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@codex.gr>
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
15namespace Eigen {
16
17namespace internal {
18
19#ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
20#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
21#endif
22
23// FIXME NEON has 16 quad registers, but since the current register allocator
24// is so bad, it is much better to reduce it to 8
25#ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
26#define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 8
27#endif
28
29typedef float32x4_t Packet4f;
30typedef int32x4_t   Packet4i;
31typedef uint32x4_t  Packet4ui;
32
33#define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
34  const Packet4f p4f_##NAME = pset1<Packet4f>(X)
35
36#define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
37  const Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int>(X))
38
39#define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
40  const Packet4i p4i_##NAME = pset1<Packet4i>(X)
41
42#if defined(__llvm__) && !defined(__clang__)
43  //Special treatment for Apple's llvm-gcc, its NEON packet types are unions
44  #define EIGEN_INIT_NEON_PACKET2(X, Y)       {{X, Y}}
45  #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {{X, Y, Z, W}}
46#else
47  //Default initializer for packets
48  #define EIGEN_INIT_NEON_PACKET2(X, Y)       {X, Y}
49  #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {X, Y, Z, W}
50#endif
51
52// arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function
53// which available on LLVM and GCC (at least)
54#if EIGEN_HAS_BUILTIN(__builtin_prefetch) || defined(__GNUC__)
55  #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR);
56#elif defined __pld
57  #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR)
58#elif !defined(__aarch64__)
59  #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ( "   pld [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" );
60#else
61  // by default no explicit prefetching
62  #define EIGEN_ARM_PREFETCH(ADDR)
63#endif
64
65template<> struct packet_traits<float>  : default_packet_traits
66{
67  typedef Packet4f type;
68  enum {
69    Vectorizable = 1,
70    AlignedOnScalar = 1,
71    size = 4,
72
73    HasDiv  = 1,
74    // FIXME check the Has*
75    HasSin  = 0,
76    HasCos  = 0,
77    HasLog  = 0,
78    HasExp  = 0,
79    HasSqrt = 0
80  };
81};
82template<> struct packet_traits<int>    : default_packet_traits
83{
84  typedef Packet4i type;
85  enum {
86    Vectorizable = 1,
87    AlignedOnScalar = 1,
88    size=4
89    // FIXME check the Has*
90  };
91};
92
93#if EIGEN_GNUC_AT_MOST(4,4) && !defined(__llvm__)
94// workaround gcc 4.2, 4.3 and 4.4 compilatin issue
95EIGEN_STRONG_INLINE float32x4_t vld1q_f32(const float* x) { return ::vld1q_f32((const float32_t*)x); }
96EIGEN_STRONG_INLINE float32x2_t vld1_f32 (const float* x) { return ::vld1_f32 ((const float32_t*)x); }
97EIGEN_STRONG_INLINE void        vst1q_f32(float* to, float32x4_t from) { ::vst1q_f32((float32_t*)to,from); }
98EIGEN_STRONG_INLINE void        vst1_f32 (float* to, float32x2_t from) { ::vst1_f32 ((float32_t*)to,from); }
99#endif
100
101template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4}; };
102template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4}; };
103
104template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) { return vdupq_n_f32(from); }
105template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   { return vdupq_n_s32(from); }
106
107template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a)
108{
109  Packet4f countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
110  return vaddq_f32(pset1<Packet4f>(a), countdown);
111}
112template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a)
113{
114  Packet4i countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3);
115  return vaddq_s32(pset1<Packet4i>(a), countdown);
116}
117
118template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vaddq_f32(a,b); }
119template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vaddq_s32(a,b); }
120
121template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vsubq_f32(a,b); }
122template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vsubq_s32(a,b); }
123
124template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return vnegq_f32(a); }
125template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return vnegq_s32(a); }
126
127template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; }
128template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; }
129
130template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmulq_f32(a,b); }
131template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmulq_s32(a,b); }
132
133template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
134{
135  Packet4f inv, restep, div;
136
137  // NEON does not offer a divide instruction, we have to do a reciprocal approximation
138  // However NEON in contrast to other SIMD engines (AltiVec/SSE), offers
139  // a reciprocal estimate AND a reciprocal step -which saves a few instructions
140  // vrecpeq_f32() returns an estimate to 1/b, which we will finetune with
141  // Newton-Raphson and vrecpsq_f32()
142  inv = vrecpeq_f32(b);
143
144  // This returns a differential, by which we will have to multiply inv to get a better
145  // approximation of 1/b.
146  restep = vrecpsq_f32(b, inv);
147  inv = vmulq_f32(restep, inv);
148
149  // Finally, multiply a by 1/b and get the wanted result of the division.
150  div = vmulq_f32(a, inv);
151
152  return div;
153}
154template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
155{ eigen_assert(false && "packet integer division are not supported by NEON");
156  return pset1<Packet4i>(0);
157}
158
159// for some weird raisons, it has to be overloaded for packet of integers
160template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vmlaq_f32(c,a,b); }
161template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return vmlaq_s32(c,a,b); }
162
163template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vminq_f32(a,b); }
164template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vminq_s32(a,b); }
165
166template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxq_f32(a,b); }
167template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmaxq_s32(a,b); }
168
169// Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
170template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b)
171{
172  return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
173}
174template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vandq_s32(a,b); }
175
176template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b)
177{
178  return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
179}
180template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vorrq_s32(a,b); }
181
182template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b)
183{
184  return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
185}
186template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return veorq_s32(a,b); }
187
188template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b)
189{
190  return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b)));
191}
192template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vbicq_s32(a,b); }
193
194template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(from); }
195template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*   from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(from); }
196
197template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f32(from); }
198template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)   { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s32(from); }
199
200template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float*   from)
201{
202  float32x2_t lo, hi;
203  lo = vld1_dup_f32(from);
204  hi = vld1_dup_f32(from+1);
205  return vcombine_f32(lo, hi);
206}
207template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int*     from)
208{
209  int32x2_t lo, hi;
210  lo = vld1_dup_s32(from);
211  hi = vld1_dup_s32(from+1);
212  return vcombine_s32(lo, hi);
213}
214
215template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_f32(to, from); }
216template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_s32(to, from); }
217
218template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from); }
219template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from); }
220
221template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_ARM_PREFETCH(addr); }
222template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { EIGEN_ARM_PREFETCH(addr); }
223
224// FIXME only store the 2 first elements ?
225template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vst1q_f32(x, a); return x[0]; }
226template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int   EIGEN_ALIGN16 x[4]; vst1q_s32(x, a); return x[0]; }
227
228template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) {
229  float32x2_t a_lo, a_hi;
230  Packet4f a_r64;
231
232  a_r64 = vrev64q_f32(a);
233  a_lo = vget_low_f32(a_r64);
234  a_hi = vget_high_f32(a_r64);
235  return vcombine_f32(a_hi, a_lo);
236}
237template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) {
238  int32x2_t a_lo, a_hi;
239  Packet4i a_r64;
240
241  a_r64 = vrev64q_s32(a);
242  a_lo = vget_low_s32(a_r64);
243  a_hi = vget_high_s32(a_r64);
244  return vcombine_s32(a_hi, a_lo);
245}
246template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vabsq_f32(a); }
247template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vabsq_s32(a); }
248
249template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
250{
251  float32x2_t a_lo, a_hi, sum;
252
253  a_lo = vget_low_f32(a);
254  a_hi = vget_high_f32(a);
255  sum = vpadd_f32(a_lo, a_hi);
256  sum = vpadd_f32(sum, sum);
257  return vget_lane_f32(sum, 0);
258}
259
260template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
261{
262  float32x4x2_t vtrn1, vtrn2, res1, res2;
263  Packet4f sum1, sum2, sum;
264
265  // NEON zip performs interleaving of the supplied vectors.
266  // We perform two interleaves in a row to acquire the transposed vector
267  vtrn1 = vzipq_f32(vecs[0], vecs[2]);
268  vtrn2 = vzipq_f32(vecs[1], vecs[3]);
269  res1 = vzipq_f32(vtrn1.val[0], vtrn2.val[0]);
270  res2 = vzipq_f32(vtrn1.val[1], vtrn2.val[1]);
271
272  // Do the addition of the resulting vectors
273  sum1 = vaddq_f32(res1.val[0], res1.val[1]);
274  sum2 = vaddq_f32(res2.val[0], res2.val[1]);
275  sum = vaddq_f32(sum1, sum2);
276
277  return sum;
278}
279
280template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
281{
282  int32x2_t a_lo, a_hi, sum;
283
284  a_lo = vget_low_s32(a);
285  a_hi = vget_high_s32(a);
286  sum = vpadd_s32(a_lo, a_hi);
287  sum = vpadd_s32(sum, sum);
288  return vget_lane_s32(sum, 0);
289}
290
291template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
292{
293  int32x4x2_t vtrn1, vtrn2, res1, res2;
294  Packet4i sum1, sum2, sum;
295
296  // NEON zip performs interleaving of the supplied vectors.
297  // We perform two interleaves in a row to acquire the transposed vector
298  vtrn1 = vzipq_s32(vecs[0], vecs[2]);
299  vtrn2 = vzipq_s32(vecs[1], vecs[3]);
300  res1 = vzipq_s32(vtrn1.val[0], vtrn2.val[0]);
301  res2 = vzipq_s32(vtrn1.val[1], vtrn2.val[1]);
302
303  // Do the addition of the resulting vectors
304  sum1 = vaddq_s32(res1.val[0], res1.val[1]);
305  sum2 = vaddq_s32(res2.val[0], res2.val[1]);
306  sum = vaddq_s32(sum1, sum2);
307
308  return sum;
309}
310
311// Other reduction functions:
312// mul
313template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
314{
315  float32x2_t a_lo, a_hi, prod;
316
317  // Get a_lo = |a1|a2| and a_hi = |a3|a4|
318  a_lo = vget_low_f32(a);
319  a_hi = vget_high_f32(a);
320  // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|
321  prod = vmul_f32(a_lo, a_hi);
322  // Multiply prod with its swapped value |a2*a4|a1*a3|
323  prod = vmul_f32(prod, vrev64_f32(prod));
324
325  return vget_lane_f32(prod, 0);
326}
327template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
328{
329  int32x2_t a_lo, a_hi, prod;
330
331  // Get a_lo = |a1|a2| and a_hi = |a3|a4|
332  a_lo = vget_low_s32(a);
333  a_hi = vget_high_s32(a);
334  // Get the product of a_lo * a_hi -> |a1*a3|a2*a4|
335  prod = vmul_s32(a_lo, a_hi);
336  // Multiply prod with its swapped value |a2*a4|a1*a3|
337  prod = vmul_s32(prod, vrev64_s32(prod));
338
339  return vget_lane_s32(prod, 0);
340}
341
342// min
343template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
344{
345  float32x2_t a_lo, a_hi, min;
346
347  a_lo = vget_low_f32(a);
348  a_hi = vget_high_f32(a);
349  min = vpmin_f32(a_lo, a_hi);
350  min = vpmin_f32(min, min);
351
352  return vget_lane_f32(min, 0);
353}
354
355template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
356{
357  int32x2_t a_lo, a_hi, min;
358
359  a_lo = vget_low_s32(a);
360  a_hi = vget_high_s32(a);
361  min = vpmin_s32(a_lo, a_hi);
362  min = vpmin_s32(min, min);
363
364  return vget_lane_s32(min, 0);
365}
366
367// max
368template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
369{
370  float32x2_t a_lo, a_hi, max;
371
372  a_lo = vget_low_f32(a);
373  a_hi = vget_high_f32(a);
374  max = vpmax_f32(a_lo, a_hi);
375  max = vpmax_f32(max, max);
376
377  return vget_lane_f32(max, 0);
378}
379
380template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
381{
382  int32x2_t a_lo, a_hi, max;
383
384  a_lo = vget_low_s32(a);
385  a_hi = vget_high_s32(a);
386  max = vpmax_s32(a_lo, a_hi);
387
388  return vget_lane_s32(max, 0);
389}
390
391// this PALIGN_NEON business is to work around a bug in LLVM Clang 3.0 causing incorrect compilation errors,
392// see bug 347 and this LLVM bug: http://llvm.org/bugs/show_bug.cgi?id=11074
393#define PALIGN_NEON(Offset,Type,Command) \
394template<>\
395struct palign_impl<Offset,Type>\
396{\
397    EIGEN_STRONG_INLINE static void run(Type& first, const Type& second)\
398    {\
399        if (Offset!=0)\
400            first = Command(first, second, Offset);\
401    }\
402};\
403
404PALIGN_NEON(0,Packet4f,vextq_f32)
405PALIGN_NEON(1,Packet4f,vextq_f32)
406PALIGN_NEON(2,Packet4f,vextq_f32)
407PALIGN_NEON(3,Packet4f,vextq_f32)
408PALIGN_NEON(0,Packet4i,vextq_s32)
409PALIGN_NEON(1,Packet4i,vextq_s32)
410PALIGN_NEON(2,Packet4i,vextq_s32)
411PALIGN_NEON(3,Packet4i,vextq_s32)
412
413#undef PALIGN_NEON
414
415} // end namespace internal
416
417} // end namespace Eigen
418
419#endif // EIGEN_PACKET_MATH_NEON_H
420