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 // Copyright (C) 2010 Konstantinos Margaritis <markos@freevec.org>
6 // Heavily based on Gael's SSE version.
7 //
8 // This Source Code Form is subject to the terms of the Mozilla
9 // Public License v. 2.0. If a copy of the MPL was not distributed
10 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11 
12 #ifndef EIGEN_PACKET_MATH_NEON_H
13 #define EIGEN_PACKET_MATH_NEON_H
14 
15 namespace Eigen {
16 
17 namespace internal {
18 
19 #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
20 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
21 #endif
22 
23 #ifndef EIGEN_HAS_SINGLE_INSTRUCTION_MADD
24 #define EIGEN_HAS_SINGLE_INSTRUCTION_MADD
25 #endif
26 
27 #ifndef EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD
28 #define EIGEN_HAS_SINGLE_INSTRUCTION_CJMADD
29 #endif
30 
31 #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
32 #if EIGEN_ARCH_ARM64
33 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 32
34 #else
35 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16
36 #endif
37 #endif
38 
39 typedef float32x2_t Packet2f;
40 typedef float32x4_t Packet4f;
41 typedef int32x4_t   Packet4i;
42 typedef int32x2_t   Packet2i;
43 typedef uint32x4_t  Packet4ui;
44 
45 #define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
46   const Packet4f p4f_##NAME = pset1<Packet4f>(X)
47 
48 #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
49   const Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int32_t>(X))
50 
51 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
52   const Packet4i p4i_##NAME = pset1<Packet4i>(X)
53 
54 #if EIGEN_ARCH_ARM64
55   // __builtin_prefetch tends to do nothing on ARM64 compilers because the
56   // prefetch instructions there are too detailed for __builtin_prefetch to map
57   // meaningfully to them.
58   #define EIGEN_ARM_PREFETCH(ADDR)  __asm__ __volatile__("prfm pldl1keep, [%[addr]]\n" ::[addr] "r"(ADDR) : );
59 #elif EIGEN_HAS_BUILTIN(__builtin_prefetch) || EIGEN_COMP_GNUC
60   #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
61 #elif defined __pld
62   #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
63 #elif EIGEN_ARCH_ARM32
64   #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ("pld [%[addr]]\n" :: [addr] "r" (ADDR) : );
65 #else
66   // by default no explicit prefetching
67   #define EIGEN_ARM_PREFETCH(ADDR)
68 #endif
69 
70 template<> struct packet_traits<float>  : default_packet_traits
71 {
72   typedef Packet4f type;
73   typedef Packet4f half; // Packet2f intrinsics not implemented yet
74   enum {
75     Vectorizable = 1,
76     AlignedOnScalar = 1,
77     size = 4,
78     HasHalfPacket=0, // Packet2f intrinsics not implemented yet
79 
80     HasDiv  = 1,
81     // FIXME check the Has*
82     HasSin  = 0,
83     HasCos  = 0,
84     HasLog  = 0,
85     HasExp  = 1,
86     HasSqrt = 0
87   };
88 };
89 template<> struct packet_traits<int32_t>    : default_packet_traits
90 {
91   typedef Packet4i type;
92   typedef Packet4i half; // Packet2i intrinsics not implemented yet
93   enum {
94     Vectorizable = 1,
95     AlignedOnScalar = 1,
96     size=4,
97     HasHalfPacket=0 // Packet2i intrinsics not implemented yet
98     // FIXME check the Has*
99   };
100 };
101 
102 #if EIGEN_GNUC_AT_MOST(4,4) && !EIGEN_COMP_LLVM
103 // workaround gcc 4.2, 4.3 and 4.4 compilatin issue
104 EIGEN_STRONG_INLINE float32x4_t vld1q_f32(const float* x) { return ::vld1q_f32((const float32_t*)x); }
105 EIGEN_STRONG_INLINE float32x2_t vld1_f32 (const float* x) { return ::vld1_f32 ((const float32_t*)x); }
106 EIGEN_STRONG_INLINE float32x2_t vld1_dup_f32 (const float* x) { return ::vld1_dup_f32 ((const float32_t*)x); }
107 EIGEN_STRONG_INLINE void        vst1q_f32(float* to, float32x4_t from) { ::vst1q_f32((float32_t*)to,from); }
108 EIGEN_STRONG_INLINE void        vst1_f32 (float* to, float32x2_t from) { ::vst1_f32 ((float32_t*)to,from); }
109 #endif
110 
111 template<> struct unpacket_traits<Packet4f> { typedef float   type; enum {size=4, alignment=Aligned16}; typedef Packet4f half; };
112 template<> struct unpacket_traits<Packet4i> { typedef int32_t type; enum {size=4, alignment=Aligned16}; typedef Packet4i half; };
113 
114 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return vdupq_n_f32(from); }
115 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int32_t&    from)   { return vdupq_n_s32(from); }
116 
117 template<> EIGEN_STRONG_INLINE Packet4f plset<Packet4f>(const float& a)
118 {
119   const float f[] = {0, 1, 2, 3};
120   Packet4f countdown = vld1q_f32(f);
121   return vaddq_f32(pset1<Packet4f>(a), countdown);
122 }
123 template<> EIGEN_STRONG_INLINE Packet4i plset<Packet4i>(const int32_t& a)
124 {
125   const int32_t i[] = {0, 1, 2, 3};
126   Packet4i countdown = vld1q_s32(i);
127   return vaddq_s32(pset1<Packet4i>(a), countdown);
128 }
129 
130 template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vaddq_f32(a,b); }
131 template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vaddq_s32(a,b); }
132 
133 template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vsubq_f32(a,b); }
134 template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vsubq_s32(a,b); }
135 
136 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return vnegq_f32(a); }
137 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return vnegq_s32(a); }
138 
139 template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
140 template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
141 
142 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmulq_f32(a,b); }
143 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmulq_s32(a,b); }
144 
145 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
146 {
147 #if EIGEN_ARCH_ARM64
148   return vdivq_f32(a,b);
149 #else
150   Packet4f inv, restep, div;
151 
152   // NEON does not offer a divide instruction, we have to do a reciprocal approximation
153   // However NEON in contrast to other SIMD engines (AltiVec/SSE), offers
154   // a reciprocal estimate AND a reciprocal step -which saves a few instructions
155   // vrecpeq_f32() returns an estimate to 1/b, which we will finetune with
156   // Newton-Raphson and vrecpsq_f32()
157   inv = vrecpeq_f32(b);
158 
159   // This returns a differential, by which we will have to multiply inv to get a better
160   // approximation of 1/b.
161   restep = vrecpsq_f32(b, inv);
162   inv = vmulq_f32(restep, inv);
163 
164   // Finally, multiply a by 1/b and get the wanted result of the division.
165   div = vmulq_f32(a, inv);
166 
167   return div;
168 #endif
169 }
170 
171 template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
172 { eigen_assert(false && "packet integer division are not supported by NEON");
173   return pset1<Packet4i>(0);
174 }
175 
176 // Clang/ARM wrongly advertises __ARM_FEATURE_FMA even when it's not available,
177 // then implements a slow software scalar fallback calling fmaf()!
178 // Filed LLVM bug:
179 //     https://llvm.org/bugs/show_bug.cgi?id=27216
180 #if (defined __ARM_FEATURE_FMA) && !(EIGEN_COMP_CLANG && EIGEN_ARCH_ARM)
181 // See bug 936.
182 // FMA is available on VFPv4 i.e. when compiling with -mfpu=neon-vfpv4.
183 // FMA is a true fused multiply-add i.e. only 1 rounding at the end, no intermediate rounding.
184 // MLA is not fused i.e. does 2 roundings.
185 // In addition to giving better accuracy, FMA also gives better performance here on a Krait (Nexus 4):
186 // MLA: 10 GFlop/s ; FMA: 12 GFlops/s.
187 template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vfmaq_f32(c,a,b); }
188 #else
189 template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) {
190 #if EIGEN_COMP_CLANG && EIGEN_ARCH_ARM
191   // Clang/ARM will replace VMLA by VMUL+VADD at least for some values of -mcpu,
192   // at least -mcpu=cortex-a8 and -mcpu=cortex-a7. Since the former is the default on
193   // -march=armv7-a, that is a very common case.
194   // See e.g. this thread:
195   //     http://lists.llvm.org/pipermail/llvm-dev/2013-December/068806.html
196   // Filed LLVM bug:
197   //     https://llvm.org/bugs/show_bug.cgi?id=27219
198   Packet4f r = c;
199   asm volatile(
200     "vmla.f32 %q[r], %q[a], %q[b]"
201     : [r] "+w" (r)
202     : [a] "w" (a),
203       [b] "w" (b)
204     : );
205   return r;
206 #else
207   return vmlaq_f32(c,a,b);
208 #endif
209 }
210 #endif
211 
212 // No FMA instruction for int, so use MLA unconditionally.
213 template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return vmlaq_s32(c,a,b); }
214 
215 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vminq_f32(a,b); }
216 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vminq_s32(a,b); }
217 
218 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxq_f32(a,b); }
219 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmaxq_s32(a,b); }
220 
221 // Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
222 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b)
223 {
224   return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
225 }
226 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vandq_s32(a,b); }
227 
228 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)
229 {
230   return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
231 }
232 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vorrq_s32(a,b); }
233 
234 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)
235 {
236   return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
237 }
238 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return veorq_s32(a,b); }
239 
240 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b)
241 {
242   return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
243 }
244 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vbicq_s32(a,b); }
245 
246 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float*    from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(from); }
247 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int32_t*  from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(from); }
248 
249 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float*   from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f32(from); }
250 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int32_t* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s32(from); }
251 
252 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from)
253 {
254   float32x2_t lo, hi;
255   lo = vld1_dup_f32(from);
256   hi = vld1_dup_f32(from+1);
257   return vcombine_f32(lo, hi);
258 }
259 template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int32_t* from)
260 {
261   int32x2_t lo, hi;
262   lo = vld1_dup_s32(from);
263   hi = vld1_dup_s32(from+1);
264   return vcombine_s32(lo, hi);
265 }
266 
267 template<> EIGEN_STRONG_INLINE void pstore<float>  (float*    to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_f32(to, from); }
268 template<> EIGEN_STRONG_INLINE void pstore<int32_t>(int32_t*  to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_s32(to, from); }
269 
270 template<> EIGEN_STRONG_INLINE void pstoreu<float>  (float*   to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from); }
271 template<> EIGEN_STRONG_INLINE void pstoreu<int32_t>(int32_t* to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from); }
272 
273 template<> EIGEN_DEVICE_FUNC inline Packet4f pgather<float, Packet4f>(const float* from, Index stride)
274 {
275   Packet4f res = pset1<Packet4f>(0.f);
276   res = vsetq_lane_f32(from[0*stride], res, 0);
277   res = vsetq_lane_f32(from[1*stride], res, 1);
278   res = vsetq_lane_f32(from[2*stride], res, 2);
279   res = vsetq_lane_f32(from[3*stride], res, 3);
280   return res;
281 }
282 template<> EIGEN_DEVICE_FUNC inline Packet4i pgather<int32_t, Packet4i>(const int32_t* from, Index stride)
283 {
284   Packet4i res = pset1<Packet4i>(0);
285   res = vsetq_lane_s32(from[0*stride], res, 0);
286   res = vsetq_lane_s32(from[1*stride], res, 1);
287   res = vsetq_lane_s32(from[2*stride], res, 2);
288   res = vsetq_lane_s32(from[3*stride], res, 3);
289   return res;
290 }
291 
292 template<> EIGEN_DEVICE_FUNC inline void pscatter<float, Packet4f>(float* to, const Packet4f& from, Index stride)
293 {
294   to[stride*0] = vgetq_lane_f32(from, 0);
295   to[stride*1] = vgetq_lane_f32(from, 1);
296   to[stride*2] = vgetq_lane_f32(from, 2);
297   to[stride*3] = vgetq_lane_f32(from, 3);
298 }
299 template<> EIGEN_DEVICE_FUNC inline void pscatter<int32_t, Packet4i>(int32_t* to, const Packet4i& from, Index stride)
300 {
301   to[stride*0] = vgetq_lane_s32(from, 0);
302   to[stride*1] = vgetq_lane_s32(from, 1);
303   to[stride*2] = vgetq_lane_s32(from, 2);
304   to[stride*3] = vgetq_lane_s32(from, 3);
305 }
306 
307 template<> EIGEN_STRONG_INLINE void prefetch<float>  (const float*    addr) { EIGEN_ARM_PREFETCH(addr); }
308 template<> EIGEN_STRONG_INLINE void prefetch<int32_t>(const int32_t*  addr) { EIGEN_ARM_PREFETCH(addr); }
309 
310 // FIXME only store the 2 first elements ?
311 template<> EIGEN_STRONG_INLINE float   pfirst<Packet4f>(const Packet4f& a) { float   EIGEN_ALIGN16 x[4]; vst1q_f32(x, a); return x[0]; }
312 template<> EIGEN_STRONG_INLINE int32_t pfirst<Packet4i>(const Packet4i& a) { int32_t EIGEN_ALIGN16 x[4]; vst1q_s32(x, a); return x[0]; }
313 
314 template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) {
315   float32x2_t a_lo, a_hi;
316   Packet4f a_r64;
317 
318   a_r64 = vrev64q_f32(a);
319   a_lo = vget_low_f32(a_r64);
320   a_hi = vget_high_f32(a_r64);
321   return vcombine_f32(a_hi, a_lo);
322 }
323 template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {
324   int32x2_t a_lo, a_hi;
325   Packet4i a_r64;
326 
327   a_r64 = vrev64q_s32(a);
328   a_lo = vget_low_s32(a_r64);
329   a_hi = vget_high_s32(a_r64);
330   return vcombine_s32(a_hi, a_lo);
331 }
332 
333 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vabsq_f32(a); }
334 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vabsq_s32(a); }
335 
336 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
337 {
338   float32x2_t a_lo, a_hi, sum;
339 
340   a_lo = vget_low_f32(a);
341   a_hi = vget_high_f32(a);
342   sum = vpadd_f32(a_lo, a_hi);
343   sum = vpadd_f32(sum, sum);
344   return vget_lane_f32(sum, 0);
345 }
346 
347 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
348 {
349   float32x4x2_t vtrn1, vtrn2, res1, res2;
350   Packet4f sum1, sum2, sum;
351 
352   // NEON zip performs interleaving of the supplied vectors.
353   // We perform two interleaves in a row to acquire the transposed vector
354   vtrn1 = vzipq_f32(vecs[0], vecs[2]);
355   vtrn2 = vzipq_f32(vecs[1], vecs[3]);
356   res1 = vzipq_f32(vtrn1.val[0], vtrn2.val[0]);
357   res2 = vzipq_f32(vtrn1.val[1], vtrn2.val[1]);
358 
359   // Do the addition of the resulting vectors
360   sum1 = vaddq_f32(res1.val[0], res1.val[1]);
361   sum2 = vaddq_f32(res2.val[0], res2.val[1]);
362   sum = vaddq_f32(sum1, sum2);
363 
364   return sum;
365 }
366 
367 template<> EIGEN_STRONG_INLINE int32_t predux<Packet4i>(const Packet4i& a)
368 {
369   int32x2_t a_lo, a_hi, sum;
370 
371   a_lo = vget_low_s32(a);
372   a_hi = vget_high_s32(a);
373   sum = vpadd_s32(a_lo, a_hi);
374   sum = vpadd_s32(sum, sum);
375   return vget_lane_s32(sum, 0);
376 }
377 
378 template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
379 {
380   int32x4x2_t vtrn1, vtrn2, res1, res2;
381   Packet4i sum1, sum2, sum;
382 
383   // NEON zip performs interleaving of the supplied vectors.
384   // We perform two interleaves in a row to acquire the transposed vector
385   vtrn1 = vzipq_s32(vecs[0], vecs[2]);
386   vtrn2 = vzipq_s32(vecs[1], vecs[3]);
387   res1 = vzipq_s32(vtrn1.val[0], vtrn2.val[0]);
388   res2 = vzipq_s32(vtrn1.val[1], vtrn2.val[1]);
389 
390   // Do the addition of the resulting vectors
391   sum1 = vaddq_s32(res1.val[0], res1.val[1]);
392   sum2 = vaddq_s32(res2.val[0], res2.val[1]);
393   sum = vaddq_s32(sum1, sum2);
394 
395   return sum;
396 }
397 
398 // Other reduction functions:
399 // mul
400 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
401 {
402   float32x2_t a_lo, a_hi, prod;
403 
404   // Get a_lo = |a1|a2| and a_hi = |a3|a4|
405   a_lo = vget_low_f32(a);
406   a_hi = vget_high_f32(a);
407   // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|
408   prod = vmul_f32(a_lo, a_hi);
409   // Multiply prod with its swapped value |a2*a4|a1*a3|
410   prod = vmul_f32(prod, vrev64_f32(prod));
411 
412   return vget_lane_f32(prod, 0);
413 }
414 template<> EIGEN_STRONG_INLINE int32_t predux_mul<Packet4i>(const Packet4i& a)
415 {
416   int32x2_t a_lo, a_hi, prod;
417 
418   // Get a_lo = |a1|a2| and a_hi = |a3|a4|
419   a_lo = vget_low_s32(a);
420   a_hi = vget_high_s32(a);
421   // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|
422   prod = vmul_s32(a_lo, a_hi);
423   // Multiply prod with its swapped value |a2*a4|a1*a3|
424   prod = vmul_s32(prod, vrev64_s32(prod));
425 
426   return vget_lane_s32(prod, 0);
427 }
428 
429 // min
430 template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
431 {
432   float32x2_t a_lo, a_hi, min;
433 
434   a_lo = vget_low_f32(a);
435   a_hi = vget_high_f32(a);
436   min = vpmin_f32(a_lo, a_hi);
437   min = vpmin_f32(min, min);
438 
439   return vget_lane_f32(min, 0);
440 }
441 
442 template<> EIGEN_STRONG_INLINE int32_t predux_min<Packet4i>(const Packet4i& a)
443 {
444   int32x2_t a_lo, a_hi, min;
445 
446   a_lo = vget_low_s32(a);
447   a_hi = vget_high_s32(a);
448   min = vpmin_s32(a_lo, a_hi);
449   min = vpmin_s32(min, min);
450 
451   return vget_lane_s32(min, 0);
452 }
453 
454 // max
455 template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
456 {
457   float32x2_t a_lo, a_hi, max;
458 
459   a_lo = vget_low_f32(a);
460   a_hi = vget_high_f32(a);
461   max = vpmax_f32(a_lo, a_hi);
462   max = vpmax_f32(max, max);
463 
464   return vget_lane_f32(max, 0);
465 }
466 
467 template<> EIGEN_STRONG_INLINE int32_t predux_max<Packet4i>(const Packet4i& a)
468 {
469   int32x2_t a_lo, a_hi, max;
470 
471   a_lo = vget_low_s32(a);
472   a_hi = vget_high_s32(a);
473   max = vpmax_s32(a_lo, a_hi);
474   max = vpmax_s32(max, max);
475 
476   return vget_lane_s32(max, 0);
477 }
478 
479 // this PALIGN_NEON business is to work around a bug in LLVM Clang 3.0 causing incorrect compilation errors,
480 // see bug 347 and this LLVM bug: http://llvm.org/bugs/show_bug.cgi?id=11074
481 #define PALIGN_NEON(Offset,Type,Command) \
482 template<>\
483 struct palign_impl<Offset,Type>\
484 {\
485     EIGEN_STRONG_INLINE static void run(Type& first, const Type& second)\
486     {\
487         if (Offset!=0)\
488             first = Command(first, second, Offset);\
489     }\
490 };\
491 
492 PALIGN_NEON(0,Packet4f,vextq_f32)
493 PALIGN_NEON(1,Packet4f,vextq_f32)
494 PALIGN_NEON(2,Packet4f,vextq_f32)
495 PALIGN_NEON(3,Packet4f,vextq_f32)
496 PALIGN_NEON(0,Packet4i,vextq_s32)
497 PALIGN_NEON(1,Packet4i,vextq_s32)
498 PALIGN_NEON(2,Packet4i,vextq_s32)
499 PALIGN_NEON(3,Packet4i,vextq_s32)
500 
501 #undef PALIGN_NEON
502 
503 EIGEN_DEVICE_FUNC inline void
504 ptranspose(PacketBlock<Packet4f,4>& kernel) {
505   float32x4x2_t tmp1 = vzipq_f32(kernel.packet[0], kernel.packet[1]);
506   float32x4x2_t tmp2 = vzipq_f32(kernel.packet[2], kernel.packet[3]);
507 
508   kernel.packet[0] = vcombine_f32(vget_low_f32(tmp1.val[0]), vget_low_f32(tmp2.val[0]));
509   kernel.packet[1] = vcombine_f32(vget_high_f32(tmp1.val[0]), vget_high_f32(tmp2.val[0]));
510   kernel.packet[2] = vcombine_f32(vget_low_f32(tmp1.val[1]), vget_low_f32(tmp2.val[1]));
511   kernel.packet[3] = vcombine_f32(vget_high_f32(tmp1.val[1]), vget_high_f32(tmp2.val[1]));
512 }
513 
514 EIGEN_DEVICE_FUNC inline void
515 ptranspose(PacketBlock<Packet4i,4>& kernel) {
516   int32x4x2_t tmp1 = vzipq_s32(kernel.packet[0], kernel.packet[1]);
517   int32x4x2_t tmp2 = vzipq_s32(kernel.packet[2], kernel.packet[3]);
518   kernel.packet[0] = vcombine_s32(vget_low_s32(tmp1.val[0]), vget_low_s32(tmp2.val[0]));
519   kernel.packet[1] = vcombine_s32(vget_high_s32(tmp1.val[0]), vget_high_s32(tmp2.val[0]));
520   kernel.packet[2] = vcombine_s32(vget_low_s32(tmp1.val[1]), vget_low_s32(tmp2.val[1]));
521   kernel.packet[3] = vcombine_s32(vget_high_s32(tmp1.val[1]), vget_high_s32(tmp2.val[1]));
522 }
523 
524 //---------- double ----------
525 
526 // Clang 3.5 in the iOS toolchain has an ICE triggered by NEON intrisics for double.
527 // Confirmed at least with __apple_build_version__ = 6000054.
528 #ifdef __apple_build_version__
529 // Let's hope that by the time __apple_build_version__ hits the 601* range, the bug will be fixed.
530 // https://gist.github.com/yamaya/2924292 suggests that the 3 first digits are only updated with
531 // major toolchain updates.
532 #define EIGEN_APPLE_DOUBLE_NEON_BUG (__apple_build_version__ < 6010000)
533 #else
534 #define EIGEN_APPLE_DOUBLE_NEON_BUG 0
535 #endif
536 
537 #if EIGEN_ARCH_ARM64 && !EIGEN_APPLE_DOUBLE_NEON_BUG
538 
539 // Bug 907: workaround missing declarations of the following two functions in the ADK
540 // Defining these functions as templates ensures that if these intrinsics are
541 // already defined in arm_neon.h, then our workaround doesn't cause a conflict
542 // and has lower priority in overload resolution.
543 template <typename T>
544 uint64x2_t vreinterpretq_u64_f64(T a)
545 {
546   return (uint64x2_t) a;
547 }
548 
549 template <typename T>
550 float64x2_t vreinterpretq_f64_u64(T a)
551 {
552   return (float64x2_t) a;
553 }
554 
555 typedef float64x2_t Packet2d;
556 typedef float64x1_t Packet1d;
557 
558 template<> struct packet_traits<double>  : default_packet_traits
559 {
560   typedef Packet2d type;
561   typedef Packet2d half;
562   enum {
563     Vectorizable = 1,
564     AlignedOnScalar = 1,
565     size = 2,
566     HasHalfPacket=0,
567 
568     HasDiv  = 1,
569     // FIXME check the Has*
570     HasSin  = 0,
571     HasCos  = 0,
572     HasLog  = 0,
573     HasExp  = 0,
574     HasSqrt = 0
575   };
576 };
577 
578 template<> struct unpacket_traits<Packet2d> { typedef double  type; enum {size=2, alignment=Aligned16}; typedef Packet2d half; };
579 
580 template<> EIGEN_STRONG_INLINE Packet2d pset1<Packet2d>(const double&  from) { return vdupq_n_f64(from); }
581 
582 template<> EIGEN_STRONG_INLINE Packet2d plset<Packet2d>(const double& a)
583 {
584   const double countdown_raw[] = {0.0,1.0};
585   const Packet2d countdown = vld1q_f64(countdown_raw);
586   return vaddq_f64(pset1<Packet2d>(a), countdown);
587 }
588 template<> EIGEN_STRONG_INLINE Packet2d padd<Packet2d>(const Packet2d& a, const Packet2d& b) { return vaddq_f64(a,b); }
589 
590 template<> EIGEN_STRONG_INLINE Packet2d psub<Packet2d>(const Packet2d& a, const Packet2d& b) { return vsubq_f64(a,b); }
591 
592 template<> EIGEN_STRONG_INLINE Packet2d pnegate(const Packet2d& a) { return vnegq_f64(a); }
593 
594 template<> EIGEN_STRONG_INLINE Packet2d pconj(const Packet2d& a) { return a; }
595 
596 template<> EIGEN_STRONG_INLINE Packet2d pmul<Packet2d>(const Packet2d& a, const Packet2d& b) { return vmulq_f64(a,b); }
597 
598 template<> EIGEN_STRONG_INLINE Packet2d pdiv<Packet2d>(const Packet2d& a, const Packet2d& b) { return vdivq_f64(a,b); }
599 
600 #ifdef __ARM_FEATURE_FMA
601 // See bug 936. See above comment about FMA for float.
602 template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vfmaq_f64(c,a,b); }
603 #else
604 template<> EIGEN_STRONG_INLINE Packet2d pmadd(const Packet2d& a, const Packet2d& b, const Packet2d& c) { return vmlaq_f64(c,a,b); }
605 #endif
606 
607 template<> EIGEN_STRONG_INLINE Packet2d pmin<Packet2d>(const Packet2d& a, const Packet2d& b) { return vminq_f64(a,b); }
608 
609 template<> EIGEN_STRONG_INLINE Packet2d pmax<Packet2d>(const Packet2d& a, const Packet2d& b) { return vmaxq_f64(a,b); }
610 
611 // Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
612 template<> EIGEN_STRONG_INLINE Packet2d pand<Packet2d>(const Packet2d& a, const Packet2d& b)
613 {
614   return vreinterpretq_f64_u64(vandq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));
615 }
616 
617 template<> EIGEN_STRONG_INLINE Packet2d por<Packet2d>(const Packet2d& a, const Packet2d& b)
618 {
619   return vreinterpretq_f64_u64(vorrq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));
620 }
621 
622 template<> EIGEN_STRONG_INLINE Packet2d pxor<Packet2d>(const Packet2d& a, const Packet2d& b)
623 {
624   return vreinterpretq_f64_u64(veorq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));
625 }
626 
627 template<> EIGEN_STRONG_INLINE Packet2d pandnot<Packet2d>(const Packet2d& a, const Packet2d& b)
628 {
629   return vreinterpretq_f64_u64(vbicq_u64(vreinterpretq_u64_f64(a),vreinterpretq_u64_f64(b)));
630 }
631 
632 template<> EIGEN_STRONG_INLINE Packet2d pload<Packet2d>(const double* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f64(from); }
633 
634 template<> EIGEN_STRONG_INLINE Packet2d ploadu<Packet2d>(const double* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f64(from); }
635 
636 template<> EIGEN_STRONG_INLINE Packet2d ploaddup<Packet2d>(const double*   from)
637 {
638   return vld1q_dup_f64(from);
639 }
640 template<> EIGEN_STRONG_INLINE void pstore<double>(double*   to, const Packet2d& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_f64(to, from); }
641 
642 template<> EIGEN_STRONG_INLINE void pstoreu<double>(double*  to, const Packet2d& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f64(to, from); }
643 
644 template<> EIGEN_DEVICE_FUNC inline Packet2d pgather<double, Packet2d>(const double* from, Index stride)
645 {
646   Packet2d res = pset1<Packet2d>(0.0);
647   res = vsetq_lane_f64(from[0*stride], res, 0);
648   res = vsetq_lane_f64(from[1*stride], res, 1);
649   return res;
650 }
651 template<> EIGEN_DEVICE_FUNC inline void pscatter<double, Packet2d>(double* to, const Packet2d& from, Index stride)
652 {
653   to[stride*0] = vgetq_lane_f64(from, 0);
654   to[stride*1] = vgetq_lane_f64(from, 1);
655 }
656 template<> EIGEN_STRONG_INLINE void prefetch<double>(const double* addr) { EIGEN_ARM_PREFETCH(addr); }
657 
658 // FIXME only store the 2 first elements ?
659 template<> EIGEN_STRONG_INLINE double pfirst<Packet2d>(const Packet2d& a) { return vgetq_lane_f64(a, 0); }
660 
661 template<> EIGEN_STRONG_INLINE Packet2d preverse(const Packet2d& a) { return vcombine_f64(vget_high_f64(a), vget_low_f64(a)); }
662 
663 template<> EIGEN_STRONG_INLINE Packet2d pabs(const Packet2d& a) { return vabsq_f64(a); }
664 
665 #if EIGEN_COMP_CLANG && defined(__apple_build_version__)
666 // workaround ICE, see bug 907
667 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { return (vget_low_f64(a) + vget_high_f64(a))[0]; }
668 #else
669 template<> EIGEN_STRONG_INLINE double predux<Packet2d>(const Packet2d& a) { return vget_lane_f64(vget_low_f64(a) + vget_high_f64(a), 0); }
670 #endif
671 
672 template<> EIGEN_STRONG_INLINE Packet2d preduxp<Packet2d>(const Packet2d* vecs)
673 {
674   float64x2_t trn1, trn2;
675 
676   // NEON zip performs interleaving of the supplied vectors.
677   // We perform two interleaves in a row to acquire the transposed vector
678   trn1 = vzip1q_f64(vecs[0], vecs[1]);
679   trn2 = vzip2q_f64(vecs[0], vecs[1]);
680 
681   // Do the addition of the resulting vectors
682   return vaddq_f64(trn1, trn2);
683 }
684 // Other reduction functions:
685 // mul
686 #if EIGEN_COMP_CLANG && defined(__apple_build_version__)
687 template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) { return (vget_low_f64(a) * vget_high_f64(a))[0]; }
688 #else
689 template<> EIGEN_STRONG_INLINE double predux_mul<Packet2d>(const Packet2d& a) { return vget_lane_f64(vget_low_f64(a) * vget_high_f64(a), 0); }
690 #endif
691 
692 // min
693 template<> EIGEN_STRONG_INLINE double predux_min<Packet2d>(const Packet2d& a) { return vgetq_lane_f64(vpminq_f64(a, a), 0); }
694 
695 // max
696 template<> EIGEN_STRONG_INLINE double predux_max<Packet2d>(const Packet2d& a) { return vgetq_lane_f64(vpmaxq_f64(a, a), 0); }
697 
698 // this PALIGN_NEON business is to work around a bug in LLVM Clang 3.0 causing incorrect compilation errors,
699 // see bug 347 and this LLVM bug: http://llvm.org/bugs/show_bug.cgi?id=11074
700 #define PALIGN_NEON(Offset,Type,Command) \
701 template<>\
702 struct palign_impl<Offset,Type>\
703 {\
704     EIGEN_STRONG_INLINE static void run(Type& first, const Type& second)\
705     {\
706         if (Offset!=0)\
707             first = Command(first, second, Offset);\
708     }\
709 };\
710 
711 PALIGN_NEON(0,Packet2d,vextq_f64)
712 PALIGN_NEON(1,Packet2d,vextq_f64)
713 #undef PALIGN_NEON
714 
715 EIGEN_DEVICE_FUNC inline void
716 ptranspose(PacketBlock<Packet2d,2>& kernel) {
717   float64x2_t trn1 = vzip1q_f64(kernel.packet[0], kernel.packet[1]);
718   float64x2_t trn2 = vzip2q_f64(kernel.packet[0], kernel.packet[1]);
719 
720   kernel.packet[0] = trn1;
721   kernel.packet[1] = trn2;
722 }
723 #endif // EIGEN_ARCH_ARM64
724 
725 } // end namespace internal
726 
727 } // end namespace Eigen
728 
729 #endif // EIGEN_PACKET_MATH_NEON_H
730