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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
+// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@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_GENERIC_PACKET_MATH_H
+#define EIGEN_GENERIC_PACKET_MATH_H
+
+namespace Eigen {
+
+namespace internal {
+
+/** \internal
+ * \file GenericPacketMath.h
+ *
+ * Default implementation for types not supported by the vectorization.
+ * In practice these functions are provided to make easier the writing
+ * of generic vectorized code.
+ */
+
+#ifndef EIGEN_DEBUG_ALIGNED_LOAD
+#define EIGEN_DEBUG_ALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
+#define EIGEN_DEBUG_UNALIGNED_LOAD
+#endif
+
+#ifndef EIGEN_DEBUG_ALIGNED_STORE
+#define EIGEN_DEBUG_ALIGNED_STORE
+#endif
+
+#ifndef EIGEN_DEBUG_UNALIGNED_STORE
+#define EIGEN_DEBUG_UNALIGNED_STORE
+#endif
+
+struct default_packet_traits
+{
+ enum {
+ HasAdd = 1,
+ HasSub = 1,
+ HasMul = 1,
+ HasNegate = 1,
+ HasAbs = 1,
+ HasAbs2 = 1,
+ HasMin = 1,
+ HasMax = 1,
+ HasConj = 1,
+ HasSetLinear = 1,
+
+ HasDiv = 0,
+ HasSqrt = 0,
+ HasExp = 0,
+ HasLog = 0,
+ HasPow = 0,
+
+ HasSin = 0,
+ HasCos = 0,
+ HasTan = 0,
+ HasASin = 0,
+ HasACos = 0,
+ HasATan = 0
+ };
+};
+
+template<typename T> struct packet_traits : default_packet_traits
+{
+ typedef T type;
+ enum {
+ Vectorizable = 0,
+ size = 1,
+ AlignedOnScalar = 0
+ };
+ enum {
+ HasAdd = 0,
+ HasSub = 0,
+ HasMul = 0,
+ HasNegate = 0,
+ HasAbs = 0,
+ HasAbs2 = 0,
+ HasMin = 0,
+ HasMax = 0,
+ HasConj = 0,
+ HasSetLinear = 0
+ };
+};
+
+/** \internal \returns a + b (coeff-wise) */
+template<typename Packet> inline Packet
+padd(const Packet& a,
+ const Packet& b) { return a+b; }
+
+/** \internal \returns a - b (coeff-wise) */
+template<typename Packet> inline Packet
+psub(const Packet& a,
+ const Packet& b) { return a-b; }
+
+/** \internal \returns -a (coeff-wise) */
+template<typename Packet> inline Packet
+pnegate(const Packet& a) { return -a; }
+
+/** \internal \returns conj(a) (coeff-wise) */
+template<typename Packet> inline Packet
+pconj(const Packet& a) { return conj(a); }
+
+/** \internal \returns a * b (coeff-wise) */
+template<typename Packet> inline Packet
+pmul(const Packet& a,
+ const Packet& b) { return a*b; }
+
+/** \internal \returns a / b (coeff-wise) */
+template<typename Packet> inline Packet
+pdiv(const Packet& a,
+ const Packet& b) { return a/b; }
+
+/** \internal \returns the min of \a a and \a b (coeff-wise) */
+template<typename Packet> inline Packet
+pmin(const Packet& a,
+ const Packet& b) { using std::min; return (min)(a, b); }
+
+/** \internal \returns the max of \a a and \a b (coeff-wise) */
+template<typename Packet> inline Packet
+pmax(const Packet& a,
+ const Packet& b) { using std::max; return (max)(a, b); }
+
+/** \internal \returns the absolute value of \a a */
+template<typename Packet> inline Packet
+pabs(const Packet& a) { return abs(a); }
+
+/** \internal \returns the bitwise and of \a a and \a b */
+template<typename Packet> inline Packet
+pand(const Packet& a, const Packet& b) { return a & b; }
+
+/** \internal \returns the bitwise or of \a a and \a b */
+template<typename Packet> inline Packet
+por(const Packet& a, const Packet& b) { return a | b; }
+
+/** \internal \returns the bitwise xor of \a a and \a b */
+template<typename Packet> inline Packet
+pxor(const Packet& a, const Packet& b) { return a ^ b; }
+
+/** \internal \returns the bitwise andnot of \a a and \a b */
+template<typename Packet> inline Packet
+pandnot(const Packet& a, const Packet& b) { return a & (!b); }
+
+/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
+template<typename Packet> inline Packet
+pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet version of \a *from, (un-aligned load) */
+template<typename Packet> inline Packet
+ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet with elements of \a *from duplicated, e.g.: (from[0],from[0],from[1],from[1]) */
+template<typename Packet> inline Packet
+ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
+
+/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
+template<typename Packet> inline Packet
+pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
+
+/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
+template<typename Scalar> inline typename packet_traits<Scalar>::type
+plset(const Scalar& a) { return a; }
+
+/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal copy the packet \a from to \a *to, (un-aligned store) */
+template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from)
+{ (*to) = from; }
+
+/** \internal tries to do cache prefetching of \a addr */
+template<typename Scalar> inline void prefetch(const Scalar* addr)
+{
+#if !defined(_MSC_VER)
+__builtin_prefetch(addr);
+#endif
+}
+
+/** \internal \returns the first element of a packet */
+template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
+{ return a; }
+
+/** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
+template<typename Packet> inline Packet
+preduxp(const Packet* vecs) { return vecs[0]; }
+
+/** \internal \returns the sum of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a)
+{ return a; }
+
+/** \internal \returns the product of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
+{ return a; }
+
+/** \internal \returns the min of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
+{ return a; }
+
+/** \internal \returns the max of the elements of \a a*/
+template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
+{ return a; }
+
+/** \internal \returns the reversed elements of \a a*/
+template<typename Packet> inline Packet preverse(const Packet& a)
+{ return a; }
+
+
+/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
+template<typename Packet> inline Packet pcplxflip(const Packet& a)
+{ return Packet(imag(a),real(a)); }
+
+/**************************
+* Special math functions
+***************************/
+
+/** \internal \returns the sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psin(const Packet& a) { return sin(a); }
+
+/** \internal \returns the cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pcos(const Packet& a) { return cos(a); }
+
+/** \internal \returns the tan of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet ptan(const Packet& a) { return tan(a); }
+
+/** \internal \returns the arc sine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pasin(const Packet& a) { return asin(a); }
+
+/** \internal \returns the arc cosine of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pacos(const Packet& a) { return acos(a); }
+
+/** \internal \returns the exp of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet pexp(const Packet& a) { return exp(a); }
+
+/** \internal \returns the log of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet plog(const Packet& a) { return log(a); }
+
+/** \internal \returns the square-root of \a a (coeff-wise) */
+template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
+Packet psqrt(const Packet& a) { return sqrt(a); }
+
+/***************************************************************************
+* The following functions might not have to be overwritten for vectorized types
+***************************************************************************/
+
+/** \internal copy a packet with constant coeficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned */
+// NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
+template<typename Packet>
+inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
+{
+ pstore(to, pset1<Packet>(a));
+}
+
+/** \internal \returns a * b + c (coeff-wise) */
+template<typename Packet> inline Packet
+pmadd(const Packet& a,
+ const Packet& b,
+ const Packet& c)
+{ return padd(pmul(a, b),c); }
+
+/** \internal \returns a packet version of \a *from.
+ * If LoadMode equals #Aligned, \a from must be 16 bytes aligned */
+template<typename Packet, int LoadMode>
+inline Packet ploadt(const typename unpacket_traits<Packet>::type* from)
+{
+ if(LoadMode == Aligned)
+ return pload<Packet>(from);
+ else
+ return ploadu<Packet>(from);
+}
+
+/** \internal copy the packet \a from to \a *to.
+ * If StoreMode equals #Aligned, \a to must be 16 bytes aligned */
+template<typename Scalar, typename Packet, int LoadMode>
+inline void pstoret(Scalar* to, const Packet& from)
+{
+ if(LoadMode == Aligned)
+ pstore(to, from);
+ else
+ pstoreu(to, from);
+}
+
+/** \internal default implementation of palign() allowing partial specialization */
+template<int Offset,typename PacketType>
+struct palign_impl
+{
+ // by default data are aligned, so there is nothing to be done :)
+ static inline void run(PacketType&, const PacketType&) {}
+};
+
+/** \internal update \a first using the concatenation of the \a Offset last elements
+ * of \a first and packet_size minus \a Offset first elements of \a second */
+template<int Offset,typename PacketType>
+inline void palign(PacketType& first, const PacketType& second)
+{
+ palign_impl<Offset,PacketType>::run(first,second);
+}
+
+/***************************************************************************
+* Fast complex products (GCC generates a function call which is very slow)
+***************************************************************************/
+
+template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
+{ return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
+
+template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
+{ return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
+
+} // end namespace internal
+
+} // end namespace Eigen
+
+#endif // EIGEN_GENERIC_PACKET_MATH_H
+