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00030 #ifndef EIGEN_MATH_FUNCTIONS_SSE_H
00031 #define EIGEN_MATH_FUNCTIONS_SSE_H
00032
00033 namespace internal {
00034
00035 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00036 Packet4f plog<Packet4f>(const Packet4f& _x)
00037 {
00038 Packet4f x = _x;
00039 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00040 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00041 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
00042
00043 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
00044
00045
00046 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
00047
00048
00049
00050
00051 _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
00052 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
00053 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
00054 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
00055 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
00056 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
00057 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
00058 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
00059 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
00060 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
00061 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
00062 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
00063
00064
00065 Packet4i emm0;
00066
00067 Packet4f invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
00068
00069 x = pmax(x, p4f_min_norm_pos);
00070 emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
00071
00072
00073 x = _mm_and_ps(x, p4f_inv_mant_mask);
00074 x = _mm_or_ps(x, p4f_half);
00075
00076 emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
00077 Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
00078
00079
00080
00081
00082
00083
00084
00085 Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
00086 Packet4f tmp = _mm_and_ps(x, mask);
00087 x = psub(x, p4f_1);
00088 e = psub(e, _mm_and_ps(p4f_1, mask));
00089 x = padd(x, tmp);
00090
00091 Packet4f x2 = pmul(x,x);
00092 Packet4f x3 = pmul(x2,x);
00093
00094 Packet4f y, y1, y2;
00095 y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
00096 y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
00097 y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
00098 y = pmadd(y , x, p4f_cephes_log_p2);
00099 y1 = pmadd(y1, x, p4f_cephes_log_p5);
00100 y2 = pmadd(y2, x, p4f_cephes_log_p8);
00101 y = pmadd(y, x3, y1);
00102 y = pmadd(y, x3, y2);
00103 y = pmul(y, x3);
00104
00105 y1 = pmul(e, p4f_cephes_log_q1);
00106 tmp = pmul(x2, p4f_half);
00107 y = padd(y, y1);
00108 x = psub(x, tmp);
00109 y2 = pmul(e, p4f_cephes_log_q2);
00110 x = padd(x, y);
00111 x = padd(x, y2);
00112 return _mm_or_ps(x, invalid_mask);
00113 }
00114
00115 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00116 Packet4f pexp<Packet4f>(const Packet4f& _x)
00117 {
00118 Packet4f x = _x;
00119 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00120 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00121 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
00122
00123
00124 _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647949f);
00125 _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
00126
00127 _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
00128 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
00129 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
00130
00131 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
00132 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
00133 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
00134 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
00135 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
00136 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
00137
00138 Packet4f tmp = _mm_setzero_ps(), fx;
00139 Packet4i emm0;
00140
00141
00142 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
00143
00144
00145 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
00146
00147
00148 emm0 = _mm_cvttps_epi32(fx);
00149 tmp = _mm_cvtepi32_ps(emm0);
00150
00151 Packet4f mask = _mm_cmpgt_ps(tmp, fx);
00152 mask = _mm_and_ps(mask, p4f_1);
00153 fx = psub(tmp, mask);
00154
00155 tmp = pmul(fx, p4f_cephes_exp_C1);
00156 Packet4f z = pmul(fx, p4f_cephes_exp_C2);
00157 x = psub(x, tmp);
00158 x = psub(x, z);
00159
00160 z = pmul(x,x);
00161
00162 Packet4f y = p4f_cephes_exp_p0;
00163 y = pmadd(y, x, p4f_cephes_exp_p1);
00164 y = pmadd(y, x, p4f_cephes_exp_p2);
00165 y = pmadd(y, x, p4f_cephes_exp_p3);
00166 y = pmadd(y, x, p4f_cephes_exp_p4);
00167 y = pmadd(y, x, p4f_cephes_exp_p5);
00168 y = pmadd(y, z, x);
00169 y = padd(y, p4f_1);
00170
00171
00172 emm0 = _mm_cvttps_epi32(fx);
00173 emm0 = _mm_add_epi32(emm0, p4i_0x7f);
00174 emm0 = _mm_slli_epi32(emm0, 23);
00175 return pmul(y, _mm_castsi128_ps(emm0));
00176 }
00177
00178
00179
00180
00181
00182
00183
00184
00185
00186
00187
00188
00189
00190 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00191 Packet4f psin<Packet4f>(const Packet4f& _x)
00192 {
00193 Packet4f x = _x;
00194 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00195 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00196
00197 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
00198 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
00199 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
00200 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
00201
00202 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
00203
00204 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
00205 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
00206 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
00207 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
00208 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
00209 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
00210 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
00211 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
00212 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
00213 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
00214
00215 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
00216
00217 Packet4i emm0, emm2;
00218 sign_bit = x;
00219
00220 x = pabs(x);
00221
00222
00223
00224
00225 sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
00226
00227
00228 y = pmul(x, p4f_cephes_FOPI);
00229
00230
00231 emm2 = _mm_cvttps_epi32(y);
00232
00233 emm2 = _mm_add_epi32(emm2, p4i_1);
00234 emm2 = _mm_and_si128(emm2, p4i_not1);
00235 y = _mm_cvtepi32_ps(emm2);
00236
00237 emm0 = _mm_and_si128(emm2, p4i_4);
00238 emm0 = _mm_slli_epi32(emm0, 29);
00239
00240
00241
00242
00243
00244
00245 emm2 = _mm_and_si128(emm2, p4i_2);
00246 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
00247
00248 Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
00249 Packet4f poly_mask = _mm_castsi128_ps(emm2);
00250 sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
00251
00252
00253
00254 xmm1 = pmul(y, p4f_minus_cephes_DP1);
00255 xmm2 = pmul(y, p4f_minus_cephes_DP2);
00256 xmm3 = pmul(y, p4f_minus_cephes_DP3);
00257 x = padd(x, xmm1);
00258 x = padd(x, xmm2);
00259 x = padd(x, xmm3);
00260
00261
00262 y = p4f_coscof_p0;
00263 Packet4f z = _mm_mul_ps(x,x);
00264
00265 y = pmadd(y, z, p4f_coscof_p1);
00266 y = pmadd(y, z, p4f_coscof_p2);
00267 y = pmul(y, z);
00268 y = pmul(y, z);
00269 Packet4f tmp = pmul(z, p4f_half);
00270 y = psub(y, tmp);
00271 y = padd(y, p4f_1);
00272
00273
00274
00275 Packet4f y2 = p4f_sincof_p0;
00276 y2 = pmadd(y2, z, p4f_sincof_p1);
00277 y2 = pmadd(y2, z, p4f_sincof_p2);
00278 y2 = pmul(y2, z);
00279 y2 = pmul(y2, x);
00280 y2 = padd(y2, x);
00281
00282
00283 y2 = _mm_and_ps(poly_mask, y2);
00284 y = _mm_andnot_ps(poly_mask, y);
00285 y = _mm_or_ps(y,y2);
00286
00287 return _mm_xor_ps(y, sign_bit);
00288 }
00289
00290
00291 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00292 Packet4f pcos<Packet4f>(const Packet4f& _x)
00293 {
00294 Packet4f x = _x;
00295 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00296 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00297
00298 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
00299 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
00300 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
00301 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
00302
00303 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
00304 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
00305 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
00306 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
00307 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
00308 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
00309 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
00310 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
00311 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
00312 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
00313
00314 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
00315 Packet4i emm0, emm2;
00316
00317 x = pabs(x);
00318
00319
00320 y = pmul(x, p4f_cephes_FOPI);
00321
00322
00323 emm2 = _mm_cvttps_epi32(y);
00324
00325 emm2 = _mm_add_epi32(emm2, p4i_1);
00326 emm2 = _mm_and_si128(emm2, p4i_not1);
00327 y = _mm_cvtepi32_ps(emm2);
00328
00329 emm2 = _mm_sub_epi32(emm2, p4i_2);
00330
00331
00332 emm0 = _mm_andnot_si128(emm2, p4i_4);
00333 emm0 = _mm_slli_epi32(emm0, 29);
00334
00335 emm2 = _mm_and_si128(emm2, p4i_2);
00336 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
00337
00338 Packet4f sign_bit = _mm_castsi128_ps(emm0);
00339 Packet4f poly_mask = _mm_castsi128_ps(emm2);
00340
00341
00342
00343 xmm1 = pmul(y, p4f_minus_cephes_DP1);
00344 xmm2 = pmul(y, p4f_minus_cephes_DP2);
00345 xmm3 = pmul(y, p4f_minus_cephes_DP3);
00346 x = padd(x, xmm1);
00347 x = padd(x, xmm2);
00348 x = padd(x, xmm3);
00349
00350
00351 y = p4f_coscof_p0;
00352 Packet4f z = pmul(x,x);
00353
00354 y = pmadd(y,z,p4f_coscof_p1);
00355 y = pmadd(y,z,p4f_coscof_p2);
00356 y = pmul(y, z);
00357 y = pmul(y, z);
00358 Packet4f tmp = _mm_mul_ps(z, p4f_half);
00359 y = psub(y, tmp);
00360 y = padd(y, p4f_1);
00361
00362
00363 Packet4f y2 = p4f_sincof_p0;
00364 y2 = pmadd(y2, z, p4f_sincof_p1);
00365 y2 = pmadd(y2, z, p4f_sincof_p2);
00366 y2 = pmul(y2, z);
00367 y2 = pmadd(y2, x, x);
00368
00369
00370 y2 = _mm_and_ps(poly_mask, y2);
00371 y = _mm_andnot_ps(poly_mask, y);
00372 y = _mm_or_ps(y,y2);
00373
00374
00375 return _mm_xor_ps(y, sign_bit);
00376 }
00377
00378
00379
00380 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00381 Packet4f psqrt<Packet4f>(const Packet4f& _x)
00382 {
00383 Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
00384
00385
00386 Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
00387 Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
00388
00389 x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
00390 return pmul(_x,x);
00391 }
00392
00393 }
00394
00395 #endif // EIGEN_MATH_FUNCTIONS_SSE_H