LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ slaruv()

 subroutine slaruv ( integer, dimension( 4 ) ISEED, integer N, real, dimension( n ) X )

SLARUV returns a vector of n random real numbers from a uniform distribution.

Purpose:
``` SLARUV returns a vector of n random real numbers from a uniform (0,1)
distribution (n <= 128).

This is an auxiliary routine called by SLARNV and CLARNV.```
Parameters
 [in,out] ISEED ``` ISEED is INTEGER array, dimension (4) On entry, the seed of the random number generator; the array elements must be between 0 and 4095, and ISEED(4) must be odd. On exit, the seed is updated.``` [in] N ``` N is INTEGER The number of random numbers to be generated. N <= 128.``` [out] X ``` X is REAL array, dimension (N) The generated random numbers.```
Further Details:
```  This routine uses a multiplicative congruential method with modulus
2**48 and multiplier 33952834046453 (see G.S.Fishman,
'Multiplicative congruential random number generators with modulus
2**b: an exhaustive analysis for b = 32 and a partial analysis for
b = 48', Math. Comp. 189, pp 331-344, 1990).

48-bit integers are stored in 4 integer array elements with 12 bits
per element. Hence the routine is portable across machines with
integers of 32 bits or more.```

Definition at line 94 of file slaruv.f.

95 *
96 * -- LAPACK auxiliary routine --
97 * -- LAPACK is a software package provided by Univ. of Tennessee, --
98 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
99 *
100 * .. Scalar Arguments ..
101  INTEGER N
102 * ..
103 * .. Array Arguments ..
104  INTEGER ISEED( 4 )
105  REAL X( N )
106 * ..
107 *
108 * =====================================================================
109 *
110 * .. Parameters ..
111  REAL ONE
112  parameter( one = 1.0e0 )
113  INTEGER LV, IPW2
114  REAL R
115  parameter( lv = 128, ipw2 = 4096, r = one / ipw2 )
116 * ..
117 * .. Local Scalars ..
118  INTEGER I, I1, I2, I3, I4, IT1, IT2, IT3, IT4, J
119 * ..
120 * .. Local Arrays ..
121  INTEGER MM( LV, 4 )
122 * ..
123 * .. Intrinsic Functions ..
124  INTRINSIC min, mod, real
125 * ..
126 * .. Data statements ..
127  DATA ( mm( 1, j ), j = 1, 4 ) / 494, 322, 2508,
128  \$ 2549 /
129  DATA ( mm( 2, j ), j = 1, 4 ) / 2637, 789, 3754,
130  \$ 1145 /
131  DATA ( mm( 3, j ), j = 1, 4 ) / 255, 1440, 1766,
132  \$ 2253 /
133  DATA ( mm( 4, j ), j = 1, 4 ) / 2008, 752, 3572,
134  \$ 305 /
135  DATA ( mm( 5, j ), j = 1, 4 ) / 1253, 2859, 2893,
136  \$ 3301 /
137  DATA ( mm( 6, j ), j = 1, 4 ) / 3344, 123, 307,
138  \$ 1065 /
139  DATA ( mm( 7, j ), j = 1, 4 ) / 4084, 1848, 1297,
140  \$ 3133 /
141  DATA ( mm( 8, j ), j = 1, 4 ) / 1739, 643, 3966,
142  \$ 2913 /
143  DATA ( mm( 9, j ), j = 1, 4 ) / 3143, 2405, 758,
144  \$ 3285 /
145  DATA ( mm( 10, j ), j = 1, 4 ) / 3468, 2638, 2598,
146  \$ 1241 /
147  DATA ( mm( 11, j ), j = 1, 4 ) / 688, 2344, 3406,
148  \$ 1197 /
149  DATA ( mm( 12, j ), j = 1, 4 ) / 1657, 46, 2922,
150  \$ 3729 /
151  DATA ( mm( 13, j ), j = 1, 4 ) / 1238, 3814, 1038,
152  \$ 2501 /
153  DATA ( mm( 14, j ), j = 1, 4 ) / 3166, 913, 2934,
154  \$ 1673 /
155  DATA ( mm( 15, j ), j = 1, 4 ) / 1292, 3649, 2091,
156  \$ 541 /
157  DATA ( mm( 16, j ), j = 1, 4 ) / 3422, 339, 2451,
158  \$ 2753 /
159  DATA ( mm( 17, j ), j = 1, 4 ) / 1270, 3808, 1580,
160  \$ 949 /
161  DATA ( mm( 18, j ), j = 1, 4 ) / 2016, 822, 1958,
162  \$ 2361 /
163  DATA ( mm( 19, j ), j = 1, 4 ) / 154, 2832, 2055,
164  \$ 1165 /
165  DATA ( mm( 20, j ), j = 1, 4 ) / 2862, 3078, 1507,
166  \$ 4081 /
167  DATA ( mm( 21, j ), j = 1, 4 ) / 697, 3633, 1078,
168  \$ 2725 /
169  DATA ( mm( 22, j ), j = 1, 4 ) / 1706, 2970, 3273,
170  \$ 3305 /
171  DATA ( mm( 23, j ), j = 1, 4 ) / 491, 637, 17,
172  \$ 3069 /
173  DATA ( mm( 24, j ), j = 1, 4 ) / 931, 2249, 854,
174  \$ 3617 /
175  DATA ( mm( 25, j ), j = 1, 4 ) / 1444, 2081, 2916,
176  \$ 3733 /
177  DATA ( mm( 26, j ), j = 1, 4 ) / 444, 4019, 3971,
178  \$ 409 /
179  DATA ( mm( 27, j ), j = 1, 4 ) / 3577, 1478, 2889,
180  \$ 2157 /
181  DATA ( mm( 28, j ), j = 1, 4 ) / 3944, 242, 3831,
182  \$ 1361 /
183  DATA ( mm( 29, j ), j = 1, 4 ) / 2184, 481, 2621,
184  \$ 3973 /
185  DATA ( mm( 30, j ), j = 1, 4 ) / 1661, 2075, 1541,
186  \$ 1865 /
187  DATA ( mm( 31, j ), j = 1, 4 ) / 3482, 4058, 893,
188  \$ 2525 /
189  DATA ( mm( 32, j ), j = 1, 4 ) / 657, 622, 736,
190  \$ 1409 /
191  DATA ( mm( 33, j ), j = 1, 4 ) / 3023, 3376, 3992,
192  \$ 3445 /
193  DATA ( mm( 34, j ), j = 1, 4 ) / 3618, 812, 787,
194  \$ 3577 /
195  DATA ( mm( 35, j ), j = 1, 4 ) / 1267, 234, 2125,
196  \$ 77 /
197  DATA ( mm( 36, j ), j = 1, 4 ) / 1828, 641, 2364,
198  \$ 3761 /
199  DATA ( mm( 37, j ), j = 1, 4 ) / 164, 4005, 2460,
200  \$ 2149 /
201  DATA ( mm( 38, j ), j = 1, 4 ) / 3798, 1122, 257,
202  \$ 1449 /
203  DATA ( mm( 39, j ), j = 1, 4 ) / 3087, 3135, 1574,
204  \$ 3005 /
205  DATA ( mm( 40, j ), j = 1, 4 ) / 2400, 2640, 3912,
206  \$ 225 /
207  DATA ( mm( 41, j ), j = 1, 4 ) / 2870, 2302, 1216,
208  \$ 85 /
209  DATA ( mm( 42, j ), j = 1, 4 ) / 3876, 40, 3248,
210  \$ 3673 /
211  DATA ( mm( 43, j ), j = 1, 4 ) / 1905, 1832, 3401,
212  \$ 3117 /
213  DATA ( mm( 44, j ), j = 1, 4 ) / 1593, 2247, 2124,
214  \$ 3089 /
215  DATA ( mm( 45, j ), j = 1, 4 ) / 1797, 2034, 2762,
216  \$ 1349 /
217  DATA ( mm( 46, j ), j = 1, 4 ) / 1234, 2637, 149,
218  \$ 2057 /
219  DATA ( mm( 47, j ), j = 1, 4 ) / 3460, 1287, 2245,
220  \$ 413 /
221  DATA ( mm( 48, j ), j = 1, 4 ) / 328, 1691, 166,
222  \$ 65 /
223  DATA ( mm( 49, j ), j = 1, 4 ) / 2861, 496, 466,
224  \$ 1845 /
225  DATA ( mm( 50, j ), j = 1, 4 ) / 1950, 1597, 4018,
226  \$ 697 /
227  DATA ( mm( 51, j ), j = 1, 4 ) / 617, 2394, 1399,
228  \$ 3085 /
229  DATA ( mm( 52, j ), j = 1, 4 ) / 2070, 2584, 190,
230  \$ 3441 /
231  DATA ( mm( 53, j ), j = 1, 4 ) / 3331, 1843, 2879,
232  \$ 1573 /
233  DATA ( mm( 54, j ), j = 1, 4 ) / 769, 336, 153,
234  \$ 3689 /
235  DATA ( mm( 55, j ), j = 1, 4 ) / 1558, 1472, 2320,
236  \$ 2941 /
237  DATA ( mm( 56, j ), j = 1, 4 ) / 2412, 2407, 18,
238  \$ 929 /
239  DATA ( mm( 57, j ), j = 1, 4 ) / 2800, 433, 712,
240  \$ 533 /
241  DATA ( mm( 58, j ), j = 1, 4 ) / 189, 2096, 2159,
242  \$ 2841 /
243  DATA ( mm( 59, j ), j = 1, 4 ) / 287, 1761, 2318,
244  \$ 4077 /
245  DATA ( mm( 60, j ), j = 1, 4 ) / 2045, 2810, 2091,
246  \$ 721 /
247  DATA ( mm( 61, j ), j = 1, 4 ) / 1227, 566, 3443,
248  \$ 2821 /
249  DATA ( mm( 62, j ), j = 1, 4 ) / 2838, 442, 1510,
250  \$ 2249 /
251  DATA ( mm( 63, j ), j = 1, 4 ) / 209, 41, 449,
252  \$ 2397 /
253  DATA ( mm( 64, j ), j = 1, 4 ) / 2770, 1238, 1956,
254  \$ 2817 /
255  DATA ( mm( 65, j ), j = 1, 4 ) / 3654, 1086, 2201,
256  \$ 245 /
257  DATA ( mm( 66, j ), j = 1, 4 ) / 3993, 603, 3137,
258  \$ 1913 /
259  DATA ( mm( 67, j ), j = 1, 4 ) / 192, 840, 3399,
260  \$ 1997 /
261  DATA ( mm( 68, j ), j = 1, 4 ) / 2253, 3168, 1321,
262  \$ 3121 /
263  DATA ( mm( 69, j ), j = 1, 4 ) / 3491, 1499, 2271,
264  \$ 997 /
265  DATA ( mm( 70, j ), j = 1, 4 ) / 2889, 1084, 3667,
266  \$ 1833 /
267  DATA ( mm( 71, j ), j = 1, 4 ) / 2857, 3438, 2703,
268  \$ 2877 /
269  DATA ( mm( 72, j ), j = 1, 4 ) / 2094, 2408, 629,
270  \$ 1633 /
271  DATA ( mm( 73, j ), j = 1, 4 ) / 1818, 1589, 2365,
272  \$ 981 /
273  DATA ( mm( 74, j ), j = 1, 4 ) / 688, 2391, 2431,
274  \$ 2009 /
275  DATA ( mm( 75, j ), j = 1, 4 ) / 1407, 288, 1113,
276  \$ 941 /
277  DATA ( mm( 76, j ), j = 1, 4 ) / 634, 26, 3922,
278  \$ 2449 /
279  DATA ( mm( 77, j ), j = 1, 4 ) / 3231, 512, 2554,
280  \$ 197 /
281  DATA ( mm( 78, j ), j = 1, 4 ) / 815, 1456, 184,
282  \$ 2441 /
283  DATA ( mm( 79, j ), j = 1, 4 ) / 3524, 171, 2099,
284  \$ 285 /
285  DATA ( mm( 80, j ), j = 1, 4 ) / 1914, 1677, 3228,
286  \$ 1473 /
287  DATA ( mm( 81, j ), j = 1, 4 ) / 516, 2657, 4012,
288  \$ 2741 /
289  DATA ( mm( 82, j ), j = 1, 4 ) / 164, 2270, 1921,
290  \$ 3129 /
291  DATA ( mm( 83, j ), j = 1, 4 ) / 303, 2587, 3452,
292  \$ 909 /
293  DATA ( mm( 84, j ), j = 1, 4 ) / 2144, 2961, 3901,
294  \$ 2801 /
295  DATA ( mm( 85, j ), j = 1, 4 ) / 3480, 1970, 572,
296  \$ 421 /
297  DATA ( mm( 86, j ), j = 1, 4 ) / 119, 1817, 3309,
298  \$ 4073 /
299  DATA ( mm( 87, j ), j = 1, 4 ) / 3357, 676, 3171,
300  \$ 2813 /
301  DATA ( mm( 88, j ), j = 1, 4 ) / 837, 1410, 817,
302  \$ 2337 /
303  DATA ( mm( 89, j ), j = 1, 4 ) / 2826, 3723, 3039,
304  \$ 1429 /
305  DATA ( mm( 90, j ), j = 1, 4 ) / 2332, 2803, 1696,
306  \$ 1177 /
307  DATA ( mm( 91, j ), j = 1, 4 ) / 2089, 3185, 1256,
308  \$ 1901 /
309  DATA ( mm( 92, j ), j = 1, 4 ) / 3780, 184, 3715,
310  \$ 81 /
311  DATA ( mm( 93, j ), j = 1, 4 ) / 1700, 663, 2077,
312  \$ 1669 /
313  DATA ( mm( 94, j ), j = 1, 4 ) / 3712, 499, 3019,
314  \$ 2633 /
315  DATA ( mm( 95, j ), j = 1, 4 ) / 150, 3784, 1497,
316  \$ 2269 /
317  DATA ( mm( 96, j ), j = 1, 4 ) / 2000, 1631, 1101,
318  \$ 129 /
319  DATA ( mm( 97, j ), j = 1, 4 ) / 3375, 1925, 717,
320  \$ 1141 /
321  DATA ( mm( 98, j ), j = 1, 4 ) / 1621, 3912, 51,
322  \$ 249 /
323  DATA ( mm( 99, j ), j = 1, 4 ) / 3090, 1398, 981,
324  \$ 3917 /
325  DATA ( mm( 100, j ), j = 1, 4 ) / 3765, 1349, 1978,
326  \$ 2481 /
327  DATA ( mm( 101, j ), j = 1, 4 ) / 1149, 1441, 1813,
328  \$ 3941 /
329  DATA ( mm( 102, j ), j = 1, 4 ) / 3146, 2224, 3881,
330  \$ 2217 /
331  DATA ( mm( 103, j ), j = 1, 4 ) / 33, 2411, 76,
332  \$ 2749 /
333  DATA ( mm( 104, j ), j = 1, 4 ) / 3082, 1907, 3846,
334  \$ 3041 /
335  DATA ( mm( 105, j ), j = 1, 4 ) / 2741, 3192, 3694,
336  \$ 1877 /
337  DATA ( mm( 106, j ), j = 1, 4 ) / 359, 2786, 1682,
338  \$ 345 /
339  DATA ( mm( 107, j ), j = 1, 4 ) / 3316, 382, 124,
340  \$ 2861 /
341  DATA ( mm( 108, j ), j = 1, 4 ) / 1749, 37, 1660,
342  \$ 1809 /
343  DATA ( mm( 109, j ), j = 1, 4 ) / 185, 759, 3997,
344  \$ 3141 /
345  DATA ( mm( 110, j ), j = 1, 4 ) / 2784, 2948, 479,
346  \$ 2825 /
347  DATA ( mm( 111, j ), j = 1, 4 ) / 2202, 1862, 1141,
348  \$ 157 /
349  DATA ( mm( 112, j ), j = 1, 4 ) / 2199, 3802, 886,
350  \$ 2881 /
351  DATA ( mm( 113, j ), j = 1, 4 ) / 1364, 2423, 3514,
352  \$ 3637 /
353  DATA ( mm( 114, j ), j = 1, 4 ) / 1244, 2051, 1301,
354  \$ 1465 /
355  DATA ( mm( 115, j ), j = 1, 4 ) / 2020, 2295, 3604,
356  \$ 2829 /
357  DATA ( mm( 116, j ), j = 1, 4 ) / 3160, 1332, 1888,
358  \$ 2161 /
359  DATA ( mm( 117, j ), j = 1, 4 ) / 2785, 1832, 1836,
360  \$ 3365 /
361  DATA ( mm( 118, j ), j = 1, 4 ) / 2772, 2405, 1990,
362  \$ 361 /
363  DATA ( mm( 119, j ), j = 1, 4 ) / 1217, 3638, 2058,
364  \$ 2685 /
365  DATA ( mm( 120, j ), j = 1, 4 ) / 1822, 3661, 692,
366  \$ 3745 /
367  DATA ( mm( 121, j ), j = 1, 4 ) / 1245, 327, 1194,
368  \$ 2325 /
369  DATA ( mm( 122, j ), j = 1, 4 ) / 2252, 3660, 20,
370  \$ 3609 /
371  DATA ( mm( 123, j ), j = 1, 4 ) / 3904, 716, 3285,
372  \$ 3821 /
373  DATA ( mm( 124, j ), j = 1, 4 ) / 2774, 1842, 2046,
374  \$ 3537 /
375  DATA ( mm( 125, j ), j = 1, 4 ) / 997, 3987, 2107,
376  \$ 517 /
377  DATA ( mm( 126, j ), j = 1, 4 ) / 2573, 1368, 3508,
378  \$ 3017 /
379  DATA ( mm( 127, j ), j = 1, 4 ) / 1148, 1848, 3525,
380  \$ 2141 /
381  DATA ( mm( 128, j ), j = 1, 4 ) / 545, 2366, 3801,
382  \$ 1537 /
383 * ..
384 * .. Executable Statements ..
385 *
386  i1 = iseed( 1 )
387  i2 = iseed( 2 )
388  i3 = iseed( 3 )
389  i4 = iseed( 4 )
390 *
391  DO 10 i = 1, min( n, lv )
392 *
393  20 CONTINUE
394 *
395 * Multiply the seed by i-th power of the multiplier modulo 2**48
396 *
397  it4 = i4*mm( i, 4 )
398  it3 = it4 / ipw2
399  it4 = it4 - ipw2*it3
400  it3 = it3 + i3*mm( i, 4 ) + i4*mm( i, 3 )
401  it2 = it3 / ipw2
402  it3 = it3 - ipw2*it2
403  it2 = it2 + i2*mm( i, 4 ) + i3*mm( i, 3 ) + i4*mm( i, 2 )
404  it1 = it2 / ipw2
405  it2 = it2 - ipw2*it1
406  it1 = it1 + i1*mm( i, 4 ) + i2*mm( i, 3 ) + i3*mm( i, 2 ) +
407  \$ i4*mm( i, 1 )
408  it1 = mod( it1, ipw2 )
409 *
410 * Convert 48-bit integer to a real number in the interval (0,1)
411 *
412  x( i ) = r*( real( it1 )+r*( real( it2 )+r*( real( it3 )+r*
413  \$ real( it4 ) ) ) )
414 *
415  IF (x( i ).EQ.1.0) THEN
416 * If a real number has n bits of precision, and the first
417 * n bits of the 48-bit integer above happen to be all 1 (which
418 * will occur about once every 2**n calls), then X( I ) will
419 * be rounded to exactly 1.0. In IEEE single precision arithmetic,
420 * this will happen relatively often since n = 24.
421 * Since X( I ) is not supposed to return exactly 0.0 or 1.0,
422 * the statistically correct thing to do in this situation is
423 * simply to iterate again.
424 * N.B. the case X( I ) = 0.0 should not be possible.
425  i1 = i1 + 2
426  i2 = i2 + 2
427  i3 = i3 + 2
428  i4 = i4 + 2
429  GOTO 20
430  END IF
431 *
432  10 CONTINUE
433 *
434 * Return final value of seed
435 *
436  iseed( 1 ) = it1
437  iseed( 2 ) = it2
438  iseed( 3 ) = it3
439  iseed( 4 ) = it4
440  RETURN
441 *
442 * End of SLARUV
443 *
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