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1.1 bertrand 1: SUBROUTINE DLARUV( ISEED, N, X )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: INTEGER N
10: * ..
11: * .. Array Arguments ..
12: INTEGER ISEED( 4 )
13: DOUBLE PRECISION X( N )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DLARUV returns a vector of n random real numbers from a uniform (0,1)
20: * distribution (n <= 128).
21: *
22: * This is an auxiliary routine called by DLARNV and ZLARNV.
23: *
24: * Arguments
25: * =========
26: *
27: * ISEED (input/output) INTEGER array, dimension (4)
28: * On entry, the seed of the random number generator; the array
29: * elements must be between 0 and 4095, and ISEED(4) must be
30: * odd.
31: * On exit, the seed is updated.
32: *
33: * N (input) INTEGER
34: * The number of random numbers to be generated. N <= 128.
35: *
36: * X (output) DOUBLE PRECISION array, dimension (N)
37: * The generated random numbers.
38: *
39: * Further Details
40: * ===============
41: *
42: * This routine uses a multiplicative congruential method with modulus
43: * 2**48 and multiplier 33952834046453 (see G.S.Fishman,
44: * 'Multiplicative congruential random number generators with modulus
45: * 2**b: an exhaustive analysis for b = 32 and a partial analysis for
46: * b = 48', Math. Comp. 189, pp 331-344, 1990).
47: *
48: * 48-bit integers are stored in 4 integer array elements with 12 bits
49: * per element. Hence the routine is portable across machines with
50: * integers of 32 bits or more.
51: *
52: * =====================================================================
53: *
54: * .. Parameters ..
55: DOUBLE PRECISION ONE
56: PARAMETER ( ONE = 1.0D0 )
57: INTEGER LV, IPW2
58: DOUBLE PRECISION R
59: PARAMETER ( LV = 128, IPW2 = 4096, R = ONE / IPW2 )
60: * ..
61: * .. Local Scalars ..
62: INTEGER I, I1, I2, I3, I4, IT1, IT2, IT3, IT4, J
63: * ..
64: * .. Local Arrays ..
65: INTEGER MM( LV, 4 )
66: * ..
67: * .. Intrinsic Functions ..
68: INTRINSIC DBLE, MIN, MOD
69: * ..
70: * .. Data statements ..
71: DATA ( MM( 1, J ), J = 1, 4 ) / 494, 322, 2508,
72: $ 2549 /
73: DATA ( MM( 2, J ), J = 1, 4 ) / 2637, 789, 3754,
74: $ 1145 /
75: DATA ( MM( 3, J ), J = 1, 4 ) / 255, 1440, 1766,
76: $ 2253 /
77: DATA ( MM( 4, J ), J = 1, 4 ) / 2008, 752, 3572,
78: $ 305 /
79: DATA ( MM( 5, J ), J = 1, 4 ) / 1253, 2859, 2893,
80: $ 3301 /
81: DATA ( MM( 6, J ), J = 1, 4 ) / 3344, 123, 307,
82: $ 1065 /
83: DATA ( MM( 7, J ), J = 1, 4 ) / 4084, 1848, 1297,
84: $ 3133 /
85: DATA ( MM( 8, J ), J = 1, 4 ) / 1739, 643, 3966,
86: $ 2913 /
87: DATA ( MM( 9, J ), J = 1, 4 ) / 3143, 2405, 758,
88: $ 3285 /
89: DATA ( MM( 10, J ), J = 1, 4 ) / 3468, 2638, 2598,
90: $ 1241 /
91: DATA ( MM( 11, J ), J = 1, 4 ) / 688, 2344, 3406,
92: $ 1197 /
93: DATA ( MM( 12, J ), J = 1, 4 ) / 1657, 46, 2922,
94: $ 3729 /
95: DATA ( MM( 13, J ), J = 1, 4 ) / 1238, 3814, 1038,
96: $ 2501 /
97: DATA ( MM( 14, J ), J = 1, 4 ) / 3166, 913, 2934,
98: $ 1673 /
99: DATA ( MM( 15, J ), J = 1, 4 ) / 1292, 3649, 2091,
100: $ 541 /
101: DATA ( MM( 16, J ), J = 1, 4 ) / 3422, 339, 2451,
102: $ 2753 /
103: DATA ( MM( 17, J ), J = 1, 4 ) / 1270, 3808, 1580,
104: $ 949 /
105: DATA ( MM( 18, J ), J = 1, 4 ) / 2016, 822, 1958,
106: $ 2361 /
107: DATA ( MM( 19, J ), J = 1, 4 ) / 154, 2832, 2055,
108: $ 1165 /
109: DATA ( MM( 20, J ), J = 1, 4 ) / 2862, 3078, 1507,
110: $ 4081 /
111: DATA ( MM( 21, J ), J = 1, 4 ) / 697, 3633, 1078,
112: $ 2725 /
113: DATA ( MM( 22, J ), J = 1, 4 ) / 1706, 2970, 3273,
114: $ 3305 /
115: DATA ( MM( 23, J ), J = 1, 4 ) / 491, 637, 17,
116: $ 3069 /
117: DATA ( MM( 24, J ), J = 1, 4 ) / 931, 2249, 854,
118: $ 3617 /
119: DATA ( MM( 25, J ), J = 1, 4 ) / 1444, 2081, 2916,
120: $ 3733 /
121: DATA ( MM( 26, J ), J = 1, 4 ) / 444, 4019, 3971,
122: $ 409 /
123: DATA ( MM( 27, J ), J = 1, 4 ) / 3577, 1478, 2889,
124: $ 2157 /
125: DATA ( MM( 28, J ), J = 1, 4 ) / 3944, 242, 3831,
126: $ 1361 /
127: DATA ( MM( 29, J ), J = 1, 4 ) / 2184, 481, 2621,
128: $ 3973 /
129: DATA ( MM( 30, J ), J = 1, 4 ) / 1661, 2075, 1541,
130: $ 1865 /
131: DATA ( MM( 31, J ), J = 1, 4 ) / 3482, 4058, 893,
132: $ 2525 /
133: DATA ( MM( 32, J ), J = 1, 4 ) / 657, 622, 736,
134: $ 1409 /
135: DATA ( MM( 33, J ), J = 1, 4 ) / 3023, 3376, 3992,
136: $ 3445 /
137: DATA ( MM( 34, J ), J = 1, 4 ) / 3618, 812, 787,
138: $ 3577 /
139: DATA ( MM( 35, J ), J = 1, 4 ) / 1267, 234, 2125,
140: $ 77 /
141: DATA ( MM( 36, J ), J = 1, 4 ) / 1828, 641, 2364,
142: $ 3761 /
143: DATA ( MM( 37, J ), J = 1, 4 ) / 164, 4005, 2460,
144: $ 2149 /
145: DATA ( MM( 38, J ), J = 1, 4 ) / 3798, 1122, 257,
146: $ 1449 /
147: DATA ( MM( 39, J ), J = 1, 4 ) / 3087, 3135, 1574,
148: $ 3005 /
149: DATA ( MM( 40, J ), J = 1, 4 ) / 2400, 2640, 3912,
150: $ 225 /
151: DATA ( MM( 41, J ), J = 1, 4 ) / 2870, 2302, 1216,
152: $ 85 /
153: DATA ( MM( 42, J ), J = 1, 4 ) / 3876, 40, 3248,
154: $ 3673 /
155: DATA ( MM( 43, J ), J = 1, 4 ) / 1905, 1832, 3401,
156: $ 3117 /
157: DATA ( MM( 44, J ), J = 1, 4 ) / 1593, 2247, 2124,
158: $ 3089 /
159: DATA ( MM( 45, J ), J = 1, 4 ) / 1797, 2034, 2762,
160: $ 1349 /
161: DATA ( MM( 46, J ), J = 1, 4 ) / 1234, 2637, 149,
162: $ 2057 /
163: DATA ( MM( 47, J ), J = 1, 4 ) / 3460, 1287, 2245,
164: $ 413 /
165: DATA ( MM( 48, J ), J = 1, 4 ) / 328, 1691, 166,
166: $ 65 /
167: DATA ( MM( 49, J ), J = 1, 4 ) / 2861, 496, 466,
168: $ 1845 /
169: DATA ( MM( 50, J ), J = 1, 4 ) / 1950, 1597, 4018,
170: $ 697 /
171: DATA ( MM( 51, J ), J = 1, 4 ) / 617, 2394, 1399,
172: $ 3085 /
173: DATA ( MM( 52, J ), J = 1, 4 ) / 2070, 2584, 190,
174: $ 3441 /
175: DATA ( MM( 53, J ), J = 1, 4 ) / 3331, 1843, 2879,
176: $ 1573 /
177: DATA ( MM( 54, J ), J = 1, 4 ) / 769, 336, 153,
178: $ 3689 /
179: DATA ( MM( 55, J ), J = 1, 4 ) / 1558, 1472, 2320,
180: $ 2941 /
181: DATA ( MM( 56, J ), J = 1, 4 ) / 2412, 2407, 18,
182: $ 929 /
183: DATA ( MM( 57, J ), J = 1, 4 ) / 2800, 433, 712,
184: $ 533 /
185: DATA ( MM( 58, J ), J = 1, 4 ) / 189, 2096, 2159,
186: $ 2841 /
187: DATA ( MM( 59, J ), J = 1, 4 ) / 287, 1761, 2318,
188: $ 4077 /
189: DATA ( MM( 60, J ), J = 1, 4 ) / 2045, 2810, 2091,
190: $ 721 /
191: DATA ( MM( 61, J ), J = 1, 4 ) / 1227, 566, 3443,
192: $ 2821 /
193: DATA ( MM( 62, J ), J = 1, 4 ) / 2838, 442, 1510,
194: $ 2249 /
195: DATA ( MM( 63, J ), J = 1, 4 ) / 209, 41, 449,
196: $ 2397 /
197: DATA ( MM( 64, J ), J = 1, 4 ) / 2770, 1238, 1956,
198: $ 2817 /
199: DATA ( MM( 65, J ), J = 1, 4 ) / 3654, 1086, 2201,
200: $ 245 /
201: DATA ( MM( 66, J ), J = 1, 4 ) / 3993, 603, 3137,
202: $ 1913 /
203: DATA ( MM( 67, J ), J = 1, 4 ) / 192, 840, 3399,
204: $ 1997 /
205: DATA ( MM( 68, J ), J = 1, 4 ) / 2253, 3168, 1321,
206: $ 3121 /
207: DATA ( MM( 69, J ), J = 1, 4 ) / 3491, 1499, 2271,
208: $ 997 /
209: DATA ( MM( 70, J ), J = 1, 4 ) / 2889, 1084, 3667,
210: $ 1833 /
211: DATA ( MM( 71, J ), J = 1, 4 ) / 2857, 3438, 2703,
212: $ 2877 /
213: DATA ( MM( 72, J ), J = 1, 4 ) / 2094, 2408, 629,
214: $ 1633 /
215: DATA ( MM( 73, J ), J = 1, 4 ) / 1818, 1589, 2365,
216: $ 981 /
217: DATA ( MM( 74, J ), J = 1, 4 ) / 688, 2391, 2431,
218: $ 2009 /
219: DATA ( MM( 75, J ), J = 1, 4 ) / 1407, 288, 1113,
220: $ 941 /
221: DATA ( MM( 76, J ), J = 1, 4 ) / 634, 26, 3922,
222: $ 2449 /
223: DATA ( MM( 77, J ), J = 1, 4 ) / 3231, 512, 2554,
224: $ 197 /
225: DATA ( MM( 78, J ), J = 1, 4 ) / 815, 1456, 184,
226: $ 2441 /
227: DATA ( MM( 79, J ), J = 1, 4 ) / 3524, 171, 2099,
228: $ 285 /
229: DATA ( MM( 80, J ), J = 1, 4 ) / 1914, 1677, 3228,
230: $ 1473 /
231: DATA ( MM( 81, J ), J = 1, 4 ) / 516, 2657, 4012,
232: $ 2741 /
233: DATA ( MM( 82, J ), J = 1, 4 ) / 164, 2270, 1921,
234: $ 3129 /
235: DATA ( MM( 83, J ), J = 1, 4 ) / 303, 2587, 3452,
236: $ 909 /
237: DATA ( MM( 84, J ), J = 1, 4 ) / 2144, 2961, 3901,
238: $ 2801 /
239: DATA ( MM( 85, J ), J = 1, 4 ) / 3480, 1970, 572,
240: $ 421 /
241: DATA ( MM( 86, J ), J = 1, 4 ) / 119, 1817, 3309,
242: $ 4073 /
243: DATA ( MM( 87, J ), J = 1, 4 ) / 3357, 676, 3171,
244: $ 2813 /
245: DATA ( MM( 88, J ), J = 1, 4 ) / 837, 1410, 817,
246: $ 2337 /
247: DATA ( MM( 89, J ), J = 1, 4 ) / 2826, 3723, 3039,
248: $ 1429 /
249: DATA ( MM( 90, J ), J = 1, 4 ) / 2332, 2803, 1696,
250: $ 1177 /
251: DATA ( MM( 91, J ), J = 1, 4 ) / 2089, 3185, 1256,
252: $ 1901 /
253: DATA ( MM( 92, J ), J = 1, 4 ) / 3780, 184, 3715,
254: $ 81 /
255: DATA ( MM( 93, J ), J = 1, 4 ) / 1700, 663, 2077,
256: $ 1669 /
257: DATA ( MM( 94, J ), J = 1, 4 ) / 3712, 499, 3019,
258: $ 2633 /
259: DATA ( MM( 95, J ), J = 1, 4 ) / 150, 3784, 1497,
260: $ 2269 /
261: DATA ( MM( 96, J ), J = 1, 4 ) / 2000, 1631, 1101,
262: $ 129 /
263: DATA ( MM( 97, J ), J = 1, 4 ) / 3375, 1925, 717,
264: $ 1141 /
265: DATA ( MM( 98, J ), J = 1, 4 ) / 1621, 3912, 51,
266: $ 249 /
267: DATA ( MM( 99, J ), J = 1, 4 ) / 3090, 1398, 981,
268: $ 3917 /
269: DATA ( MM( 100, J ), J = 1, 4 ) / 3765, 1349, 1978,
270: $ 2481 /
271: DATA ( MM( 101, J ), J = 1, 4 ) / 1149, 1441, 1813,
272: $ 3941 /
273: DATA ( MM( 102, J ), J = 1, 4 ) / 3146, 2224, 3881,
274: $ 2217 /
275: DATA ( MM( 103, J ), J = 1, 4 ) / 33, 2411, 76,
276: $ 2749 /
277: DATA ( MM( 104, J ), J = 1, 4 ) / 3082, 1907, 3846,
278: $ 3041 /
279: DATA ( MM( 105, J ), J = 1, 4 ) / 2741, 3192, 3694,
280: $ 1877 /
281: DATA ( MM( 106, J ), J = 1, 4 ) / 359, 2786, 1682,
282: $ 345 /
283: DATA ( MM( 107, J ), J = 1, 4 ) / 3316, 382, 124,
284: $ 2861 /
285: DATA ( MM( 108, J ), J = 1, 4 ) / 1749, 37, 1660,
286: $ 1809 /
287: DATA ( MM( 109, J ), J = 1, 4 ) / 185, 759, 3997,
288: $ 3141 /
289: DATA ( MM( 110, J ), J = 1, 4 ) / 2784, 2948, 479,
290: $ 2825 /
291: DATA ( MM( 111, J ), J = 1, 4 ) / 2202, 1862, 1141,
292: $ 157 /
293: DATA ( MM( 112, J ), J = 1, 4 ) / 2199, 3802, 886,
294: $ 2881 /
295: DATA ( MM( 113, J ), J = 1, 4 ) / 1364, 2423, 3514,
296: $ 3637 /
297: DATA ( MM( 114, J ), J = 1, 4 ) / 1244, 2051, 1301,
298: $ 1465 /
299: DATA ( MM( 115, J ), J = 1, 4 ) / 2020, 2295, 3604,
300: $ 2829 /
301: DATA ( MM( 116, J ), J = 1, 4 ) / 3160, 1332, 1888,
302: $ 2161 /
303: DATA ( MM( 117, J ), J = 1, 4 ) / 2785, 1832, 1836,
304: $ 3365 /
305: DATA ( MM( 118, J ), J = 1, 4 ) / 2772, 2405, 1990,
306: $ 361 /
307: DATA ( MM( 119, J ), J = 1, 4 ) / 1217, 3638, 2058,
308: $ 2685 /
309: DATA ( MM( 120, J ), J = 1, 4 ) / 1822, 3661, 692,
310: $ 3745 /
311: DATA ( MM( 121, J ), J = 1, 4 ) / 1245, 327, 1194,
312: $ 2325 /
313: DATA ( MM( 122, J ), J = 1, 4 ) / 2252, 3660, 20,
314: $ 3609 /
315: DATA ( MM( 123, J ), J = 1, 4 ) / 3904, 716, 3285,
316: $ 3821 /
317: DATA ( MM( 124, J ), J = 1, 4 ) / 2774, 1842, 2046,
318: $ 3537 /
319: DATA ( MM( 125, J ), J = 1, 4 ) / 997, 3987, 2107,
320: $ 517 /
321: DATA ( MM( 126, J ), J = 1, 4 ) / 2573, 1368, 3508,
322: $ 3017 /
323: DATA ( MM( 127, J ), J = 1, 4 ) / 1148, 1848, 3525,
324: $ 2141 /
325: DATA ( MM( 128, J ), J = 1, 4 ) / 545, 2366, 3801,
326: $ 1537 /
327: * ..
328: * .. Executable Statements ..
329: *
330: I1 = ISEED( 1 )
331: I2 = ISEED( 2 )
332: I3 = ISEED( 3 )
333: I4 = ISEED( 4 )
334: *
335: DO 10 I = 1, MIN( N, LV )
336: *
337: 20 CONTINUE
338: *
339: * Multiply the seed by i-th power of the multiplier modulo 2**48
340: *
341: IT4 = I4*MM( I, 4 )
342: IT3 = IT4 / IPW2
343: IT4 = IT4 - IPW2*IT3
344: IT3 = IT3 + I3*MM( I, 4 ) + I4*MM( I, 3 )
345: IT2 = IT3 / IPW2
346: IT3 = IT3 - IPW2*IT2
347: IT2 = IT2 + I2*MM( I, 4 ) + I3*MM( I, 3 ) + I4*MM( I, 2 )
348: IT1 = IT2 / IPW2
349: IT2 = IT2 - IPW2*IT1
350: IT1 = IT1 + I1*MM( I, 4 ) + I2*MM( I, 3 ) + I3*MM( I, 2 ) +
351: $ I4*MM( I, 1 )
352: IT1 = MOD( IT1, IPW2 )
353: *
354: * Convert 48-bit integer to a real number in the interval (0,1)
355: *
356: X( I ) = R*( DBLE( IT1 )+R*( DBLE( IT2 )+R*( DBLE( IT3 )+R*
357: $ DBLE( IT4 ) ) ) )
358: *
359: IF (X( I ).EQ.1.0D0) THEN
360: * If a real number has n bits of precision, and the first
361: * n bits of the 48-bit integer above happen to be all 1 (which
362: * will occur about once every 2**n calls), then X( I ) will
363: * be rounded to exactly 1.0.
364: * Since X( I ) is not supposed to return exactly 0.0 or 1.0,
365: * the statistically correct thing to do in this situation is
366: * simply to iterate again.
367: * N.B. the case X( I ) = 0.0 should not be possible.
368: I1 = I1 + 2
369: I2 = I2 + 2
370: I3 = I3 + 2
371: I4 = I4 + 2
372: GOTO 20
373: END IF
374: *
375: 10 CONTINUE
376: *
377: * Return final value of seed
378: *
379: ISEED( 1 ) = IT1
380: ISEED( 2 ) = IT2
381: ISEED( 3 ) = IT3
382: ISEED( 4 ) = IT4
383: RETURN
384: *
385: * End of DLARUV
386: *
387: END