Eigen  5.0.1-dev+284dcc12
 
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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 <gael.guennebaud@inria.fr>
6// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
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
26EIGEN_DOUBLE_PACKET_FUNCTION(atanh, Packet2d)
27EIGEN_DOUBLE_PACKET_FUNCTION(log, Packet2d)
28EIGEN_DOUBLE_PACKET_FUNCTION(log2, Packet2d)
29EIGEN_DOUBLE_PACKET_FUNCTION(tanh, Packet2d)
30
31EIGEN_FLOAT_PACKET_FUNCTION(atanh, Packet4f)
32EIGEN_FLOAT_PACKET_FUNCTION(log, Packet4f)
33EIGEN_FLOAT_PACKET_FUNCTION(log2, Packet4f)
34
35EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet2d)
36EIGEN_GENERIC_PACKET_FUNCTION(atan, Packet4f)
37EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet2d)
38EIGEN_GENERIC_PACKET_FUNCTION(exp2, Packet4f)
39
40#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
41static EIGEN_DECLARE_CONST_Packet4f(1, 1.0f);
42static EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
43static EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
44static EIGEN_DECLARE_CONST_Packet4i(23, 23);
45
46static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
47
48/* the smallest non denormalized float number */
49static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
50static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f
51static EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);
52
53/* natural logarithm computed for 4 simultaneous float
54 return NaN for x <= 0
55*/
56static EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
57static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
58static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, -1.1514610310E-1f);
59static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
60static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, -1.2420140846E-1f);
61static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, +1.4249322787E-1f);
62static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, -1.6668057665E-1f);
63static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, +2.0000714765E-1f);
64static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, -2.4999993993E-1f);
65static EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, +3.3333331174E-1f);
66static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
67static EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
68
69static EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
70static EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
71
72static EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
73static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
74static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
75
76static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
77static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
78static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
79static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
80static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
81static EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
82#endif
83
84static EIGEN_DECLARE_CONST_Packet2d(1, 1.0);
85static EIGEN_DECLARE_CONST_Packet2d(2, 2.0);
86static EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
87
88static EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
89static EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
90
91static EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
92
93static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
94static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
95static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
96
97static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
98static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
99static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
100static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
101
102static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
103static EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
104
105template <>
106EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d pexp<Packet2d>(const Packet2d& _x) {
107 Packet2d x = _x;
108
109 Packet2d tmp, fx;
110 Packet2l emm0;
111
112 // clamp x
113 x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
114 /* express exp(x) as exp(g + n*log(2)) */
115 fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
116
117 fx = vec_floor(fx);
118
119 tmp = pmul(fx, p2d_cephes_exp_C1);
120 Packet2d z = pmul(fx, p2d_cephes_exp_C2);
121 x = psub(x, tmp);
122 x = psub(x, z);
123
124 Packet2d x2 = pmul(x, x);
125
126 Packet2d px = p2d_cephes_exp_p0;
127 px = pmadd(px, x2, p2d_cephes_exp_p1);
128 px = pmadd(px, x2, p2d_cephes_exp_p2);
129 px = pmul(px, x);
130
131 Packet2d qx = p2d_cephes_exp_q0;
132 qx = pmadd(qx, x2, p2d_cephes_exp_q1);
133 qx = pmadd(qx, x2, p2d_cephes_exp_q2);
134 qx = pmadd(qx, x2, p2d_cephes_exp_q3);
135
136 x = pdiv(px, psub(qx, px));
137 x = pmadd(p2d_2, x, p2d_1);
138
139 // build 2^n
140 emm0 = vec_ctsl(fx, 0);
141
142 static const Packet2l p2l_1023 = {1023, 1023};
143 static const Packet2ul p2ul_52 = {52, 52};
144
145 emm0 = emm0 + p2l_1023;
146 emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
147
148 // Altivec's max & min operators just drop silent NaNs. Check NaNs in
149 // inputs and return them unmodified.
150 Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
151 return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x), isnumber_mask);
152}
153
154template <>
155EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f pexp<Packet4f>(const Packet4f& _x) {
156#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
157 Packet4f x = _x;
158
159 Packet4f tmp, fx;
160 Packet4i emm0;
161
162 // clamp x
163 x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
164
165 // express exp(x) as exp(g + n*log(2))
166 fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
167
168 fx = pfloor(fx);
169
170 tmp = pmul(fx, p4f_cephes_exp_C1);
171 Packet4f z = pmul(fx, p4f_cephes_exp_C2);
172 x = psub(x, tmp);
173 x = psub(x, z);
174
175 z = pmul(x, x);
176
177 Packet4f y = p4f_cephes_exp_p0;
178 y = pmadd(y, x, p4f_cephes_exp_p1);
179 y = pmadd(y, x, p4f_cephes_exp_p2);
180 y = pmadd(y, x, p4f_cephes_exp_p3);
181 y = pmadd(y, x, p4f_cephes_exp_p4);
182 y = pmadd(y, x, p4f_cephes_exp_p5);
183 y = pmadd(y, z, x);
184 y = padd(y, p4f_1);
185
186 // build 2^n
187 emm0 = Packet4i{(int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3]};
188 emm0 = emm0 + p4i_0x7f;
189 emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);
190
191 return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);
192#else
193 Packet4f res;
194 res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);
195 res.v4f[1] = pexp<Packet2d>(_x.v4f[1]);
196 return res;
197#endif
198}
199
200template <>
201EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d psqrt<Packet2d>(const Packet2d& x) {
202 return vec_sqrt(x);
203}
204
205template <>
206EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f psqrt<Packet4f>(const Packet4f& x) {
207 Packet4f res;
208#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
209 res = vec_sqrt(x);
210#else
211 res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
212 res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
213#endif
214 return res;
215}
216
217template <>
218EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet2d prsqrt<Packet2d>(const Packet2d& x) {
219 return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
220}
221
222template <>
223EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f prsqrt<Packet4f>(const Packet4f& x) {
224 Packet4f res;
225#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
226 res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);
227#else
228 res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
229 res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
230#endif
231 return res;
232}
233
234// Hyperbolic Tangent function.
235template <>
236EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet4f ptanh<Packet4f>(const Packet4f& x) {
237 return ptanh_float(x);
238}
239
240} // end namespace internal
241
242} // end namespace Eigen
243
244#endif // EIGEN_MATH_FUNCTIONS_ZVECTOR_H
Eigen
Namespace containing all symbols from the Eigen library.
Definition B01_Experimental.dox:1
Eigen::atanh
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_atanh_op< typename Derived::Scalar >, const Derived > atanh(const Eigen::ArrayBase< Derived > &x)
Eigen::log2
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log2_op< typename Derived::Scalar >, const Derived > log2(const Eigen::ArrayBase< Derived > &x)
Eigen::atan
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_atan_op< typename Derived::Scalar >, const Derived > atan(const Eigen::ArrayBase< Derived > &x)
Eigen::log
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log_op< typename Derived::Scalar >, const Derived > log(const Eigen::ArrayBase< Derived > &x)
Eigen::tanh
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tanh_op< typename Derived::Scalar >, const Derived > tanh(const Eigen::ArrayBase< Derived > &x)
Eigen::exp2
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_exp2_op< typename Derived::Scalar >, const Derived > exp2(const Eigen::ArrayBase< Derived > &x)