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00030 #ifndef EIGEN_MATH_FUNCTIONS_SSE_H
00031 #define EIGEN_MATH_FUNCTIONS_SSE_H
00032
00033 namespace Eigen {
00034
00035 namespace internal {
00036
00037 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00038 Packet4f plog<Packet4f>(const Packet4f& _x)
00039 {
00040 Packet4f x = _x;
00041 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00042 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00043 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
00044
00045 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
00046
00047
00048 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
00049
00050
00051
00052
00053 _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
00054 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
00055 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
00056 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
00057 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
00058 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
00059 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
00060 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
00061 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
00062 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
00063 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
00064 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
00065
00066
00067 Packet4i emm0;
00068
00069 Packet4f invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
00070
00071 x = pmax(x, p4f_min_norm_pos);
00072 emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
00073
00074
00075 x = _mm_and_ps(x, p4f_inv_mant_mask);
00076 x = _mm_or_ps(x, p4f_half);
00077
00078 emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
00079 Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
00080
00081
00082
00083
00084
00085
00086
00087 Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
00088 Packet4f tmp = _mm_and_ps(x, mask);
00089 x = psub(x, p4f_1);
00090 e = psub(e, _mm_and_ps(p4f_1, mask));
00091 x = padd(x, tmp);
00092
00093 Packet4f x2 = pmul(x,x);
00094 Packet4f x3 = pmul(x2,x);
00095
00096 Packet4f y, y1, y2;
00097 y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
00098 y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
00099 y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
00100 y = pmadd(y , x, p4f_cephes_log_p2);
00101 y1 = pmadd(y1, x, p4f_cephes_log_p5);
00102 y2 = pmadd(y2, x, p4f_cephes_log_p8);
00103 y = pmadd(y, x3, y1);
00104 y = pmadd(y, x3, y2);
00105 y = pmul(y, x3);
00106
00107 y1 = pmul(e, p4f_cephes_log_q1);
00108 tmp = pmul(x2, p4f_half);
00109 y = padd(y, y1);
00110 x = psub(x, tmp);
00111 y2 = pmul(e, p4f_cephes_log_q2);
00112 x = padd(x, y);
00113 x = padd(x, y2);
00114 return _mm_or_ps(x, invalid_mask);
00115 }
00116
00117 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00118 Packet4f pexp<Packet4f>(const Packet4f& _x)
00119 {
00120 Packet4f x = _x;
00121 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00122 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00123 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
00124
00125
00126 _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647949f);
00127 _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
00128
00129 _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
00130 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
00131 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
00132
00133 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
00134 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
00135 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
00136 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
00137 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
00138 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
00139
00140 Packet4f tmp = _mm_setzero_ps(), fx;
00141 Packet4i emm0;
00142
00143
00144 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
00145
00146
00147 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
00148
00149
00150 emm0 = _mm_cvttps_epi32(fx);
00151 tmp = _mm_cvtepi32_ps(emm0);
00152
00153 Packet4f mask = _mm_cmpgt_ps(tmp, fx);
00154 mask = _mm_and_ps(mask, p4f_1);
00155 fx = psub(tmp, mask);
00156
00157 tmp = pmul(fx, p4f_cephes_exp_C1);
00158 Packet4f z = pmul(fx, p4f_cephes_exp_C2);
00159 x = psub(x, tmp);
00160 x = psub(x, z);
00161
00162 z = pmul(x,x);
00163
00164 Packet4f y = p4f_cephes_exp_p0;
00165 y = pmadd(y, x, p4f_cephes_exp_p1);
00166 y = pmadd(y, x, p4f_cephes_exp_p2);
00167 y = pmadd(y, x, p4f_cephes_exp_p3);
00168 y = pmadd(y, x, p4f_cephes_exp_p4);
00169 y = pmadd(y, x, p4f_cephes_exp_p5);
00170 y = pmadd(y, z, x);
00171 y = padd(y, p4f_1);
00172
00173
00174 emm0 = _mm_cvttps_epi32(fx);
00175 emm0 = _mm_add_epi32(emm0, p4i_0x7f);
00176 emm0 = _mm_slli_epi32(emm0, 23);
00177 return pmul(y, _mm_castsi128_ps(emm0));
00178 }
00179
00180
00181
00182
00183
00184
00185
00186
00187
00188
00189
00190
00191
00192 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00193 Packet4f psin<Packet4f>(const Packet4f& _x)
00194 {
00195 Packet4f x = _x;
00196 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00197 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00198
00199 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
00200 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
00201 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
00202 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
00203
00204 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
00205
00206 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
00207 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
00208 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
00209 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
00210 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
00211 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
00212 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
00213 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
00214 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
00215 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
00216
00217 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
00218
00219 Packet4i emm0, emm2;
00220 sign_bit = x;
00221
00222 x = pabs(x);
00223
00224
00225
00226
00227 sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
00228
00229
00230 y = pmul(x, p4f_cephes_FOPI);
00231
00232
00233 emm2 = _mm_cvttps_epi32(y);
00234
00235 emm2 = _mm_add_epi32(emm2, p4i_1);
00236 emm2 = _mm_and_si128(emm2, p4i_not1);
00237 y = _mm_cvtepi32_ps(emm2);
00238
00239 emm0 = _mm_and_si128(emm2, p4i_4);
00240 emm0 = _mm_slli_epi32(emm0, 29);
00241
00242
00243
00244
00245
00246
00247 emm2 = _mm_and_si128(emm2, p4i_2);
00248 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
00249
00250 Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
00251 Packet4f poly_mask = _mm_castsi128_ps(emm2);
00252 sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
00253
00254
00255
00256 xmm1 = pmul(y, p4f_minus_cephes_DP1);
00257 xmm2 = pmul(y, p4f_minus_cephes_DP2);
00258 xmm3 = pmul(y, p4f_minus_cephes_DP3);
00259 x = padd(x, xmm1);
00260 x = padd(x, xmm2);
00261 x = padd(x, xmm3);
00262
00263
00264 y = p4f_coscof_p0;
00265 Packet4f z = _mm_mul_ps(x,x);
00266
00267 y = pmadd(y, z, p4f_coscof_p1);
00268 y = pmadd(y, z, p4f_coscof_p2);
00269 y = pmul(y, z);
00270 y = pmul(y, z);
00271 Packet4f tmp = pmul(z, p4f_half);
00272 y = psub(y, tmp);
00273 y = padd(y, p4f_1);
00274
00275
00276
00277 Packet4f y2 = p4f_sincof_p0;
00278 y2 = pmadd(y2, z, p4f_sincof_p1);
00279 y2 = pmadd(y2, z, p4f_sincof_p2);
00280 y2 = pmul(y2, z);
00281 y2 = pmul(y2, x);
00282 y2 = padd(y2, x);
00283
00284
00285 y2 = _mm_and_ps(poly_mask, y2);
00286 y = _mm_andnot_ps(poly_mask, y);
00287 y = _mm_or_ps(y,y2);
00288
00289 return _mm_xor_ps(y, sign_bit);
00290 }
00291
00292
00293 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00294 Packet4f pcos<Packet4f>(const Packet4f& _x)
00295 {
00296 Packet4f x = _x;
00297 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00298 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00299
00300 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
00301 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
00302 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
00303 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
00304
00305 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
00306 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
00307 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
00308 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
00309 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
00310 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
00311 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
00312 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
00313 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
00314 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
00315
00316 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
00317 Packet4i emm0, emm2;
00318
00319 x = pabs(x);
00320
00321
00322 y = pmul(x, p4f_cephes_FOPI);
00323
00324
00325 emm2 = _mm_cvttps_epi32(y);
00326
00327 emm2 = _mm_add_epi32(emm2, p4i_1);
00328 emm2 = _mm_and_si128(emm2, p4i_not1);
00329 y = _mm_cvtepi32_ps(emm2);
00330
00331 emm2 = _mm_sub_epi32(emm2, p4i_2);
00332
00333
00334 emm0 = _mm_andnot_si128(emm2, p4i_4);
00335 emm0 = _mm_slli_epi32(emm0, 29);
00336
00337 emm2 = _mm_and_si128(emm2, p4i_2);
00338 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
00339
00340 Packet4f sign_bit = _mm_castsi128_ps(emm0);
00341 Packet4f poly_mask = _mm_castsi128_ps(emm2);
00342
00343
00344
00345 xmm1 = pmul(y, p4f_minus_cephes_DP1);
00346 xmm2 = pmul(y, p4f_minus_cephes_DP2);
00347 xmm3 = pmul(y, p4f_minus_cephes_DP3);
00348 x = padd(x, xmm1);
00349 x = padd(x, xmm2);
00350 x = padd(x, xmm3);
00351
00352
00353 y = p4f_coscof_p0;
00354 Packet4f z = pmul(x,x);
00355
00356 y = pmadd(y,z,p4f_coscof_p1);
00357 y = pmadd(y,z,p4f_coscof_p2);
00358 y = pmul(y, z);
00359 y = pmul(y, z);
00360 Packet4f tmp = _mm_mul_ps(z, p4f_half);
00361 y = psub(y, tmp);
00362 y = padd(y, p4f_1);
00363
00364
00365 Packet4f y2 = p4f_sincof_p0;
00366 y2 = pmadd(y2, z, p4f_sincof_p1);
00367 y2 = pmadd(y2, z, p4f_sincof_p2);
00368 y2 = pmul(y2, z);
00369 y2 = pmadd(y2, x, x);
00370
00371
00372 y2 = _mm_and_ps(poly_mask, y2);
00373 y = _mm_andnot_ps(poly_mask, y);
00374 y = _mm_or_ps(y,y2);
00375
00376
00377 return _mm_xor_ps(y, sign_bit);
00378 }
00379
00380
00381
00382 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00383 Packet4f psqrt<Packet4f>(const Packet4f& _x)
00384 {
00385 Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
00386
00387
00388 Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
00389 Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
00390
00391 x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
00392 return pmul(_x,x);
00393 }
00394
00395 }
00396
00397 }
00398
00399 #endif // EIGEN_MATH_FUNCTIONS_SSE_H