3169578969));
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CHECK(Math::acosh((T)450.0) == doctest::Approx((T)6.8023935287));
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CHECK(Math::is_inf(Math::atanh((T)-2.0)));
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CHECK(Math::atanh((T)-2.0) < (T)0.0);
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CHECK(Math::is_inf(Math::atanh((T)-1.0)));
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CHECK(Math::atanh((T)-1.0) < (T)0.0);
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CHECK(Math::atanh((T)-0.1) == doctest::Approx((T)-0.1003353477));
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CHECK(Math::atanh((T)0.1) == doctest::Approx((T)0.1003353477));
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CHECK(Math::atanh((T)0.5) == doctest::Approx((T)0.5493061443));
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CHECK(Math::is_inf(Math::atanh((T)1.0)));
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CHECK(Math::atanh((T)1.0) > (T)0.0);
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CHECK(Math::is_inf(Math::atanh((T)1.5)));
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CHECK(Math::atanh((T)1.5) > (T)0.0);
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CHECK(Math::is_inf(Math::atanh((T)450.0)));
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CHECK(Math::atanh((T)450.0) > (T)0.0);
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}
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TEST_CASE_TEMPLATE("[Math] sinc/sincn/atan2", T, float, double) {
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TEST_CASE_TEMPLATE("[Math] sinc/sincn/atan2", T, float, double) {
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CHECK(Math::sinc((T)-0.1) == doctest::Approx((T)0.9983341665));
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CHECK(Math::sinc((T)-0.1) == doctest::Approx((T)0.9983341665));
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CHECK(Math::sinc((T)0.1) == doctest::Approx((T)0.9983341665));
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CHECK(Math::sinc((T)0.1) == doctest::Approx((T)0.9983341665));
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