Add special functions to Eigen: lgamma, erf, erfc.

Includes CUDA support and unit tests.

10 files changed, 330 insertions, 1 deletions

diff --git a/Eigen/Core b/Eigen/Core
index 1ec749452..63602f4c3 100644
--- a/Eigen/Core
+++ b/Eigen/Core
@@ -300,6 +300,7 @@ using std::ptrdiff_t;
 
 #include "src/Core/NumTraits.h"
 #include "src/Core/MathFunctions.h"
+#include "src/Core/SpecialFunctions.h"
 #include "src/Core/GenericPacketMath.h"
 
 #if defined EIGEN_VECTORIZE_AVX
diff --git a/Eigen/src/Core/GenericPacketMath.h b/Eigen/src/Core/GenericPacketMath.h
index 5f27d8166..0e7dd29ed 100644
--- a/Eigen/src/Core/GenericPacketMath.h
+++ b/Eigen/src/Core/GenericPacketMath.h
@@ -74,6 +74,9 @@ struct default_packet_traits
     HasSinh    = 0,
     HasCosh    = 0,
     HasTanh    = 0,
+    HasLGamma = 0,
+    HasErf = 0,
+    HasErfc = 0
 
     HasRound  = 0,
     HasFloor  = 0,
@@ -432,6 +435,18 @@ Packet pfloor(const Packet& a) { using numext::floor; return floor(a); }
 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
 Packet pceil(const Packet& a) { using numext::ceil; return ceil(a); }
 
+/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plgamma(const Packet& a) { return numext::lgamma(a); }
+
+/** \internal \returns the erf(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet perf(const Packet& a) { return numext::erf(a); }
+
+/** \internal \returns the erfc(\a a) (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet perfc(const Packet& a) { return numext::erfc(a); }
+
 /***************************************************************************
 * The following functions might not have to be overwritten for vectorized types
 ***************************************************************************/
diff --git a/Eigen/src/Core/GlobalFunctions.h b/Eigen/src/Core/GlobalFunctions.h
index 585974809..62fec7008 100644
--- a/Eigen/src/Core/GlobalFunctions.h
+++ b/Eigen/src/Core/GlobalFunctions.h
@@ -49,6 +49,9 @@ namespace Eigen
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sinh,scalar_sinh_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cosh,scalar_cosh_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tanh,scalar_tanh_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(lgamma,scalar_lgamma_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erf,scalar_erf_op)
+  EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(erfc,scalar_erfc_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op)
   EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log10,scalar_log10_op)
diff --git a/Eigen/src/Core/SpecialFunctions.h b/Eigen/src/Core/SpecialFunctions.h
new file mode 100644
index 000000000..d481f2e06
--- /dev/null
+++ b/Eigen/src/Core/SpecialFunctions.h
@@ -0,0 +1,144 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
+// Copyright (C) 2015 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_SPECIAL_FUNCTIONS_H
+#define EIGEN_SPECIAL_FUNCTIONS_H
+
+namespace Eigen {
+
+namespace internal {
+
+template <typename Scalar>
+EIGEN_STRONG_INLINE Scalar __lgamma(Scalar x) {
+  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+                      THIS_TYPE_IS_NOT_SUPPORTED);
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float __lgamma<float>(float x) { return lgammaf(x); }
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double __lgamma<double>(double x) { return lgamma(x); }
+
+template <typename Scalar>
+EIGEN_STRONG_INLINE Scalar __erf(Scalar x) {
+  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+                      THIS_TYPE_IS_NOT_SUPPORTED);
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float __erf<float>(float x) { return erff(x); }
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double __erf<double>(double x) { return erf(x); }
+
+template <typename Scalar>
+EIGEN_STRONG_INLINE Scalar __erfc(Scalar x) {
+  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
+                      THIS_TYPE_IS_NOT_SUPPORTED);
+}
+
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float __erfc<float>(float x) { return erfcf(x); }
+template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double __erfc<double>(double x) { return erfc(x); }
+
+}  // end namespace internal
+
+/****************************************************************************
+ * Implementations                                                           *
+ ****************************************************************************/
+
+namespace internal {
+
+/****************************************************************************
+ * Implementation of
+ * lgamma                                                  *
+ ****************************************************************************/
+
+template<typename Scalar>
+struct lgamma_impl
+{
+  EIGEN_DEVICE_FUNC
+  static EIGEN_STRONG_INLINE Scalar run(const Scalar& x)
+  {
+    return __lgamma<Scalar>(x);
+  }
+};
+
+template<typename Scalar>
+struct lgamma_retval
+{
+  typedef Scalar type;
+};
+
+/****************************************************************************
+ * Implementation of
+ * erf                                                  *
+ ****************************************************************************/
+
+template<typename Scalar>
+struct erf_impl
+{
+  EIGEN_DEVICE_FUNC
+  static EIGEN_STRONG_INLINE Scalar run(const Scalar& x)
+  {
+    return __erf<Scalar>(x);
+  }
+};
+
+template<typename Scalar>
+struct erf_retval
+{
+  typedef Scalar type;
+};
+
+/****************************************************************************
+* Implementation of erfc                                                  *
+****************************************************************************/
+
+template<typename Scalar>
+struct erfc_impl
+{
+  EIGEN_DEVICE_FUNC
+  static EIGEN_STRONG_INLINE Scalar run(const Scalar& x)
+  {
+    return __erfc<Scalar>(x);
+  }
+};
+
+template<typename Scalar>
+struct erfc_retval
+{
+  typedef Scalar type;
+};
+
+}  // end namespace internal
+
+namespace numext {
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(lgamma, Scalar) lgamma(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(lgamma, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(erf, Scalar) erf(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(erf, Scalar)::run(x);
+}
+
+template<typename Scalar>
+EIGEN_DEVICE_FUNC
+inline EIGEN_MATHFUNC_RETVAL(erfc, Scalar) erfc(const Scalar& x)
+{
+  return EIGEN_MATHFUNC_IMPL(erfc, Scalar)::run(x);
+}
+
+}  // end namespace numext
+
+}  // end namespace Eigen
+
+#endif  // EIGEN_SPECIAL_FUNCTIONS_H
diff --git a/Eigen/src/Core/arch/CUDA/MathFunctions.h b/Eigen/src/Core/arch/CUDA/MathFunctions.h
index 3bea88bea..ecd5c444e 100644
--- a/Eigen/src/Core/arch/CUDA/MathFunctions.h
+++ b/Eigen/src/Core/arch/CUDA/MathFunctions.h
@@ -66,6 +66,43 @@ double2 prsqrt<double2>(const double2& a)
   return make_double2(rsqrt(a.x), rsqrt(a.y));
 }
 
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 plgamma<float4>(const float4& a)
+{
+  return make_float4(lgammaf(a.x), lgammaf(a.y), lgammaf(a.z), lgammaf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 plgamma<double2>(const double2& a)
+{
+  return make_double2(lgamma(a.x), lgamma(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 perf<float4>(const float4& a)
+{
+  return make_float4(erf(a.x), erf(a.y), erf(a.z), erf(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 perf<double2>(const double2& a)
+{
+  return make_double2(erf(a.x), erf(a.y));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+float4 perfc<float4>(const float4& a)
+{
+  return make_float4(erfc(a.x), erfc(a.y), erfc(a.z), erfc(a.w));
+}
+
+template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
+double2 perfc<double2>(const double2& a)
+{
+  return make_double2(erfc(a.x), erfc(a.y));
+}
+
+
 #endif
 
 } // end namespace internal
diff --git a/Eigen/src/Core/arch/CUDA/PacketMath.h b/Eigen/src/Core/arch/CUDA/PacketMath.h
index 0d2c2fef0..cb1b547e0 100644
--- a/Eigen/src/Core/arch/CUDA/PacketMath.h
+++ b/Eigen/src/Core/arch/CUDA/PacketMath.h
@@ -39,6 +39,9 @@ template<> struct packet_traits<float> : default_packet_traits
     HasExp  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasLGamma = 1,
+    HasErf = 1,
+    HasErfc = 1,
 
     HasBlend = 0,
   };
@@ -59,6 +62,9 @@ template<> struct packet_traits<double> : default_packet_traits
     HasExp  = 1,
     HasSqrt = 1,
     HasRsqrt = 1,
+    HasLGamma = 1,
+    HasErf = 1,
+    HasErfc = 1,
 
     HasBlend = 0,
   };
diff --git a/Eigen/src/Core/functors/UnaryFunctors.h b/Eigen/src/Core/functors/UnaryFunctors.h
index e6c665fb6..e16bdd589 100644
--- a/Eigen/src/Core/functors/UnaryFunctors.h
+++ b/Eigen/src/Core/functors/UnaryFunctors.h
@@ -403,6 +403,77 @@ struct functor_traits<scalar_asin_op<Scalar> >
   };
 };
 
+
+/** \internal
+ * \brief Template functor to compute the natural log of the absolute
+ * value of Gamma of a scalar
+ * \sa class CwiseUnaryOp, Cwise::lgamma()
+ */
+template<typename Scalar> struct scalar_lgamma_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_lgamma_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {
+    using numext::lgamma; return lgamma(a);
+  }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::plgamma(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_lgamma_op<Scalar> >
+{
+  enum {
+    // Guesstimate
+    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasLGamma
+  };
+};
+
+/** \internal
+ * \brief Template functor to compute the Gauss error function of a
+ * scalar
+ * \sa class CwiseUnaryOp, Cwise::erf()
+ */
+template<typename Scalar> struct scalar_erf_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_erf_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {
+    using numext::erf; return erf(a);
+  }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::perf(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_erf_op<Scalar> >
+{
+  enum {
+    // Guesstimate
+    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasErf
+  };
+};
+
+/** \internal
+ * \brief Template functor to compute the Complementary Error Function
+ * of a scalar
+ * \sa class CwiseUnaryOp, Cwise::erfc()
+ */
+template<typename Scalar> struct scalar_erfc_op {
+  EIGEN_EMPTY_STRUCT_CTOR(scalar_erfc_op)
+  EIGEN_DEVICE_FUNC inline const Scalar operator() (const Scalar& a) const {
+    using numext::erfc; return erfc(a);
+  }
+  typedef typename packet_traits<Scalar>::type Packet;
+  inline Packet packetOp(const Packet& a) const { return internal::perfc(a); }
+};
+template<typename Scalar>
+struct functor_traits<scalar_erfc_op<Scalar> >
+{
+  enum {
+    // Guesstimate
+    Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
+    PacketAccess = packet_traits<Scalar>::HasErfc
+  };
+};
+
+
 /** \internal
   * \brief Template functor to compute the atan of a scalar
   * \sa class CwiseUnaryOp, ArrayBase::atan()
@@ -422,6 +493,7 @@ struct functor_traits<scalar_atan_op<Scalar> >
   };
 };
 
+
 /** \internal
   * \brief Template functor to compute the tanh of a scalar
   * \sa class CwiseUnaryOp, ArrayBase::tanh()
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 483af876f..27c7907fc 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -294,6 +294,12 @@ struct stem_function
 };
 }
 
+// SpecialFunctions forward declarations
+namespace internal {
+template <typename Scalar> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar __lgamma(Scalar x);
+template <typename Scalar> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar __erf(Scalar x);
+template <typename Scalar> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Scalar __erfc(Scalar x);
+
 } // end namespace Eigen
 
 #endif // EIGEN_FORWARDDECLARATIONS_H
diff --git a/Eigen/src/Core/util/StaticAssert.h b/Eigen/src/Core/util/StaticAssert.h
index 108181419..1fe365aa7 100644
--- a/Eigen/src/Core/util/StaticAssert.h
+++ b/Eigen/src/Core/util/StaticAssert.h
@@ -96,7 +96,8 @@
         STORAGE_LAYOUT_DOES_NOT_MATCH,
         EIGEN_INTERNAL_ERROR_PLEASE_FILE_A_BUG_REPORT__INVALID_COST_VALUE,
         THIS_COEFFICIENT_ACCESSOR_TAKING_ONE_ACCESS_IS_ONLY_FOR_EXPRESSIONS_ALLOWING_LINEAR_ACCESS,
-        MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY
+        MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY,
+        THIS_TYPE_IS_NOT_SUPPORTED
       };
     };
 
diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
index 45e826b0c..ed9818dd1 100644
--- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h
+++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h
@@ -21,6 +21,9 @@ typedef CwiseUnaryOp<internal::scalar_atan_op<Scalar>, const Derived> AtanReturn
 typedef CwiseUnaryOp<internal::scalar_tanh_op<Scalar>, const Derived> TanhReturnType;
 typedef CwiseUnaryOp<internal::scalar_sinh_op<Scalar>, const Derived> SinhReturnType;
 typedef CwiseUnaryOp<internal::scalar_cosh_op<Scalar>, const Derived> CoshReturnType;
+typedef CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, const Derived> LgammaReturnType;
+typedef CwiseUnaryOp<internal::scalar_erf_op<Scalar>, const Derived> ErfReturnType;
+typedef CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, const Derived> ErfcReturnType;
 typedef CwiseUnaryOp<internal::scalar_pow_op<Scalar>, const Derived> PowReturnType;
 typedef CwiseUnaryOp<internal::scalar_square_op<Scalar>, const Derived> SquareReturnType;
 typedef CwiseUnaryOp<internal::scalar_cube_op<Scalar>, const Derived> CubeReturnType;
@@ -302,6 +305,47 @@ cosh() const
   return CoshReturnType(derived());
 }
 
+/** \returns an expression of the coefficient-wise ln(|gamma(*this)|).
+ *
+ * Example: \include Cwise_lgamma.cpp
+ * Output: \verbinclude Cwise_lgamma.out
+ *
+ * \sa cos(), sin(), tan()
+ */
+inline const CwiseUnaryOp<internal::scalar_lgamma_op<Scalar>, Derived>
+lgamma() const
+{
+  return LgammaReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise Gauss error
+ * function of *this.
+ *
+ * Example: \include Cwise_erf.cpp
+ * Output: \verbinclude Cwise_erf.out
+ *
+ * \sa cos(), sin(), tan()
+ */
+inline const CwiseUnaryOp<internal::scalar_erf_op<Scalar>, Derived>
+erf() const
+{
+  return ErfReturnType(derived());
+}
+
+/** \returns an expression of the coefficient-wise Complementary error
+ * function of *this.
+ *
+ * Example: \include Cwise_erfc.cpp
+ * Output: \verbinclude Cwise_erfc.out
+ *
+ * \sa cos(), sin(), tan()
+ */
+inline const CwiseUnaryOp<internal::scalar_erfc_op<Scalar>, Derived>
+erfc() const
+{
+  return ErfcReturnType(derived());
+}
+
 /** \returns an expression of the coefficient-wise power of *this to the given exponent.
   *
   * This function computes the coefficient-wise power. The function MatrixBase::pow() in the