[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2007 Julien Pommier
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| 5 | // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | /* The sin, cos, exp, and log functions of this file come from
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| 12 | * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
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| 13 | */
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| 14 |
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| 15 | #ifndef EIGEN_MATH_FUNCTIONS_SSE_H
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| 16 | #define EIGEN_MATH_FUNCTIONS_SSE_H
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| 17 |
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| 18 | namespace Eigen {
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| 19 |
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| 20 | namespace internal {
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| 21 |
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| 22 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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| 23 | Packet4f plog<Packet4f>(const Packet4f& _x)
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| 24 | {
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| 25 | Packet4f x = _x;
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| 26 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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| 27 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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| 28 | _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
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| 29 |
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| 30 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
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| 31 |
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| 32 | /* the smallest non denormalized float number */
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| 33 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
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| 34 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000);//-1.f/0.f);
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| 35 |
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| 36 | /* natural logarithm computed for 4 simultaneous float
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| 37 | return NaN for x <= 0
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| 38 | */
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| 39 | _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
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| 40 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
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| 41 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
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| 42 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
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| 43 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
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| 44 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
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| 45 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
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| 46 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
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| 47 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
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| 48 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
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| 49 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
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| 50 | _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
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| 51 |
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| 52 |
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| 53 | Packet4i emm0;
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| 54 |
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| 55 | Packet4f invalid_mask = _mm_cmpnge_ps(x, _mm_setzero_ps()); // not greater equal is true if x is NaN
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| 56 | Packet4f iszero_mask = _mm_cmpeq_ps(x, _mm_setzero_ps());
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| 57 |
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| 58 | x = pmax(x, p4f_min_norm_pos); /* cut off denormalized stuff */
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| 59 | emm0 = _mm_srli_epi32(_mm_castps_si128(x), 23);
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| 60 |
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| 61 | /* keep only the fractional part */
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| 62 | x = _mm_and_ps(x, p4f_inv_mant_mask);
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| 63 | x = _mm_or_ps(x, p4f_half);
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| 64 |
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| 65 | emm0 = _mm_sub_epi32(emm0, p4i_0x7f);
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| 66 | Packet4f e = padd(_mm_cvtepi32_ps(emm0), p4f_1);
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| 67 |
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| 68 | /* part2:
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| 69 | if( x < SQRTHF ) {
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| 70 | e -= 1;
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| 71 | x = x + x - 1.0;
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| 72 | } else { x = x - 1.0; }
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| 73 | */
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| 74 | Packet4f mask = _mm_cmplt_ps(x, p4f_cephes_SQRTHF);
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| 75 | Packet4f tmp = _mm_and_ps(x, mask);
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| 76 | x = psub(x, p4f_1);
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| 77 | e = psub(e, _mm_and_ps(p4f_1, mask));
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| 78 | x = padd(x, tmp);
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| 79 |
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| 80 | Packet4f x2 = pmul(x,x);
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| 81 | Packet4f x3 = pmul(x2,x);
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| 82 |
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| 83 | Packet4f y, y1, y2;
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| 84 | y = pmadd(p4f_cephes_log_p0, x, p4f_cephes_log_p1);
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| 85 | y1 = pmadd(p4f_cephes_log_p3, x, p4f_cephes_log_p4);
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| 86 | y2 = pmadd(p4f_cephes_log_p6, x, p4f_cephes_log_p7);
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| 87 | y = pmadd(y , x, p4f_cephes_log_p2);
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| 88 | y1 = pmadd(y1, x, p4f_cephes_log_p5);
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| 89 | y2 = pmadd(y2, x, p4f_cephes_log_p8);
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| 90 | y = pmadd(y, x3, y1);
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| 91 | y = pmadd(y, x3, y2);
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| 92 | y = pmul(y, x3);
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| 93 |
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| 94 | y1 = pmul(e, p4f_cephes_log_q1);
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| 95 | tmp = pmul(x2, p4f_half);
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| 96 | y = padd(y, y1);
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| 97 | x = psub(x, tmp);
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| 98 | y2 = pmul(e, p4f_cephes_log_q2);
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| 99 | x = padd(x, y);
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| 100 | x = padd(x, y2);
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| 101 | // negative arg will be NAN, 0 will be -INF
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| 102 | return _mm_or_ps(_mm_andnot_ps(iszero_mask, _mm_or_ps(x, invalid_mask)),
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| 103 | _mm_and_ps(iszero_mask, p4f_minus_inf));
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| 104 | }
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| 105 |
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| 106 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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| 107 | Packet4f pexp<Packet4f>(const Packet4f& _x)
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| 108 | {
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| 109 | Packet4f x = _x;
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| 110 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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| 111 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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| 112 | _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
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| 113 |
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| 114 |
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| 115 | _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
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| 116 | _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
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| 117 |
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| 118 | _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
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| 119 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
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| 120 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
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| 121 |
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| 122 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
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| 123 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
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| 124 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
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| 125 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
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| 126 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
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| 127 | _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
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| 128 |
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| 129 | Packet4f tmp, fx;
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| 130 | Packet4i emm0;
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| 131 |
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| 132 | // clamp x
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| 133 | x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
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| 134 |
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| 135 | /* express exp(x) as exp(g + n*log(2)) */
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| 136 | fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
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| 137 |
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| 138 | #ifdef EIGEN_VECTORIZE_SSE4_1
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| 139 | fx = _mm_floor_ps(fx);
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| 140 | #else
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| 141 | emm0 = _mm_cvttps_epi32(fx);
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| 142 | tmp = _mm_cvtepi32_ps(emm0);
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| 143 | /* if greater, substract 1 */
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| 144 | Packet4f mask = _mm_cmpgt_ps(tmp, fx);
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| 145 | mask = _mm_and_ps(mask, p4f_1);
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| 146 | fx = psub(tmp, mask);
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| 147 | #endif
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| 148 |
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| 149 | tmp = pmul(fx, p4f_cephes_exp_C1);
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| 150 | Packet4f z = pmul(fx, p4f_cephes_exp_C2);
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| 151 | x = psub(x, tmp);
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| 152 | x = psub(x, z);
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| 153 |
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| 154 | z = pmul(x,x);
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| 155 |
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| 156 | Packet4f y = p4f_cephes_exp_p0;
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| 157 | y = pmadd(y, x, p4f_cephes_exp_p1);
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| 158 | y = pmadd(y, x, p4f_cephes_exp_p2);
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| 159 | y = pmadd(y, x, p4f_cephes_exp_p3);
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| 160 | y = pmadd(y, x, p4f_cephes_exp_p4);
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| 161 | y = pmadd(y, x, p4f_cephes_exp_p5);
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| 162 | y = pmadd(y, z, x);
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| 163 | y = padd(y, p4f_1);
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| 164 |
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| 165 | // build 2^n
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| 166 | emm0 = _mm_cvttps_epi32(fx);
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| 167 | emm0 = _mm_add_epi32(emm0, p4i_0x7f);
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| 168 | emm0 = _mm_slli_epi32(emm0, 23);
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| 169 | return pmax(pmul(y, Packet4f(_mm_castsi128_ps(emm0))), _x);
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| 170 | }
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| 171 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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| 172 | Packet2d pexp<Packet2d>(const Packet2d& _x)
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| 173 | {
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| 174 | Packet2d x = _x;
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| 175 |
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| 176 | _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
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| 177 | _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
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| 178 | _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
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| 179 |
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| 180 | _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
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| 181 | _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
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| 182 |
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| 183 | _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
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| 184 |
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| 185 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
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| 186 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
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| 187 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
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| 188 |
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| 189 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
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| 190 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
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| 191 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
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| 192 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
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| 193 |
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| 194 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
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| 195 | _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
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| 196 | static const __m128i p4i_1023_0 = _mm_setr_epi32(1023, 1023, 0, 0);
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| 197 |
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| 198 | Packet2d tmp, fx;
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| 199 | Packet4i emm0;
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| 200 |
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| 201 | // clamp x
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| 202 | x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
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| 203 | /* express exp(x) as exp(g + n*log(2)) */
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| 204 | fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
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| 205 |
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| 206 | #ifdef EIGEN_VECTORIZE_SSE4_1
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| 207 | fx = _mm_floor_pd(fx);
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| 208 | #else
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| 209 | emm0 = _mm_cvttpd_epi32(fx);
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| 210 | tmp = _mm_cvtepi32_pd(emm0);
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| 211 | /* if greater, substract 1 */
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| 212 | Packet2d mask = _mm_cmpgt_pd(tmp, fx);
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| 213 | mask = _mm_and_pd(mask, p2d_1);
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| 214 | fx = psub(tmp, mask);
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| 215 | #endif
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| 216 |
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| 217 | tmp = pmul(fx, p2d_cephes_exp_C1);
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| 218 | Packet2d z = pmul(fx, p2d_cephes_exp_C2);
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| 219 | x = psub(x, tmp);
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| 220 | x = psub(x, z);
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| 221 |
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| 222 | Packet2d x2 = pmul(x,x);
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| 223 |
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| 224 | Packet2d px = p2d_cephes_exp_p0;
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| 225 | px = pmadd(px, x2, p2d_cephes_exp_p1);
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| 226 | px = pmadd(px, x2, p2d_cephes_exp_p2);
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| 227 | px = pmul (px, x);
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| 228 |
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| 229 | Packet2d qx = p2d_cephes_exp_q0;
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| 230 | qx = pmadd(qx, x2, p2d_cephes_exp_q1);
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| 231 | qx = pmadd(qx, x2, p2d_cephes_exp_q2);
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| 232 | qx = pmadd(qx, x2, p2d_cephes_exp_q3);
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| 233 |
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| 234 | x = pdiv(px,psub(qx,px));
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| 235 | x = pmadd(p2d_2,x,p2d_1);
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| 236 |
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| 237 | // build 2^n
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| 238 | emm0 = _mm_cvttpd_epi32(fx);
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| 239 | emm0 = _mm_add_epi32(emm0, p4i_1023_0);
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| 240 | emm0 = _mm_slli_epi32(emm0, 20);
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| 241 | emm0 = _mm_shuffle_epi32(emm0, _MM_SHUFFLE(1,2,0,3));
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| 242 | return pmax(pmul(x, Packet2d(_mm_castsi128_pd(emm0))), _x);
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| 243 | }
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| 244 |
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| 245 | /* evaluation of 4 sines at onces, using SSE2 intrinsics.
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| 246 |
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| 247 | The code is the exact rewriting of the cephes sinf function.
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| 248 | Precision is excellent as long as x < 8192 (I did not bother to
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| 249 | take into account the special handling they have for greater values
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| 250 | -- it does not return garbage for arguments over 8192, though, but
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| 251 | the extra precision is missing).
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| 252 |
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| 253 | Note that it is such that sinf((float)M_PI) = 8.74e-8, which is the
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| 254 | surprising but correct result.
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| 255 | */
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| 256 |
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| 257 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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| 258 | Packet4f psin<Packet4f>(const Packet4f& _x)
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| 259 | {
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| 260 | Packet4f x = _x;
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| 261 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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| 262 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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| 263 |
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| 264 | _EIGEN_DECLARE_CONST_Packet4i(1, 1);
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| 265 | _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
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| 266 | _EIGEN_DECLARE_CONST_Packet4i(2, 2);
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| 267 | _EIGEN_DECLARE_CONST_Packet4i(4, 4);
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| 268 |
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| 269 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
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| 270 |
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| 271 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
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| 272 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
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| 273 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
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| 274 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
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| 275 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
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| 276 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
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| 277 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
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| 278 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
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| 279 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
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| 280 | _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
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| 281 |
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| 282 | Packet4f xmm1, xmm2, xmm3, sign_bit, y;
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| 283 |
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| 284 | Packet4i emm0, emm2;
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| 285 | sign_bit = x;
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| 286 | /* take the absolute value */
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| 287 | x = pabs(x);
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| 288 |
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| 289 | /* take the modulo */
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| 290 |
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| 291 | /* extract the sign bit (upper one) */
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| 292 | sign_bit = _mm_and_ps(sign_bit, p4f_sign_mask);
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| 293 |
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| 294 | /* scale by 4/Pi */
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| 295 | y = pmul(x, p4f_cephes_FOPI);
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| 296 |
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| 297 | /* store the integer part of y in mm0 */
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| 298 | emm2 = _mm_cvttps_epi32(y);
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| 299 | /* j=(j+1) & (~1) (see the cephes sources) */
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| 300 | emm2 = _mm_add_epi32(emm2, p4i_1);
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| 301 | emm2 = _mm_and_si128(emm2, p4i_not1);
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| 302 | y = _mm_cvtepi32_ps(emm2);
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| 303 | /* get the swap sign flag */
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| 304 | emm0 = _mm_and_si128(emm2, p4i_4);
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| 305 | emm0 = _mm_slli_epi32(emm0, 29);
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| 306 | /* get the polynom selection mask
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| 307 | there is one polynom for 0 <= x <= Pi/4
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| 308 | and another one for Pi/4<x<=Pi/2
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| 309 |
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| 310 | Both branches will be computed.
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| 311 | */
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| 312 | emm2 = _mm_and_si128(emm2, p4i_2);
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| 313 | emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
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| 314 |
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| 315 | Packet4f swap_sign_bit = _mm_castsi128_ps(emm0);
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| 316 | Packet4f poly_mask = _mm_castsi128_ps(emm2);
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| 317 | sign_bit = _mm_xor_ps(sign_bit, swap_sign_bit);
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| 318 |
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| 319 | /* The magic pass: "Extended precision modular arithmetic"
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| 320 | x = ((x - y * DP1) - y * DP2) - y * DP3; */
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| 321 | xmm1 = pmul(y, p4f_minus_cephes_DP1);
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| 322 | xmm2 = pmul(y, p4f_minus_cephes_DP2);
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| 323 | xmm3 = pmul(y, p4f_minus_cephes_DP3);
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| 324 | x = padd(x, xmm1);
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| 325 | x = padd(x, xmm2);
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| 326 | x = padd(x, xmm3);
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| 327 |
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| 328 | /* Evaluate the first polynom (0 <= x <= Pi/4) */
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| 329 | y = p4f_coscof_p0;
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| 330 | Packet4f z = _mm_mul_ps(x,x);
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| 331 |
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| 332 | y = pmadd(y, z, p4f_coscof_p1);
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| 333 | y = pmadd(y, z, p4f_coscof_p2);
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| 334 | y = pmul(y, z);
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| 335 | y = pmul(y, z);
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| 336 | Packet4f tmp = pmul(z, p4f_half);
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| 337 | y = psub(y, tmp);
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| 338 | y = padd(y, p4f_1);
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| 339 |
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| 340 | /* Evaluate the second polynom (Pi/4 <= x <= 0) */
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| 341 |
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| 342 | Packet4f y2 = p4f_sincof_p0;
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| 343 | y2 = pmadd(y2, z, p4f_sincof_p1);
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| 344 | y2 = pmadd(y2, z, p4f_sincof_p2);
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| 345 | y2 = pmul(y2, z);
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| 346 | y2 = pmul(y2, x);
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| 347 | y2 = padd(y2, x);
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| 348 |
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| 349 | /* select the correct result from the two polynoms */
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| 350 | y2 = _mm_and_ps(poly_mask, y2);
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| 351 | y = _mm_andnot_ps(poly_mask, y);
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| 352 | y = _mm_or_ps(y,y2);
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| 353 | /* update the sign */
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| 354 | return _mm_xor_ps(y, sign_bit);
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| 355 | }
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| 356 |
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| 357 | /* almost the same as psin */
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| 358 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
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| 359 | Packet4f pcos<Packet4f>(const Packet4f& _x)
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| 360 | {
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| 361 | Packet4f x = _x;
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| 362 | _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
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| 363 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
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| 364 |
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| 365 | _EIGEN_DECLARE_CONST_Packet4i(1, 1);
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| 366 | _EIGEN_DECLARE_CONST_Packet4i(not1, ~1);
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| 367 | _EIGEN_DECLARE_CONST_Packet4i(2, 2);
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| 368 | _EIGEN_DECLARE_CONST_Packet4i(4, 4);
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| 369 |
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| 370 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP1,-0.78515625f);
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| 371 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP2, -2.4187564849853515625e-4f);
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| 372 | _EIGEN_DECLARE_CONST_Packet4f(minus_cephes_DP3, -3.77489497744594108e-8f);
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| 373 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p0, -1.9515295891E-4f);
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| 374 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p1, 8.3321608736E-3f);
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| 375 | _EIGEN_DECLARE_CONST_Packet4f(sincof_p2, -1.6666654611E-1f);
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| 376 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p0, 2.443315711809948E-005f);
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| 377 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p1, -1.388731625493765E-003f);
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| 378 | _EIGEN_DECLARE_CONST_Packet4f(coscof_p2, 4.166664568298827E-002f);
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| 379 | _EIGEN_DECLARE_CONST_Packet4f(cephes_FOPI, 1.27323954473516f); // 4 / M_PI
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| 380 |
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| 381 | Packet4f xmm1, xmm2, xmm3, y;
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| 382 | Packet4i emm0, emm2;
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| 383 |
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| 384 | x = pabs(x);
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| 385 |
|
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| 386 | /* scale by 4/Pi */
|
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| 387 | y = pmul(x, p4f_cephes_FOPI);
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| 388 |
|
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| 389 | /* get the integer part of y */
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| 390 | emm2 = _mm_cvttps_epi32(y);
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| 391 | /* j=(j+1) & (~1) (see the cephes sources) */
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| 392 | emm2 = _mm_add_epi32(emm2, p4i_1);
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| 393 | emm2 = _mm_and_si128(emm2, p4i_not1);
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| 394 | y = _mm_cvtepi32_ps(emm2);
|
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| 395 |
|
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| 396 | emm2 = _mm_sub_epi32(emm2, p4i_2);
|
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| 397 |
|
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| 398 | /* get the swap sign flag */
|
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| 399 | emm0 = _mm_andnot_si128(emm2, p4i_4);
|
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| 400 | emm0 = _mm_slli_epi32(emm0, 29);
|
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| 401 | /* get the polynom selection mask */
|
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| 402 | emm2 = _mm_and_si128(emm2, p4i_2);
|
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| 403 | emm2 = _mm_cmpeq_epi32(emm2, _mm_setzero_si128());
|
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| 404 |
|
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| 405 | Packet4f sign_bit = _mm_castsi128_ps(emm0);
|
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| 406 | Packet4f poly_mask = _mm_castsi128_ps(emm2);
|
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| 407 |
|
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| 408 | /* The magic pass: "Extended precision modular arithmetic"
|
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| 409 | x = ((x - y * DP1) - y * DP2) - y * DP3; */
|
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| 410 | xmm1 = pmul(y, p4f_minus_cephes_DP1);
|
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| 411 | xmm2 = pmul(y, p4f_minus_cephes_DP2);
|
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| 412 | xmm3 = pmul(y, p4f_minus_cephes_DP3);
|
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| 413 | x = padd(x, xmm1);
|
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| 414 | x = padd(x, xmm2);
|
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| 415 | x = padd(x, xmm3);
|
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| 416 |
|
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| 417 | /* Evaluate the first polynom (0 <= x <= Pi/4) */
|
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| 418 | y = p4f_coscof_p0;
|
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| 419 | Packet4f z = pmul(x,x);
|
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| 420 |
|
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| 421 | y = pmadd(y,z,p4f_coscof_p1);
|
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| 422 | y = pmadd(y,z,p4f_coscof_p2);
|
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| 423 | y = pmul(y, z);
|
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| 424 | y = pmul(y, z);
|
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| 425 | Packet4f tmp = _mm_mul_ps(z, p4f_half);
|
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| 426 | y = psub(y, tmp);
|
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| 427 | y = padd(y, p4f_1);
|
---|
| 428 |
|
---|
| 429 | /* Evaluate the second polynom (Pi/4 <= x <= 0) */
|
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| 430 | Packet4f y2 = p4f_sincof_p0;
|
---|
| 431 | y2 = pmadd(y2, z, p4f_sincof_p1);
|
---|
| 432 | y2 = pmadd(y2, z, p4f_sincof_p2);
|
---|
| 433 | y2 = pmul(y2, z);
|
---|
| 434 | y2 = pmadd(y2, x, x);
|
---|
| 435 |
|
---|
| 436 | /* select the correct result from the two polynoms */
|
---|
| 437 | y2 = _mm_and_ps(poly_mask, y2);
|
---|
| 438 | y = _mm_andnot_ps(poly_mask, y);
|
---|
| 439 | y = _mm_or_ps(y,y2);
|
---|
| 440 |
|
---|
| 441 | /* update the sign */
|
---|
| 442 | return _mm_xor_ps(y, sign_bit);
|
---|
| 443 | }
|
---|
| 444 |
|
---|
| 445 | #if EIGEN_FAST_MATH
|
---|
| 446 |
|
---|
| 447 | // This is based on Quake3's fast inverse square root.
|
---|
| 448 | // For detail see here: http://www.beyond3d.com/content/articles/8/
|
---|
| 449 | // It lacks 1 (or 2 bits in some rare cases) of precision, and does not handle negative, +inf, or denormalized numbers correctly.
|
---|
| 450 | template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
|
---|
| 451 | Packet4f psqrt<Packet4f>(const Packet4f& _x)
|
---|
| 452 | {
|
---|
| 453 | Packet4f half = pmul(_x, pset1<Packet4f>(.5f));
|
---|
| 454 |
|
---|
| 455 | /* select only the inverse sqrt of non-zero inputs */
|
---|
| 456 | Packet4f non_zero_mask = _mm_cmpge_ps(_x, pset1<Packet4f>((std::numeric_limits<float>::min)()));
|
---|
| 457 | Packet4f x = _mm_and_ps(non_zero_mask, _mm_rsqrt_ps(_x));
|
---|
| 458 |
|
---|
| 459 | x = pmul(x, psub(pset1<Packet4f>(1.5f), pmul(half, pmul(x,x))));
|
---|
| 460 | return pmul(_x,x);
|
---|
| 461 | }
|
---|
| 462 |
|
---|
| 463 | #else
|
---|
| 464 |
|
---|
| 465 | template<> EIGEN_STRONG_INLINE Packet4f psqrt<Packet4f>(const Packet4f& x) { return _mm_sqrt_ps(x); }
|
---|
| 466 |
|
---|
| 467 | #endif
|
---|
| 468 |
|
---|
| 469 | template<> EIGEN_STRONG_INLINE Packet2d psqrt<Packet2d>(const Packet2d& x) { return _mm_sqrt_pd(x); }
|
---|
| 470 |
|
---|
| 471 | } // end namespace internal
|
---|
| 472 |
|
---|
| 473 | } // end namespace Eigen
|
---|
| 474 |
|
---|
| 475 | #endif // EIGEN_MATH_FUNCTIONS_SSE_H
|
---|