Add TernaryFunctors and the betainc SpecialFunction.

TernaryFunctors and their executors allow operations on 3-tuples of inputs.
API fully implemented for Arrays and Tensors based on binary functors.

Ported the cephes betainc function (regularized incomplete beta
integral) to Eigen, with support for CPU and GPU, floats, doubles, and
half types.

Added unit tests in array.cpp and cxx11_tensor_cuda.cu


Collapsed revision
* Merged helper methods for betainc across floats and doubles.
* Added TensorGlobalFunctions with betainc().  Removed betainc() from TensorBase.
* Clean up CwiseTernaryOp checks, change igamma_helper to cephes_helper.
* betainc: merge incbcf and incbd into incbeta_cfe.  and more cleanup.
* Update TernaryOp and SpecialFunctions (betainc) based on review comments.

1 files changed, 22 insertions, 0 deletions

diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 9c97ccb0e..e489cefec 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -213,6 +213,28 @@ namespace Eigen
     );
   }
 
+  /** \cpp11 \returns an expression of the coefficient-wise betainc(\a x, \a a, \a b) to the given arrays.
+    *
+    * This function computes the regularized incomplete beta function (integral).
+    *
+    * \note This function supports only float and double scalar types in c++11 mode. To support other scalar types,
+    * or float/double in non c++11 mode, the user has to provide implementations of betainc(T,T,T) for any scalar
+    * type T to be supported.
+    *
+    * \sa Eigen::betainc(), Eigen::lgamma()
+    */
+  template<typename ArgADerived, typename ArgBDerived, typename ArgXDerived>
+  inline const Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>
+  betainc(const Eigen::ArrayBase<ArgADerived>& a, const Eigen::ArrayBase<ArgBDerived>& b, const Eigen::ArrayBase<ArgXDerived>& x)
+  {
+    return Eigen::CwiseTernaryOp<Eigen::internal::scalar_betainc_op<typename ArgXDerived::Scalar>, const ArgADerived, const ArgBDerived, const ArgXDerived>(
+      a.derived(),
+      b.derived(),
+      x.derived()
+    );
+  }
+
+
   /** \returns an expression of the coefficient-wise zeta(\a x, \a q) to the given arrays.
     *
     * It returns the Riemann zeta function of two arguments \a x and \a q: