c--------------------------------------------------------------------- double precision function randlc (x, a) c--------------------------------------------------------------------- c--------------------------------------------------------------------- c c This routine returns a uniform pseudorandom double precision number in the c range (0, 1) by using the linear congruential generator c c x_{k+1} = a x_k (mod 2^46) c c where 0 < x_k < 2^46 and 0 < a < 2^46. This scheme generates 2^44 numbers c before repeating. The argument A is the same as 'a' in the above formula, c and X is the same as x_0. A and X must be odd double precision integers c in the range (1, 2^46). The returned value RANDLC is normalized to be c between 0 and 1, i.e. RANDLC = 2^(-46) * x_1. X is updated to contain c the new seed x_1, so that subsequent calls to RANDLC using the same c arguments will generate a continuous sequence. c c This routine should produce the same results on any computer with at least c 48 mantissa bits in double precision floating point data. On 64 bit c systems, double precision should be disabled. c c David H. Bailey October 26, 1990 c c--------------------------------------------------------------------- implicit none double precision r23,r46,t23,t46,a,x,t1,t2,t3,t4,a1,a2,x1,x2,z parameter (r23 = 0.5d0 ** 23, r46 = r23 ** 2, t23 = 2.d0 ** 23, > t46 = t23 ** 2) c--------------------------------------------------------------------- c Break A into two parts such that A = 2^23 * A1 + A2. c--------------------------------------------------------------------- t1 = r23 * a a1 = int (t1) a2 = a - t23 * a1 c--------------------------------------------------------------------- c Break X into two parts such that X = 2^23 * X1 + X2, compute c Z = A1 * X2 + A2 * X1 (mod 2^23), and then c X = 2^23 * Z + A2 * X2 (mod 2^46). c--------------------------------------------------------------------- t1 = r23 * x x1 = int (t1) x2 = x - t23 * x1 t1 = a1 * x2 + a2 * x1 t2 = int (r23 * t1) z = t1 - t23 * t2 t3 = t23 * z + a2 * x2 t4 = int (r46 * t3) x = t3 - t46 * t4 randlc = r46 * x return end c--------------------------------------------------------------------- c--------------------------------------------------------------------- subroutine vranlc (n, x, a, y) c--------------------------------------------------------------------- c--------------------------------------------------------------------- c--------------------------------------------------------------------- c This routine generates N uniform pseudorandom double precision numbers in c the range (0, 1) by using the linear congruential generator c c x_{k+1} = a x_k (mod 2^46) c c where 0 < x_k < 2^46 and 0 < a < 2^46. This scheme generates 2^44 numbers c before repeating. The argument A is the same as 'a' in the above formula, c and X is the same as x_0. A and X must be odd double precision integers c in the range (1, 2^46). The N results are placed in Y and are normalized c to be between 0 and 1. X is updated to contain the new seed, so that c subsequent calls to RANDLC using the same arguments will generate a c continuous sequence. c c This routine generates the output sequence in batches of length NV, for c convenience on vector computers. This routine should produce the same c results on any computer with at least 48 mantissa bits in double precision c floating point data. On Cray systems, double precision should be disabled. c c David H. Bailey August 30, 1990 c--------------------------------------------------------------------- integer n double precision x, a, y(*) double precision r23, r46, t23, t46 integer nv parameter (r23 = 2.d0 ** (-23), r46 = r23 * r23, t23 = 2.d0 ** 23, > t46 = t23 * t23, nv = 64) double precision xv(nv), t1, t2, t3, t4, an, a1, a2, x1, x2, yy integer n1, i, j external randlc double precision randlc c--------------------------------------------------------------------- c Compute the first NV elements of the sequence using RANDLC. c--------------------------------------------------------------------- t1 = x n1 = min (n, nv) do i = 1, n1 xv(i) = t46 * randlc (t1, a) enddo c--------------------------------------------------------------------- c It is not necessary to compute AN, A1 or A2 unless N is greater than NV. c--------------------------------------------------------------------- if (n .gt. nv) then c--------------------------------------------------------------------- c Compute AN = AA ^ NV (mod 2^46) using successive calls to RANDLC. c--------------------------------------------------------------------- t1 = a t2 = r46 * a do i = 1, nv - 1 t2 = randlc (t1, a) enddo an = t46 * t2 c--------------------------------------------------------------------- c Break AN into two parts such that AN = 2^23 * A1 + A2. c--------------------------------------------------------------------- t1 = r23 * an a1 = aint (t1) a2 = an - t23 * a1 endif c--------------------------------------------------------------------- c Compute N pseudorandom results in batches of size NV. c--------------------------------------------------------------------- do j = 0, n - 1, nv n1 = min (nv, n - j) c--------------------------------------------------------------------- c Compute up to NV results based on the current seed vector XV. c--------------------------------------------------------------------- do i = 1, n1 y(i+j) = r46 * xv(i) enddo c--------------------------------------------------------------------- c If this is the last pass through the 140 loop, it is not necessary to c update the XV vector. c--------------------------------------------------------------------- if (j + n1 .eq. n) goto 150 c--------------------------------------------------------------------- c Update the XV vector by multiplying each element by AN (mod 2^46). c--------------------------------------------------------------------- do i = 1, nv t1 = r23 * xv(i) x1 = aint (t1) x2 = xv(i) - t23 * x1 t1 = a1 * x2 + a2 * x1 t2 = aint (r23 * t1) yy = t1 - t23 * t2 t3 = t23 * yy + a2 * x2 t4 = aint (r46 * t3) xv(i) = t3 - t46 * t4 enddo enddo c--------------------------------------------------------------------- c Save the last seed in X so that subsequent calls to VRANLC will generate c a continuous sequence. c--------------------------------------------------------------------- 150 x = xv(n1) return end c----- end of program ------------------------------------------------