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_Packet2d(NAME,X) \
52   const Packet2d p2d_##NAME = pset1<Packet2d>(X)
53 
54 #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
55   const Packet4f p4f_##NAME = _mm_castsi128_ps(pset1<Packet4i>(X))
56 
57 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
58   const Packet4i p4i_##NAME = pset1<Packet4i>(X)
59 
60 
61 template<> struct packet_traits<float>  : default_packet_traits
62 {
63   typedef Packet4f type;
64   enum {
65     Vectorizable = 1,
66     AlignedOnScalar = 1,
67     size=4,
68 
69     HasDiv  = 1,
70     HasSin  = EIGEN_FAST_MATH,
71     HasCos  = EIGEN_FAST_MATH,
72     HasLog  = 1,
73     HasExp  = 1,
74     HasSqrt = 1
75   };
76 };
77 template<> struct packet_traits<double> : default_packet_traits
78 {
79   typedef Packet2d type;
80   enum {
81     Vectorizable = 1,
82     AlignedOnScalar = 1,
83     size=2,
84 
85     HasDiv  = 1,
86     HasExp  = 1,
87     HasSqrt = 1
88   };
89 };
90 template<> struct packet_traits<int>    : default_packet_traits
91 {
92   typedef Packet4i type;
93   enum {
94     // FIXME check the Has*
95     Vectorizable = 1,
96     AlignedOnScalar = 1,
97     size=4
98   };
99 };
100 
101 template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4}; };
102 template<> struct unpacket_traits<Packet2d> { typedef double type; enum {size=2}; };
103 template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4}; };
104 
105 #if defined(_MSC_VER) && (_MSC_VER==1500)
106 // Workaround MSVC 9 internal compiler error.
107 // TODO: It has been detected with win64 builds (amd64), so let's check whether it also happens in 32bits+SSE mode
108 // TODO: let's check whether there does not exist a better fix, like adding a pset0() function. (it crashed on pset1(0)).
109 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return _mm_set_ps(from,from,from,from); }
110 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set_pd(from,from); }
111 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set_epi32(from,from,from,from); }
112 #else
113 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return _mm_set1_ps(from); }
114 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double& from) { return _mm_set1_pd(from); }
115 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from) { return _mm_set1_epi32(from); }
116 #endif
117 
118 template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) { return _mm_add_ps(pset1<Packet4f>(a), _mm_set_ps(3,2,1,0)); }
119 template<> EIGEN_STRONG_INLINE Packet2d plset<double>(const double& a) { return _mm_add_pd(pset1<Packet2d>(a),_mm_set_pd(1,0)); }
120 template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a) { return _mm_add_epi32(pset1<Packet4i>(a),_mm_set_epi32(3,2,1,0)); }
121 
122 template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_add_ps(a,b); }
123 template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_add_pd(a,b); }
124 template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_add_epi32(a,b); }
125 
126 template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_sub_ps(a,b); }
127 template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_sub_pd(a,b); }
128 template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_sub_epi32(a,b); }
129 
130 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a)
131 {
132   const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x80000000,0x80000000,0x80000000,0x80000000));
133   return _mm_xor_ps(a,mask);
134 }
135 template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a)
136 {
137   const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0x0,0x80000000,0x0,0x80000000));
138   return _mm_xor_pd(a,mask);
139 }
140 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a)
141 {
142   return psub(_mm_setr_epi32(0,0,0,0), a);
143 }
144 
145 template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
146 template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
147 template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
148 
149 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_mul_ps(a,b); }
150 template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_mul_pd(a,b); }
151 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
152 {
153 #ifdef EIGEN_VECTORIZE_SSE4_1
154   return _mm_mullo_epi32(a,b);
155 #else
156   // this version is slightly faster than 4 scalar products
157   return vec4i_swizzle1(
158             vec4i_swizzle2(
159               _mm_mul_epu32(a,b),
160               _mm_mul_epu32(vec4i_swizzle1(a,1,0,3,2),
161                             vec4i_swizzle1(b,1,0,3,2)),
162               0,2,0,2),
163             0,2,1,3);
164 #endif
165 }
166 
167 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_div_ps(a,b); }
168 template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_div_pd(a,b); }
169 template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
170 { eigen_assert(false && "packet integer division are not supported by SSE");
171   return pset1<Packet4i>(0);
172 }
173 
174 // for some weird raisons, it has to be overloaded for packet of integers
175 template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
176 
177 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_min_ps(a,b); }
178 template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_min_pd(a,b); }
179 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b)
180 {
181 #ifdef EIGEN_VECTORIZE_SSE4_1
182   return _mm_min_epi32(a,b);
183 #else
184   // after some bench, this version *is* faster than a scalar implementation
185   Packet4i mask = _mm_cmplt_epi32(a,b);
186   return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
187 #endif
188 }
189 
190 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_max_ps(a,b); }
191 template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_max_pd(a,b); }
192 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b)
193 {
194 #ifdef EIGEN_VECTORIZE_SSE4_1
195   return _mm_max_epi32(a,b);
196 #else
197   // after some bench, this version *is* faster than a scalar implementation
198   Packet4i mask = _mm_cmpgt_epi32(a,b);
199   return _mm_or_si128(_mm_and_si128(mask,a),_mm_andnot_si128(mask,b));
200 #endif
201 }
202 
203 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_and_ps(a,b); }
204 template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_and_pd(a,b); }
205 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_and_si128(a,b); }
206 
207 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_or_ps(a,b); }
208 template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_or_pd(a,b); }
209 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_or_si128(a,b); }
210 
211 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_xor_ps(a,b); }
212 template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_xor_pd(a,b); }
213 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_xor_si128(a,b); }
214 
215 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return _mm_andnot_ps(a,b); }
216 template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b) { return _mm_andnot_pd(a,b); }
217 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return _mm_andnot_si128(a,b); }
218 
219 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*   from) {
220   EIGEN_DEBUG_ALIGNED_LOAD
221 #ifdef EIGEN_ANDROID_SSE_WR
222 // Workaround for X86 on Android crash on aligned operation.
223   return _mm_loadu_ps(from);
224 #else
225   return _mm_load_ps(from);
226 #endif
227   }
228 template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double*  from) {
229   EIGEN_DEBUG_ALIGNED_LOAD
230 #ifdef EIGEN_ANDROID_SSE_WR
231 // Workaround for X86 on Android crash on aligned operation.
232   return _mm_loadu_pd(from);
233 #else
234   return _mm_load_pd(from);
235 #endif
236   }
237 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) {
238   EIGEN_DEBUG_ALIGNED_LOAD
239 #ifdef EIGEN_ANDROID_SSE_WR
240 // Workaround for X86 on Android crash on aligned operation.
241   return _mm_loadu_si128(reinterpret_cast<const Packet4i*>(from));
242 #else
243   return _mm_load_si128(reinterpret_cast<const Packet4i*>(from));
244 #endif
245   }
246 
247 #if defined(_MSC_VER)
248   template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float*  from) {
249     EIGEN_DEBUG_UNALIGNED_LOAD
250     #if (_MSC_VER==1600)
251     // NOTE Some version of MSVC10 generates bad code when using _mm_loadu_ps
252     // (i.e., it does not generate an unaligned load!!
253     // TODO On most architectures this version should also be faster than a single _mm_loadu_ps
254     // so we could also enable it for MSVC08 but first we have to make this later does not generate crap when doing so...
255     __m128 res = _mm_loadl_pi(_mm_set1_ps(0.0f), (const __m64*)(from));
256     res = _mm_loadh_pi(res, (const __m64*)(from+2));
257     return res;
258     #else
259     return _mm_loadu_ps(from);
260     #endif
261   }
262   template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_pd(from); }
263   template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int*    from) { EIGEN_DEBUG_UNALIGNED_LOAD return _mm_loadu_si128(reinterpret_cast<const Packet4i*>(from)); }
264 #else
265 // Fast unaligned loads. Note that here we cannot directly use intrinsics: this would
266 // require pointer casting to incompatible pointer types and leads to invalid code
267 // because of the strict aliasing rule. The "dummy" stuff are required to enforce
268 // a correct instruction dependency.
269 // TODO: do the same for MSVC (ICC is compatible)
270 // NOTE: with the code below, MSVC's compiler crashes!
271 
272 #if defined(__GNUC__) && defined(__i386__)
273   // bug 195: gcc/i386 emits weird x87 fldl/fstpl instructions for _mm_load_sd
274   #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
275 #elif defined(__clang__)
276   // bug 201: Segfaults in __mm_loadh_pd with clang 2.8
277   #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 1
278 #else
279   #define EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS 0
280 #endif
281 
282 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
283 {
284   EIGEN_DEBUG_UNALIGNED_LOAD
285 #if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
286   return _mm_loadu_ps(from);
287 #else
288   __m128d res;
289 #ifdef EIGEN_ANDROID_SSE_WR
290 // Workaround for X86 on Android crash on aligned operation.
291   res =  _mm_loadu_sd((const double*)(from)) ;
292 #else
293   res =  _mm_load_sd((const double*)(from)) ;
294 #endif
295   res =  _mm_loadh_pd(res, (const double*)(from+2)) ;
296   return _mm_castpd_ps(res);
297 #endif
298 }
299 template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from)
300 {
301   EIGEN_DEBUG_UNALIGNED_LOAD
302 #if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
303   return _mm_loadu_pd(from);
304 #else
305   __m128d res;
306 #ifdef EIGEN_ANDROID_SSE_WR
307 // Workaround for X86 on Android crash on aligned operation.
308   res = _mm_loadu_sd(from) ;
309 #else
310   res = _mm_load_sd(from) ;
311 #endif
312   res = _mm_loadh_pd(res,from+1);
313   return res;
314 #endif
315 }
316 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
317 {
318   EIGEN_DEBUG_UNALIGNED_LOAD
319 #if EIGEN_AVOID_CUSTOM_UNALIGNED_LOADS
320   return _mm_loadu_si128(reinterpret_cast<const Packet4i*>(from));
321 #else
322   __m128d res;
323 #ifdef EIGEN_ANDROID_SSE_WR
324 // Workaround for X86 on Android crash on aligned operation.
325   res =  _mm_loadu_sd((const double*)(from)) ;
326 #else
327   res =  _mm_load_sd((const double*)(from)) ;
328 #endif
329   res =  _mm_loadh_pd(res, (const double*)(from+2)) ;
330   return _mm_castpd_si128(res);
331 #endif
332 }
333 #endif
334 
335 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
336 {
337   return vec4f_swizzle1(_mm_castpd_ps(_mm_load_sd(reinterpret_cast<const double*>(from))), 0, 0, 1, 1);
338 }
339 template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*  from)
340 { return pset1<Packet2d>(from[0]); }
341 template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
342 {
343   Packet4i tmp;
344   tmp = _mm_loadl_epi64(reinterpret_cast<const Packet4i*>(from));
345   return vec4i_swizzle1(tmp, 0, 0, 1, 1);
346 }
347 
348 template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) {
349   EIGEN_DEBUG_ALIGNED_STORE
350 #ifdef EIGEN_ANDROID_SSE_WR
351 // Workaround for X86 on Android crash on aligned operation.
352   _mm_storeu_ps(to, from);
353 #else
354   _mm_store_ps(to, from);
355 #endif
356   }
357 template<> EIGEN_STRONG_INLINE void pstore<double>(double* to, const Packet2d& from) {
358   EIGEN_DEBUG_ALIGNED_STORE
359 #ifdef EIGEN_ANDROID_SSE_WR
360 // Workaround for X86 on Android crash on aligned operation.
361   _mm_storeu_pd(to, from);
362 #else
363   _mm_store_pd(to, from);
364 #endif
365   }
366 template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) {
367   EIGEN_DEBUG_ALIGNED_STORE
368 #ifdef EIGEN_ANDROID_SSE_WR
369 // Workaround for X86 on Android crash on aligned operation.
370   _mm_storeu_si128(reinterpret_cast<Packet4i*>(to), from);
371 #else
372   _mm_store_si128(reinterpret_cast<Packet4i*>(to), from);
373 #endif
374   }
375 
376 template<> EIGEN_STRONG_INLINE void pstoreu<double>(double* to, const Packet2d& from) {
377   EIGEN_DEBUG_UNALIGNED_STORE
378   _mm_storel_pd((to), from);
379   _mm_storeh_pd((to+1), from);
380 }
381 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)); }
382 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)); }
383 
384 // some compilers might be tempted to perform multiple moves instead of using a vector path.
385 template<> EIGEN_STRONG_INLINE void pstore1<Packet4f>(float* to, const float& a)
386 {
387   Packet4f pa = _mm_set_ss(a);
388   pstore(to, vec4f_swizzle1(pa,0,0,0,0));
389 }
390 // some compilers might be tempted to perform multiple moves instead of using a vector path.
391 template<> EIGEN_STRONG_INLINE void pstore1<Packet2d>(double* to, const double& a)
392 {
393   Packet2d pa = _mm_set_sd(a);
394   pstore(to, vec2d_swizzle1(pa,0,0));
395 }
396 
397 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float*   addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
398 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
399 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*       addr) { _mm_prefetch((const char*)(addr), _MM_HINT_T0); }
400 
401 #if defined(_MSC_VER) && defined(_WIN64) && !defined(__INTEL_COMPILER)
402 // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
403 // Direct of the struct members fixed bug #62.
404 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { return a.m128_f32[0]; }
405 template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return a.m128d_f64[0]; }
406 template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
407 #elif defined(_MSC_VER) && !defined(__INTEL_COMPILER)
408 // The temporary variable fixes an internal compilation error in vs <= 2008 and a wrong-result bug in vs 2010
409 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float x = _mm_cvtss_f32(a); return x; }
410 template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { double x = _mm_cvtsd_f64(a); return x; }
411 template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int x = _mm_cvtsi128_si32(a); return x; }
412 #else
413 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { return _mm_cvtss_f32(a); }
414 template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return _mm_cvtsd_f64(a); }
415 template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { return _mm_cvtsi128_si32(a); }
416 #endif
417 
418 template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a)
419 { return _mm_shuffle_ps(a,a,0x1B); }
420 template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a)
421 { return _mm_shuffle_pd(a,a,0x1); }
422 template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a)
423 { return _mm_shuffle_epi32(a,0x1B); }
424 
425 
426 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a)
427 {
428   const Packet4f mask = _mm_castsi128_ps(_mm_setr_epi32(0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF,0x7FFFFFFF));
429   return _mm_and_ps(a,mask);
430 }
431 template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a)
432 {
433   const Packet2d mask = _mm_castsi128_pd(_mm_setr_epi32(0xFFFFFFFF,0x7FFFFFFF,0xFFFFFFFF,0x7FFFFFFF));
434   return _mm_and_pd(a,mask);
435 }
436 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a)
437 {
438   #ifdef EIGEN_VECTORIZE_SSSE3
439   return _mm_abs_epi32(a);
440   #else
441   Packet4i aux = _mm_srai_epi32(a,31);
442   return _mm_sub_epi32(_mm_xor_si128(a,aux),aux);
443   #endif
444 }
445 
446 EIGEN_STRONG_INLINE void punpackp(Packet4f* vecs)
447 {
448   vecs[1] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x55));
449   vecs[2] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xAA));
450   vecs[3] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0xFF));
451   vecs[0] = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(vecs[0]), 0x00));
452 }
453 
454 #ifdef EIGEN_VECTORIZE_SSE3
455 // TODO implement SSE2 versions as well as integer versions
456 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
457 {
458   return _mm_hadd_ps(_mm_hadd_ps(vecs[0], vecs[1]),_mm_hadd_ps(vecs[2], vecs[3]));
459 }
460 template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
461 {
462   return _mm_hadd_pd(vecs[0], vecs[1]);
463 }
464 // SSSE3 version:
465 // EIGEN_STRONG_INLINE Packet4i preduxp(const Packet4i* vecs)
466 // {
467 //   return _mm_hadd_epi32(_mm_hadd_epi32(vecs[0], vecs[1]),_mm_hadd_epi32(vecs[2], vecs[3]));
468 // }
469 
470 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
471 {
472   Packet4f tmp0 = _mm_hadd_ps(a,a);
473   return pfirst(_mm_hadd_ps(tmp0, tmp0));
474 }
475 
476 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { return pfirst(_mm_hadd_pd(a, a)); }
477 
478 // SSSE3 version:
479 // EIGEN_STRONG_INLINE float predux(const Packet4i& a)
480 // {
481 //   Packet4i tmp0 = _mm_hadd_epi32(a,a);
482 //   return pfirst(_mm_hadd_epi32(tmp0, tmp0));
483 // }
484 #else
485 // SSE2 versions
486 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
487 {
488   Packet4f tmp = _mm_add_ps(a, _mm_movehl_ps(a,a));
489   return pfirst(_mm_add_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
490 }
491 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a)
492 {
493   return pfirst(_mm_add_sd(a, _mm_unpackhi_pd(a,a)));
494 }
495 
496 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
497 {
498   Packet4f tmp0, tmp1, tmp2;
499   tmp0 = _mm_unpacklo_ps(vecs[0], vecs[1]);
500   tmp1 = _mm_unpackhi_ps(vecs[0], vecs[1]);
501   tmp2 = _mm_unpackhi_ps(vecs[2], vecs[3]);
502   tmp0 = _mm_add_ps(tmp0, tmp1);
503   tmp1 = _mm_unpacklo_ps(vecs[2], vecs[3]);
504   tmp1 = _mm_add_ps(tmp1, tmp2);
505   tmp2 = _mm_movehl_ps(tmp1, tmp0);
506   tmp0 = _mm_movelh_ps(tmp0, tmp1);
507   return _mm_add_ps(tmp0, tmp2);
508 }
509 
510 template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
511 {
512   return _mm_add_pd(_mm_unpacklo_pd(vecs[0], vecs[1]), _mm_unpackhi_pd(vecs[0], vecs[1]));
513 }
514 #endif  // SSE3
515 
516 template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
517 {
518   Packet4i tmp = _mm_add_epi32(a, _mm_unpackhi_epi64(a,a));
519   return pfirst(tmp) + pfirst(_mm_shuffle_epi32(tmp, 1));
520 }
521 
522 template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
523 {
524   Packet4i tmp0, tmp1, tmp2;
525   tmp0 = _mm_unpacklo_epi32(vecs[0], vecs[1]);
526   tmp1 = _mm_unpackhi_epi32(vecs[0], vecs[1]);
527   tmp2 = _mm_unpackhi_epi32(vecs[2], vecs[3]);
528   tmp0 = _mm_add_epi32(tmp0, tmp1);
529   tmp1 = _mm_unpacklo_epi32(vecs[2], vecs[3]);
530   tmp1 = _mm_add_epi32(tmp1, tmp2);
531   tmp2 = _mm_unpacklo_epi64(tmp0, tmp1);
532   tmp0 = _mm_unpackhi_epi64(tmp0, tmp1);
533   return _mm_add_epi32(tmp0, tmp2);
534 }
535 
536 // Other reduction functions:
537 
538 // mul
539 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
540 {
541   Packet4f tmp = _mm_mul_ps(a, _mm_movehl_ps(a,a));
542   return pfirst(_mm_mul_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
543 }
544 template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a)
545 {
546   return pfirst(_mm_mul_sd(a, _mm_unpackhi_pd(a,a)));
547 }
548 template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
549 {
550   // after some experiments, it is seems this is the fastest way to implement it
551   // for GCC (eg., reusing pmul is very slow !)
552   // TODO try to call _mm_mul_epu32 directly
553   EIGEN_ALIGN16 int aux[4];
554   pstore(aux, a);
555   return  (aux[0] * aux[1]) * (aux[2] * aux[3]);;
556 }
557 
558 // min
559 template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
560 {
561   Packet4f tmp = _mm_min_ps(a, _mm_movehl_ps(a,a));
562   return pfirst(_mm_min_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
563 }
564 template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a)
565 {
566   return pfirst(_mm_min_sd(a, _mm_unpackhi_pd(a,a)));
567 }
568 template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
569 {
570   // after some experiments, it is seems this is the fastest way to implement it
571   // for GCC (eg., it does not like using std::min after the pstore !!)
572   EIGEN_ALIGN16 int aux[4];
573   pstore(aux, a);
574   int aux0 = aux[0]<aux[1] ? aux[0] : aux[1];
575   int aux2 = aux[2]<aux[3] ? aux[2] : aux[3];
576   return aux0<aux2 ? aux0 : aux2;
577 }
578 
579 // max
580 template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
581 {
582   Packet4f tmp = _mm_max_ps(a, _mm_movehl_ps(a,a));
583   return pfirst(_mm_max_ss(tmp, _mm_shuffle_ps(tmp,tmp, 1)));
584 }
585 template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a)
586 {
587   return pfirst(_mm_max_sd(a, _mm_unpackhi_pd(a,a)));
588 }
589 template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
590 {
591   // after some experiments, it is seems this is the fastest way to implement it
592   // for GCC (eg., it does not like using std::min after the pstore !!)
593   EIGEN_ALIGN16 int aux[4];
594   pstore(aux, a);
595   int aux0 = aux[0]>aux[1] ? aux[0] : aux[1];
596   int aux2 = aux[2]>aux[3] ? aux[2] : aux[3];
597   return aux0>aux2 ? aux0 : aux2;
598 }
599 
600 #if (defined __GNUC__)
601 // template <> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f&  a, const Packet4f&  b, const Packet4f&  c)
602 // {
603 //   Packet4f res = b;
604 //   asm("mulps %[a], %[b] \n\taddps %[c], %[b]" : [b] "+x" (res) : [a] "x" (a), [c] "x" (c));
605 //   return res;
606 // }
607 // EIGEN_STRONG_INLINE Packet4i _mm_alignr_epi8(const Packet4i&  a, const Packet4i&  b, const int i)
608 // {
609 //   Packet4i res = a;
610 //   asm("palignr %[i], %[a], %[b] " : [b] "+x" (res) : [a] "x" (a), [i] "i" (i));
611 //   return res;
612 // }
613 #endif
614 
615 #ifdef EIGEN_VECTORIZE_SSSE3
616 // SSSE3 versions
617 template<int Offset>
618 struct palign_impl<Offset,Packet4f>
619 {
620   static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
621   {
622     if (Offset!=0)
623       first = _mm_castsi128_ps(_mm_alignr_epi8(_mm_castps_si128(second), _mm_castps_si128(first), Offset*4));
624   }
625 };
626 
627 template<int Offset>
628 struct palign_impl<Offset,Packet4i>
629 {
630   static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
631   {
632     if (Offset!=0)
633       first = _mm_alignr_epi8(second,first, Offset*4);
634   }
635 };
636 
637 template<int Offset>
638 struct palign_impl<Offset,Packet2d>
639 {
640   static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
641   {
642     if (Offset==1)
643       first = _mm_castsi128_pd(_mm_alignr_epi8(_mm_castpd_si128(second), _mm_castpd_si128(first), 8));
644   }
645 };
646 #else
647 // SSE2 versions
648 template<int Offset>
649 struct palign_impl<Offset,Packet4f>
650 {
651   static EIGEN_STRONG_INLINE void run(Packet4f& first, const Packet4f& second)
652   {
653     if (Offset==1)
654     {
655       first = _mm_move_ss(first,second);
656       first = _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(first),0x39));
657     }
658     else if (Offset==2)
659     {
660       first = _mm_movehl_ps(first,first);
661       first = _mm_movelh_ps(first,second);
662     }
663     else if (Offset==3)
664     {
665       first = _mm_move_ss(first,second);
666       first = _mm_shuffle_ps(first,second,0x93);
667     }
668   }
669 };
670 
671 template<int Offset>
672 struct palign_impl<Offset,Packet4i>
673 {
674   static EIGEN_STRONG_INLINE void run(Packet4i& first, const Packet4i& second)
675   {
676     if (Offset==1)
677     {
678       first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
679       first = _mm_shuffle_epi32(first,0x39);
680     }
681     else if (Offset==2)
682     {
683       first = _mm_castps_si128(_mm_movehl_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(first)));
684       first = _mm_castps_si128(_mm_movelh_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
685     }
686     else if (Offset==3)
687     {
688       first = _mm_castps_si128(_mm_move_ss(_mm_castsi128_ps(first),_mm_castsi128_ps(second)));
689       first = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(first),_mm_castsi128_ps(second),0x93));
690     }
691   }
692 };
693 
694 template<int Offset>
695 struct palign_impl<Offset,Packet2d>
696 {
697   static EIGEN_STRONG_INLINE void run(Packet2d& first, const Packet2d& second)
698   {
699     if (Offset==1)
700     {
701       first = _mm_castps_pd(_mm_movehl_ps(_mm_castpd_ps(first),_mm_castpd_ps(first)));
702       first = _mm_castps_pd(_mm_movelh_ps(_mm_castpd_ps(first),_mm_castpd_ps(second)));
703     }
704   }
705 };
706 #endif
707 
708 } // end namespace internal
709 
710 } // end namespace Eigen
711 
712 #endif // EIGEN_PACKET_MATH_SSE_H
713