1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2007 Julien Pommier
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2016 Konstantinos Margaritis <markos@freevec.org>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
/* The sin, cos, exp, and log functions of this file come from
* Julien Pommier's sse math library: http://gruntthepeon.free.fr/ssemath/
*/
#ifndef EIGEN_MATH_FUNCTIONS_ALTIVEC_H
#define EIGEN_MATH_FUNCTIONS_ALTIVEC_H
namespace Eigen {
namespace internal {
#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
static _EIGEN_DECLARE_CONST_Packet4f(1 , 1.0f);
static _EIGEN_DECLARE_CONST_Packet4f(half, 0.5f);
static _EIGEN_DECLARE_CONST_Packet4i(0x7f, 0x7f);
static _EIGEN_DECLARE_CONST_Packet4i(23, 23);
static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(inv_mant_mask, ~0x7f800000);
/* the smallest non denormalized float number */
static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(min_norm_pos, 0x00800000);
static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_inf, 0xff800000); // -1.f/0.f
static _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(minus_nan, 0xffffffff);
/* natural logarithm computed for 4 simultaneous float
return NaN for x <= 0
*/
static _EIGEN_DECLARE_CONST_Packet4f(cephes_SQRTHF, 0.707106781186547524f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p0, 7.0376836292E-2f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p1, - 1.1514610310E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p2, 1.1676998740E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p3, - 1.2420140846E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p4, + 1.4249322787E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p5, - 1.6668057665E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p6, + 2.0000714765E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p7, - 2.4999993993E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_p8, + 3.3333331174E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q1, -2.12194440e-4f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_log_q2, 0.693359375f);
static _EIGEN_DECLARE_CONST_Packet4f(exp_hi, 88.3762626647950f);
static _EIGEN_DECLARE_CONST_Packet4f(exp_lo, -88.3762626647949f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_LOG2EF, 1.44269504088896341f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C1, 0.693359375f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_C2, -2.12194440e-4f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p0, 1.9875691500E-4f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p1, 1.3981999507E-3f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p2, 8.3334519073E-3f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p3, 4.1665795894E-2f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p4, 1.6666665459E-1f);
static _EIGEN_DECLARE_CONST_Packet4f(cephes_exp_p5, 5.0000001201E-1f);
#endif
static _EIGEN_DECLARE_CONST_Packet2d(1 , 1.0);
static _EIGEN_DECLARE_CONST_Packet2d(2 , 2.0);
static _EIGEN_DECLARE_CONST_Packet2d(half, 0.5);
static _EIGEN_DECLARE_CONST_Packet2d(exp_hi, 709.437);
static _EIGEN_DECLARE_CONST_Packet2d(exp_lo, -709.436139303);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_LOG2EF, 1.4426950408889634073599);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p0, 1.26177193074810590878e-4);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p1, 3.02994407707441961300e-2);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_p2, 9.99999999999999999910e-1);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q0, 3.00198505138664455042e-6);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q1, 2.52448340349684104192e-3);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q2, 2.27265548208155028766e-1);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_q3, 2.00000000000000000009e0);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C1, 0.693145751953125);
static _EIGEN_DECLARE_CONST_Packet2d(cephes_exp_C2, 1.42860682030941723212e-6);
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet2d pexp<Packet2d>(const Packet2d& _x)
{
Packet2d x = _x;
Packet2d tmp, fx;
Packet2l emm0;
// clamp x
x = pmax(pmin(x, p2d_exp_hi), p2d_exp_lo);
/* express exp(x) as exp(g + n*log(2)) */
fx = pmadd(p2d_cephes_LOG2EF, x, p2d_half);
fx = vec_floor(fx);
tmp = pmul(fx, p2d_cephes_exp_C1);
Packet2d z = pmul(fx, p2d_cephes_exp_C2);
x = psub(x, tmp);
x = psub(x, z);
Packet2d x2 = pmul(x,x);
Packet2d px = p2d_cephes_exp_p0;
px = pmadd(px, x2, p2d_cephes_exp_p1);
px = pmadd(px, x2, p2d_cephes_exp_p2);
px = pmul (px, x);
Packet2d qx = p2d_cephes_exp_q0;
qx = pmadd(qx, x2, p2d_cephes_exp_q1);
qx = pmadd(qx, x2, p2d_cephes_exp_q2);
qx = pmadd(qx, x2, p2d_cephes_exp_q3);
x = pdiv(px,psub(qx,px));
x = pmadd(p2d_2,x,p2d_1);
// build 2^n
emm0 = vec_ctsl(fx, 0);
static const Packet2l p2l_1023 = { 1023, 1023 };
static const Packet2ul p2ul_52 = { 52, 52 };
emm0 = emm0 + p2l_1023;
emm0 = emm0 << reinterpret_cast<Packet2l>(p2ul_52);
// Altivec's max & min operators just drop silent NaNs. Check NaNs in
// inputs and return them unmodified.
Packet2ul isnumber_mask = reinterpret_cast<Packet2ul>(vec_cmpeq(_x, _x));
return vec_sel(_x, pmax(pmul(x, reinterpret_cast<Packet2d>(emm0)), _x),
isnumber_mask);
}
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet4f pexp<Packet4f>(const Packet4f& _x)
{
#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
Packet4f x = _x;
Packet4f tmp, fx;
Packet4i emm0;
// clamp x
x = pmax(pmin(x, p4f_exp_hi), p4f_exp_lo);
// express exp(x) as exp(g + n*log(2))
fx = pmadd(x, p4f_cephes_LOG2EF, p4f_half);
fx = pfloor(fx);
tmp = pmul(fx, p4f_cephes_exp_C1);
Packet4f z = pmul(fx, p4f_cephes_exp_C2);
x = psub(x, tmp);
x = psub(x, z);
z = pmul(x,x);
Packet4f y = p4f_cephes_exp_p0;
y = pmadd(y, x, p4f_cephes_exp_p1);
y = pmadd(y, x, p4f_cephes_exp_p2);
y = pmadd(y, x, p4f_cephes_exp_p3);
y = pmadd(y, x, p4f_cephes_exp_p4);
y = pmadd(y, x, p4f_cephes_exp_p5);
y = pmadd(y, z, x);
y = padd(y, p4f_1);
// build 2^n
emm0 = (Packet4i){ (int)fx[0], (int)fx[1], (int)fx[2], (int)fx[3] };
emm0 = emm0 + p4i_0x7f;
emm0 = emm0 << reinterpret_cast<Packet4i>(p4i_23);
return pmax(pmul(y, reinterpret_cast<Packet4f>(emm0)), _x);
#else
Packet4f res;
res.v4f[0] = pexp<Packet2d>(_x.v4f[0]);
res.v4f[1] = pexp<Packet2d>(_x.v4f[1]);
return res;
#endif
}
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet2d psqrt<Packet2d>(const Packet2d& x)
{
return vec_sqrt(x);
}
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet4f psqrt<Packet4f>(const Packet4f& x)
{
Packet4f res;
#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
res = vec_sqrt(x);
#else
res.v4f[0] = psqrt<Packet2d>(x.v4f[0]);
res.v4f[1] = psqrt<Packet2d>(x.v4f[1]);
#endif
return res;
}
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet2d prsqrt<Packet2d>(const Packet2d& x) {
return pset1<Packet2d>(1.0) / psqrt<Packet2d>(x);
}
template<> EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED
Packet4f prsqrt<Packet4f>(const Packet4f& x) {
Packet4f res;
#if !defined(__ARCH__) || (defined(__ARCH__) && __ARCH__ >= 12)
res = pset1<Packet4f>(1.0) / psqrt<Packet4f>(x);
#else
res.v4f[0] = prsqrt<Packet2d>(x.v4f[0]);
res.v4f[1] = prsqrt<Packet2d>(x.v4f[1]);
#endif
return res;
}
// Hyperbolic Tangent function.
template <>
EIGEN_DEFINE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS EIGEN_UNUSED Packet4f
ptanh<Packet4f>(const Packet4f& x) {
return internal::generic_fast_tanh_float(x);
}
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_MATH_FUNCTIONS_ALTIVEC_H
|
