Eigen  3.4.90 (git rev 5a9f66fb35d03a4da9ef8976e67a61b30aa16dcf)
 
Loading...
Searching...
No Matches
arch/ZVector/MathFunctions.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2007 Julien Pommier
5// Copyright (C) 2009 Gael Guennebaud <[email protected]>
6// Copyright (C) 2016 Konstantinos Margaritis <[email protected]>
7//
8// This Source Code Form is subject to the terms of the Mozilla
9// Public License v. 2.0. If a copy of the MPL was not distributed
10// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11
12/* The sin, cos, exp, and log functions of this file come from
13 * Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
14 */
15
16#ifndef EIGEN_MATH_FUNCTIONS_ZVECTOR_H
17#define EIGEN_MATH_FUNCTIONS_ZVECTOR_H
18
19// IWYU pragma: private
20#include "../../InternalHeaderCheck.h"
21
22namespace Eigen {
23
24namespace internal {
25
26#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
27static EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
28static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
29static EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
30static EIGEN_DECLARE_CONST_Packet4i(23, 23);
31
32static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
33
34/* the smallest non denormalized float number */
35static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
36static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f
37static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);
38
39/* natural logarithm computed for 4 simultaneous float
40 return NaN for x <= 0
41*/
42static EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
43static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
44static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310E-1f);
45static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
46static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846E-1f);
47static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787E-1f);
48static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665E-1f);
49static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765E-1f);
50static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993E-1f);
51static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174E-1f);
52static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
53static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
54
55static EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
56static EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
57
58static EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
59static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
60static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
61
62static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
63static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
64static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
65static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
66static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
67static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
68#endif
69
70static EIGEN_DECLARE_CONST_Packet2d(1, 1.0);
71static EIGEN_DECLARE_CONST_Packet2d(2, 2.0);
72static EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
73
74static EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
75static EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
76
77static EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
78
79static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
80static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
81static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
82
83static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
84static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
85static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
86static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
87
88static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
89static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
90
91template <>
92EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d pexp<Packet2d>(const Packet2d& _x) {
93 Packet2d x = _x;
94
95 Packet2d tmp, fx;
96 Packet2l emm0;
97
98 // clamp x
99 x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
100 /* express exp(x) as exp(g + n*log(2)) */
101 fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
102
103 fx = vec_floor(fx);
104
105 tmp = pmul(fx, p2d_cephes_exp_C1);
106 Packet2d z = pmul(fx, p2d_cephes_exp_C2);
107 x = psub(x, tmp);
108 x = psub(x, z);
109
110 Packet2d x2 = pmul(x, x);
111
112 Packet2d px = p2d_cephes_exp_p0;
113 px = pmadd(px, x2, p2d_cephes_exp_p1);
114 px = pmadd(px, x2, p2d_cephes_exp_p2);
115 px = pmul(px, x);
116
117 Packet2d qx = p2d_cephes_exp_q0;
118 qx = pmadd(qx, x2, p2d_cephes_exp_q1);
119 qx = pmadd(qx, x2, p2d_cephes_exp_q2);
120 qx = pmadd(qx, x2, p2d_cephes_exp_q3);
121
122 x = pdiv(px, psub(qx, px));
123 x = pmadd(p2d_2, x, p2d_1);
124
125 // build 2^n
126 emm0 = vec_ctsl(fx, 0);
127
128 static const Packet2l p2l_1023 = {1023, 1023};
129 static const Packet2ul p2ul_52 = {52, 52};
130
131 emm0 = emm0 + p2l_1023;
132 emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
133
134 // Altivec's max & min operators just drop silent NaNs. Check NaNs in
135 // inputs and return them unmodified.
136 Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
137 return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x), isnumber_mask);
138}
139
140template <>
141EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pexp<Packet4f>(const Packet4f& _x) {
142#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
143 Packet4f x = _x;
144
145 Packet4f tmp, fx;
146 Packet4i emm0;
147
148 // clamp x
149 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
150
151 // express exp(x) as exp(g + n*log(2))
152 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
153
154 fx = pfloor(fx);
155
156 tmp = pmul(fx, p4f_cephes_exp_C1);
157 Packet4f z = pmul(fx, p4f_cephes_exp_C2);
158 x = psub(x, tmp);
159 x = psub(x, z);
160
161 z = pmul(x, x);
162
163 Packet4f y = p4f_cephes_exp_p0;
164 y = pmadd(y, x, p4f_cephes_exp_p1);
165 y = pmadd(y, x, p4f_cephes_exp_p2);
166 y = pmadd(y, x, p4f_cephes_exp_p3);
167 y = pmadd(y, x, p4f_cephes_exp_p4);
168 y = pmadd(y, x, p4f_cephes_exp_p5);
169 y = pmadd(y, z, x);
170 y = padd(y, p4f_1);
171
172 // build 2^n
173 emm0 = (Packet4i){(int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3]};
174 emm0 = emm0 + p4i_0x7f;
175 emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);
176
177 return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);
178#else
179 Packet4f res;
180 res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);
181 res.v4f[1] = pexp<Packet2d>(_x.v4f[1]);
182 return res;
183#endif
184}
185
186template <>
187EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d psqrt<Packet2d>(const Packet2d& x) {
188 return vec_sqrt(x);
189}
190
191template <>
192EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f psqrt<Packet4f>(const Packet4f& x) {
193 Packet4f res;
194#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
195 res = vec_sqrt(x);
196#else
197 res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
198 res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
199#endif
200 return res;
201}
202
203template <>
204EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d prsqrt<Packet2d>(const Packet2d& x) {
205 return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
206}
207
208template <>
209EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f prsqrt<Packet4f>(const Packet4f& x) {
210 Packet4f res;
211#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
212 res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);
213#else
214 res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
215 res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
216#endif
217 return res;
218}
219
220// Hyperbolic Tangent function.
221template <>
222EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f ptanh<Packet4f>(const Packet4f& x) {
223 return ptanh_float(x);
224}
225
226} // end namespace internal
227
228} // end namespace Eigen
229
230#endif // EIGEN_MATH_FUNCTIONS_ZVECTOR_H
Eigen
Namespace containing all symbols from the Eigen library.
Definition Core:137