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authorNao Pross <np@0hm.ch>2024-02-12 15:23:24 +0100
committerNao Pross <np@0hm.ch>2024-02-12 15:23:24 +0100
commitfbd6758fb4649b146176dbbc2dfe9384c69ef58d (patch)
tree0993d5c74a5cd1773ff9a572e4926d3102c0299f /src/EigenUnsupported/src/SpecialFunctions
parentMove into version control (diff)
downloadfsisotool-fbd6758fb4649b146176dbbc2dfe9384c69ef58d.tar.gz
fsisotool-fbd6758fb4649b146176dbbc2dfe9384c69ef58d.zip
Remove old stuff with Eigen
Diffstat (limited to 'src/EigenUnsupported/src/SpecialFunctions')
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsArrayAPI.h286
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsBFloat16.h68
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsFunctors.h357
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsHalf.h66
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsImpl.h1959
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsPacketMath.h118
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/HipVectorCompatibility.h67
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsArrayAPI.h167
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsBFloat16.h58
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsFunctors.h330
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsHalf.h58
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsImpl.h2045
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsPacketMath.h79
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/arch/AVX/BesselFunctions.h46
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/arch/AVX/SpecialFunctions.h16
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/BesselFunctions.h46
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h16
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/arch/GPU/SpecialFunctions.h369
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/arch/NEON/BesselFunctions.h54
-rw-r--r--src/EigenUnsupported/src/SpecialFunctions/arch/NEON/SpecialFunctions.h34
20 files changed, 0 insertions, 6239 deletions
diff --git a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsArrayAPI.h b/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsArrayAPI.h
deleted file mode 100644
index 41d2bf6..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsArrayAPI.h
+++ /dev/null
@@ -1,286 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
-//
-// 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_BESSELFUNCTIONS_ARRAYAPI_H
-#define EIGEN_BESSELFUNCTIONS_ARRAYAPI_H
-
-namespace Eigen {
-
-/** \returns an expression of the coefficient-wise i0(\a x) to the given
- * arrays.
- *
- * It returns the modified Bessel function of the first kind of order zero.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of i0(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_i0()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i0_op<typename Derived::Scalar>, const Derived>
-bessel_i0(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i0_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise i0e(\a x) to the given
- * arrays.
- *
- * It returns the exponentially scaled modified Bessel
- * function of the first kind of order zero.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of i0e(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_i0e()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i0e_op<typename Derived::Scalar>, const Derived>
-bessel_i0e(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i0e_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise i1(\a x) to the given
- * arrays.
- *
- * It returns the modified Bessel function of the first kind of order one.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of i1(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_i1()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i1_op<typename Derived::Scalar>, const Derived>
-bessel_i1(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i1_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise i1e(\a x) to the given
- * arrays.
- *
- * It returns the exponentially scaled modified Bessel
- * function of the first kind of order one.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of i1e(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_i1e()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i1e_op<typename Derived::Scalar>, const Derived>
-bessel_i1e(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_i1e_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise k0(\a x) to the given
- * arrays.
- *
- * It returns the modified Bessel function of the second kind of order zero.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of k0(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_k0()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k0_op<typename Derived::Scalar>, const Derived>
-bessel_k0(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k0_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise k0e(\a x) to the given
- * arrays.
- *
- * It returns the exponentially scaled modified Bessel
- * function of the second kind of order zero.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of k0e(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_k0e()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k0e_op<typename Derived::Scalar>, const Derived>
-bessel_k0e(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k0e_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise k1(\a x) to the given
- * arrays.
- *
- * It returns the modified Bessel function of the second kind of order one.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of k1(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_k1()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k1_op<typename Derived::Scalar>, const Derived>
-bessel_k1(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k1_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise k1e(\a x) to the given
- * arrays.
- *
- * It returns the exponentially scaled modified Bessel
- * function of the second kind of order one.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of k1e(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_k1e()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k1e_op<typename Derived::Scalar>, const Derived>
-bessel_k1e(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_k1e_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise j0(\a x) to the given
- * arrays.
- *
- * It returns the Bessel function of the first kind of order zero.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of j0(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_j0()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_j0_op<typename Derived::Scalar>, const Derived>
-bessel_j0(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_j0_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise y0(\a x) to the given
- * arrays.
- *
- * It returns the Bessel function of the second kind of order zero.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of y0(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_y0()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_y0_op<typename Derived::Scalar>, const Derived>
-bessel_y0(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_y0_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise j1(\a x) to the given
- * arrays.
- *
- * It returns the modified Bessel function of the first kind of order one.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of j1(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_j1()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_j1_op<typename Derived::Scalar>, const Derived>
-bessel_j1(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_j1_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-/** \returns an expression of the coefficient-wise y1(\a x) to the given
- * arrays.
- *
- * It returns the Bessel function of the second kind of order one.
- *
- * \param x is the argument
- *
- * \note This function supports only float and double scalar types. To support
- * other scalar types, the user has to provide implementations of y1(T) for
- * any scalar type T to be supported.
- *
- * \sa ArrayBase::bessel_y1()
- */
-template <typename Derived>
-EIGEN_STRONG_INLINE const Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_y1_op<typename Derived::Scalar>, const Derived>
-bessel_y1(const Eigen::ArrayBase<Derived>& x) {
- return Eigen::CwiseUnaryOp<
- Eigen::internal::scalar_bessel_y1_op<typename Derived::Scalar>,
- const Derived>(x.derived());
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_BESSELFUNCTIONS_ARRAYAPI_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsBFloat16.h b/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsBFloat16.h
deleted file mode 100644
index 6049cc2..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsBFloat16.h
+++ /dev/null
@@ -1,68 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// 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_BESSELFUNCTIONS_BFLOAT16_H
-#define EIGEN_BESSELFUNCTIONS_BFLOAT16_H
-
-namespace Eigen {
-namespace numext {
-
-#if EIGEN_HAS_C99_MATH
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i0(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_i0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i0e(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_i0e(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i1(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_i1(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_i1e(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_i1e(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_j0(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_j0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_j1(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_j1(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_y0(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_y0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_y1(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_y1(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k0(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_k0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k0e(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_k0e(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k1(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_k1(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 bessel_k1e(const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::bessel_k1e(static_cast<float>(x)));
-}
-#endif
-
-} // end namespace numext
-} // end namespace Eigen
-
-#endif // EIGEN_BESSELFUNCTIONS_BFLOAT16_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsFunctors.h b/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsFunctors.h
deleted file mode 100644
index 8606a9f..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsFunctors.h
+++ /dev/null
@@ -1,357 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
-// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
-//
-// 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_BESSELFUNCTIONS_FUNCTORS_H
-#define EIGEN_BESSELFUNCTIONS_FUNCTORS_H
-
-namespace Eigen {
-
-namespace internal {
-
-/** \internal
- * \brief Template functor to compute the modified Bessel function of the first
- * kind of order zero.
- * \sa class CwiseUnaryOp, Cwise::bessel_i0()
- */
-template <typename Scalar>
-struct scalar_bessel_i0_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i0_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_i0;
- return bessel_i0(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_i0(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_i0_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=20 is computed.
- // The cost is N multiplications and 2N additions. We also add
- // the cost of an additional exp over i0e.
- Cost = 28 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the exponentially scaled modified Bessel
- * function of the first kind of order zero
- * \sa class CwiseUnaryOp, Cwise::bessel_i0e()
- */
-template <typename Scalar>
-struct scalar_bessel_i0e_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i0e_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_i0e;
- return bessel_i0e(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_i0e(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_i0e_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=20 is computed.
- // The cost is N multiplications and 2N additions.
- Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the modified Bessel function of the first
- * kind of order one
- * \sa class CwiseUnaryOp, Cwise::bessel_i1()
- */
-template <typename Scalar>
-struct scalar_bessel_i1_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i1_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_i1;
- return bessel_i1(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_i1(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_i1_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=20 is computed.
- // The cost is N multiplications and 2N additions. We also add
- // the cost of an additional exp over i1e.
- Cost = 28 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the exponentially scaled modified Bessel
- * function of the first kind of order zero
- * \sa class CwiseUnaryOp, Cwise::bessel_i1e()
- */
-template <typename Scalar>
-struct scalar_bessel_i1e_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i1e_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_i1e;
- return bessel_i1e(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_i1e(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_i1e_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=20 is computed.
- // The cost is N multiplications and 2N additions.
- Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the Bessel function of the second kind of
- * order zero
- * \sa class CwiseUnaryOp, Cwise::bessel_j0()
- */
-template <typename Scalar>
-struct scalar_bessel_j0_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_j0_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_j0;
- return bessel_j0(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_j0(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_j0_op<Scalar> > {
- enum {
- // 6 polynomial of order ~N=8 is computed.
- // The cost is N multiplications and N additions each, along with a
- // sine, cosine and rsqrt cost.
- Cost = 63 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the Bessel function of the second kind of
- * order zero
- * \sa class CwiseUnaryOp, Cwise::bessel_y0()
- */
-template <typename Scalar>
-struct scalar_bessel_y0_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_y0_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_y0;
- return bessel_y0(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_y0(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_y0_op<Scalar> > {
- enum {
- // 6 polynomial of order ~N=8 is computed.
- // The cost is N multiplications and N additions each, along with a
- // sine, cosine, rsqrt and j0 cost.
- Cost = 126 * NumTraits<Scalar>::MulCost + 96 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the Bessel function of the first kind of
- * order one
- * \sa class CwiseUnaryOp, Cwise::bessel_j1()
- */
-template <typename Scalar>
-struct scalar_bessel_j1_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_j1_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_j1;
- return bessel_j1(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_j1(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_j1_op<Scalar> > {
- enum {
- // 6 polynomial of order ~N=8 is computed.
- // The cost is N multiplications and N additions each, along with a
- // sine, cosine and rsqrt cost.
- Cost = 63 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the Bessel function of the second kind of
- * order one
- * \sa class CwiseUnaryOp, Cwise::bessel_j1e()
- */
-template <typename Scalar>
-struct scalar_bessel_y1_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_y1_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_y1;
- return bessel_y1(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_y1(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_y1_op<Scalar> > {
- enum {
- // 6 polynomial of order ~N=8 is computed.
- // The cost is N multiplications and N additions each, along with a
- // sine, cosine, rsqrt and j1 cost.
- Cost = 126 * NumTraits<Scalar>::MulCost + 96 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the modified Bessel function of the second
- * kind of order zero
- * \sa class CwiseUnaryOp, Cwise::bessel_k0()
- */
-template <typename Scalar>
-struct scalar_bessel_k0_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k0_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_k0;
- return bessel_k0(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_k0(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_k0_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=10 is computed.
- // The cost is N multiplications and 2N additions. In addition we compute
- // i0, a log, exp and prsqrt and sin and cos.
- Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the exponentially scaled modified Bessel
- * function of the second kind of order zero
- * \sa class CwiseUnaryOp, Cwise::bessel_k0e()
- */
-template <typename Scalar>
-struct scalar_bessel_k0e_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k0e_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_k0e;
- return bessel_k0e(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_k0e(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_k0e_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=10 is computed.
- // The cost is N multiplications and 2N additions. In addition we compute
- // i0, a log, exp and prsqrt and sin and cos.
- Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the modified Bessel function of the
- * second kind of order one
- * \sa class CwiseUnaryOp, Cwise::bessel_k1()
- */
-template <typename Scalar>
-struct scalar_bessel_k1_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k1_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_k1;
- return bessel_k1(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_k1(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_k1_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=10 is computed.
- // The cost is N multiplications and 2N additions. In addition we compute
- // i1, a log, exp and prsqrt and sin and cos.
- Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-/** \internal
- * \brief Template functor to compute the exponentially scaled modified Bessel
- * function of the second kind of order one
- * \sa class CwiseUnaryOp, Cwise::bessel_k1e()
- */
-template <typename Scalar>
-struct scalar_bessel_k1e_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k1e_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
- using numext::bessel_k1e;
- return bessel_k1e(x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return internal::pbessel_k1e(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_bessel_k1e_op<Scalar> > {
- enum {
- // On average, a Chebyshev polynomial of order N=10 is computed.
- // The cost is N multiplications and 2N additions. In addition we compute
- // i1, a log, exp and prsqrt and sin and cos.
- Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasBessel
- };
-};
-
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_BESSELFUNCTIONS_FUNCTORS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsHalf.h b/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsHalf.h
deleted file mode 100644
index 8930d1a..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsHalf.h
+++ /dev/null
@@ -1,66 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// 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_BESSELFUNCTIONS_HALF_H
-#define EIGEN_BESSELFUNCTIONS_HALF_H
-
-namespace Eigen {
-namespace numext {
-
-#if EIGEN_HAS_C99_MATH
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i0(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_i0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i0e(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_i0e(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i1(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_i1(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_i1e(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_i1e(static_cast<float>(x)));
-}
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_j0(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_j0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_j1(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_j1(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_y0(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_y0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_y1(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_y1(static_cast<float>(x)));
-}
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k0(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_k0(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k0e(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_k0e(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k1(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_k1(static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half bessel_k1e(const Eigen::half& x) {
- return Eigen::half(Eigen::numext::bessel_k1e(static_cast<float>(x)));
-}
-#endif
-
-} // end namespace numext
-} // end namespace Eigen
-
-#endif // EIGEN_BESSELFUNCTIONS_HALF_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsImpl.h b/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsImpl.h
deleted file mode 100644
index 24812be..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsImpl.h
+++ /dev/null
@@ -1,1959 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// 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_BESSEL_FUNCTIONS_H
-#define EIGEN_BESSEL_FUNCTIONS_H
-
-namespace Eigen {
-namespace internal {
-
-// Parts of this code are based on the Cephes Math Library.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
-//
-// Permission has been kindly provided by the original author
-// to incorporate the Cephes software into the Eigen codebase:
-//
-// From: Stephen Moshier
-// To: Eugene Brevdo
-// Subject: Re: Permission to wrap several cephes functions in Eigen
-//
-// Hello Eugene,
-//
-// Thank you for writing.
-//
-// If your licensing is similar to BSD, the formal way that has been
-// handled is simply to add a statement to the effect that you are incorporating
-// the Cephes software by permission of the author.
-//
-// Good luck with your project,
-// Steve
-
-
-/****************************************************************************
- * Implementation of Bessel function, based on Cephes *
- ****************************************************************************/
-
-template <typename Scalar>
-struct bessel_i0e_retval {
- typedef Scalar type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_i0e {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_i0e<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* i0ef.c
- *
- * Modified Bessel function of order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i0ef();
- *
- * y = i0ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order zero of the argument.
- *
- * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 100000 3.7e-7 7.0e-8
- * See i0f().
- *
- */
-
- const float A[] = {-1.30002500998624804212E-8f, 6.04699502254191894932E-8f,
- -2.67079385394061173391E-7f, 1.11738753912010371815E-6f,
- -4.41673835845875056359E-6f, 1.64484480707288970893E-5f,
- -5.75419501008210370398E-5f, 1.88502885095841655729E-4f,
- -5.76375574538582365885E-4f, 1.63947561694133579842E-3f,
- -4.32430999505057594430E-3f, 1.05464603945949983183E-2f,
- -2.37374148058994688156E-2f, 4.93052842396707084878E-2f,
- -9.49010970480476444210E-2f, 1.71620901522208775349E-1f,
- -3.04682672343198398683E-1f, 6.76795274409476084995E-1f};
-
- const float B[] = {3.39623202570838634515E-9f, 2.26666899049817806459E-8f,
- 2.04891858946906374183E-7f, 2.89137052083475648297E-6f,
- 6.88975834691682398426E-5f, 3.36911647825569408990E-3f,
- 8.04490411014108831608E-1f};
- T y = pabs(x);
- T y_le_eight = internal::pchebevl<T, 18>::run(
- pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A);
- T y_gt_eight = pmul(
- internal::pchebevl<T, 7>::run(
- psub(pdiv(pset1<T>(32.0f), y), pset1<T>(2.0f)), B),
- prsqrt(y));
- // TODO: Perhaps instead check whether all packet elements are in
- // [-8, 8] and evaluate a branch based off of that. It's possible
- // in practice most elements are in this region.
- return pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight);
- }
-};
-
-template <typename T>
-struct generic_i0e<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* i0e.c
- *
- * Modified Bessel function of order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i0e();
- *
- * y = i0e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order zero of the argument.
- *
- * The function is defined as i0e(x) = exp(-|x|) j0( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 30000 5.4e-16 1.2e-16
- * See i0().
- *
- */
-
- const double A[] = {-4.41534164647933937950E-18, 3.33079451882223809783E-17,
- -2.43127984654795469359E-16, 1.71539128555513303061E-15,
- -1.16853328779934516808E-14, 7.67618549860493561688E-14,
- -4.85644678311192946090E-13, 2.95505266312963983461E-12,
- -1.72682629144155570723E-11, 9.67580903537323691224E-11,
- -5.18979560163526290666E-10, 2.65982372468238665035E-9,
- -1.30002500998624804212E-8, 6.04699502254191894932E-8,
- -2.67079385394061173391E-7, 1.11738753912010371815E-6,
- -4.41673835845875056359E-6, 1.64484480707288970893E-5,
- -5.75419501008210370398E-5, 1.88502885095841655729E-4,
- -5.76375574538582365885E-4, 1.63947561694133579842E-3,
- -4.32430999505057594430E-3, 1.05464603945949983183E-2,
- -2.37374148058994688156E-2, 4.93052842396707084878E-2,
- -9.49010970480476444210E-2, 1.71620901522208775349E-1,
- -3.04682672343198398683E-1, 6.76795274409476084995E-1};
- const double B[] = {
- -7.23318048787475395456E-18, -4.83050448594418207126E-18,
- 4.46562142029675999901E-17, 3.46122286769746109310E-17,
- -2.82762398051658348494E-16, -3.42548561967721913462E-16,
- 1.77256013305652638360E-15, 3.81168066935262242075E-15,
- -9.55484669882830764870E-15, -4.15056934728722208663E-14,
- 1.54008621752140982691E-14, 3.85277838274214270114E-13,
- 7.18012445138366623367E-13, -1.79417853150680611778E-12,
- -1.32158118404477131188E-11, -3.14991652796324136454E-11,
- 1.18891471078464383424E-11, 4.94060238822496958910E-10,
- 3.39623202570838634515E-9, 2.26666899049817806459E-8,
- 2.04891858946906374183E-7, 2.89137052083475648297E-6,
- 6.88975834691682398426E-5, 3.36911647825569408990E-3,
- 8.04490411014108831608E-1};
- T y = pabs(x);
- T y_le_eight = internal::pchebevl<T, 30>::run(
- pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A);
- T y_gt_eight = pmul(
- internal::pchebevl<T, 25>::run(
- psub(pdiv(pset1<T>(32.0), y), pset1<T>(2.0)), B),
- prsqrt(y));
- // TODO: Perhaps instead check whether all packet elements are in
- // [-8, 8] and evaluate a branch based off of that. It's possible
- // in practice most elements are in this region.
- return pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight);
- }
-};
-
-template <typename T>
-struct bessel_i0e_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_i0e<T>::run(x);
- }
-};
-
-template <typename Scalar>
-struct bessel_i0_retval {
- typedef Scalar type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_i0 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- return pmul(
- pexp(pabs(x)),
- generic_i0e<T, ScalarType>::run(x));
- }
-};
-
-template <typename T>
-struct bessel_i0_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_i0<T>::run(x);
- }
-};
-
-template <typename Scalar>
-struct bessel_i1e_retval {
- typedef Scalar type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type >
-struct generic_i1e {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_i1e<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* i1ef.c
- *
- * Modified Bessel function of order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, i1ef();
- *
- * y = i1ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order one of the argument.
- *
- * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 1.5e-6 1.5e-7
- * See i1().
- *
- */
- const float A[] = {9.38153738649577178388E-9f, -4.44505912879632808065E-8f,
- 2.00329475355213526229E-7f, -8.56872026469545474066E-7f,
- 3.47025130813767847674E-6f, -1.32731636560394358279E-5f,
- 4.78156510755005422638E-5f, -1.61760815825896745588E-4f,
- 5.12285956168575772895E-4f, -1.51357245063125314899E-3f,
- 4.15642294431288815669E-3f, -1.05640848946261981558E-2f,
- 2.47264490306265168283E-2f, -5.29459812080949914269E-2f,
- 1.02643658689847095384E-1f, -1.76416518357834055153E-1f,
- 2.52587186443633654823E-1f};
-
- const float B[] = {-3.83538038596423702205E-9f, -2.63146884688951950684E-8f,
- -2.51223623787020892529E-7f, -3.88256480887769039346E-6f,
- -1.10588938762623716291E-4f, -9.76109749136146840777E-3f,
- 7.78576235018280120474E-1f};
-
-
- T y = pabs(x);
- T y_le_eight = pmul(y, internal::pchebevl<T, 17>::run(
- pmadd(pset1<T>(0.5f), y, pset1<T>(-2.0f)), A));
- T y_gt_eight = pmul(
- internal::pchebevl<T, 7>::run(
- psub(pdiv(pset1<T>(32.0f), y),
- pset1<T>(2.0f)), B),
- prsqrt(y));
- // TODO: Perhaps instead check whether all packet elements are in
- // [-8, 8] and evaluate a branch based off of that. It's possible
- // in practice most elements are in this region.
- y = pselect(pcmp_le(y, pset1<T>(8.0f)), y_le_eight, y_gt_eight);
- return pselect(pcmp_lt(x, pset1<T>(0.0f)), pnegate(y), y);
- }
-};
-
-template <typename T>
-struct generic_i1e<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* i1e.c
- *
- * Modified Bessel function of order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, i1e();
- *
- * y = i1e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of order one of the argument.
- *
- * The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 2.0e-15 2.0e-16
- * See i1().
- *
- */
- const double A[] = {2.77791411276104639959E-18, -2.11142121435816608115E-17,
- 1.55363195773620046921E-16, -1.10559694773538630805E-15,
- 7.60068429473540693410E-15, -5.04218550472791168711E-14,
- 3.22379336594557470981E-13, -1.98397439776494371520E-12,
- 1.17361862988909016308E-11, -6.66348972350202774223E-11,
- 3.62559028155211703701E-10, -1.88724975172282928790E-9,
- 9.38153738649577178388E-9, -4.44505912879632808065E-8,
- 2.00329475355213526229E-7, -8.56872026469545474066E-7,
- 3.47025130813767847674E-6, -1.32731636560394358279E-5,
- 4.78156510755005422638E-5, -1.61760815825896745588E-4,
- 5.12285956168575772895E-4, -1.51357245063125314899E-3,
- 4.15642294431288815669E-3, -1.05640848946261981558E-2,
- 2.47264490306265168283E-2, -5.29459812080949914269E-2,
- 1.02643658689847095384E-1, -1.76416518357834055153E-1,
- 2.52587186443633654823E-1};
- const double B[] = {
- 7.51729631084210481353E-18, 4.41434832307170791151E-18,
- -4.65030536848935832153E-17, -3.20952592199342395980E-17,
- 2.96262899764595013876E-16, 3.30820231092092828324E-16,
- -1.88035477551078244854E-15, -3.81440307243700780478E-15,
- 1.04202769841288027642E-14, 4.27244001671195135429E-14,
- -2.10154184277266431302E-14, -4.08355111109219731823E-13,
- -7.19855177624590851209E-13, 2.03562854414708950722E-12,
- 1.41258074366137813316E-11, 3.25260358301548823856E-11,
- -1.89749581235054123450E-11, -5.58974346219658380687E-10,
- -3.83538038596423702205E-9, -2.63146884688951950684E-8,
- -2.51223623787020892529E-7, -3.88256480887769039346E-6,
- -1.10588938762623716291E-4, -9.76109749136146840777E-3,
- 7.78576235018280120474E-1};
- T y = pabs(x);
- T y_le_eight = pmul(y, internal::pchebevl<T, 29>::run(
- pmadd(pset1<T>(0.5), y, pset1<T>(-2.0)), A));
- T y_gt_eight = pmul(
- internal::pchebevl<T, 25>::run(
- psub(pdiv(pset1<T>(32.0), y),
- pset1<T>(2.0)), B),
- prsqrt(y));
- // TODO: Perhaps instead check whether all packet elements are in
- // [-8, 8] and evaluate a branch based off of that. It's possible
- // in practice most elements are in this region.
- y = pselect(pcmp_le(y, pset1<T>(8.0)), y_le_eight, y_gt_eight);
- return pselect(pcmp_lt(x, pset1<T>(0.0)), pnegate(y), y);
- }
-};
-
-template <typename T>
-struct bessel_i1e_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_i1e<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_i1_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_i1 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- return pmul(
- pexp(pabs(x)),
- generic_i1e<T, ScalarType>::run(x));
- }
-};
-
-template <typename T>
-struct bessel_i1_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_i1<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_k0e_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_k0e {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_k0e<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* k0ef.c
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0ef();
- *
- * y = k0ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 8.1e-7 7.8e-8
- * See k0().
- *
- */
-
- const float A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,
- 2.28621210311945178607E-5f, 1.26461541144692592338E-3f,
- 3.59799365153615016266E-2f, 3.44289899924628486886E-1f,
- -5.35327393233902768720E-1f};
-
- const float B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,
- -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,
- -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,
- -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,
- -3.14481013119645005427E-2f, 2.44030308206595545468E0f};
- const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = internal::pchebevl<T, 7>::run(
- pmadd(x, x, pset1<T>(-2.0)), A);
- x_le_two = pmadd(
- generic_i0<T, float>::run(x), pnegate(
- plog(pmul(pset1<T>(0.5), x))), x_le_two);
- x_le_two = pmul(pexp(x), x_le_two);
- T x_gt_two = pmul(
- internal::pchebevl<T, 10>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B),
- prsqrt(x));
- return pselect(
- pcmp_le(x, pset1<T>(0.0)),
- MAXNUM,
- pselect(pcmp_le(x, two), x_le_two, x_gt_two));
- }
-};
-
-template <typename T>
-struct generic_k0e<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* k0e.c
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k0e();
- *
- * y = k0e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 1.4e-15 1.4e-16
- * See k0().
- *
- */
-
- const double A[] = {
- 1.37446543561352307156E-16,
- 4.25981614279661018399E-14,
- 1.03496952576338420167E-11,
- 1.90451637722020886025E-9,
- 2.53479107902614945675E-7,
- 2.28621210311945178607E-5,
- 1.26461541144692592338E-3,
- 3.59799365153615016266E-2,
- 3.44289899924628486886E-1,
- -5.35327393233902768720E-1};
- const double B[] = {
- 5.30043377268626276149E-18, -1.64758043015242134646E-17,
- 5.21039150503902756861E-17, -1.67823109680541210385E-16,
- 5.51205597852431940784E-16, -1.84859337734377901440E-15,
- 6.34007647740507060557E-15, -2.22751332699166985548E-14,
- 8.03289077536357521100E-14, -2.98009692317273043925E-13,
- 1.14034058820847496303E-12, -4.51459788337394416547E-12,
- 1.85594911495471785253E-11, -7.95748924447710747776E-11,
- 3.57739728140030116597E-10, -1.69753450938905987466E-9,
- 8.57403401741422608519E-9, -4.66048989768794782956E-8,
- 2.76681363944501510342E-7, -1.83175552271911948767E-6,
- 1.39498137188764993662E-5, -1.28495495816278026384E-4,
- 1.56988388573005337491E-3, -3.14481013119645005427E-2,
- 2.44030308206595545468E0
- };
- const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = internal::pchebevl<T, 10>::run(
- pmadd(x, x, pset1<T>(-2.0)), A);
- x_le_two = pmadd(
- generic_i0<T, double>::run(x), pmul(
- pset1<T>(-1.0), plog(pmul(pset1<T>(0.5), x))), x_le_two);
- x_le_two = pmul(pexp(x), x_le_two);
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
- T x_gt_two = pmul(
- internal::pchebevl<T, 25>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B),
- prsqrt(x));
- return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct bessel_k0e_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_k0e<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_k0_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_k0 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_k0<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* k0f.c
- * Modified Bessel function, third kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0f();
- *
- * y = k0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order zero of the argument.
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at 2000 random points between 0 and 8. Peak absolute
- * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 7.8e-7 8.5e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * K0 domain x <= 0 MAXNUM
- *
- */
-
- const float A[] = {1.90451637722020886025E-9f, 2.53479107902614945675E-7f,
- 2.28621210311945178607E-5f, 1.26461541144692592338E-3f,
- 3.59799365153615016266E-2f, 3.44289899924628486886E-1f,
- -5.35327393233902768720E-1f};
-
- const float B[] = {-1.69753450938905987466E-9f, 8.57403401741422608519E-9f,
- -4.66048989768794782956E-8f, 2.76681363944501510342E-7f,
- -1.83175552271911948767E-6f, 1.39498137188764993662E-5f,
- -1.28495495816278026384E-4f, 1.56988388573005337491E-3f,
- -3.14481013119645005427E-2f, 2.44030308206595545468E0f};
- const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = internal::pchebevl<T, 7>::run(
- pmadd(x, x, pset1<T>(-2.0)), A);
- x_le_two = pmadd(
- generic_i0<T, float>::run(x), pnegate(
- plog(pmul(pset1<T>(0.5), x))), x_le_two);
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
- T x_gt_two = pmul(
- pmul(
- pexp(pnegate(x)),
- internal::pchebevl<T, 10>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B)),
- prsqrt(x));
- return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct generic_k0<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /*
- *
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k0();
- *
- * y = k0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 1.4e-15 1.4e-16
- * See k0().
- *
- */
- const double A[] = {
- 1.37446543561352307156E-16,
- 4.25981614279661018399E-14,
- 1.03496952576338420167E-11,
- 1.90451637722020886025E-9,
- 2.53479107902614945675E-7,
- 2.28621210311945178607E-5,
- 1.26461541144692592338E-3,
- 3.59799365153615016266E-2,
- 3.44289899924628486886E-1,
- -5.35327393233902768720E-1};
- const double B[] = {
- 5.30043377268626276149E-18, -1.64758043015242134646E-17,
- 5.21039150503902756861E-17, -1.67823109680541210385E-16,
- 5.51205597852431940784E-16, -1.84859337734377901440E-15,
- 6.34007647740507060557E-15, -2.22751332699166985548E-14,
- 8.03289077536357521100E-14, -2.98009692317273043925E-13,
- 1.14034058820847496303E-12, -4.51459788337394416547E-12,
- 1.85594911495471785253E-11, -7.95748924447710747776E-11,
- 3.57739728140030116597E-10, -1.69753450938905987466E-9,
- 8.57403401741422608519E-9, -4.66048989768794782956E-8,
- 2.76681363944501510342E-7, -1.83175552271911948767E-6,
- 1.39498137188764993662E-5, -1.28495495816278026384E-4,
- 1.56988388573005337491E-3, -3.14481013119645005427E-2,
- 2.44030308206595545468E0
- };
- const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = internal::pchebevl<T, 10>::run(
- pmadd(x, x, pset1<T>(-2.0)), A);
- x_le_two = pmadd(
- generic_i0<T, double>::run(x), pnegate(
- plog(pmul(pset1<T>(0.5), x))), x_le_two);
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
- T x_gt_two = pmul(
- pmul(
- pexp(-x),
- internal::pchebevl<T, 25>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B)),
- prsqrt(x));
- return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct bessel_k0_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_k0<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_k1e_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_k1e {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_k1e<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* k1ef.c
- *
- * Modified Bessel function, third kind, order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k1ef();
- *
- * y = k1ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order one of the argument:
- *
- * k1e(x) = exp(x) * k1(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 4.9e-7 6.7e-8
- * See k1().
- *
- */
-
- const float A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,
- -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,
- -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,
- 1.52530022733894777053E0f};
- const float B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,
- 5.74108412545004946722E-8f, -3.50196060308781257119E-7f,
- 2.40648494783721712015E-6f, -1.93619797416608296024E-5f,
- 1.95215518471351631108E-4f, -2.85781685962277938680E-3f,
- 1.03923736576817238437E-1f, 2.72062619048444266945E0f};
- const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = pdiv(internal::pchebevl<T, 7>::run(
- pmadd(x, x, pset1<T>(-2.0)), A), x);
- x_le_two = pmadd(
- generic_i1<T, float>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
- x_le_two = pmul(x_le_two, pexp(x));
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
- T x_gt_two = pmul(
- internal::pchebevl<T, 10>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B),
- prsqrt(x));
- return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct generic_k1e<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* k1e.c
- *
- * Modified Bessel function, third kind, order one,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, k1e();
- *
- * y = k1e( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order one of the argument:
- *
- * k1e(x) = exp(x) * k1(x).
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 7.8e-16 1.2e-16
- * See k1().
- *
- */
- const double A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,
- -6.66690169419932900609E-13, -1.41148839263352776110E-10,
- -2.21338763073472585583E-8, -2.43340614156596823496E-6,
- -1.73028895751305206302E-4, -6.97572385963986435018E-3,
- -1.22611180822657148235E-1, -3.53155960776544875667E-1,
- 1.52530022733894777053E0};
- const double B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,
- -5.68946255844285935196E-17, 1.83809354436663880070E-16,
- -6.05704724837331885336E-16, 2.03870316562433424052E-15,
- -7.01983709041831346144E-15, 2.47715442448130437068E-14,
- -8.97670518232499435011E-14, 3.34841966607842919884E-13,
- -1.28917396095102890680E-12, 5.13963967348173025100E-12,
- -2.12996783842756842877E-11, 9.21831518760500529508E-11,
- -4.19035475934189648750E-10, 2.01504975519703286596E-9,
- -1.03457624656780970260E-8, 5.74108412545004946722E-8,
- -3.50196060308781257119E-7, 2.40648494783721712015E-6,
- -1.93619797416608296024E-5, 1.95215518471351631108E-4,
- -2.85781685962277938680E-3, 1.03923736576817238437E-1,
- 2.72062619048444266945E0};
- const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = pdiv(internal::pchebevl<T, 11>::run(
- pmadd(x, x, pset1<T>(-2.0)), A), x);
- x_le_two = pmadd(
- generic_i1<T, double>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
- x_le_two = pmul(x_le_two, pexp(x));
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
- T x_gt_two = pmul(
- internal::pchebevl<T, 25>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B),
- prsqrt(x));
- return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct bessel_k1e_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_k1e<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_k1_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_k1 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_k1<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* k1f.c
- * Modified Bessel function, third kind, order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k1f();
- *
- * y = k1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the modified Bessel function of the third kind
- * of order one of the argument.
- *
- * The range is partitioned into the two intervals [0,2] and
- * (2, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 4.6e-7 7.6e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * k1 domain x <= 0 MAXNUM
- *
- */
-
- const float A[] = {-2.21338763073472585583E-8f, -2.43340614156596823496E-6f,
- -1.73028895751305206302E-4f, -6.97572385963986435018E-3f,
- -1.22611180822657148235E-1f, -3.53155960776544875667E-1f,
- 1.52530022733894777053E0f};
- const float B[] = {2.01504975519703286596E-9f, -1.03457624656780970260E-8f,
- 5.74108412545004946722E-8f, -3.50196060308781257119E-7f,
- 2.40648494783721712015E-6f, -1.93619797416608296024E-5f,
- 1.95215518471351631108E-4f, -2.85781685962277938680E-3f,
- 1.03923736576817238437E-1f, 2.72062619048444266945E0f};
- const T MAXNUM = pset1<T>(NumTraits<float>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = pdiv(internal::pchebevl<T, 7>::run(
- pmadd(x, x, pset1<T>(-2.0)), A), x);
- x_le_two = pmadd(
- generic_i1<T, float>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
- T x_gt_two = pmul(
- pexp(pnegate(x)),
- pmul(
- internal::pchebevl<T, 10>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B),
- prsqrt(x)));
- return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct generic_k1<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* k1.c
- * Modified Bessel function, third kind, order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k1f();
- *
- * y = k1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Computes the modified Bessel function of the third kind
- * of order one of the argument.
- *
- * The range is partitioned into the two intervals [0,2] and
- * (2, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 4.6e-7 7.6e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * k1 domain x <= 0 MAXNUM
- *
- */
- const double A[] = {-7.02386347938628759343E-18, -2.42744985051936593393E-15,
- -6.66690169419932900609E-13, -1.41148839263352776110E-10,
- -2.21338763073472585583E-8, -2.43340614156596823496E-6,
- -1.73028895751305206302E-4, -6.97572385963986435018E-3,
- -1.22611180822657148235E-1, -3.53155960776544875667E-1,
- 1.52530022733894777053E0};
- const double B[] = {-5.75674448366501715755E-18, 1.79405087314755922667E-17,
- -5.68946255844285935196E-17, 1.83809354436663880070E-16,
- -6.05704724837331885336E-16, 2.03870316562433424052E-15,
- -7.01983709041831346144E-15, 2.47715442448130437068E-14,
- -8.97670518232499435011E-14, 3.34841966607842919884E-13,
- -1.28917396095102890680E-12, 5.13963967348173025100E-12,
- -2.12996783842756842877E-11, 9.21831518760500529508E-11,
- -4.19035475934189648750E-10, 2.01504975519703286596E-9,
- -1.03457624656780970260E-8, 5.74108412545004946722E-8,
- -3.50196060308781257119E-7, 2.40648494783721712015E-6,
- -1.93619797416608296024E-5, 1.95215518471351631108E-4,
- -2.85781685962277938680E-3, 1.03923736576817238437E-1,
- 2.72062619048444266945E0};
- const T MAXNUM = pset1<T>(NumTraits<double>::infinity());
- const T two = pset1<T>(2.0);
- T x_le_two = pdiv(internal::pchebevl<T, 11>::run(
- pmadd(x, x, pset1<T>(-2.0)), A), x);
- x_le_two = pmadd(
- generic_i1<T, double>::run(x), plog(pmul(pset1<T>(0.5), x)), x_le_two);
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), MAXNUM, x_le_two);
- T x_gt_two = pmul(
- pexp(-x),
- pmul(
- internal::pchebevl<T, 25>::run(
- psub(pdiv(pset1<T>(8.0), x), two), B),
- prsqrt(x)));
- return pselect(pcmp_le(x, two), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct bessel_k1_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_k1<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_j0_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_j0 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_j0<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j0f.c
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, j0f();
- *
- * y = j0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order zero of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval the following polynomial
- * approximation is used:
- *
- *
- * 2 2 2
- * (w - r ) (w - r ) (w - r ) P(w)
- * 1 2 3
- *
- * 2
- * where w = x and the three r's are zeros of the function.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x R(1/x^2) - pi/4. The function is
- *
- * j0(x) = Modulus(x) cos( Phase(x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 1.3e-7 3.6e-8
- * IEEE 2, 32 100000 1.9e-7 5.4e-8
- *
- */
-
- const float JP[] = {-6.068350350393235E-008f, 6.388945720783375E-006f,
- -3.969646342510940E-004f, 1.332913422519003E-002f,
- -1.729150680240724E-001f};
- const float MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,
- -2.145007480346739E-001f, 1.197549369473540E-001f,
- -3.560281861530129E-003f, -4.969382655296620E-002f,
- -3.355424622293709E-006f, 7.978845717621440E-001f};
- const float PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,
- 1.756221482109099E+001f, -4.974978466280903E+000f,
- 1.001973420681837E+000f, -1.939906941791308E-001f,
- 6.490598792654666E-002f, -1.249992184872738E-001f};
- const T DR1 = pset1<T>(5.78318596294678452118f);
- const T NEG_PIO4F = pset1<T>(-0.7853981633974483096f); /* -pi / 4 */
- T y = pabs(x);
- T z = pmul(y, y);
- T y_le_two = pselect(
- pcmp_lt(y, pset1<T>(1.0e-3f)),
- pmadd(z, pset1<T>(-0.25f), pset1<T>(1.0f)),
- pmul(psub(z, DR1), internal::ppolevl<T, 4>::run(z, JP)));
- T q = pdiv(pset1<T>(1.0f), y);
- T w = prsqrt(y);
- T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO));
- w = pmul(q, q);
- T yn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH), NEG_PIO4F);
- T y_gt_two = pmul(p, pcos(padd(yn, y)));
- return pselect(pcmp_le(y, pset1<T>(2.0)), y_le_two, y_gt_two);
- }
-};
-
-template <typename T>
-struct generic_j0<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j0.c
- * Bessel function of order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j0();
- *
- * y = j0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order zero of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval the following rational
- * approximation is used:
- *
- *
- * 2 2
- * (w - r ) (w - r ) P (w) / Q (w)
- * 1 2 3 8
- *
- * 2
- * where w = x and the two r's are zeros of the function.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 4.4e-17 6.3e-18
- * IEEE 0, 30 60000 4.2e-16 1.1e-16
- *
- */
- const double PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,
- 1.23953371646414299388E0, 5.44725003058768775090E0,
- 8.74716500199817011941E0, 5.30324038235394892183E0,
- 9.99999999999999997821E-1};
- const double PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,
- 1.25352743901058953537E0, 5.47097740330417105182E0,
- 8.76190883237069594232E0, 5.30605288235394617618E0,
- 1.00000000000000000218E0};
- const double QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,
- -1.95539544257735972385E1, -9.32060152123768231369E1,
- -1.77681167980488050595E2, -1.47077505154951170175E2,
- -5.14105326766599330220E1, -6.05014350600728481186E0};
- const double QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,
- 8.56430025976980587198E2, 3.88240183605401609683E3,
- 7.24046774195652478189E3, 5.93072701187316984827E3,
- 2.06209331660327847417E3, 2.42005740240291393179E2};
- const double RP[] = {-4.79443220978201773821E9, 1.95617491946556577543E12,
- -2.49248344360967716204E14, 9.70862251047306323952E15};
- const double RQ[] = {1.00000000000000000000E0, 4.99563147152651017219E2,
- 1.73785401676374683123E5, 4.84409658339962045305E7,
- 1.11855537045356834862E10, 2.11277520115489217587E12,
- 3.10518229857422583814E14, 3.18121955943204943306E16,
- 1.71086294081043136091E18};
- const T DR1 = pset1<T>(5.78318596294678452118E0);
- const T DR2 = pset1<T>(3.04712623436620863991E1);
- const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1); /* sqrt(2 / pi) */
- const T NEG_PIO4 = pset1<T>(-0.7853981633974483096); /* pi / 4 */
-
- T y = pabs(x);
- T z = pmul(y, y);
- T y_le_five = pselect(
- pcmp_lt(y, pset1<T>(1.0e-5)),
- pmadd(z, pset1<T>(-0.25), pset1<T>(1.0)),
- pmul(pmul(psub(z, DR1), psub(z, DR2)),
- pdiv(internal::ppolevl<T, 3>::run(z, RP),
- internal::ppolevl<T, 8>::run(z, RQ))));
- T s = pdiv(pset1<T>(25.0), z);
- T p = pdiv(
- internal::ppolevl<T, 6>::run(s, PP),
- internal::ppolevl<T, 6>::run(s, PQ));
- T q = pdiv(
- internal::ppolevl<T, 7>::run(s, QP),
- internal::ppolevl<T, 7>::run(s, QQ));
- T yn = padd(y, NEG_PIO4);
- T w = pdiv(pset1<T>(-5.0), y);
- p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));
- T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));
- return pselect(pcmp_le(y, pset1<T>(5.0)), y_le_five, y_gt_five);
- }
-};
-
-template <typename T>
-struct bessel_j0_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_j0<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_y0_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_y0 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_y0<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j0f.c
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, y0f();
- *
- * y = y0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *
- * 2 2 2
- * y0(x) = (w - r ) (w - r ) (w - r ) R(x) + 2/pi ln(x) j0(x).
- * 1 2 3
- *
- * Thus a call to j0() is required. The three zeros are removed
- * from R(x) to improve its numerical stability.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x S(1/x^2) - pi/4. Then the function is
- *
- * y0(x) = Modulus(x) sin( Phase(x) ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 2.4e-7 3.4e-8
- * IEEE 2, 32 100000 1.8e-7 5.3e-8
- *
- */
-
- const float YP[] = {9.454583683980369E-008f, -9.413212653797057E-006f,
- 5.344486707214273E-004f, -1.584289289821316E-002f,
- 1.707584643733568E-001f};
- const float MO[] = {-6.838999669318810E-002f, 1.864949361379502E-001f,
- -2.145007480346739E-001f, 1.197549369473540E-001f,
- -3.560281861530129E-003f, -4.969382655296620E-002f,
- -3.355424622293709E-006f, 7.978845717621440E-001f};
- const float PH[] = {3.242077816988247E+001f, -3.630592630518434E+001f,
- 1.756221482109099E+001f, -4.974978466280903E+000f,
- 1.001973420681837E+000f, -1.939906941791308E-001f,
- 6.490598792654666E-002f, -1.249992184872738E-001f};
- const T YZ1 = pset1<T>(0.43221455686510834878f);
- const T TWOOPI = pset1<T>(0.636619772367581343075535f); /* 2 / pi */
- const T NEG_PIO4F = pset1<T>(-0.7853981633974483096f); /* -pi / 4 */
- const T NEG_MAXNUM = pset1<T>(-NumTraits<float>::infinity());
- T z = pmul(x, x);
- T x_le_two = pmul(TWOOPI, pmul(plog(x), generic_j0<T, float>::run(x)));
- x_le_two = pmadd(
- psub(z, YZ1), internal::ppolevl<T, 4>::run(z, YP), x_le_two);
- x_le_two = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_two);
- T q = pdiv(pset1<T>(1.0), x);
- T w = prsqrt(x);
- T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO));
- T u = pmul(q, q);
- T xn = pmadd(q, internal::ppolevl<T, 7>::run(u, PH), NEG_PIO4F);
- T x_gt_two = pmul(p, psin(padd(xn, x)));
- return pselect(pcmp_le(x, pset1<T>(2.0)), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct generic_y0<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j0.c
- * Bessel function of the second kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y0();
- *
- * y = y0( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind, of order
- * zero, of the argument.
- *
- * The domain is divided into the intervals [0, 5] and
- * (5, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- * y0(x) = R(x) + 2 * log(x) * j0(x) / PI.
- * Thus a call to j0() is required.
- *
- * In the second interval, the Hankel asymptotic expansion
- * is employed with two rational functions of degree 6/6
- * and 7/7.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error, when y0(x) < 1; else relative error:
- *
- * arithmetic domain # trials peak rms
- * DEC 0, 30 9400 7.0e-17 7.9e-18
- * IEEE 0, 30 30000 1.3e-15 1.6e-16
- *
- */
- const double PP[] = {7.96936729297347051624E-4, 8.28352392107440799803E-2,
- 1.23953371646414299388E0, 5.44725003058768775090E0,
- 8.74716500199817011941E0, 5.30324038235394892183E0,
- 9.99999999999999997821E-1};
- const double PQ[] = {9.24408810558863637013E-4, 8.56288474354474431428E-2,
- 1.25352743901058953537E0, 5.47097740330417105182E0,
- 8.76190883237069594232E0, 5.30605288235394617618E0,
- 1.00000000000000000218E0};
- const double QP[] = {-1.13663838898469149931E-2, -1.28252718670509318512E0,
- -1.95539544257735972385E1, -9.32060152123768231369E1,
- -1.77681167980488050595E2, -1.47077505154951170175E2,
- -5.14105326766599330220E1, -6.05014350600728481186E0};
- const double QQ[] = {1.00000000000000000000E0, 6.43178256118178023184E1,
- 8.56430025976980587198E2, 3.88240183605401609683E3,
- 7.24046774195652478189E3, 5.93072701187316984827E3,
- 2.06209331660327847417E3, 2.42005740240291393179E2};
- const double YP[] = {1.55924367855235737965E4, -1.46639295903971606143E7,
- 5.43526477051876500413E9, -9.82136065717911466409E11,
- 8.75906394395366999549E13, -3.46628303384729719441E15,
- 4.42733268572569800351E16, -1.84950800436986690637E16};
- const double YQ[] = {1.00000000000000000000E0, 1.04128353664259848412E3,
- 6.26107330137134956842E5, 2.68919633393814121987E8,
- 8.64002487103935000337E10, 2.02979612750105546709E13,
- 3.17157752842975028269E15, 2.50596256172653059228E17};
- const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1); /* sqrt(2 / pi) */
- const T TWOOPI = pset1<T>(0.636619772367581343075535); /* 2 / pi */
- const T NEG_PIO4 = pset1<T>(-0.7853981633974483096); /* -pi / 4 */
- const T NEG_MAXNUM = pset1<T>(-NumTraits<double>::infinity());
-
- T z = pmul(x, x);
- T x_le_five = pdiv(internal::ppolevl<T, 7>::run(z, YP),
- internal::ppolevl<T, 7>::run(z, YQ));
- x_le_five = pmadd(
- pmul(TWOOPI, plog(x)), generic_j0<T, double>::run(x), x_le_five);
- x_le_five = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_five);
- T s = pdiv(pset1<T>(25.0), z);
- T p = pdiv(
- internal::ppolevl<T, 6>::run(s, PP),
- internal::ppolevl<T, 6>::run(s, PQ));
- T q = pdiv(
- internal::ppolevl<T, 7>::run(s, QP),
- internal::ppolevl<T, 7>::run(s, QQ));
- T xn = padd(x, NEG_PIO4);
- T w = pdiv(pset1<T>(5.0), x);
- p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));
- T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));
- return pselect(pcmp_le(x, pset1<T>(5.0)), x_le_five, x_gt_five);
- }
-};
-
-template <typename T>
-struct bessel_y0_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_y0<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_j1_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_j1 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_j1<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j1f.c
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, j1f();
- *
- * y = j1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a polynomial approximation
- * 2
- * (w - r ) x P(w)
- * 1
- * 2
- * is used, where w = x and r is the first zero of the function.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4. The function is
- *
- * j0(x) = Modulus(x) cos( Phase(x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 1.2e-7 2.5e-8
- * IEEE 2, 32 100000 2.0e-7 5.3e-8
- *
- *
- */
-
- const float JP[] = {-4.878788132172128E-009f, 6.009061827883699E-007f,
- -4.541343896997497E-005f, 1.937383947804541E-003f,
- -3.405537384615824E-002f};
- const float MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,
- 3.138238455499697E-001f, -2.102302420403875E-001f,
- 5.435364690523026E-003f, 1.493389585089498E-001f,
- 4.976029650847191E-006f, 7.978845453073848E-001f};
- const float PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,
- -2.485774108720340E+001f, 7.222973196770240E+000f,
- -1.544842782180211E+000f, 3.503787691653334E-001f,
- -1.637986776941202E-001f, 3.749989509080821E-001f};
- const T Z1 = pset1<T>(1.46819706421238932572E1f);
- const T NEG_THPIO4F = pset1<T>(-2.35619449019234492885f); /* -3*pi/4 */
-
- T y = pabs(x);
- T z = pmul(y, y);
- T y_le_two = pmul(
- psub(z, Z1),
- pmul(x, internal::ppolevl<T, 4>::run(z, JP)));
- T q = pdiv(pset1<T>(1.0f), y);
- T w = prsqrt(y);
- T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO1));
- w = pmul(q, q);
- T yn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH1), NEG_THPIO4F);
- T y_gt_two = pmul(p, pcos(padd(yn, y)));
- // j1 is an odd function. This implementation differs from cephes to
- // take this fact in to account. Cephes returns -j1(x) for y > 2 range.
- y_gt_two = pselect(
- pcmp_lt(x, pset1<T>(0.0f)), pnegate(y_gt_two), y_gt_two);
- return pselect(pcmp_le(y, pset1<T>(2.0f)), y_le_two, y_gt_two);
- }
-};
-
-template <typename T>
-struct generic_j1<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j1.c
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, j1();
- *
- * y = j1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 24 term Chebyshev
- * expansion is used. In the second, the asymptotic
- * trigonometric representation is employed using two
- * rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 4.0e-17 1.1e-17
- * IEEE 0, 30 30000 2.6e-16 1.1e-16
- *
- */
- const double PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,
- 1.12719608129684925192E0, 5.11207951146807644818E0,
- 8.42404590141772420927E0, 5.21451598682361504063E0,
- 1.00000000000000000254E0};
- const double PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,
- 1.10514232634061696926E0, 5.07386386128601488557E0,
- 8.39985554327604159757E0, 5.20982848682361821619E0,
- 9.99999999999999997461E-1};
- const double QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,
- 7.58238284132545283818E1, 3.66779609360150777800E2,
- 7.10856304998926107277E2, 5.97489612400613639965E2,
- 2.11688757100572135698E2, 2.52070205858023719784E1};
- const double QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,
- 1.05644886038262816351E3, 4.98641058337653607651E3,
- 9.56231892404756170795E3, 7.99704160447350683650E3,
- 2.82619278517639096600E3, 3.36093607810698293419E2};
- const double RP[] = {-8.99971225705559398224E8, 4.52228297998194034323E11,
- -7.27494245221818276015E13, 3.68295732863852883286E15};
- const double RQ[] = {1.00000000000000000000E0, 6.20836478118054335476E2,
- 2.56987256757748830383E5, 8.35146791431949253037E7,
- 2.21511595479792499675E10, 4.74914122079991414898E12,
- 7.84369607876235854894E14, 8.95222336184627338078E16,
- 5.32278620332680085395E18};
- const T Z1 = pset1<T>(1.46819706421238932572E1);
- const T Z2 = pset1<T>(4.92184563216946036703E1);
- const T NEG_THPIO4 = pset1<T>(-2.35619449019234492885); /* -3*pi/4 */
- const T SQ2OPI = pset1<T>(7.9788456080286535587989E-1); /* sqrt(2 / pi) */
- T y = pabs(x);
- T z = pmul(y, y);
- T y_le_five = pdiv(internal::ppolevl<T, 3>::run(z, RP),
- internal::ppolevl<T, 8>::run(z, RQ));
- y_le_five = pmul(pmul(pmul(y_le_five, x), psub(z, Z1)), psub(z, Z2));
- T s = pdiv(pset1<T>(25.0), z);
- T p = pdiv(
- internal::ppolevl<T, 6>::run(s, PP),
- internal::ppolevl<T, 6>::run(s, PQ));
- T q = pdiv(
- internal::ppolevl<T, 7>::run(s, QP),
- internal::ppolevl<T, 7>::run(s, QQ));
- T yn = padd(y, NEG_THPIO4);
- T w = pdiv(pset1<T>(-5.0), y);
- p = pmadd(p, pcos(yn), pmul(w, pmul(q, psin(yn))));
- T y_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(y)));
- // j1 is an odd function. This implementation differs from cephes to
- // take this fact in to account. Cephes returns -j1(x) for y > 5 range.
- y_gt_five = pselect(
- pcmp_lt(x, pset1<T>(0.0)), pnegate(y_gt_five), y_gt_five);
- return pselect(pcmp_le(y, pset1<T>(5.0)), y_le_five, y_gt_five);
- }
-};
-
-template <typename T>
-struct bessel_j1_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_j1<T>::run(x);
- }
-};
-
-template <typename T>
-struct bessel_y1_retval {
- typedef T type;
-};
-
-template <typename T, typename ScalarType = typename unpacket_traits<T>::type>
-struct generic_y1 {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T&) {
- EIGEN_STATIC_ASSERT((internal::is_same<T, T>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return ScalarType(0);
- }
-};
-
-template <typename T>
-struct generic_y1<T, float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j1f.c
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *
- * 2
- * y0(x) = (w - r ) x R(x^2) + 2/pi (ln(x) j1(x) - 1/x) .
- * 1
- *
- * Thus a call to j1() is required.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4. Then the function is
- *
- * y0(x) = Modulus(x) sin( Phase(x) ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 2.2e-7 4.6e-8
- * IEEE 2, 32 100000 1.9e-7 5.3e-8
- *
- * (error criterion relative when |y1| > 1).
- *
- */
-
- const float YP[] = {8.061978323326852E-009f, -9.496460629917016E-007f,
- 6.719543806674249E-005f, -2.641785726447862E-003f,
- 4.202369946500099E-002f};
- const float MO1[] = {6.913942741265801E-002f, -2.284801500053359E-001f,
- 3.138238455499697E-001f, -2.102302420403875E-001f,
- 5.435364690523026E-003f, 1.493389585089498E-001f,
- 4.976029650847191E-006f, 7.978845453073848E-001f};
- const float PH1[] = {-4.497014141919556E+001f, 5.073465654089319E+001f,
- -2.485774108720340E+001f, 7.222973196770240E+000f,
- -1.544842782180211E+000f, 3.503787691653334E-001f,
- -1.637986776941202E-001f, 3.749989509080821E-001f};
- const T YO1 = pset1<T>(4.66539330185668857532f);
- const T NEG_THPIO4F = pset1<T>(-2.35619449019234492885f); /* -3*pi/4 */
- const T TWOOPI = pset1<T>(0.636619772367581343075535f); /* 2/pi */
- const T NEG_MAXNUM = pset1<T>(-NumTraits<float>::infinity());
-
- T z = pmul(x, x);
- T x_le_two = pmul(psub(z, YO1), internal::ppolevl<T, 4>::run(z, YP));
- x_le_two = pmadd(
- x_le_two, x,
- pmul(TWOOPI, pmadd(
- generic_j1<T, float>::run(x), plog(x),
- pdiv(pset1<T>(-1.0f), x))));
- x_le_two = pselect(pcmp_lt(x, pset1<T>(0.0f)), NEG_MAXNUM, x_le_two);
-
- T q = pdiv(pset1<T>(1.0), x);
- T w = prsqrt(x);
- T p = pmul(w, internal::ppolevl<T, 7>::run(q, MO1));
- w = pmul(q, q);
- T xn = pmadd(q, internal::ppolevl<T, 7>::run(w, PH1), NEG_THPIO4F);
- T x_gt_two = pmul(p, psin(padd(xn, x)));
- return pselect(pcmp_le(x, pset1<T>(2.0)), x_le_two, x_gt_two);
- }
-};
-
-template <typename T>
-struct generic_y1<T, double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- /* j1.c
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 8] and
- * (8, infinity). In the first interval a 25 term Chebyshev
- * expansion is used, and a call to j1() is required.
- * In the second, the asymptotic trigonometric representation
- * is employed using two rational functions of degree 5/5.
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * DEC 0, 30 10000 8.6e-17 1.3e-17
- * IEEE 0, 30 30000 1.0e-15 1.3e-16
- *
- * (error criterion relative when |y1| > 1).
- *
- */
- const double PP[] = {7.62125616208173112003E-4, 7.31397056940917570436E-2,
- 1.12719608129684925192E0, 5.11207951146807644818E0,
- 8.42404590141772420927E0, 5.21451598682361504063E0,
- 1.00000000000000000254E0};
- const double PQ[] = {5.71323128072548699714E-4, 6.88455908754495404082E-2,
- 1.10514232634061696926E0, 5.07386386128601488557E0,
- 8.39985554327604159757E0, 5.20982848682361821619E0,
- 9.99999999999999997461E-1};
- const double QP[] = {5.10862594750176621635E-2, 4.98213872951233449420E0,
- 7.58238284132545283818E1, 3.66779609360150777800E2,
- 7.10856304998926107277E2, 5.97489612400613639965E2,
- 2.11688757100572135698E2, 2.52070205858023719784E1};
- const double QQ[] = {1.00000000000000000000E0, 7.42373277035675149943E1,
- 1.05644886038262816351E3, 4.98641058337653607651E3,
- 9.56231892404756170795E3, 7.99704160447350683650E3,
- 2.82619278517639096600E3, 3.36093607810698293419E2};
- const double YP[] = {1.26320474790178026440E9, -6.47355876379160291031E11,
- 1.14509511541823727583E14, -8.12770255501325109621E15,
- 2.02439475713594898196E17, -7.78877196265950026825E17};
- const double YQ[] = {1.00000000000000000000E0, 5.94301592346128195359E2,
- 2.35564092943068577943E5, 7.34811944459721705660E7,
- 1.87601316108706159478E10, 3.88231277496238566008E12,
- 6.20557727146953693363E14, 6.87141087355300489866E16,
- 3.97270608116560655612E18};
- const T SQ2OPI = pset1<T>(.79788456080286535588);
- const T NEG_THPIO4 = pset1<T>(-2.35619449019234492885); /* -3*pi/4 */
- const T TWOOPI = pset1<T>(0.636619772367581343075535); /* 2/pi */
- const T NEG_MAXNUM = pset1<T>(-NumTraits<double>::infinity());
-
- T z = pmul(x, x);
- T x_le_five = pdiv(internal::ppolevl<T, 5>::run(z, YP),
- internal::ppolevl<T, 8>::run(z, YQ));
- x_le_five = pmadd(
- x_le_five, x, pmul(
- TWOOPI, pmadd(generic_j1<T, double>::run(x), plog(x),
- pdiv(pset1<T>(-1.0), x))));
-
- x_le_five = pselect(pcmp_le(x, pset1<T>(0.0)), NEG_MAXNUM, x_le_five);
- T s = pdiv(pset1<T>(25.0), z);
- T p = pdiv(
- internal::ppolevl<T, 6>::run(s, PP),
- internal::ppolevl<T, 6>::run(s, PQ));
- T q = pdiv(
- internal::ppolevl<T, 7>::run(s, QP),
- internal::ppolevl<T, 7>::run(s, QQ));
- T xn = padd(x, NEG_THPIO4);
- T w = pdiv(pset1<T>(5.0), x);
- p = pmadd(p, psin(xn), pmul(w, pmul(q, pcos(xn))));
- T x_gt_five = pmul(p, pmul(SQ2OPI, prsqrt(x)));
- return pselect(pcmp_le(x, pset1<T>(5.0)), x_le_five, x_gt_five);
- }
-};
-
-template <typename T>
-struct bessel_y1_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T x) {
- return generic_y1<T>::run(x);
- }
-};
-
-} // end namespace internal
-
-namespace numext {
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i0, Scalar)
- bessel_i0(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_i0, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i0e, Scalar)
- bessel_i0e(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_i0e, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i1, Scalar)
- bessel_i1(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_i1, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_i1e, Scalar)
- bessel_i1e(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_i1e, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k0, Scalar)
- bessel_k0(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_k0, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k0e, Scalar)
- bessel_k0e(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_k0e, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k1, Scalar)
- bessel_k1(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_k1, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_k1e, Scalar)
- bessel_k1e(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_k1e, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_j0, Scalar)
- bessel_j0(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_j0, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_y0, Scalar)
- bessel_y0(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_y0, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_j1, Scalar)
- bessel_j1(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_j1, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(bessel_y1, Scalar)
- bessel_y1(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(bessel_y1, Scalar)::run(x);
-}
-
-} // end namespace numext
-
-} // end namespace Eigen
-
-#endif // EIGEN_BESSEL_FUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsPacketMath.h b/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsPacketMath.h
deleted file mode 100644
index 943d10f..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/BesselFunctionsPacketMath.h
+++ /dev/null
@@ -1,118 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
-//
-// 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_BESSELFUNCTIONS_PACKETMATH_H
-#define EIGEN_BESSELFUNCTIONS_PACKETMATH_H
-
-namespace Eigen {
-
-namespace internal {
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order zero i0(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_i0(const Packet& x) {
- return numext::bessel_i0(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order zero i0e(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_i0e(const Packet& x) {
- return numext::bessel_i0e(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order one i1(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_i1(const Packet& x) {
- return numext::bessel_i1(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order one i1e(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_i1e(const Packet& x) {
- return numext::bessel_i1e(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order zero j0(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_j0(const Packet& x) {
- return numext::bessel_j0(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order zero j1(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_j1(const Packet& x) {
- return numext::bessel_j1(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order one y0(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_y0(const Packet& x) {
- return numext::bessel_y0(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order one y1(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_y1(const Packet& x) {
- return numext::bessel_y1(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order zero k0(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_k0(const Packet& x) {
- return numext::bessel_k0(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order zero k0e(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_k0e(const Packet& x) {
- return numext::bessel_k0e(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order one k1e(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_k1(const Packet& x) {
- return numext::bessel_k1(x);
-}
-
-/** \internal \returns the exponentially scaled modified Bessel function of
- * order one k1e(\a a) (coeff-wise) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pbessel_k1e(const Packet& x) {
- return numext::bessel_k1e(x);
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_BESSELFUNCTIONS_PACKETMATH_H
-
diff --git a/src/EigenUnsupported/src/SpecialFunctions/HipVectorCompatibility.h b/src/EigenUnsupported/src/SpecialFunctions/HipVectorCompatibility.h
deleted file mode 100644
index d7b231a..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/HipVectorCompatibility.h
+++ /dev/null
@@ -1,67 +0,0 @@
-#ifndef HIP_VECTOR_COMPATIBILITY_H
-#define HIP_VECTOR_COMPATIBILITY_H
-
-namespace hip_impl {
- template <typename, typename, unsigned int> struct Scalar_accessor;
-} // end namespace hip_impl
-
-namespace Eigen {
-namespace internal {
-
-#define HIP_SCALAR_ACCESSOR_BUILDER(NAME) \
-template <typename T, typename U, unsigned int n> \
-struct NAME <hip_impl::Scalar_accessor<T, U, n>> : NAME <T> {};
-
-#define HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(NAME) \
-template <typename T, typename U, unsigned int n> \
-struct NAME##_impl <hip_impl::Scalar_accessor<T, U, n>> : NAME##_impl <T> {}; \
-template <typename T, typename U, unsigned int n> \
-struct NAME##_retval <hip_impl::Scalar_accessor<T, U, n>> : NAME##_retval <T> {};
-
-#define HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(NAME) \
-template <typename T, typename U, unsigned int n, IgammaComputationMode mode> \
-struct NAME <hip_impl::Scalar_accessor<T, U, n>, mode> : NAME <T, mode> {};
-
-#if EIGEN_HAS_C99_MATH
-HIP_SCALAR_ACCESSOR_BUILDER(betainc_helper)
-HIP_SCALAR_ACCESSOR_BUILDER(incbeta_cfe)
-
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(erf)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(erfc)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(igammac)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(lgamma)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(ndtri)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(polygamma)
-
-HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(igamma_generic_impl)
-#endif
-
-HIP_SCALAR_ACCESSOR_BUILDER(digamma_impl_maybe_poly)
-HIP_SCALAR_ACCESSOR_BUILDER(zeta_impl_series)
-
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i0)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i0e)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i1)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_i1e)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_j0)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_j1)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k0)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k0e)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k1)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_k1e)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_y0)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(bessel_y1)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(betainc)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(digamma)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(gamma_sample_der_alpha)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(igamma_der_a)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(igamma)
-HIP_SCALAR_ACCESSOR_BUILDER_RETVAL(zeta)
-
-HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(igamma_series_impl)
-HIP_SCALAR_ACCESSOR_BUILDER_IGAMMA(igammac_cf_impl)
-
-} // end namespace internal
-} // end namespace Eigen
-
-#endif // HIP_VECTOR_COMPATIBILITY_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsArrayAPI.h b/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
deleted file mode 100644
index 691ff4d..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsArrayAPI.h
+++ /dev/null
@@ -1,167 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
-//
-// 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_SPECIALFUNCTIONS_ARRAYAPI_H
-#define EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H
-
-namespace Eigen {
-
-/** \cpp11 \returns an expression of the coefficient-wise igamma(\a a, \a x) to the given arrays.
- *
- * This function computes the coefficient-wise incomplete gamma function.
- *
- * \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 igammac(T,T) for any scalar
- * type T to be supported.
- *
- * \sa Eigen::igammac(), Eigen::lgamma()
- */
-template<typename Derived,typename ExponentDerived>
-EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
-igamma(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
-{
- return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
- a.derived(),
- x.derived()
- );
-}
-
-/** \cpp11 \returns an expression of the coefficient-wise igamma_der_a(\a a, \a x) to the given arrays.
- *
- * This function computes the coefficient-wise derivative of the incomplete
- * gamma function with respect to the parameter a.
- *
- * \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 igamma_der_a(T,T) for any scalar
- * type T to be supported.
- *
- * \sa Eigen::igamma(), Eigen::lgamma()
- */
-template <typename Derived, typename ExponentDerived>
-EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
-igamma_der_a(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x) {
- return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igamma_der_a_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
- a.derived(),
- x.derived());
-}
-
-/** \cpp11 \returns an expression of the coefficient-wise gamma_sample_der_alpha(\a alpha, \a sample) to the given arrays.
- *
- * This function computes the coefficient-wise derivative of the sample
- * of a Gamma(alpha, 1) random variable with respect to the parameter alpha.
- *
- * \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 gamma_sample_der_alpha(T,T) for any scalar
- * type T to be supported.
- *
- * \sa Eigen::igamma(), Eigen::lgamma()
- */
-template <typename AlphaDerived, typename SampleDerived>
-EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>, const AlphaDerived, const SampleDerived>
-gamma_sample_der_alpha(const Eigen::ArrayBase<AlphaDerived>& alpha, const Eigen::ArrayBase<SampleDerived>& sample) {
- return Eigen::CwiseBinaryOp<Eigen::internal::scalar_gamma_sample_der_alpha_op<typename AlphaDerived::Scalar>, const AlphaDerived, const SampleDerived>(
- alpha.derived(),
- sample.derived());
-}
-
-/** \cpp11 \returns an expression of the coefficient-wise igammac(\a a, \a x) to the given arrays.
- *
- * This function computes the coefficient-wise complementary incomplete gamma function.
- *
- * \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 igammac(T,T) for any scalar
- * type T to be supported.
- *
- * \sa Eigen::igamma(), Eigen::lgamma()
- */
-template<typename Derived,typename ExponentDerived>
-EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>
-igammac(const Eigen::ArrayBase<Derived>& a, const Eigen::ArrayBase<ExponentDerived>& x)
-{
- return Eigen::CwiseBinaryOp<Eigen::internal::scalar_igammac_op<typename Derived::Scalar>, const Derived, const ExponentDerived>(
- a.derived(),
- x.derived()
- );
-}
-
-/** \cpp11 \returns an expression of the coefficient-wise polygamma(\a n, \a x) to the given arrays.
- *
- * It returns the \a n -th derivative of the digamma(psi) evaluated at \c x.
- *
- * \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 polygamma(T,T) for any scalar
- * type T to be supported.
- *
- * \sa Eigen::digamma()
- */
-// * \warning Be careful with the order of the parameters: x.polygamma(n) is equivalent to polygamma(n,x)
-// * \sa ArrayBase::polygamma()
-template<typename DerivedN,typename DerivedX>
-EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>
-polygamma(const Eigen::ArrayBase<DerivedN>& n, const Eigen::ArrayBase<DerivedX>& x)
-{
- return Eigen::CwiseBinaryOp<Eigen::internal::scalar_polygamma_op<typename DerivedX::Scalar>, const DerivedN, const DerivedX>(
- n.derived(),
- x.derived()
- );
-}
-
-/** \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>
-EIGEN_STRONG_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:
- *
- * \param x is the exponent, it must be > 1
- * \param q is the shift, it must be > 0
- *
- * \note This function supports only float and double scalar types. To support other scalar types, the user has
- * to provide implementations of zeta(T,T) for any scalar type T to be supported.
- *
- * \sa ArrayBase::zeta()
- */
-template<typename DerivedX,typename DerivedQ>
-EIGEN_STRONG_INLINE const Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>
-zeta(const Eigen::ArrayBase<DerivedX>& x, const Eigen::ArrayBase<DerivedQ>& q)
-{
- return Eigen::CwiseBinaryOp<Eigen::internal::scalar_zeta_op<typename DerivedX::Scalar>, const DerivedX, const DerivedQ>(
- x.derived(),
- q.derived()
- );
-}
-
-
-} // end namespace Eigen
-
-#endif // EIGEN_SPECIALFUNCTIONS_ARRAYAPI_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsBFloat16.h b/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsBFloat16.h
deleted file mode 100644
index 2d94231..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsBFloat16.h
+++ /dev/null
@@ -1,58 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// 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_SPECIALFUNCTIONS_BFLOAT16_H
-#define EIGEN_SPECIALFUNCTIONS_BFLOAT16_H
-
-namespace Eigen {
-namespace numext {
-
-#if EIGEN_HAS_C99_MATH
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 lgamma(const Eigen::bfloat16& a) {
- return Eigen::bfloat16(Eigen::numext::lgamma(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 digamma(const Eigen::bfloat16& a) {
- return Eigen::bfloat16(Eigen::numext::digamma(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 zeta(const Eigen::bfloat16& x, const Eigen::bfloat16& q) {
- return Eigen::bfloat16(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 polygamma(const Eigen::bfloat16& n, const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 erf(const Eigen::bfloat16& a) {
- return Eigen::bfloat16(Eigen::numext::erf(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 erfc(const Eigen::bfloat16& a) {
- return Eigen::bfloat16(Eigen::numext::erfc(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 ndtri(const Eigen::bfloat16& a) {
- return Eigen::bfloat16(Eigen::numext::ndtri(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 igamma(const Eigen::bfloat16& a, const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 igamma_der_a(const Eigen::bfloat16& a, const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::igamma_der_a(static_cast<float>(a), static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 gamma_sample_der_alpha(const Eigen::bfloat16& alpha, const Eigen::bfloat16& sample) {
- return Eigen::bfloat16(Eigen::numext::gamma_sample_der_alpha(static_cast<float>(alpha), static_cast<float>(sample)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 igammac(const Eigen::bfloat16& a, const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::igammac(static_cast<float>(a), static_cast<float>(x)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::bfloat16 betainc(const Eigen::bfloat16& a, const Eigen::bfloat16& b, const Eigen::bfloat16& x) {
- return Eigen::bfloat16(Eigen::numext::betainc(static_cast<float>(a), static_cast<float>(b), static_cast<float>(x)));
-}
-#endif
-
-} // end namespace numext
-} // end namespace Eigen
-
-#endif // EIGEN_SPECIALFUNCTIONS_BFLOAT16_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsFunctors.h b/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsFunctors.h
deleted file mode 100644
index abefe99..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsFunctors.h
+++ /dev/null
@@ -1,330 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
-// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
-//
-// 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_SPECIALFUNCTIONS_FUNCTORS_H
-#define EIGEN_SPECIALFUNCTIONS_FUNCTORS_H
-
-namespace Eigen {
-
-namespace internal {
-
-
-/** \internal
- * \brief Template functor to compute the incomplete gamma function igamma(a, x)
- *
- * \sa class CwiseBinaryOp, Cwise::igamma
- */
-template<typename Scalar> struct scalar_igamma_op : binary_op_base<Scalar,Scalar>
-{
- EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
- using numext::igamma; return igamma(a, x);
- }
- template<typename Packet>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
- return internal::pigamma(a, x);
- }
-};
-template<typename Scalar>
-struct functor_traits<scalar_igamma_op<Scalar> > {
- enum {
- // Guesstimate
- Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasIGamma
- };
-};
-
-/** \internal
- * \brief Template functor to compute the derivative of the incomplete gamma
- * function igamma_der_a(a, x)
- *
- * \sa class CwiseBinaryOp, Cwise::igamma_der_a
- */
-template <typename Scalar>
-struct scalar_igamma_der_a_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_igamma_der_a_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& a, const Scalar& x) const {
- using numext::igamma_der_a;
- return igamma_der_a(a, x);
- }
- template <typename Packet>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const {
- return internal::pigamma_der_a(a, x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_igamma_der_a_op<Scalar> > {
- enum {
- // 2x the cost of igamma
- Cost = 40 * NumTraits<Scalar>::MulCost + 20 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasIGammaDerA
- };
-};
-
-/** \internal
- * \brief Template functor to compute the derivative of the sample
- * of a Gamma(alpha, 1) random variable with respect to the parameter alpha
- * gamma_sample_der_alpha(alpha, sample)
- *
- * \sa class CwiseBinaryOp, Cwise::gamma_sample_der_alpha
- */
-template <typename Scalar>
-struct scalar_gamma_sample_der_alpha_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_gamma_sample_der_alpha_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& alpha, const Scalar& sample) const {
- using numext::gamma_sample_der_alpha;
- return gamma_sample_der_alpha(alpha, sample);
- }
- template <typename Packet>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& alpha, const Packet& sample) const {
- return internal::pgamma_sample_der_alpha(alpha, sample);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_gamma_sample_der_alpha_op<Scalar> > {
- enum {
- // 2x the cost of igamma, minus the lgamma cost (the lgamma cancels out)
- Cost = 30 * NumTraits<Scalar>::MulCost + 15 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasGammaSampleDerAlpha
- };
-};
-
-/** \internal
- * \brief Template functor to compute the complementary incomplete gamma function igammac(a, x)
- *
- * \sa class CwiseBinaryOp, Cwise::igammac
- */
-template<typename Scalar> struct scalar_igammac_op : binary_op_base<Scalar,Scalar>
-{
- EIGEN_EMPTY_STRUCT_CTOR(scalar_igammac_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a, const Scalar& x) const {
- using numext::igammac; return igammac(a, x);
- }
- template<typename Packet>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a, const Packet& x) const
- {
- return internal::pigammac(a, x);
- }
-};
-template<typename Scalar>
-struct functor_traits<scalar_igammac_op<Scalar> > {
- enum {
- // Guesstimate
- Cost = 20 * NumTraits<Scalar>::MulCost + 10 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasIGammac
- };
-};
-
-
-/** \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
- };
-};
-
-
-/** \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 EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
- using numext::lgamma; return lgamma(a);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_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 psi, the derivative of lgamma of a scalar.
- * \sa class CwiseUnaryOp, Cwise::digamma()
- */
-template<typename Scalar> struct scalar_digamma_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_digamma_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
- using numext::digamma; return digamma(a);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::pdigamma(a); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_digamma_op<Scalar> >
-{
- enum {
- // Guesstimate
- Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasDiGamma
- };
-};
-
-/** \internal
- * \brief Template functor to compute the Riemann Zeta function of two arguments.
- * \sa class CwiseUnaryOp, Cwise::zeta()
- */
-template<typename Scalar> struct scalar_zeta_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_zeta_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& x, const Scalar& q) const {
- using numext::zeta; return zeta(x, q);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x, const Packet& q) const { return internal::pzeta(x, q); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_zeta_op<Scalar> >
-{
- enum {
- // Guesstimate
- Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasZeta
- };
-};
-
-/** \internal
- * \brief Template functor to compute the polygamma function.
- * \sa class CwiseUnaryOp, Cwise::polygamma()
- */
-template<typename Scalar> struct scalar_polygamma_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_polygamma_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& n, const Scalar& x) const {
- using numext::polygamma; return polygamma(n, x);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& n, const Packet& x) const { return internal::ppolygamma(n, x); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_polygamma_op<Scalar> >
-{
- enum {
- // Guesstimate
- Cost = 10 * NumTraits<Scalar>::MulCost + 5 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasPolygamma
- };
-};
-
-/** \internal
- * \brief Template functor to compute the error function of a scalar
- * \sa class CwiseUnaryOp, ArrayBase::erf()
- */
-template<typename Scalar> struct scalar_erf_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_erf_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar
- operator()(const Scalar& a) const {
- return numext::erf(a);
- }
- template <typename Packet>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
- return perf(x);
- }
-};
-template <typename Scalar>
-struct functor_traits<scalar_erf_op<Scalar> > {
- enum {
- PacketAccess = packet_traits<Scalar>::HasErf,
- Cost =
- (PacketAccess
-#ifdef EIGEN_VECTORIZE_FMA
- // TODO(rmlarsen): Move the FMA cost model to a central location.
- // Haswell can issue 2 add/mul/madd per cycle.
- // 10 pmadd, 2 pmul, 1 div, 2 other
- ? (2 * NumTraits<Scalar>::AddCost +
- 7 * NumTraits<Scalar>::MulCost +
- scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
-#else
- ? (12 * NumTraits<Scalar>::AddCost +
- 12 * NumTraits<Scalar>::MulCost +
- scalar_div_cost<Scalar, packet_traits<Scalar>::HasDiv>::value)
-#endif
- // Assume for simplicity that this is as expensive as an exp().
- : (functor_traits<scalar_exp_op<Scalar> >::Cost))
- };
-};
-
-/** \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 EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
- using numext::erfc; return erfc(a);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_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 Inverse of the normal distribution
- * function of a scalar
- * \sa class CwiseUnaryOp, Cwise::ndtri()
- */
-template<typename Scalar> struct scalar_ndtri_op {
- EIGEN_EMPTY_STRUCT_CTOR(scalar_ndtri_op)
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const {
- using numext::ndtri; return ndtri(a);
- }
- typedef typename packet_traits<Scalar>::type Packet;
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& a) const { return internal::pndtri(a); }
-};
-template<typename Scalar>
-struct functor_traits<scalar_ndtri_op<Scalar> >
-{
- enum {
- // On average, We are evaluating rational functions with degree N=9 in the
- // numerator and denominator. This results in 2*N additions and 2*N
- // multiplications.
- Cost = 18 * NumTraits<Scalar>::MulCost + 18 * NumTraits<Scalar>::AddCost,
- PacketAccess = packet_traits<Scalar>::HasNdtri
- };
-};
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_SPECIALFUNCTIONS_FUNCTORS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsHalf.h b/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsHalf.h
deleted file mode 100644
index 2a3a531..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsHalf.h
+++ /dev/null
@@ -1,58 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// 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_SPECIALFUNCTIONS_HALF_H
-#define EIGEN_SPECIALFUNCTIONS_HALF_H
-
-namespace Eigen {
-namespace numext {
-
-#if EIGEN_HAS_C99_MATH
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half lgamma(const Eigen::half& a) {
- return Eigen::half(Eigen::numext::lgamma(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half digamma(const Eigen::half& a) {
- return Eigen::half(Eigen::numext::digamma(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half zeta(const Eigen::half& x, const Eigen::half& q) {
- return Eigen::half(Eigen::numext::zeta(static_cast<float>(x), static_cast<float>(q)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half polygamma(const Eigen::half& n, const Eigen::half& x) {
- return Eigen::half(Eigen::numext::polygamma(static_cast<float>(n), static_cast<float>(x)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erf(const Eigen::half& a) {
- return Eigen::half(Eigen::numext::erf(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half erfc(const Eigen::half& a) {
- return Eigen::half(Eigen::numext::erfc(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half ndtri(const Eigen::half& a) {
- return Eigen::half(Eigen::numext::ndtri(static_cast<float>(a)));
-}
-template<> EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma(const Eigen::half& a, const Eigen::half& x) {
- return Eigen::half(Eigen::numext::igamma(static_cast<float>(a), static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half igamma_der_a(const Eigen::half& a, const Eigen::half& x) {
- return Eigen::half(Eigen::numext::igamma_der_a(static_cast<float>(a), static_cast<float>(x)));
-}
-template <>
-EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Eigen::half gamma_sample_der_alpha(const Eigen::half& alpha, const Eigen::half& sample) {
- return Eigen::half(Eigen::numext::gamma_sample_der_alpha(static_cast<float>(alpha), static_cast<float>(sample)));
-}
-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
-} // end namespace Eigen
-
-#endif // EIGEN_SPECIALFUNCTIONS_HALF_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsImpl.h b/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsImpl.h
deleted file mode 100644
index f1c260e..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsImpl.h
+++ /dev/null
@@ -1,2045 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// 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 {
-
-// Parts of this code are based on the Cephes Math Library.
-//
-// Cephes Math Library Release 2.8: June, 2000
-// Copyright 1984, 1987, 1992, 2000 by Stephen L. Moshier
-//
-// Permission has been kindly provided by the original author
-// to incorporate the Cephes software into the Eigen codebase:
-//
-// From: Stephen Moshier
-// To: Eugene Brevdo
-// Subject: Re: Permission to wrap several cephes functions in Eigen
-//
-// Hello Eugene,
-//
-// Thank you for writing.
-//
-// If your licensing is similar to BSD, the formal way that has been
-// handled is simply to add a statement to the effect that you are incorporating
-// the Cephes software by permission of the author.
-//
-// Good luck with your project,
-// Steve
-
-
-/****************************************************************************
- * Implementation of lgamma, requires C++11/C99 *
- ****************************************************************************/
-
-template <typename Scalar>
-struct lgamma_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-template <typename Scalar>
-struct lgamma_retval {
- typedef Scalar type;
-};
-
-#if EIGEN_HAS_C99_MATH
-// Since glibc 2.19
-#if defined(__GLIBC__) && ((__GLIBC__>=2 && __GLIBC_MINOR__ >= 19) || __GLIBC__>2) \
- && (defined(_DEFAULT_SOURCE) || defined(_BSD_SOURCE) || defined(_SVID_SOURCE))
-#define EIGEN_HAS_LGAMMA_R
-#endif
-
-// Glibc versions before 2.19
-#if defined(__GLIBC__) && ((__GLIBC__==2 && __GLIBC_MINOR__ < 19) || __GLIBC__<2) \
- && (defined(_BSD_SOURCE) || defined(_SVID_SOURCE))
-#define EIGEN_HAS_LGAMMA_R
-#endif
-
-template <>
-struct lgamma_impl<float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float run(float x) {
-#if !defined(EIGEN_GPU_COMPILE_PHASE) && defined (EIGEN_HAS_LGAMMA_R) && !defined(__APPLE__)
- int dummy;
- return ::lgammaf_r(x, &dummy);
-#elif defined(SYCL_DEVICE_ONLY)
- return cl::sycl::lgamma(x);
-#else
- return ::lgammaf(x);
-#endif
- }
-};
-
-template <>
-struct lgamma_impl<double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double run(double x) {
-#if !defined(EIGEN_GPU_COMPILE_PHASE) && defined(EIGEN_HAS_LGAMMA_R) && !defined(__APPLE__)
- int dummy;
- return ::lgamma_r(x, &dummy);
-#elif defined(SYCL_DEVICE_ONLY)
- return cl::sycl::lgamma(x);
-#else
- return ::lgamma(x);
-#endif
- }
-};
-
-#undef EIGEN_HAS_LGAMMA_R
-#endif
-
-/****************************************************************************
- * Implementation of digamma (psi), based on Cephes *
- ****************************************************************************/
-
-template <typename Scalar>
-struct digamma_retval {
- typedef Scalar type;
-};
-
-/*
- *
- * Polynomial evaluation helper for the Psi (digamma) function.
- *
- * digamma_impl_maybe_poly::run(s) evaluates the asymptotic Psi expansion for
- * input Scalar s, assuming s is above 10.0.
- *
- * If s is above a certain threshold for the given Scalar type, zero
- * is returned. Otherwise the polynomial is evaluated with enough
- * coefficients for results matching Scalar machine precision.
- *
- *
- */
-template <typename Scalar>
-struct digamma_impl_maybe_poly {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-
-template <>
-struct digamma_impl_maybe_poly<float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float run(const float s) {
- const float A[] = {
- -4.16666666666666666667E-3f,
- 3.96825396825396825397E-3f,
- -8.33333333333333333333E-3f,
- 8.33333333333333333333E-2f
- };
-
- float z;
- if (s < 1.0e8f) {
- z = 1.0f / (s * s);
- return z * internal::ppolevl<float, 3>::run(z, A);
- } else return 0.0f;
- }
-};
-
-template <>
-struct digamma_impl_maybe_poly<double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double run(const double s) {
- const double A[] = {
- 8.33333333333333333333E-2,
- -2.10927960927960927961E-2,
- 7.57575757575757575758E-3,
- -4.16666666666666666667E-3,
- 3.96825396825396825397E-3,
- -8.33333333333333333333E-3,
- 8.33333333333333333333E-2
- };
-
- double z;
- if (s < 1.0e17) {
- z = 1.0 / (s * s);
- return z * internal::ppolevl<double, 6>::run(z, A);
- }
- else return 0.0;
- }
-};
-
-template <typename Scalar>
-struct digamma_impl {
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar x) {
- /*
- *
- * Psi (digamma) function (modified for Eigen)
- *
- *
- * SYNOPSIS:
- *
- * double x, y, psi();
- *
- * y = psi( x );
- *
- *
- * DESCRIPTION:
- *
- * d -
- * psi(x) = -- ln | (x)
- * dx
- *
- * is the logarithmic derivative of the gamma function.
- * For integer x,
- * n-1
- * -
- * psi(n) = -EUL + > 1/k.
- * -
- * k=1
- *
- * If x is negative, it is transformed to a positive argument by the
- * reflection formula psi(1-x) = psi(x) + pi cot(pi x).
- * For general positive x, the argument is made greater than 10
- * using the recurrence psi(x+1) = psi(x) + 1/x.
- * Then the following asymptotic expansion is applied:
- *
- * inf. B
- * - 2k
- * psi(x) = log(x) - 1/2x - > -------
- * - 2k
- * k=1 2k x
- *
- * where the B2k are Bernoulli numbers.
- *
- * ACCURACY (float):
- * Relative error (except absolute when |psi| < 1):
- * arithmetic domain # trials peak rms
- * IEEE 0,30 30000 1.3e-15 1.4e-16
- * IEEE -30,0 40000 1.5e-15 2.2e-16
- *
- * ACCURACY (double):
- * Absolute error, relative when |psi| > 1 :
- * arithmetic domain # trials peak rms
- * IEEE -33,0 30000 8.2e-7 1.2e-7
- * IEEE 0,33 100000 7.3e-7 7.7e-8
- *
- * ERROR MESSAGES:
- * message condition value returned
- * psi singularity x integer <=0 INFINITY
- */
-
- Scalar p, q, nz, s, w, y;
- bool negative = false;
-
- const Scalar nan = NumTraits<Scalar>::quiet_NaN();
- const Scalar m_pi = Scalar(EIGEN_PI);
-
- const Scalar zero = Scalar(0);
- const Scalar one = Scalar(1);
- const Scalar half = Scalar(0.5);
- nz = zero;
-
- if (x <= zero) {
- negative = true;
- q = x;
- p = numext::floor(q);
- if (p == q) {
- return nan;
- }
- /* Remove the zeros of tan(m_pi x)
- * by subtracting the nearest integer from x
- */
- nz = q - p;
- if (nz != half) {
- if (nz > half) {
- p += one;
- nz = q - p;
- }
- nz = m_pi / numext::tan(m_pi * nz);
- }
- else {
- nz = zero;
- }
- x = one - x;
- }
-
- /* use the recurrence psi(x+1) = psi(x) + 1/x. */
- s = x;
- w = zero;
- while (s < Scalar(10)) {
- w += one / s;
- s += one;
- }
-
- y = digamma_impl_maybe_poly<Scalar>::run(s);
-
- y = numext::log(s) - (half / s) - y - w;
-
- return (negative) ? y - nz : y;
- }
-};
-
-/****************************************************************************
- * Implementation of erf, requires C++11/C99 *
- ****************************************************************************/
-
-/** \internal \returns the error function of \a a (coeff-wise)
- Doesn't do anything fancy, just a 13/8-degree rational interpolant which
- is accurate up to a couple of ulp in the range [-4, 4], outside of which
- fl(erf(x)) = +/-1.
-
- This implementation works on both scalars and Ts.
-*/
-template <typename T>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T generic_fast_erf_float(const T& a_x) {
- // Clamp the inputs to the range [-4, 4] since anything outside
- // this range is +/-1.0f in single-precision.
- const T plus_4 = pset1<T>(4.f);
- const T minus_4 = pset1<T>(-4.f);
- const T x = pmax(pmin(a_x, plus_4), minus_4);
- // The monomial coefficients of the numerator polynomial (odd).
- const T alpha_1 = pset1<T>(-1.60960333262415e-02f);
- const T alpha_3 = pset1<T>(-2.95459980854025e-03f);
- const T alpha_5 = pset1<T>(-7.34990630326855e-04f);
- const T alpha_7 = pset1<T>(-5.69250639462346e-05f);
- const T alpha_9 = pset1<T>(-2.10102402082508e-06f);
- const T alpha_11 = pset1<T>(2.77068142495902e-08f);
- const T alpha_13 = pset1<T>(-2.72614225801306e-10f);
-
- // The monomial coefficients of the denominator polynomial (even).
- const T beta_0 = pset1<T>(-1.42647390514189e-02f);
- const T beta_2 = pset1<T>(-7.37332916720468e-03f);
- const T beta_4 = pset1<T>(-1.68282697438203e-03f);
- const T beta_6 = pset1<T>(-2.13374055278905e-04f);
- const T beta_8 = pset1<T>(-1.45660718464996e-05f);
-
- // Since the polynomials are odd/even, we need x^2.
- const T x2 = pmul(x, x);
-
- // Evaluate the numerator polynomial p.
- T p = pmadd(x2, alpha_13, alpha_11);
- p = pmadd(x2, p, alpha_9);
- p = pmadd(x2, p, alpha_7);
- p = pmadd(x2, p, alpha_5);
- p = pmadd(x2, p, alpha_3);
- p = pmadd(x2, p, alpha_1);
- p = pmul(x, p);
-
- // Evaluate the denominator polynomial p.
- T q = pmadd(x2, beta_8, beta_6);
- q = pmadd(x2, q, beta_4);
- q = pmadd(x2, q, beta_2);
- q = pmadd(x2, q, beta_0);
-
- // Divide the numerator by the denominator.
- return pdiv(p, q);
-}
-
-template <typename T>
-struct erf_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE T run(const T& x) {
- return generic_fast_erf_float(x);
- }
-};
-
-template <typename Scalar>
-struct erf_retval {
- typedef Scalar type;
-};
-
-#if EIGEN_HAS_C99_MATH
-template <>
-struct erf_impl<float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float run(float x) {
-#if defined(SYCL_DEVICE_ONLY)
- return cl::sycl::erf(x);
-#else
- return generic_fast_erf_float(x);
-#endif
- }
-};
-
-template <>
-struct erf_impl<double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double run(double x) {
-#if defined(SYCL_DEVICE_ONLY)
- return cl::sycl::erf(x);
-#else
- return ::erf(x);
-#endif
- }
-};
-#endif // EIGEN_HAS_C99_MATH
-
-/***************************************************************************
-* Implementation of erfc, requires C++11/C99 *
-****************************************************************************/
-
-template <typename Scalar>
-struct erfc_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-template <typename Scalar>
-struct erfc_retval {
- typedef Scalar type;
-};
-
-#if EIGEN_HAS_C99_MATH
-template <>
-struct erfc_impl<float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float run(const float x) {
-#if defined(SYCL_DEVICE_ONLY)
- return cl::sycl::erfc(x);
-#else
- return ::erfcf(x);
-#endif
- }
-};
-
-template <>
-struct erfc_impl<double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double run(const double x) {
-#if defined(SYCL_DEVICE_ONLY)
- return cl::sycl::erfc(x);
-#else
- return ::erfc(x);
-#endif
- }
-};
-#endif // EIGEN_HAS_C99_MATH
-
-
-/***************************************************************************
-* Implementation of ndtri. *
-****************************************************************************/
-
-/* Inverse of Normal distribution function (modified for Eigen).
- *
- *
- * SYNOPSIS:
- *
- * double x, y, ndtri();
- *
- * x = ndtri( y );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns the argument, x, for which the area under the
- * Gaussian probability density function (integrated from
- * minus infinity to x) is equal to y.
- *
- *
- * For small arguments 0 < y < exp(-2), the program computes
- * z = sqrt( -2.0 * log(y) ); then the approximation is
- * x = z - log(z)/z - (1/z) P(1/z) / Q(1/z).
- * There are two rational functions P/Q, one for 0 < y < exp(-32)
- * and the other for y up to exp(-2). For larger arguments,
- * w = y - 0.5, and x/sqrt(2pi) = w + w**3 R(w**2)/S(w**2)).
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * DEC 0.125, 1 5500 9.5e-17 2.1e-17
- * DEC 6e-39, 0.135 3500 5.7e-17 1.3e-17
- * IEEE 0.125, 1 20000 7.2e-16 1.3e-16
- * IEEE 3e-308, 0.135 50000 4.6e-16 9.8e-17
- *
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * ndtri domain x <= 0 -MAXNUM
- * ndtri domain x >= 1 MAXNUM
- *
- */
- /*
- Cephes Math Library Release 2.2: June, 1992
- Copyright 1985, 1987, 1992 by Stephen L. Moshier
- Direct inquiries to 30 Frost Street, Cambridge, MA 02140
- */
-
-
-// TODO: Add a cheaper approximation for float.
-
-
-template<typename T>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T flipsign(
- const T& should_flipsign, const T& x) {
- typedef typename unpacket_traits<T>::type Scalar;
- const T sign_mask = pset1<T>(Scalar(-0.0));
- T sign_bit = pand<T>(should_flipsign, sign_mask);
- return pxor<T>(sign_bit, x);
-}
-
-template<>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double flipsign<double>(
- const double& should_flipsign, const double& x) {
- return should_flipsign == 0 ? x : -x;
-}
-
-template<>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float flipsign<float>(
- const float& should_flipsign, const float& x) {
- return should_flipsign == 0 ? x : -x;
-}
-
-// We split this computation in to two so that in the scalar path
-// only one branch is evaluated (due to our template specialization of pselect
-// being an if statement.)
-
-template <typename T, typename ScalarType>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T generic_ndtri_gt_exp_neg_two(const T& b) {
- const ScalarType p0[] = {
- ScalarType(-5.99633501014107895267e1),
- ScalarType(9.80010754185999661536e1),
- ScalarType(-5.66762857469070293439e1),
- ScalarType(1.39312609387279679503e1),
- ScalarType(-1.23916583867381258016e0)
- };
- const ScalarType q0[] = {
- ScalarType(1.0),
- ScalarType(1.95448858338141759834e0),
- ScalarType(4.67627912898881538453e0),
- ScalarType(8.63602421390890590575e1),
- ScalarType(-2.25462687854119370527e2),
- ScalarType(2.00260212380060660359e2),
- ScalarType(-8.20372256168333339912e1),
- ScalarType(1.59056225126211695515e1),
- ScalarType(-1.18331621121330003142e0)
- };
- const T sqrt2pi = pset1<T>(ScalarType(2.50662827463100050242e0));
- const T half = pset1<T>(ScalarType(0.5));
- T c, c2, ndtri_gt_exp_neg_two;
-
- c = psub(b, half);
- c2 = pmul(c, c);
- ndtri_gt_exp_neg_two = pmadd(c, pmul(
- c2, pdiv(
- internal::ppolevl<T, 4>::run(c2, p0),
- internal::ppolevl<T, 8>::run(c2, q0))), c);
- return pmul(ndtri_gt_exp_neg_two, sqrt2pi);
-}
-
-template <typename T, typename ScalarType>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE T generic_ndtri_lt_exp_neg_two(
- const T& b, const T& should_flipsign) {
- /* Approximation for interval z = sqrt(-2 log a ) between 2 and 8
- * i.e., a between exp(-2) = .135 and exp(-32) = 1.27e-14.
- */
- const ScalarType p1[] = {
- ScalarType(4.05544892305962419923e0),
- ScalarType(3.15251094599893866154e1),
- ScalarType(5.71628192246421288162e1),
- ScalarType(4.40805073893200834700e1),
- ScalarType(1.46849561928858024014e1),
- ScalarType(2.18663306850790267539e0),
- ScalarType(-1.40256079171354495875e-1),
- ScalarType(-3.50424626827848203418e-2),
- ScalarType(-8.57456785154685413611e-4)
- };
- const ScalarType q1[] = {
- ScalarType(1.0),
- ScalarType(1.57799883256466749731e1),
- ScalarType(4.53907635128879210584e1),
- ScalarType(4.13172038254672030440e1),
- ScalarType(1.50425385692907503408e1),
- ScalarType(2.50464946208309415979e0),
- ScalarType(-1.42182922854787788574e-1),
- ScalarType(-3.80806407691578277194e-2),
- ScalarType(-9.33259480895457427372e-4)
- };
- /* Approximation for interval z = sqrt(-2 log a ) between 8 and 64
- * i.e., a between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
- */
- const ScalarType p2[] = {
- ScalarType(3.23774891776946035970e0),
- ScalarType(6.91522889068984211695e0),
- ScalarType(3.93881025292474443415e0),
- ScalarType(1.33303460815807542389e0),
- ScalarType(2.01485389549179081538e-1),
- ScalarType(1.23716634817820021358e-2),
- ScalarType(3.01581553508235416007e-4),
- ScalarType(2.65806974686737550832e-6),
- ScalarType(6.23974539184983293730e-9)
- };
- const ScalarType q2[] = {
- ScalarType(1.0),
- ScalarType(6.02427039364742014255e0),
- ScalarType(3.67983563856160859403e0),
- ScalarType(1.37702099489081330271e0),
- ScalarType(2.16236993594496635890e-1),
- ScalarType(1.34204006088543189037e-2),
- ScalarType(3.28014464682127739104e-4),
- ScalarType(2.89247864745380683936e-6),
- ScalarType(6.79019408009981274425e-9)
- };
- const T eight = pset1<T>(ScalarType(8.0));
- const T one = pset1<T>(ScalarType(1));
- const T neg_two = pset1<T>(ScalarType(-2));
- T x, x0, x1, z;
-
- x = psqrt(pmul(neg_two, plog(b)));
- x0 = psub(x, pdiv(plog(x), x));
- z = pdiv(one, x);
- x1 = pmul(
- z, pselect(
- pcmp_lt(x, eight),
- pdiv(internal::ppolevl<T, 8>::run(z, p1),
- internal::ppolevl<T, 8>::run(z, q1)),
- pdiv(internal::ppolevl<T, 8>::run(z, p2),
- internal::ppolevl<T, 8>::run(z, q2))));
- return flipsign(should_flipsign, psub(x0, x1));
-}
-
-template <typename T, typename ScalarType>
-EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE
-T generic_ndtri(const T& a) {
- const T maxnum = pset1<T>(NumTraits<ScalarType>::infinity());
- const T neg_maxnum = pset1<T>(-NumTraits<ScalarType>::infinity());
-
- const T zero = pset1<T>(ScalarType(0));
- const T one = pset1<T>(ScalarType(1));
- // exp(-2)
- const T exp_neg_two = pset1<T>(ScalarType(0.13533528323661269189));
- T b, ndtri, should_flipsign;
-
- should_flipsign = pcmp_le(a, psub(one, exp_neg_two));
- b = pselect(should_flipsign, a, psub(one, a));
-
- ndtri = pselect(
- pcmp_lt(exp_neg_two, b),
- generic_ndtri_gt_exp_neg_two<T, ScalarType>(b),
- generic_ndtri_lt_exp_neg_two<T, ScalarType>(b, should_flipsign));
-
- return pselect(
- pcmp_le(a, zero), neg_maxnum,
- pselect(pcmp_le(one, a), maxnum, ndtri));
-}
-
-template <typename Scalar>
-struct ndtri_retval {
- typedef Scalar type;
-};
-
-#if !EIGEN_HAS_C99_MATH
-
-template <typename Scalar>
-struct ndtri_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-# else
-
-template <typename Scalar>
-struct ndtri_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(const Scalar x) {
- return generic_ndtri<Scalar, Scalar>(x);
- }
-};
-
-#endif // EIGEN_HAS_C99_MATH
-
-
-/**************************************************************************************************************
- * Implementation of igammac (complemented incomplete gamma integral), based on Cephes but requires C++11/C99 *
- **************************************************************************************************************/
-
-template <typename Scalar>
-struct igammac_retval {
- typedef Scalar type;
-};
-
-// NOTE: cephes_helper is also used to implement zeta
-template <typename Scalar>
-struct cephes_helper {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar machep() { assert(false && "machep not supported for this type"); return 0.0; }
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar big() { assert(false && "big not supported for this type"); return 0.0; }
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar biginv() { assert(false && "biginv not supported for this type"); return 0.0; }
-};
-
-template <>
-struct cephes_helper<float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float machep() {
- return NumTraits<float>::epsilon() / 2; // 1.0 - machep == 1.0
- }
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float big() {
- // use epsneg (1.0 - epsneg == 1.0)
- return 1.0f / (NumTraits<float>::epsilon() / 2);
- }
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float biginv() {
- // epsneg
- return machep();
- }
-};
-
-template <>
-struct cephes_helper<double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double machep() {
- return NumTraits<double>::epsilon() / 2; // 1.0 - machep == 1.0
- }
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double big() {
- return 1.0 / NumTraits<double>::epsilon();
- }
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double biginv() {
- // inverse of eps
- return NumTraits<double>::epsilon();
- }
-};
-
-enum IgammaComputationMode { VALUE, DERIVATIVE, SAMPLE_DERIVATIVE };
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC
-static EIGEN_STRONG_INLINE Scalar main_igamma_term(Scalar a, Scalar x) {
- /* Compute x**a * exp(-x) / gamma(a) */
- Scalar logax = a * numext::log(x) - x - lgamma_impl<Scalar>::run(a);
- if (logax < -numext::log(NumTraits<Scalar>::highest()) ||
- // Assuming x and a aren't Nan.
- (numext::isnan)(logax)) {
- return Scalar(0);
- }
- return numext::exp(logax);
-}
-
-template <typename Scalar, IgammaComputationMode mode>
-EIGEN_DEVICE_FUNC
-int igamma_num_iterations() {
- /* Returns the maximum number of internal iterations for igamma computation.
- */
- if (mode == VALUE) {
- return 2000;
- }
-
- if (internal::is_same<Scalar, float>::value) {
- return 200;
- } else if (internal::is_same<Scalar, double>::value) {
- return 500;
- } else {
- return 2000;
- }
-}
-
-template <typename Scalar, IgammaComputationMode mode>
-struct igammac_cf_impl {
- /* Computes igamc(a, x) or derivative (depending on the mode)
- * using the continued fraction expansion of the complementary
- * incomplete Gamma function.
- *
- * Preconditions:
- * a > 0
- * x >= 1
- * x >= a
- */
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar a, Scalar x) {
- const Scalar zero = 0;
- const Scalar one = 1;
- const Scalar two = 2;
- const Scalar machep = cephes_helper<Scalar>::machep();
- const Scalar big = cephes_helper<Scalar>::big();
- const Scalar biginv = cephes_helper<Scalar>::biginv();
-
- if ((numext::isinf)(x)) {
- return zero;
- }
-
- Scalar ax = main_igamma_term<Scalar>(a, x);
- // This is independent of mode. If this value is zero,
- // then the function value is zero. If the function value is zero,
- // then we are in a neighborhood where the function value evalutes to zero,
- // so the derivative is zero.
- if (ax == zero) {
- return zero;
- }
-
- // continued fraction
- Scalar y = one - a;
- Scalar z = x + y + one;
- Scalar c = zero;
- Scalar pkm2 = one;
- Scalar qkm2 = x;
- Scalar pkm1 = x + one;
- Scalar qkm1 = z * x;
- Scalar ans = pkm1 / qkm1;
-
- Scalar dpkm2_da = zero;
- Scalar dqkm2_da = zero;
- Scalar dpkm1_da = zero;
- Scalar dqkm1_da = -x;
- Scalar dans_da = (dpkm1_da - ans * dqkm1_da) / qkm1;
-
- for (int i = 0; i < igamma_num_iterations<Scalar, mode>(); i++) {
- c += one;
- y += one;
- z += two;
-
- Scalar yc = y * c;
- Scalar pk = pkm1 * z - pkm2 * yc;
- Scalar qk = qkm1 * z - qkm2 * yc;
-
- Scalar dpk_da = dpkm1_da * z - pkm1 - dpkm2_da * yc + pkm2 * c;
- Scalar dqk_da = dqkm1_da * z - qkm1 - dqkm2_da * yc + qkm2 * c;
-
- if (qk != zero) {
- Scalar ans_prev = ans;
- ans = pk / qk;
-
- Scalar dans_da_prev = dans_da;
- dans_da = (dpk_da - ans * dqk_da) / qk;
-
- if (mode == VALUE) {
- if (numext::abs(ans_prev - ans) <= machep * numext::abs(ans)) {
- break;
- }
- } else {
- if (numext::abs(dans_da - dans_da_prev) <= machep) {
- break;
- }
- }
- }
-
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- dpkm2_da = dpkm1_da;
- dpkm1_da = dpk_da;
- dqkm2_da = dqkm1_da;
- dqkm1_da = dqk_da;
-
- if (numext::abs(pk) > big) {
- pkm2 *= biginv;
- pkm1 *= biginv;
- qkm2 *= biginv;
- qkm1 *= biginv;
-
- dpkm2_da *= biginv;
- dpkm1_da *= biginv;
- dqkm2_da *= biginv;
- dqkm1_da *= biginv;
- }
- }
-
- /* Compute x**a * exp(-x) / gamma(a) */
- Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a);
- Scalar dax_da = ax * dlogax_da;
-
- switch (mode) {
- case VALUE:
- return ans * ax;
- case DERIVATIVE:
- return ans * dax_da + dans_da * ax;
- case SAMPLE_DERIVATIVE:
- default: // this is needed to suppress clang warning
- return -(dans_da + ans * dlogax_da) * x;
- }
- }
-};
-
-template <typename Scalar, IgammaComputationMode mode>
-struct igamma_series_impl {
- /* Computes igam(a, x) or its derivative (depending on the mode)
- * using the series expansion of the incomplete Gamma function.
- *
- * Preconditions:
- * x > 0
- * a > 0
- * !(x > 1 && x > a)
- */
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar a, Scalar x) {
- const Scalar zero = 0;
- const Scalar one = 1;
- const Scalar machep = cephes_helper<Scalar>::machep();
-
- Scalar ax = main_igamma_term<Scalar>(a, x);
-
- // This is independent of mode. If this value is zero,
- // then the function value is zero. If the function value is zero,
- // then we are in a neighborhood where the function value evalutes to zero,
- // so the derivative is zero.
- if (ax == zero) {
- return zero;
- }
-
- ax /= a;
-
- /* power series */
- Scalar r = a;
- Scalar c = one;
- Scalar ans = one;
-
- Scalar dc_da = zero;
- Scalar dans_da = zero;
-
- for (int i = 0; i < igamma_num_iterations<Scalar, mode>(); i++) {
- r += one;
- Scalar term = x / r;
- Scalar dterm_da = -x / (r * r);
- dc_da = term * dc_da + dterm_da * c;
- dans_da += dc_da;
- c *= term;
- ans += c;
-
- if (mode == VALUE) {
- if (c <= machep * ans) {
- break;
- }
- } else {
- if (numext::abs(dc_da) <= machep * numext::abs(dans_da)) {
- break;
- }
- }
- }
-
- Scalar dlogax_da = numext::log(x) - digamma_impl<Scalar>::run(a + one);
- Scalar dax_da = ax * dlogax_da;
-
- switch (mode) {
- case VALUE:
- return ans * ax;
- case DERIVATIVE:
- return ans * dax_da + dans_da * ax;
- case SAMPLE_DERIVATIVE:
- default: // this is needed to suppress clang warning
- return -(dans_da + ans * dlogax_da) * x / a;
- }
- }
-};
-
-#if !EIGEN_HAS_C99_MATH
-
-template <typename Scalar>
-struct igammac_impl {
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar a, Scalar x) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-#else
-
-template <typename Scalar>
-struct igammac_impl {
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar a, Scalar x) {
- /* igamc()
- *
- * Incomplete gamma integral (modified for Eigen)
- *
- *
- *
- * SYNOPSIS:
- *
- * double a, x, y, igamc();
- *
- * y = igamc( a, x );
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- *
- * igamc(a,x) = 1 - igam(a,x)
- *
- * inf.
- * -
- * 1 | | -t a-1
- * = ----- | e t dt.
- * - | |
- * | (a) -
- * x
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- * ACCURACY (float):
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 30000 7.8e-6 5.9e-7
- *
- *
- * ACCURACY (double):
- *
- * Tested at random a, x.
- * a x Relative error:
- * arithmetic domain domain # trials peak rms
- * IEEE 0.5,100 0,100 200000 1.9e-14 1.7e-15
- * IEEE 0.01,0.5 0,100 200000 1.4e-13 1.6e-15
- *
- */
- /*
- Cephes Math Library Release 2.2: June, 1992
- Copyright 1985, 1987, 1992 by Stephen L. Moshier
- Direct inquiries to 30 Frost Street, Cambridge, MA 02140
- */
- const Scalar zero = 0;
- const Scalar one = 1;
- const Scalar nan = NumTraits<Scalar>::quiet_NaN();
-
- if ((x < zero) || (a <= zero)) {
- // domain error
- return nan;
- }
-
- if ((numext::isnan)(a) || (numext::isnan)(x)) { // propagate nans
- return nan;
- }
-
- if ((x < one) || (x < a)) {
- return (one - igamma_series_impl<Scalar, VALUE>::run(a, x));
- }
-
- return igammac_cf_impl<Scalar, VALUE>::run(a, x);
- }
-};
-
-#endif // EIGEN_HAS_C99_MATH
-
-/************************************************************************************************
- * Implementation of igamma (incomplete gamma integral), based on Cephes but requires C++11/C99 *
- ************************************************************************************************/
-
-#if !EIGEN_HAS_C99_MATH
-
-template <typename Scalar, IgammaComputationMode mode>
-struct igamma_generic_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar x) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-#else
-
-template <typename Scalar, IgammaComputationMode mode>
-struct igamma_generic_impl {
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar a, Scalar x) {
- /* Depending on the mode, returns
- * - VALUE: incomplete Gamma function igamma(a, x)
- * - DERIVATIVE: derivative of incomplete Gamma function d/da igamma(a, x)
- * - SAMPLE_DERIVATIVE: implicit derivative of a Gamma random variable
- * x ~ Gamma(x | a, 1), dx/da = -1 / Gamma(x | a, 1) * d igamma(a, x) / dx
- *
- * Derivatives are implemented by forward-mode differentiation.
- */
- const Scalar zero = 0;
- const Scalar one = 1;
- const Scalar nan = NumTraits<Scalar>::quiet_NaN();
-
- if (x == zero) return zero;
-
- if ((x < zero) || (a <= zero)) { // domain error
- return nan;
- }
-
- if ((numext::isnan)(a) || (numext::isnan)(x)) { // propagate nans
- return nan;
- }
-
- if ((x > one) && (x > a)) {
- Scalar ret = igammac_cf_impl<Scalar, mode>::run(a, x);
- if (mode == VALUE) {
- return one - ret;
- } else {
- return -ret;
- }
- }
-
- return igamma_series_impl<Scalar, mode>::run(a, x);
- }
-};
-
-#endif // EIGEN_HAS_C99_MATH
-
-template <typename Scalar>
-struct igamma_retval {
- typedef Scalar type;
-};
-
-template <typename Scalar>
-struct igamma_impl : igamma_generic_impl<Scalar, VALUE> {
- /* igam()
- * Incomplete gamma integral.
- *
- * The CDF of Gamma(a, 1) random variable at the point x.
- *
- * Accuracy estimation. For each a in [10^-2, 10^-1...10^3] we sample
- * 50 Gamma random variables x ~ Gamma(x | a, 1), a total of 300 points.
- * The ground truth is computed by mpmath. Mean absolute error:
- * float: 1.26713e-05
- * double: 2.33606e-12
- *
- * Cephes documentation below.
- *
- * SYNOPSIS:
- *
- * double a, x, y, igam();
- *
- * y = igam( a, x );
- *
- * DESCRIPTION:
- *
- * The function is defined by
- *
- * x
- * -
- * 1 | | -t a-1
- * igam(a,x) = ----- | e t dt.
- * - | |
- * | (a) -
- * 0
- *
- *
- * In this implementation both arguments must be positive.
- * The integral is evaluated by either a power series or
- * continued fraction expansion, depending on the relative
- * values of a and x.
- *
- * ACCURACY (double):
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 200000 3.6e-14 2.9e-15
- * IEEE 0,100 300000 9.9e-14 1.5e-14
- *
- *
- * ACCURACY (float):
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0,30 20000 7.8e-6 5.9e-7
- *
- */
- /*
- Cephes Math Library Release 2.2: June, 1992
- Copyright 1985, 1987, 1992 by Stephen L. Moshier
- Direct inquiries to 30 Frost Street, Cambridge, MA 02140
- */
-
- /* left tail of incomplete gamma function:
- *
- * inf. k
- * a -x - x
- * x e > ----------
- * - -
- * k=0 | (a+k+1)
- *
- */
-};
-
-template <typename Scalar>
-struct igamma_der_a_retval : igamma_retval<Scalar> {};
-
-template <typename Scalar>
-struct igamma_der_a_impl : igamma_generic_impl<Scalar, DERIVATIVE> {
- /* Derivative of the incomplete Gamma function with respect to a.
- *
- * Computes d/da igamma(a, x) by forward differentiation of the igamma code.
- *
- * Accuracy estimation. For each a in [10^-2, 10^-1...10^3] we sample
- * 50 Gamma random variables x ~ Gamma(x | a, 1), a total of 300 points.
- * The ground truth is computed by mpmath. Mean absolute error:
- * float: 6.17992e-07
- * double: 4.60453e-12
- *
- * Reference:
- * R. Moore. "Algorithm AS 187: Derivatives of the incomplete gamma
- * integral". Journal of the Royal Statistical Society. 1982
- */
-};
-
-template <typename Scalar>
-struct gamma_sample_der_alpha_retval : igamma_retval<Scalar> {};
-
-template <typename Scalar>
-struct gamma_sample_der_alpha_impl
- : igamma_generic_impl<Scalar, SAMPLE_DERIVATIVE> {
- /* Derivative of a Gamma random variable sample with respect to alpha.
- *
- * Consider a sample of a Gamma random variable with the concentration
- * parameter alpha: sample ~ Gamma(alpha, 1). The reparameterization
- * derivative that we want to compute is dsample / dalpha =
- * d igammainv(alpha, u) / dalpha, where u = igamma(alpha, sample).
- * However, this formula is numerically unstable and expensive, so instead
- * we use implicit differentiation:
- *
- * igamma(alpha, sample) = u, where u ~ Uniform(0, 1).
- * Apply d / dalpha to both sides:
- * d igamma(alpha, sample) / dalpha
- * + d igamma(alpha, sample) / dsample * dsample/dalpha = 0
- * d igamma(alpha, sample) / dalpha
- * + Gamma(sample | alpha, 1) dsample / dalpha = 0
- * dsample/dalpha = - (d igamma(alpha, sample) / dalpha)
- * / Gamma(sample | alpha, 1)
- *
- * Here Gamma(sample | alpha, 1) is the PDF of the Gamma distribution
- * (note that the derivative of the CDF w.r.t. sample is the PDF).
- * See the reference below for more details.
- *
- * The derivative of igamma(alpha, sample) is computed by forward
- * differentiation of the igamma code. Division by the Gamma PDF is performed
- * in the same code, increasing the accuracy and speed due to cancellation
- * of some terms.
- *
- * Accuracy estimation. For each alpha in [10^-2, 10^-1...10^3] we sample
- * 50 Gamma random variables sample ~ Gamma(sample | alpha, 1), a total of 300
- * points. The ground truth is computed by mpmath. Mean absolute error:
- * float: 2.1686e-06
- * double: 1.4774e-12
- *
- * Reference:
- * M. Figurnov, S. Mohamed, A. Mnih "Implicit Reparameterization Gradients".
- * 2018
- */
-};
-
-/*****************************************************************************
- * Implementation of Riemann zeta function of two arguments, based on Cephes *
- *****************************************************************************/
-
-template <typename Scalar>
-struct zeta_retval {
- typedef Scalar type;
-};
-
-template <typename Scalar>
-struct zeta_impl_series {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(const Scalar) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-template <>
-struct zeta_impl_series<float> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE bool run(float& a, float& b, float& s, const float x, const float machep) {
- int i = 0;
- while(i < 9)
- {
- i += 1;
- a += 1.0f;
- b = numext::pow( a, -x );
- s += b;
- if( numext::abs(b/s) < machep )
- return true;
- }
-
- //Return whether we are done
- return false;
- }
-};
-
-template <>
-struct zeta_impl_series<double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE bool run(double& a, double& b, double& s, const double x, const double machep) {
- int i = 0;
- while( (i < 9) || (a <= 9.0) )
- {
- i += 1;
- a += 1.0;
- b = numext::pow( a, -x );
- s += b;
- if( numext::abs(b/s) < machep )
- return true;
- }
-
- //Return whether we are done
- return false;
- }
-};
-
-template <typename Scalar>
-struct zeta_impl {
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar x, Scalar q) {
- /* zeta.c
- *
- * Riemann zeta function of two arguments
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, q, y, zeta();
- *
- * y = zeta( x, q );
- *
- *
- *
- * DESCRIPTION:
- *
- *
- *
- * inf.
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=0
- *
- * where x > 1 and q is not a negative integer or zero.
- * The Euler-Maclaurin summation formula is used to obtain
- * the expansion
- *
- * n
- * - -x
- * zeta(x,q) = > (k+q)
- * -
- * k=1
- *
- * 1-x inf. B x(x+1)...(x+2j)
- * (n+q) 1 - 2j
- * + --------- - ------- + > --------------------
- * x-1 x - x+2j+1
- * 2(n+q) j=1 (2j)! (n+q)
- *
- * where the B2j are Bernoulli numbers. Note that (see zetac.c)
- * zeta(x,1) = zetac(x) + 1.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error for single precision:
- * arithmetic domain # trials peak rms
- * IEEE 0,25 10000 6.9e-7 1.0e-7
- *
- * Large arguments may produce underflow in powf(), in which
- * case the results are inaccurate.
- *
- * REFERENCE:
- *
- * Gradshteyn, I. S., and I. M. Ryzhik, Tables of Integrals,
- * Series, and Products, p. 1073; Academic Press, 1980.
- *
- */
-
- int i;
- Scalar p, r, a, b, k, s, t, w;
-
- const Scalar A[] = {
- Scalar(12.0),
- Scalar(-720.0),
- Scalar(30240.0),
- Scalar(-1209600.0),
- Scalar(47900160.0),
- Scalar(-1.8924375803183791606e9), /*1.307674368e12/691*/
- Scalar(7.47242496e10),
- Scalar(-2.950130727918164224e12), /*1.067062284288e16/3617*/
- Scalar(1.1646782814350067249e14), /*5.109094217170944e18/43867*/
- Scalar(-4.5979787224074726105e15), /*8.028576626982912e20/174611*/
- Scalar(1.8152105401943546773e17), /*1.5511210043330985984e23/854513*/
- Scalar(-7.1661652561756670113e18) /*1.6938241367317436694528e27/236364091*/
- };
-
- const Scalar maxnum = NumTraits<Scalar>::infinity();
- const Scalar zero = 0.0, half = 0.5, one = 1.0;
- const Scalar machep = cephes_helper<Scalar>::machep();
- const Scalar nan = NumTraits<Scalar>::quiet_NaN();
-
- if( x == one )
- return maxnum;
-
- if( x < one )
- {
- return nan;
- }
-
- if( q <= zero )
- {
- if(q == numext::floor(q))
- {
- if (x == numext::floor(x) && long(x) % 2 == 0) {
- return maxnum;
- }
- else {
- return nan;
- }
- }
- p = x;
- r = numext::floor(p);
- if (p != r)
- return nan;
- }
-
- /* Permit negative q but continue sum until n+q > +9 .
- * This case should be handled by a reflection formula.
- * If q<0 and x is an integer, there is a relation to
- * the polygamma function.
- */
- s = numext::pow( q, -x );
- a = q;
- b = zero;
- // Run the summation in a helper function that is specific to the floating precision
- if (zeta_impl_series<Scalar>::run(a, b, s, x, machep)) {
- return s;
- }
-
- w = a;
- s += b*w/(x-one);
- s -= half * b;
- a = one;
- k = zero;
- for( i=0; i<12; i++ )
- {
- a *= x + k;
- b /= w;
- t = a*b/A[i];
- s = s + t;
- t = numext::abs(t/s);
- if( t < machep ) {
- break;
- }
- k += one;
- a *= x + k;
- b /= w;
- k += one;
- }
- return s;
- }
-};
-
-/****************************************************************************
- * Implementation of polygamma function, requires C++11/C99 *
- ****************************************************************************/
-
-template <typename Scalar>
-struct polygamma_retval {
- typedef Scalar type;
-};
-
-#if !EIGEN_HAS_C99_MATH
-
-template <typename Scalar>
-struct polygamma_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(Scalar n, Scalar x) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-#else
-
-template <typename Scalar>
-struct polygamma_impl {
- EIGEN_DEVICE_FUNC
- static Scalar run(Scalar n, Scalar x) {
- Scalar zero = 0.0, one = 1.0;
- Scalar nplus = n + one;
- const Scalar nan = NumTraits<Scalar>::quiet_NaN();
-
- // Check that n is a non-negative integer
- if (numext::floor(n) != n || n < zero) {
- return nan;
- }
- // Just return the digamma function for n = 0
- else if (n == zero) {
- return digamma_impl<Scalar>::run(x);
- }
- // Use the same implementation as scipy
- else {
- Scalar factorial = numext::exp(lgamma_impl<Scalar>::run(nplus));
- return numext::pow(-one, nplus) * factorial * zeta_impl<Scalar>::run(nplus, x);
- }
- }
-};
-
-#endif // EIGEN_HAS_C99_MATH
-
-/************************************************************************************************
- * Implementation of betainc (incomplete beta integral), based on Cephes but requires C++11/C99 *
- ************************************************************************************************/
-
-template <typename Scalar>
-struct betainc_retval {
- typedef Scalar type;
-};
-
-#if !EIGEN_HAS_C99_MATH
-
-template <typename Scalar>
-struct betainc_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar b, Scalar x) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-#else
-
-template <typename Scalar>
-struct betainc_impl {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(Scalar, Scalar, Scalar) {
- /* betaincf.c
- *
- * Incomplete beta integral
- *
- *
- * SYNOPSIS:
- *
- * float a, b, x, y, betaincf();
- *
- * y = betaincf( a, b, x );
- *
- *
- * DESCRIPTION:
- *
- * Returns incomplete beta integral of the arguments, evaluated
- * from zero to x. The function is defined as
- *
- * x
- * - -
- * | (a+b) | | a-1 b-1
- * ----------- | t (1-t) dt.
- * - - | |
- * | (a) | (b) -
- * 0
- *
- * The domain of definition is 0 <= x <= 1. In this
- * implementation a and b are restricted to positive values.
- * The integral from x to 1 may be obtained by the symmetry
- * relation
- *
- * 1 - betainc( a, b, x ) = betainc( b, a, 1-x ).
- *
- * The integral is evaluated by a continued fraction expansion.
- * If a < 1, the function calls itself recursively after a
- * transformation to increase a to a+1.
- *
- * ACCURACY (float):
- *
- * Tested at random points (a,b,x) with a and b in the indicated
- * interval and x between 0 and 1.
- *
- * arithmetic domain # trials peak rms
- * Relative error:
- * IEEE 0,30 10000 3.7e-5 5.1e-6
- * IEEE 0,100 10000 1.7e-4 2.5e-5
- * The useful domain for relative error is limited by underflow
- * of the single precision exponential function.
- * Absolute error:
- * IEEE 0,30 100000 2.2e-5 9.6e-7
- * IEEE 0,100 10000 6.5e-5 3.7e-6
- *
- * Larger errors may occur for extreme ratios of a and b.
- *
- * ACCURACY (double):
- * arithmetic domain # trials peak rms
- * IEEE 0,5 10000 6.9e-15 4.5e-16
- * IEEE 0,85 250000 2.2e-13 1.7e-14
- * IEEE 0,1000 30000 5.3e-12 6.3e-13
- * IEEE 0,10000 250000 9.3e-11 7.1e-12
- * IEEE 0,100000 10000 8.7e-10 4.8e-11
- * Outputs smaller than the IEEE gradual underflow threshold
- * were excluded from these statistics.
- *
- * ERROR MESSAGES:
- * message condition value returned
- * incbet domain x<0, x>1 nan
- * incbet underflow nan
- */
-
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, Scalar>::value == false),
- THIS_TYPE_IS_NOT_SUPPORTED);
- return Scalar(0);
- }
-};
-
-/* Continued fraction expansion #1 for incomplete beta integral (small_branch = True)
- * Continued fraction expansion #2 for incomplete beta integral (small_branch = False)
- */
-template <typename Scalar>
-struct incbeta_cfe {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE Scalar run(Scalar a, Scalar b, Scalar x, bool small_branch) {
- EIGEN_STATIC_ASSERT((internal::is_same<Scalar, float>::value ||
- internal::is_same<Scalar, double>::value),
- THIS_TYPE_IS_NOT_SUPPORTED);
- const Scalar big = cephes_helper<Scalar>::big();
- const Scalar machep = cephes_helper<Scalar>::machep();
- const Scalar biginv = cephes_helper<Scalar>::biginv();
-
- const Scalar zero = 0;
- const Scalar one = 1;
- const Scalar two = 2;
-
- Scalar xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
- Scalar k1, k2, k3, k4, k5, k6, k7, k8, k26update;
- Scalar ans;
- int n;
-
- const int num_iters = (internal::is_same<Scalar, float>::value) ? 100 : 300;
- const Scalar thresh =
- (internal::is_same<Scalar, float>::value) ? machep : Scalar(3) * machep;
- Scalar r = (internal::is_same<Scalar, float>::value) ? zero : one;
-
- if (small_branch) {
- k1 = a;
- k2 = a + b;
- k3 = a;
- k4 = a + one;
- k5 = one;
- k6 = b - one;
- k7 = k4;
- k8 = a + two;
- k26update = one;
- } else {
- k1 = a;
- k2 = b - one;
- k3 = a;
- k4 = a + one;
- k5 = one;
- k6 = a + b;
- k7 = a + one;
- k8 = a + two;
- k26update = -one;
- x = x / (one - x);
- }
-
- pkm2 = zero;
- qkm2 = one;
- pkm1 = one;
- qkm1 = one;
- ans = one;
- n = 0;
-
- do {
- xk = -(x * k1 * k2) / (k3 * k4);
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- xk = (x * k5 * k6) / (k7 * k8);
- pk = pkm1 + pkm2 * xk;
- qk = qkm1 + qkm2 * xk;
- pkm2 = pkm1;
- pkm1 = pk;
- qkm2 = qkm1;
- qkm1 = qk;
-
- if (qk != zero) {
- r = pk / qk;
- if (numext::abs(ans - r) < numext::abs(r) * thresh) {
- return r;
- }
- ans = r;
- }
-
- k1 += one;
- k2 += k26update;
- k3 += two;
- k4 += two;
- k5 += one;
- k6 -= k26update;
- k7 += two;
- k8 += two;
-
- if ((numext::abs(qk) + numext::abs(pk)) > big) {
- pkm2 *= biginv;
- pkm1 *= biginv;
- qkm2 *= biginv;
- qkm1 *= biginv;
- }
- if ((numext::abs(qk) < biginv) || (numext::abs(pk) < biginv)) {
- pkm2 *= big;
- pkm1 *= big;
- qkm2 *= big;
- qkm1 *= big;
- }
- } while (++n < num_iters);
-
- return ans;
- }
-};
-
-/* Helper functions depending on the Scalar type */
-template <typename Scalar>
-struct betainc_helper {};
-
-template <>
-struct betainc_helper<float> {
- /* Core implementation, assumes a large (> 1.0) */
- EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE float incbsa(float aa, float bb,
- float xx) {
- float ans, a, b, t, x, onemx;
- bool reversed_a_b = false;
-
- onemx = 1.0f - xx;
-
- /* see if x is greater than the mean */
- if (xx > (aa / (aa + bb))) {
- reversed_a_b = true;
- a = bb;
- b = aa;
- t = xx;
- x = onemx;
- } else {
- a = aa;
- b = bb;
- t = onemx;
- x = xx;
- }
-
- /* Choose expansion for optimal convergence */
- if (b > 10.0f) {
- if (numext::abs(b * x / a) < 0.3f) {
- t = betainc_helper<float>::incbps(a, b, x);
- if (reversed_a_b) t = 1.0f - t;
- return t;
- }
- }
-
- ans = x * (a + b - 2.0f) / (a - 1.0f);
- if (ans < 1.0f) {
- ans = incbeta_cfe<float>::run(a, b, x, true /* small_branch */);
- t = b * numext::log(t);
- } else {
- ans = incbeta_cfe<float>::run(a, b, x, false /* small_branch */);
- t = (b - 1.0f) * numext::log(t);
- }
-
- t += a * numext::log(x) + lgamma_impl<float>::run(a + b) -
- lgamma_impl<float>::run(a) - lgamma_impl<float>::run(b);
- t += numext::log(ans / a);
- t = numext::exp(t);
-
- if (reversed_a_b) t = 1.0f - t;
- return t;
- }
-
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE float incbps(float a, float b, float x) {
- float t, u, y, s;
- const float machep = cephes_helper<float>::machep();
-
- y = a * numext::log(x) + (b - 1.0f) * numext::log1p(-x) - numext::log(a);
- y -= lgamma_impl<float>::run(a) + lgamma_impl<float>::run(b);
- y += lgamma_impl<float>::run(a + b);
-
- t = x / (1.0f - x);
- s = 0.0f;
- u = 1.0f;
- do {
- b -= 1.0f;
- if (b == 0.0f) {
- break;
- }
- a += 1.0f;
- u *= t * b / a;
- s += u;
- } while (numext::abs(u) > machep);
-
- return numext::exp(y) * (1.0f + s);
- }
-};
-
-template <>
-struct betainc_impl<float> {
- EIGEN_DEVICE_FUNC
- static float run(float a, float b, float x) {
- const float nan = NumTraits<float>::quiet_NaN();
- float ans, t;
-
- if (a <= 0.0f) return nan;
- if (b <= 0.0f) return nan;
- if ((x <= 0.0f) || (x >= 1.0f)) {
- if (x == 0.0f) return 0.0f;
- if (x == 1.0f) return 1.0f;
- // mtherr("betaincf", DOMAIN);
- return nan;
- }
-
- /* transformation for small aa */
- if (a <= 1.0f) {
- ans = betainc_helper<float>::incbsa(a + 1.0f, b, x);
- t = a * numext::log(x) + b * numext::log1p(-x) +
- lgamma_impl<float>::run(a + b) - lgamma_impl<float>::run(a + 1.0f) -
- lgamma_impl<float>::run(b);
- return (ans + numext::exp(t));
- } else {
- return betainc_helper<float>::incbsa(a, b, x);
- }
- }
-};
-
-template <>
-struct betainc_helper<double> {
- EIGEN_DEVICE_FUNC
- static EIGEN_STRONG_INLINE double incbps(double a, double b, double x) {
- const double machep = cephes_helper<double>::machep();
-
- double s, t, u, v, n, t1, z, ai;
-
- ai = 1.0 / a;
- u = (1.0 - b) * x;
- v = u / (a + 1.0);
- t1 = v;
- t = u;
- n = 2.0;
- s = 0.0;
- z = machep * ai;
- while (numext::abs(v) > z) {
- u = (n - b) * x / n;
- t *= u;
- v = t / (a + n);
- s += v;
- n += 1.0;
- }
- s += t1;
- s += ai;
-
- u = a * numext::log(x);
- // TODO: gamma() is not directly implemented in Eigen.
- /*
- if ((a + b) < maxgam && numext::abs(u) < maxlog) {
- t = gamma(a + b) / (gamma(a) * gamma(b));
- s = s * t * pow(x, a);
- }
- */
- t = lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) -
- lgamma_impl<double>::run(b) + u + numext::log(s);
- return s = numext::exp(t);
- }
-};
-
-template <>
-struct betainc_impl<double> {
- EIGEN_DEVICE_FUNC
- static double run(double aa, double bb, double xx) {
- const double nan = NumTraits<double>::quiet_NaN();
- const double machep = cephes_helper<double>::machep();
- // const double maxgam = 171.624376956302725;
-
- double a, b, t, x, xc, w, y;
- bool reversed_a_b = false;
-
- if (aa <= 0.0 || bb <= 0.0) {
- return nan; // goto domerr;
- }
-
- if ((xx <= 0.0) || (xx >= 1.0)) {
- if (xx == 0.0) return (0.0);
- if (xx == 1.0) return (1.0);
- // mtherr("incbet", DOMAIN);
- return nan;
- }
-
- if ((bb * xx) <= 1.0 && xx <= 0.95) {
- return betainc_helper<double>::incbps(aa, bb, xx);
- }
-
- w = 1.0 - xx;
-
- /* Reverse a and b if x is greater than the mean. */
- if (xx > (aa / (aa + bb))) {
- reversed_a_b = true;
- a = bb;
- b = aa;
- xc = xx;
- x = w;
- } else {
- a = aa;
- b = bb;
- xc = w;
- x = xx;
- }
-
- if (reversed_a_b && (b * x) <= 1.0 && x <= 0.95) {
- t = betainc_helper<double>::incbps(a, b, x);
- if (t <= machep) {
- t = 1.0 - machep;
- } else {
- t = 1.0 - t;
- }
- return t;
- }
-
- /* Choose expansion for better convergence. */
- y = x * (a + b - 2.0) - (a - 1.0);
- if (y < 0.0) {
- w = incbeta_cfe<double>::run(a, b, x, true /* small_branch */);
- } else {
- w = incbeta_cfe<double>::run(a, b, x, false /* small_branch */) / xc;
- }
-
- /* Multiply w by the factor
- a b _ _ _
- x (1-x) | (a+b) / ( a | (a) | (b) ) . */
-
- y = a * numext::log(x);
- t = b * numext::log(xc);
- // TODO: gamma is not directly implemented in Eigen.
- /*
- if ((a + b) < maxgam && numext::abs(y) < maxlog && numext::abs(t) < maxlog)
- {
- t = pow(xc, b);
- t *= pow(x, a);
- t /= a;
- t *= w;
- t *= gamma(a + b) / (gamma(a) * gamma(b));
- } else {
- */
- /* Resort to logarithms. */
- y += t + lgamma_impl<double>::run(a + b) - lgamma_impl<double>::run(a) -
- lgamma_impl<double>::run(b);
- y += numext::log(w / a);
- t = numext::exp(y);
-
- /* } */
- // done:
-
- if (reversed_a_b) {
- if (t <= machep) {
- t = 1.0 - machep;
- } else {
- t = 1.0 - t;
- }
- }
- return t;
- }
-};
-
-#endif // EIGEN_HAS_C99_MATH
-
-} // 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(digamma, Scalar)
- digamma(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(digamma, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(zeta, Scalar)
-zeta(const Scalar& x, const Scalar& q) {
- return EIGEN_MATHFUNC_IMPL(zeta, Scalar)::run(x, q);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(polygamma, Scalar)
-polygamma(const Scalar& n, const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(polygamma, Scalar)::run(n, 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);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(ndtri, Scalar)
- ndtri(const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(ndtri, Scalar)::run(x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma, Scalar)
- igamma(const Scalar& a, const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(igamma, Scalar)::run(a, x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igamma_der_a, Scalar)
- igamma_der_a(const Scalar& a, const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(igamma_der_a, Scalar)::run(a, x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(gamma_sample_der_alpha, Scalar)
- gamma_sample_der_alpha(const Scalar& a, const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(gamma_sample_der_alpha, Scalar)::run(a, x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(igammac, Scalar)
- igammac(const Scalar& a, const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(igammac, Scalar)::run(a, x);
-}
-
-template <typename Scalar>
-EIGEN_DEVICE_FUNC inline EIGEN_MATHFUNC_RETVAL(betainc, Scalar)
- betainc(const Scalar& a, const Scalar& b, const Scalar& x) {
- return EIGEN_MATHFUNC_IMPL(betainc, Scalar)::run(a, b, x);
-}
-
-} // end namespace numext
-} // end namespace Eigen
-
-#endif // EIGEN_SPECIAL_FUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsPacketMath.h b/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsPacketMath.h
deleted file mode 100644
index 2bb0179..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/SpecialFunctionsPacketMath.h
+++ /dev/null
@@ -1,79 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
-//
-// 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_SPECIALFUNCTIONS_PACKETMATH_H
-#define EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
-
-namespace Eigen {
-
-namespace internal {
-
-/** \internal \returns the ln(|gamma(\a a)|) (coeff-wise) */
-template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet plgamma(const Packet& a) { using numext::lgamma; return lgamma(a); }
-
-/** \internal \returns the derivative of lgamma, psi(\a a) (coeff-wise) */
-template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pdigamma(const Packet& a) { using numext::digamma; return digamma(a); }
-
-/** \internal \returns the zeta function of two arguments (coeff-wise) */
-template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pzeta(const Packet& x, const Packet& q) { using numext::zeta; return zeta(x, q); }
-
-/** \internal \returns the polygamma function (coeff-wise) */
-template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet ppolygamma(const Packet& n, const Packet& x) { using numext::polygamma; return polygamma(n, x); }
-
-/** \internal \returns the erf(\a a) (coeff-wise) */
-template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet perf(const Packet& a) { using numext::erf; return erf(a); }
-
-/** \internal \returns the erfc(\a a) (coeff-wise) */
-template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet perfc(const Packet& a) { using numext::erfc; return erfc(a); }
-
-/** \internal \returns the ndtri(\a a) (coeff-wise) */
-template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
-Packet pndtri(const Packet& a) {
- typedef typename unpacket_traits<Packet>::type ScalarType;
- using internal::generic_ndtri; return generic_ndtri<Packet, ScalarType>(a);
-}
-
-/** \internal \returns the incomplete gamma function igamma(\a a, \a x) */
-template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-Packet pigamma(const Packet& a, const Packet& x) { using numext::igamma; return igamma(a, x); }
-
-/** \internal \returns the derivative of the incomplete gamma function
- * igamma_der_a(\a a, \a x) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pigamma_der_a(const Packet& a, const Packet& x) {
- using numext::igamma_der_a; return igamma_der_a(a, x);
-}
-
-/** \internal \returns compute the derivative of the sample
- * of Gamma(alpha, 1) random variable with respect to the parameter a
- * gamma_sample_der_alpha(\a alpha, \a sample) */
-template <typename Packet>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet pgamma_sample_der_alpha(const Packet& alpha, const Packet& sample) {
- using numext::gamma_sample_der_alpha; return gamma_sample_der_alpha(alpha, sample);
-}
-
-/** \internal \returns the complementary incomplete gamma function igammac(\a a, \a x) */
-template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-Packet pigammac(const Packet& a, const Packet& x) { using numext::igammac; return igammac(a, x); }
-
-/** \internal \returns the complementary incomplete gamma function betainc(\a a, \a b, \a x) */
-template<typename Packet> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-Packet pbetainc(const Packet& a, const Packet& b,const Packet& x) { using numext::betainc; return betainc(a, b, x); }
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_SPECIALFUNCTIONS_PACKETMATH_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX/BesselFunctions.h b/src/EigenUnsupported/src/SpecialFunctions/arch/AVX/BesselFunctions.h
deleted file mode 100644
index 2d76692..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX/BesselFunctions.h
+++ /dev/null
@@ -1,46 +0,0 @@
-#ifndef EIGEN_AVX_BESSELFUNCTIONS_H
-#define EIGEN_AVX_BESSELFUNCTIONS_H
-
-namespace Eigen {
-namespace internal {
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i0)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i0)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i0e)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i0e)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i1)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i1)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_i1e)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_i1e)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_j0)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_j0)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_j1)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_j1)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k0)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k0)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k0e)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k0e)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k1)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k1)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_k1e)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_k1e)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_y0)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_y0)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pbessel_y1)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pbessel_y1)
-
-} // namespace internal
-} // namespace Eigen
-
-#endif // EIGEN_AVX_BESSELFUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX/SpecialFunctions.h b/src/EigenUnsupported/src/SpecialFunctions/arch/AVX/SpecialFunctions.h
deleted file mode 100644
index 35e62a8..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX/SpecialFunctions.h
+++ /dev/null
@@ -1,16 +0,0 @@
-#ifndef EIGEN_AVX_SPECIALFUNCTIONS_H
-#define EIGEN_AVX_SPECIALFUNCTIONS_H
-
-namespace Eigen {
-namespace internal {
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, perf)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, perf)
-
-F16_PACKET_FUNCTION(Packet8f, Packet8h, pndtri)
-BF16_PACKET_FUNCTION(Packet8f, Packet8bf, pndtri)
-
-} // namespace internal
-} // namespace Eigen
-
-#endif // EIGEN_AVX_SPECIAL_FUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/BesselFunctions.h b/src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/BesselFunctions.h
deleted file mode 100644
index 7dd3c3e..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/BesselFunctions.h
+++ /dev/null
@@ -1,46 +0,0 @@
-#ifndef EIGEN_AVX512_BESSELFUNCTIONS_H
-#define EIGEN_AVX512_BESSELFUNCTIONS_H
-
-namespace Eigen {
-namespace internal {
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i0)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i0)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i0e)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i0e)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i1)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i1)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_i1e)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_i1e)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_j0)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_j0)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_j1)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_j1)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k0)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k0)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k0e)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k0e)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k1)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k1)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_k1e)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_k1e)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_y0)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_y0)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pbessel_y1)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pbessel_y1)
-
-} // namespace internal
-} // namespace Eigen
-
-#endif // EIGEN_AVX512_BESSELFUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h b/src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h
deleted file mode 100644
index 79878f2..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/arch/AVX512/SpecialFunctions.h
+++ /dev/null
@@ -1,16 +0,0 @@
-#ifndef EIGEN_AVX512_SPECIALFUNCTIONS_H
-#define EIGEN_AVX512_SPECIALFUNCTIONS_H
-
-namespace Eigen {
-namespace internal {
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, perf)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, perf)
-
-F16_PACKET_FUNCTION(Packet16f, Packet16h, pndtri)
-BF16_PACKET_FUNCTION(Packet16f, Packet16bf, pndtri)
-
-} // namespace internal
-} // namespace Eigen
-
-#endif // EIGEN_AVX512_SPECIAL_FUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/arch/GPU/SpecialFunctions.h b/src/EigenUnsupported/src/SpecialFunctions/arch/GPU/SpecialFunctions.h
deleted file mode 100644
index dd3bf4d..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/arch/GPU/SpecialFunctions.h
+++ /dev/null
@@ -1,369 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@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_GPU_SPECIALFUNCTIONS_H
-#define EIGEN_GPU_SPECIALFUNCTIONS_H
-
-namespace Eigen {
-
-namespace internal {
-
-// Make sure this is only available when targeting a GPU: we don't want to
-// introduce conflicts between these packet_traits definitions and the ones
-// we'll use on the host side (SSE, AVX, ...)
-#if defined(EIGEN_GPUCC) && defined(EIGEN_USE_GPU)
-
-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)
-{
- using numext::lgamma;
- return make_double2(lgamma(a.x), lgamma(a.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 pdigamma<float4>(const float4& a)
-{
- using numext::digamma;
- return make_float4(digamma(a.x), digamma(a.y), digamma(a.z), digamma(a.w));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-double2 pdigamma<double2>(const double2& a)
-{
- using numext::digamma;
- return make_double2(digamma(a.x), digamma(a.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 pzeta<float4>(const float4& x, const float4& q)
-{
- using numext::zeta;
- return make_float4(zeta(x.x, q.x), zeta(x.y, q.y), zeta(x.z, q.z), zeta(x.w, q.w));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-double2 pzeta<double2>(const double2& x, const double2& q)
-{
- using numext::zeta;
- return make_double2(zeta(x.x, q.x), zeta(x.y, q.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 ppolygamma<float4>(const float4& n, const float4& x)
-{
- using numext::polygamma;
- return make_float4(polygamma(n.x, x.x), polygamma(n.y, x.y), polygamma(n.z, x.z), polygamma(n.w, x.w));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-double2 ppolygamma<double2>(const double2& n, const double2& x)
-{
- using numext::polygamma;
- return make_double2(polygamma(n.x, x.x), polygamma(n.y, x.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 perf<float4>(const float4& a)
-{
- return make_float4(erff(a.x), erff(a.y), erff(a.z), erff(a.w));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-double2 perf<double2>(const double2& a)
-{
- using numext::erf;
- return make_double2(erf(a.x), erf(a.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 perfc<float4>(const float4& a)
-{
- using numext::erfc;
- 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)
-{
- using numext::erfc;
- return make_double2(erfc(a.x), erfc(a.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 pndtri<float4>(const float4& a)
-{
- using numext::ndtri;
- return make_float4(ndtri(a.x), ndtri(a.y), ndtri(a.z), ndtri(a.w));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-double2 pndtri<double2>(const double2& a)
-{
- using numext::ndtri;
- return make_double2(ndtri(a.x), ndtri(a.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 pigamma<float4>(const float4& a, const float4& x)
-{
- using numext::igamma;
- return make_float4(
- igamma(a.x, x.x),
- igamma(a.y, x.y),
- igamma(a.z, x.z),
- igamma(a.w, x.w));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-double2 pigamma<double2>(const double2& a, const double2& x)
-{
- using numext::igamma;
- return make_double2(igamma(a.x, x.x), igamma(a.y, x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pigamma_der_a<float4>(
- const float4& a, const float4& x) {
- using numext::igamma_der_a;
- return make_float4(igamma_der_a(a.x, x.x), igamma_der_a(a.y, x.y),
- igamma_der_a(a.z, x.z), igamma_der_a(a.w, x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pigamma_der_a<double2>(const double2& a, const double2& x) {
- using numext::igamma_der_a;
- return make_double2(igamma_der_a(a.x, x.x), igamma_der_a(a.y, x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pgamma_sample_der_alpha<float4>(
- const float4& alpha, const float4& sample) {
- using numext::gamma_sample_der_alpha;
- return make_float4(
- gamma_sample_der_alpha(alpha.x, sample.x),
- gamma_sample_der_alpha(alpha.y, sample.y),
- gamma_sample_der_alpha(alpha.z, sample.z),
- gamma_sample_der_alpha(alpha.w, sample.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pgamma_sample_der_alpha<double2>(const double2& alpha, const double2& sample) {
- using numext::gamma_sample_der_alpha;
- return make_double2(
- gamma_sample_der_alpha(alpha.x, sample.x),
- gamma_sample_der_alpha(alpha.y, sample.y));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-float4 pigammac<float4>(const float4& a, const float4& x)
-{
- using numext::igammac;
- return make_float4(
- igammac(a.x, x.x),
- igammac(a.y, x.y),
- igammac(a.z, x.z),
- igammac(a.w, x.w));
-}
-
-template<> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
-double2 pigammac<double2>(const double2& a, const double2& x)
-{
- using numext::igammac;
- 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));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i0e<float4>(const float4& x) {
- using numext::bessel_i0e;
- return make_float4(bessel_i0e(x.x), bessel_i0e(x.y), bessel_i0e(x.z), bessel_i0e(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_i0e<double2>(const double2& x) {
- using numext::bessel_i0e;
- return make_double2(bessel_i0e(x.x), bessel_i0e(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i0<float4>(const float4& x) {
- using numext::bessel_i0;
- return make_float4(bessel_i0(x.x), bessel_i0(x.y), bessel_i0(x.z), bessel_i0(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_i0<double2>(const double2& x) {
- using numext::bessel_i0;
- return make_double2(bessel_i0(x.x), bessel_i0(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i1e<float4>(const float4& x) {
- using numext::bessel_i1e;
- return make_float4(bessel_i1e(x.x), bessel_i1e(x.y), bessel_i1e(x.z), bessel_i1e(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_i1e<double2>(const double2& x) {
- using numext::bessel_i1e;
- return make_double2(bessel_i1e(x.x), bessel_i1e(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_i1<float4>(const float4& x) {
- using numext::bessel_i1;
- return make_float4(bessel_i1(x.x), bessel_i1(x.y), bessel_i1(x.z), bessel_i1(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_i1<double2>(const double2& x) {
- using numext::bessel_i1;
- return make_double2(bessel_i1(x.x), bessel_i1(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k0e<float4>(const float4& x) {
- using numext::bessel_k0e;
- return make_float4(bessel_k0e(x.x), bessel_k0e(x.y), bessel_k0e(x.z), bessel_k0e(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_k0e<double2>(const double2& x) {
- using numext::bessel_k0e;
- return make_double2(bessel_k0e(x.x), bessel_k0e(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k0<float4>(const float4& x) {
- using numext::bessel_k0;
- return make_float4(bessel_k0(x.x), bessel_k0(x.y), bessel_k0(x.z), bessel_k0(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_k0<double2>(const double2& x) {
- using numext::bessel_k0;
- return make_double2(bessel_k0(x.x), bessel_k0(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k1e<float4>(const float4& x) {
- using numext::bessel_k1e;
- return make_float4(bessel_k1e(x.x), bessel_k1e(x.y), bessel_k1e(x.z), bessel_k1e(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_k1e<double2>(const double2& x) {
- using numext::bessel_k1e;
- return make_double2(bessel_k1e(x.x), bessel_k1e(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_k1<float4>(const float4& x) {
- using numext::bessel_k1;
- return make_float4(bessel_k1(x.x), bessel_k1(x.y), bessel_k1(x.z), bessel_k1(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_k1<double2>(const double2& x) {
- using numext::bessel_k1;
- return make_double2(bessel_k1(x.x), bessel_k1(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_j0<float4>(const float4& x) {
- using numext::bessel_j0;
- return make_float4(bessel_j0(x.x), bessel_j0(x.y), bessel_j0(x.z), bessel_j0(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_j0<double2>(const double2& x) {
- using numext::bessel_j0;
- return make_double2(bessel_j0(x.x), bessel_j0(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_j1<float4>(const float4& x) {
- using numext::bessel_j1;
- return make_float4(bessel_j1(x.x), bessel_j1(x.y), bessel_j1(x.z), bessel_j1(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_j1<double2>(const double2& x) {
- using numext::bessel_j1;
- return make_double2(bessel_j1(x.x), bessel_j1(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_y0<float4>(const float4& x) {
- using numext::bessel_y0;
- return make_float4(bessel_y0(x.x), bessel_y0(x.y), bessel_y0(x.z), bessel_y0(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_y0<double2>(const double2& x) {
- using numext::bessel_y0;
- return make_double2(bessel_y0(x.x), bessel_y0(x.y));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE float4 pbessel_y1<float4>(const float4& x) {
- using numext::bessel_y1;
- return make_float4(bessel_y1(x.x), bessel_y1(x.y), bessel_y1(x.z), bessel_y1(x.w));
-}
-
-template <>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE double2
-pbessel_y1<double2>(const double2& x) {
- using numext::bessel_y1;
- return make_double2(bessel_y1(x.x), bessel_y1(x.y));
-}
-
-#endif
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_GPU_SPECIALFUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/arch/NEON/BesselFunctions.h b/src/EigenUnsupported/src/SpecialFunctions/arch/NEON/BesselFunctions.h
deleted file mode 100644
index 67433b0..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/arch/NEON/BesselFunctions.h
+++ /dev/null
@@ -1,54 +0,0 @@
-#ifndef EIGEN_NEON_BESSELFUNCTIONS_H
-#define EIGEN_NEON_BESSELFUNCTIONS_H
-
-namespace Eigen {
-namespace internal {
-
-#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
-
-#define NEON_HALF_TO_FLOAT_FUNCTIONS(METHOD) \
-template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
-Packet8hf METHOD<Packet8hf>(const Packet8hf& x) { \
- const Packet4f lo = METHOD<Packet4f>(vcvt_f32_f16(vget_low_f16(x))); \
- const Packet4f hi = METHOD<Packet4f>(vcvt_f32_f16(vget_high_f16(x))); \
- return vcombine_f16(vcvt_f16_f32(lo), vcvt_f16_f32(hi)); \
-} \
- \
-template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
-Packet4hf METHOD<Packet4hf>(const Packet4hf& x) { \
- return vcvt_f16_f32(METHOD<Packet4f>(vcvt_f32_f16(x))); \
-}
-
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i0)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i0e)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i1)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_i1e)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_j0)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_j1)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k0)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k0e)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k1)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_k1e)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_y0)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pbessel_y1)
-
-#undef NEON_HALF_TO_FLOAT_FUNCTIONS
-#endif
-
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i0)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i0e)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i1)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_i1e)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_j0)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_j1)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k0)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k0e)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k1)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_k1e)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_y0)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pbessel_y1)
-
-} // namespace internal
-} // namespace Eigen
-
-#endif // EIGEN_NEON_BESSELFUNCTIONS_H
diff --git a/src/EigenUnsupported/src/SpecialFunctions/arch/NEON/SpecialFunctions.h b/src/EigenUnsupported/src/SpecialFunctions/arch/NEON/SpecialFunctions.h
deleted file mode 100644
index ec92951..0000000
--- a/src/EigenUnsupported/src/SpecialFunctions/arch/NEON/SpecialFunctions.h
+++ /dev/null
@@ -1,34 +0,0 @@
-#ifndef EIGEN_NEON_SPECIALFUNCTIONS_H
-#define EIGEN_NEON_SPECIALFUNCTIONS_H
-
-namespace Eigen {
-namespace internal {
-
-#if EIGEN_HAS_ARM64_FP16_VECTOR_ARITHMETIC
-
-#define NEON_HALF_TO_FLOAT_FUNCTIONS(METHOD) \
-template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
-Packet8hf METHOD<Packet8hf>(const Packet8hf& x) { \
- const Packet4f lo = METHOD<Packet4f>(vcvt_f32_f16(vget_low_f16(x))); \
- const Packet4f hi = METHOD<Packet4f>(vcvt_f32_f16(vget_high_f16(x))); \
- return vcombine_f16(vcvt_f16_f32(lo), vcvt_f16_f32(hi)); \
-} \
- \
-template <> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE \
-Packet4hf METHOD<Packet4hf>(const Packet4hf& x) { \
- return vcvt_f16_f32(METHOD<Packet4f>(vcvt_f32_f16(x))); \
-}
-
-NEON_HALF_TO_FLOAT_FUNCTIONS(perf)
-NEON_HALF_TO_FLOAT_FUNCTIONS(pndtri)
-
-#undef NEON_HALF_TO_FLOAT_FUNCTIONS
-#endif
-
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, perf)
-BF16_PACKET_FUNCTION(Packet4f, Packet4bf, pndtri)
-
-} // namespace internal
-} // namespace Eigen
-
-#endif // EIGEN_NEON_SPECIALFUNCTIONS_H