SSE/PacketMath.h
1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #ifndef EIGEN_PACKET_MATH_SSE_H
11 #define EIGEN_PACKET_MATH_SSE_H
12 
13 namespace Eigen {
14 
15 namespace internal {
16 
17 #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
18 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
19 #endif
20 
21 #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
22 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS (2*sizeof(void*))
23 #endif
24 
25 typedef __m128 Packet4f;
26 typedef __m128i Packet4i;
27 typedef __m128d Packet2d;
28 
29 template<> struct is_arithmetic<__m128> { enum { value = true }; };
30 template<> struct is_arithmetic<__m128i> { enum { value = true }; };
31 template<> struct is_arithmetic<__m128d> { enum { value = true }; };
32 
33 #define vec4f_swizzle1(v,p,q,r,s) \
34  (_mm_castsi128_ps(_mm_shuffle_epi32( _mm_castps_si128(v), ((s)<<6|(r)<<4|(q)<<2|(p)))))
35 
36 #define vec4i_swizzle1(v,p,q,r,s) \
37  (_mm_shuffle_epi32( v, ((s)<<6|(r)<<4|(q)<<2|(p))))
38 
39 #define vec2d_swizzle1(v,p,q) \
40  (_mm_castsi128_pd(_mm_shuffle_epi32( _mm_castpd_si128(v), ((q*2+1)<<6|(q*2)<<4|(p*2+1)<<2|(p*2)))))
41 
42 #define vec4f_swizzle2(a,b,p,q,r,s) \
43  (_mm_shuffle_ps( (a), (b), ((s)<<6|(r)<<4|(q)<<2|(p))))
44 
45 #define vec4i_swizzle2(a,b,p,q,r,s) \
46  (_mm_castps_si128( (_mm_shuffle_ps( _mm_castsi128_ps(a), _mm_castsi128_ps(b), ((s)<<6|(r)<<4|(q)<<2|(p))))))
47 
48 #define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
49  const Packet4f p4f_##NAME = pset1<Packet4f>(X)
50 
51 #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
52  const Packet4f p4f_##NAME = _mm_castsi128_ps(pset1<Packet4i>(X))
53 
54 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
55  const Packet4i p4i_##NAME = pset1<Packet4i>(X)
56 
57 
58 template<> struct packet_traits<float> : default_packet_traits
59 {
60  typedef Packet4f type;
61  enum {
62  Vectorizable = 1,
63  AlignedOnScalar = 1,
64  size=4,
65 
66  HasDiv = 1,
67  HasSin = EIGEN_FAST_MATH,
68  HasCos = EIGEN_FAST_MATH,
69  HasLog = 1,
70  HasExp = 1,
71  HasSqrt = 1
72  };
73 };
74 template<> struct packet_traits<double> : default_packet_traits
75 {
76  typedef Packet2d type;
77  enum {
78  Vectorizable = 1,
79  AlignedOnScalar = 1,
80  size=2,
81 
82  HasDiv = 1
83  };
84 };
85 template<> struct packet_traits<int> : default_packet_traits
86 {
87  typedef Packet4i type;
88  enum {
89  // FIXME check the Has*
90  Vectorizable = 1,
91  AlignedOnScalar = 1,
92  size=4
93  };
94 };
95 
96 template<> struct unpacket_traits<Packet4f> { typedef float type; enum {size=4}; };
97 template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2}; };
98 template<> struct unpacket_traits<Packet4i> { typedef int type; enum {size=4}; };
99 
100 #if defined(_MSC_VER) && (_MSC_VER==1500)
101 // Workaround MSVC 9 internal compiler error.
102 // TODO: It has been detected with win64 builds (amd64), so let's check whether it also happens in 32bits+SSE mode
103 // TODO: let's check whether there does not exist a better fix, like adding a pset0() function. (it crashed on pset1(0)).
104 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return _mm_set_ps(from,from,from,from); }
105 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set_pd(from,from); }
106 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return _mm_set_epi32(from,from,from,from); }
107 #else
108 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return _mm_set1_ps(from); }
109 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }
110 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return _mm_set1_epi32(from); }
111 #endif
112 
113 template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3,2,1,0)); }
114 template<> EIGEN_STRONG_INLINE Packet2d plset<double>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a),_mm_set_pd(1,0)); }
115 template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a) { return _mm_add_epi32(pset1<Packet4i>(a),_mm_set_epi32(3,2,1,0)); }
116 
117 template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a,b); }
118 template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a,b); }
119 template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a,b); }
120 
121 template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a,b); }
122 template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a,b); }
123 template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a,b); }
124 
125 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
126 {
127  const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
128  return _mm_xor_ps(a,mask);
129 }
130 template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)
131 {
132  const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x80000000));
133  return _mm_xor_pd(a,mask);
134 }
135 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)
136 {
137  return psub(_mm_setr_epi32(0,0,0,0), a);
138 }
139 
140 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }
141 template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }
142 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
143 {
144 #ifdef EIGEN_VECTORIZE_SSE4_1
145  return _mm_mullo_epi32(a,b);
146 #else
147  // this version is slightly faster than 4 scalar products
148  return vec4i_swizzle1(
149  vec4i_swizzle2(
150  _mm_mul_epu32(a,b),
151  _mm_mul_epu32(vec4i_swizzle1(a,1,0,3,2),
152  vec4i_swizzle1(b,1,0,3,2)),
153  0,2,0,2),
154  0,2,1,3);
155 #endif
156 }
157 
158 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a,b); }
159 template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a,b); }
160 template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
161 { eigen_assert(false && "packet integer division are not supported by SSE");
162  return pset1<Packet4i>(0);
163 }
164 
165 // for some weird raisons, it has to be overloaded for packet of integers
166 template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
167 
168 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_min_ps(a,b); }
169 template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_min_pd(a,b); }
170 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
171 {
172  // after some bench, this version *is* faster than a scalar implementation
173  Packet4i mask = _mm_cmplt_epi32(a,b);
174  return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
175 }
176 
177 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_max_ps(a,b); }
178 template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_max_pd(a,b); }
179 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
180 {
181  // after some bench, this version *is* faster than a scalar implementation
182  Packet4i mask = _mm_cmpgt_epi32(a,b);
183  return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
184 }
185 
186 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
187 template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
188 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
189 
190 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
191 template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
192 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
193 
194 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
195 template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
196 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
197 
198 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(a,b); }
199 template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(a,b); }
200 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(a,b); }
201 
202 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_ps(from); }
203 template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_pd(from); }
204 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return _mm_load_si128(reinterpret_cast<const Packet4i*>(from)); }
205 
206 #if defined(_MSC_VER)
207  template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) {
208  EIGEN_DEBUG_UNALIGNED_LOAD
209  #if (_MSC_VER==1600)
210  // NOTE Some version of MSVC10 generates bad code when using _mm_loadu_ps
211  // (i.e., it does not generate an unaligned load!!
212  // TODO On most architectures this version should also be faster than a single _mm_loadu_ps
213  // so we could also enable it for MSVC08 but first we have to make this later does not generate crap when doing so...
214  __m128 res = _mm_loadl_pi(_mm_set1_ps(0.0f), (const __m64*)(from));
215  res = _mm_loadh_pi(res, (const __m64*)(from+2));
216  return res;
217  #else
218  return _mm_loadu_ps(from);
219  #endif
220  }
221  template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_pd(from); }
222  template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_si128(reinterpret_cast<const Packet4i*>(from)); }
223 #else
224 // Fast unaligned loads. Note that here we cannot directly use intrinsics: this would
225 // require pointer casting to incompatible pointer types and leads to invalid code
226 // because of the strict aliasing rule. The "dummy" stuff are required to enforce
227 // a correct instruction dependency.
228 // TODO: do the same for MSVC (ICC is compatible)
229 // NOTE: with the code below, MSVC's compiler crashes!
230 
231 #if defined(__GNUC__) && defined(__i386__)
232  // bug 195: gcc/i386 emits weird x87 fldl/fstpl instructions for _mm_load_sd
233  #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
234 #elif defined(__clang__)
235  // bug 201: Segfaults in __mm_loadh_pd with clang 2.8
236  #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
237 #else
238  #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 0
239 #endif
240 
241 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
242 {
243  EIGEN_DEBUG_UNALIGNED_LOAD
244 #if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
245  return _mm_loadu_ps(from);
246 #else
247  __m128d res;
248  res = _mm_load_sd((const double*)(from)) ;
249  res = _mm_loadh_pd(res, (const double*)(from+2)) ;
250  return _mm_castpd_ps(res);
251 #endif
252 }
253 template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
254 {
255  EIGEN_DEBUG_UNALIGNED_LOAD
256 #if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
257  return _mm_loadu_pd(from);
258 #else
259  __m128d res;
260  res = _mm_load_sd(from) ;
261  res = _mm_loadh_pd(res,from+1);
262  return res;
263 #endif
264 }
265 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
266 {
267  EIGEN_DEBUG_UNALIGNED_LOAD
268 #if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
269  return _mm_loadu_si128(reinterpret_cast<const Packet4i*>(from));
270 #else
271  __m128d res;
272  res = _mm_load_sd((const double*)(from)) ;
273  res = _mm_loadh_pd(res, (const double*)(from+2)) ;
274  return _mm_castpd_si128(res);
275 #endif
276 }
277 #endif
278 
279 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
280 {
281  return vec4f_swizzle1(_mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))), 0, 0, 1, 1);
282 }
283 template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double* from)
284 { return pset1<Packet2d>(from[0]); }
285 template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from)
286 {
287  Packet4i tmp;
288  tmp = _mm_loadl_epi64(reinterpret_cast<const Packet4i*>(from));
289  return vec4i_swizzle1(tmp, 0, 0, 1, 1);
290 }
291 
292 template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_ps(to, from); }
293 template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_pd(to, from); }
294 template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE _mm_store_si128(reinterpret_cast<Packet4i*>(to), from); }
295 
296 template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) {
297  EIGEN_DEBUG_UNALIGNED_STORE
298  _mm_storel_pd((to), from);
299  _mm_storeh_pd((to+1), from);
300 }
301 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<double*>(to), _mm_castps_pd(from)); }
302 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE pstoreu(reinterpret_cast<double*>(to), _mm_castsi128_pd(from)); }
303 
304 // some compilers might be tempted to perform multiple moves instead of using a vector path.
305 template<> EIGEN_STRONG_INLINE void pstore1<Packet4f>(float* to, const float& a)
306 {
307  Packet4f pa = _mm_set_ss(a);
308  pstore(to, vec4f_swizzle1(pa,0,0,0,0));
309 }
310 // some compilers might be tempted to perform multiple moves instead of using a vector path.
311 template<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double& a)
312 {
313  Packet2d pa = _mm_set_sd(a);
314  pstore(to, vec2d_swizzle1(pa,0,0));
315 }
316 
317 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
318 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
319 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
320 
321 #if defined(_MSC_VER) && defined(_WIN64) && !defined(__INTEL_COMPILER)
322 // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
323 // Direct of the struct members fixed bug #62.
324 template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }
325 template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }
326 template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
327 #elif defined(_MSC_VER) && !defined(__INTEL_COMPILER)
328 // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
329 template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }
330 template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }
331 template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
332 #else
333 template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }
334 template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }
335 template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }
336 #endif
337 
338 template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
339 { return _mm_shuffle_ps(a,a,0x1B); }
340 template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
341 { return _mm_shuffle_pd(a,a,0x1); }
342 template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
343 { return _mm_shuffle_epi32(a,0x1B); }
344 
345 
346 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a)
347 {
348  const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
349  return _mm_and_ps(a,mask);
350 }
351 template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a)
352 {
353  const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
354  return _mm_and_pd(a,mask);
355 }
356 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)
357 {
358  #ifdef EIGEN_VECTORIZE_SSSE3
359  return _mm_abs_epi32(a);
360  #else
361  Packet4i aux = _mm_srai_epi32(a,31);
362  return _mm_sub_epi32(_mm_xor_si128(a,aux),aux);
363  #endif
364 }
365 
366 EIGEN_STRONG_INLINE void punpackp(Packet4f* vecs)
367 {
368  vecs[1] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x55));
369  vecs[2] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xAA));
370  vecs[3] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xFF));
371  vecs[0] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x00));
372 }
373 
374 #ifdef EIGEN_VECTORIZE_SSE3
375 // TODO implement SSE2 versions as well as integer versions
376 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
377 {
378  return _mm_hadd_ps(_mm_hadd_ps(vecs[0], vecs[1]),_mm_hadd_ps(vecs[2], vecs[3]));
379 }
380 template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
381 {
382  return _mm_hadd_pd(vecs[0], vecs[1]);
383 }
384 // SSSE3 version:
385 // EIGEN_STRONG_INLINE Packet4i preduxp(const Packet4i* vecs)
386 // {
387 // return _mm_hadd_epi32(_mm_hadd_epi32(vecs[0], vecs[1]),_mm_hadd_epi32(vecs[2], vecs[3]));
388 // }
389 
390 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
391 {
392  Packet4f tmp0 = _mm_hadd_ps(a,a);
393  return pfirst(_mm_hadd_ps(tmp0, tmp0));
394 }
395 
396 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { return pfirst(_mm_hadd_pd(a, a)); }
397 
398 // SSSE3 version:
399 // EIGEN_STRONG_INLINE float predux(const Packet4i& a)
400 // {
401 // Packet4i tmp0 = _mm_hadd_epi32(a,a);
402 // return pfirst(_mm_hadd_epi32(tmp0, tmp0));
403 // }
404 #else
405 // SSE2 versions
406 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
407 {
408  Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a,a));
409  return pfirst(_mm_add_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
410 }
411 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
412 {
413  return pfirst(_mm_add_sd(a, _mm_unpackhi_pd(a,a)));
414 }
415 
416 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
417 {
418  Packet4f tmp0, tmp1, tmp2;
419  tmp0 = _mm_unpacklo_ps(vecs[0], vecs[1]);
420  tmp1 = _mm_unpackhi_ps(vecs[0], vecs[1]);
421  tmp2 = _mm_unpackhi_ps(vecs[2], vecs[3]);
422  tmp0 = _mm_add_ps(tmp0, tmp1);
423  tmp1 = _mm_unpacklo_ps(vecs[2], vecs[3]);
424  tmp1 = _mm_add_ps(tmp1, tmp2);
425  tmp2 = _mm_movehl_ps(tmp1, tmp0);
426  tmp0 = _mm_movelh_ps(tmp0, tmp1);
427  return _mm_add_ps(tmp0, tmp2);
428 }
429 
430 template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
431 {
432  return _mm_add_pd(_mm_unpacklo_pd(vecs[0], vecs[1]), _mm_unpackhi_pd(vecs[0], vecs[1]));
433 }
434 #endif // SSE3
435 
436 template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
437 {
438  Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a,a));
439  return pfirst(tmp) + pfirst(_mm_shuffle_epi32(tmp, 1));
440 }
441 
442 template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
443 {
444  Packet4i tmp0, tmp1, tmp2;
445  tmp0 = _mm_unpacklo_epi32(vecs[0], vecs[1]);
446  tmp1 = _mm_unpackhi_epi32(vecs[0], vecs[1]);
447  tmp2 = _mm_unpackhi_epi32(vecs[2], vecs[3]);
448  tmp0 = _mm_add_epi32(tmp0, tmp1);
449  tmp1 = _mm_unpacklo_epi32(vecs[2], vecs[3]);
450  tmp1 = _mm_add_epi32(tmp1, tmp2);
451  tmp2 = _mm_unpacklo_epi64(tmp0, tmp1);
452  tmp0 = _mm_unpackhi_epi64(tmp0, tmp1);
453  return _mm_add_epi32(tmp0, tmp2);
454 }
455 
456 // Other reduction functions:
457 
458 // mul
459 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
460 {
461  Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));
462  return pfirst(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
463 }
464 template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
465 {
466  return pfirst(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));
467 }
468 template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
469 {
470  // after some experiments, it is seems this is the fastest way to implement it
471  // for GCC (eg., reusing pmul is very slow !)
472  // TODO try to call _mm_mul_epu32 directly
473  EIGEN_ALIGN16 int aux[4];
474  pstore(aux, a);
475  return (aux[0] * aux[1]) * (aux[2] * aux[3]);;
476 }
477 
478 // min
479 template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
480 {
481  Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a,a));
482  return pfirst(_mm_min_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
483 }
484 template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
485 {
486  return pfirst(_mm_min_sd(a, _mm_unpackhi_pd(a,a)));
487 }
488 template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
489 {
490  // after some experiments, it is seems this is the fastest way to implement it
491  // for GCC (eg., it does not like using std::min after the pstore !!)
492  EIGEN_ALIGN16 int aux[4];
493  pstore(aux, a);
494  register int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
495  register int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
496  return aux0<aux2 ? aux0 : aux2;
497 }
498 
499 // max
500 template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
501 {
502  Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a,a));
503  return pfirst(_mm_max_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
504 }
505 template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
506 {
507  return pfirst(_mm_max_sd(a, _mm_unpackhi_pd(a,a)));
508 }
509 template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
510 {
511  // after some experiments, it is seems this is the fastest way to implement it
512  // for GCC (eg., it does not like using std::min after the pstore !!)
513  EIGEN_ALIGN16 int aux[4];
514  pstore(aux, a);
515  register int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
516  register int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
517  return aux0>aux2 ? aux0 : aux2;
518 }
519 
520 #if (defined __GNUC__)
521 // template <> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c)
522 // {
523 // Packet4f res = b;
524 // asm("mulps %[a], %[b] \n\taddps %[c], %[b]" : [b] "+x" (res) : [a] "x" (a), [c] "x" (c));
525 // return res;
526 // }
527 // EIGEN_STRONG_INLINE Packet4i _mm_alignr_epi8(const Packet4i& a, const Packet4i& b, const int i)
528 // {
529 // Packet4i res = a;
530 // asm("palignr %[i], %[a], %[b] " : [b] "+x" (res) : [a] "x" (a), [i] "i" (i));
531 // return res;
532 // }
533 #endif
534 
535 #ifdef EIGEN_VECTORIZE_SSSE3
536 // SSSE3 versions
537 template<int Offset>
538 struct palign_impl<Offset,Packet4f>
539 {
540  static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
541  {
542  if (Offset!=0)
543  first = _mm_castsi128_ps(_mm_alignr_epi8(_mm_castps_si128(second), _mm_castps_si128(first), Offset*4));
544  }
545 };
546 
547 template<int Offset>
548 struct palign_impl<Offset,Packet4i>
549 {
550  static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
551  {
552  if (Offset!=0)
553  first = _mm_alignr_epi8(second,first, Offset*4);
554  }
555 };
556 
557 template<int Offset>
558 struct palign_impl<Offset,Packet2d>
559 {
560  static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
561  {
562  if (Offset==1)
563  first = _mm_castsi128_pd(_mm_alignr_epi8(_mm_castpd_si128(second), _mm_castpd_si128(first), 8));
564  }
565 };
566 #else
567 // SSE2 versions
568 template<int Offset>
569 struct palign_impl<Offset,Packet4f>
570 {
571  static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
572  {
573  if (Offset==1)
574  {
575  first = _mm_move_ss(first,second);
576  first = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(first),0x39));
577  }
578  else if (Offset==2)
579  {
580  first = _mm_movehl_ps(first,first);
581  first = _mm_movelh_ps(first,second);
582  }
583  else if (Offset==3)
584  {
585  first = _mm_move_ss(first,second);
586  first = _mm_shuffle_ps(first,second,0x93);
587  }
588  }
589 };
590 
591 template<int Offset>
592 struct palign_impl<Offset,Packet4i>
593 {
594  static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
595  {
596  if (Offset==1)
597  {
598  first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
599  first = _mm_shuffle_epi32(first,0x39);
600  }
601  else if (Offset==2)
602  {
603  first = _mm_castps_si128(_mm_movehl_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(first)));
604  first = _mm_castps_si128(_mm_movelh_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
605  }
606  else if (Offset==3)
607  {
608  first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
609  first = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second),0x93));
610  }
611  }
612 };
613 
614 template<int Offset>
615 struct palign_impl<Offset,Packet2d>
616 {
617  static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
618  {
619  if (Offset==1)
620  {
621  first = _mm_castps_pd(_mm_movehl_ps(_mm_castpd_ps(first),_mm_castpd_ps(first)));
622  first = _mm_castps_pd(_mm_movelh_ps(_mm_castpd_ps(first),_mm_castpd_ps(second)));
623  }
624  }
625 };
626 #endif
627 
628 } // end namespace internal
629 
630 } // end namespace Eigen
631 
632 #endif // EIGEN_PACKET_MATH_SSE_H