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465 lines
15 KiB
C++
465 lines
15 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2007 Julien Pommier
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// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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/* The sin, cos, exp, and log functions of this file come from
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* Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
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*/
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#ifndef EIGEN_MATH_FUNCTIONS_SSE_H
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#define EIGEN_MATH_FUNCTIONS_SSE_H
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namespace Eigen {
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namespace internal {
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template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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Packet4f plog<Packet4f>(const Packet4f& _x)
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{
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Packet4f x = _x;
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_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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_EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
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_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
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/* the smallest non denormalized float number */
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_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
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_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);//-1.f/0.f);
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/* natural logarithm computed for 4 simultaneous float
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return NaN for x <= 0
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*/
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_EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
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Packet4i emm0;
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Packet4f invalid_mask = _mm_cmplt_ps(x, _mm_setzero_ps());
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Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());
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x = pmax(x, p4f_min_norm_pos); /* cut off denormalized stuff */
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emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
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/* keep only the fractional part */
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x = _mm_and_ps(x, p4f_inv_mant_mask);
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x = _mm_or_ps(x, p4f_half);
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emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
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Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
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/* part2:
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if( x < SQRTHF ) {
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e -= 1;
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x = x + x - 1.0;
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} else { x = x - 1.0; }
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*/
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Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
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Packet4f tmp = _mm_and_ps(x, mask);
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x = psub(x, p4f_1);
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e = psub(e, _mm_and_ps(p4f_1, mask));
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x = padd(x, tmp);
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Packet4f x2 = pmul(x,x);
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Packet4f x3 = pmul(x2,x);
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Packet4f y, y1, y2;
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y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
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y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
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y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
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y = pmadd(y , x, p4f_cephes_log_p2);
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y1 = pmadd(y1, x, p4f_cephes_log_p5);
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y2 = pmadd(y2, x, p4f_cephes_log_p8);
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y = pmadd(y, x3, y1);
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y = pmadd(y, x3, y2);
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y = pmul(y, x3);
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y1 = pmul(e, p4f_cephes_log_q1);
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tmp = pmul(x2, p4f_half);
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y = padd(y, y1);
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x = psub(x, tmp);
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y2 = pmul(e, p4f_cephes_log_q2);
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x = padd(x, y);
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x = padd(x, y2);
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// negative arg will be NAN, 0 will be -INF
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return _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)),
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_mm_and_ps(iszero_mask, p4f_minus_inf));
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}
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template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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Packet4f pexp<Packet4f>(const Packet4f& _x)
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{
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Packet4f x = _x;
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_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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_EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
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_EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
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_EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
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Packet4f tmp = _mm_setzero_ps(), fx;
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Packet4i emm0;
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// clamp x
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x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
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/* express exp(x) as exp(g + n*log(2)) */
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fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
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#ifdef EIGEN_VECTORIZE_SSE4_1
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fx = _mm_floor_ps(fx);
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#else
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emm0 = _mm_cvttps_epi32(fx);
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tmp = _mm_cvtepi32_ps(emm0);
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/* if greater, substract 1 */
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Packet4f mask = _mm_cmpgt_ps(tmp, fx);
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mask = _mm_and_ps(mask, p4f_1);
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fx = psub(tmp, mask);
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#endif
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tmp = pmul(fx, p4f_cephes_exp_C1);
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Packet4f z = pmul(fx, p4f_cephes_exp_C2);
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x = psub(x, tmp);
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x = psub(x, z);
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z = pmul(x,x);
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Packet4f y = p4f_cephes_exp_p0;
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y = pmadd(y, x, p4f_cephes_exp_p1);
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y = pmadd(y, x, p4f_cephes_exp_p2);
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y = pmadd(y, x, p4f_cephes_exp_p3);
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y = pmadd(y, x, p4f_cephes_exp_p4);
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y = pmadd(y, x, p4f_cephes_exp_p5);
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y = pmadd(y, z, x);
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y = padd(y, p4f_1);
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// build 2^n
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emm0 = _mm_cvttps_epi32(fx);
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emm0 = _mm_add_epi32(emm0, p4i_0x7f);
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emm0 = _mm_slli_epi32(emm0, 23);
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return pmul(y, _mm_castsi128_ps(emm0));
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}
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template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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Packet2d pexp<Packet2d>(const Packet2d& _x)
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{
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Packet2d x = _x;
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_EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
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_EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
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_EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
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_EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
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_EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
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_EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
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static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);
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Packet2d tmp = _mm_setzero_pd(), fx;
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Packet4i emm0;
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// clamp x
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x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
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/* express exp(x) as exp(g + n*log(2)) */
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fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
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#ifdef EIGEN_VECTORIZE_SSE4_1
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fx = _mm_floor_pd(fx);
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#else
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emm0 = _mm_cvttpd_epi32(fx);
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tmp = _mm_cvtepi32_pd(emm0);
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/* if greater, substract 1 */
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Packet2d mask = _mm_cmpgt_pd(tmp, fx);
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mask = _mm_and_pd(mask, p2d_1);
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fx = psub(tmp, mask);
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#endif
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tmp = pmul(fx, p2d_cephes_exp_C1);
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Packet2d z = pmul(fx, p2d_cephes_exp_C2);
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x = psub(x, tmp);
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x = psub(x, z);
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Packet2d x2 = pmul(x,x);
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Packet2d px = p2d_cephes_exp_p0;
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px = pmadd(px, x2, p2d_cephes_exp_p1);
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px = pmadd(px, x2, p2d_cephes_exp_p2);
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px = pmul (px, x);
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Packet2d qx = p2d_cephes_exp_q0;
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qx = pmadd(qx, x2, p2d_cephes_exp_q1);
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qx = pmadd(qx, x2, p2d_cephes_exp_q2);
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qx = pmadd(qx, x2, p2d_cephes_exp_q3);
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x = pdiv(px,psub(qx,px));
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x = pmadd(p2d_2,x,p2d_1);
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// build 2^n
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emm0 = _mm_cvttpd_epi32(fx);
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emm0 = _mm_add_epi32(emm0, p4i_1023_0);
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emm0 = _mm_slli_epi32(emm0, 20);
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emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));
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return pmul(x, _mm_castsi128_pd(emm0));
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}
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/* evaluation of 4 sines at onces, using SSE2 intrinsics.
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The code is the exact rewriting of the cephes sinf function.
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Precision is excellent as long as x < 8192 (I did not bother to
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take into account the special handling they have for greater values
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-- it does not return garbage for arguments over 8192, though, but
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the extra precision is missing).
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Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
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surprising but correct result.
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*/
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template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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Packet4f psin<Packet4f>(const Packet4f& _x)
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{
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Packet4f x = _x;
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_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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_EIGEN_DECLARE_CONST_Packet4i(1, 1);
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_EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
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_EIGEN_DECLARE_CONST_Packet4i(2, 2);
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_EIGEN_DECLARE_CONST_Packet4i(4, 4);
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_EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
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_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
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_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
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_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
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_EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
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_EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
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_EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
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_EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
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_EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
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Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, sign_bit, y;
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Packet4i emm0, emm2;
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sign_bit = x;
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/* take the absolute value */
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x = pabs(x);
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/* take the modulo */
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/* extract the sign bit (upper one) */
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sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
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/* scale by 4/Pi */
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y = pmul(x, p4f_cephes_FOPI);
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/* store the integer part of y in mm0 */
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emm2 = _mm_cvttps_epi32(y);
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/* j=(j+1) & (~1) (see the cephes sources) */
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emm2 = _mm_add_epi32(emm2, p4i_1);
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emm2 = _mm_and_si128(emm2, p4i_not1);
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y = _mm_cvtepi32_ps(emm2);
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/* get the swap sign flag */
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emm0 = _mm_and_si128(emm2, p4i_4);
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emm0 = _mm_slli_epi32(emm0, 29);
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/* get the polynom selection mask
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there is one polynom for 0 <= x <= Pi/4
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and another one for Pi/4<x<=Pi/2
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Both branches will be computed.
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*/
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emm2 = _mm_and_si128(emm2, p4i_2);
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emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
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Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
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Packet4f poly_mask = _mm_castsi128_ps(emm2);
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sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
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/* The magic pass: "Extended precision modular arithmetic"
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x = ((x - y * DP1) - y * DP2) - y * DP3; */
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xmm1 = pmul(y, p4f_minus_cephes_DP1);
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xmm2 = pmul(y, p4f_minus_cephes_DP2);
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xmm3 = pmul(y, p4f_minus_cephes_DP3);
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x = padd(x, xmm1);
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x = padd(x, xmm2);
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x = padd(x, xmm3);
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/* Evaluate the first polynom (0 <= x <= Pi/4) */
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y = p4f_coscof_p0;
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Packet4f z = _mm_mul_ps(x,x);
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y = pmadd(y, z, p4f_coscof_p1);
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y = pmadd(y, z, p4f_coscof_p2);
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y = pmul(y, z);
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y = pmul(y, z);
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Packet4f tmp = pmul(z, p4f_half);
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y = psub(y, tmp);
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y = padd(y, p4f_1);
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/* Evaluate the second polynom (Pi/4 <= x <= 0) */
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Packet4f y2 = p4f_sincof_p0;
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y2 = pmadd(y2, z, p4f_sincof_p1);
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y2 = pmadd(y2, z, p4f_sincof_p2);
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y2 = pmul(y2, z);
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y2 = pmul(y2, x);
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y2 = padd(y2, x);
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/* select the correct result from the two polynoms */
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y2 = _mm_and_ps(poly_mask, y2);
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y = _mm_andnot_ps(poly_mask, y);
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y = _mm_or_ps(y,y2);
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/* update the sign */
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return _mm_xor_ps(y, sign_bit);
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}
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/* almost the same as psin */
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template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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Packet4f pcos<Packet4f>(const Packet4f& _x)
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{
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Packet4f x = _x;
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_EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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_EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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_EIGEN_DECLARE_CONST_Packet4i(1, 1);
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_EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
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_EIGEN_DECLARE_CONST_Packet4i(2, 2);
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_EIGEN_DECLARE_CONST_Packet4i(4, 4);
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_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
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_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
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_EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
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_EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
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_EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
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_EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
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_EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
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_EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
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_EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
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_EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
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Packet4f xmm1, xmm2 = _mm_setzero_ps(), xmm3, y;
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Packet4i emm0, emm2;
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x = pabs(x);
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/* scale by 4/Pi */
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y = pmul(x, p4f_cephes_FOPI);
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/* get the integer part of y */
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emm2 = _mm_cvttps_epi32(y);
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/* j=(j+1) & (~1) (see the cephes sources) */
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emm2 = _mm_add_epi32(emm2, p4i_1);
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emm2 = _mm_and_si128(emm2, p4i_not1);
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y = _mm_cvtepi32_ps(emm2);
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emm2 = _mm_sub_epi32(emm2, p4i_2);
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/* get the swap sign flag */
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emm0 = _mm_andnot_si128(emm2, p4i_4);
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emm0 = _mm_slli_epi32(emm0, 29);
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/* get the polynom selection mask */
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emm2 = _mm_and_si128(emm2, p4i_2);
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emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
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Packet4f sign_bit = _mm_castsi128_ps(emm0);
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Packet4f poly_mask = _mm_castsi128_ps(emm2);
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/* The magic pass: "Extended precision modular arithmetic"
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x = ((x - y * DP1) - y * DP2) - y * DP3; */
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xmm1 = pmul(y, p4f_minus_cephes_DP1);
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xmm2 = pmul(y, p4f_minus_cephes_DP2);
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xmm3 = pmul(y, p4f_minus_cephes_DP3);
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x = padd(x, xmm1);
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x = padd(x, xmm2);
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x = padd(x, xmm3);
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/* Evaluate the first polynom (0 <= x <= Pi/4) */
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y = p4f_coscof_p0;
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Packet4f z = pmul(x,x);
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y = pmadd(y,z,p4f_coscof_p1);
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y = pmadd(y,z,p4f_coscof_p2);
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y = pmul(y, z);
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y = pmul(y, z);
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Packet4f tmp = _mm_mul_ps(z, p4f_half);
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y = psub(y, tmp);
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y = padd(y, p4f_1);
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/* Evaluate the second polynom (Pi/4 <= x <= 0) */
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Packet4f y2 = p4f_sincof_p0;
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y2 = pmadd(y2, z, p4f_sincof_p1);
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y2 = pmadd(y2, z, p4f_sincof_p2);
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y2 = pmul(y2, z);
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y2 = pmadd(y2, x, x);
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/* select the correct result from the two polynoms */
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y2 = _mm_and_ps(poly_mask, y2);
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y = _mm_andnot_ps(poly_mask, y);
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y = _mm_or_ps(y,y2);
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/* update the sign */
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return _mm_xor_ps(y, sign_bit);
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}
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// This is based on Quake3's fast inverse square root.
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// For detail see here: http://www.beyond3d.com/content/articles/8/
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template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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Packet4f psqrt<Packet4f>(const Packet4f& _x)
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{
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Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
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/* select only the inverse sqrt of non-zero inputs */
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Packet4f non_zero_mask = _mm_cmpgt_ps(_x, pset1<Packet4f>(std::numeric_limits<float>::epsilon()));
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Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
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x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
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return pmul(_x,x);
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}
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} // end namespace internal
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} // end namespace Eigen
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#endif // EIGEN_MATH_FUNCTIONS_SSE_H
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