Math: use __builtin_sincos for sincos() on GCC.

Makes this thing faster on Debug. But I'm not sure whether it's due to
less function calls or this intrinsic being actually faster, heh.
Probably a combination of both.

doc/changelog.dox

@@ -315,6 +315,9 @@ See also:
 -   Changed the way @ref Math::operator<<(Corrade::Utility::Debug&, const BoolVector<size>&)
     works --- the output now has the same bit order as when constructing it
     using binary literals
+-   @ref Math::sincos() now uses the `__builtin_sincos` intrinsic on GCC,
+    making it potentially faster in case the optimizer doesn't figure out the
+    same
 
 @subsubsection changelog-latest-changes-meshtools MeshTools library
 

src/Magnum/Math/Functions.h

@@ -114,17 +114,44 @@ template<class T> inline T cos(Unit<Rad, T> angle) { return std::cos(T(angle));
 template<class T> inline T cos(Unit<Deg, T> angle) { return cos(Rad<T>(angle)); }
 #endif
 
+#if defined(__GNUC__) && !defined(__clang__)
+namespace Implementation {
+    /* GCC builtin since 3.4 (https://stackoverflow.com/a/2742861),
+       unfortunately either Clang nor MSVC have any alternative which wouldn't
+       involve inline assembly. */
+    inline void sincos(Float rad, Float& sin, Float& cos) {
+        __builtin_sincosf(rad, &sin, &cos);
+    }
+    inline void sincos(Double rad, Double& sin, Double& cos) {
+        __builtin_sincos(rad, &sin, &cos);
+    }
+    inline void sincos(long double rad, long double& sin, long double& cos) {
+        __builtin_sincosl(rad, &sin, &cos);
+    }
+    /* Assuming there's no other floating-point type */
+}
+#endif
+
 /**
 @brief Sine and cosine
 
-On some architectures might be faster than doing both computations separately.
+On GCC, this uses the `__builtin_sincos` intrinsic (or its `f` / `l` suffixed
+variants), which may be faster than calculating sine and cosine separately. On
+other compilers this *might* result in the optimizer picking up the combined
+instruction as well.
 @see @ref sin(), @ref cos(), @ref sincos(const Dual<Rad<T>>&)
 */
 #ifdef DOXYGEN_GENERATING_OUTPUT
 template<class T> inline std::pair<T, T> sincos(Rad<T> angle);
 #else
 template<class T> inline std::pair<T, T> sincos(Unit<Rad, T> angle) {
-    return {std::sin(T(angle)) ,std::cos(T(angle))};
+    #if defined(__GNUC__) && !defined(__clang__)
+    std::pair<T, T> out;
+    Implementation::sincos(T(angle), out.first, out.second);
+    return out;
+    #else
+    return {std::sin(T(angle)), std::cos(T(angle))};
+    #endif
 }
 template<class T> inline std::pair<T, T> sincos(Unit<Deg, T> angle) { return sincos(Rad<T>(angle)); }
 #endif

src/Magnum/Math/Test/FunctionsTest.cpp

@@ -24,6 +24,7 @@
 */
 
 #include <Corrade/TestSuite/Tester.h>
+#include <Corrade/TestSuite/Compare/Numeric.h>
 
 #include "Magnum/Math/Functions.h"
 #include "Magnum/Math/Vector4.h"
@@ -67,8 +68,13 @@ struct FunctionsTest: Corrade::TestSuite::Tester {
     void isInfVector();
     void isNan();
     void isNanfVector();
+
     void trigonometric();
     void trigonometricWithBase();
+    template<class T> void sincos();
+
+    void sinCosSeparateBenchmark();
+    void sinCosCombinedBenchmark();
 };
 
 using namespace Literals;
@@ -118,8 +124,18 @@ FunctionsTest::FunctionsTest() {
               &FunctionsTest::isInfVector,
               &FunctionsTest::isNan,
               &FunctionsTest::isNanfVector,
+
               &FunctionsTest::trigonometric,
-              &FunctionsTest::trigonometricWithBase});
+              &FunctionsTest::trigonometricWithBase,
+              &FunctionsTest::sincos<Float>,
+              &FunctionsTest::sincos<Double>,
+              #ifndef CORRADE_TARGET_EMSCRIPTEN
+              &FunctionsTest::sincos<long double>,
+              #endif
+              });
+
+    addBenchmarks({&FunctionsTest::sinCosSeparateBenchmark,
+                   &FunctionsTest::sinCosCombinedBenchmark}, 100);
 }
 
 void FunctionsTest::powIntegral() {
@@ -463,6 +479,38 @@ void FunctionsTest::trigonometricWithBase() {
     CORRADE_COMPARE(Math::tan(2*Rad(Constants::pi()/8)), 1.0f);
 }
 
+template<class T> void FunctionsTest::sincos() {
+    setTestCaseTemplateName(TypeTraits<T>::name());
+
+    /* For GCC's __builtin_sincos this verifies that all specializations are
+       correct */
+    CORRADE_COMPARE(Math::sincos(Math::Deg<T>(T(30.0))).first, T(0.5));
+    CORRADE_COMPARE(Math::sincos(Math::Deg<T>(T(30.0))).second, T(0.8660254037844386));
+}
+
+void FunctionsTest::sinCosSeparateBenchmark() {
+    Float sin{}, cos{}, a{};
+    CORRADE_BENCHMARK(1000) {
+        sin += Math::sin(Rad(a));
+        cos += Math::cos(Rad(a));
+        a += 0.1f;
+    }
+
+    CORRADE_COMPARE_AS(a, 10.0f, Corrade::TestSuite::Compare::Greater);
+}
+
+void FunctionsTest::sinCosCombinedBenchmark() {
+    Float sin{}, cos{}, a{};
+    CORRADE_BENCHMARK(1000) {
+        auto sincos = Math::sincos(Rad(a));
+        sin += sincos.first;
+        cos += sincos.second;
+        a += 0.1f;
+    }
+
+    CORRADE_COMPARE_AS(a, 10.0f, Corrade::TestSuite::Compare::Greater);
+}
+
 }}}}
 
 CORRADE_TEST_MAIN(Magnum::Math::Test::FunctionsTest)