1// This file is part of Eigen, a lightweight C++ template library 2// for linear algebra. 3// 4// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com) 5// 6// This Source Code Form is subject to the terms of the Mozilla 7// Public License v. 2.0. If a copy of the MPL was not distributed 8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10#ifndef EIGEN_MATH_FUNCTIONS_AVX_H 11#define EIGEN_MATH_FUNCTIONS_AVX_H 12 13/* The sin, cos, exp, and log functions of this file are loosely derived from 14 * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ 15 */ 16 17namespace Eigen { 18 19namespace internal { 20 21inline Packet8i pshiftleft(Packet8i v, int n) 22{ 23#ifdef EIGEN_VECTORIZE_AVX2 24 return _mm256_slli_epi32(v, n); 25#else 26 __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(v, 0), n); 27 __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(v, 1), n); 28 return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1); 29#endif 30} 31 32inline Packet8f pshiftright(Packet8f v, int n) 33{ 34#ifdef EIGEN_VECTORIZE_AVX2 35 return _mm256_cvtepi32_ps(_mm256_srli_epi32(_mm256_castps_si256(v), n)); 36#else 37 __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 0), n); 38 __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 1), n); 39 return _mm256_cvtepi32_ps(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1)); 40#endif 41} 42 43// Sine function 44// Computes sin(x) by wrapping x to the interval [-Pi/4,3*Pi/4] and 45// evaluating interpolants in [-Pi/4,Pi/4] or [Pi/4,3*Pi/4]. The interpolants 46// are (anti-)symmetric and thus have only odd/even coefficients 47template <> 48EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f 49psin<Packet8f>(const Packet8f& _x) { 50 Packet8f x = _x; 51 52 // Some useful values. 53 _EIGEN_DECLARE_CONST_Packet8i(one, 1); 54 _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f); 55 _EIGEN_DECLARE_CONST_Packet8f(two, 2.0f); 56 _EIGEN_DECLARE_CONST_Packet8f(one_over_four, 0.25f); 57 _EIGEN_DECLARE_CONST_Packet8f(one_over_pi, 3.183098861837907e-01f); 58 _EIGEN_DECLARE_CONST_Packet8f(neg_pi_first, -3.140625000000000e+00f); 59 _EIGEN_DECLARE_CONST_Packet8f(neg_pi_second, -9.670257568359375e-04f); 60 _EIGEN_DECLARE_CONST_Packet8f(neg_pi_third, -6.278329571784980e-07f); 61 _EIGEN_DECLARE_CONST_Packet8f(four_over_pi, 1.273239544735163e+00f); 62 63 // Map x from [-Pi/4,3*Pi/4] to z in [-1,3] and subtract the shifted period. 64 Packet8f z = pmul(x, p8f_one_over_pi); 65 Packet8f shift = _mm256_floor_ps(padd(z, p8f_one_over_four)); 66 x = pmadd(shift, p8f_neg_pi_first, x); 67 x = pmadd(shift, p8f_neg_pi_second, x); 68 x = pmadd(shift, p8f_neg_pi_third, x); 69 z = pmul(x, p8f_four_over_pi); 70 71 // Make a mask for the entries that need flipping, i.e. wherever the shift 72 // is odd. 73 Packet8i shift_ints = _mm256_cvtps_epi32(shift); 74 Packet8i shift_isodd = _mm256_castps_si256(_mm256_and_ps(_mm256_castsi256_ps(shift_ints), _mm256_castsi256_ps(p8i_one))); 75 Packet8i sign_flip_mask = pshiftleft(shift_isodd, 31); 76 77 // Create a mask for which interpolant to use, i.e. if z > 1, then the mask 78 // is set to ones for that entry. 79 Packet8f ival_mask = _mm256_cmp_ps(z, p8f_one, _CMP_GT_OQ); 80 81 // Evaluate the polynomial for the interval [1,3] in z. 82 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_0, 9.999999724233232e-01f); 83 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_2, -3.084242535619928e-01f); 84 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_4, 1.584991525700324e-02f); 85 _EIGEN_DECLARE_CONST_Packet8f(coeff_right_6, -3.188805084631342e-04f); 86 Packet8f z_minus_two = psub(z, p8f_two); 87 Packet8f z_minus_two2 = pmul(z_minus_two, z_minus_two); 88 Packet8f right = pmadd(p8f_coeff_right_6, z_minus_two2, p8f_coeff_right_4); 89 right = pmadd(right, z_minus_two2, p8f_coeff_right_2); 90 right = pmadd(right, z_minus_two2, p8f_coeff_right_0); 91 92 // Evaluate the polynomial for the interval [-1,1] in z. 93 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_1, 7.853981525427295e-01f); 94 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_3, -8.074536727092352e-02f); 95 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_5, 2.489871967827018e-03f); 96 _EIGEN_DECLARE_CONST_Packet8f(coeff_left_7, -3.587725841214251e-05f); 97 Packet8f z2 = pmul(z, z); 98 Packet8f left = pmadd(p8f_coeff_left_7, z2, p8f_coeff_left_5); 99 left = pmadd(left, z2, p8f_coeff_left_3); 100 left = pmadd(left, z2, p8f_coeff_left_1); 101 left = pmul(left, z); 102 103 // Assemble the results, i.e. select the left and right polynomials. 104 left = _mm256_andnot_ps(ival_mask, left); 105 right = _mm256_and_ps(ival_mask, right); 106 Packet8f res = _mm256_or_ps(left, right); 107 108 // Flip the sign on the odd intervals and return the result. 109 res = _mm256_xor_ps(res, _mm256_castsi256_ps(sign_flip_mask)); 110 return res; 111} 112 113// Natural logarithm 114// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2) 115// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can 116// be easily approximated by a polynomial centered on m=1 for stability. 117// TODO(gonnet): Further reduce the interval allowing for lower-degree 118// polynomial interpolants -> ... -> profit! 119template <> 120EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f 121plog<Packet8f>(const Packet8f& _x) { 122 Packet8f x = _x; 123 _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f); 124 _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f); 125 _EIGEN_DECLARE_CONST_Packet8f(126f, 126.0f); 126 127 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inv_mant_mask, ~0x7f800000); 128 129 // The smallest non denormalized float number. 130 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(min_norm_pos, 0x00800000); 131 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(minus_inf, 0xff800000); 132 133 // Polynomial coefficients. 134 _EIGEN_DECLARE_CONST_Packet8f(cephes_SQRTHF, 0.707106781186547524f); 135 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p0, 7.0376836292E-2f); 136 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p1, -1.1514610310E-1f); 137 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p2, 1.1676998740E-1f); 138 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p3, -1.2420140846E-1f); 139 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p4, +1.4249322787E-1f); 140 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p5, -1.6668057665E-1f); 141 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p6, +2.0000714765E-1f); 142 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p7, -2.4999993993E-1f); 143 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p8, +3.3333331174E-1f); 144 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q1, -2.12194440e-4f); 145 _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q2, 0.693359375f); 146 147 Packet8f invalid_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_NGE_UQ); // not greater equal is true if x is NaN 148 Packet8f iszero_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_EQ_OQ); 149 150 // Truncate input values to the minimum positive normal. 151 x = pmax(x, p8f_min_norm_pos); 152 153 Packet8f emm0 = pshiftright(x,23); 154 Packet8f e = _mm256_sub_ps(emm0, p8f_126f); 155 156 // Set the exponents to -1, i.e. x are in the range [0.5,1). 157 x = _mm256_and_ps(x, p8f_inv_mant_mask); 158 x = _mm256_or_ps(x, p8f_half); 159 160 // part2: Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2)) 161 // and shift by -1. The values are then centered around 0, which improves 162 // the stability of the polynomial evaluation. 163 // if( x < SQRTHF ) { 164 // e -= 1; 165 // x = x + x - 1.0; 166 // } else { x = x - 1.0; } 167 Packet8f mask = _mm256_cmp_ps(x, p8f_cephes_SQRTHF, _CMP_LT_OQ); 168 Packet8f tmp = _mm256_and_ps(x, mask); 169 x = psub(x, p8f_1); 170 e = psub(e, _mm256_and_ps(p8f_1, mask)); 171 x = padd(x, tmp); 172 173 Packet8f x2 = pmul(x, x); 174 Packet8f x3 = pmul(x2, x); 175 176 // Evaluate the polynomial approximant of degree 8 in three parts, probably 177 // to improve instruction-level parallelism. 178 Packet8f y, y1, y2; 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); 187 y = pmul(y, x3); 188 189 // Add the logarithm of the exponent back to the result of the interpolation. 190 y1 = pmul(e, p8f_cephes_log_q1); 191 tmp = pmul(x2, p8f_half); 192 y = padd(y, y1); 193 x = psub(x, tmp); 194 y2 = pmul(e, p8f_cephes_log_q2); 195 x = padd(x, y); 196 x = padd(x, y2); 197 198 // Filter out invalid inputs, i.e. negative arg will be NAN, 0 will be -INF. 199 return _mm256_or_ps( 200 _mm256_andnot_ps(iszero_mask, _mm256_or_ps(x, invalid_mask)), 201 _mm256_and_ps(iszero_mask, p8f_minus_inf)); 202} 203 204// Exponential function. Works by writing "x = m*log(2) + r" where 205// "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then 206// "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1). 207template <> 208EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f 209pexp<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); 213 214 _EIGEN_DECLARE_CONST_Packet8f(exp_hi, 88.3762626647950f); 215 _EIGEN_DECLARE_CONST_Packet8f(exp_lo, -88.3762626647949f); 216 217 _EIGEN_DECLARE_CONST_Packet8f(cephes_LOG2EF, 1.44269504088896341f); 218 219 _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); 225 226 // Clamp x. 227 Packet8f x = pmax(pmin(_x, p8f_exp_hi), p8f_exp_lo); 228 229 // Express exp(x) as exp(m*ln(2) + r), start by extracting 230 // m = floor(x/ln(2) + 0.5). 231 Packet8f m = _mm256_floor_ps(pmadd(x, p8f_cephes_LOG2EF, p8f_half)); 232 233// Get r = x - m*ln(2). If no FMA instructions are available, m*ln(2) is 234// subtracted out in two parts, m*C1+m*C2 = m*ln(2), to avoid accumulating 235// truncation errors. Note that we don't use the "pmadd" function here to 236// ensure that a precision-preserving FMA instruction is used. 237#ifdef EIGEN_VECTORIZE_FMA 238 _EIGEN_DECLARE_CONST_Packet8f(nln2, -0.6931471805599453f); 239 Packet8f r = _mm256_fmadd_ps(m, p8f_nln2, x); 240#else 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)); 245#endif 246 247 Packet8f r2 = pmul(r, r); 248 249 // TODO(gonnet): Split into odd/even polynomials and try to exploit 250 // instruction-level parallelism. 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); 257 y = pmadd(y, r2, r); 258 y = padd(y, p8f_1); 259 260 // Build emm0 = 2^m. 261 Packet8i emm0 = _mm256_cvttps_epi32(padd(m, p8f_127)); 262 emm0 = pshiftleft(emm0, 23); 263 264 // Return 2^m * exp(r). 265 return pmax(pmul(y, _mm256_castsi256_ps(emm0)), _x); 266} 267 268// Hyperbolic Tangent function. 269template <> 270EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f 271ptanh<Packet8f>(const Packet8f& x) { 272 return internal::generic_fast_tanh_float(x); 273} 274 275template <> 276EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d 277pexp<Packet4d>(const Packet4d& _x) { 278 Packet4d x = _x; 279 280 _EIGEN_DECLARE_CONST_Packet4d(1, 1.0); 281 _EIGEN_DECLARE_CONST_Packet4d(2, 2.0); 282 _EIGEN_DECLARE_CONST_Packet4d(half, 0.5); 283 284 _EIGEN_DECLARE_CONST_Packet4d(exp_hi, 709.437); 285 _EIGEN_DECLARE_CONST_Packet4d(exp_lo, -709.436139303); 286 287 _EIGEN_DECLARE_CONST_Packet4d(cephes_LOG2EF, 1.4426950408889634073599); 288 289 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p0, 1.26177193074810590878e-4); 290 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p1, 3.02994407707441961300e-2); 291 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p2, 9.99999999999999999910e-1); 292 293 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q0, 3.00198505138664455042e-6); 294 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q1, 2.52448340349684104192e-3); 295 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q2, 2.27265548208155028766e-1); 296 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q3, 2.00000000000000000009e0); 297 298 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C1, 0.693145751953125); 299 _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C2, 1.42860682030941723212e-6); 300 _EIGEN_DECLARE_CONST_Packet4i(1023, 1023); 301 302 Packet4d tmp, fx; 303 304 // clamp x 305 x = pmax(pmin(x, p4d_exp_hi), p4d_exp_lo); 306 // Express exp(x) as exp(g + n*log(2)). 307 fx = pmadd(p4d_cephes_LOG2EF, x, p4d_half); 308 309 // Get the integer modulus of log(2), i.e. the "n" described above. 310 fx = _mm256_floor_pd(fx); 311 312 // Get the remainder modulo log(2), i.e. the "g" described above. Subtract 313 // n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last 314 // digits right. 315 tmp = pmul(fx, p4d_cephes_exp_C1); 316 Packet4d z = pmul(fx, p4d_cephes_exp_C2); 317 x = psub(x, tmp); 318 x = psub(x, z); 319 320 Packet4d x2 = pmul(x, x); 321 322 // Evaluate the numerator polynomial of the rational interpolant. 323 Packet4d px = p4d_cephes_exp_p0; 324 px = pmadd(px, x2, p4d_cephes_exp_p1); 325 px = pmadd(px, x2, p4d_cephes_exp_p2); 326 px = pmul(px, x); 327 328 // Evaluate the denominator polynomial of the rational interpolant. 329 Packet4d qx = p4d_cephes_exp_q0; 330 qx = pmadd(qx, x2, p4d_cephes_exp_q1); 331 qx = pmadd(qx, x2, p4d_cephes_exp_q2); 332 qx = pmadd(qx, x2, p4d_cephes_exp_q3); 333 334 // I don't really get this bit, copied from the SSE2 routines, so... 335 // TODO(gonnet): Figure out what is going on here, perhaps find a better 336 // rational interpolant? 337 x = _mm256_div_pd(px, psub(qx, px)); 338 x = pmadd(p4d_2, x, p4d_1); 339 340 // Build e=2^n by constructing the exponents in a 128-bit vector and 341 // shifting them to where they belong in double-precision values. 342 __m128i emm0 = _mm256_cvtpd_epi32(fx); 343 emm0 = _mm_add_epi32(emm0, p4i_1023); 344 emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(3, 1, 2, 0)); 345 __m128i lo = _mm_slli_epi64(emm0, 52); 346 __m128i hi = _mm_slli_epi64(_mm_srli_epi64(emm0, 32), 52); 347 __m256i e = _mm256_insertf128_si256(_mm256_setzero_si256(), lo, 0); 348 e = _mm256_insertf128_si256(e, hi, 1); 349 350 // Construct the result 2^n * exp(g) = e * x. The max is used to catch 351 // non-finite values in the input. 352 return pmax(pmul(x, _mm256_castsi256_pd(e)), _x); 353} 354 355// Functions for sqrt. 356// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step 357// of Newton's method, at a cost of 1-2 bits of precision as opposed to the 358// exact solution. It does not handle +inf, or denormalized numbers correctly. 359// The main advantage of this approach is not just speed, but also the fact that 360// it can be inlined and pipelined with other computations, further reducing its 361// effective latency. This is similar to Quake3's fast inverse square root. 362// For detail see here: http://www.beyond3d.com/content/articles/8/ 363#if EIGEN_FAST_MATH 364template <> 365EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f 366psqrt<Packet8f>(const Packet8f& _x) { 367 Packet8f half = pmul(_x, pset1<Packet8f>(.5f)); 368 Packet8f denormal_mask = _mm256_and_ps( 369 _mm256_cmp_ps(_x, pset1<Packet8f>((std::numeric_limits<float>::min)()), 370 _CMP_LT_OQ), 371 _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_GE_OQ)); 372 373 // Compute approximate reciprocal sqrt. 374 Packet8f x = _mm256_rsqrt_ps(_x); 375 // Do a single step of Newton's iteration. 376 x = pmul(x, psub(pset1<Packet8f>(1.5f), pmul(half, pmul(x,x)))); 377 // Flush results for denormals to zero. 378 return _mm256_andnot_ps(denormal_mask, pmul(_x,x)); 379} 380#else 381template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 382Packet8f psqrt<Packet8f>(const Packet8f& x) { 383 return _mm256_sqrt_ps(x); 384} 385#endif 386template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 387Packet4d psqrt<Packet4d>(const Packet4d& x) { 388 return _mm256_sqrt_pd(x); 389} 390#if EIGEN_FAST_MATH 391 392template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 393Packet8f prsqrt<Packet8f>(const Packet8f& _x) { 394 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inf, 0x7f800000); 395 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(nan, 0x7fc00000); 396 _EIGEN_DECLARE_CONST_Packet8f(one_point_five, 1.5f); 397 _EIGEN_DECLARE_CONST_Packet8f(minus_half, -0.5f); 398 _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(flt_min, 0x00800000); 399 400 Packet8f neg_half = pmul(_x, p8f_minus_half); 401 402 // select only the inverse sqrt of positive normal inputs (denormals are 403 // flushed to zero and cause infs as well). 404 Packet8f le_zero_mask = _mm256_cmp_ps(_x, p8f_flt_min, _CMP_LT_OQ); 405 Packet8f x = _mm256_andnot_ps(le_zero_mask, _mm256_rsqrt_ps(_x)); 406 407 // Fill in NaNs and Infs for the negative/zero entries. 408 Packet8f neg_mask = _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_LT_OQ); 409 Packet8f zero_mask = _mm256_andnot_ps(neg_mask, le_zero_mask); 410 Packet8f infs_and_nans = _mm256_or_ps(_mm256_and_ps(neg_mask, p8f_nan), 411 _mm256_and_ps(zero_mask, p8f_inf)); 412 413 // Do a single step of Newton's iteration. 414 x = pmul(x, pmadd(neg_half, pmul(x, x), p8f_one_point_five)); 415 416 // Insert NaNs and Infs in all the right places. 417 return _mm256_or_ps(x, infs_and_nans); 418} 419 420#else 421template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 422Packet8f prsqrt<Packet8f>(const Packet8f& x) { 423 _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f); 424 return _mm256_div_ps(p8f_one, _mm256_sqrt_ps(x)); 425} 426#endif 427 428template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED 429Packet4d prsqrt<Packet4d>(const Packet4d& x) { 430 _EIGEN_DECLARE_CONST_Packet4d(one, 1.0); 431 return _mm256_div_pd(p4d_one, _mm256_sqrt_pd(x)); 432} 433 434 435} // end namespace internal 436 437} // end namespace Eigen 438 439#endif // EIGEN_MATH_FUNCTIONS_AVX_H 440