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.

3 files changed, 26 insertions, 1 deletions

diff --git a/Eigen/src/Core/arch/CUDA/Half.h b/Eigen/src/Core/arch/CUDA/Half.h
index d4ce2eaf9..87bdbfd1e 100644
--- a/Eigen/src/Core/arch/CUDA/Half.h
+++ b/Eigen/src/Core/arch/CUDA/Half.h
@@ -480,6 +480,9 @@ template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen:
 template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igammac(const Eigen::half& a, const Eigen::half& x) {
   return Eigen::half(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x)));
 }
+template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half betainc(const Eigen::half& a, const Eigen::half& b, const Eigen::half& x) {
+  return Eigen::half(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x)));
+}
 #endif
 } // end namespace numext
 
diff --git a/Eigen/src/Core/arch/CUDA/MathFunctions.h b/Eigen/src/Core/arch/CUDA/MathFunctions.h
index c90ec96a0..8b5e8204f 100644
--- a/Eigen/src/Core/arch/CUDA/MathFunctions.h
+++ b/Eigen/src/Core/arch/CUDA/MathFunctions.h
@@ -181,6 +181,24 @@ double2 pigammac<double2>(const double2& a, const double2& x)
   return make_double2(igammac(a.x, x.x), igammac(a.y, x.y));
 }
 
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 pbetainc<float4>(const float4& a, const float4& b, const float4& x)
+{
+  using numext::betainc;
+  return make_float4(
+      betainc(a.x, b.x, x.x),
+      betainc(a.y, b.y, x.y),
+      betainc(a.z, b.z, x.z),
+      betainc(a.w, b.w, x.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 pbetainc<double2>(const double2& a, const double2& b, const double2& x)
+{
+  using numext::betainc;
+  return make_double2(betainc(a.x, b.x, x.x), betainc(a.y, b.y, x.y));
+}
+
 #endif
 
 } // end namespace internal
diff --git a/Eigen/src/Core/arch/CUDA/PacketMath.h b/Eigen/src/Core/arch/CUDA/PacketMath.h
index 25a59066c..ad66399e0 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMath.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMath.h
@@ -44,8 +44,9 @@ template<> struct packet_traits<float> : default_packet_traits
     HasPolygamma = 1,
     HasErf = 1,
     HasErfc = 1,
-    HasIgamma = 1,
+    HasIGamma = 1,
     HasIGammac = 1,
+    HasBetaInc = 1,
 
     HasBlend = 0,
   };
@@ -68,10 +69,13 @@ template<> struct packet_traits<double> : default_packet_traits
     HasRsqrt = 1,
     HasLGamma = 1,
     HasDiGamma = 1,
+    HasZeta = 1,
+    HasPolygamma = 1,
     HasErf = 1,
     HasErfc = 1,
     HasIGamma = 1,
     HasIGammac = 1,
+    HasBetaInc = 1,
 
     HasBlend = 0,
   };