-
Notifications
You must be signed in to change notification settings - Fork 59
/
Copy pathlinpack_bench.html
429 lines (388 loc) · 13.3 KB
/
linpack_bench.html
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
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
<html>
<head>
<title>
LINPACK_BENCH - The LINPACK Benchmark
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
LINPACK_BENCH <br> The LINPACK Benchmark
</h1>
<hr>
<p>
<b>LINPACK_BENCH</b>
is a FORTRAN90 program which
carries out the LINPACK Benchmark.
</p>
<p>
The LINPACK benchmark is a test problem used to rate the performance
of a computer on a simple linear algebra problem.
</p>
<p>
The test problem requires the user to set up a random dense matrix
<b>A</b> of size <b>N</b> = 1000, and a right hand side vector <b>B</b>
which is the product of <b>A</b> and a vector <b>X</b> of all 1's.
The first task is to compute an LU factorization of <b>A</b>. The
second task is to use the LU factorization to solve the linear system
<blockquote>
<b>A</b> * <b>X</b> = <b>B</b>.
</blockquote>
</p>
<p>
The number of floating point operations required for these two
tasks is roughly
<blockquote>
ops = 2 * N*N*N / 3 + 2 * N * N,
</blockquote>
therefore, the "MegaFLOPS" rating, or millions of floating point
operations per second, can be found as
<blockquote>
mflops = ops / ( cpu * 1000000 ).
</blockquote>
</p>
<p>
On a given computer, if you run the benchmark for a sequence of increasing
values of N, the behavior of the MegaFLOPS rating will vary as you pass through
three main zones of behavior:
<ul>
<li>
a <i>rising</i> zone, as both the local cache memory and the processor
are not challenged.
</li>
<li>
a <i>flat</i> zone, where the processor is challenged, that is, it is
performing at top efficiency.
</li>
<li>
a <i>decaying</i> zone, where the local cache memory is also challenged,
that is the matrix is so large that the cache is not big enough to
keep the necessary data close enough to the processor to keep it running
at top speed.
</li>
</ul>
</p>
<p>
<table border="1">
<tr>
<th>Language</th><th>Precision</th><th>Type</th><th>Machine</th><th>Comment</t><th>MegaFLOPS</th>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>Chili</td><td>(rewritten)</td><td>240</td>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>Kachina</td><td> </td><td>196</td>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>Chili</td><td> </td><td>194</td>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>Eclipse</td><td>(1 processor)</td><td>127</td>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>DHCP95 (Apple G5)</td><td>gfortran</td><td>118</td>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>Yankee (Apple G4)</td><td> </td><td>36</td>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>Teragold</td><td>(1 processor)</td><td>18</td>
</tr>
<tr>
<td>Fortran90</td><td>Single</td><td>Real</td><td>Sgi</td><td> </td><td>16</td>
</tr>
<tr>
<td> </td><td> </td><td> </td><td> </td><td> </td><td> </td>
</tr>
<tr>
<td>Fortran90</td><td>Double</td><td>Real</td><td>DHCP95 (Apple G5)</td><td>gfortran</td><td>149</td>
</tr>
<tr>
<td>Fortran90</td><td>Double</td><td>Real</td><td>Chili</td><td>fort -fast</td><td>104</td>
</tr>
<tr>
<td>Fortran90</td><td>Double</td><td>Real</td><td>Kachina</td><td> </td><td>87</td>
</tr>
<tr>
<td>Fortran90</td><td>Double</td><td>Real</td><td>Chili</td><td> </td><td>77</td>
</tr>
<tr>
<td> </td><td> </td><td> </td><td> </td><td> </td><td> </td>
</tr>
<tr>
<td>Fortran90</td><td>Quad</td><td>Real</td><td>DHCP95 (Apple G5)</td><td>gfortran</td><td>23</td>
</tr>
<tr>
<td>Fortran90</td><td>Quad</td><td>Real</td><td>Chili</td><td> </td><td>10</td>
</tr>
</table>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>LINPACK_BENCH</b> is available in
<a href = "../../c_src/linpack_bench/linpack_bench.html">a C version</a> and
<a href = "../../cpp_src/linpack_bench/linpack_bench.html">a C++ version</a> and
<a href = "../../f77_src/linpack_bench/linpack_bench.html">a FORTRAN77 version</a> and
<a href = "../../f_src/linpack_bench/linpack_bench.html">a FORTRAN90 version</a> and
<a href = "../../j_src/linpack_bench/linpack_bench.html">a JAVA version</a> and
<a href = "../../m_src/linpack_bench/linpack_bench.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/linpack_d/linpack_d.html">
LINPACK_D</a>,
a FORTRAN90 library which
supplies the solvers used by <b>LINPACK_BENCH</b>.
</p>
<p>
<a href = "../../f_src/matmul/matmul.html">
MATMUL</a>,
a FORTRAN90 program which
is an interactive matrix multiplication benchmark program.
</p>
<p>
<a href = "../../f77_src/mdbnch/mdbnch.html">
MDBNCH</a>,
a FORTRAN77 program which
is a benchmark code for a molecular dynamics calculation.
</p>
<p>
<a href = "../../f_src/memory_test/memory_test.html">
MEMORY_TEST</a>,
a FORTRAN90 program which
declares and uses a sequence of larger
and larger vectors, to see how big a vector can be used on a given
machine and compiler.
</p>
<p>
<a href = "../../f_src/mxm/mxm.html">
MXM</a>,
a FORTRAN90 program which
sets up a matrix multiplication problem A=B*C of arbitrary size,
and compares the time required for IJK, IKJ, JIK, JKI, KIJ and KJI orderings
of the loops.
</p>
<p>
<a href = "../../f_src/mxv/mxv.html">
MXV</a>,
a FORTRAN90 program which
compares the performance of (DO I, DO J) loops, (DO J, DO I) loops,
and MATMUL for computing the product of an MxN matrix A and an N vector X.
</p>
<p>
<a href = "../../f_src/nas/nas.html">
NAS</a>,
a FORTRAN90 program which
runs the NASA kernel benchmark.
</p>
<p>
<a href = "../../f_src/sum_million/sum_million.html">
SUM_MILLION</a>,
a FORTRAN90 program which
sums the integers from 1 to 1,000,000, as a demonstration of how
to rate a computer's speed;
</p>
<p>
<a href = "../../f_src/timer/timer.html">
TIMER</a>,
a FORTRAN90 example which
demonstrates how to measure CPU time or elapsed time.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
<a href = "http://www.netlib.org/benchmark/1000s">
http://www.netlib.org/benchmark/1000s</a>
the LINPACK benchmark website (single precision).
</li>
<li>
<a href = "http://www.netlib.org/benchmark/1000d">
http://www.netlib.org/benchmark/1000d</a>
the LINPACK benchmark website (double precision).
</li>
<li>
Jack Dongarra,<br>
Performance of Various Computers Using Standard Linear Equations Software,
Technical Report CS-89-85,<br>
Electrical Engineering and Computer Science Department,<br>
University of Tennessee, 2008.
</li>
<li>
Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,<br>
LINPACK User's Guide,<br>
SIAM, 1979,<br>
ISBN13: 978-0-898711-72-1,<br>
LC: QA214.L56.
</li>
<li>
George Fishman,<br>
Multiplicative congruential random number generators with modulus
2**b: an exhaustive analysis for b = 32 and a partial analysis for b = 48,<br>
Mathematics of Computation,<br>
Volume 189, 1990, pages 331-344.
</li>
<li>
Charles Lawson, Richard Hanson, David Kincaid, Fred Krogh,<br>
Algorithm 539:
Basic Linear Algebra Subprograms for Fortran Usage,<br>
ACM Transactions on Mathematical Software,<br>
Volume 5, Number 3, September 1979, pages 308-323.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<b>LINPACK_BENCH_S</b> is the single precision version:
<ul>
<li>
<a href = "linpack_bench_s.f90">linpack_bench_s.f90</a>,
the source code.
</li>
<li>
<a href = "linpack_bench_s.sh">linpack_bench_s.sh</a>,
commands to compile and load the source code.
</li>
<li>
<a href = "linpack_bench_s.ll">linpack_bench_s.ll</a>,
commands to compile and load the source code on a system
that uses IBM's LoadLeveler batch queueing system.
</li>
<li>
<a href = "linpack_bench_s_chili_output.txt">
linpack_bench_s_chili_output.txt</a>,
the output from an ALPHA named "Chili".
</li>
<li>
<a href = "linpack_bench_s_dhcp95_output.txt">
linpack_bench_s_dhcp95_output.txt</a>,
the output from an Apple G5 named "DHCP95".
</li>
<li>
<a href = "linpack_bench_s_eclipse_output.txt">
linpack_bench_s_eclipse_output.txt</a>,
the output from one (Power4) processor
of ECLIPSE, an IBM pSeries 690.
</li>
<li>
<a href = "linpack_bench_s_kachina_output.txt">
linpack_bench_s_kachina_output.txt</a>,
the output from an ALPHA named "Kachina".
</li>
<li>
<a href = "linpack_bench_s_sgi_output.txt">
linpack_bench_s_sgi_output.txt</a>,
the output from an SGI.
</li>
<li>
<a href = "linpack_bench_s_teragold_output.txt">
linpack_bench_s_teragold_output.txt</a>,
the output from one (Power3) processor
of TERAGOLD, an IBM pSeries 690.
</li>
</ul>
</p>
<p>
<b>LINPACK_BENCH_D</b> is the double precision version:
<ul>
<li>
<a href = "linpack_bench_d.f90">linpack_bench_d.f90</a>,
the source code.
</li>
<li>
<a href = "linpack_bench_d.sh">linpack_bench_d.sh</a>,
commands to compile and load the source code.
</li>
<li>
<a href = "linpack_bench_d_chili_output.txt">
linpack_bench_d_chili_output.txt</a>,
the output an ALPHA named "Chili".
</li>
<li>
<a href = "linpack_bench_d_dhcp95_output.txt">
linpack_bench_d_dhcp95_output.txt</a>,
the output from an Apple G5 named "DHCP95".
</li>
<li>
<a href = "linpack_bench_d_kachina_output.txt">
linpack_bench_d_kachina_output.txt</a>,
the output from an ALPHA named "Kachina".
</li>
</ul>
</p>
<p>
<b>LINPACK_BENCH_Q</b> is the quad precision version (your compiler might not allow this
arithmetic type, or you may have to change the syntax of the program
to get it):
<ul>
<li>
<a href = "linpack_bench_q.f90">linpack_bench_q.f90</a>,
the source code.
</li>
<li>
<a href = "linpack_bench_q.sh">linpack_bench_q.sh</a>,
commands to compile and load the source code.
</li>
<li>
<a href = "linpack_bench_q_chili_output.txt">
linpack_bench_q_chili_output.txt</a>,
the output from an ALPHA named "Chili".
</li>
<li>
<a href = "linpack_bench_q_dhcp95_output.txt">
linpack_bench_q_dhcp95_output.txt</a>,
the output from an Apple G5 named "DHCP95".
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
This is the list of routines for the double precision version of the
benchmark program. The single and quad precision names are similar.
<ul>
<li>
<b>LINPACK_BENCH_D</b> drives the double precision LINPACK benchmark program.
</li>
<li>
<b>D_MATGEN</b> generates a random matrix.
</li>
<li>
<b>D_RANDOM</b> returns a uniformly distributed random number between 0 and 1.
</li>
<li>
<b>DAXPY</b> adds a constant times one vector to another.
</li>
<li>
<b>DGEFA</b> factors a real matrix.
</li>
<li>
<b>DGESL</b> solves a real general linear system A * X = B.
</li>
<li>
<b>IDAMAX</b> finds the index of the vector element of maximum absolute value.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 07 March 2008.
</i>
<!-- John Burkardt -->
</body>
</html>