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
|
/*
* Copyright (C) 2014, The University of Texas at Austin
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are
* met:
* - Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* - Neither the name of The University of Texas at Austin nor the names
* of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
*/
/*
* Copyright (C) 2014-2015, Michael Lehn
*
* ulmBLAS adopted general ideas from BLIS. Using micro kernels from BLIS
* only requires minor modifications,
*
*/
#ifndef ULMBLAS_IMPL_LEVEL1_NRM2_TCC
#define ULMBLAS_IMPL_LEVEL1_NRM2_TCC 1
#include <complex>
#include <cmath>
#include <ulmblas/impl/auxiliary/pow.h>
#include <ulmblas/impl/level1/nrm2.h>
namespace ulmBLAS {
template <typename IndexType, typename VX>
VX
nrm2(IndexType n,
const VX *x,
IndexType incX)
{
VX result;
nrm2(n, x, incX, result);
return result;
}
template <typename IndexType, typename VX>
VX
nrm2(IndexType n,
const std::complex<VX> *x,
IndexType incX)
{
VX result;
nrm2(n, x, incX, result);
return result;
}
template <typename IndexType, typename VX, typename Result>
void
nrm2(IndexType n,
const VX *x,
IndexType incX,
Result &result)
{
using std::abs;
using std::sqrt;
const Result Zero(0), One(1);
if (n<1) {
result = Zero;
} else if (n==1) {
result = abs(*x);
} else {
Result scale = 0;
Result ssq = 1;
for (IndexType i=0; i<n; ++i) {
if (x[i*incX]!=Zero) {
Result absXi = abs(x[i*incX]);
if (scale<absXi) {
ssq = One + ssq * pow(scale/absXi, 2);
scale = absXi;
} else {
ssq += pow(absXi/scale, 2);
}
}
}
result = scale*sqrt(ssq);
}
}
template <typename IndexType, typename VX, typename Result>
void
nrm2(IndexType n,
const std::complex<VX> *x,
IndexType incX,
Result &result)
{
using std::abs;
using std::imag;
using std::real;
using std::pow;
const Result Zero(0), One(1);
if (n<1) {
result = Zero;
} else if (n==1) {
result = abs(*x);
} else {
Result scale = 0;
Result ssq = 1;
for (IndexType i=0; i<n; ++i) {
if (real(x[i*incX]) != Zero) {
Result absXi = abs(real(x[i*incX]));
if (scale<absXi) {
ssq = One + ssq * pow(scale/absXi, 2);
scale = absXi;
} else {
ssq += pow(absXi/scale, 2);
}
}
if (imag(x[i*incX]) != Zero) {
Result absXi = abs(imag(x[i*incX]));
if (scale<absXi) {
ssq = One + ssq * pow(scale/absXi, 2);
scale = absXi;
} else {
ssq += pow(absXi/scale, 2);
}
}
}
result = scale*sqrt(ssq);
}
}
} // namespace ulmBLAS
#endif // ULMBLAS_IMPL_LEVEL1_NRM2_TCC 1
|