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, 47 insertions, 0 deletions

diff --git a/Eigen/src/Core/functors/TernaryFunctors.h b/Eigen/src/Core/functors/TernaryFunctors.h
new file mode 100644
index 000000000..8b9e53062
--- /dev/null
+++ b/Eigen/src/Core/functors/TernaryFunctors.h
@@ -0,0 +1,47 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_TERNARY_FUNCTORS_H
+#define EIGEN_TERNARY_FUNCTORS_H
+
+namespace Eigen {
+
+namespace internal {
+
+//---------- associative ternary functors ----------
+
+/** \internal
+  * \brief Template functor to compute the incomplete beta integral betainc(a, b, x)
+  *
+  */
+template<typename Scalar> struct scalar_betainc_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_betainc_op)
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& x, const Scalar& a, const Scalar& b) const {
+    using numext::betainc; return betainc(x, a, b);
+  }
+  template<typename Packet>
+  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& x, const Packet& a, const Packet& b) const
+  {
+    return internal::pbetainc(x, a, b);
+  }
+};
+template<typename Scalar>
+struct functor_traits<scalar_betainc_op<Scalar> > {
+  enum {
+    // Guesstimate
+    Cost = 400 * NumTraits<Scalar>::MulCost + 400 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasBetaInc
+  };
+};
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_TERNARY_FUNCTORS_H