SRC/dlaruv.f

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      SUBROUTINE DLARUV( ISEED, N, X )
*
*  -- LAPACK auxiliary routine (version 3.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2006
*
*     .. Scalar Arguments ..
      INTEGER            N
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      DOUBLE PRECISION   X( N )
*     ..
*
*  Purpose
*  =======
*
*  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.
*
*  Arguments
*  =========
*
*  ISEED   (input/output) 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.
*
*  N       (input) INTEGER
*          The number of random numbers to be generated. N <= 128.
*
*  X       (output) DOUBLE PRECISION 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.
*
*  =====================================================================
*
*     .. 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 ..
*
      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