untemplate binomial & and assert test

src/Magnum/CMakeLists.txt

@@ -111,11 +111,11 @@ set(MagnumMath_SRCS
     Math/Angle.cpp
     Math/Color.cpp
     Math/Half.cpp
-    Math/Functions.cpp
     Math/Packing.cpp
     Math/instantiation.cpp)
 
 set(MagnumMath_GracefulAssert_SRCS
+    Math/Functions.cpp
     Math/PackingBatch.cpp)
 
 # Objects shared between main and math test library

src/Magnum/Math/Functions.cpp

@@ -23,6 +23,8 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#include <Corrade/Utility/Debug.h>
+
 #include "Functions.h"
 
 namespace Magnum { namespace Math {
@@ -41,4 +43,20 @@ UnsignedInt log2(UnsignedInt number) {
     return log;
 }
 
+
+UnsignedLong binomialCoefficient(UnsignedInt n, UnsignedInt k) {
+    if (k > n) return 0;
+    if (k * 2 > n)
+        k = n-k;
+    if (k == 0) return 1;
+
+    UnsignedLong result = n;
+    for(UnsignedInt i = 2; i <= k; ++i ) {
+        CORRADE_ASSERT(result < ~UnsignedLong{} / (n-i+1), "Math::binomialCoefficient(): overflow for (" << Corrade::Utility::Debug::nospace << n << "choose" << k << Corrade::Utility::Debug::nospace << ")", 0ul);
+        result *= (n-i+1);
+        result /= i;
+    }
+    return result;
+}
+
 }}

src/Magnum/Math/Functions.h

@@ -34,7 +34,6 @@
 #include <cstdlib> /* std::div() */
 #include <type_traits>
 #include <utility>
-#include <limits>
 #include <Corrade/Utility/StlMath.h>
 
 #include "Magnum/visibility.h"
@@ -413,30 +412,15 @@ template<std::size_t size, class T> inline Vector<size, T> ceil(const Vector<siz
 
 
 /**
-@brief Computes a Binomial Coefficient
+@brief [Binomial Coefficient](https://en.wikipedia.org/wiki/Binomial_coefficient)
 
-Given n elements computes the number of ways to choose k elements
-without replacement. The number of ways to do this is
-given by
+Returns the number of combinations of @f$ n @f$ things taken @f$ k @f$ at a time.
+The number of ways to do this is given by
 @f[
     \begin{pmatrix} n \\ k \end{pmatrix} = \frac{n! \cdot (n-k)!}{k!} = \frac{n \cdot (n-1) \cdots (n - k + 1)}{k \cdots 1}.
 @f]
 */
-template<class T> inline typename std::enable_if<IsIntegral<T>::value, T>::type binomialCoefficient(T n, T k) {
-    CORRADE_ASSERT(k >= 0, "k must be positive to compute the Binomial Coefficient", T{0});
-    if (k > n) return 0;
-    if (k * 2 > n)
-        k = n-k;
-    if (k == 0) return 1;
-
-    T result = n;
-    for(T i = 2; i <= k; ++i ) {
-        CORRADE_ASSERT(result < std::numeric_limits<T>::max()/(n-i+1), "Overflow In Binomial Coefficient", T{0});
-        result *= (n-i+1);
-        result /= i;
-    }
-    return result;
-}
+UnsignedLong MAGNUM_EXPORT binomialCoefficient(UnsignedInt n, UnsignedInt k);
 
 /**
 @brief Floating point division remainder

src/Magnum/Math/Test/FunctionsTest.cpp

@@ -54,6 +54,7 @@ struct FunctionsTest: Corrade::TestSuite::Tester {
     void fmod();
 
     void binomialCoefficient();
+    void binomialCoefficientOverflow();
 
     void sqrt();
     void sqrtInverted();
@@ -118,6 +119,7 @@ FunctionsTest::FunctionsTest() {
               &FunctionsTest::fmod,
 
               &FunctionsTest::binomialCoefficient,
+              &FunctionsTest::binomialCoefficientOverflow,
 
               &FunctionsTest::sqrt,
               &FunctionsTest::sqrtInverted,
@@ -298,12 +300,24 @@ void FunctionsTest::ceil() {
 }
 
 void FunctionsTest::binomialCoefficient() {
-    CORRADE_COMPARE(Math::binomialCoefficient(1, 1), 1);
-    CORRADE_COMPARE(Math::binomialCoefficient(1, 0), 1);
-    CORRADE_COMPARE(Math::binomialCoefficient(19, 11), 75582);
-    CORRADE_COMPARE(Math::binomialCoefficient(1000, 999), 1000);
-    CORRADE_COMPARE(Math::binomialCoefficient(0, 0), 1);
-    CORRADE_COMPARE(Math::binomialCoefficient(32, 11), 129024480);
+    CORRADE_COMPARE(Math::binomialCoefficient(1, 1), 1ul);
+    CORRADE_COMPARE(Math::binomialCoefficient(1, 0), 1ul);
+    CORRADE_COMPARE(Math::binomialCoefficient(19, 11), 75582ul);
+    CORRADE_COMPARE(Math::binomialCoefficient(1000, 999), 1000ul);
+    CORRADE_COMPARE(Math::binomialCoefficient(0, 0), 1ul);
+    CORRADE_COMPARE(Math::binomialCoefficient(32, 11), 129024480ul);
+    CORRADE_COMPARE(Math::binomialCoefficient(62, 31), 465428353255261088ul);
+}
+
+void FunctionsTest::binomialCoefficientOverflow() {
+    #ifdef CORRADE_NO_ASSERT
+    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
+    #endif
+
+    std::ostringstream out;
+    Error redirectError{&out};
+    Math::binomialCoefficient(63, 31);
+    CORRADE_COMPARE(out.str(), "Math::binomialCoefficient(): overflow for (63 choose 31)\n");
 }
 
 void FunctionsTest::fmod() {