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@inria.fr>
5// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@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
14namespace Eigen {
15
16namespace 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
42struct 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
71template<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) */
94template<typename Packet> inline Packet
95padd(const Packet& a,
96        const Packet& b) { return a+b; }
97
98/** \internal \returns a - b (coeff-wise) */
99template<typename Packet> inline Packet
100psub(const Packet& a,
101        const Packet& b) { return a-b; }
102
103/** \internal \returns -a (coeff-wise) */
104template<typename Packet> inline Packet
105pnegate(const Packet& a) { return -a; }
106
107/** \internal \returns conj(a) (coeff-wise) */
108template<typename Packet> inline Packet
109pconj(const Packet& a) { return numext::conj(a); }
110
111/** \internal \returns a * b (coeff-wise) */
112template<typename Packet> inline Packet
113pmul(const Packet& a,
114        const Packet& b) { return a*b; }
115
116/** \internal \returns a / b (coeff-wise) */
117template<typename Packet> inline Packet
118pdiv(const Packet& a,
119        const Packet& b) { return a/b; }
120
121/** \internal \returns the min of \a a and \a b  (coeff-wise) */
122template<typename Packet> inline Packet
123pmin(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) */
127template<typename Packet> inline Packet
128pmax(const Packet& a,
129        const Packet& b) { using std::max; return (max)(a, b); }
130
131/** \internal \returns the absolute value of \a a */
132template<typename Packet> inline Packet
133pabs(const Packet& a) { using std::abs; return abs(a); }
134
135/** \internal \returns the bitwise and of \a a and \a b */
136template<typename Packet> inline Packet
137pand(const Packet& a, const Packet& b) { return a & b; }
138
139/** \internal \returns the bitwise or of \a a and \a b */
140template<typename Packet> inline Packet
141por(const Packet& a, const Packet& b) { return a | b; }
142
143/** \internal \returns the bitwise xor of \a a and \a b */
144template<typename Packet> inline Packet
145pxor(const Packet& a, const Packet& b) { return a ^ b; }
146
147/** \internal \returns the bitwise andnot of \a a and \a b */
148template<typename Packet> inline Packet
149pandnot(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 */
152template<typename Packet> inline Packet
153pload(const typename unpacket_traits<Packet>::type* from) { return *from; }
154
155/** \internal \returns a packet version of \a *from, (un-aligned load) */
156template<typename Packet> inline Packet
157ploadu(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 */
164template<typename Packet> inline Packet
165ploaddup(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) */
168template<typename Packet> inline Packet
169pset1(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). */
172template<typename Scalar> inline typename packet_traits<Scalar>::type
173plset(const Scalar& a) { return a; }
174
175/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
176template<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) */
180template<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 */
184template<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 */
192template<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] */
196template<typename Packet> inline Packet
197preduxp(const Packet* vecs) { return vecs[0]; }
198
199/** \internal \returns the sum of the elements of \a a*/
200template<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*/
204template<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*/
208template<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*/
212template<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*/
216template<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) */
221template<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) */
234template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
235Packet psin(const Packet& a) { using std::sin; return sin(a); }
236
237/** \internal \returns the cosine of \a a (coeff-wise) */
238template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
239Packet pcos(const Packet& a) { using std::cos; return cos(a); }
240
241/** \internal \returns the tan of \a a (coeff-wise) */
242template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
243Packet ptan(const Packet& a) { using std::tan; return tan(a); }
244
245/** \internal \returns the arc sine of \a a (coeff-wise) */
246template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
247Packet pasin(const Packet& a) { using std::asin; return asin(a); }
248
249/** \internal \returns the arc cosine of \a a (coeff-wise) */
250template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
251Packet pacos(const Packet& a) { using std::acos; return acos(a); }
252
253/** \internal \returns the exp of \a a (coeff-wise) */
254template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
255Packet pexp(const Packet& a) { using std::exp; return exp(a); }
256
257/** \internal \returns the log of \a a (coeff-wise) */
258template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
259Packet plog(const Packet& a) { using std::log; return log(a); }
260
261/** \internal \returns the square-root of \a a (coeff-wise) */
262template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
263Packet 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)
271template<typename Packet>
272inline 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) */
278template<typename Packet> inline Packet
279pmadd(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 */
286template<typename Packet, int LoadMode>
287inline 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 */
297template<typename Scalar, typename Packet, int LoadMode>
298inline 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 */
307template<int Offset,typename PacketType>
308struct 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  */
329template<int Offset,typename PacketType>
330inline 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
339template<> 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
342template<> 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