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Library of Fortran Routines for Random Number Generation
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Base Generator Documentation
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Compiled and Written by:
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Department of Biomathematics, Box 237
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The University of Texas, M.D. Anderson Cancer Center
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1515 Holcombe Boulevard
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This work was supported by grant CA-16672 from the National Cancer Institute.
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Base Random Number Generator
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I. OVERVIEW AND DEFAULT BEHAVIOR
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This set of programs contains 32 virtual random number generators.
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Each generator can provide 1,048,576 blocks of numbers, and each block
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is of length 1,073,741,824. Any generator can be set to the beginning
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or end of the current block or to its starting value. The methods are
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from the paper cited immediately below, and most of the code is a
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transliteration from the Pascal of the paper into Fortran.
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P. L'Ecuyer and S. Cote. Implementing a Random Number Package with
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Splitting Facilities. ACM Transactions on Mathematical Software 17:1,
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Most users won't need the sophisticated capabilities of this package,
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and will desire a single generator. This single generator (which will
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have a non-repeating length of 2.3 X 10^18 numbers) is the default.
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In order to accommodate this use, the concept of the current generator
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is added to those of the cited paper; references to a generator are
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always to the current generator. The current generator is initially
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generator number 1; it can be changed by SETCGN, and the ordinal
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number of the current generator can be obtained from GETCGN.
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The user of the default can set the initial values of the two integer
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seeds with SETALL. If the user does not set the seeds, the random
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number generation will use the default values, 1234567890 and
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123456789. The values of the current seeds can be achieved by a call
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to GETSD. Random number may be obtained as integers ranging from 1 to
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a large integer by reference to function IGNLGI or as a floating point
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number between 0 and 1 by a reference to function RANF. These are the
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only routines needed by a user desiring a single stream of random
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A stream of pseudo-random numbers is a sequence, each member of which
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can be obtained either as an integer in the range 1..2,147,483,563 or
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as a floating point number in the range [0..1]. The user is in charge
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of which representation is desired.
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The method contains an algorithm for generating a stream with a very
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long period, 2.3 X 10^18. This stream in partitioned into G (=32)
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virtual generators. Each virtual generator contains 2^20 (=1,048,576)
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blocks of non-overlapping random numbers. Each block is 2^30
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(=1,073,741,824) in length.
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Base Random Number Generator Page 2
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The state of a generator is determined by two integers called seeds.
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The seeds can be initialized by the user; the initial values of the
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first must lie between 1 and 2,147,483,562, that of the second between
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1 and 2,147,483,398. Each time a number is generated, the values of
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the seeds change. Three values of seeds are remembered by the
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generators at all times: the value with which the generator was
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initialized, the value at the beginning of the current block, and the
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value at the beginning of the next block. The seeds of any generator
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can be set to any of these three values at any time.
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Of the 32 virtual generators, exactly one will be the current
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generator, i.e., that one will be used to generate values for IGNLGI
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and RANDF. Initially, the current generator is set to number one.
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The current generator may be changed by calling SETCGN, and the number
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of the current generator can be obtained using GETCGN.
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An example of the need for these capabilities is as follows. Two
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statistical techniques are being compared on data of different sizes.
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The first technique uses bootstrapping and is thought to be as
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accurate using less data than the second method which employs only
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For the first method, a data set of size uniformly distributed between
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25 and 50 will be generated. Then the data set of the specified size
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will be generated and alalyzed. The second method will choose a data
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set size between 100 and 200, generate the data and alalyze it. This
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process will be repeated 1000 times.
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For variance reduction, we want the random numbers used in the two
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methods to be the same for each of the 1000 comparisons. But method
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two will use more random numbers than method one and without this
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package, synchronization might be difficult.
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With the package, it is a snap. Use generator 1 to obtain the sample
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size for method one and generator 2 to obtain the data. Then reset
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the state to the beginning of the current block and do the same for
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the second method. This assures that the initial data for method two
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is that used by method one. When both have concluded, advance the
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block for both generators.
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A random number is obtained either as a random integer between 1 and
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2,147,483,562 by invoking integer function IGNLGI (I GeNerate LarGe
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Integer) or as a random floating point number between 0 and 1 by
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invoking real function RANF. Neither function has arguments.
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The seed of the first generator can be set by invoking subroutine
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SETALL; the values of the seeds of the other 31 generators are
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calculated from this value.
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Base Random Number Generator Page 3
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The number of the current generator can be set by calling subroutine
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SETCGN, which takes a single argument, the integer generator number in
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the range 1..32. The number of the current generator can be obtained
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by invoking subroutine GETCGN which returns the number in its single
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A. SETTING THE SEED OF ALL GENERATORS
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C**********************************************************************
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C SUBROUTINE SETALL(ISEED1,ISEED2)
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C SET ALL random number generators
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C Sets the initial seed of generator 1 to ISEED1 and ISEED2. The
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C initial seeds of the other generators are set accordingly, and
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C all generators states are set to these seeds.
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C ISEED1 -> First of two integer seeds
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C ISEED2 -> Second of two integer seeds
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C**********************************************************************
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B. OBTAINING RANDOM NUMBERS
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C**********************************************************************
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C INTEGER FUNCTION IGNLGI()
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C GeNerate LarGe Integer
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C Returns a random integer following a uniform distribution over
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C (1, 2147483562) using the current generator.
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C**********************************************************************
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C**********************************************************************
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C REAL FUNCTION RANF()
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C RANDom number generator as a Function
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C Returns a random floating point number from a uniform distribution
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C over 0 - 1 (endpoints of this interval are not returned) using the
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C**********************************************************************
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Base Random Number Generator Page 4
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C. SETTING AND OBTAINING THE NUMBER OF THE CURRENT GENERATOR
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C**********************************************************************
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C SUBROUTINE SETCGN( G )
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C Sets the current generator to G. All references to a generator
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C are to the current generator.
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C G --> Number of the current random number generator (1..32)
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C**********************************************************************
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C**********************************************************************
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C SUBROUTINE GETCGN(G)
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C Returns in G the number of the current random number generator
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C G <-- Number of the current random number generator (1..32)
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C**********************************************************************
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D. OBTAINING OR CHANGING SEEDS IN CURRENT GENERATOR
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C**********************************************************************
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C SUBROUTINE ADVNST(K)
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C Advances the state of the current generator by 2^K values and
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C resets the initial seed to that value.
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C K -> The generator is advanced by 2^K values
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C**********************************************************************
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Base Random Number Generator Page 5
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C**********************************************************************
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C SUBROUTINE GETSD(ISEED1,ISEED2)
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C Returns the value of two integer seeds of the current generator
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C ISEED1 <- First integer seed of generator G
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C ISEED2 <- Second integer seed of generator G
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C**********************************************************************
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C**********************************************************************
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C SUBROUTINE INITGN(ISDTYP)
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C INIT-ialize current G-e-N-erator
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C Reinitializes the state of the current generator
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C ISDTYP -> The state to which the generator is to be set
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C ISDTYP = -1 => sets the seeds to their initial value
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C ISDTYP = 0 => sets the seeds to the first value of
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C ISDTYP = 1 => sets the seeds to the first value of
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C**********************************************************************
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C**********************************************************************
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C SUBROUTINE SETSD(ISEED1,ISEED2)
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C SET S-ee-D of current generator
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C Resets the initial seed of the current generator to ISEED1 and
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C ISEED2. The seeds of the other generators remain unchanged.
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C ISEED1 -> First integer seed
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C ISEED2 -> Second integer seed
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C**********************************************************************
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C**********************************************************************
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C INTEGER FUNCTION MLTMOD(A,S,M)
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C Returns (A*S) MOD M
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C**********************************************************************
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C**********************************************************************
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C SUBROUTINE SETANT(QVALUE)
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C Sets whether the current generator produces antithetic values. If
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C X is the value normally returned from a uniform [0,1] random
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C number generator then 1 - X is the antithetic value. If X is the
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C value normally returned from a uniform [0,N] random number
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C generator then N - 1 - X is the antithetic value.
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C All generators are initialized to NOT generate antithetic values.
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C QVALUE -> .TRUE. if generator G is to generating antithetic
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C values, otherwise .FALSE.
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C**********************************************************************
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liboctave/cruft/ranlib/Basegen.doc
