V104 Uniform Random Numbers

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V104 Uniform Random Numbers

Routine ID: V104
Author(s): CDC: H. von Eicken, IBM: T. Lindelöf	Library: KERNLIB
Submitter:	Submitted: 07.12.1970
Language: Assembler	Revised: 15.09.1978

OBSOLETE

Please note that this routine has been obsoleted in CNL 215. Users are advised not to use it any longer and to replace it in older programs. No maintenance for it will take place and it will eventually disappear.
Suggested replacement:
RANMAR (V113) or RANECU (V114) or RANLUX (V115)

RNDM generates uniformly distributed pseudo-random numbers in the interval (0,1) in type REAL and in the interval $(1,2$ ⁴⁷-1) (CDC) or $(1,2$ ³¹-1) (IBM) in type INTEGER. The CDC version has a period of more than $10$ ¹³ . The IBM period, however, is only about $5 x10$ ⁸ which may not be good enough for some calculations. In that case RNDM2 (V107) should be used instead.

Structure:

SUBROUTINE subprogram
User Entry Names: IRNDM, RNDM, RDMIN, RDMOUT

Usage:

    Y = RNDM(X)

where X is a dummy argument (see Notes), sets Y to a pseudo-random number in the interval (0,1). X and Y are of type REAL.

    I = IRNDM(X)

where X is a dummy argument (see Notes), sets I to an integer pseudo-random number in the interval

(1,2

⁴⁷-1) on CDC,

(1,2

³¹-1) on IBM. X is of type REAL and I is of type INTEGER.

    CALL RDMOUT(SEED)

replaces SEED by the current value of the integer pseudo-random number. This SEED may then be used to restart the sequence at this point, by a call to RDMIN. SEED is of type REAL.

    CALL RDMIN(SEED)

replaces the current value of the integer pseudo-random number by the value of the variable SEED. SEED is of type REAL. The value of SEED should not be chosen by the user but should be obtained by a previous call to RDMOUT. If this is not complied with, the numbers generated may have serious defects in their randomness.

Method:

CDC:
Consider the sequence:

$r$ _i $=$ $αr$ _i-1( mod 2⁴⁷) for i=1,2,...

$with r$ ₀ $=$ $2000 0000 0110 6047 1625$ ₈

$and α$ $=$ $2000 0000 3432 7724 4615$ ₈

where $r$ ₀ and $α$ are the unnormalised floating-point representation of the starting number and $5$ ¹⁵ respectively. The j-th floating-point number $R$ _j is obtained by packing $r$ _j

with an exponent $(-47)$ and normalising it. This ensures that $R$ _j

falls in the interval (0,1).

The product $αr$ _j-1 is generated in a 96 bit accumulator. The integer number $N$ _j returned is the low order 47 bits of the contents of this accumulator, except that the right-most 11 bits are replaced by those occupying bit positions 48-58. This replacement is done in order to increase the time period of the low order bits.
IBM: See write-up for RNDM2 (V107).

Notes:

While the argument is dummy, in the sense that the generator makes no use of it, it must be noted that if a reference to RNDM occurs

$•$: more than once within a Fortran statement, the argument to it should be different in each case;
$•$: in a DO-loop, the argument must depend either directly or indirectly on the index of this loop.

These rules must be observed since the compilers, in their attempt to optimise the object code, assume that functions called with identical arguments return the same function value.

•

V105

Next: V105 Arrays of Up: CERNLIB Previous: V103 Random Bits

Janne Saarela
Mon Apr 3 15:06:23 METDST 1995

$r$ _i	$=$	$αr$ _i-1( mod 2⁴⁷) for i=1,2,...
$with r$ ₀	$=$	$2000 0000 0110 6047 1625$ ₈
$and α$	$=$	$2000 0000 3432 7724 4615$ ₈