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author | Nao Pross <np@0hm.ch> | 2024-02-12 15:23:24 +0100 |
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committer | Nao Pross <np@0hm.ch> | 2024-02-12 15:23:24 +0100 |
commit | fbd6758fb4649b146176dbbc2dfe9384c69ef58d (patch) | |
tree | 0993d5c74a5cd1773ff9a572e4926d3102c0299f /src/EigenUnsupported/src/SpecialFunctions | |
parent | Move into version control (diff) | |
download | fsisotool-fbd6758fb4649b146176dbbc2dfe9384c69ef58d.tar.gz fsisotool-fbd6758fb4649b146176dbbc2dfe9384c69ef58d.zip |
Remove old stuff with Eigen
Diffstat (limited to 'src/EigenUnsupported/src/SpecialFunctions')
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 |