rand.f
FUNCTION RAND (R)
C***BEGIN PROLOGUE RAND
C***PURPOSE Generate a uniformly distributed random number.
C***LIBRARY SLATEC (FNLIB)
C***CATEGORY L6A21
C***TYPE SINGLE PRECISION (RAND-S)
C***KEYWORDS FNLIB, RANDOM NUMBER, SPECIAL FUNCTIONS, UNIFORM
C***AUTHOR Fullerton, W., (LANL)
C***DESCRIPTION
C
C This pseudo-random number generator is portable among a wide
C variety of computers. RAND(R) undoubtedly is not as good as many
C readily available installation dependent versions, and so this
C routine is not recommended for widespread usage. Its redeeming
C feature is that the exact same random numbers (to within final round-
C off error) can be generated from machine to machine. Thus, programs
C that make use of random numbers can be easily transported to and
C checked in a new environment.
C
C The random numbers are generated by the linear congruential
C method described, e.g., by Knuth in Seminumerical Methods (p.9),
C Addison-Wesley, 1969. Given the I-th number of a pseudo-random
C sequence, the I+1 -st number is generated from
C X(I+1) = (A*X(I) + C) MOD M,
C where here M = 2**22 = 4194304, C = 1731 and several suitable values
C of the multiplier A are discussed below. Both the multiplier A and
C random number X are represented in double precision as two 11-bit
C words. The constants are chosen so that the period is the maximum
C possible, 4194304.
C
C In order that the same numbers be generated from machine to
C machine, it is necessary that 23-bit integers be reducible modulo
C 2**11 exactly, that 23-bit integers be added exactly, and that 11-bit
C integers be multiplied exactly. Furthermore, if the restart option
C is used (where R is between 0 and 1), then the product R*2**22 =
C R*4194304 must be correct to the nearest integer.
C
C The first four random numbers should be .0004127026,
C .6750836372, .1614754200, and .9086198807. The tenth random number
C is .5527787209, and the hundredth is .3600893021 . The thousandth
C number should be .2176990509 .
C
C In order to generate several effectively independent sequences
C with the same generator, it is necessary to know the random number
C for several widely spaced calls. The I-th random number times 2**22,
C where I=K*P/8 and P is the period of the sequence (P = 2**22), is
C still of the form L*P/8. In particular we find the I-th random
C number multiplied by 2**22 is given by
C I = 0 1*P/8 2*P/8 3*P/8 4*P/8 5*P/8 6*P/8 7*P/8 8*P/8
C RAND= 0 5*P/8 2*P/8 7*P/8 4*P/8 1*P/8 6*P/8 3*P/8 0
C Thus the 4*P/8 = 2097152 random number is 2097152/2**22.
C
C Several multipliers have been subjected to the spectral test
C (see Knuth, p. 82). Four suitable multipliers roughly in order of
C goodness according to the spectral test are
C 3146757 = 1536*2048 + 1029 = 2**21 + 2**20 + 2**10 + 5
C 2098181 = 1024*2048 + 1029 = 2**21 + 2**10 + 5
C 3146245 = 1536*2048 + 517 = 2**21 + 2**20 + 2**9 + 5
C 2776669 = 1355*2048 + 1629 = 5**9 + 7**7 + 1
C
C In the table below LOG10(NU(I)) gives roughly the number of
C random decimal digits in the random numbers considered I at a time.
C C is the primary measure of goodness. In both cases bigger is better.
C
C LOG10 NU(I) C(I)
C A I=2 I=3 I=4 I=5 I=2 I=3 I=4 I=5
C
C 3146757 3.3 2.0 1.6 1.3 3.1 1.3 4.6 2.6
C 2098181 3.3 2.0 1.6 1.2 3.2 1.3 4.6 1.7
C 3146245 3.3 2.2 1.5 1.1 3.2 4.2 1.1 0.4
C 2776669 3.3 2.1 1.6 1.3 2.5 2.0 1.9 2.6
C Best
C Possible 3.3 2.3 1.7 1.4 3.6 5.9 9.7 14.9
C
C Input Argument --
C R If R=0., the next random number of the sequence is generated.
C If R .LT. 0., the last generated number will be returned for
C possible use in a restart procedure.
C If R .GT. 0., the sequence of random numbers will start with
C the seed R mod 1. This seed is also returned as the value of
C RAND provided the arithmetic is done exactly.
C
C Output Value --
C RAND a pseudo-random number between 0. and 1.
C
C***REFERENCES (NONE)
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 770401 DATE WRITTEN
C 890531 Changed all specific intrinsics to generic. (WRB)
C 890531 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C***END PROLOGUE RAND