*> \brief \b SLARUV returns a vector of n random real numbers from a uniform distribution.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SLARUV + dependencies
*>
*> [TGZ]
*>
*> [ZIP]
*>
*> [TXT]
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SLARUV( ISEED, N, X )
*
* .. Scalar Arguments ..
* INTEGER N
* ..
* .. Array Arguments ..
* INTEGER ISEED( 4 )
* REAL X( N )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in,out] ISEED
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of random numbers to be generated. N <= 128.
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is REAL array, dimension (N)
*> The generated random numbers.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup auxOTHERauxiliary
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> 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.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE SLARUV( ISEED, N, X )
*
* -- LAPACK auxiliary routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER N
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
REAL X( N )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E0 )
INTEGER LV, IPW2
REAL R
PARAMETER ( LV = 128, IPW2 = 4096, R = ONE / IPW2 )
* ..
* .. Local Scalars ..
INTEGER I, I1, I2, I3, I4, IT1, IT2, IT3, IT4, J
* ..
* .. Local Arrays ..
INTEGER MM( LV, 4 )
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, MOD, REAL
* ..
* .. Data statements ..
DATA ( MM( 1, J ), J = 1, 4 ) / 494, 322, 2508,
$ 2549 /
DATA ( MM( 2, J ), J = 1, 4 ) / 2637, 789, 3754,
$ 1145 /
DATA ( MM( 3, J ), J = 1, 4 ) / 255, 1440, 1766,
$ 2253 /
DATA ( MM( 4, J ), J = 1, 4 ) / 2008, 752, 3572,
$ 305 /
DATA ( MM( 5, J ), J = 1, 4 ) / 1253, 2859, 2893,
$ 3301 /
DATA ( MM( 6, J ), J = 1, 4 ) / 3344, 123, 307,
$ 1065 /
DATA ( MM( 7, J ), J = 1, 4 ) / 4084, 1848, 1297,
$ 3133 /
DATA ( MM( 8, J ), J = 1, 4 ) / 1739, 643, 3966,
$ 2913 /
DATA ( MM( 9, J ), J = 1, 4 ) / 3143, 2405, 758,
$ 3285 /
DATA ( MM( 10, J ), J = 1, 4 ) / 3468, 2638, 2598,
$ 1241 /
DATA ( MM( 11, J ), J = 1, 4 ) / 688, 2344, 3406,
$ 1197 /
DATA ( MM( 12, J ), J = 1, 4 ) / 1657, 46, 2922,
$ 3729 /
DATA ( MM( 13, J ), J = 1, 4 ) / 1238, 3814, 1038,
$ 2501 /
DATA ( MM( 14, J ), J = 1, 4 ) / 3166, 913, 2934,
$ 1673 /
DATA ( MM( 15, J ), J = 1, 4 ) / 1292, 3649, 2091,
$ 541 /
DATA ( MM( 16, J ), J = 1, 4 ) / 3422, 339, 2451,
$ 2753 /
DATA ( MM( 17, J ), J = 1, 4 ) / 1270, 3808, 1580,
$ 949 /
DATA ( MM( 18, J ), J = 1, 4 ) / 2016, 822, 1958,
$ 2361 /
DATA ( MM( 19, J ), J = 1, 4 ) / 154, 2832, 2055,
$ 1165 /
DATA ( MM( 20, J ), J = 1, 4 ) / 2862, 3078, 1507,
$ 4081 /
DATA ( MM( 21, J ), J = 1, 4 ) / 697, 3633, 1078,
$ 2725 /
DATA ( MM( 22, J ), J = 1, 4 ) / 1706, 2970, 3273,
$ 3305 /
DATA ( MM( 23, J ), J = 1, 4 ) / 491, 637, 17,
$ 3069 /
DATA ( MM( 24, J ), J = 1, 4 ) / 931, 2249, 854,
$ 3617 /
DATA ( MM( 25, J ), J = 1, 4 ) / 1444, 2081, 2916,
$ 3733 /
DATA ( MM( 26, J ), J = 1, 4 ) / 444, 4019, 3971,
$ 409 /
DATA ( MM( 27, J ), J = 1, 4 ) / 3577, 1478, 2889,
$ 2157 /
DATA ( MM( 28, J ), J = 1, 4 ) / 3944, 242, 3831,
$ 1361 /
DATA ( MM( 29, J ), J = 1, 4 ) / 2184, 481, 2621,
$ 3973 /
DATA ( MM( 30, J ), J = 1, 4 ) / 1661, 2075, 1541,
$ 1865 /
DATA ( MM( 31, J ), J = 1, 4 ) / 3482, 4058, 893,
$ 2525 /
DATA ( MM( 32, J ), J = 1, 4 ) / 657, 622, 736,
$ 1409 /
DATA ( MM( 33, J ), J = 1, 4 ) / 3023, 3376, 3992,
$ 3445 /
DATA ( MM( 34, J ), J = 1, 4 ) / 3618, 812, 787,
$ 3577 /
DATA ( MM( 35, J ), J = 1, 4 ) / 1267, 234, 2125,
$ 77 /
DATA ( MM( 36, J ), J = 1, 4 ) / 1828, 641, 2364,
$ 3761 /
DATA ( MM( 37, J ), J = 1, 4 ) / 164, 4005, 2460,
$ 2149 /
DATA ( MM( 38, J ), J = 1, 4 ) / 3798, 1122, 257,
$ 1449 /
DATA ( MM( 39, J ), J = 1, 4 ) / 3087, 3135, 1574,
$ 3005 /
DATA ( MM( 40, J ), J = 1, 4 ) / 2400, 2640, 3912,
$ 225 /
DATA ( MM( 41, J ), J = 1, 4 ) / 2870, 2302, 1216,
$ 85 /
DATA ( MM( 42, J ), J = 1, 4 ) / 3876, 40, 3248,
$ 3673 /
DATA ( MM( 43, J ), J = 1, 4 ) / 1905, 1832, 3401,
$ 3117 /
DATA ( MM( 44, J ), J = 1, 4 ) / 1593, 2247, 2124,
$ 3089 /
DATA ( MM( 45, J ), J = 1, 4 ) / 1797, 2034, 2762,
$ 1349 /
DATA ( MM( 46, J ), J = 1, 4 ) / 1234, 2637, 149,
$ 2057 /
DATA ( MM( 47, J ), J = 1, 4 ) / 3460, 1287, 2245,
$ 413 /
DATA ( MM( 48, J ), J = 1, 4 ) / 328, 1691, 166,
$ 65 /
DATA ( MM( 49, J ), J = 1, 4 ) / 2861, 496, 466,
$ 1845 /
DATA ( MM( 50, J ), J = 1, 4 ) / 1950, 1597, 4018,
$ 697 /
DATA ( MM( 51, J ), J = 1, 4 ) / 617, 2394, 1399,
$ 3085 /
DATA ( MM( 52, J ), J = 1, 4 ) / 2070, 2584, 190,
$ 3441 /
DATA ( MM( 53, J ), J = 1, 4 ) / 3331, 1843, 2879,
$ 1573 /
DATA ( MM( 54, J ), J = 1, 4 ) / 769, 336, 153,
$ 3689 /
DATA ( MM( 55, J ), J = 1, 4 ) / 1558, 1472, 2320,
$ 2941 /
DATA ( MM( 56, J ), J = 1, 4 ) / 2412, 2407, 18,
$ 929 /
DATA ( MM( 57, J ), J = 1, 4 ) / 2800, 433, 712,
$ 533 /
DATA ( MM( 58, J ), J = 1, 4 ) / 189, 2096, 2159,
$ 2841 /
DATA ( MM( 59, J ), J = 1, 4 ) / 287, 1761, 2318,
$ 4077 /
DATA ( MM( 60, J ), J = 1, 4 ) / 2045, 2810, 2091,
$ 721 /
DATA ( MM( 61, J ), J = 1, 4 ) / 1227, 566, 3443,
$ 2821 /
DATA ( MM( 62, J ), J = 1, 4 ) / 2838, 442, 1510,
$ 2249 /
DATA ( MM( 63, J ), J = 1, 4 ) / 209, 41, 449,
$ 2397 /
DATA ( MM( 64, J ), J = 1, 4 ) / 2770, 1238, 1956,
$ 2817 /
DATA ( MM( 65, J ), J = 1, 4 ) / 3654, 1086, 2201,
$ 245 /
DATA ( MM( 66, J ), J = 1, 4 ) / 3993, 603, 3137,
$ 1913 /
DATA ( MM( 67, J ), J = 1, 4 ) / 192, 840, 3399,
$ 1997 /
DATA ( MM( 68, J ), J = 1, 4 ) / 2253, 3168, 1321,
$ 3121 /
DATA ( MM( 69, J ), J = 1, 4 ) / 3491, 1499, 2271,
$ 997 /
DATA ( MM( 70, J ), J = 1, 4 ) / 2889, 1084, 3667,
$ 1833 /
DATA ( MM( 71, J ), J = 1, 4 ) / 2857, 3438, 2703,
$ 2877 /
DATA ( MM( 72, J ), J = 1, 4 ) / 2094, 2408, 629,
$ 1633 /
DATA ( MM( 73, J ), J = 1, 4 ) / 1818, 1589, 2365,
$ 981 /
DATA ( MM( 74, J ), J = 1, 4 ) / 688, 2391, 2431,
$ 2009 /
DATA ( MM( 75, J ), J = 1, 4 ) / 1407, 288, 1113,
$ 941 /
DATA ( MM( 76, J ), J = 1, 4 ) / 634, 26, 3922,
$ 2449 /
DATA ( MM( 77, J ), J = 1, 4 ) / 3231, 512, 2554,
$ 197 /
DATA ( MM( 78, J ), J = 1, 4 ) / 815, 1456, 184,
$ 2441 /
DATA ( MM( 79, J ), J = 1, 4 ) / 3524, 171, 2099,
$ 285 /
DATA ( MM( 80, J ), J = 1, 4 ) / 1914, 1677, 3228,
$ 1473 /
DATA ( MM( 81, J ), J = 1, 4 ) / 516, 2657, 4012,
$ 2741 /
DATA ( MM( 82, J ), J = 1, 4 ) / 164, 2270, 1921,
$ 3129 /
DATA ( MM( 83, J ), J = 1, 4 ) / 303, 2587, 3452,
$ 909 /
DATA ( MM( 84, J ), J = 1, 4 ) / 2144, 2961, 3901,
$ 2801 /
DATA ( MM( 85, J ), J = 1, 4 ) / 3480, 1970, 572,
$ 421 /
DATA ( MM( 86, J ), J = 1, 4 ) / 119, 1817, 3309,
$ 4073 /
DATA ( MM( 87, J ), J = 1, 4 ) / 3357, 676, 3171,
$ 2813 /
DATA ( MM( 88, J ), J = 1, 4 ) / 837, 1410, 817,
$ 2337 /
DATA ( MM( 89, J ), J = 1, 4 ) / 2826, 3723, 3039,
$ 1429 /
DATA ( MM( 90, J ), J = 1, 4 ) / 2332, 2803, 1696,
$ 1177 /
DATA ( MM( 91, J ), J = 1, 4 ) / 2089, 3185, 1256,
$ 1901 /
DATA ( MM( 92, J ), J = 1, 4 ) / 3780, 184, 3715,
$ 81 /
DATA ( MM( 93, J ), J = 1, 4 ) / 1700, 663, 2077,
$ 1669 /
DATA ( MM( 94, J ), J = 1, 4 ) / 3712, 499, 3019,
$ 2633 /
DATA ( MM( 95, J ), J = 1, 4 ) / 150, 3784, 1497,
$ 2269 /
DATA ( MM( 96, J ), J = 1, 4 ) / 2000, 1631, 1101,
$ 129 /
DATA ( MM( 97, J ), J = 1, 4 ) / 3375, 1925, 717,
$ 1141 /
DATA ( MM( 98, J ), J = 1, 4 ) / 1621, 3912, 51,
$ 249 /
DATA ( MM( 99, J ), J = 1, 4 ) / 3090, 1398, 981,
$ 3917 /
DATA ( MM( 100, J ), J = 1, 4 ) / 3765, 1349, 1978,
$ 2481 /
DATA ( MM( 101, J ), J = 1, 4 ) / 1149, 1441, 1813,
$ 3941 /
DATA ( MM( 102, J ), J = 1, 4 ) / 3146, 2224, 3881,
$ 2217 /
DATA ( MM( 103, J ), J = 1, 4 ) / 33, 2411, 76,
$ 2749 /
DATA ( MM( 104, J ), J = 1, 4 ) / 3082, 1907, 3846,
$ 3041 /
DATA ( MM( 105, J ), J = 1, 4 ) / 2741, 3192, 3694,
$ 1877 /
DATA ( MM( 106, J ), J = 1, 4 ) / 359, 2786, 1682,
$ 345 /
DATA ( MM( 107, J ), J = 1, 4 ) / 3316, 382, 124,
$ 2861 /
DATA ( MM( 108, J ), J = 1, 4 ) / 1749, 37, 1660,
$ 1809 /
DATA ( MM( 109, J ), J = 1, 4 ) / 185, 759, 3997,
$ 3141 /
DATA ( MM( 110, J ), J = 1, 4 ) / 2784, 2948, 479,
$ 2825 /
DATA ( MM( 111, J ), J = 1, 4 ) / 2202, 1862, 1141,
$ 157 /
DATA ( MM( 112, J ), J = 1, 4 ) / 2199, 3802, 886,
$ 2881 /
DATA ( MM( 113, J ), J = 1, 4 ) / 1364, 2423, 3514,
$ 3637 /
DATA ( MM( 114, J ), J = 1, 4 ) / 1244, 2051, 1301,
$ 1465 /
DATA ( MM( 115, J ), J = 1, 4 ) / 2020, 2295, 3604,
$ 2829 /
DATA ( MM( 116, J ), J = 1, 4 ) / 3160, 1332, 1888,
$ 2161 /
DATA ( MM( 117, J ), J = 1, 4 ) / 2785, 1832, 1836,
$ 3365 /
DATA ( MM( 118, J ), J = 1, 4 ) / 2772, 2405, 1990,
$ 361 /
DATA ( MM( 119, J ), J = 1, 4 ) / 1217, 3638, 2058,
$ 2685 /
DATA ( MM( 120, J ), J = 1, 4 ) / 1822, 3661, 692,
$ 3745 /
DATA ( MM( 121, J ), J = 1, 4 ) / 1245, 327, 1194,
$ 2325 /
DATA ( MM( 122, J ), J = 1, 4 ) / 2252, 3660, 20,
$ 3609 /
DATA ( MM( 123, J ), J = 1, 4 ) / 3904, 716, 3285,
$ 3821 /
DATA ( MM( 124, J ), J = 1, 4 ) / 2774, 1842, 2046,
$ 3537 /
DATA ( MM( 125, J ), J = 1, 4 ) / 997, 3987, 2107,
$ 517 /
DATA ( MM( 126, J ), J = 1, 4 ) / 2573, 1368, 3508,
$ 3017 /
DATA ( MM( 127, J ), J = 1, 4 ) / 1148, 1848, 3525,
$ 2141 /
DATA ( MM( 128, J ), J = 1, 4 ) / 545, 2366, 3801,
$ 1537 /
* ..
* .. Executable Statements ..
*
I1 = ISEED( 1 )
I2 = ISEED( 2 )
I3 = ISEED( 3 )
I4 = ISEED( 4 )
*
DO 10 I = 1, MIN( N, LV )
*
20 CONTINUE
*
* Multiply the seed by i-th power of the multiplier modulo 2**48
*
IT4 = I4*MM( I, 4 )
IT3 = IT4 / IPW2
IT4 = IT4 - IPW2*IT3
IT3 = IT3 + I3*MM( I, 4 ) + I4*MM( I, 3 )
IT2 = IT3 / IPW2
IT3 = IT3 - IPW2*IT2
IT2 = IT2 + I2*MM( I, 4 ) + I3*MM( I, 3 ) + I4*MM( I, 2 )
IT1 = IT2 / IPW2
IT2 = IT2 - IPW2*IT1
IT1 = IT1 + I1*MM( I, 4 ) + I2*MM( I, 3 ) + I3*MM( I, 2 ) +
$ I4*MM( I, 1 )
IT1 = MOD( IT1, IPW2 )
*
* Convert 48-bit integer to a real number in the interval (0,1)
*
X( I ) = R*( REAL( IT1 )+R*( REAL( IT2 )+R*( REAL( IT3 )+R*
$ REAL( IT4 ) ) ) )
*
IF (X( I ).EQ.1.0) THEN
* If a real number has n bits of precision, and the first
* n bits of the 48-bit integer above happen to be all 1 (which
* will occur about once every 2**n calls), then X( I ) will
* be rounded to exactly 1.0. In IEEE single precision arithmetic,
* this will happen relatively often since n = 24.
* Since X( I ) is not supposed to return exactly 0.0 or 1.0,
* the statistically correct thing to do in this situation is
* simply to iterate again.
* N.B. the case X( I ) = 0.0 should not be possible.
I1 = I1 + 2
I2 = I2 + 2
I3 = I3 + 2
I4 = I4 + 2
GOTO 20
END IF
*
10 CONTINUE
*
* Return final value of seed
*
ISEED( 1 ) = IT1
ISEED( 2 ) = IT2
ISEED( 3 ) = IT3
ISEED( 4 ) = IT4
RETURN
*
* End of SLARUV
*
END