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dlaruv_dev.f90
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!> \brief \b DLARUV 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 DLARUV + dependencies
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaruv.f">
!> [TGZ]</a>
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaruv.f">
!> [ZIP]</a>
!> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaruv.f">
!> [TXT]</a>
!> \endhtmlonly
!
! Definition:
! ===========
!
! SUBROUTINE DLARUV( ISEED, N, X )
!
! .. Scalar Arguments ..
! INTEGER N
! ..
! .. Array Arguments ..
! INTEGER ISEED( 4 )
! DOUBLE PRECISION X( N )
! ..
!
!
!> \par Purpose:
! =============
!>
!> \verbatim
!>
!> DLARUV returns a vector of n random real numbers from a uniform (0,1)
!> distribution (n <= 128).
!>
!> This is an auxiliary routine called by DLARNV and ZLARNV.
!> \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 DOUBLE PRECISION 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.
!
!> \ingroup OTHERauxiliary
!
!> \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
!>
! =====================================================================
#if defined(__CUDA)
ATTRIBUTES(DEVICE) SUBROUTINE DLARUV_XG( ISEED, N, X )
#else
SUBROUTINE DLARUV_XG( ISEED, N, X )
#endif
!
! -- LAPACK auxiliary routine --
! -- LAPACK is a software package provided by Univ. of Tennessee, --
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
!
! .. Scalar Arguments ..
INTEGER N
! ..
! .. Array Arguments ..
INTEGER ISEED( 4 )
DOUBLE PRECISION X( N )
! ..
!
! =====================================================================
!
! .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
INTEGER LV, IPW2
DOUBLE PRECISION 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 DBLE, MIN, MOD
! ..
! .. 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 ..
!
#if defined(__CUDA)
ATTRIBUTES(VALUE) :: N
ATTRIBUTES(DEVICE) :: ISEED, X
#endif
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*( DBLE( IT1 )+R*( DBLE( IT2 )+R*( DBLE( IT3 )+R* &
DBLE( IT4 ) ) ) )
!
IF (X( I ).EQ.1.0D0) 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.
! 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 DLARUV
!
END