[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | #ifndef EIGEN_GENERIC_PACKET_MATH_H
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| 12 | #define EIGEN_GENERIC_PACKET_MATH_H
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| 13 |
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| 14 | namespace Eigen {
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| 15 |
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| 16 | namespace internal {
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| 17 |
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| 18 | /** \internal
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| 19 | * \file GenericPacketMath.h
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| 20 | *
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| 21 | * Default implementation for types not supported by the vectorization.
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| 22 | * In practice these functions are provided to make easier the writing
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| 23 | * of generic vectorized code.
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| 24 | */
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| 25 |
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| 26 | #ifndef EIGEN_DEBUG_ALIGNED_LOAD
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| 27 | #define EIGEN_DEBUG_ALIGNED_LOAD
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| 28 | #endif
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| 29 |
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| 30 | #ifndef EIGEN_DEBUG_UNALIGNED_LOAD
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| 31 | #define EIGEN_DEBUG_UNALIGNED_LOAD
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| 32 | #endif
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| 33 |
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| 34 | #ifndef EIGEN_DEBUG_ALIGNED_STORE
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| 35 | #define EIGEN_DEBUG_ALIGNED_STORE
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| 36 | #endif
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| 37 |
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| 38 | #ifndef EIGEN_DEBUG_UNALIGNED_STORE
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| 39 | #define EIGEN_DEBUG_UNALIGNED_STORE
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| 40 | #endif
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| 41 |
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| 42 | struct default_packet_traits
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| 43 | {
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| 44 | enum {
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| 45 | HasAdd = 1,
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| 46 | HasSub = 1,
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| 47 | HasMul = 1,
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| 48 | HasNegate = 1,
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| 49 | HasAbs = 1,
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| 50 | HasAbs2 = 1,
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| 51 | HasMin = 1,
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| 52 | HasMax = 1,
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| 53 | HasConj = 1,
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| 54 | HasSetLinear = 1,
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| 55 |
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| 56 | HasDiv = 0,
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| 57 | HasSqrt = 0,
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| 58 | HasExp = 0,
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| 59 | HasLog = 0,
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| 60 | HasPow = 0,
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| 61 |
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| 62 | HasSin = 0,
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| 63 | HasCos = 0,
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| 64 | HasTan = 0,
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| 65 | HasASin = 0,
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| 66 | HasACos = 0,
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| 67 | HasATan = 0
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| 68 | };
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| 69 | };
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| 70 |
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| 71 | template<typename T> struct packet_traits : default_packet_traits
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| 72 | {
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| 73 | typedef T type;
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| 74 | enum {
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| 75 | Vectorizable = 0,
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| 76 | size = 1,
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| 77 | AlignedOnScalar = 0
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| 78 | };
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| 79 | enum {
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| 80 | HasAdd = 0,
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| 81 | HasSub = 0,
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| 82 | HasMul = 0,
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| 83 | HasNegate = 0,
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| 84 | HasAbs = 0,
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| 85 | HasAbs2 = 0,
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| 86 | HasMin = 0,
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| 87 | HasMax = 0,
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| 88 | HasConj = 0,
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| 89 | HasSetLinear = 0
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| 90 | };
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| 91 | };
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| 92 |
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| 93 | /** \internal \returns a + b (coeff-wise) */
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| 94 | template<typename Packet> inline Packet
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| 95 | padd(const Packet& a,
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| 96 | const Packet& b) { return a+b; }
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| 97 |
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| 98 | /** \internal \returns a - b (coeff-wise) */
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| 99 | template<typename Packet> inline Packet
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| 100 | psub(const Packet& a,
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| 101 | const Packet& b) { return a-b; }
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| 102 |
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| 103 | /** \internal \returns -a (coeff-wise) */
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| 104 | template<typename Packet> inline Packet
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| 105 | pnegate(const Packet& a) { return -a; }
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| 106 |
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| 107 | /** \internal \returns conj(a) (coeff-wise) */
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| 108 | template<typename Packet> inline Packet
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| 109 | pconj(const Packet& a) { return numext::conj(a); }
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| 110 |
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| 111 | /** \internal \returns a * b (coeff-wise) */
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| 112 | template<typename Packet> inline Packet
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| 113 | pmul(const Packet& a,
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| 114 | const Packet& b) { return a*b; }
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| 115 |
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| 116 | /** \internal \returns a / b (coeff-wise) */
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| 117 | template<typename Packet> inline Packet
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| 118 | pdiv(const Packet& a,
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| 119 | const Packet& b) { return a/b; }
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| 120 |
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| 121 | /** \internal \returns the min of \a a and \a b (coeff-wise) */
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| 122 | template<typename Packet> inline Packet
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| 123 | pmin(const Packet& a,
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| 124 | const Packet& b) { using std::min; return (min)(a, b); }
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| 125 |
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| 126 | /** \internal \returns the max of \a a and \a b (coeff-wise) */
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| 127 | template<typename Packet> inline Packet
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| 128 | pmax(const Packet& a,
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| 129 | const Packet& b) { using std::max; return (max)(a, b); }
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| 130 |
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| 131 | /** \internal \returns the absolute value of \a a */
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| 132 | template<typename Packet> inline Packet
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| 133 | pabs(const Packet& a) { using std::abs; return abs(a); }
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| 134 |
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| 135 | /** \internal \returns the bitwise and of \a a and \a b */
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| 136 | template<typename Packet> inline Packet
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| 137 | pand(const Packet& a, const Packet& b) { return a & b; }
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| 138 |
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| 139 | /** \internal \returns the bitwise or of \a a and \a b */
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| 140 | template<typename Packet> inline Packet
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| 141 | por(const Packet& a, const Packet& b) { return a | b; }
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| 142 |
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| 143 | /** \internal \returns the bitwise xor of \a a and \a b */
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| 144 | template<typename Packet> inline Packet
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| 145 | pxor(const Packet& a, const Packet& b) { return a ^ b; }
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| 146 |
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| 147 | /** \internal \returns the bitwise andnot of \a a and \a b */
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| 148 | template<typename Packet> inline Packet
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| 149 | pandnot(const Packet& a, const Packet& b) { return a & (!b); }
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| 150 |
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| 151 | /** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
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| 152 | template<typename Packet> inline Packet
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| 153 | pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
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| 154 |
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| 155 | /** \internal \returns a packet version of \a *from, (un-aligned load) */
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| 156 | template<typename Packet> inline Packet
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| 157 | ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
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| 158 |
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| 159 | /** \internal \returns a packet with elements of \a *from duplicated.
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| 160 | * For instance, for a packet of 8 elements, 4 scalar will be read from \a *from and
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| 161 | * duplicated to form: {from[0],from[0],from[1],from[1],,from[2],from[2],,from[3],from[3]}
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| 162 | * Currently, this function is only used for scalar * complex products.
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| 163 | */
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| 164 | template<typename Packet> inline Packet
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| 165 | ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
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| 166 |
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| 167 | /** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
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| 168 | template<typename Packet> inline Packet
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| 169 | pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
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| 170 |
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| 171 | /** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
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| 172 | template<typename Scalar> inline typename packet_traits<Scalar>::type
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| 173 | plset(const Scalar& a) { return a; }
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| 174 |
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| 175 | /** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
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| 176 | template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from)
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| 177 | { (*to) = from; }
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| 178 |
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| 179 | /** \internal copy the packet \a from to \a *to, (un-aligned store) */
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| 180 | template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from)
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| 181 | { (*to) = from; }
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| 182 |
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| 183 | /** \internal tries to do cache prefetching of \a addr */
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| 184 | template<typename Scalar> inline void prefetch(const Scalar* addr)
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| 185 | {
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| 186 | #if !defined(_MSC_VER)
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| 187 | __builtin_prefetch(addr);
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| 188 | #endif
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| 189 | }
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| 190 |
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| 191 | /** \internal \returns the first element of a packet */
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| 192 | template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
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| 193 | { return a; }
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| 194 |
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| 195 | /** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
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| 196 | template<typename Packet> inline Packet
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| 197 | preduxp(const Packet* vecs) { return vecs[0]; }
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| 198 |
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| 199 | /** \internal \returns the sum of the elements of \a a*/
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| 200 | template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a)
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| 201 | { return a; }
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| 202 |
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| 203 | /** \internal \returns the product of the elements of \a a*/
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| 204 | template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
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| 205 | { return a; }
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| 206 |
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| 207 | /** \internal \returns the min of the elements of \a a*/
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| 208 | template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
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| 209 | { return a; }
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| 210 |
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| 211 | /** \internal \returns the max of the elements of \a a*/
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| 212 | template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
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| 213 | { return a; }
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| 214 |
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| 215 | /** \internal \returns the reversed elements of \a a*/
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| 216 | template<typename Packet> inline Packet preverse(const Packet& a)
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| 217 | { return a; }
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| 218 |
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| 219 |
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| 220 | /** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
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| 221 | template<typename Packet> inline Packet pcplxflip(const Packet& a)
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| 222 | {
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| 223 | // FIXME: uncomment the following in case we drop the internal imag and real functions.
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| 224 | // using std::imag;
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| 225 | // using std::real;
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| 226 | return Packet(imag(a),real(a));
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| 227 | }
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| 228 |
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| 229 | /**************************
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| 230 | * Special math functions
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| 231 | ***************************/
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| 232 |
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| 233 | /** \internal \returns the sine of \a a (coeff-wise) */
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| 234 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 235 | Packet psin(const Packet& a) { using std::sin; return sin(a); }
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| 236 |
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| 237 | /** \internal \returns the cosine of \a a (coeff-wise) */
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| 238 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 239 | Packet pcos(const Packet& a) { using std::cos; return cos(a); }
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| 240 |
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| 241 | /** \internal \returns the tan of \a a (coeff-wise) */
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| 242 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 243 | Packet ptan(const Packet& a) { using std::tan; return tan(a); }
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| 244 |
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| 245 | /** \internal \returns the arc sine of \a a (coeff-wise) */
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| 246 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 247 | Packet pasin(const Packet& a) { using std::asin; return asin(a); }
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| 248 |
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| 249 | /** \internal \returns the arc cosine of \a a (coeff-wise) */
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| 250 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 251 | Packet pacos(const Packet& a) { using std::acos; return acos(a); }
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| 252 |
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| 253 | /** \internal \returns the exp of \a a (coeff-wise) */
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| 254 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 255 | Packet pexp(const Packet& a) { using std::exp; return exp(a); }
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| 256 |
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| 257 | /** \internal \returns the log of \a a (coeff-wise) */
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| 258 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 259 | Packet plog(const Packet& a) { using std::log; return log(a); }
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| 260 |
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| 261 | /** \internal \returns the square-root of \a a (coeff-wise) */
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| 262 | template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
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| 263 | Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }
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| 264 |
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| 265 | /***************************************************************************
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| 266 | * The following functions might not have to be overwritten for vectorized types
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| 267 | ***************************************************************************/
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| 268 |
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| 269 | /** \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 */
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| 270 | // NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
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| 271 | template<typename Packet>
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| 272 | inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
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| 273 | {
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| 274 | pstore(to, pset1<Packet>(a));
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| 275 | }
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| 276 |
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| 277 | /** \internal \returns a * b + c (coeff-wise) */
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| 278 | template<typename Packet> inline Packet
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| 279 | pmadd(const Packet& a,
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| 280 | const Packet& b,
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| 281 | const Packet& c)
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| 282 | { return padd(pmul(a, b),c); }
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| 283 |
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| 284 | /** \internal \returns a packet version of \a *from.
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| 285 | * If LoadMode equals #Aligned, \a from must be 16 bytes aligned */
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| 286 | template<typename Packet, int LoadMode>
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| 287 | inline Packet ploadt(const typename unpacket_traits<Packet>::type* from)
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| 288 | {
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| 289 | if(LoadMode == Aligned)
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| 290 | return pload<Packet>(from);
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| 291 | else
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| 292 | return ploadu<Packet>(from);
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| 293 | }
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| 294 |
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| 295 | /** \internal copy the packet \a from to \a *to.
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| 296 | * If StoreMode equals #Aligned, \a to must be 16 bytes aligned */
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| 297 | template<typename Scalar, typename Packet, int LoadMode>
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| 298 | inline void pstoret(Scalar* to, const Packet& from)
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| 299 | {
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| 300 | if(LoadMode == Aligned)
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| 301 | pstore(to, from);
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| 302 | else
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| 303 | pstoreu(to, from);
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| 304 | }
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| 305 |
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| 306 | /** \internal default implementation of palign() allowing partial specialization */
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| 307 | template<int Offset,typename PacketType>
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| 308 | struct palign_impl
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| 309 | {
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| 310 | // by default data are aligned, so there is nothing to be done :)
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| 311 | static inline void run(PacketType&, const PacketType&) {}
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| 312 | };
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| 313 |
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| 314 | /** \internal update \a first using the concatenation of the packet_size minus \a Offset last elements
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| 315 | * of \a first and \a Offset first elements of \a second.
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| 316 | *
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| 317 | * This function is currently only used to optimize matrix-vector products on unligned matrices.
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| 318 | * It takes 2 packets that represent a contiguous memory array, and returns a packet starting
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| 319 | * at the position \a Offset. For instance, for packets of 4 elements, we have:
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| 320 | * Input:
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| 321 | * - first = {f0,f1,f2,f3}
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| 322 | * - second = {s0,s1,s2,s3}
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| 323 | * Output:
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| 324 | * - if Offset==0 then {f0,f1,f2,f3}
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| 325 | * - if Offset==1 then {f1,f2,f3,s0}
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| 326 | * - if Offset==2 then {f2,f3,s0,s1}
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| 327 | * - if Offset==3 then {f3,s0,s1,s3}
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| 328 | */
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| 329 | template<int Offset,typename PacketType>
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| 330 | inline void palign(PacketType& first, const PacketType& second)
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| 331 | {
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| 332 | palign_impl<Offset,PacketType>::run(first,second);
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| 333 | }
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| 334 |
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| 335 | /***************************************************************************
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| 336 | * Fast complex products (GCC generates a function call which is very slow)
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| 337 | ***************************************************************************/
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| 338 |
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| 339 | template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
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| 340 | { return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
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| 341 |
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| 342 | template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
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| 343 | { return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
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| 344 |
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| 345 | } // end namespace internal
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| 346 |
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| 347 | } // end namespace Eigen
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| 348 |
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| 349 | #endif // EIGEN_GENERIC_PACKET_MATH_H
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| 350 |
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