10 #ifndef EIGEN_MATH_FUNCTIONS_AVX_H
11 #define EIGEN_MATH_FUNCTIONS_AVX_H
15 #define _mm256_setr_m128(lo, hi) \
16 _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1)
31 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
32 psin<Packet8f>(
const Packet8f& _x) {
36 _EIGEN_DECLARE_CONST_Packet8i(one, 1);
37 _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f);
38 _EIGEN_DECLARE_CONST_Packet8f(two, 2.0f);
39 _EIGEN_DECLARE_CONST_Packet8f(one_over_four, 0.25f);
40 _EIGEN_DECLARE_CONST_Packet8f(one_over_pi, 3.183098861837907e-01f);
41 _EIGEN_DECLARE_CONST_Packet8f(neg_pi_first, -3.140625000000000e+00);
42 _EIGEN_DECLARE_CONST_Packet8f(neg_pi_second, -9.670257568359375e-04);
43 _EIGEN_DECLARE_CONST_Packet8f(neg_pi_third, -6.278329571784980e-07);
44 _EIGEN_DECLARE_CONST_Packet8f(four_over_pi, 1.273239544735163e+00);
47 Packet8f z = pmul(x, p8f_one_over_pi);
48 Packet8f shift = _mm256_floor_ps(padd(z, p8f_one_over_four));
49 x = pmadd(shift, p8f_neg_pi_first, x);
50 x = pmadd(shift, p8f_neg_pi_second, x);
51 x = pmadd(shift, p8f_neg_pi_third, x);
52 z = pmul(x, p8f_four_over_pi);
56 Packet8i shift_ints = _mm256_cvtps_epi32(shift);
57 Packet8i shift_isodd =
58 (__m256i)_mm256_and_ps((__m256)shift_ints, (__m256)p8i_one);
59 #ifdef EIGEN_VECTORIZE_AVX2
60 Packet8i sign_flip_mask = _mm256_slli_epi32(shift_isodd, 31);
63 _mm_slli_epi32(_mm256_extractf128_si256((__m256i)shift_isodd, 0), 31);
65 _mm_slli_epi32(_mm256_extractf128_si256((__m256i)shift_isodd, 1), 31);
66 Packet8i sign_flip_mask = _mm256_setr_m128(lo, hi);
71 Packet8f ival_mask = _mm256_cmp_ps(z, p8f_one, _CMP_GT_OQ);
74 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_0, 9.999999724233232e-01f);
75 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_2, -3.084242535619928e-01);
76 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_4, 1.584991525700324e-02);
77 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_6, -3.188805084631342e-04);
78 Packet8f z_minus_two = psub(z, p8f_two);
79 Packet8f z_minus_two2 = pmul(z_minus_two, z_minus_two);
80 Packet8f right = pmadd(p8f_coeff_right_6, z_minus_two2, p8f_coeff_right_4);
81 right = pmadd(right, z_minus_two2, p8f_coeff_right_2);
82 right = pmadd(right, z_minus_two2, p8f_coeff_right_0);
85 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_1, 7.853981525427295e-01);
86 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_3, -8.074536727092352e-02);
87 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_5, 2.489871967827018e-03);
88 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_7, -3.587725841214251e-05);
89 Packet8f z2 = pmul(z, z);
90 Packet8f left = pmadd(p8f_coeff_left_7, z2, p8f_coeff_left_5);
91 left = pmadd(left, z2, p8f_coeff_left_3);
92 left = pmadd(left, z2, p8f_coeff_left_1);
96 left = _mm256_andnot_ps(ival_mask, left);
97 right = _mm256_and_ps(ival_mask, right);
98 Packet8f res = _mm256_or_ps(left, right);
101 res = _mm256_xor_ps(res, (__m256)sign_flip_mask);
112 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
113 plog<Packet8f>(
const Packet8f& _x) {
115 _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f);
116 _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f);
117 _EIGEN_DECLARE_CONST_Packet8f(126f, 126.0f);
119 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inv_mant_mask, ~0x7f800000);
122 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(min_norm_pos, 0x00800000);
123 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(minus_inf, 0xff800000);
126 _EIGEN_DECLARE_CONST_Packet8f(cephes_SQRTHF, 0.707106781186547524f);
127 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p0, 7.0376836292E-2f);
128 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p1, -1.1514610310E-1f);
129 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p2, 1.1676998740E-1f);
130 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p3, -1.2420140846E-1f);
131 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p4, +1.4249322787E-1f);
132 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p5, -1.6668057665E-1f);
133 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p6, +2.0000714765E-1f);
134 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p7, -2.4999993993E-1f);
135 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p8, +3.3333331174E-1f);
136 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q1, -2.12194440e-4f);
137 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q2, 0.693359375f);
139 Packet8f invalid_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_NGE_UQ);
140 Packet8f iszero_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_EQ_OQ);
143 x = pmax(x, p8f_min_norm_pos);
147 #ifdef EIGEN_VECTORIZE_AVX2
148 Packet8f emm0 = _mm256_cvtepi32_ps(_mm256_srli_epi32((__m256i)x, 23));
150 __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256((__m256i)x, 0), 23);
151 __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256((__m256i)x, 1), 23);
152 Packet8f emm0 = _mm256_cvtepi32_ps(_mm256_setr_m128(lo, hi));
154 Packet8f e = _mm256_sub_ps(emm0, p8f_126f);
157 x = _mm256_and_ps(x, p8f_inv_mant_mask);
158 x = _mm256_or_ps(x, p8f_half);
167 Packet8f mask = _mm256_cmp_ps(x, p8f_cephes_SQRTHF, _CMP_LT_OQ);
168 Packet8f tmp = _mm256_and_ps(x, mask);
170 e = psub(e, _mm256_and_ps(p8f_1, mask));
173 Packet8f x2 = pmul(x, x);
174 Packet8f x3 = pmul(x2, x);
179 y = pmadd(p8f_cephes_log_p0, x, p8f_cephes_log_p1);
180 y1 = pmadd(p8f_cephes_log_p3, x, p8f_cephes_log_p4);
181 y2 = pmadd(p8f_cephes_log_p6, x, p8f_cephes_log_p7);
182 y = pmadd(y, x, p8f_cephes_log_p2);
183 y1 = pmadd(y1, x, p8f_cephes_log_p5);
184 y2 = pmadd(y2, x, p8f_cephes_log_p8);
185 y = pmadd(y, x3, y1);
186 y = pmadd(y, x3, y2);
190 y1 = pmul(e, p8f_cephes_log_q1);
191 tmp = pmul(x2, p8f_half);
194 y2 = pmul(e, p8f_cephes_log_q2);
200 _mm256_andnot_ps(iszero_mask, _mm256_or_ps(x, invalid_mask)),
201 _mm256_and_ps(iszero_mask, p8f_minus_inf));
208 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
209 pexp<Packet8f>(
const Packet8f& _x) {
210 _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f);
211 _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f);
212 _EIGEN_DECLARE_CONST_Packet8f(127, 127.0f);
214 _EIGEN_DECLARE_CONST_Packet8f(exp_hi, 88.3762626647950f);
215 _EIGEN_DECLARE_CONST_Packet8f(exp_lo, -88.3762626647949f);
217 _EIGEN_DECLARE_CONST_Packet8f(cephes_LOG2EF, 1.44269504088896341f);
219 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p0, 1.9875691500E-4f);
220 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p1, 1.3981999507E-3f);
221 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p2, 8.3334519073E-3f);
222 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p3, 4.1665795894E-2f);
223 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p4, 1.6666665459E-1f);
224 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p5, 5.0000001201E-1f);
227 Packet8f x = pmax(pmin(_x, p8f_exp_hi), p8f_exp_lo);
231 Packet8f m = _mm256_floor_ps(pmadd(x, p8f_cephes_LOG2EF, p8f_half));
237 #ifdef EIGEN_VECTORIZE_FMA
238 _EIGEN_DECLARE_CONST_Packet8f(nln2, -0.6931471805599453f);
239 Packet8f r = _mm256_fmadd_ps(m, p8f_nln2, x);
241 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C1, 0.693359375f);
242 _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C2, -2.12194440e-4f);
243 Packet8f r = psub(x, pmul(m, p8f_cephes_exp_C1));
244 r = psub(r, pmul(m, p8f_cephes_exp_C2));
247 Packet8f r2 = pmul(r, r);
251 Packet8f y = p8f_cephes_exp_p0;
252 y = pmadd(y, r, p8f_cephes_exp_p1);
253 y = pmadd(y, r, p8f_cephes_exp_p2);
254 y = pmadd(y, r, p8f_cephes_exp_p3);
255 y = pmadd(y, r, p8f_cephes_exp_p4);
256 y = pmadd(y, r, p8f_cephes_exp_p5);
261 Packet8i emm0 = _mm256_cvttps_epi32(padd(m, p8f_127));
262 #ifdef EIGEN_VECTORIZE_AVX2
263 emm0 = _mm256_slli_epi32(emm0, 23);
265 __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(emm0, 0), 23);
266 __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(emm0, 1), 23);
267 emm0 = _mm256_setr_m128(lo, hi);
271 return pmax(pmul(y, _mm256_castsi256_ps(emm0)), _x);
275 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d
276 pexp<Packet4d>(
const Packet4d& _x) {
279 _EIGEN_DECLARE_CONST_Packet4d(1, 1.0);
280 _EIGEN_DECLARE_CONST_Packet4d(2, 2.0);
281 _EIGEN_DECLARE_CONST_Packet4d(half, 0.5);
283 _EIGEN_DECLARE_CONST_Packet4d(exp_hi, 709.437);
284 _EIGEN_DECLARE_CONST_Packet4d(exp_lo, -709.436139303);
286 _EIGEN_DECLARE_CONST_Packet4d(cephes_LOG2EF, 1.4426950408889634073599);
288 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p0, 1.26177193074810590878e-4);
289 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p1, 3.02994407707441961300e-2);
290 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p2, 9.99999999999999999910e-1);
292 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q0, 3.00198505138664455042e-6);
293 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q1, 2.52448340349684104192e-3);
294 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q2, 2.27265548208155028766e-1);
295 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q3, 2.00000000000000000009e0);
297 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C1, 0.693145751953125);
298 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C2, 1.42860682030941723212e-6);
299 _EIGEN_DECLARE_CONST_Packet4i(1023, 1023);
304 x = pmax(pmin(x, p4d_exp_hi), p4d_exp_lo);
306 fx = pmadd(p4d_cephes_LOG2EF, x, p4d_half);
309 fx = _mm256_floor_pd(fx);
314 tmp = pmul(fx, p4d_cephes_exp_C1);
315 Packet4d z = pmul(fx, p4d_cephes_exp_C2);
319 Packet4d x2 = pmul(x, x);
322 Packet4d px = p4d_cephes_exp_p0;
323 px = pmadd(px, x2, p4d_cephes_exp_p1);
324 px = pmadd(px, x2, p4d_cephes_exp_p2);
328 Packet4d qx = p4d_cephes_exp_q0;
329 qx = pmadd(qx, x2, p4d_cephes_exp_q1);
330 qx = pmadd(qx, x2, p4d_cephes_exp_q2);
331 qx = pmadd(qx, x2, p4d_cephes_exp_q3);
336 x = _mm256_div_pd(px, psub(qx, px));
337 x = pmadd(p4d_2, x, p4d_1);
341 __m128i emm0 = _mm256_cvtpd_epi32(fx);
342 emm0 = _mm_add_epi32(emm0, p4i_1023);
343 emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(3, 1, 2, 0));
344 __m128i lo = _mm_slli_epi64(emm0, 52);
345 __m128i hi = _mm_slli_epi64(_mm_srli_epi64(emm0, 32), 52);
346 __m256i e = _mm256_insertf128_si256(_mm256_setzero_si256(), lo, 0);
347 e = _mm256_insertf128_si256(e, hi, 1);
351 return pmax(pmul(x, Packet4d(e)), _x);
362 EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f
363 psqrt<Packet8f>(
const Packet8f& _x) {
364 _EIGEN_DECLARE_CONST_Packet8f(one_point_five, 1.5f);
365 _EIGEN_DECLARE_CONST_Packet8f(minus_half, -0.5f);
366 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(flt_min, 0x00800000);
368 Packet8f neg_half = pmul(_x, p8f_minus_half);
372 Packet8f non_zero_mask = _mm256_cmp_ps(_x, p8f_flt_min, _CMP_GE_OQ);
373 Packet8f x = _mm256_and_ps(non_zero_mask, _mm256_rsqrt_ps(_x));
376 x = pmul(x, pmadd(neg_half, pmul(x, x), p8f_one_point_five));
383 template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
384 Packet8f psqrt<Packet8f>(
const Packet8f& x) {
385 return _mm256_sqrt_ps(x);
388 template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
389 Packet4d psqrt<Packet4d>(
const Packet4d& x) {
390 return _mm256_sqrt_pd(x);
394 template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
395 Packet8f prsqrt<Packet8f>(
const Packet8f& _x) {
396 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inf, 0x7f800000);
397 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(nan, 0x7fc00000);
398 _EIGEN_DECLARE_CONST_Packet8f(one_point_five, 1.5f);
399 _EIGEN_DECLARE_CONST_Packet8f(minus_half, -0.5f);
400 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(flt_min, 0x00800000);
402 Packet8f neg_half = pmul(_x, p8f_minus_half);
406 Packet8f le_zero_mask = _mm256_cmp_ps(_x, p8f_flt_min, _CMP_LT_OQ);
407 Packet8f x = _mm256_andnot_ps(le_zero_mask, _mm256_rsqrt_ps(_x));
410 Packet8f neg_mask = _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_LT_OQ);
411 Packet8f zero_mask = _mm256_andnot_ps(neg_mask, le_zero_mask);
412 Packet8f infs_and_nans = _mm256_or_ps(_mm256_and_ps(neg_mask, p8f_nan),
413 _mm256_and_ps(zero_mask, p8f_inf));
416 x = pmul(x, pmadd(neg_half, pmul(x, x), p8f_one_point_five));
419 return _mm256_or_ps(x, infs_and_nans);
423 template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
424 Packet8f prsqrt<Packet8f>(
const Packet8f& x) {
425 _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f);
426 return _mm256_div_ps(p8f_one, _mm256_sqrt_ps(x));
430 template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
431 Packet4d prsqrt<Packet4d>(
const Packet4d& x) {
432 _EIGEN_DECLARE_CONST_Packet4d(one, 1.0);
433 return _mm256_div_pd(p4d_one, _mm256_sqrt_pd(x));
441 #endif // EIGEN_MATH_FUNCTIONS_AVX_H
Definition: Eigen_Colamd.h:54