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00001 // This file is part of Eigen, a lightweight C++ template library 00002 // for linear algebra. 00003 // 00004 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr> 00005 // Copyright (C) 2010 Konstantinos Margaritis <markos@codex.gr> 00006 // Heavily based on Gael's SSE version. 00007 // 00008 // This Source Code Form is subject to the terms of the Mozilla 00009 // Public License v. 2.0. If a copy of the MPL was not distributed 00010 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 00011 00012 #ifndef EIGEN_PACKET_MATH_NEON_H 00013 #define EIGEN_PACKET_MATH_NEON_H 00014 00015 namespace Eigen { 00016 00017 namespace internal { 00018 00019 #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 00020 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8 00021 #endif 00022 00023 // FIXME NEON has 16 quad registers, but since the current register allocator 00024 // is so bad, it is much better to reduce it to 8 00025 #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 00026 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 8 00027 #endif 00028 00029 typedef float32x4_t Packet4f; 00030 typedef int32x4_t Packet4i; 00031 typedef uint32x4_t Packet4ui; 00032 00033 #define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \ 00034 const Packet4f p4f_##NAME = pset1<Packet4f>(X) 00035 00036 #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \ 00037 const Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int>(X)) 00038 00039 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \ 00040 const Packet4i p4i_##NAME = pset1<Packet4i>(X) 00041 00042 #if defined(__llvm__) && !defined(__clang__) 00043 //Special treatment for Apple's llvm-gcc, its NEON packet types are unions 00044 #define EIGEN_INIT_NEON_PACKET2(X, Y) {{X, Y}} 00045 #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {{X, Y, Z, W}} 00046 #else 00047 //Default initializer for packets 00048 #define EIGEN_INIT_NEON_PACKET2(X, Y) {X, Y} 00049 #define EIGEN_INIT_NEON_PACKET4(X, Y, Z, W) {X, Y, Z, W} 00050 #endif 00051 00052 // arm64 does have the pld instruction. If available, let's trust the __builtin_prefetch built-in function 00053 // which available on LLVM and GCC (at least) 00054 #if EIGEN_HAS_BUILTIN(__builtin_prefetch) || defined(__GNUC__) 00055 #define EIGEN_ARM_PREFETCH(ADDR) __builtin_prefetch(ADDR); 00056 #elif defined __pld 00057 #define EIGEN_ARM_PREFETCH(ADDR) __pld(ADDR) 00058 #elif !defined(__aarch64__) 00059 #define EIGEN_ARM_PREFETCH(ADDR) __asm__ __volatile__ ( " pld [%[addr]]\n" :: [addr] "r" (ADDR) : "cc" ); 00060 #else 00061 // by default no explicit prefetching 00062 #define EIGEN_ARM_PREFETCH(ADDR) 00063 #endif 00064 00065 template<> struct packet_traits<float> : default_packet_traits 00066 { 00067 typedef Packet4f type; 00068 enum { 00069 Vectorizable = 1, 00070 AlignedOnScalar = 1, 00071 size = 4, 00072 00073 HasDiv = 1, 00074 // FIXME check the Has* 00075 HasSin = 0, 00076 HasCos = 0, 00077 HasLog = 0, 00078 HasExp = 0, 00079 HasSqrt = 0 00080 }; 00081 }; 00082 template<> struct packet_traits<int> : default_packet_traits 00083 { 00084 typedef Packet4i type; 00085 enum { 00086 Vectorizable = 1, 00087 AlignedOnScalar = 1, 00088 size=4 00089 // FIXME check the Has* 00090 }; 00091 }; 00092 00093 #if EIGEN_GNUC_AT_MOST(4,4) && !defined(__llvm__) 00094 // workaround gcc 4.2, 4.3 and 4.4 compilatin issue 00095 EIGEN_STRONG_INLINE float32x4_t vld1q_f32(const float* x) { return ::vld1q_f32((const float32_t*)x); } 00096 EIGEN_STRONG_INLINE float32x2_t vld1_f32 (const float* x) { return ::vld1_f32 ((const float32_t*)x); } 00097 EIGEN_STRONG_INLINE void vst1q_f32(float* to, float32x4_t from) { ::vst1q_f32((float32_t*)to,from); } 00098 EIGEN_STRONG_INLINE void vst1_f32 (float* to, float32x2_t from) { ::vst1_f32 ((float32_t*)to,from); } 00099 #endif 00100 00101 template<> struct unpacket_traits<Packet4f> { typedef float type; enum {size=4}; }; 00102 template<> struct unpacket_traits<Packet4i> { typedef int type; enum {size=4}; }; 00103 00104 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float& from) { return vdupq_n_f32(from); } 00105 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int& from) { return vdupq_n_s32(from); } 00106 00107 template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) 00108 { 00109 Packet4f countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3); 00110 return vaddq_f32(pset1<Packet4f>(a), countdown); 00111 } 00112 template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a) 00113 { 00114 Packet4i countdown = EIGEN_INIT_NEON_PACKET4(0, 1, 2, 3); 00115 return vaddq_s32(pset1<Packet4i>(a), countdown); 00116 } 00117 00118 template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vaddq_f32(a,b); } 00119 template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vaddq_s32(a,b); } 00120 00121 template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vsubq_f32(a,b); } 00122 template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vsubq_s32(a,b); } 00123 00124 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return vnegq_f32(a); } 00125 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return vnegq_s32(a); } 00126 00127 template<> EIGEN_STRONG_INLINE Packet4f pconj(const Packet4f& a) { return a; } 00128 template<> EIGEN_STRONG_INLINE Packet4i pconj(const Packet4i& a) { return a; } 00129 00130 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmulq_f32(a,b); } 00131 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmulq_s32(a,b); } 00132 00133 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b) 00134 { 00135 Packet4f inv, restep, div; 00136 00137 // NEON does not offer a divide instruction, we have to do a reciprocal approximation 00138 // However NEON in contrast to other SIMD engines (AltiVec/SSE), offers 00139 // a reciprocal estimate AND a reciprocal step -which saves a few instructions 00140 // vrecpeq_f32() returns an estimate to 1/b, which we will finetune with 00141 // Newton-Raphson and vrecpsq_f32() 00142 inv = vrecpeq_f32(b); 00143 00144 // This returns a differential, by which we will have to multiply inv to get a better 00145 // approximation of 1/b. 00146 restep = vrecpsq_f32(b, inv); 00147 inv = vmulq_f32(restep, inv); 00148 00149 // Finally, multiply a by 1/b and get the wanted result of the division. 00150 div = vmulq_f32(a, inv); 00151 00152 return div; 00153 } 00154 template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/) 00155 { eigen_assert(false && "packet integer division are not supported by NEON"); 00156 return pset1<Packet4i>(0); 00157 } 00158 00159 // for some weird raisons, it has to be overloaded for packet of integers 00160 template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vmlaq_f32(c,a,b); } 00161 template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return vmlaq_s32(c,a,b); } 00162 00163 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vminq_f32(a,b); } 00164 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vminq_s32(a,b); } 00165 00166 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vmaxq_f32(a,b); } 00167 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vmaxq_s32(a,b); } 00168 00169 // Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics 00170 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) 00171 { 00172 return vreinterpretq_f32_u32(vandq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); 00173 } 00174 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vandq_s32(a,b); } 00175 00176 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) 00177 { 00178 return vreinterpretq_f32_u32(vorrq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); 00179 } 00180 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vorrq_s32(a,b); } 00181 00182 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) 00183 { 00184 return vreinterpretq_f32_u32(veorq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); 00185 } 00186 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return veorq_s32(a,b); } 00187 00188 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) 00189 { 00190 return vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(a),vreinterpretq_u32_f32(b))); 00191 } 00192 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vbicq_s32(a,b); } 00193 00194 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_f32(from); } 00195 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int* from) { EIGEN_DEBUG_ALIGNED_LOAD return vld1q_s32(from); } 00196 00197 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_f32(from); } 00198 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from) { EIGEN_DEBUG_UNALIGNED_LOAD return vld1q_s32(from); } 00199 00200 template<> EIGEN_STRONG_INLINE Packet4f ploaddup<Packet4f>(const float* from) 00201 { 00202 float32x2_t lo, hi; 00203 lo = vld1_dup_f32(from); 00204 hi = vld1_dup_f32(from+1); 00205 return vcombine_f32(lo, hi); 00206 } 00207 template<> EIGEN_STRONG_INLINE Packet4i ploaddup<Packet4i>(const int* from) 00208 { 00209 int32x2_t lo, hi; 00210 lo = vld1_dup_s32(from); 00211 hi = vld1_dup_s32(from+1); 00212 return vcombine_s32(lo, hi); 00213 } 00214 00215 template<> EIGEN_STRONG_INLINE void pstore<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_f32(to, from); } 00216 template<> EIGEN_STRONG_INLINE void pstore<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vst1q_s32(to, from); } 00217 00218 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float* to, const Packet4f& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_f32(to, from); } 00219 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int* to, const Packet4i& from) { EIGEN_DEBUG_UNALIGNED_STORE vst1q_s32(to, from); } 00220 00221 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { EIGEN_ARM_PREFETCH(addr); } 00222 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int* addr) { EIGEN_ARM_PREFETCH(addr); } 00223 00224 // FIXME only store the 2 first elements ? 00225 template<> EIGEN_STRONG_INLINE float pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vst1q_f32(x, a); return x[0]; } 00226 template<> EIGEN_STRONG_INLINE int pfirst<Packet4i>(const Packet4i& a) { int EIGEN_ALIGN16 x[4]; vst1q_s32(x, a); return x[0]; } 00227 00228 template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { 00229 float32x2_t a_lo, a_hi; 00230 Packet4f a_r64; 00231 00232 a_r64 = vrev64q_f32(a); 00233 a_lo = vget_low_f32(a_r64); 00234 a_hi = vget_high_f32(a_r64); 00235 return vcombine_f32(a_hi, a_lo); 00236 } 00237 template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { 00238 int32x2_t a_lo, a_hi; 00239 Packet4i a_r64; 00240 00241 a_r64 = vrev64q_s32(a); 00242 a_lo = vget_low_s32(a_r64); 00243 a_hi = vget_high_s32(a_r64); 00244 return vcombine_s32(a_hi, a_lo); 00245 } 00246 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vabsq_f32(a); } 00247 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vabsq_s32(a); } 00248 00249 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a) 00250 { 00251 float32x2_t a_lo, a_hi, sum; 00252 00253 a_lo = vget_low_f32(a); 00254 a_hi = vget_high_f32(a); 00255 sum = vpadd_f32(a_lo, a_hi); 00256 sum = vpadd_f32(sum, sum); 00257 return vget_lane_f32(sum, 0); 00258 } 00259 00260 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs) 00261 { 00262 float32x4x2_t vtrn1, vtrn2, res1, res2; 00263 Packet4f sum1, sum2, sum; 00264 00265 // NEON zip performs interleaving of the supplied vectors. 00266 // We perform two interleaves in a row to acquire the transposed vector 00267 vtrn1 = vzipq_f32(vecs[0], vecs[2]); 00268 vtrn2 = vzipq_f32(vecs[1], vecs[3]); 00269 res1 = vzipq_f32(vtrn1.val[0], vtrn2.val[0]); 00270 res2 = vzipq_f32(vtrn1.val[1], vtrn2.val[1]); 00271 00272 // Do the addition of the resulting vectors 00273 sum1 = vaddq_f32(res1.val[0], res1.val[1]); 00274 sum2 = vaddq_f32(res2.val[0], res2.val[1]); 00275 sum = vaddq_f32(sum1, sum2); 00276 00277 return sum; 00278 } 00279 00280 template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a) 00281 { 00282 int32x2_t a_lo, a_hi, sum; 00283 00284 a_lo = vget_low_s32(a); 00285 a_hi = vget_high_s32(a); 00286 sum = vpadd_s32(a_lo, a_hi); 00287 sum = vpadd_s32(sum, sum); 00288 return vget_lane_s32(sum, 0); 00289 } 00290 00291 template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs) 00292 { 00293 int32x4x2_t vtrn1, vtrn2, res1, res2; 00294 Packet4i sum1, sum2, sum; 00295 00296 // NEON zip performs interleaving of the supplied vectors. 00297 // We perform two interleaves in a row to acquire the transposed vector 00298 vtrn1 = vzipq_s32(vecs[0], vecs[2]); 00299 vtrn2 = vzipq_s32(vecs[1], vecs[3]); 00300 res1 = vzipq_s32(vtrn1.val[0], vtrn2.val[0]); 00301 res2 = vzipq_s32(vtrn1.val[1], vtrn2.val[1]); 00302 00303 // Do the addition of the resulting vectors 00304 sum1 = vaddq_s32(res1.val[0], res1.val[1]); 00305 sum2 = vaddq_s32(res2.val[0], res2.val[1]); 00306 sum = vaddq_s32(sum1, sum2); 00307 00308 return sum; 00309 } 00310 00311 // Other reduction functions: 00312 // mul 00313 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a) 00314 { 00315 float32x2_t a_lo, a_hi, prod; 00316 00317 // Get a_lo = |a1|a2| and a_hi = |a3|a4| 00318 a_lo = vget_low_f32(a); 00319 a_hi = vget_high_f32(a); 00320 // Get the product of a_lo * a_hi -> |a1*a3|a2*a4| 00321 prod = vmul_f32(a_lo, a_hi); 00322 // Multiply prod with its swapped value |a2*a4|a1*a3| 00323 prod = vmul_f32(prod, vrev64_f32(prod)); 00324 00325 return vget_lane_f32(prod, 0); 00326 } 00327 template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a) 00328 { 00329 int32x2_t a_lo, a_hi, prod; 00330 00331 // Get a_lo = |a1|a2| and a_hi = |a3|a4| 00332 a_lo = vget_low_s32(a); 00333 a_hi = vget_high_s32(a); 00334 // Get the product of a_lo * a_hi -> |a1*a3|a2*a4| 00335 prod = vmul_s32(a_lo, a_hi); 00336 // Multiply prod with its swapped value |a2*a4|a1*a3| 00337 prod = vmul_s32(prod, vrev64_s32(prod)); 00338 00339 return vget_lane_s32(prod, 0); 00340 } 00341 00342 // min 00343 template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a) 00344 { 00345 float32x2_t a_lo, a_hi, min; 00346 00347 a_lo = vget_low_f32(a); 00348 a_hi = vget_high_f32(a); 00349 min = vpmin_f32(a_lo, a_hi); 00350 min = vpmin_f32(min, min); 00351 00352 return vget_lane_f32(min, 0); 00353 } 00354 00355 template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a) 00356 { 00357 int32x2_t a_lo, a_hi, min; 00358 00359 a_lo = vget_low_s32(a); 00360 a_hi = vget_high_s32(a); 00361 min = vpmin_s32(a_lo, a_hi); 00362 min = vpmin_s32(min, min); 00363 00364 return vget_lane_s32(min, 0); 00365 } 00366 00367 // max 00368 template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a) 00369 { 00370 float32x2_t a_lo, a_hi, max; 00371 00372 a_lo = vget_low_f32(a); 00373 a_hi = vget_high_f32(a); 00374 max = vpmax_f32(a_lo, a_hi); 00375 max = vpmax_f32(max, max); 00376 00377 return vget_lane_f32(max, 0); 00378 } 00379 00380 template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a) 00381 { 00382 int32x2_t a_lo, a_hi, max; 00383 00384 a_lo = vget_low_s32(a); 00385 a_hi = vget_high_s32(a); 00386 max = vpmax_s32(a_lo, a_hi); 00387 00388 return vget_lane_s32(max, 0); 00389 } 00390 00391 // this PALIGN_NEON business is to work around a bug in LLVM Clang 3.0 causing incorrect compilation errors, 00392 // see bug 347 and this LLVM bug: http://llvm.org/bugs/show_bug.cgi?id=11074 00393 #define PALIGN_NEON(Offset,Type,Command) \ 00394 template<>\ 00395 struct palign_impl<Offset,Type>\ 00396 {\ 00397 EIGEN_STRONG_INLINE static void run(Type& first, const Type& second)\ 00398 {\ 00399 if (Offset!=0)\ 00400 first = Command(first, second, Offset);\ 00401 }\ 00402 };\ 00403 00404 PALIGN_NEON(0,Packet4f,vextq_f32) 00405 PALIGN_NEON(1,Packet4f,vextq_f32) 00406 PALIGN_NEON(2,Packet4f,vextq_f32) 00407 PALIGN_NEON(3,Packet4f,vextq_f32) 00408 PALIGN_NEON(0,Packet4i,vextq_s32) 00409 PALIGN_NEON(1,Packet4i,vextq_s32) 00410 PALIGN_NEON(2,Packet4i,vextq_s32) 00411 PALIGN_NEON(3,Packet4i,vextq_s32) 00412 00413 #undef PALIGN_NEON 00414 00415 } // end namespace internal 00416 00417 } // end namespace Eigen 00418 00419 #endif // EIGEN_PACKET_MATH_NEON_H