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PacketMath.h

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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 Konstantinos Margaritis <markos@codex.gr>
00005 //
00006 // Eigen is free software; you can redistribute it and/or
00007 // modify it under the terms of the GNU Lesser General Public
00008 // License as published by the Free Software Foundation; either
00009 // version 3 of the License, or (at your option) any later version.
00010 //
00011 // Alternatively, you can redistribute it and/or
00012 // modify it under the terms of the GNU General Public License as
00013 // published by the Free Software Foundation; either version 2 of
00014 // the License, or (at your option) any later version.
00015 //
00016 // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
00017 // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
00018 // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
00019 // GNU General Public License for more details.
00020 //
00021 // You should have received a copy of the GNU Lesser General Public
00022 // License and a copy of the GNU General Public License along with
00023 // Eigen. If not, see <http://www.gnu.org/licenses/>.
00024 
00025 #ifndef EIGEN_PACKET_MATH_ALTIVEC_H
00026 #define EIGEN_PACKET_MATH_ALTIVEC_H
00027 
00028 namespace internal {
00029 
00030 #ifndef EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD
00031 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 4
00032 #endif
00033 
00034 #ifndef EIGEN_HAS_FUSE_CJMADD
00035 #define EIGEN_HAS_FUSE_CJMADD 1
00036 #endif
00037 
00038 #ifndef EIGEN_TUNE_FOR_CPU_CACHE_SIZE
00039 #define EIGEN_TUNE_FOR_CPU_CACHE_SIZE 8*256*256
00040 #endif
00041 
00042 // NOTE Altivec has 32 registers, but Eigen only accepts a value of 8 or 16
00043 #ifndef EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS
00044 #define EIGEN_ARCH_DEFAULT_NUMBER_OF_REGISTERS 16
00045 #endif
00046 
00047 typedef __vector float          Packet4f;
00048 typedef __vector int            Packet4i;
00049 typedef __vector unsigned int   Packet4ui;
00050 typedef __vector __bool int     Packet4bi;
00051 typedef __vector short int      Packet8i;
00052 typedef __vector unsigned char  Packet16uc;
00053 
00054 // We don't want to write the same code all the time, but we need to reuse the constants
00055 // and it doesn't really work to declare them global, so we define macros instead
00056 
00057 #define _EIGEN_DECLARE_CONST_FAST_Packet4f(NAME,X) \
00058   Packet4f p4f_##NAME = (Packet4f) vec_splat_s32(X)
00059 
00060 #define _EIGEN_DECLARE_CONST_FAST_Packet4i(NAME,X) \
00061   Packet4i p4i_##NAME = vec_splat_s32(X)
00062 
00063 #define _EIGEN_DECLARE_CONST_Packet4f(NAME,X) \
00064   Packet4f p4f_##NAME = pset1<Packet4f>(X)
00065 
00066 #define _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(NAME,X) \
00067   Packet4f p4f_##NAME = vreinterpretq_f32_u32(pset1<int>(X))
00068 
00069 #define _EIGEN_DECLARE_CONST_Packet4i(NAME,X) \
00070   Packet4i p4i_##NAME = pset1<Packet4i>(X)
00071 
00072 #define DST_CHAN 1
00073 #define DST_CTRL(size, count, stride) (((size) << 24) | ((count) << 16) | (stride))
00074 
00075 // Define global static constants:
00076 static Packet4f p4f_COUNTDOWN = { 3.0, 2.0, 1.0, 0.0 };
00077 static Packet4i p4i_COUNTDOWN = { 3, 2, 1, 0 };
00078 static Packet16uc p16uc_REVERSE = {12,13,14,15, 8,9,10,11, 4,5,6,7, 0,1,2,3};
00079 static Packet16uc p16uc_FORWARD = vec_lvsl(0, (float*)0);
00080 
00081 static _EIGEN_DECLARE_CONST_FAST_Packet4f(ZERO, 0);
00082 static _EIGEN_DECLARE_CONST_FAST_Packet4i(ZERO, 0);
00083 static _EIGEN_DECLARE_CONST_FAST_Packet4i(ONE,1);
00084 static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS16,-16);
00085 static _EIGEN_DECLARE_CONST_FAST_Packet4i(MINUS1,-1);
00086 static Packet4f p4f_ONE = vec_ctf(p4i_ONE, 0);
00087 static Packet4f p4f_ZERO_ = (Packet4f) vec_sl((Packet4ui)p4i_MINUS1, (Packet4ui)p4i_MINUS1);
00088 
00089 template<> struct packet_traits<float>  : default_packet_traits
00090 {
00091   typedef Packet4f type;
00092   enum {
00093     Vectorizable = 1,
00094     AlignedOnScalar = 1,
00095     size=4,
00096 
00097     // FIXME check the Has*
00098     HasSin  = 0,
00099     HasCos  = 0,
00100     HasLog  = 0,
00101     HasExp  = 0,
00102     HasSqrt = 0
00103   };
00104 };
00105 template<> struct packet_traits<int>    : default_packet_traits
00106 {
00107   typedef Packet4i type;
00108   enum {
00109     // FIXME check the Has*
00110     Vectorizable = 1,
00111     AlignedOnScalar = 1,
00112     size=4
00113   };
00114 };
00115 
00116 template<> struct unpacket_traits<Packet4f> { typedef float  type; enum {size=4}; };
00117 template<> struct unpacket_traits<Packet4i> { typedef int    type; enum {size=4}; };
00118 /*
00119 inline std::ostream & operator <<(std::ostream & s, const Packet4f & v)
00120 {
00121   union {
00122     Packet4f   v;
00123     float n[4];
00124   } vt;
00125   vt.v = v;
00126   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
00127   return s;
00128 }
00129 
00130 inline std::ostream & operator <<(std::ostream & s, const Packet4i & v)
00131 {
00132   union {
00133     Packet4i   v;
00134     int n[4];
00135   } vt;
00136   vt.v = v;
00137   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
00138   return s;
00139 }
00140 
00141 inline std::ostream & operator <<(std::ostream & s, const Packet4ui & v)
00142 {
00143   union {
00144     Packet4ui   v;
00145     unsigned int n[4];
00146   } vt;
00147   vt.v = v;
00148   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
00149   return s;
00150 }
00151 
00152 inline std::ostream & operator <<(std::ostream & s, const Packetbi & v)
00153 {
00154   union {
00155     Packet4bi v;
00156     unsigned int n[4];
00157   } vt;
00158   vt.v = v;
00159   s << vt.n[0] << ", " << vt.n[1] << ", " << vt.n[2] << ", " << vt.n[3];
00160   return s;
00161 }
00162 */
00163 template<> EIGEN_STRONG_INLINE Packet4f pset1<Packet4f>(const float&  from) {
00164   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
00165   float EIGEN_ALIGN16 af[4];
00166   af[0] = from;
00167   Packet4f vc = vec_ld(0, af);
00168   vc = vec_splat(vc, 0);
00169   return vc;
00170 }
00171 
00172 template<> EIGEN_STRONG_INLINE Packet4i pset1<Packet4i>(const int&    from)   {
00173   int EIGEN_ALIGN16 ai[4];
00174   ai[0] = from;
00175   Packet4i vc = vec_ld(0, ai);
00176   vc = vec_splat(vc, 0);
00177   return vc;
00178 }
00179 
00180 template<> EIGEN_STRONG_INLINE Packet4f plset<float>(const float& a) { return vec_add(pset1<Packet4f>(a), p4f_COUNTDOWN); }
00181 template<> EIGEN_STRONG_INLINE Packet4i plset<int>(const int& a)     { return vec_add(pset1<Packet4i>(a), p4i_COUNTDOWN); }
00182 
00183 template<> EIGEN_STRONG_INLINE Packet4f padd<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_add(a,b); }
00184 template<> EIGEN_STRONG_INLINE Packet4i padd<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_add(a,b); }
00185 
00186 template<> EIGEN_STRONG_INLINE Packet4f psub<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_sub(a,b); }
00187 template<> EIGEN_STRONG_INLINE Packet4i psub<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_sub(a,b); }
00188 
00189 template<> EIGEN_STRONG_INLINE Packet4f pnegate(const Packet4f& a) { return psub<Packet4f>(p4f_ZERO, a); }
00190 template<> EIGEN_STRONG_INLINE Packet4i pnegate(const Packet4i& a) { return psub<Packet4i>(p4i_ZERO, a); }
00191 
00192 template<> EIGEN_STRONG_INLINE Packet4f pmul<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_madd(a,b,p4f_ZERO); }
00193 /* Commented out: it's actually slower than processing it scalar
00194  *
00195 template<> EIGEN_STRONG_INLINE Packet4i pmul<Packet4i>(const Packet4i& a, const Packet4i& b)
00196 {
00197   // Detailed in: http://freevec.org/content/32bit_signed_integer_multiplication_altivec
00198   //Set up constants, variables
00199   Packet4i a1, b1, bswap, low_prod, high_prod, prod, prod_, v1sel;
00200 
00201   // Get the absolute values
00202   a1  = vec_abs(a);
00203   b1  = vec_abs(b);
00204 
00205   // Get the signs using xor
00206   Packet4bi sgn = (Packet4bi) vec_cmplt(vec_xor(a, b), p4i_ZERO);
00207 
00208   // Do the multiplication for the asbolute values.
00209   bswap = (Packet4i) vec_rl((Packet4ui) b1, (Packet4ui) p4i_MINUS16 );
00210   low_prod = vec_mulo((Packet8i) a1, (Packet8i)b1);
00211   high_prod = vec_msum((Packet8i) a1, (Packet8i) bswap, p4i_ZERO);
00212   high_prod = (Packet4i) vec_sl((Packet4ui) high_prod, (Packet4ui) p4i_MINUS16);
00213   prod = vec_add( low_prod, high_prod );
00214 
00215   // NOR the product and select only the negative elements according to the sign mask
00216   prod_ = vec_nor(prod, prod);
00217   prod_ = vec_sel(p4i_ZERO, prod_, sgn);
00218 
00219   // Add 1 to the result to get the negative numbers
00220   v1sel = vec_sel(p4i_ZERO, p4i_ONE, sgn);
00221   prod_ = vec_add(prod_, v1sel);
00222 
00223   // Merge the results back to the final vector.
00224   prod = vec_sel(prod, prod_, sgn);
00225 
00226   return prod;
00227 }
00228 */
00229 template<> EIGEN_STRONG_INLINE Packet4f pdiv<Packet4f>(const Packet4f& a, const Packet4f& b)
00230 {
00231   Packet4f t, y_0, y_1, res;
00232 
00233   // Altivec does not offer a divide instruction, we have to do a reciprocal approximation
00234   y_0 = vec_re(b);
00235 
00236   // Do one Newton-Raphson iteration to get the needed accuracy
00237   t   = vec_nmsub(y_0, b, p4f_ONE);
00238   y_1 = vec_madd(y_0, t, y_0);
00239 
00240   res = vec_madd(a, y_1, p4f_ZERO);
00241   return res;
00242 }
00243 
00244 template<> EIGEN_STRONG_INLINE Packet4i pdiv<Packet4i>(const Packet4i& /*a*/, const Packet4i& /*b*/)
00245 { eigen_assert(false && "packet integer division are not supported by AltiVec");
00246   return pset1<Packet4i>(0);
00247 }
00248 
00249 // for some weird raisons, it has to be overloaded for packet of integers
00250 template<> EIGEN_STRONG_INLINE Packet4f pmadd(const Packet4f& a, const Packet4f& b, const Packet4f& c) { return vec_madd(a, b, c); }
00251 template<> EIGEN_STRONG_INLINE Packet4i pmadd(const Packet4i& a, const Packet4i& b, const Packet4i& c) { return padd(pmul(a,b), c); }
00252 
00253 template<> EIGEN_STRONG_INLINE Packet4f pmin<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_min(a, b); }
00254 template<> EIGEN_STRONG_INLINE Packet4i pmin<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_min(a, b); }
00255 
00256 template<> EIGEN_STRONG_INLINE Packet4f pmax<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_max(a, b); }
00257 template<> EIGEN_STRONG_INLINE Packet4i pmax<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_max(a, b); }
00258 
00259 // Logical Operations are not supported for float, so we have to reinterpret casts using NEON intrinsics
00260 template<> EIGEN_STRONG_INLINE Packet4f pand<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, b); }
00261 template<> EIGEN_STRONG_INLINE Packet4i pand<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, b); }
00262 
00263 template<> EIGEN_STRONG_INLINE Packet4f por<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_or(a, b); }
00264 template<> EIGEN_STRONG_INLINE Packet4i por<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_or(a, b); }
00265 
00266 template<> EIGEN_STRONG_INLINE Packet4f pxor<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_xor(a, b); }
00267 template<> EIGEN_STRONG_INLINE Packet4i pxor<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_xor(a, b); }
00268 
00269 template<> EIGEN_STRONG_INLINE Packet4f pandnot<Packet4f>(const Packet4f& a, const Packet4f& b) { return vec_and(a, vec_nor(b, b)); }
00270 template<> EIGEN_STRONG_INLINE Packet4i pandnot<Packet4i>(const Packet4i& a, const Packet4i& b) { return vec_and(a, vec_nor(b, b)); }
00271 
00272 template<> EIGEN_STRONG_INLINE Packet4f pload<Packet4f>(const float* from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
00273 template<> EIGEN_STRONG_INLINE Packet4i pload<Packet4i>(const int*     from) { EIGEN_DEBUG_ALIGNED_LOAD return vec_ld(0, from); }
00274 
00275 template<> EIGEN_STRONG_INLINE Packet4f ploadu<Packet4f>(const float* from)
00276 {
00277   EIGEN_DEBUG_ALIGNED_LOAD
00278   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
00279   Packet16uc MSQ, LSQ;
00280   Packet16uc mask;
00281   MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
00282   LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
00283   mask = vec_lvsl(0, from);                        // create the permute mask
00284   return (Packet4f) vec_perm(MSQ, LSQ, mask);           // align the data
00285 
00286 }
00287 template<> EIGEN_STRONG_INLINE Packet4i ploadu<Packet4i>(const int* from)
00288 {
00289   EIGEN_DEBUG_ALIGNED_LOAD
00290   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
00291   Packet16uc MSQ, LSQ;
00292   Packet16uc mask;
00293   MSQ = vec_ld(0, (unsigned char *)from);          // most significant quadword
00294   LSQ = vec_ld(15, (unsigned char *)from);         // least significant quadword
00295   mask = vec_lvsl(0, from);                        // create the permute mask
00296   return (Packet4i) vec_perm(MSQ, LSQ, mask);    // align the data
00297 }
00298 
00299 template<> EIGEN_STRONG_INLINE void pstore<float>(float*   to, const Packet4f& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
00300 template<> EIGEN_STRONG_INLINE void pstore<int>(int*       to, const Packet4i& from) { EIGEN_DEBUG_ALIGNED_STORE vec_st(from, 0, to); }
00301 
00302 template<> EIGEN_STRONG_INLINE void pstoreu<float>(float*  to, const Packet4f& from)
00303 {
00304   EIGEN_DEBUG_UNALIGNED_STORE
00305   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
00306   // Warning: not thread safe!
00307   Packet16uc MSQ, LSQ, edges;
00308   Packet16uc edgeAlign, align;
00309 
00310   MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
00311   LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
00312   edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
00313   edges=vec_perm(LSQ,MSQ,edgeAlign);                        // extract the edges
00314   align = vec_lvsr( 0, to );                                // permute map to misalign data
00315   MSQ = vec_perm(edges,(Packet16uc)from,align);             // misalign the data (MSQ)
00316   LSQ = vec_perm((Packet16uc)from,edges,align);             // misalign the data (LSQ)
00317   vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
00318   vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
00319 }
00320 template<> EIGEN_STRONG_INLINE void pstoreu<int>(int*      to, const Packet4i& from)
00321 {
00322   EIGEN_DEBUG_UNALIGNED_STORE
00323   // Taken from http://developer.apple.com/hardwaredrivers/ve/alignment.html
00324   // Warning: not thread safe!
00325   Packet16uc MSQ, LSQ, edges;
00326   Packet16uc edgeAlign, align;
00327 
00328   MSQ = vec_ld(0, (unsigned char *)to);                     // most significant quadword
00329   LSQ = vec_ld(15, (unsigned char *)to);                    // least significant quadword
00330   edgeAlign = vec_lvsl(0, to);                              // permute map to extract edges
00331   edges=vec_perm(LSQ, MSQ, edgeAlign);                      // extract the edges
00332   align = vec_lvsr( 0, to );                                // permute map to misalign data
00333   MSQ = vec_perm(edges, (Packet16uc) from, align);          // misalign the data (MSQ)
00334   LSQ = vec_perm((Packet16uc) from, edges, align);          // misalign the data (LSQ)
00335   vec_st( LSQ, 15, (unsigned char *)to );                   // Store the LSQ part first
00336   vec_st( MSQ, 0, (unsigned char *)to );                    // Store the MSQ part
00337 }
00338 
00339 template<> EIGEN_STRONG_INLINE void prefetch<float>(const float* addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
00340 template<> EIGEN_STRONG_INLINE void prefetch<int>(const int*     addr) { vec_dstt(addr, DST_CTRL(2,2,32), DST_CHAN); }
00341 
00342 template<> EIGEN_STRONG_INLINE float  pfirst<Packet4f>(const Packet4f& a) { float EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
00343 template<> EIGEN_STRONG_INLINE int    pfirst<Packet4i>(const Packet4i& a) { int   EIGEN_ALIGN16 x[4]; vec_st(a, 0, x); return x[0]; }
00344 
00345 template<> EIGEN_STRONG_INLINE Packet4f preverse(const Packet4f& a) { return (Packet4f)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE); }
00346 template<> EIGEN_STRONG_INLINE Packet4i preverse(const Packet4i& a) { return (Packet4i)vec_perm((Packet16uc)a,(Packet16uc)a, p16uc_REVERSE); }
00347 
00348 template<> EIGEN_STRONG_INLINE Packet4f pabs(const Packet4f& a) { return vec_abs(a); }
00349 template<> EIGEN_STRONG_INLINE Packet4i pabs(const Packet4i& a) { return vec_abs(a); }
00350 
00351 template<> EIGEN_STRONG_INLINE float predux<Packet4f>(const Packet4f& a)
00352 {
00353   Packet4f b, sum;
00354   b   = (Packet4f) vec_sld(a, a, 8);
00355   sum = vec_add(a, b);
00356   b   = (Packet4f) vec_sld(sum, sum, 4);
00357   sum = vec_add(sum, b);
00358   return pfirst(sum);
00359 }
00360 
00361 template<> EIGEN_STRONG_INLINE Packet4f preduxp<Packet4f>(const Packet4f* vecs)
00362 {
00363   Packet4f v[4], sum[4];
00364 
00365   // It's easier and faster to transpose then add as columns
00366   // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
00367   // Do the transpose, first set of moves
00368   v[0] = vec_mergeh(vecs[0], vecs[2]);
00369   v[1] = vec_mergel(vecs[0], vecs[2]);
00370   v[2] = vec_mergeh(vecs[1], vecs[3]);
00371   v[3] = vec_mergel(vecs[1], vecs[3]);
00372   // Get the resulting vectors
00373   sum[0] = vec_mergeh(v[0], v[2]);
00374   sum[1] = vec_mergel(v[0], v[2]);
00375   sum[2] = vec_mergeh(v[1], v[3]);
00376   sum[3] = vec_mergel(v[1], v[3]);
00377 
00378   // Now do the summation:
00379   // Lines 0+1
00380   sum[0] = vec_add(sum[0], sum[1]);
00381   // Lines 2+3
00382   sum[1] = vec_add(sum[2], sum[3]);
00383   // Add the results
00384   sum[0] = vec_add(sum[0], sum[1]);
00385 
00386   return sum[0];
00387 }
00388 
00389 template<> EIGEN_STRONG_INLINE int predux<Packet4i>(const Packet4i& a)
00390 {
00391   Packet4i sum;
00392   sum = vec_sums(a, p4i_ZERO);
00393   sum = vec_sld(sum, p4i_ZERO, 12);
00394   return pfirst(sum);
00395 }
00396 
00397 template<> EIGEN_STRONG_INLINE Packet4i preduxp<Packet4i>(const Packet4i* vecs)
00398 {
00399   Packet4i v[4], sum[4];
00400 
00401   // It's easier and faster to transpose then add as columns
00402   // Check: http://www.freevec.org/function/matrix_4x4_transpose_floats for explanation
00403   // Do the transpose, first set of moves
00404   v[0] = vec_mergeh(vecs[0], vecs[2]);
00405   v[1] = vec_mergel(vecs[0], vecs[2]);
00406   v[2] = vec_mergeh(vecs[1], vecs[3]);
00407   v[3] = vec_mergel(vecs[1], vecs[3]);
00408   // Get the resulting vectors
00409   sum[0] = vec_mergeh(v[0], v[2]);
00410   sum[1] = vec_mergel(v[0], v[2]);
00411   sum[2] = vec_mergeh(v[1], v[3]);
00412   sum[3] = vec_mergel(v[1], v[3]);
00413 
00414   // Now do the summation:
00415   // Lines 0+1
00416   sum[0] = vec_add(sum[0], sum[1]);
00417   // Lines 2+3
00418   sum[1] = vec_add(sum[2], sum[3]);
00419   // Add the results
00420   sum[0] = vec_add(sum[0], sum[1]);
00421 
00422   return sum[0];
00423 }
00424 
00425 // Other reduction functions:
00426 // mul
00427 template<> EIGEN_STRONG_INLINE float predux_mul<Packet4f>(const Packet4f& a)
00428 {
00429   Packet4f prod;
00430   prod = pmul(a, (Packet4f)vec_sld(a, a, 8));
00431   return pfirst(pmul(prod, (Packet4f)vec_sld(prod, prod, 4)));
00432 }
00433 
00434 template<> EIGEN_STRONG_INLINE int predux_mul<Packet4i>(const Packet4i& a)
00435 {
00436   EIGEN_ALIGN16 int aux[4];
00437   pstore(aux, a);
00438   return aux[0] * aux[1] * aux[2] * aux[3];
00439 }
00440 
00441 // min
00442 template<> EIGEN_STRONG_INLINE float predux_min<Packet4f>(const Packet4f& a)
00443 {
00444   Packet4f b, res;
00445   b = vec_min(a, vec_sld(a, a, 8));
00446   res = vec_min(b, vec_sld(b, b, 4));
00447   return pfirst(res);
00448 }
00449 
00450 template<> EIGEN_STRONG_INLINE int predux_min<Packet4i>(const Packet4i& a)
00451 {
00452   Packet4i b, res;
00453   b = vec_min(a, vec_sld(a, a, 8));
00454   res = vec_min(b, vec_sld(b, b, 4));
00455   return pfirst(res);
00456 }
00457 
00458 // max
00459 template<> EIGEN_STRONG_INLINE float predux_max<Packet4f>(const Packet4f& a)
00460 {
00461   Packet4f b, res;
00462   b = vec_max(a, vec_sld(a, a, 8));
00463   res = vec_max(b, vec_sld(b, b, 4));
00464   return pfirst(res);
00465 }
00466 
00467 template<> EIGEN_STRONG_INLINE int predux_max<Packet4i>(const Packet4i& a)
00468 {
00469   Packet4i b, res;
00470   b = vec_max(a, vec_sld(a, a, 8));
00471   res = vec_max(b, vec_sld(b, b, 4));
00472   return pfirst(res);
00473 }
00474 
00475 template<int Offset>
00476 struct palign_impl<Offset,Packet4f>
00477 {
00478   EIGEN_STRONG_INLINE static void run(Packet4f& first, const Packet4f& second)
00479   {
00480     if (Offset!=0)
00481       first = vec_sld(first, second, Offset*4);
00482   }
00483 };
00484 
00485 template<int Offset>
00486 struct palign_impl<Offset,Packet4i>
00487 {
00488   EIGEN_STRONG_INLINE static void run(Packet4i& first, const Packet4i& second)
00489   {
00490     if (Offset!=0)
00491       first = vec_sld(first, second, Offset*4);
00492   }
00493 };
00494 
00495 } // end namespace internal
00496 
00497 #endif // EIGEN_PACKET_MATH_ALTIVEC_H



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