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RANLIB.C Library of C Routines for Random Number Generation Base Generator Documentation Compiled and Written by: Barry W. Brown James Lovato Department of Biomathematics, Box 237 The University of Texas, M.D. Anderson Cancer Center 1515 Holcombe Boulevard Houston, TX 77030 This work was supported by grant CA-16672 from the National Cancer Institute. Base Random Number GeneratorI. OVERVIEW AND DEFAULT BEHAVIORThis set of programs contains 32 virtual random number generators.Each generator can provide 1,048,576 blocks of numbers, and each blockis of length 1,073,741,824. Any generator can be set to the beginningor end of the current block or to its starting value. The methods arefrom the paper cited immediately below, and most of the code is atransliteration from the Pascal of the paper into Fortran.P. L'Ecuyer and S. Cote. Implementing a Random Number Package withSplitting Facilities. ACM Transactions on Mathematical Software 17:1,pp 98-111.Most users won't need the sophisticated capabilities of this package,and will desire a single generator. This single generator (which willhave a non-repeating length of 2.3 X 10^18 numbers) is the default.In order to accommodate this use, the concept of the current generatoris added to those of the cited paper; references to a generator arealways to the current generator. The current generator is initiallygenerator number 1; it can be changed by setcgn, and the ordinalnumber of the current generator can be obtained from getcgn.The user of the default can set the initial values of the two integerseeds with setall. If the user does not set the seeds, the randomnumber generation will use the default values, 1234567890 and123456789. The values of the current seeds can be achieved by a callto GETSD. Random number may be obtained as integers ranging from 1 toa large integer by reference to function ignlgi or as a floating pointnumber between 0 and 1 by a reference to function ranf. These are theonly routines needed by a user desiring a single stream of randomnumbers.II. CONCEPTSA stream of pseudo-random numbers is a sequence, each member of whichcan be obtained either as an integer in the range 1..2,147,483,563 oras a floating point number in the range [0..1]. The user is in chargeof which representation is desired.The method contains an algorithm for generating a stream with a verylong period, 2.3 X 10^18. This stream in partitioned into G (=32)virtual generators. Each virtual generator contains 2^20 (=1,048,576)blocks of non-overlapping random numbers. Each block is 2^30(=1,073,741,824) in length. Base Random Number Generator Page 2The state of a generator is determined by two integers called seeds.The seeds can be initialized by the user; the initial values of thefirst must lie between 1 and 2,147,483,562, that of the second between1 and 2,147,483,398. Each time a number is generated, the values ofthe seeds change. Three values of seeds are remembered by thegenerators at all times: the value with which the generator wasinitialized, the value at the beginning of the current block, and thevalue at the beginning of the next block. The seeds of any generatorcan be set to any of these three values at any time.Of the 32 virtual generators, exactly one will be the currentgenerator, i.e., that one will be used to generate values for ignlgiand randf. Initially, the current generator is set to number one.The current generator may be changed by calling setcgn, and the numberof the current generator can be obtained using getcgn.III. AN EXAMPLEAn example of the need for these capabilities is as follows. Twostatistical techniques are being compared on data of different sizes.The first technique uses bootstrapping and is thought to be asaccurate using less data than the second method which employs onlybrute force.For the first method, a data set of size uniformly distributed between25 and 50 will be generated. Then the data set of the specified sizewill be generated and alalyzed. The second method will choose a dataset size between 100 and 200, generate the data and alalyze it. Thisprocess will be repeated 1000 times.For variance reduction, we want the random numbers used in the twomethods to be the same for each of the 1000 comparisons. But methodtwo will use more random numbers than method one and without thispackage, synchronization might be difficult.With the package, it is a snap. Use generator 1 to obtain the samplesize for method one and generator 2 to obtain the data. Then resetthe state to the beginning of the current block and do the same forthe second method. This assures that the initial data for method twois that used by method one. When both have concluded, advance theblock for both generators.IV. THE INTERFACEA random number is obtained either as a random integer between 1 and2,147,483,562 by invoking integer function ignlgi (I GeNerate LarGeInteger) or as a random floating point number between 0 and 1 byinvoking real function RANF. Neither function has arguments.The seed of the first generator can be set by invoking subroutineSETALL; the values of the seeds of the other 31 generators arecalculated from this value. Base Random Number Generator Page 3The number of the current generator can be set by calling subroutineSETCGN, which takes a single argument, the integer generator number inthe range 1..32. The number of the current generator can be obtainedby invoking subroutine getcgn which returns the number in its singleinteger argument.V. CALLING SEQUENCES A. SETTING THE SEED OF ALL GENERATORS********************************************************************** void setall(long iseed1,long iseed2) SET ALL random number generators Sets the initial seed of generator 1 to ISEED1 and ISEED2. The initial seeds of the other generators are set accordingly, and all generators states are set to these seeds. This is a transcription from Pascal to Fortran of routine Set_Initial_Seed from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991) Arguments iseed1 -> First of two integer seeds iseed2 -> Second of two integer seeds********************************************************************** B. OBTAINING RANDOM NUMBERS********************************************************************** long ignlgi(void) GeNerate LarGe Integer Returns a random integer following a uniform distribution over (1, 2147483562) using the current generator. This is a transcription from Pascal to Fortran of routine Random from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991)********************************************************************** Base Random Number Generator Page 4********************************************************************** float ranf(void) RANDom number generator as a Function Returns a random floating point number from a uniform distribution over 0 - 1 (endpoints of this interval are not returned) using the current generator This is a transcription from Pascal to Fortran of routine Uniform_01 from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991)********************************************************************** C. SETTING AND OBTAINING THE NUMBER OF THE CURRENT GENERATOR********************************************************************** void gscgn(long getset,long *g) Get/Set GeNerator Gets or returns in G the number of the current generator Arguments getset --> 0 Get 1 Set g <-- Number of the current random number generator (1..32)********************************************************************** D. OBTAINING OR CHANGING SEEDS IN CURRENT GENERATOR*********************************************************************** void advnst(long k) ADV-a-N-ce ST-ate Advances the state of the current generator by 2^K values and resets the initial seed to that value. This is a transcription from Pascal to Fortran of routine Advance_State from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991) Arguments k -> The generator is advanced by2^K values********************************************************************** Base Random Number Generator Page 5********************************************************************** void getsd(long *iseed1,long *iseed2) GET SeeD Returns the value of two integer seeds of the current generator This is a transcription from Pascal to Fortran of routine Get_State from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991) Arguments iseed1 <- First integer seed of generator G iseed2 <- Second integer seed of generator G******************************************************************************************************************************************** void initgn(long isdtyp) INIT-ialize current G-e-N-erator Reinitializes the state of the current generator This is a transcription from Pascal to Fortran of routine Init_Generator from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991) Arguments isdtyp -> The state to which the generator is to be set isdtyp = -1 => sets the seeds to their initial value isdtyp = 0 => sets the seeds to the first value of the current block isdtyp = 1 => sets the seeds to the first value of the next block********************************************************************** Base Random Number Generator Page 6********************************************************************** void setsd(long iseed1,long iseed2) SET S-ee-D of current generator Resets the initial seed of the current generator to ISEED1 and ISEED2. The seeds of the other generators remain unchanged. This is a transcription from Pascal to Fortran of routine Set_Seed from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991) Arguments iseed1 -> First integer seed iseed2 -> Second integer seed********************************************************************** E. MISCELLANY********************************************************************** long mltmod(long a,long s,long m) Returns (A*S) MOD M This is a transcription from Pascal to Fortran of routine MULtMod_Decompos from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991) Arguments a, s, m -->********************************************************************** Base Random Number Generator Page 7********************************************************************** void setant(long qvalue) SET ANTithetic Sets whether the current generator produces antithetic values. If X is the value normally returned from a uniform [0,1] random number generator then 1 - X is the antithetic value. If X is the value normally returned from a uniform [0,N] random number generator then N - 1 - X is the antithetic value. All generators are initialized to NOT generate antithetic values. This is a transcription from Pascal to Fortran of routine Set_Antithetic from the paper L'Ecuyer, P. and Cote, S. "Implementing a Random Number Package with Splitting Facilities." ACM Transactions on Mathematical Software, 17:98-111 (1991) Arguments qvalue -> nonzero if generator G is to generating antithetic values, otherwise zero**********************************************************************⌨️ 快捷键说明
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