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
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2016 Eugene Brevdo <ebrevdo@gmail.com>
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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/.
#ifndef EIGEN_BESSELFUNCTIONS_FUNCTORS_H
#define EIGEN_BESSELFUNCTIONS_FUNCTORS_H
namespace Eigen {
namespace internal {
/** \internal
* \brief Template functor to compute the modified Bessel function of the first
* kind of order zero.
* \sa class CwiseUnaryOp, Cwise::bessel_i0()
*/
template <typename Scalar>
struct scalar_bessel_i0_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i0_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_i0;
return bessel_i0(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_i0(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_i0_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=20 is computed.
// The cost is N multiplications and 2N additions. We also add
// the cost of an additional exp over i0e.
Cost = 28 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the exponentially scaled modified Bessel
* function of the first kind of order zero
* \sa class CwiseUnaryOp, Cwise::bessel_i0e()
*/
template <typename Scalar>
struct scalar_bessel_i0e_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i0e_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_i0e;
return bessel_i0e(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_i0e(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_i0e_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=20 is computed.
// The cost is N multiplications and 2N additions.
Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the modified Bessel function of the first
* kind of order one
* \sa class CwiseUnaryOp, Cwise::bessel_i1()
*/
template <typename Scalar>
struct scalar_bessel_i1_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i1_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_i1;
return bessel_i1(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_i1(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_i1_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=20 is computed.
// The cost is N multiplications and 2N additions. We also add
// the cost of an additional exp over i1e.
Cost = 28 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the exponentially scaled modified Bessel
* function of the first kind of order zero
* \sa class CwiseUnaryOp, Cwise::bessel_i1e()
*/
template <typename Scalar>
struct scalar_bessel_i1e_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_i1e_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_i1e;
return bessel_i1e(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_i1e(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_i1e_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=20 is computed.
// The cost is N multiplications and 2N additions.
Cost = 20 * NumTraits<Scalar>::MulCost + 40 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the Bessel function of the second kind of
* order zero
* \sa class CwiseUnaryOp, Cwise::bessel_j0()
*/
template <typename Scalar>
struct scalar_bessel_j0_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_j0_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_j0;
return bessel_j0(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_j0(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_j0_op<Scalar> > {
enum {
// 6 polynomial of order ~N=8 is computed.
// The cost is N multiplications and N additions each, along with a
// sine, cosine and rsqrt cost.
Cost = 63 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the Bessel function of the second kind of
* order zero
* \sa class CwiseUnaryOp, Cwise::bessel_y0()
*/
template <typename Scalar>
struct scalar_bessel_y0_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_y0_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_y0;
return bessel_y0(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_y0(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_y0_op<Scalar> > {
enum {
// 6 polynomial of order ~N=8 is computed.
// The cost is N multiplications and N additions each, along with a
// sine, cosine, rsqrt and j0 cost.
Cost = 126 * NumTraits<Scalar>::MulCost + 96 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the Bessel function of the first kind of
* order one
* \sa class CwiseUnaryOp, Cwise::bessel_j1()
*/
template <typename Scalar>
struct scalar_bessel_j1_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_j1_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_j1;
return bessel_j1(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_j1(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_j1_op<Scalar> > {
enum {
// 6 polynomial of order ~N=8 is computed.
// The cost is N multiplications and N additions each, along with a
// sine, cosine and rsqrt cost.
Cost = 63 * NumTraits<Scalar>::MulCost + 48 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the Bessel function of the second kind of
* order one
* \sa class CwiseUnaryOp, Cwise::bessel_j1e()
*/
template <typename Scalar>
struct scalar_bessel_y1_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_y1_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_y1;
return bessel_y1(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_y1(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_y1_op<Scalar> > {
enum {
// 6 polynomial of order ~N=8 is computed.
// The cost is N multiplications and N additions each, along with a
// sine, cosine, rsqrt and j1 cost.
Cost = 126 * NumTraits<Scalar>::MulCost + 96 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the modified Bessel function of the second
* kind of order zero
* \sa class CwiseUnaryOp, Cwise::bessel_k0()
*/
template <typename Scalar>
struct scalar_bessel_k0_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k0_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_k0;
return bessel_k0(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_k0(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_k0_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=10 is computed.
// The cost is N multiplications and 2N additions. In addition we compute
// i0, a log, exp and prsqrt and sin and cos.
Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the exponentially scaled modified Bessel
* function of the second kind of order zero
* \sa class CwiseUnaryOp, Cwise::bessel_k0e()
*/
template <typename Scalar>
struct scalar_bessel_k0e_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k0e_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_k0e;
return bessel_k0e(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_k0e(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_k0e_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=10 is computed.
// The cost is N multiplications and 2N additions. In addition we compute
// i0, a log, exp and prsqrt and sin and cos.
Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the modified Bessel function of the
* second kind of order one
* \sa class CwiseUnaryOp, Cwise::bessel_k1()
*/
template <typename Scalar>
struct scalar_bessel_k1_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k1_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_k1;
return bessel_k1(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_k1(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_k1_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=10 is computed.
// The cost is N multiplications and 2N additions. In addition we compute
// i1, a log, exp and prsqrt and sin and cos.
Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
/** \internal
* \brief Template functor to compute the exponentially scaled modified Bessel
* function of the second kind of order one
* \sa class CwiseUnaryOp, Cwise::bessel_k1e()
*/
template <typename Scalar>
struct scalar_bessel_k1e_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_bessel_k1e_op)
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator()(const Scalar& x) const {
using numext::bessel_k1e;
return bessel_k1e(x);
}
typedef typename packet_traits<Scalar>::type Packet;
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet packetOp(const Packet& x) const {
return internal::pbessel_k1e(x);
}
};
template <typename Scalar>
struct functor_traits<scalar_bessel_k1e_op<Scalar> > {
enum {
// On average, a Chebyshev polynomial of order N=10 is computed.
// The cost is N multiplications and 2N additions. In addition we compute
// i1, a log, exp and prsqrt and sin and cos.
Cost = 68 * NumTraits<Scalar>::MulCost + 88 * NumTraits<Scalar>::AddCost,
PacketAccess = packet_traits<Scalar>::HasBessel
};
};
} // end namespace internal
} // end namespace Eigen
#endif // EIGEN_BESSELFUNCTIONS_FUNCTORS_H
|
