December 2003 - cypherpunks-legacy

(fwd) Re: BSD random() - any good (source included)?
by Jim choate 17 Dec '03

17 Dec '03

Newsgroups: sci.math,sci.stat.math Path: bga.com!news.sprintlink.net!hookup!europa.eng.gtefsd.com!howland.reston.ans.net!spool.mu.edu!agate!library.ucla.edu!csulb.edu!csus.edu!netcom.com!deleyd From: deleyd(a)netcom.com Subject: Re: BSD random() - any good (source included)? Message-ID: <deleydCs1L9A.2L6(a)netcom.com> Followup-To: sci.math,sci.stat.math Organization: NETCOM On-line Communication Services (408 261-4700 guest) X-Newsreader: TIN [version 1.2 PL1] References: <2ua9ln$4lv(a)news.tamu.edu> Date: Mon, 27 Jun 1994 06:12:45 GMT Lines: 13 Xref: bga.com sci.math:14916 sci.stat.math:1219 I did a research paper on Computer Generated Random Number Sequences in 1991. Included are the results of testing numerous popular generators. The code used for testing the generators is also available if one is so inclined to do some testing of a particular generator. (The only thing is a thorough test to determine the limits of the generator can take many hours of CPU time). Perhaps later this week I'll post the paper and see what the response is. I'm always a bit apprehensive to post. Never sure what the response will be. Maybe someone will think it's interesting. David Deley deleyd(a)netcom.com

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(fwd) BSD random() - any good (source included)?
by Jim choate 17 Dec '03

17 Dec '03

Path: bga.com!news.sprintlink.net!news.onramp.net!convex!cs.utexas.edu!bcm!news.tamu.edu!henrik From: henrik(a)stat.tamu.edu (Henrik Schmiediche) Newsgroups: sci.math,sci.stat.math Subject: BSD random() - any good (source included)? Date: 22 Jun 1994 21:15:35 GMT Organization: Department of Statistics, Texas A&M University Lines: 140 Message-ID: <2ua9ln$4lv(a)news.tamu.edu> NNTP-Posting-Host: picard.tamu.edu Xref: bga.com sci.math:14740 sci.stat.math:1193 Hello, the BSD random() function returns a pseudo random number. I would like to know if anyone knows how good this random number generator is and if it has been thouroughly tested. Below are two descriptions of the generator for two different sources. Looking at the source code it is obvious that this generator is seeded using a linear congruetial generator that leaves much to be desired (low bits alternate). I remember reading somewhere that the trinomials used by random() are not optimal but I can't remember the source. The generator does have some great advantages like being very fast and having a very long period, but both these advantages are meaningless if the random numbers it produces are not very good. Anyone know more about random() and if it is any good? I have include a source code implementation below (I wrote it originally so I could inline the code into my own application which spend a significant amount of time generating random numbers). - henrik According to the SunOS doc's: "random () uses a non-linear additive feedback random number generator employing a default table of size 31 long integers to return successive pseudo-random numbers in the range from 0 to (2**31)-1. The period of this random number generator is very large, approximately 16*((2**31)-1)." The BSD source code (from glibc) says: "The random number generation technique is a linear feedback shift register approach, employing trinomials (since there are fewer terms to sum up that way). In this approach, the least significant bit of all the numbers in the state table will act as a linear feedback shift register, and will have period 2^deg - 1 (where deg is the degree of the polynomial being used, assuming that the polynomial is irreducible and primitive). The higher order bits will have longer periods, since their values are also influenced by pseudo-random carries out of the lower bits. The total period of the generator is approximately deg*(2**deg - 1); thus doubling the amount of state information has a vast influence on the period of the generator." For table size of 31 long ints random() use the trinomial: x**31 + x**3 + 1. For 63 long ints it uses the trinomial x**63 + x + 1. ***************************************************************************** /*** Code to implement random() & srandom() of BSD Unix. It was taken (though coded somewhat differently) from the Gnu BSD implementation. ***/ #include <stdio.h> #include <stdlib.h> #ifdef LONG31 /* x^31 + x^3 + 1 */ #define SIZE 31 #define SIZE1 30 #define P1 3 #define P2 0 #else /* LONG63: x^63 + x + 1 */ #define SIZE 63 #define SIZE1 62 #define P1 1 #define P2 0 #endif #define LONG_MAX 0x7fffffff int p1=P1, p2=P2; long table[SIZE]; /*** return a "random" number in range [0, LONG_MAX] */ long xrand () { int r; table[p1] = table[p1] + table[p2]; /* add two table elements */ r = (table[p1] >> 1) & LONG_MAX; /* throw least significant bit away */ if (p1 == SIZE1) { /* increment the table indexes */ p1 = 0; p2 = p2 + 1; } else if (p2 == SIZE1) { p1 = p1 + 1; p2 = 0; } else { p1 = p1 + 1; p2 = p2 + 1; } return (r); } /*** use a linear congruential type generator to seed the state table & cycle the entire table 10 times */ void sxrand (seed) long seed; { int i; table[0] = seed; for (i=1; i<SIZE; ++i) table[i] = (table[i-1] * 1103515145) + 12345; /* lousy */ for (i=0; i<10*SIZE; ++i) (void) xrand(); } /*** a small test program */ void main () { int i; sxrand (1); /* BSD default */ for (i=1; i<=40; ++i) printf ("%ld", xrand() % 10 ); /* least random bits ? */ /* 6714066113586447326208220248220881760069 (cc -DLONG63) */ /* 9418752338157675324663485137890734831064 (cc -DLONG31) */ printf ("\n"); } -- Henrik Schmiediche, Dept. of Statistics, Texas A&M, College Station, TX 77843 E-mail: henrik(a)stat.tamu.edu | Tel: (409) 862-1764 | Fax: (409) 845-3144 Finger for pgp 2.5 key, fingerprint: CE8F BD6C 59FC DA85 376A BB96 2E83 FF5E

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(fwd) Re: BSD random() - any good (source included)?
by Jim choate 17 Dec '03

17 Dec '03

Path: bga.com!news.sprintlink.net!hookup!europa.eng.gtefsd.com!newsxfer.itd.umich.edu!nntp.cs.ubc.ca!mala.bc.ca!hakatac!rbursey Newsgroups: sci.math,sci.stat.math Subject: Re: BSD random() - any good (source included)? Message-ID: <iFwLoc3w165w(a)hakatac.almanac.bc.ca> From: rbursey(a)hakatac.almanac.bc.ca (robert bursey) Date: Mon, 27 Jun 94 18:24:29 PDT References: <deleydCs1L9A.2L6(a)netcom.com> Distribution: na Organization: Sir HackAlot's UNIX BBS, Port Alberni, B.C. Lines: 18 Xref: bga.com sci.math:14978 sci.stat.math:1239 deleyd(a)netcom.com writes: > I did a research paper on Computer Generated Random Number Sequences in > 1991. Included are the results of testing numerous popular generators. > The code used for testing the generators is also available if one > is so inclined to do some testing of a particular generator. (The only > thing is a thorough test to determine the limits of the generator can > take many hours of CPU time). > > Perhaps later this week I'll post the paper and see what the response > is. I'm always a bit apprehensive to post. Never sure what the > response will be. Maybe someone will think it's interesting. > > David Deley > deleyd(a)netcom.com Does anybody know of a good test for randomness? I would definitely like to know how good computer RNG's are. Post away!

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(fwd) Re: BSD random() - any good (source included)?
by Jim choate 17 Dec '03

17 Dec '03

Newsgroups: sci.math,sci.stat.math Path: bga.com!news.sprintlink.net!hookup!ames!lll-winken.llnl.gov!overload.lbl.gov!dog.ee.lbl.gov!ihnp4.ucsd.edu!usc!howland.reston.ans.net!europa.eng.gtefsd.com!MathWorks.Com!news.kei.com!ssd.intel.com!carr From: carr(a)ssd.intel.com (George Carr) Subject: Re: BSD random() - any good (source included)? Message-ID: <Cs4B6w.IqE(a)SSD.intel.com> Sender: usenet(a)SSD.intel.com Nntp-Posting-Host: shiva Organization: Supercomputer Systems Divison, Intel Corp. References: <deleydCs1L9A.2L6(a)netcom.com> <iFwLoc3w165w(a)hakatac.almanac.bc.ca> Distribution: na Date: Tue, 28 Jun 1994 17:28:08 GMT Lines: 34 Xref: bga.com sci.math:14998 sci.stat.math:1241 In article <iFwLoc3w165w(a)hakatac.almanac.bc.ca>, rbursey(a)hakatac.almanac.bc.ca (robert bursey) writes: |> deleyd(a)netcom.com writes: |> |> > I did a research paper on Computer Generated Random Number Sequences in |> > 1991. Included are the results of testing numerous popular generators. |> > The code used for testing the generators is also available if one |> > is so inclined to do some testing of a particular generator. (The only |> > thing is a thorough test to determine the limits of the generator can |> > take many hours of CPU time). |> > |> > Perhaps later this week I'll post the paper and see what the response |> > is. I'm always a bit apprehensive to post. Never sure what the |> > response will be. Maybe someone will think it's interesting. |> > |> > David Deley |> > deleyd(a)netcom.com |> |> Does anybody know of a good test for randomness? I would definitely like to |> know how good computer RNG's are. Post away! The classic reference is Volume 2 of Donald Knuth's The Art of Computer Programming, Second Edition, Seminumerical Algorithms. I highly recommend it to anyone wanting to know what "random" is all about. If you really need to know whether your generator is random-enough for your application you should expect to do your own testing and yes it will require many hours of your time in addition to that of your computer. -- George R. Carr, Jr. Intel Supercomputer Systems Division Parallel Systems Engineer NOAA Forecast Systems Laboratory carr(a)ssd.intel.com Research Lab 3, Rm A227 carr(a)neko.fsl.noaa.gov 3100 Marine St, R/E/FS5 voice: 303-497-6130 Boulder, CO 80303 fax: 303-497-6821

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(fwd) Re: BSD random() - any good (source included)?
by Jim choate 17 Dec '03

17 Dec '03

Path: bga.com!news.sprintlink.net!hookup!ames!lll-winken.llnl.gov!noc.near.net!pad-thai.aktis.com!la-jiao.aktis.com!not-for-mail From: don(a)cam.ov.com (Donald T. Davis) Newsgroups: sci.math,sci.stat.math Subject: Re: BSD random() - any good (source included)? Date: 28 Jun 1994 17:52:48 -0400 Organization: OpenVision Technologies, Inc. Lines: 65 Distribution: na Message-ID: <2uq63g$g5c(a)la-jiao.aktis.com> References: <deleydCs1L9A.2L6(a)netcom.com> <iFwLoc3w165w(a)hakatac.almanac.bc.ca> <Cs4B6w.IqE(a)SSD.intel.com> NNTP-Posting-Host: la-jiao.aktis.com Xref: bga.com sci.math:15008 sci.stat.math:1243 (George Carr) writes: >(robert bursey) writes: >|> deleyd(a)netcom.com writes: >|> >|> > I did a research paper on Computer Generated Random Number Sequences in >|> > 1991. Included are the results of testing numerous popular generators. >|> > The code used for testing the generators is also available if one >|> > is so inclined to do some testing of a particular generator. (The only >|> > thing is a thorough test to determine the limits of the generator can >|> > take many hours of CPU time). >|> > >|> > Perhaps later this week I'll post the paper and see what the response >|> > is. I'm always a bit apprehensive to post. Never sure what the >|> > response will be. Maybe someone will think it's interesting. >|> > >|> > David Deley >|> > deleyd(a)netcom.com >|> >|> Does anybody know of a good test for randomness? I would definitely like to >|> know how good computer RNG's are. Post away! > >The classic reference is Volume 2 of Donald Knuth's The Art of Computer >Programming, Second Edition, Seminumerical Algorithms. I highly recommend >it to anyone wanting to know what "random" is all about. > >If you really need to know whether your generator is random-enough for >your application you should expect to do your own testing and yes it will >require many hours of your time in addition to that of your computer. >-- knuth's chapter's practical results are about linear-congruential rngs, their optimization and testing. though these rngs are still distressingly common, nonlinear rngs are the way to go for two burgeoning areas that consume random numbers: graphics and cryptography. both areas are concerned with getting extremely long periods, but cryptography is also concerned with proving unpredictability of secure rngs. that is, knowing some outputs of an rng as applied to a given seed, it should be impossible to deduce or predict other outputs' values. so, you see, the "good test for randomness" depends strongly on which features of a random variable you want to use. if you're careful, knuth's approach will work fine for some statistical applications, like monte-carlo techniques. but knuth's is by no means the last word on the subject. btw, for cryptographic purposes, the received wisdom is that there is NO adequate test for randomness; if an rng passes lots of tests, that's very nice, but the presumption is that the variable's deterministic structure is simply hidden, and that the clever-enough test was not yet applied or devised. nevertheless, in the cryptographic field, the list of tests used is long. typically, you design the test to probe the weaknesses of a specific rng algorithm. period tests, runs tests, and substring-interarrival tests are common, and some people like entropy estimates. one of the trusted names in the crypto-rng literature is marsaglia; he has published extensively on the subject of rng-testing. i don't know what the graphics literature on rngs is like; i only know that if you want to simulate textured surfaces, like grass, a bad rng makes a striped texture. be forwarned: the rng literature is amazingly vast, with a low signal- to-noise ratio. it seems that everyone thinks he can design a "good" rng. btw, i favor hardware rngs. -don davis openvision technologies cambridge, ma

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real live Detweiler messages- anyone?
by jamiel＠sybase.com 17 Dec '03

17 Dec '03

I have a writing assignment coming up (nothing to do with much that is talked about on this list), and some example posts by Detweiler could be really handy as references. I have one from a long time ago, but could use some others- anybody save any for posterity? If so, could you forward me a couple of juicy ones? thanks- -j -- "Blah Blah Blah" ___________________________________________________________________ Jamie Lawrence <jamiel(a)sybase.com>

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Re: (fwd) Re: BSD random() - any good (source included)?
by jamiel＠sybase.com 17 Dec '03

17 Dec '03

At 3:20 PM 07/07/94 -0500, Jim choate wrote 69K of forwards (so far) that I would much rather look at in sci.math or sci.stat.math than in my mailbox, unrequested. Didn't we have a little forwarding talk recently enough for your avarage televangelist viewer to remember it? Kindly cut it out. -j -- "Blah Blah Blah" ___________________________________________________________________ Jamie Lawrence <jamiel(a)sybase.com>

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(fwd) Random Numbers - CHIKSN.FOR
by Jim choate 17 Dec '03

17 Dec '03

Newsgroups: sci.stat.math,sci.math,sci.math.num-analysis Path: bga.com!news.sprintlink.net!news.onramp.net!convex!cs.utexas.edu!swrinde!ihnp4.ucsd.edu!library.ucla.edu!csulb.edu!csus.edu!netcom.com!deleyd From: deleyd(a)netcom.com Subject: Random Numbers - CHIKSN.FOR Message-ID: <deleydCsIBAp.KuF(a)netcom.com> Organization: NETCOM On-line Communication Services (408 261-4700 guest) Date: Wed, 6 Jul 1994 06:56:49 GMT Lines: 526 Xref: bga.com sci.stat.math:1316 sci.math:15354 sci.math.num-analysis:3355 {Approx. 520 lines} C CHIKSN.FOR C C This is the program which impliments the chi-square test used to test C random number generators. Presented here if you would wish to play C with it yourself, maybe do some testing of your own. See the paper C "Computer Generated Random Numbers" sections 4 and 6 for an explanation C of what this program does. C C This is not polished code you put on a shelf and admire, this is code C you dig your hands into and work with to make it do what you want it to. C C The main routine is the one to tinker with. This code is meant to be C modified to suit your needs. The goal is to fill up the bins with C balls. Here's a brief outline: C C 1. ASK USER INPUT: C a. Number of dimensions? NDIM C b. Number of bins per dimension? NBINSPD C c. Total number of balls to throw at bins? NBALLS C d. Number of tests to run? NCHITESTS C e. Random number generator to use (if more than one defined) C f. SEED value to initialize generator with C C 2. CREATE ARRAY BINS and ZERO ARRAY C C 3. THROW THE BALLS AT THE BINS and CALCULATE PROBABILITY: C C LOOP (do CHITEST=1 to NCHITESTS) C zero BIN array C LOOP (do J=1 to NBALLS) C get random numbers r1,r2,...,rn) C increment BIN(r1,r2,...,rn) C ENDLOOP C CALL CHSONE to calculate chi-square probability C ENDLOOP C CALL KSONE to calculate Kolmogorov-Smirnov probability C C The main routine here is where you put a call to your random number C generator, or for speed you can attempt a direct implimentation of your C random number generator to save the overhead of a call. (It can make a C difference when you call the random number generator 100 million times C in one test). C C The main routine defines a large one-dimensional array called BINS, the C maximum size of which would depend on your account quotas and machine C specific limitations. The array BINS keeps track of how many balls have C fallen into each bin. The size of array BINS determines the maximum C number of bins a user may select for a test. (10,000,000 bins is a C typical number you may want to use if possible.) C C So steps are: C C 1. Check definition of one-dimensional array NBINS C that it's not too large for your account quotas C or system limitations. C C 2. Place your random number generator to be tested where it C bluntly says "PLACE YOUR RANDOM NUMBER GENERATOR HERE". C The output is an integer IRANDOM between 0 and NBINS-1 C (NBINS is the number of bins chosen by the user). C C Currently the program is set up to use subroutine RAN1, a portable C random number generator from the book "NUMERICAL RECIPES: The Art C of Scientific Computing". I've had trouble on our UNIX system C not making array R(97) static even though the code says to. C Compiling with the -static qualifier works. C C The random number generator being tested is used to "randomly" select a C bin for the ball to fall in, and the counter for that bin is C incremented. Note for a multi-dimensional test we calculate the C appropriate index into the linear array BINS by hand. After all the C balls are thrown we call the subroutines to do the heavy math. C C All the subroutines should be fairly standard FORTRAN-77 modified C versions of routines from the book "NUMERICAL RECIPES: The Art of C Scientific Computing" by William H. Press, Brian P. Flannery, Saul A. C Teukolsky, and William T. Vetterling, and you should look there for C further reference as to what the routines are doing. (Note: the book C comes in several programming language forms including C, PASCAL, BASIC, C as well as FORTRAN, so you can take your pick and rewrite this code in C any language you please.) C C Note: C CHIKSN.FOR is currently set up to be run by a process with a very C large page file quota (pgflquo). If you get a 'exceed quota' error C attempting to run this then all you need to do is change the line C which reads: C C INTEGER*2 BINS(20 000 000) !The bins. C C to something smaller like: C C INTEGER*2 BINS(1 000 000) !The bins. C C C To compile: C $ FORTRAN CHIKSN C $ LINK CHIKSN C or C % f77 chiksn.f !(Some UNIX F77 compilers require -save option) C C Sample run: C Test MTH$RANDOM in 3-D with 10 bins per dimension and 10 balls per bin: C C $ RUN CHIKSN C Input number of dimensions NDIM: 3 C Input number of bins per dimension NBINSPD: 10 C Total number of bins = NBINSPD**NDIM = 1000 C Minimum number of balls = 5*NBINS = 5000 C Input total number of balls NBALLS: 10000 C Input number of Chi-Square tests NCHITESTS (min=2) : 2 C Choose random number generator to test C (1) MTH$RANDOM, C (2) RANDU, C (3) ANSI C, C (4) Microsoft C C (5) Turbo Pascal C (6) DES C : 1 C Input starting SEED value: 1 C C BALLS= 10000 CHISQ= 993.0002441 PROB= 0.4524292 C BALLS= 10000 CHISQ= 974.0001831 PROB= 0.2915459 C KS D= 0.5475708 PROB= 0.5863269 C C----------------------------------------------------------------------- PROGRAM CHIKSN C Perform a CHI-SQUARE test on a sequence of sets of N random numbers C NDIM = number of dimensions C NBINSPD = number of bins per dimension C NBINS = total number of bins. NBINS = NBINSPD**NDIM C NBALLS = total number of balls. Should be at least 5*(NBINS**NDIM) C NCHITESTS = Number of chi-square tests to do. Must be 2 or more. C EBINS = Expected value for each bin. EBINS = NBALLS/NBINS C SEED = Initial seed value for random number generator C C Note 1: The maximum size of array NBINS may be determined by the users C page file quota (pgflquo in AUTHORIZE). Also, it is recommended C the user have a very large working set quota (wsquo,wsextent) C to reduce page faulting. This can greatly improve speed. C We use INTEGER*2 array here to save space. C C Note 2: The maximum number of Chi-Square tests that can be saved is C arbitrary (array SAVEPROB). The user may choose any value. C C Note 3: The user may choose any starting seed value. Some restrictions C may apply depending upon the particular random number generator C being used. For example, RANDU should always be started with C an odd value of SEED. MTH$RANDOM may be started with any value C of SEED. C C Note 4: The MTH$RANDOM generator is used by the VAX FORTRAN intrinsic C function RAN and the VAX BASIC function RND. It is defined as: C C SEED = 69069*SEED + 1 mod 2**32 C X = SEED/2**32 C C Note 5: The RANDU generator is obsolite due to very strong correlation C in 3d space. ( Prove to yourself using 65539 = 2**16 + 3 that C SEED[i+2] = 6*SEED[i+1] - 9*SEED[i] ). It is defined as: C C SEED = 65539*SEED mod 2**31 C X = SEED/2**31 C C The RANDU generator should be started with an odd value of SEED. C C Note 6: The C standard library function rand() is defined as: C C SEED = 1103515245*SEED + 12345 mod 2**32 C IX = SEED mod 2**31 C C This standard random number generator is defined in the book: C The C Programming Language C Brian W. Kernighan and Dennis M. Ritchie C Prentice Hall, 1978 C C The same generator is defined in the ANSI C version by the same C authors above, and the same generator is used in VAX C. C C Note 7: The Microsoft C version 4.0 library function rand() impliments C the following: C C SEED = 214013*SEED + 2531011 mod 2**32 C IX = bits 16-31 of SEED C C Note 8: The Turbo Pascal version 6.0 function impliments the following: C C SEED = 134775813*SEED + 1 mod 2**32 C IX = bits 16-32 of SEED C IMPLICIT NONE INTEGER NDIM !Number of dimensions INTEGER NBINS !Number of bins INTEGER NBINSPD !Number of bins per dimension INTEGER NBALLS !Number of random numbers per !chi-square test. INTEGER NCHITESTS !Number of chi-square tests to do C INTEGER*2 BINS(20 000 000) !The bins. (see note 1) INTEGER*2 BINS(200 000) !Less bins. (see note 1) REAL EBINS !Expected number of balls per bin REAL SAVEPROB(100) !Array to save results of !chi-square tests (see note 2) INTEGER*4 SEED(2) !Only SEED(1) result is ever used. INTEGER*2 W(4) !Seeds for RANDU EQUIVALENCE(SEED,W) !for RANDU COMMON / SEEDSTORE / SEED INTEGER I,J,K,MRANDO,NBYTES,CLEAR,CHITEST,INDEX,IRANDOM,NCLEAR REAL*4 FRANDOM, RRANDOM CHARACTER*8 TIMEBUF EQUIVALENCE (IRANDOM,FRANDOM) REAL FOR$IRAN !The RANDU random number generator REAL RAND !UNIX rand() INTEGER*4 xrand !BSD random() REAL RAN1 !test generator supplied REAL D INTEGER JISHFT,IRANDOM2,COUNT REAL RANDES !DES FUNCTION (not supplied) INTEGER KEY(2) REAL CHSQ,PROB !Chi-square value, !chi-square probability REAL*4 FNBINSPD !float(NBINSPD) REAL*4 TWO31F REAL*4 TWO16F REAL*4 TWO15F TWO31F = 2.0**31.0 TWO16F = 2.0**16.0 TWO15F = 2.0**15.0 C*DES KEY(1) = 12345 !Choose any number you want C*DES KEY(2) = 678901 !to initialize DES with C*DES CALL DES_INIT(KEY) !DES code not included. 104 FORMAT(' Input number of dimensions NDIM: ',$) 100 FORMAT(' Input number of bins per dimension NBINSPD: ',$) 105 FORMAT(' Total number of bins = NBINSPD**NDIM = ',I) 106 FORMAT(' Minimum number of balls = 5*NBINS = ',I) 101 FORMAT(' Input total number of balls NBALLS: ',$) 103 FORMAT(' Input number of Chi-Square tests NCHITESTS (min=2) : ',$) 102 FORMAT(' Choose random number generator to test'/, 1 ' /*(1)*/ xrand(),'/ 1 ' /*(2)*/ UNIX rand(),'/ 1 ' /*(3)*/ MTH$RANDOM,'/ 2 ' /*(4)*/ RANDU,'/ 3 ' /*(5)*/ ANSI C,'/ 4 ' /*(6)*/ Microsoft C'/ 5 ' /*(7)*/ Turbo Pascal'/ 7 ' /*(8)*/ DES'/ 8 ' (9) another random number generator (choose this one)'/ 6 ' : ',$) 107 FORMAT(' Input starting SEED value: ',$) 200 FORMAT(BN,I) C ***GET USER INPUT*** 10 WRITE(6,104) !Input number of dimensions READ(5,200) NDIM WRITE(6,100) !Input number of bins per dimension READ(5,200) NBINSPD FNBINSPD = FLOAT(NBINSPD) NBINS = NBINSPD**NDIM !Calculate total number of bins WRITE(6,105) NBINS !Total number of bins is... WRITE(6,106) 5*NBINS !Minimum number of balls is... WRITE(6,101) !Input total number of balls READ(5,200) NBALLS WRITE(6,103) !Input number of chi-square tests to do READ(5,200) NCHITESTS WRITE(6,102) !Choose random number generator to test READ(5,200) MRANDO WRITE(6,107) !Starting SEED value READ(5,200) SEED(1) SEED(2) = 1 !Used only if random number generator !uses bigger than 32 bits C INITIALIZE GENERATOR IF NEEDED C*XRAND CALL sxrand(SEED(1)) !Initialize xrand() CALL RAN1(-SEED(1)) !Initialize RAN1 generator C Calculate expected average number of balls for each bin EBINS = FLOAT(NBALLS)/FLOAT(NBINS) C CALL TIME(TIMEBUF) C WRITE(6,201) TIMEBUF C201 FORMAT(1X,A8) DO CHITEST=1,NCHITESTS C *** ZERO BIN ARRAY *** DO I=1,NBINS BINS(I) = 0 ENDDO C*VMS !Quickly set BINS(k) = 0, k=1,...NBINS C*VMS !Does the equivalent of above C*VMS !but a lot faster. C*VMS K = 1 C*VMS NBYTES = NBINS*2 !total number of bytes to zero C*VMS DO WHILE (NBYTES .GT. 0) C*VMS IF (NBYTES .LE. 65534) THEN !maximum number of bytes we can clear C*VMS NCLEAR = NBYTES !in one call to LIB$MOVC5 is 65535 C*VMS ELSE C*VMS NCLEAR = 65534 !max that LIB$MOVC3 can do in one call C*VMS ENDIF !(make nclear an even number so we can divide evenly by 2) C*VMS CALL LIB$MOVC5(0,0,0,NCLEAR,BINS(K)) !Clear a block of memory C*VMS NBYTES = NBYTES - NCLEAR !Number of bytes still left to clear C*VMS K = K + NCLEAR/2 !Number of bytes cleared so far + 1 C*VMS ENDDO C Main Loop DO J=1,NBALLS INDEX = 1 DO I=0,NDIM-1 C ***PLACE YOUR RANDOM NUMBER GENERATOR HERE*** C Set IRANDOM using whatever random number generator you choose C IRANDOM = integer between 0 and NBINS-1 c IF (MRANDO .EQ. 1) THEN c IRANDOM = INT( ( float( xrand() ) /TWO31F ) *FNBINSPD) c ELSEIF (MRANDO .EQ. 2) THEN c IRANDOM = INT( RAND(SEED(1)) *FNBINSPD) !UNIX rand() c ELSEIF (MRANDO .EQ. 3) THEN c IRANDOM = INT( RAN(SEED(1)) *FNBINSPD) !VMS mth$random c ELSEIF (MRANDO .EQ. 4) THEN c IRANDOM = INT( FOR$IRAN(W(2),W(1)) *FNBINSPD) !Infamous randu c ELSEIF (MRANDO .EQ. 5) THEN c CALL LIB$EMUL(1103515245,SEED,12345,SEED) !ANSI C c IRANDOM = SEED(1) .AND. '7FFFFFFF'X c IRANDOM = INT( FLOAT(IRANDOM)/(TWO31F) *FNBINSPD) c ELSEIF (MRANDO .EQ. 6) THEN c CALL LIB$EMUL(214013,SEED,2531011,SEED) !Microsoft C 4.0 c IRANDOM = W(2) .AND. '7FFF'X c IRANDOM = INT( FLOAT(IRANDOM)/(TWO15F) *FNBINSPD) c ELSEIF (MRANDO .EQ. 7) THEN c CALL LIB$EMUL(134775813,SEED,1,SEED) !Turbo Pascal 6.0 c IRANDOM = SEED(1) .AND. 'FFFF0000'X c IRANDOM = JISHFT(IRANDOM,-16) c IRANDOM = INT( FLOAT(IRANDOM)/(TWO16F) * FNBINSPD) c ELSEIF (MRANDO .EQ. 8) THEN c IRANDOM = INT( RANDES() * FNBINSPD ) !DES (not supplied) c ELSEIF (MRANDO .EQ. 9) THEN IRANDOM = INT( RAN1(SEED(1)) * FNBINSPD ) c ENDIF C Calculate index by hand. INDEX = INDEX + IRANDOM*(NBINSPD**I) ENDDO BINS(INDEX) = BINS(INDEX) + 1 !ball fell in this bin C IF ( MOD(J, 1 000 000) .EQ. 0 ) THEN C CALL TIME(TIMEBUF) C WRITE(6,302) J, TIMEBUF 302 FORMAT(1X,'AT BALL:',I,3X,'TIME=',A8) C WRITE(6,303) SEED(2), SEED(1) 303 FORMAT(1X,'HEX: SEED(2)= ',Z,' SEED(1)= ',Z) C WRITE(6,304) SEED(2), SEED(1) 304 FORMAT(1X,'DEC: SEED(2)= ',I,' SEED(1)= ',I) C ENDIF ENDDO 400 CALL CHSONE(BINS,EBINS,NBINS,CHSQ,PROB) SAVEPROB(CHITEST) = PROB WRITE(6,1) NBALLS,CHSQ,PROB 1 FORMAT(' BALLS=',I,' CHISQ=',F,' PROB=',F) ENDDO C Now see if all the chi-square values are chi-square distributed: IF (NCHITESTS .GT. 1) THEN CALL KSONE(SAVEPROB,NCHITESTS,D,PROB) WRITE(6,2) D,PROB 2 FORMAT(1X,'KS D=',F,' PROB=',F) ENDIF END C============================================================================ C From book NUMERICAL RECIPES: The Art of Scientific Computing C Here for demonstration purposes C Replace this with whatever random number generator you want to test C Initialize with negative number FUNCTION RAN1(IDUM) REAL R(97) SAVE R !(Some UNIX F77 compilers require -save option on compile) PARAMETER (M1=259200,IA1=7141,IC1=54773,RM1=3.8580247E-6) PARAMETER (M2=134456,IA2=8121,IC2=28411,RM2=7.4373773E-6) PARAMETER (M3=243000,IA3=4561,IC3=51349) DATA IFF /0/ IF (IDUM.LT.0.OR.IFF.EQ.0) THEN IFF=1 IX1=MOD(IC1-IDUM,M1) IX1=MOD(IA1*IX1+IC1,M1) IX2=MOD(IX1,M2) IX1=MOD(IA1*IX1+IC1,M1) IX3=MOD(IX1,M3) DO 11 J=1,97 IX1=MOD(IA1*IX1+IC1,M1) IX2=MOD(IA2*IX2+IC2,M2) R(J)=(FLOAT(IX1)+FLOAT(IX2)*RM2)*RM1 11 CONTINUE IDUM=1 ENDIF IX1=MOD(IA1*IX1+IC1,M1) IX2=MOD(IA2*IX2+IC2,M2) IX3=MOD(IA3*IX3+IC3,M3) J=1+(97*IX3)/M3 IF(J.GT.97.OR.J.LT.1)PAUSE write(1,100) R write(1,102) R(J) 100 format(f) 102 format(1x,'RAN1 = ', F) RAN1=R(J) R(J)=(FLOAT(IX1)+FLOAT(IX2)*RM2)*RM1 RETURN END C---------------------------------------------------------------------------- C CALCULATE THE CHI-SQUARE PROBABILITY. SINCE NBINS IS LARGE, IT IS JUST C THE CUMULATIVE GAUSSIAN DISTRIBUTION AFTER WE NORMALIZE THE VARIABLES. C OR ERROR FUNCTION. FUNCTION CHIPROB(NBINS,CHISQ) C Formula is the inverse of one given in Knuth for going the other way. INTEGER NBINS,DF REAL*4 CHISQ,Z DF = NBINS-1 Z = ( SQRT(24.0*CHISQ - 6.0*DF + 16.0) - 3*SQRT(2.0*DF) ) / 4.0 CHIPROB = ERF(Z) RETURN END FUNCTION ERF(X) C Return approximation to the complimentary error function erfc(X). C Return is not normalized err function. See book for details. C Adapted from book NUMERICAL RECIPES: The Art of Scientific Computing C Modified to return normalized error function erf(X) C (It's a polynomial approximation) REAL ERFCC,Z,T Z=ABS(X/1.414213) !Normalize T=1./(1.+0.5*Z) ERFCC=T*EXP(-Z*Z-1.26551223+T*(1.00002368+T*(.37409196+ * T*(.09678418+T*(-.18628806+T*(.27886807+T*(-1.13520398+ * T*(1.48851587+T*(-.82215223+T*.17087277))))))))) IF (X.LT.0.) ERFCC=2.-ERFCC ERF = 1.0 - ERFCC/2.0 !Normalize and compliment RETURN END C---------------------------------------------------------------------------- C THE FOLLOWING SUBROUTINES CALCULATE THE CHI-SQUARE VALUE: SUBROUTINE CHSONE(BINS,EBINS,NBINS,CHSQ,PROB) C Adapted from book NUMERICAL RECIPES: The Art of Scientific Computing INTEGER NBINS INTEGER*2 BINS(NBINS) REAL EBINS,CHSQ,PROB CHSQ=0. IF(EBINS.LE.0.) PAUSE 'CHSONE: EBINS must be > 0' DO 11 J=1,NBINS CHSQ=CHSQ+(BINS(J)-EBINS)**2/EBINS 11 CONTINUE PROB=CHIPROB(NBINS,CHSQ) RETURN END C============================================================================ C THE FOLLOWING SUBROUTINES CALCULATE THE KOLMOGOROV-SMIRNOV PROBABILITY SUBROUTINE KSONE(DATA,N,D,PROB) C Adapted from book NUMERICAL RECIPES: The Art of Scientific Computing C DF - degrees of freedom. Passsed to FUNC INTEGER N REAL DATA(N) REAL D,PROB CALL PIKSRT(N,DATA) EN=N D=0. FO=0. DO 11 J=1,N FN=J/EN FF=DATA(J) DT=AMAX1(ABS(FO-FF),ABS(FN-FF)) IF(DT.GT.D)D=DT FO=FN 11 CONTINUE PROB=PROBKS(SQRT(EN)*D) RETURN END C---------------------------------------------------------------------------- FUNCTION PROBKS(ALAM) C Adapted from book NUMERICAL RECIPES: The Art of Scientific Computing C Note the routine in the Numerical Recipes book erronously returns C 1 instead of 0 for large values of ALAM. PARAMETER (EPS1=0.001, EPS2=1.E-8) A2=-2.*ALAM**2 FAC=2. PROBKS=0. TERMBF=0. DO 11 J=1,100 TERM=FAC*EXP(A2*J**2) PROBKS=PROBKS+TERM C Error in Numerical Recipes book. Terminate if TERM underflows. C** IF(ABS(TERM).LT.EPS1*TERMBF.OR.ABS(TERM).LT.EPS2*PROBKS)RETURN IF(ABS(TERM).LE.EPS1*TERMBF.OR.ABS(TERM).LE.EPS2*PROBKS)RETURN FAC=-FAC TERMBF=ABS(TERM) 11 CONTINUE PROBKS=1.0 RETURN END C---------------------------------------------------------------------------- SUBROUTINE PIKSRT(N,ARR) C Adapted from book NUMERICAL RECIPES: The Art of Scientific Computing C See book for details. INTEGER N REAL ARR(N) DO 12 J=2,N A=ARR(J) DO 11 I=J-1,1,-1 IF(ARR(I).LE.A)GO TO 10 ARR(I+1)=ARR(I) 11 CONTINUE I=0 10 ARR(I+1)=A 12 CONTINUE RETURN END

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(fwd) New ITAR Indictment
by Anonymous User 17 Dec '03

17 Dec '03

Are you serious? (fwd) From: chuckles(a)MCS.COM (Jason Skiles) Newsgroups: alt.security.pgp,comp.org.eff.talk,comp.org.cpsr.talk Subject: New ITAR Indictment Date: 8 Jul 1994 01:02:56 -0500 Reprinted with permission from the Chicago Sun-Tribune, 5 July 1994: >From Sun-Tribune Wires Washington, D.C.- In a Rose Garden press conference early this morning, Justice Department spokesmen announced the indictment of a Washington, DC. computer bulletin board system (BBS) operator, one Mr. Gil Bates, for violation of ITAR munitions export laws in connection with the operation of the infamous 'We got yer nudes here' BBS. According to federal authorities, many of the graphics files, or 'gif' files, named for their storage format, contained, when examined with a common hex editor, the value 0xAAAA, which can be used to encrypt data in such a way as to make it extremely difficult for intelligence and law enforcement agencies to recover the encrypted data. "0xAAAA first came to our attention a few weeks ago," explained Deputncrypted] file, by using a complicated algorithm known as 'exclusive or' and a 'mask' or encryption key, of, for example, "0xAAAA." Agents were stunned. "It's an entirely new and sinister turn of events in the field," said Miller. "We'd be helpless against such an attack." Miller went on to explain just how secure such a scheme would be. "When we need to crack some encrypted data, for example, email someone sends to his lawyer that we think may contain incriminating evidence," we usually just hand it to thenstitutional issues involved there, but we're working on it." He refused to elaborate. Once the technique was known, news spread quickly throughout the law-enforcement community. "This was a shot across the bow, a real wake-up call for us," said one Justice Department source. "We moved immediately, meeting with the vice-president and a professor from Georgetown. They were reluctant at first, but we mentioned organized crime and terrorists and they came around to our point of view." But why forbid the 'mask' or 'key' instead of the algorithm itself, the 'exclusive-or' technique? "That's sort of a funny story," explained Miller. "We were going to at first, but it turns out that the Clipper and Capstone chips [part of a government-designed key escrow system] make use of the algorithm in places. Of course, there were a few 0xAAAA's too, but the NSA assures us they've got a workaround." Bates loudly proclaims his innocence. "This is stupid, really stupid. It's just a 16-bit value, like any other. They can't restrict it. I'm... I'm at a loss. This is just too stupid to comment on." The case got weaker late this afternoon when it was revealed that the file in question didn't actually leave the country, but was retrieved by an FBI agent in Virginia. "Obviously this compromises our case somewhat," admitted Miller, "since Virginia isn't a foreign country. But someone in another country could have done the same thing, easily. That should count for something." Schneider noted that "Even though we'll probably have to drop the ITAR case, we did come up with something. He had a copy of PGP [a 'guerilla freeware' encryption package popular with subversives and criminals] and some files he'd protected with it." "We think they were maybe lists of children he an FBI agent in Virginia. "Obviously this compromises our case somewhat," admitted Miller, "since Virginia isn't a foreign country. But someone in another country could have done the same thing, easily. That should count for something." Schneider noted that "Even though we'll probably have to drop the ITAR case, we did come up with something. He had a copy of PGP [a 'guerilla freeware' encryption package popular with subversives and criminals] and some files he'd protected with it." "We think they were maybe lists of children he abused, or something," says Schneider. "Yeah, or something," added Miller. [Pre-flame apologies go out to those who object to the inclusion of 'serious' groups in the newsgroups list. If you know any silly ones where this would be more welcome, feel free to send it along.] ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ | Jason "Chuckles" Skiles | <Insert a clever quotation here.> | | chuckles(a)mcs.com | - <misattribute it here> | ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ | Any opinions I express are also those of every single school, company, | | and organization I've ever been in any way associated with. Honest. | ++++++++++++++++++++++++++finger for PGP public key+++++++++++++++++++++++++ ------------ To respond to the sender of this message, send mail to remailer(a)soda.berkeley.edu, starting your message with the following 8 lines: :: Response-Key: ideaclipper ====Encrypted-Sender-Begin==== MI@```%ES^P;+]AB?X9TW6\8WR:2P&2%`$A:^X<=%.A'J%;"Y7E2J[QT=&)]L M0`F:L=MI*O?R!?N6/E3TTZ6WF^B=ZP9][Y)B)J)4PF/%M3XOVYT^Y;!E*9Y9 $\U3XF@`` ====Encrypted-Sender-End====

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Re: (fwd) Re: BSD random() - any good (source included)
by jamiel＠sybase.com 17 Dec '03

17 Dec '03

At 1:11 AM 07/08/94 +0200, Nobody wrote: >I guess cypherpunks would rather not write or even read code, but >simply gossip about usenet kooks and pedophiles. Nobody either - Is baiting for fun or - Actually thinks mailbombing 700+ people with easily accessible information on a subject tangental to this list is a Good Idea, and - doesn't have the slightest clue what proper conduct in a public forum is. For Nobody's sake, I hope it is the former. But if it happens to be the latter- Nobody, write me with an address I can reach you at and I'll send you lots and lots of code for you to read, every day, if you choose. That will help your productivity *immensely*. >c@lib@n -j -- "Blah Blah Blah" ___________________________________________________________________ Jamie Lawrence <jamiel(a)sybase.com>

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