diff options
Diffstat (limited to 'Eigen/src/Core/arch/AVX/MathFunctions.h')
| -rw-r--r-- | Eigen/src/Core/arch/AVX/MathFunctions.h | 439 |
1 files changed, 439 insertions, 0 deletions
diff --git a/Eigen/src/Core/arch/AVX/MathFunctions.h b/Eigen/src/Core/arch/AVX/MathFunctions.h new file mode 100644 index 000000000..6af67ce2d --- /dev/null +++ b/Eigen/src/Core/arch/AVX/MathFunctions.h @@ -0,0 +1,439 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2014 Pedro Gonnet (pedro.gonnet@gmail.com) +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_MATH_FUNCTIONS_AVX_H +#define EIGEN_MATH_FUNCTIONS_AVX_H + +/* The sin, cos, exp, and log functions of this file are loosely derived from + * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/ + */ + +namespace Eigen { + +namespace internal { + +inline Packet8i pshiftleft(Packet8i v, int n) +{ +#ifdef EIGEN_VECTORIZE_AVX2 + return _mm256_slli_epi32(v, n); +#else + __m128i lo = _mm_slli_epi32(_mm256_extractf128_si256(v, 0), n); + __m128i hi = _mm_slli_epi32(_mm256_extractf128_si256(v, 1), n); + return _mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1); +#endif +} + +inline Packet8f pshiftright(Packet8f v, int n) +{ +#ifdef EIGEN_VECTORIZE_AVX2 + return _mm256_cvtepi32_ps(_mm256_srli_epi32(_mm256_castps_si256(v), n)); +#else + __m128i lo = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 0), n); + __m128i hi = _mm_srli_epi32(_mm256_extractf128_si256(_mm256_castps_si256(v), 1), n); + return _mm256_cvtepi32_ps(_mm256_insertf128_si256(_mm256_castsi128_si256(lo), (hi), 1)); +#endif +} + +// Sine function +// Computes sin(x) by wrapping x to the interval [-Pi/4,3*Pi/4] and +// evaluating interpolants in [-Pi/4,Pi/4] or [Pi/4,3*Pi/4]. The interpolants +// are (anti-)symmetric and thus have only odd/even coefficients +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +psin<Packet8f>(const Packet8f& _x) { + Packet8f x = _x; + + // Some useful values. + _EIGEN_DECLARE_CONST_Packet8i(one, 1); + _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f); + _EIGEN_DECLARE_CONST_Packet8f(two, 2.0f); + _EIGEN_DECLARE_CONST_Packet8f(one_over_four, 0.25f); + _EIGEN_DECLARE_CONST_Packet8f(one_over_pi, 3.183098861837907e-01f); + _EIGEN_DECLARE_CONST_Packet8f(neg_pi_first, -3.140625000000000e+00f); + _EIGEN_DECLARE_CONST_Packet8f(neg_pi_second, -9.670257568359375e-04f); + _EIGEN_DECLARE_CONST_Packet8f(neg_pi_third, -6.278329571784980e-07f); + _EIGEN_DECLARE_CONST_Packet8f(four_over_pi, 1.273239544735163e+00f); + + // Map x from [-Pi/4,3*Pi/4] to z in [-1,3] and subtract the shifted period. + Packet8f z = pmul(x, p8f_one_over_pi); + Packet8f shift = _mm256_floor_ps(padd(z, p8f_one_over_four)); + x = pmadd(shift, p8f_neg_pi_first, x); + x = pmadd(shift, p8f_neg_pi_second, x); + x = pmadd(shift, p8f_neg_pi_third, x); + z = pmul(x, p8f_four_over_pi); + + // Make a mask for the entries that need flipping, i.e. wherever the shift + // is odd. + Packet8i shift_ints = _mm256_cvtps_epi32(shift); + Packet8i shift_isodd = _mm256_castps_si256(_mm256_and_ps(_mm256_castsi256_ps(shift_ints), _mm256_castsi256_ps(p8i_one))); + Packet8i sign_flip_mask = pshiftleft(shift_isodd, 31); + + // Create a mask for which interpolant to use, i.e. if z > 1, then the mask + // is set to ones for that entry. + Packet8f ival_mask = _mm256_cmp_ps(z, p8f_one, _CMP_GT_OQ); + + // Evaluate the polynomial for the interval [1,3] in z. + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_0, 9.999999724233232e-01f); + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_2, -3.084242535619928e-01f); + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_4, 1.584991525700324e-02f); + _EIGEN_DECLARE_CONST_Packet8f(coeff_right_6, -3.188805084631342e-04f); + Packet8f z_minus_two = psub(z, p8f_two); + Packet8f z_minus_two2 = pmul(z_minus_two, z_minus_two); + Packet8f right = pmadd(p8f_coeff_right_6, z_minus_two2, p8f_coeff_right_4); + right = pmadd(right, z_minus_two2, p8f_coeff_right_2); + right = pmadd(right, z_minus_two2, p8f_coeff_right_0); + + // Evaluate the polynomial for the interval [-1,1] in z. + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_1, 7.853981525427295e-01f); + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_3, -8.074536727092352e-02f); + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_5, 2.489871967827018e-03f); + _EIGEN_DECLARE_CONST_Packet8f(coeff_left_7, -3.587725841214251e-05f); + Packet8f z2 = pmul(z, z); + Packet8f left = pmadd(p8f_coeff_left_7, z2, p8f_coeff_left_5); + left = pmadd(left, z2, p8f_coeff_left_3); + left = pmadd(left, z2, p8f_coeff_left_1); + left = pmul(left, z); + + // Assemble the results, i.e. select the left and right polynomials. + left = _mm256_andnot_ps(ival_mask, left); + right = _mm256_and_ps(ival_mask, right); + Packet8f res = _mm256_or_ps(left, right); + + // Flip the sign on the odd intervals and return the result. + res = _mm256_xor_ps(res, _mm256_castsi256_ps(sign_flip_mask)); + return res; +} + +// Natural logarithm +// Computes log(x) as log(2^e * m) = C*e + log(m), where the constant C =log(2) +// and m is in the range [sqrt(1/2),sqrt(2)). In this range, the logarithm can +// be easily approximated by a polynomial centered on m=1 for stability. +// TODO(gonnet): Further reduce the interval allowing for lower-degree +// polynomial interpolants -> ... -> profit! +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +plog<Packet8f>(const Packet8f& _x) { + Packet8f x = _x; + _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f); + _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet8f(126f, 126.0f); + + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inv_mant_mask, ~0x7f800000); + + // The smallest non denormalized float number. + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(min_norm_pos, 0x00800000); + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(minus_inf, 0xff800000); + + // Polynomial coefficients. + _EIGEN_DECLARE_CONST_Packet8f(cephes_SQRTHF, 0.707106781186547524f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p0, 7.0376836292E-2f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p1, -1.1514610310E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p2, 1.1676998740E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p3, -1.2420140846E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p4, +1.4249322787E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p5, -1.6668057665E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p6, +2.0000714765E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p7, -2.4999993993E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_p8, +3.3333331174E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q1, -2.12194440e-4f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_log_q2, 0.693359375f); + + Packet8f invalid_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_NGE_UQ); // not greater equal is true if x is NaN + Packet8f iszero_mask = _mm256_cmp_ps(x, _mm256_setzero_ps(), _CMP_EQ_OQ); + + // Truncate input values to the minimum positive normal. + x = pmax(x, p8f_min_norm_pos); + + Packet8f emm0 = pshiftright(x,23); + Packet8f e = _mm256_sub_ps(emm0, p8f_126f); + + // Set the exponents to -1, i.e. x are in the range [0.5,1). + x = _mm256_and_ps(x, p8f_inv_mant_mask); + x = _mm256_or_ps(x, p8f_half); + + // part2: Shift the inputs from the range [0.5,1) to [sqrt(1/2),sqrt(2)) + // and shift by -1. The values are then centered around 0, which improves + // the stability of the polynomial evaluation. + // if( x < SQRTHF ) { + // e -= 1; + // x = x + x - 1.0; + // } else { x = x - 1.0; } + Packet8f mask = _mm256_cmp_ps(x, p8f_cephes_SQRTHF, _CMP_LT_OQ); + Packet8f tmp = _mm256_and_ps(x, mask); + x = psub(x, p8f_1); + e = psub(e, _mm256_and_ps(p8f_1, mask)); + x = padd(x, tmp); + + Packet8f x2 = pmul(x, x); + Packet8f x3 = pmul(x2, x); + + // Evaluate the polynomial approximant of degree 8 in three parts, probably + // to improve instruction-level parallelism. + Packet8f y, y1, y2; + y = pmadd(p8f_cephes_log_p0, x, p8f_cephes_log_p1); + y1 = pmadd(p8f_cephes_log_p3, x, p8f_cephes_log_p4); + y2 = pmadd(p8f_cephes_log_p6, x, p8f_cephes_log_p7); + y = pmadd(y, x, p8f_cephes_log_p2); + y1 = pmadd(y1, x, p8f_cephes_log_p5); + y2 = pmadd(y2, x, p8f_cephes_log_p8); + y = pmadd(y, x3, y1); + y = pmadd(y, x3, y2); + y = pmul(y, x3); + + // Add the logarithm of the exponent back to the result of the interpolation. + y1 = pmul(e, p8f_cephes_log_q1); + tmp = pmul(x2, p8f_half); + y = padd(y, y1); + x = psub(x, tmp); + y2 = pmul(e, p8f_cephes_log_q2); + x = padd(x, y); + x = padd(x, y2); + + // Filter out invalid inputs, i.e. negative arg will be NAN, 0 will be -INF. + return _mm256_or_ps( + _mm256_andnot_ps(iszero_mask, _mm256_or_ps(x, invalid_mask)), + _mm256_and_ps(iszero_mask, p8f_minus_inf)); +} + +// Exponential function. Works by writing "x = m*log(2) + r" where +// "m = floor(x/log(2)+1/2)" and "r" is the remainder. The result is then +// "exp(x) = 2^m*exp(r)" where exp(r) is in the range [-1,1). +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +pexp<Packet8f>(const Packet8f& _x) { + _EIGEN_DECLARE_CONST_Packet8f(1, 1.0f); + _EIGEN_DECLARE_CONST_Packet8f(half, 0.5f); + _EIGEN_DECLARE_CONST_Packet8f(127, 127.0f); + + _EIGEN_DECLARE_CONST_Packet8f(exp_hi, 88.3762626647950f); + _EIGEN_DECLARE_CONST_Packet8f(exp_lo, -88.3762626647949f); + + _EIGEN_DECLARE_CONST_Packet8f(cephes_LOG2EF, 1.44269504088896341f); + + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p0, 1.9875691500E-4f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p1, 1.3981999507E-3f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p2, 8.3334519073E-3f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p3, 4.1665795894E-2f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p4, 1.6666665459E-1f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_p5, 5.0000001201E-1f); + + // Clamp x. + Packet8f x = pmax(pmin(_x, p8f_exp_hi), p8f_exp_lo); + + // Express exp(x) as exp(m*ln(2) + r), start by extracting + // m = floor(x/ln(2) + 0.5). + Packet8f m = _mm256_floor_ps(pmadd(x, p8f_cephes_LOG2EF, p8f_half)); + +// Get r = x - m*ln(2). If no FMA instructions are available, m*ln(2) is +// subtracted out in two parts, m*C1+m*C2 = m*ln(2), to avoid accumulating +// truncation errors. Note that we don't use the "pmadd" function here to +// ensure that a precision-preserving FMA instruction is used. +#ifdef EIGEN_VECTORIZE_FMA + _EIGEN_DECLARE_CONST_Packet8f(nln2, -0.6931471805599453f); + Packet8f r = _mm256_fmadd_ps(m, p8f_nln2, x); +#else + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C1, 0.693359375f); + _EIGEN_DECLARE_CONST_Packet8f(cephes_exp_C2, -2.12194440e-4f); + Packet8f r = psub(x, pmul(m, p8f_cephes_exp_C1)); + r = psub(r, pmul(m, p8f_cephes_exp_C2)); +#endif + + Packet8f r2 = pmul(r, r); + + // TODO(gonnet): Split into odd/even polynomials and try to exploit + // instruction-level parallelism. + Packet8f y = p8f_cephes_exp_p0; + y = pmadd(y, r, p8f_cephes_exp_p1); + y = pmadd(y, r, p8f_cephes_exp_p2); + y = pmadd(y, r, p8f_cephes_exp_p3); + y = pmadd(y, r, p8f_cephes_exp_p4); + y = pmadd(y, r, p8f_cephes_exp_p5); + y = pmadd(y, r2, r); + y = padd(y, p8f_1); + + // Build emm0 = 2^m. + Packet8i emm0 = _mm256_cvttps_epi32(padd(m, p8f_127)); + emm0 = pshiftleft(emm0, 23); + + // Return 2^m * exp(r). + return pmax(pmul(y, _mm256_castsi256_ps(emm0)), _x); +} + +// Hyperbolic Tangent function. +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +ptanh<Packet8f>(const Packet8f& x) { + return internal::generic_fast_tanh_float(x); +} + +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4d +pexp<Packet4d>(const Packet4d& _x) { + Packet4d x = _x; + + _EIGEN_DECLARE_CONST_Packet4d(1, 1.0); + _EIGEN_DECLARE_CONST_Packet4d(2, 2.0); + _EIGEN_DECLARE_CONST_Packet4d(half, 0.5); + + _EIGEN_DECLARE_CONST_Packet4d(exp_hi, 709.437); + _EIGEN_DECLARE_CONST_Packet4d(exp_lo, -709.436139303); + + _EIGEN_DECLARE_CONST_Packet4d(cephes_LOG2EF, 1.4426950408889634073599); + + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p0, 1.26177193074810590878e-4); + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p1, 3.02994407707441961300e-2); + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_p2, 9.99999999999999999910e-1); + + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q0, 3.00198505138664455042e-6); + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q1, 2.52448340349684104192e-3); + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q2, 2.27265548208155028766e-1); + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_q3, 2.00000000000000000009e0); + + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C1, 0.693145751953125); + _EIGEN_DECLARE_CONST_Packet4d(cephes_exp_C2, 1.42860682030941723212e-6); + _EIGEN_DECLARE_CONST_Packet4i(1023, 1023); + + Packet4d tmp, fx; + + // clamp x + x = pmax(pmin(x, p4d_exp_hi), p4d_exp_lo); + // Express exp(x) as exp(g + n*log(2)). + fx = pmadd(p4d_cephes_LOG2EF, x, p4d_half); + + // Get the integer modulus of log(2), i.e. the "n" described above. + fx = _mm256_floor_pd(fx); + + // Get the remainder modulo log(2), i.e. the "g" described above. Subtract + // n*log(2) out in two steps, i.e. n*C1 + n*C2, C1+C2=log2 to get the last + // digits right. + tmp = pmul(fx, p4d_cephes_exp_C1); + Packet4d z = pmul(fx, p4d_cephes_exp_C2); + x = psub(x, tmp); + x = psub(x, z); + + Packet4d x2 = pmul(x, x); + + // Evaluate the numerator polynomial of the rational interpolant. + Packet4d px = p4d_cephes_exp_p0; + px = pmadd(px, x2, p4d_cephes_exp_p1); + px = pmadd(px, x2, p4d_cephes_exp_p2); + px = pmul(px, x); + + // Evaluate the denominator polynomial of the rational interpolant. + Packet4d qx = p4d_cephes_exp_q0; + qx = pmadd(qx, x2, p4d_cephes_exp_q1); + qx = pmadd(qx, x2, p4d_cephes_exp_q2); + qx = pmadd(qx, x2, p4d_cephes_exp_q3); + + // I don't really get this bit, copied from the SSE2 routines, so... + // TODO(gonnet): Figure out what is going on here, perhaps find a better + // rational interpolant? + x = _mm256_div_pd(px, psub(qx, px)); + x = pmadd(p4d_2, x, p4d_1); + + // Build e=2^n by constructing the exponents in a 128-bit vector and + // shifting them to where they belong in double-precision values. + __m128i emm0 = _mm256_cvtpd_epi32(fx); + emm0 = _mm_add_epi32(emm0, p4i_1023); + emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(3, 1, 2, 0)); + __m128i lo = _mm_slli_epi64(emm0, 52); + __m128i hi = _mm_slli_epi64(_mm_srli_epi64(emm0, 32), 52); + __m256i e = _mm256_insertf128_si256(_mm256_setzero_si256(), lo, 0); + e = _mm256_insertf128_si256(e, hi, 1); + + // Construct the result 2^n * exp(g) = e * x. The max is used to catch + // non-finite values in the input. + return pmax(pmul(x, _mm256_castsi256_pd(e)), _x); +} + +// Functions for sqrt. +// The EIGEN_FAST_MATH version uses the _mm_rsqrt_ps approximation and one step +// of Newton's method, at a cost of 1-2 bits of precision as opposed to the +// exact solution. It does not handle +inf, or denormalized numbers correctly. +// The main advantage of this approach is not just speed, but also the fact that +// it can be inlined and pipelined with other computations, further reducing its +// effective latency. This is similar to Quake3's fast inverse square root. +// For detail see here: http://www.beyond3d.com/content/articles/8/ +#if EIGEN_FAST_MATH +template <> +EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet8f +psqrt<Packet8f>(const Packet8f& _x) { + Packet8f half = pmul(_x, pset1<Packet8f>(.5f)); + Packet8f denormal_mask = _mm256_and_ps( + _mm256_cmp_ps(_x, pset1<Packet8f>((std::numeric_limits<float>::min)()), + _CMP_LT_OQ), + _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_GE_OQ)); + + // Compute approximate reciprocal sqrt. + Packet8f x = _mm256_rsqrt_ps(_x); + // Do a single step of Newton's iteration. + x = pmul(x, psub(pset1<Packet8f>(1.5f), pmul(half, pmul(x,x)))); + // Flush results for denormals to zero. + return _mm256_andnot_ps(denormal_mask, pmul(_x,x)); +} +#else +template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet8f psqrt<Packet8f>(const Packet8f& x) { + return _mm256_sqrt_ps(x); +} +#endif +template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4d psqrt<Packet4d>(const Packet4d& x) { + return _mm256_sqrt_pd(x); +} +#if EIGEN_FAST_MATH + +template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet8f prsqrt<Packet8f>(const Packet8f& _x) { + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(inf, 0x7f800000); + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(nan, 0x7fc00000); + _EIGEN_DECLARE_CONST_Packet8f(one_point_five, 1.5f); + _EIGEN_DECLARE_CONST_Packet8f(minus_half, -0.5f); + _EIGEN_DECLARE_CONST_Packet8f_FROM_INT(flt_min, 0x00800000); + + Packet8f neg_half = pmul(_x, p8f_minus_half); + + // select only the inverse sqrt of positive normal inputs (denormals are + // flushed to zero and cause infs as well). + Packet8f le_zero_mask = _mm256_cmp_ps(_x, p8f_flt_min, _CMP_LT_OQ); + Packet8f x = _mm256_andnot_ps(le_zero_mask, _mm256_rsqrt_ps(_x)); + + // Fill in NaNs and Infs for the negative/zero entries. + Packet8f neg_mask = _mm256_cmp_ps(_x, _mm256_setzero_ps(), _CMP_LT_OQ); + Packet8f zero_mask = _mm256_andnot_ps(neg_mask, le_zero_mask); + Packet8f infs_and_nans = _mm256_or_ps(_mm256_and_ps(neg_mask, p8f_nan), + _mm256_and_ps(zero_mask, p8f_inf)); + + // Do a single step of Newton's iteration. + x = pmul(x, pmadd(neg_half, pmul(x, x), p8f_one_point_five)); + + // Insert NaNs and Infs in all the right places. + return _mm256_or_ps(x, infs_and_nans); +} + +#else +template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet8f prsqrt<Packet8f>(const Packet8f& x) { + _EIGEN_DECLARE_CONST_Packet8f(one, 1.0f); + return _mm256_div_ps(p8f_one, _mm256_sqrt_ps(x)); +} +#endif + +template <> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED +Packet4d prsqrt<Packet4d>(const Packet4d& x) { + _EIGEN_DECLARE_CONST_Packet4d(one, 1.0); + return _mm256_div_pd(p4d_one, _mm256_sqrt_pd(x)); +} + + +} // end namespace internal + +} // end namespace Eigen + +#endif // EIGEN_MATH_FUNCTIONS_AVX_H |