GenericPacketMath.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
00006 //
00007 // This Source Code Form is subject to the terms of the Mozilla
00008 // Public License v. 2.0. If a copy of the MPL was not distributed
00009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00010 
00011 #ifndef EIGEN_GENERIC_PACKET_MATH_H
00012 #define EIGEN_GENERIC_PACKET_MATH_H
00013 
00014 namespace Eigen {
00015 
00016 namespace internal {
00017 
00018 /** \internal
00019   * \file GenericPacketMath.h
00020   *
00021   * Default implementation for types not supported by the vectorization.
00022   * In practice these functions are provided to make easier the writing
00023   * of generic vectorized code.
00024   */
00025 
00026 #ifndef EIGEN_DEBUG_ALIGNED_LOAD
00027 #define EIGEN_DEBUG_ALIGNED_LOAD
00028 #endif
00029 
00030 #ifndef EIGEN_DEBUG_UNALIGNED_LOAD
00031 #define EIGEN_DEBUG_UNALIGNED_LOAD
00032 #endif
00033 
00034 #ifndef EIGEN_DEBUG_ALIGNED_STORE
00035 #define EIGEN_DEBUG_ALIGNED_STORE
00036 #endif
00037 
00038 #ifndef EIGEN_DEBUG_UNALIGNED_STORE
00039 #define EIGEN_DEBUG_UNALIGNED_STORE
00040 #endif
00041 
00042 struct default_packet_traits
00043 {
00044   enum {
00045     HasAdd    = 1,
00046     HasSub    = 1,
00047     HasMul    = 1,
00048     HasNegate = 1,
00049     HasAbs    = 1,
00050     HasAbs2   = 1,
00051     HasMin    = 1,
00052     HasMax    = 1,
00053     HasConj   = 1,
00054     HasSetLinear = 1,
00055 
00056     HasDiv    = 0,
00057     HasSqrt   = 0,
00058     HasExp    = 0,
00059     HasLog    = 0,
00060     HasPow    = 0,
00061 
00062     HasSin    = 0,
00063     HasCos    = 0,
00064     HasTan    = 0,
00065     HasASin   = 0,
00066     HasACos   = 0,
00067     HasATan   = 0
00068   };
00069 };
00070 
00071 template<typename T> struct packet_traits : default_packet_traits
00072 {
00073   typedef T type;
00074   enum {
00075     Vectorizable = 0,
00076     size = 1,
00077     AlignedOnScalar = 0
00078   };
00079   enum {
00080     HasAdd    = 0,
00081     HasSub    = 0,
00082     HasMul    = 0,
00083     HasNegate = 0,
00084     HasAbs    = 0,
00085     HasAbs2   = 0,
00086     HasMin    = 0,
00087     HasMax    = 0,
00088     HasConj   = 0,
00089     HasSetLinear = 0
00090   };
00091 };
00092 
00093 /** \internal \returns a + b (coeff-wise) */
00094 template<typename Packet> inline Packet
00095 padd(const Packet& a,
00096         const Packet& b) { return a+b; }
00097 
00098 /** \internal \returns a - b (coeff-wise) */
00099 template<typename Packet> inline Packet
00100 psub(const Packet& a,
00101         const Packet& b) { return a-b; }
00102 
00103 /** \internal \returns -a (coeff-wise) */
00104 template<typename Packet> inline Packet
00105 pnegate(const Packet& a) { return -a; }
00106 
00107 /** \internal \returns conj(a) (coeff-wise) */
00108 template<typename Packet> inline Packet
00109 pconj(const Packet& a) { return numext::conj(a); }
00110 
00111 /** \internal \returns a * b (coeff-wise) */
00112 template<typename Packet> inline Packet
00113 pmul(const Packet& a,
00114         const Packet& b) { return a*b; }
00115 
00116 /** \internal \returns a / b (coeff-wise) */
00117 template<typename Packet> inline Packet
00118 pdiv(const Packet& a,
00119         const Packet& b) { return a/b; }
00120 
00121 /** \internal \returns the min of \a a and \a b  (coeff-wise) */
00122 template<typename Packet> inline Packet
00123 pmin(const Packet& a,
00124         const Packet& b) { using std::min; return (min)(a, b); }
00125 
00126 /** \internal \returns the max of \a a and \a b  (coeff-wise) */
00127 template<typename Packet> inline Packet
00128 pmax(const Packet& a,
00129         const Packet& b) { using std::max; return (max)(a, b); }
00130 
00131 /** \internal \returns the absolute value of \a a */
00132 template<typename Packet> inline Packet
00133 pabs(const Packet& a) { using std::abs; return abs(a); }
00134 
00135 /** \internal \returns the bitwise and of \a a and \a b */
00136 template<typename Packet> inline Packet
00137 pand(const Packet& a, const Packet& b) { return a & b; }
00138 
00139 /** \internal \returns the bitwise or of \a a and \a b */
00140 template<typename Packet> inline Packet
00141 por(const Packet& a, const Packet& b) { return a | b; }
00142 
00143 /** \internal \returns the bitwise xor of \a a and \a b */
00144 template<typename Packet> inline Packet
00145 pxor(const Packet& a, const Packet& b) { return a ^ b; }
00146 
00147 /** \internal \returns the bitwise andnot of \a a and \a b */
00148 template<typename Packet> inline Packet
00149 pandnot(const Packet& a, const Packet& b) { return a & (!b); }
00150 
00151 /** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
00152 template<typename Packet> inline Packet
00153 pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
00154 
00155 /** \internal \returns a packet version of \a *from, (un-aligned load) */
00156 template<typename Packet> inline Packet
00157 ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; }
00158 
00159 /** \internal \returns a packet with elements of \a *from duplicated.
00160   * For instance, for a packet of 8 elements, 4 scalar will be read from \a *from and
00161   * duplicated to form: {from[0],from[0],from[1],from[1],,from[2],from[2],,from[3],from[3]}
00162   * Currently, this function is only used for scalar * complex products.
00163  */
00164 template<typename Packet> inline Packet
00165 ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; }
00166 
00167 /** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
00168 template<typename Packet> inline Packet
00169 pset1(const typename unpacket_traits<Packet>::type& a) { return a; }
00170 
00171 /** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
00172 template<typename Scalar> inline typename packet_traits<Scalar>::type
00173 plset(const Scalar& a) { return a; }
00174 
00175 /** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
00176 template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from)
00177 { (*to) = from; }
00178 
00179 /** \internal copy the packet \a from to \a *to, (un-aligned store) */
00180 template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from)
00181 { (*to) = from; }
00182 
00183 /** \internal tries to do cache prefetching of \a addr */
00184 template<typename Scalar> inline void prefetch(const Scalar* addr)
00185 {
00186 #if !defined(_MSC_VER)
00187 __builtin_prefetch(addr);
00188 #endif
00189 }
00190 
00191 /** \internal \returns the first element of a packet */
00192 template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a)
00193 { return a; }
00194 
00195 /** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */
00196 template<typename Packet> inline Packet
00197 preduxp(const Packet* vecs) { return vecs[0]; }
00198 
00199 /** \internal \returns the sum of the elements of \a a*/
00200 template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a)
00201 { return a; }
00202 
00203 /** \internal \returns the product of the elements of \a a*/
00204 template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a)
00205 { return a; }
00206 
00207 /** \internal \returns the min of the elements of \a a*/
00208 template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a)
00209 { return a; }
00210 
00211 /** \internal \returns the max of the elements of \a a*/
00212 template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a)
00213 { return a; }
00214 
00215 /** \internal \returns the reversed elements of \a a*/
00216 template<typename Packet> inline Packet preverse(const Packet& a)
00217 { return a; }
00218 
00219 
00220 /** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
00221 template<typename Packet> inline Packet pcplxflip(const Packet& a)
00222 {
00223   // FIXME: uncomment the following in case we drop the internal imag and real functions.
00224 //   using std::imag;
00225 //   using std::real;
00226   return Packet(imag(a),real(a));
00227 }
00228 
00229 /**************************
00230 * Special math functions
00231 ***************************/
00232 
00233 /** \internal \returns the sine of \a a (coeff-wise) */
00234 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00235 Packet psin(const Packet& a) { using std::sin; return sin(a); }
00236 
00237 /** \internal \returns the cosine of \a a (coeff-wise) */
00238 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00239 Packet pcos(const Packet& a) { using std::cos; return cos(a); }
00240 
00241 /** \internal \returns the tan of \a a (coeff-wise) */
00242 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00243 Packet ptan(const Packet& a) { using std::tan; return tan(a); }
00244 
00245 /** \internal \returns the arc sine of \a a (coeff-wise) */
00246 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00247 Packet pasin(const Packet& a) { using std::asin; return asin(a); }
00248 
00249 /** \internal \returns the arc cosine of \a a (coeff-wise) */
00250 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00251 Packet pacos(const Packet& a) { using std::acos; return acos(a); }
00252 
00253 /** \internal \returns the exp of \a a (coeff-wise) */
00254 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00255 Packet pexp(const Packet& a) { using std::exp; return exp(a); }
00256 
00257 /** \internal \returns the log of \a a (coeff-wise) */
00258 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00259 Packet plog(const Packet& a) { using std::log; return log(a); }
00260 
00261 /** \internal \returns the square-root of \a a (coeff-wise) */
00262 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
00263 Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }
00264 
00265 /***************************************************************************
00266 * The following functions might not have to be overwritten for vectorized types
00267 ***************************************************************************/
00268 
00269 /** \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 */
00270 // NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type)
00271 template<typename Packet>
00272 inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
00273 {
00274   pstore(to, pset1<Packet>(a));
00275 }
00276 
00277 /** \internal \returns a * b + c (coeff-wise) */
00278 template<typename Packet> inline Packet
00279 pmadd(const Packet&  a,
00280          const Packet&  b,
00281          const Packet&  c)
00282 { return padd(pmul(a, b),c); }
00283 
00284 /** \internal \returns a packet version of \a *from.
00285   * If LoadMode equals #Aligned, \a from must be 16 bytes aligned */
00286 template<typename Packet, int LoadMode>
00287 inline Packet ploadt(const typename unpacket_traits<Packet>::type* from)
00288 {
00289   if(LoadMode == Aligned)
00290     return pload<Packet>(from);
00291   else
00292     return ploadu<Packet>(from);
00293 }
00294 
00295 /** \internal copy the packet \a from to \a *to.
00296   * If StoreMode equals #Aligned, \a to must be 16 bytes aligned */
00297 template<typename Scalar, typename Packet, int LoadMode>
00298 inline void pstoret(Scalar* to, const Packet& from)
00299 {
00300   if(LoadMode == Aligned)
00301     pstore(to, from);
00302   else
00303     pstoreu(to, from);
00304 }
00305 
00306 /** \internal default implementation of palign() allowing partial specialization */
00307 template<int Offset,typename PacketType>
00308 struct palign_impl
00309 {
00310   // by default data are aligned, so there is nothing to be done :)
00311   static inline void run(PacketType&, const PacketType&) {}
00312 };
00313 
00314 /** \internal update \a first using the concatenation of the packet_size minus \a Offset last elements
00315   * of \a first and \a Offset first elements of \a second.
00316   * 
00317   * This function is currently only used to optimize matrix-vector products on unligned matrices.
00318   * It takes 2 packets that represent a contiguous memory array, and returns a packet starting
00319   * at the position \a Offset. For instance, for packets of 4 elements, we have:
00320   *  Input:
00321   *  - first = {f0,f1,f2,f3}
00322   *  - second = {s0,s1,s2,s3}
00323   * Output: 
00324   *   - if Offset==0 then {f0,f1,f2,f3}
00325   *   - if Offset==1 then {f1,f2,f3,s0}
00326   *   - if Offset==2 then {f2,f3,s0,s1}
00327   *   - if Offset==3 then {f3,s0,s1,s3}
00328   */
00329 template<int Offset,typename PacketType>
00330 inline void palign(PacketType& first, const PacketType& second)
00331 {
00332   palign_impl<Offset,PacketType>::run(first,second);
00333 }
00334 
00335 /***************************************************************************
00336 * Fast complex products (GCC generates a function call which is very slow)
00337 ***************************************************************************/
00338 
00339 template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b)
00340 { return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
00341 
00342 template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b)
00343 { return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); }
00344 
00345 } // end namespace internal
00346 
00347 } // end namespace Eigen
00348 
00349 #endif // EIGEN_GENERIC_PACKET_MATH_H