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
|
/* dlasq5.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Subroutine */ int dlasq5_(integer *i0, integer *n0, doublereal *z__,
integer *pp, doublereal *tau, doublereal *dmin__, doublereal *dmin1,
doublereal *dmin2, doublereal *dn, doublereal *dnm1, doublereal *dnm2,
logical *ieee)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Local variables */
doublereal d__;
integer j4, j4p2;
doublereal emin, temp;
/* -- LAPACK routine (version 3.2) -- */
/* -- Contributed by Osni Marques of the Lawrence Berkeley National -- */
/* -- Laboratory and Beresford Parlett of the Univ. of California at -- */
/* -- Berkeley -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLASQ5 computes one dqds transform in ping-pong form, one */
/* version for IEEE machines another for non IEEE machines. */
/* Arguments */
/* ========= */
/* I0 (input) INTEGER */
/* First index. */
/* N0 (input) INTEGER */
/* Last index. */
/* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) */
/* Z holds the qd array. EMIN is stored in Z(4*N0) to avoid */
/* an extra argument. */
/* PP (input) INTEGER */
/* PP=0 for ping, PP=1 for pong. */
/* TAU (input) DOUBLE PRECISION */
/* This is the shift. */
/* DMIN (output) DOUBLE PRECISION */
/* Minimum value of d. */
/* DMIN1 (output) DOUBLE PRECISION */
/* Minimum value of d, excluding D( N0 ). */
/* DMIN2 (output) DOUBLE PRECISION */
/* Minimum value of d, excluding D( N0 ) and D( N0-1 ). */
/* DN (output) DOUBLE PRECISION */
/* d(N0), the last value of d. */
/* DNM1 (output) DOUBLE PRECISION */
/* d(N0-1). */
/* DNM2 (output) DOUBLE PRECISION */
/* d(N0-2). */
/* IEEE (input) LOGICAL */
/* Flag for IEEE or non IEEE arithmetic. */
/* ===================================================================== */
/* .. Parameter .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--z__;
/* Function Body */
if (*n0 - *i0 - 1 <= 0) {
return 0;
}
j4 = (*i0 << 2) + *pp - 3;
emin = z__[j4 + 4];
d__ = z__[j4] - *tau;
*dmin__ = d__;
*dmin1 = -z__[j4];
if (*ieee) {
/* Code for IEEE arithmetic. */
if (*pp == 0) {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 2] = d__ + z__[j4 - 1];
temp = z__[j4 + 1] / z__[j4 - 2];
d__ = d__ * temp - *tau;
*dmin__ = min(*dmin__,d__);
z__[j4] = z__[j4 - 1] * temp;
/* Computing MIN */
d__1 = z__[j4];
emin = min(d__1,emin);
/* L10: */
}
} else {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 3] = d__ + z__[j4];
temp = z__[j4 + 2] / z__[j4 - 3];
d__ = d__ * temp - *tau;
*dmin__ = min(*dmin__,d__);
z__[j4 - 1] = z__[j4] * temp;
/* Computing MIN */
d__1 = z__[j4 - 1];
emin = min(d__1,emin);
/* L20: */
}
}
/* Unroll last two steps. */
*dnm2 = d__;
*dmin2 = *dmin__;
j4 = (*n0 - 2 << 2) - *pp;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm2 + z__[j4p2];
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau;
*dmin__ = min(*dmin__,*dnm1);
*dmin1 = *dmin__;
j4 += 4;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm1 + z__[j4p2];
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau;
*dmin__ = min(*dmin__,*dn);
} else {
/* Code for non IEEE arithmetic. */
if (*pp == 0) {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 2] = d__ + z__[j4 - 1];
if (d__ < 0.) {
return 0;
} else {
z__[j4] = z__[j4 + 1] * (z__[j4 - 1] / z__[j4 - 2]);
d__ = z__[j4 + 1] * (d__ / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,d__);
/* Computing MIN */
d__1 = emin, d__2 = z__[j4];
emin = min(d__1,d__2);
/* L30: */
}
} else {
i__1 = *n0 - 3 << 2;
for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
z__[j4 - 3] = d__ + z__[j4];
if (d__ < 0.) {
return 0;
} else {
z__[j4 - 1] = z__[j4 + 2] * (z__[j4] / z__[j4 - 3]);
d__ = z__[j4 + 2] * (d__ / z__[j4 - 3]) - *tau;
}
*dmin__ = min(*dmin__,d__);
/* Computing MIN */
d__1 = emin, d__2 = z__[j4 - 1];
emin = min(d__1,d__2);
/* L40: */
}
}
/* Unroll last two steps. */
*dnm2 = d__;
*dmin2 = *dmin__;
j4 = (*n0 - 2 << 2) - *pp;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm2 + z__[j4p2];
if (*dnm2 < 0.) {
return 0;
} else {
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dnm1 = z__[j4p2 + 2] * (*dnm2 / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,*dnm1);
*dmin1 = *dmin__;
j4 += 4;
j4p2 = j4 + (*pp << 1) - 1;
z__[j4 - 2] = *dnm1 + z__[j4p2];
if (*dnm1 < 0.) {
return 0;
} else {
z__[j4] = z__[j4p2 + 2] * (z__[j4p2] / z__[j4 - 2]);
*dn = z__[j4p2 + 2] * (*dnm1 / z__[j4 - 2]) - *tau;
}
*dmin__ = min(*dmin__,*dn);
}
z__[j4 + 2] = *dn;
z__[(*n0 << 2) - *pp] = emin;
return 0;
/* End of DLASQ5 */
} /* dlasq5_ */
|
