1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.fr> 5 // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #ifndef EIGEN_GENERIC_PACKET_MATH_H 12 #define EIGEN_GENERIC_PACKET_MATH_H 13 14 namespace Eigen { 15 16 namespace internal { 17 18 /** \internal 19 * \file GenericPacketMath.h 20 * 21 * Default implementation for types not supported by the vectorization. 22 * In practice these functions are provided to make easier the writing 23 * of generic vectorized code. 24 */ 25 26 #ifndef EIGEN_DEBUG_ALIGNED_LOAD 27 #define EIGEN_DEBUG_ALIGNED_LOAD 28 #endif 29 30 #ifndef EIGEN_DEBUG_UNALIGNED_LOAD 31 #define EIGEN_DEBUG_UNALIGNED_LOAD 32 #endif 33 34 #ifndef EIGEN_DEBUG_ALIGNED_STORE 35 #define EIGEN_DEBUG_ALIGNED_STORE 36 #endif 37 38 #ifndef EIGEN_DEBUG_UNALIGNED_STORE 39 #define EIGEN_DEBUG_UNALIGNED_STORE 40 #endif 41 42 struct default_packet_traits 43 { 44 enum { 45 HasAdd = 1, 46 HasSub = 1, 47 HasMul = 1, 48 HasNegate = 1, 49 HasAbs = 1, 50 HasAbs2 = 1, 51 HasMin = 1, 52 HasMax = 1, 53 HasConj = 1, 54 HasSetLinear = 1, 55 56 HasDiv = 0, 57 HasSqrt = 0, 58 HasExp = 0, 59 HasLog = 0, 60 HasPow = 0, 61 62 HasSin = 0, 63 HasCos = 0, 64 HasTan = 0, 65 HasASin = 0, 66 HasACos = 0, 67 HasATan = 0 68 }; 69 }; 70 71 template<typename T> struct packet_traits : default_packet_traits 72 { 73 typedef T type; 74 enum { 75 Vectorizable = 0, 76 size = 1, 77 AlignedOnScalar = 0 78 }; 79 enum { 80 HasAdd = 0, 81 HasSub = 0, 82 HasMul = 0, 83 HasNegate = 0, 84 HasAbs = 0, 85 HasAbs2 = 0, 86 HasMin = 0, 87 HasMax = 0, 88 HasConj = 0, 89 HasSetLinear = 0 90 }; 91 }; 92 93 /** \internal \returns a + b (coeff-wise) */ 94 template<typename Packet> inline Packet 95 padd(const Packet& a, 96 const Packet& b) { return a+b; } 97 98 /** \internal \returns a - b (coeff-wise) */ 99 template<typename Packet> inline Packet 100 psub(const Packet& a, 101 const Packet& b) { return a-b; } 102 103 /** \internal \returns -a (coeff-wise) */ 104 template<typename Packet> inline Packet 105 pnegate(const Packet& a) { return -a; } 106 107 /** \internal \returns conj(a) (coeff-wise) */ 108 template<typename Packet> inline Packet 109 pconj(const Packet& a) { return numext::conj(a); } 110 111 /** \internal \returns a * b (coeff-wise) */ 112 template<typename Packet> inline Packet 113 pmul(const Packet& a, 114 const Packet& b) { return a*b; } 115 116 /** \internal \returns a / b (coeff-wise) */ 117 template<typename Packet> inline Packet 118 pdiv(const Packet& a, 119 const Packet& b) { return a/b; } 120 121 /** \internal \returns the min of \a a and \a b (coeff-wise) */ 122 template<typename Packet> inline Packet 123 pmin(const Packet& a, 124 const Packet& b) { using std::min; return (min)(a, b); } 125 126 /** \internal \returns the max of \a a and \a b (coeff-wise) */ 127 template<typename Packet> inline Packet 128 pmax(const Packet& a, 129 const Packet& b) { using std::max; return (max)(a, b); } 130 131 /** \internal \returns the absolute value of \a a */ 132 template<typename Packet> inline Packet 133 pabs(const Packet& a) { using std::abs; return abs(a); } 134 135 /** \internal \returns the bitwise and of \a a and \a b */ 136 template<typename Packet> inline Packet 137 pand(const Packet& a, const Packet& b) { return a & b; } 138 139 /** \internal \returns the bitwise or of \a a and \a b */ 140 template<typename Packet> inline Packet 141 por(const Packet& a, const Packet& b) { return a | b; } 142 143 /** \internal \returns the bitwise xor of \a a and \a b */ 144 template<typename Packet> inline Packet 145 pxor(const Packet& a, const Packet& b) { return a ^ b; } 146 147 /** \internal \returns the bitwise andnot of \a a and \a b */ 148 template<typename Packet> inline Packet 149 pandnot(const Packet& a, const Packet& b) { return a & (!b); } 150 151 /** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */ 152 template<typename Packet> inline Packet 153 pload(const typename unpacket_traits<Packet>::type* from) { return *from; } 154 155 /** \internal \returns a packet version of \a *from, (un-aligned load) */ 156 template<typename Packet> inline Packet 157 ploadu(const typename unpacket_traits<Packet>::type* from) { return *from; } 158 159 /** \internal \returns a packet with elements of \a *from duplicated. 160 * For instance, for a packet of 8 elements, 4 scalar will be read from \a *from and 161 * duplicated to form: {from[0],from[0],from[1],from[1],,from[2],from[2],,from[3],from[3]} 162 * Currently, this function is only used for scalar * complex products. 163 */ 164 template<typename Packet> inline Packet 165 ploaddup(const typename unpacket_traits<Packet>::type* from) { return *from; } 166 167 /** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */ 168 template<typename Packet> inline Packet 169 pset1(const typename unpacket_traits<Packet>::type& a) { return a; } 170 171 /** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */ 172 template<typename Scalar> inline typename packet_traits<Scalar>::type 173 plset(const Scalar& a) { return a; } 174 175 /** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */ 176 template<typename Scalar, typename Packet> inline void pstore(Scalar* to, const Packet& from) 177 { (*to) = from; } 178 179 /** \internal copy the packet \a from to \a *to, (un-aligned store) */ 180 template<typename Scalar, typename Packet> inline void pstoreu(Scalar* to, const Packet& from) 181 { (*to) = from; } 182 183 /** \internal tries to do cache prefetching of \a addr */ 184 template<typename Scalar> inline void prefetch(const Scalar* addr) 185 { 186 #if !defined(_MSC_VER) 187 __builtin_prefetch(addr); 188 #endif 189 } 190 191 /** \internal \returns the first element of a packet */ 192 template<typename Packet> inline typename unpacket_traits<Packet>::type pfirst(const Packet& a) 193 { return a; } 194 195 /** \internal \returns a packet where the element i contains the sum of the packet of \a vec[i] */ 196 template<typename Packet> inline Packet 197 preduxp(const Packet* vecs) { return vecs[0]; } 198 199 /** \internal \returns the sum of the elements of \a a*/ 200 template<typename Packet> inline typename unpacket_traits<Packet>::type predux(const Packet& a) 201 { return a; } 202 203 /** \internal \returns the product of the elements of \a a*/ 204 template<typename Packet> inline typename unpacket_traits<Packet>::type predux_mul(const Packet& a) 205 { return a; } 206 207 /** \internal \returns the min of the elements of \a a*/ 208 template<typename Packet> inline typename unpacket_traits<Packet>::type predux_min(const Packet& a) 209 { return a; } 210 211 /** \internal \returns the max of the elements of \a a*/ 212 template<typename Packet> inline typename unpacket_traits<Packet>::type predux_max(const Packet& a) 213 { return a; } 214 215 /** \internal \returns the reversed elements of \a a*/ 216 template<typename Packet> inline Packet preverse(const Packet& a) 217 { return a; } 218 219 220 /** \internal \returns \a a with real and imaginary part flipped (for complex type only) */ 221 template<typename Packet> inline Packet pcplxflip(const Packet& a) 222 { 223 // FIXME: uncomment the following in case we drop the internal imag and real functions. 224 // using std::imag; 225 // using std::real; 226 return Packet(imag(a),real(a)); 227 } 228 229 /************************** 230 * Special math functions 231 ***************************/ 232 233 /** \internal \returns the sine of \a a (coeff-wise) */ 234 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 235 Packet psin(const Packet& a) { using std::sin; return sin(a); } 236 237 /** \internal \returns the cosine of \a a (coeff-wise) */ 238 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 239 Packet pcos(const Packet& a) { using std::cos; return cos(a); } 240 241 /** \internal \returns the tan of \a a (coeff-wise) */ 242 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 243 Packet ptan(const Packet& a) { using std::tan; return tan(a); } 244 245 /** \internal \returns the arc sine of \a a (coeff-wise) */ 246 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 247 Packet pasin(const Packet& a) { using std::asin; return asin(a); } 248 249 /** \internal \returns the arc cosine of \a a (coeff-wise) */ 250 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 251 Packet pacos(const Packet& a) { using std::acos; return acos(a); } 252 253 /** \internal \returns the exp of \a a (coeff-wise) */ 254 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 255 Packet pexp(const Packet& a) { using std::exp; return exp(a); } 256 257 /** \internal \returns the log of \a a (coeff-wise) */ 258 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 259 Packet plog(const Packet& a) { using std::log; return log(a); } 260 261 /** \internal \returns the square-root of \a a (coeff-wise) */ 262 template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS 263 Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); } 264 265 /*************************************************************************** 266 * The following functions might not have to be overwritten for vectorized types 267 ***************************************************************************/ 268 269 /** \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 */ 270 // NOTE: this function must really be templated on the packet type (think about different packet types for the same scalar type) 271 template<typename Packet> 272 inline void pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a) 273 { 274 pstore(to, pset1<Packet>(a)); 275 } 276 277 /** \internal \returns a * b + c (coeff-wise) */ 278 template<typename Packet> inline Packet 279 pmadd(const Packet& a, 280 const Packet& b, 281 const Packet& c) 282 { return padd(pmul(a, b),c); } 283 284 /** \internal \returns a packet version of \a *from. 285 * If LoadMode equals #Aligned, \a from must be 16 bytes aligned */ 286 template<typename Packet, int LoadMode> 287 inline Packet ploadt(const typename unpacket_traits<Packet>::type* from) 288 { 289 if(LoadMode == Aligned) 290 return pload<Packet>(from); 291 else 292 return ploadu<Packet>(from); 293 } 294 295 /** \internal copy the packet \a from to \a *to. 296 * If StoreMode equals #Aligned, \a to must be 16 bytes aligned */ 297 template<typename Scalar, typename Packet, int LoadMode> 298 inline void pstoret(Scalar* to, const Packet& from) 299 { 300 if(LoadMode == Aligned) 301 pstore(to, from); 302 else 303 pstoreu(to, from); 304 } 305 306 /** \internal default implementation of palign() allowing partial specialization */ 307 template<int Offset,typename PacketType> 308 struct palign_impl 309 { 310 // by default data are aligned, so there is nothing to be done :) 311 static inline void run(PacketType&, const PacketType&) {} 312 }; 313 314 /** \internal update \a first using the concatenation of the packet_size minus \a Offset last elements 315 * of \a first and \a Offset first elements of \a second. 316 * 317 * This function is currently only used to optimize matrix-vector products on unligned matrices. 318 * It takes 2 packets that represent a contiguous memory array, and returns a packet starting 319 * at the position \a Offset. For instance, for packets of 4 elements, we have: 320 * Input: 321 * - first = {f0,f1,f2,f3} 322 * - second = {s0,s1,s2,s3} 323 * Output: 324 * - if Offset==0 then {f0,f1,f2,f3} 325 * - if Offset==1 then {f1,f2,f3,s0} 326 * - if Offset==2 then {f2,f3,s0,s1} 327 * - if Offset==3 then {f3,s0,s1,s3} 328 */ 329 template<int Offset,typename PacketType> 330 inline void palign(PacketType& first, const PacketType& second) 331 { 332 palign_impl<Offset,PacketType>::run(first,second); 333 } 334 335 /*************************************************************************** 336 * Fast complex products (GCC generates a function call which is very slow) 337 ***************************************************************************/ 338 339 template<> inline std::complex<float> pmul(const std::complex<float>& a, const std::complex<float>& b) 340 { return std::complex<float>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); } 341 342 template<> inline std::complex<double> pmul(const std::complex<double>& a, const std::complex<double>& b) 343 { return std::complex<double>(real(a)*real(b) - imag(a)*imag(b), imag(a)*real(b) + real(a)*imag(b)); } 344 345 } // end namespace internal 346 347 } // end namespace Eigen 348 349 #endif // EIGEN_GENERIC_PACKET_MATH_H 350 351
