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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_GENERIC_PACKET_MATH_H
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#define EIGEN_GENERIC_PACKET_MATH_H
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namespace Eigen {
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namespace internal {
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/** \internal
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* \file GenericPacketMath.h
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*
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* Default implementation for types not supported by the vectorization.
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* In practice these functions are provided to make easier the writing
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* of generic vectorized code.
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*/
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#ifndef EIGEN_DEBUG_ALIGNED_LOAD
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#define EIGEN_DEBUG_ALIGNED_LOAD
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#endif
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#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
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#define EIGEN_DEBUG_UNALIGNED_LOAD
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#endif
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#ifndef EIGEN_DEBUG_ALIGNED_STORE
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#define EIGEN_DEBUG_ALIGNED_STORE
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#endif
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#ifndef EIGEN_DEBUG_UNALIGNED_STORE
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#define EIGEN_DEBUG_UNALIGNED_STORE
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#endif
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struct default_packet_traits
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{
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enum {
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HasAdd = 1,
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HasSub = 1,
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HasMul = 1,
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HasNegate = 1,
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HasAbs = 1,
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HasAbs2 = 1,
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HasMin = 1,
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HasMax = 1,
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HasConj = 1,
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HasSetLinear = 1,
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HasDiv = 0,
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HasSqrt = 0,
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HasExp = 0,
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HasLog = 0,
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HasPow = 0,
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HasSin = 0,
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HasCos = 0,
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HasTan = 0,
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HasASin = 0,
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HasACos = 0,
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HasATan = 0
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};
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};
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template<typename T> struct packet_traits : default_packet_traits
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{
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typedef T type;
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enum {
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Vectorizable = 0,
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size = 1,
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AlignedOnScalar = 0
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};
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enum {
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HasAdd = 0,
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HasSub = 0,
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HasMul = 0,
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HasNegate = 0,
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HasAbs = 0,
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HasAbs2 = 0,
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HasMin = 0,
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HasMax = 0,
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HasConj = 0,
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HasSetLinear = 0
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};
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};
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/** \internal \returns a + b (coeff-wise) */
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template<typename Packet> inline Packet
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padd(const Packet& a,
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const Packet& b) { return a+b; }
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/** \internal \returns a - b (coeff-wise) */
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template<typename Packet> inline Packet
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psub(const Packet& a,
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const Packet& b) { return a-b; }
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/** \internal \returns -a (coeff-wise) */
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template<typename Packet> inline Packet
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pnegate(const Packet& a) { return -a; }
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/** \internal \returns conj(a) (coeff-wise) */
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template<typename Packet> inline Packet
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pconj(const Packet& a) { return numext::conj(a); }
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/** \internal \returns a * b (coeff-wise) */
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template<typename Packet> inline Packet
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pmul(const Packet& a,
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const Packet& b) { return a*b; }
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/** \internal \returns a / b (coeff-wise) */
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template<typename Packet> inline Packet
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pdiv(const Packet& a,
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const Packet& b) { return a/b; }
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/** \internal \returns the min of \a a and \a b (coeff-wise) */
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template<typename Packet> inline Packet
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pmin(const Packet& a,
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const Packet& b) { using std::min; return (min)(a, b); }
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/** \internal \returns the max of \a a and \a b (coeff-wise) */
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template<typename Packet> inline Packet
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pmax(const Packet& a,
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const Packet& b) { using std::max; return (max)(a, b); }
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/** \internal \returns the absolute value of \a a */
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template<typename Packet> inline Packet
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pabs(const Packet& a) { using std::abs; return abs(a); }
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/** \internal \returns the bitwise and of \a a and \a b */
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template<typename Packet> inline Packet
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pand(const Packet& a, const Packet& b) { return a & b; }
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/** \internal \returns the bitwise or of \a a and \a b */
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template<typename Packet> inline Packet
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por(const Packet& a, const Packet& b) { return a | b; }
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/** \internal \returns the bitwise xor of \a a and \a b */
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template<typename Packet> inline Packet
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pxor(const Packet& a, const Packet& b) { return a ^ b; }
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/** \internal \returns the bitwise andnot of \a a and \a b */
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template<typename Packet> inline Packet
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pandnot(const Packet& a, const Packet& b) { return a & (!b); }
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/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
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template<typename Packet> inline Packet
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pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
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/** \internal \returns a packet version of \a *from, (un-aligned load) */
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template<typename Packet> inline Packet
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ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
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/** \internal \returns a packet with elements of \a *from duplicated.
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* For instance, for a packet of 8 elements, 4 scalar will be read from \a *from and
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* duplicated to form: {from[0],from[0],from[1],from[1],,from[2],from[2],,from[3],from[3]}
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* Currently, this function is only used for scalar * complex products.
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*/
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template<typename Packet> inline Packet
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ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
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/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
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template<typename Packet> inline Packet
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pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
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/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
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template<typename Scalar> inline typename packet_traits<Scalar>::type
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plset(const Scalar& a) { return a; }
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/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
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template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from)
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{ (*to) = from; }
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/** \internal copy the packet \a from to \a *to, (un-aligned store) */
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template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from)
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{ (*to) = from; }
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/** \internal tries to do cache prefetching of \a addr */
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template<typename Scalar> inline void prefetch(const Scalar* addr)
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{
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#if !defined(_MSC_VER)
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__builtin_prefetch(addr);
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#endif
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}
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/** \internal \returns the first element of a packet */
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template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
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{ return a; }
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/** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
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template<typename Packet> inline Packet
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preduxp(const Packet* vecs) { return vecs[0]; }
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/** \internal \returns the sum of the elements of \a a*/
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template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a)
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{ return a; }
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/** \internal \returns the product of the elements of \a a*/
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template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
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{ return a; }
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/** \internal \returns the min of the elements of \a a*/
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template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
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209
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{ return a; }
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210
|
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211
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/** \internal \returns the max of the elements of \a a*/
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212
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template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
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213
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{ 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
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template<typename Packet> inline Packet preverse(const Packet& a)
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217
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{ return a; }
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|
218
|
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|
219
|
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220
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/** \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
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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
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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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0:13a5d365ba16
|
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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0:13a5d365ba16
|
249
|
/** \internal \returns the arc cosine of \a a (coeff-wise) */
|
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0:13a5d365ba16
|
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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0:13a5d365ba16
|
253
|
/** \internal \returns the exp of \a a (coeff-wise) */
|
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0:13a5d365ba16
|
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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0:13a5d365ba16
|
256
|
|
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0:13a5d365ba16
|
257
|
/** \internal \returns the log of \a a (coeff-wise) */
|
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0:13a5d365ba16
|
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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0:13a5d365ba16
|
260
|
|
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0:13a5d365ba16
|
261
|
/** \internal \returns the square-root of \a a (coeff-wise) */
|
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0:13a5d365ba16
|
262
|
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
|
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0:13a5d365ba16
|
263
|
Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }
|
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0:13a5d365ba16
|
264
|
|
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0:13a5d365ba16
|
265
|
/***************************************************************************
|
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0:13a5d365ba16
|
266
|
* The following functions might not have to be overwritten for vectorized types
|
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0:13a5d365ba16
|
267
|
***************************************************************************/
|
ykuroda |
0:13a5d365ba16
|
268
|
|
ykuroda |
0:13a5d365ba16
|
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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0:13a5d365ba16
|
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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0:13a5d365ba16
|
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)
|
ykuroda |
0:13a5d365ba16
|
273
|
{
|
ykuroda |
0:13a5d365ba16
|
274
|
pstore(to, pset1<Packet>(a));
|
ykuroda |
0:13a5d365ba16
|
275
|
}
|
ykuroda |
0:13a5d365ba16
|
276
|
|
ykuroda |
0:13a5d365ba16
|
277
|
/** \internal \returns a * b + c (coeff-wise) */
|
ykuroda |
0:13a5d365ba16
|
278
|
template<typename Packet> inline Packet
|
ykuroda |
0:13a5d365ba16
|
279
|
pmadd(const Packet& a,
|
ykuroda |
0:13a5d365ba16
|
280
|
const Packet& b,
|
ykuroda |
0:13a5d365ba16
|
281
|
const Packet& c)
|
ykuroda |
0:13a5d365ba16
|
282
|
{ return padd(pmul(a, b),c); }
|
ykuroda |
0:13a5d365ba16
|
283
|
|
ykuroda |
0:13a5d365ba16
|
284
|
/** \internal \returns a packet version of \a *from.
|
ykuroda |
0:13a5d365ba16
|
285
|
* If LoadMode equals #Aligned, \a from must be 16 bytes aligned */
|
ykuroda |
0:13a5d365ba16
|
286
|
template<typename Packet, int LoadMode>
|
ykuroda |
0:13a5d365ba16
|
287
|
inline Packet ploadt(const typename unpacket_traits<Packet>::type* from)
|
ykuroda |
0:13a5d365ba16
|
288
|
{
|
ykuroda |
0:13a5d365ba16
|
289
|
if(LoadMode == Aligned)
|
ykuroda |
0:13a5d365ba16
|
290
|
return pload<Packet>(from);
|
ykuroda |
0:13a5d365ba16
|
291
|
else
|
ykuroda |
0:13a5d365ba16
|
292
|
return ploadu<Packet>(from);
|
ykuroda |
0:13a5d365ba16
|
293
|
}
|
ykuroda |
0:13a5d365ba16
|
294
|
|
ykuroda |
0:13a5d365ba16
|
295
|
/** \internal copy the packet \a from to \a *to.
|
ykuroda |
0:13a5d365ba16
|
296
|
* If StoreMode equals #Aligned, \a to must be 16 bytes aligned */
|
ykuroda |
0:13a5d365ba16
|
297
|
template<typename Scalar, typename Packet, int LoadMode>
|
ykuroda |
0:13a5d365ba16
|
298
|
inline void pstoret(Scalar* to, const Packet& from)
|
ykuroda |
0:13a5d365ba16
|
299
|
{
|
ykuroda |
0:13a5d365ba16
|
300
|
if(LoadMode == Aligned)
|
ykuroda |
0:13a5d365ba16
|
301
|
pstore(to, from);
|
ykuroda |
0:13a5d365ba16
|
302
|
else
|
ykuroda |
0:13a5d365ba16
|
303
|
pstoreu(to, from);
|
ykuroda |
0:13a5d365ba16
|
304
|
}
|
ykuroda |
0:13a5d365ba16
|
305
|
|
ykuroda |
0:13a5d365ba16
|
306
|
/** \internal default implementation of palign() allowing partial specialization */
|
ykuroda |
0:13a5d365ba16
|
307
|
template<int Offset,typename PacketType>
|
ykuroda |
0:13a5d365ba16
|
308
|
struct palign_impl
|
ykuroda |
0:13a5d365ba16
|
309
|
{
|
ykuroda |
0:13a5d365ba16
|
310
|
// by default data are aligned, so there is nothing to be done :)
|
ykuroda |
0:13a5d365ba16
|
311
|
static inline void run(PacketType&, const PacketType&) {}
|
ykuroda |
0:13a5d365ba16
|
312
|
};
|
ykuroda |
0:13a5d365ba16
|
313
|
|
ykuroda |
0:13a5d365ba16
|
314
|
/** \internal update \a first using the concatenation of the packet_size minus \a Offset last elements
|
ykuroda |
0:13a5d365ba16
|
315
|
* of \a first and \a Offset first elements of \a second.
|
ykuroda |
0:13a5d365ba16
|
316
|
*
|
ykuroda |
0:13a5d365ba16
|
317
|
* This function is currently only used to optimize matrix-vector products on unligned matrices.
|
ykuroda |
0:13a5d365ba16
|
318
|
* It takes 2 packets that represent a contiguous memory array, and returns a packet starting
|
ykuroda |
0:13a5d365ba16
|
319
|
* at the position \a Offset. For instance, for packets of 4 elements, we have:
|
ykuroda |
0:13a5d365ba16
|
320
|
* Input:
|
ykuroda |
0:13a5d365ba16
|
321
|
* - first = {f0,f1,f2,f3}
|
ykuroda |
0:13a5d365ba16
|
322
|
* - second = {s0,s1,s2,s3}
|
ykuroda |
0:13a5d365ba16
|
323
|
* Output:
|
ykuroda |
0:13a5d365ba16
|
324
|
* - if Offset==0 then {f0,f1,f2,f3}
|
ykuroda |
0:13a5d365ba16
|
325
|
* - if Offset==1 then {f1,f2,f3,s0}
|
ykuroda |
0:13a5d365ba16
|
326
|
* - if Offset==2 then {f2,f3,s0,s1}
|
ykuroda |
0:13a5d365ba16
|
327
|
* - if Offset==3 then {f3,s0,s1,s3}
|
ykuroda |
0:13a5d365ba16
|
328
|
*/
|
ykuroda |
0:13a5d365ba16
|
329
|
template<int Offset,typename PacketType>
|
ykuroda |
0:13a5d365ba16
|
330
|
inline void palign(PacketType& first, const PacketType& second)
|
ykuroda |
0:13a5d365ba16
|
331
|
{
|
ykuroda |
0:13a5d365ba16
|
332
|
palign_impl<Offset,PacketType>::run(first,second);
|
ykuroda |
0:13a5d365ba16
|
333
|
}
|
ykuroda |
0:13a5d365ba16
|
334
|
|
ykuroda |
0:13a5d365ba16
|
335
|
/***************************************************************************
|
ykuroda |
0:13a5d365ba16
|
336
|
* Fast complex products (GCC generates a function call which is very slow)
|
ykuroda |
0:13a5d365ba16
|
337
|
***************************************************************************/
|
ykuroda |
0:13a5d365ba16
|
338
|
|
ykuroda |
0:13a5d365ba16
|
339
|
template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
|
ykuroda |
0:13a5d365ba16
|
340
|
{ return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
|
ykuroda |
0:13a5d365ba16
|
341
|
|
ykuroda |
0:13a5d365ba16
|
342
|
template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
|
ykuroda |
0:13a5d365ba16
|
343
|
{ return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
|
ykuroda |
0:13a5d365ba16
|
344
|
|
ykuroda |
0:13a5d365ba16
|
345
|
} // end namespace internal
|
ykuroda |
0:13a5d365ba16
|
346
|
|
ykuroda |
0:13a5d365ba16
|
347
|
} // end namespace Eigen
|
ykuroda |
0:13a5d365ba16
|
348
|
|
ykuroda |
0:13a5d365ba16
|
349
|
#endif // EIGEN_GENERIC_PACKET_MATH_H
|