00001
00002
00003
00004
00005
00006
00007
00008
00009
00010
00011
00012
00013
00014
00015 #ifndef EIGEN_MATH_FUNCTIONS_SSE_H
00016 #define EIGEN_MATH_FUNCTIONS_SSE_H
00017
00018 namespace Eigen {
00019
00020 namespace internal {
00021
00022 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00023 Packet4f plog<Packet4f>(const Packet4f& _x)
00024 {
00025 Packet4f x = _x;
00026 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00027 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00028 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
00029
00030 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
00031
00032
00033 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
00034
00035
00036
00037
00038 _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
00039 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
00040 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
00041 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
00042 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
00043 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
00044 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
00045 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
00046 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
00047 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
00048 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
00049 _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
00050
00051
00052 Packet4i emm0;
00053
00054 Packet4f invalid_mask = _mm_cmple_ps(x, _mm_setzero_ps());
00055
00056 x = pmax(x, p4f_min_norm_pos);
00057 emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
00058
00059
00060 x = _mm_and_ps(x, p4f_inv_mant_mask);
00061 x = _mm_or_ps(x, p4f_half);
00062
00063 emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
00064 Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
00065
00066
00067
00068
00069
00070
00071
00072 Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
00073 Packet4f tmp = _mm_and_ps(x, mask);
00074 x = psub(x, p4f_1);
00075 e = psub(e, _mm_and_ps(p4f_1, mask));
00076 x = padd(x, tmp);
00077
00078 Packet4f x2 = pmul(x,x);
00079 Packet4f x3 = pmul(x2,x);
00080
00081 Packet4f y, y1, y2;
00082 y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
00083 y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
00084 y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
00085 y = pmadd(y , x, p4f_cephes_log_p2);
00086 y1 = pmadd(y1, x, p4f_cephes_log_p5);
00087 y2 = pmadd(y2, x, p4f_cephes_log_p8);
00088 y = pmadd(y, x3, y1);
00089 y = pmadd(y, x3, y2);
00090 y = pmul(y, x3);
00091
00092 y1 = pmul(e, p4f_cephes_log_q1);
00093 tmp = pmul(x2, p4f_half);
00094 y = padd(y, y1);
00095 x = psub(x, tmp);
00096 y2 = pmul(e, p4f_cephes_log_q2);
00097 x = padd(x, y);
00098 x = padd(x, y2);
00099 return _mm_or_ps(x, invalid_mask);
00100 }
00101
00102 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00103 Packet4f pexp<Packet4f>(const Packet4f& _x)
00104 {
00105 Packet4f x = _x;
00106 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00107 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00108 _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
00109
00110
00111 _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
00112 _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
00113
00114 _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
00115 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
00116 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
00117
00118 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
00119 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
00120 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
00121 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
00122 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
00123 _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
00124
00125 Packet4f tmp = _mm_setzero_ps(), fx;
00126 Packet4i emm0;
00127
00128
00129 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
00130
00131
00132 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
00133
00134
00135 emm0 = _mm_cvttps_epi32(fx);
00136 tmp = _mm_cvtepi32_ps(emm0);
00137
00138 Packet4f mask = _mm_cmpgt_ps(tmp, fx);
00139 mask = _mm_and_ps(mask, p4f_1);
00140 fx = psub(tmp, mask);
00141
00142 tmp = pmul(fx, p4f_cephes_exp_C1);
00143 Packet4f z = pmul(fx, p4f_cephes_exp_C2);
00144 x = psub(x, tmp);
00145 x = psub(x, z);
00146
00147 z = pmul(x,x);
00148
00149 Packet4f y = p4f_cephes_exp_p0;
00150 y = pmadd(y, x, p4f_cephes_exp_p1);
00151 y = pmadd(y, x, p4f_cephes_exp_p2);
00152 y = pmadd(y, x, p4f_cephes_exp_p3);
00153 y = pmadd(y, x, p4f_cephes_exp_p4);
00154 y = pmadd(y, x, p4f_cephes_exp_p5);
00155 y = pmadd(y, z, x);
00156 y = padd(y, p4f_1);
00157
00158
00159 emm0 = _mm_cvttps_epi32(fx);
00160 emm0 = _mm_add_epi32(emm0, p4i_0x7f);
00161 emm0 = _mm_slli_epi32(emm0, 23);
00162 return pmul(y, _mm_castsi128_ps(emm0));
00163 }
00164
00165
00166
00167
00168
00169
00170
00171
00172
00173
00174
00175
00176
00177 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00178 Packet4f psin<Packet4f>(const Packet4f& _x)
00179 {
00180 Packet4f x = _x;
00181 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00182 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00183
00184 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
00185 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
00186 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
00187 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
00188
00189 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
00190
00191 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
00192 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
00193 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
00194 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
00195 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
00196 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
00197 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
00198 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
00199 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
00200 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
00201
00202 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
00203
00204 Packet4i emm0, emm2;
00205 sign_bit = x;
00206
00207 x = pabs(x);
00208
00209
00210
00211
00212 sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
00213
00214
00215 y = pmul(x, p4f_cephes_FOPI);
00216
00217
00218 emm2 = _mm_cvttps_epi32(y);
00219
00220 emm2 = _mm_add_epi32(emm2, p4i_1);
00221 emm2 = _mm_and_si128(emm2, p4i_not1);
00222 y = _mm_cvtepi32_ps(emm2);
00223
00224 emm0 = _mm_and_si128(emm2, p4i_4);
00225 emm0 = _mm_slli_epi32(emm0, 29);
00226
00227
00228
00229
00230
00231
00232 emm2 = _mm_and_si128(emm2, p4i_2);
00233 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
00234
00235 Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
00236 Packet4f poly_mask = _mm_castsi128_ps(emm2);
00237 sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
00238
00239
00240
00241 xmm1 = pmul(y, p4f_minus_cephes_DP1);
00242 xmm2 = pmul(y, p4f_minus_cephes_DP2);
00243 xmm3 = pmul(y, p4f_minus_cephes_DP3);
00244 x = padd(x, xmm1);
00245 x = padd(x, xmm2);
00246 x = padd(x, xmm3);
00247
00248
00249 y = p4f_coscof_p0;
00250 Packet4f z = _mm_mul_ps(x,x);
00251
00252 y = pmadd(y, z, p4f_coscof_p1);
00253 y = pmadd(y, z, p4f_coscof_p2);
00254 y = pmul(y, z);
00255 y = pmul(y, z);
00256 Packet4f tmp = pmul(z, p4f_half);
00257 y = psub(y, tmp);
00258 y = padd(y, p4f_1);
00259
00260
00261
00262 Packet4f y2 = p4f_sincof_p0;
00263 y2 = pmadd(y2, z, p4f_sincof_p1);
00264 y2 = pmadd(y2, z, p4f_sincof_p2);
00265 y2 = pmul(y2, z);
00266 y2 = pmul(y2, x);
00267 y2 = padd(y2, x);
00268
00269
00270 y2 = _mm_and_ps(poly_mask, y2);
00271 y = _mm_andnot_ps(poly_mask, y);
00272 y = _mm_or_ps(y,y2);
00273
00274 return _mm_xor_ps(y, sign_bit);
00275 }
00276
00277
00278 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00279 Packet4f pcos<Packet4f>(const Packet4f& _x)
00280 {
00281 Packet4f x = _x;
00282 _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
00283 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
00284
00285 _EIGEN_DECLARE_CONST_Packet4i(1, 1);
00286 _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
00287 _EIGEN_DECLARE_CONST_Packet4i(2, 2);
00288 _EIGEN_DECLARE_CONST_Packet4i(4, 4);
00289
00290 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
00291 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
00292 _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
00293 _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
00294 _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
00295 _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
00296 _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
00297 _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
00298 _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
00299 _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f);
00300
00301 Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
00302 Packet4i emm0, emm2;
00303
00304 x = pabs(x);
00305
00306
00307 y = pmul(x, p4f_cephes_FOPI);
00308
00309
00310 emm2 = _mm_cvttps_epi32(y);
00311
00312 emm2 = _mm_add_epi32(emm2, p4i_1);
00313 emm2 = _mm_and_si128(emm2, p4i_not1);
00314 y = _mm_cvtepi32_ps(emm2);
00315
00316 emm2 = _mm_sub_epi32(emm2, p4i_2);
00317
00318
00319 emm0 = _mm_andnot_si128(emm2, p4i_4);
00320 emm0 = _mm_slli_epi32(emm0, 29);
00321
00322 emm2 = _mm_and_si128(emm2, p4i_2);
00323 emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
00324
00325 Packet4f sign_bit = _mm_castsi128_ps(emm0);
00326 Packet4f poly_mask = _mm_castsi128_ps(emm2);
00327
00328
00329
00330 xmm1 = pmul(y, p4f_minus_cephes_DP1);
00331 xmm2 = pmul(y, p4f_minus_cephes_DP2);
00332 xmm3 = pmul(y, p4f_minus_cephes_DP3);
00333 x = padd(x, xmm1);
00334 x = padd(x, xmm2);
00335 x = padd(x, xmm3);
00336
00337
00338 y = p4f_coscof_p0;
00339 Packet4f z = pmul(x,x);
00340
00341 y = pmadd(y,z,p4f_coscof_p1);
00342 y = pmadd(y,z,p4f_coscof_p2);
00343 y = pmul(y, z);
00344 y = pmul(y, z);
00345 Packet4f tmp = _mm_mul_ps(z, p4f_half);
00346 y = psub(y, tmp);
00347 y = padd(y, p4f_1);
00348
00349
00350 Packet4f y2 = p4f_sincof_p0;
00351 y2 = pmadd(y2, z, p4f_sincof_p1);
00352 y2 = pmadd(y2, z, p4f_sincof_p2);
00353 y2 = pmul(y2, z);
00354 y2 = pmadd(y2, x, x);
00355
00356
00357 y2 = _mm_and_ps(poly_mask, y2);
00358 y = _mm_andnot_ps(poly_mask, y);
00359 y = _mm_or_ps(y,y2);
00360
00361
00362 return _mm_xor_ps(y, sign_bit);
00363 }
00364
00365
00366
00367 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
00368 Packet4f psqrt<Packet4f>(const Packet4f& _x)
00369 {
00370 Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
00371
00372
00373 Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
00374 Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
00375
00376 x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
00377 return pmul(_x,x);
00378 }
00379
00380 }
00381
00382 }
00383
00384 #endif // EIGEN_MATH_FUNCTIONS_SSE_H