Math: add popcount().

doc/changelog.dox

@@ -70,6 +70,7 @@ See also:
 
 -   Added @ref Math::fmod() (see [mosra/magnum#454](https://github.com/mosra/magnum/pull/454))
 -   Added @ref Math::binomialCoefficient() (see [mosra/magnum#461](https://github.com/mosra/magnum/pull/461))
+-   Added @ref Math::popcount()
 
 @subsubsection changelog-latest-new-meshtools MeshTools library
 

src/Magnum/Math/Functions.cpp

@@ -30,6 +30,30 @@
 
 namespace Magnum { namespace Math {
 
+#if !defined(CORRADE_TARGET_GCC) && !defined(CORRADE_TARGET_CLANG)
+namespace {
+
+/* https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel
+   there's also https://stackoverflow.com/a/109025 which mostly just copies
+   parts of this together with a lot of noise and syntax errors. */
+template<class T> inline UnsignedInt popcountImplementation(T v) {
+    v = v - ((v >> 1) & ~T(0)/3);
+    v = (v & ~T(0)/15*3) + ((v >> 2) & ~T(0)/15*3);
+    v = (v + (v >> 4)) & ~T(0)/255*15;
+    return (v*(~T(0)/255)) >> (sizeof(T) - 1)*8;
+}
+
+}
+
+UnsignedInt popcount(UnsignedInt number) {
+    return popcountImplementation(number);
+}
+
+UnsignedInt popcount(UnsignedLong number) {
+    return popcountImplementation(number);
+}
+#endif
+
 UnsignedInt log(UnsignedInt base, UnsignedInt number) {
     UnsignedInt log = 0;
     while(number /= base)

src/Magnum/Math/Functions.h

@@ -93,6 +93,36 @@ time, with @f$ n \ge k \ge 0 @f$: @f[
 */
 UnsignedLong MAGNUM_EXPORT binomialCoefficient(UnsignedInt n, UnsignedInt k);
 
+/**
+@brief Count of bits set in a number
+@m_since_latest
+
+Expands to `__builtin_popcount` / `__builtin_popcountll` on GCC and Clang, uses
+the [Counting bits set, in parallel](https://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel)
+implementation from Sean Eron Anderson Bit Twiddling Hacks page on MSVC and
+elsewhere.
+*/
+/* Explicitly checking for Clang in addition to GCC to catch also clang-cl */
+#if defined(CORRADE_TARGET_GCC) || defined(CORRADE_TARGET_CLANG)
+inline UnsignedInt popcount(UnsignedInt number) {
+    return __builtin_popcount(number);
+}
+#else
+MAGNUM_EXPORT UnsignedInt popcount(UnsignedInt number);
+#endif
+
+/**
+@overload
+@m_since_latest
+*/
+#if defined(CORRADE_TARGET_GCC) || defined(CORRADE_TARGET_CLANG)
+inline UnsignedInt popcount(UnsignedLong number) {
+    return __builtin_popcountll(number);
+}
+#else
+MAGNUM_EXPORT UnsignedInt popcount(UnsignedLong number);
+#endif
+
 /**
 @{ @name Trigonometric functions
 

src/Magnum/Math/Test/FunctionsTest.cpp

@@ -36,6 +36,8 @@ namespace Magnum { namespace Math { namespace Test { namespace {
 struct FunctionsTest: Corrade::TestSuite::Tester {
     explicit FunctionsTest();
 
+    template<class T> void popcount();
+
     void powIntegral();
     void pow();
 
@@ -99,6 +101,10 @@ typedef Math::Vector3<Byte> Vector3b;
 typedef Math::Vector3<Int> Vector3i;
 
 FunctionsTest::FunctionsTest() {
+    addRepeatedTests<FunctionsTest>({
+        &FunctionsTest::popcount<UnsignedInt>,
+        &FunctionsTest::popcount<UnsignedLong>}, 8);
+
     addTests({&FunctionsTest::powIntegral,
               &FunctionsTest::pow,
 
@@ -154,6 +160,17 @@ FunctionsTest::FunctionsTest() {
               });
 }
 
+template<class T> void FunctionsTest::popcount() {
+    setTestCaseTemplateName(TypeTraits<T>::name());
+
+    /* Trivial cases */
+    CORRADE_COMPARE(Math::popcount(T(0)), 0);
+    CORRADE_COMPARE(Math::popcount(~T{}), sizeof(T)*8);
+
+    /* 0x101101011101000110010100 */
+    CORRADE_COMPARE(Math::popcount(T(0xb5d194) << testCaseRepeatId()), 12);
+}
+
 void FunctionsTest::powIntegral() {
     CORRADE_COMPARE(Math::pow<10>(2ul), 1024ul);
     CORRADE_COMPARE(Math::pow<0>(3ul), 1ul);