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Eigen  3.4.0
 
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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 <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_ALTIVEC_H
17#define EIGEN_MATH_FUNCTIONS_ALTIVEC_H
18
19namespace Eigen {
20
21namespace internal {
22
23#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
24static _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
25static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
26static _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
27static _EIGEN_DECLARE_CONST_Packet4i(23, 23);
28
29static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
30
31/* the smallest non denormalized float number */
32static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
33static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f
34static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);
35
36/* natural logarithm computed for 4 simultaneous float
37 return NaN for x <= 0
38*/
39static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
40static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
41static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
42static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
43static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
44static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
45static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
46static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
47static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
48static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
49static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
50static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
51
52static _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
53static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
54
55static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
56static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
57static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
58
59static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
60static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
61static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
62static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
63static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
64static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
65#endif
66
67static _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
68static _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
69static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
70
71static _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
72static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
73
74static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
75
76static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
77static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
78static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
79
80static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
81static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
82static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
83static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
84
85static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
86static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
87
88template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
89Packet2d pexp<Packet2d>(const Packet2d& _x)
90{
91 Packet2d x = _x;
92
93 Packet2d tmp, fx;
94 Packet2l emm0;
95
96 // clamp x
97 x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
98 /* express exp(x) as exp(g + n*log(2)) */
99 fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
100
101 fx = vec_floor(fx);
102
103 tmp = pmul(fx, p2d_cephes_exp_C1);
104 Packet2d z = pmul(fx, p2d_cephes_exp_C2);
105 x = psub(x, tmp);
106 x = psub(x, z);
107
108 Packet2d x2 = pmul(x,x);
109
110 Packet2d px = p2d_cephes_exp_p0;
111 px = pmadd(px, x2, p2d_cephes_exp_p1);
112 px = pmadd(px, x2, p2d_cephes_exp_p2);
113 px = pmul (px, x);
114
115 Packet2d qx = p2d_cephes_exp_q0;
116 qx = pmadd(qx, x2, p2d_cephes_exp_q1);
117 qx = pmadd(qx, x2, p2d_cephes_exp_q2);
118 qx = pmadd(qx, x2, p2d_cephes_exp_q3);
119
120 x = pdiv(px,psub(qx,px));
121 x = pmadd(p2d_2,x,p2d_1);
122
123 // build 2^n
124 emm0 = vec_ctsl(fx, 0);
125
126 static const Packet2l p2l_1023 = { 1023, 1023 };
127 static const Packet2ul p2ul_52 = { 52, 52 };
128
129 emm0 = emm0 + p2l_1023;
130 emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
131
132 // Altivec's max & min operators just drop silent NaNs. Check NaNs in
133 // inputs and return them unmodified.
134 Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
135 return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),
136 isnumber_mask);
137}
138
139template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
140Packet4f pexp<Packet4f>(const Packet4f& _x)
141{
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<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
187Packet2d psqrt<Packet2d>(const Packet2d& x)
188{
189 return vec_sqrt(x);
190}
191
192template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
193Packet4f psqrt<Packet4f>(const Packet4f& x)
194{
195 Packet4f res;
196#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
197 res = vec_sqrt(x);
198#else
199 res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
200 res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
201#endif
202 return res;
203}
204
205template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
206Packet2d prsqrt<Packet2d>(const Packet2d& x) {
207 return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
208}
209
210template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
211Packet4f prsqrt<Packet4f>(const Packet4f& x) {
212 Packet4f res;
213#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
214 res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);
215#else
216 res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
217 res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
218#endif
219 return res;
220}
221
222// Hyperbolic Tangent function.
223template <>
224EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
225ptanh<Packet4f>(const Packet4f& x) {
226 return internal::generic_fast_tanh_float(x);
227}
228
229} // end namespace internal
230
231} // end namespace Eigen
232
233#endif // EIGEN_MATH_FUNCTIONS_ALTIVEC_H
Namespace containing all symbols from the Eigen library.
Definition: Core:141