Provided by: dieharder_3.31.1.1-1build1_amd64 
NAME
dieharder - A testing and benchmarking tool for random number generators.
SYNOPSIS
dieharder [-a] [-d dieharder test number] [-f filename] [-B]
[-D output flag [-D output flag] ... ] [-F] [-c separator]
[-g generator number or -1] [-h] [-k ks_flag] [-l]
[-L overlap] [-m multiply_p] [-n ntuple]
[-p number of p samples] [-P Xoff]
[-o filename] [-s seed strategy] [-S random number seed]
[-n ntuple] [-p number of p samples] [-o filename]
[-s seed strategy] [-S random number seed]
[-t number of test samples] [-v verbose flag]
[-W weak] [-X fail] [-Y Xtrategy]
[-x xvalue] [-y yvalue] [-z zvalue]
dieharder OPTIONS
-a runs all the tests with standard/default options to create a
user-controllable report. To control the formatting of the report, see -D below.
To control the power of the test (which uses default values for tsamples that
cannot generally be varied and psamples which generally can) see -m below as a
"multiplier" of the default number of psamples (used only in a -a run).
-d test number - selects specific diehard test.
-f filename - generators 201 or 202 permit either raw binary or
formatted ASCII numbers to be read in from a file for testing. generator 200 reads
in raw binary numbers from stdin. Note well: many tests with default parameters
require a lot of rands! To see a sample of the (required) header for ASCII
formatted input, run
dieharder -o -f example.input -t 10
and then examine the contents of example.input. Raw binary input reads 32 bit
increments of the specified data stream. stdin_input_raw accepts a pipe from a raw
binary stream.
-B binary mode (used with -o below) causes output rands to be written in raw binary, not
formatted ascii.
-D output flag - permits fields to be selected for inclusion in
dieharder output. Each flag can be entered as a binary number that turns on a
specific output field or header or by flag name; flags are aggregated. To see all
currently known flags use the -F command.
-F - lists all known flags by name and number.
-c table separator - where separator is e.g. ',' (CSV) or ' ' (whitespace).
-g generator number - selects a specific generator for testing. Using
-g -1 causes all known generators to be printed out to the display.
-h prints context-sensitive help -- usually Usage (this message) or a
test synopsis if entered as e.g. dieharder -d 3 -h.
-k ks_flag - ks_flag
0 is fast but slightly sloppy for psamples > 4999 (default).
1 is MUCH slower but more accurate for larger numbers of psamples.
2 is slower still, but (we hope) accurate to machine precision for any number of
psamples up to some as yet unknown numerical upper limit (it has been tested out to
at least hundreds of thousands).
3 is kuiper ks, fast, quite inaccurate for small samples, deprecated.
-l list all known tests.
-L overlap
1 (use overlap, default)
0 (don't use overlap)
in operm5 or other tests that support overlapping and non-overlapping sample modes.
-m multiply_p - multiply default # of psamples in -a(ll) runs to crank
up the resolution of failure. -n ntuple - set ntuple length for tests on short bit
strings that permit the length to be varied (e.g. rgb bitdist).
-o filename - output -t count random numbers from current generator to file.
-p count - sets the number of p-value samples per test (default 100).
-P Xoff - sets the number of psamples that will cumulate before deciding
that a generator is "good" and really, truly passes even a -Y 2 T2D run. Currently
the default is 100000; eventually it will be set from AES-derived T2D test failure
thresholds for fully automated reliable operation, but for now it is more a
"boredom" threshold set by how long one might reasonably want to wait on any given
test run.
-S seed - where seed is a uint. Overrides the default random seed
selection. Ignored for file or stdin input.
-s strategy - if strategy is the (default) 0, dieharder reseeds (or
rewinds) once at the beginning when the random number generator is selected and
then never again. If strategy is nonzero, the generator is reseeded or rewound at
the beginning of EACH TEST. If -S seed was specified, or a file is used, this
means every test is applied to the same sequence (which is useful for validation
and testing of dieharder, but not a good way to test rngs). Otherwise a new random
seed is selected for each test.
-t count - sets the number of random entities used in each test, where
possible. Be warned -- some tests have fixed sample sizes; others are variable but
have practical minimum sizes. It is suggested you begin with the values used in -a
and experiment carefully on a test by test basis.
-W weak - sets the "weak" threshold to make the test(s) more or less
forgiving during e.g. a test-to-destruction run. Default is currently 0.005.
-X fail - sets the "fail" threshold to make the test(s) more or less
forgiving during e.g. a test-to-destruction run. Default is currently 0.000001,
which is basically "certain failure of the null hypothesis", the desired mode of
reproducible generator failure.
-Y Xtrategy - the Xtrategy flag controls the new "test to failure" (T2F)
modes. These flags and their modes act as follows:
0 - just run dieharder with the specified number of tsamples and psamples, do not
dynamically modify a run based on results. This is the way it has always run, and
is the default.
1 - "resolve ambiguity" (RA) mode. If a test returns "weak", this is an
undesired result. What does that mean, after all? If you run a long test series,
you will see occasional weak returns for a perfect generators because p is
uniformly distributed and will appear in any finite interval from time to time.
Even if a test run returns more than one weak result, you cannot be certain that
the generator is failing. RA mode adds psamples (usually in blocks of 100) until
the test result ends up solidly not weak or proceeds to unambiguous failure. This
is morally equivalent to running the test several times to see if a weak result is
reproducible, but eliminates the bias of personal judgement in the process since
the default failure threshold is very small and very unlikely to be reached by
random chance even in many runs.
This option should only be used with -k 2.
2 - "test to destruction" mode. Sometimes you just want to know where or if a
generator will .I ever fail a test (or test series). -Y 2 causes psamples to be
added 100 at a time until a test returns an overall pvalue lower than the failure
threshold or a specified maximum number of psamples (see -P) is reached.
Note well! In this mode one may well fail due to the alternate null hypothesis --
the test itself is a bad test and fails! Many dieharder tests, despite our best
efforts, are numerically unstable or have only approximately known target
statistics or are straight up asymptotic results, and will eventually return a
failing result even for a gold-standard generator (such as AES), or for the
hypercautious the XOR generator with AES, threefish, kiss, all loaded at once and
xor'd together. It is therefore safest to use this mode .I comparatively,
executing a T2D run on AES to get an idea of the test failure threshold(s)
(something I will eventually do and publish on the web so everybody doesn't have to
do it independently) and then running it on your target generator. Failure with
numbers of psamples within an order of magnitude of the AES thresholds should
probably be considered possible test failures, not generator failures. Failures at
levels significantly less than the known gold standard generator failure thresholds
are, of course, probably failures of the generator.
This option should only be used with -k 2.
-v verbose flag -- controls the verbosity of the output for debugging
only. Probably of little use to non-developers, and developers can read the
enum(s) in dieharder.h and the test sources to see which flag values turn on output
on which routines. 1 is result in a highly detailed trace of program activity.
-x,-y,-z number - Some tests have parameters that can safely be varied
from their default value. For example, in the diehard birthdays test, one can vary
the number of length, which can also be varied. -x 2048 -y 30 alters these two
values but should still run fine. These parameters should be documented internally
(where they exist) in the e.g. -d 0 -h visible notes.
NOTE WELL: The assessment(s) for the rngs may, in fact, be completely incorrect or
misleading. There are still "bad tests" in dieharder, although we are working to
fix and improve them (and try to document them in the test descriptions visible
with -g testnumber -h). In particular, 'Weak' pvalues should occur one test in two
hundred, and 'Failed' pvalues should occur one test in a million with the default
thresholds - that's what p MEANS. Use them at your Own Risk! Be Warned!
Or better yet, use the new -Y 1 and -Y 2 resolve ambiguity or test to destruction
modes above, comparing to similar runs on one of the as-good-as-it-gets
cryptographic generators, AES or threefish.
DESCRIPTION
dieharder
Welcome to the current snapshot of the dieharder random number tester. It encapsulates
all of the Gnu Scientific Library (GSL) random number generators (rngs) as well as a
number of generators from the R statistical library, hardware sources such as
/dev/*random, "gold standard" cryptographic quality generators (useful for testing
dieharder and for purposes of comparison to new generators) as well as generators
contributed by users or found in the literature into a single harness that can time them
and subject them to various tests for randomness. These tests are variously drawn from
George Marsaglia's "Diehard battery of random number tests", the NIST Statistical Test
Suite, and again from other sources such as personal invention, user contribution, other
(open source) test suites, or the literature.
The primary point of dieharder is to make it easy to time and test (pseudo)random number
generators, including both software and hardware rngs, with a fully open source tool. In
addition to providing "instant" access to testing of all built-in generators, users can
choose one of three ways to test their own random number generators or sources: a unix
pipe of a raw binary (presumed random) bitstream; a file containing a (presumed random)
raw binary bitstream or formatted ascii uints or floats; and embedding your generator in
dieharder's GSL-compatible rng harness and adding it to the list of built-in generators.
The stdin and file input methods are described below in their own section, as is suggested
"best practice" for newbies to random number generator testing.
An important motivation for using dieharder is that the entire test suite is fully Gnu
Public License (GPL) open source code and hence rather than being prohibited from "looking
underneath the hood" all users are openly encouraged to critically examine the dieharder
code for errors, add new tests or generators or user interfaces, or use it freely as is to
test their own favorite candidate rngs subject only to the constraints of the GPL. As a
result of its openness, literally hundreds of improvements and bug fixes have been
contributed by users to date, resulting in a far stronger and more reliable test suite
than would have been possible with closed and locked down sources or even open sources
(such as STS) that lack the dynamical feedback mechanism permitting corrections to be
shared.
Even small errors in test statistics permit the alternative (usually unstated) null
hypothesis to become an important factor in rng testing -- the unwelcome possibility that
your generator is just fine but it is the test that is failing. One extremely useful
feature of dieharder is that it is at least moderately self validating. Using the "gold
standard" aes and threefish cryptographic generators, you can observe how these generators
perform on dieharder runs to the same general degree of accuracy that you wish to use on
the generators you are testing. In general, dieharder tests that consistently fail at any
given level of precision (selected with e.g. -a -m 10) on both of the gold standard rngs
(and/or the better GSL generators, mt19937, gfsr4, taus) are probably unreliable at that
precision and it would hardly be surprising if they failed your generator as well.
Experts in statistics are encouraged to give the suite a try, perhaps using any of the
example calls below at first and then using it freely on their own generators or as a
harness for adding their own tests. Novices (to either statistics or random number
generator testing) are strongly encouraged to read the next section on p-values and the
null hypothesis and running the test suite a few times with a more verbose output report
to learn how the whole thing works.
QUICK START EXAMPLES
Examples for how to set up pipe or file input are given below. However, it is recommended
that a user play with some of the built in generators to gain familiarity with dieharder
reports and tests before tackling their own favorite generator or file full of possibly
random numbers.
To see dieharder's default standard test report for its default generator (mt19937) simply
run:
dieharder -a
To increase the resolution of possible failures of the standard -a(ll) test, use the -m
"multiplier" for the test default numbers of pvalues (which are selected more to make a
full test run take an hour or so instead of days than because it is truly an exhaustive
test sequence) run:
dieharder -a -m 10
To test a different generator (say the gold standard AES_OFB) simply specify the generator
on the command line with a flag:
dieharder -g 205 -a -m 10
Arguments can be in any order. The generator can also be selected by name:
dieharder -g AES_OFB -a
To apply only the diehard opso test to the AES_OFB generator, specify the test by name or
number:
dieharder -g 205 -d 5
or
dieharder -g 205 -d diehard_opso
Nearly every aspect or field in dieharder's output report format is user-selectable by
means of display option flags. In addition, the field separator character can be selected
by the user to make the output particularly easy for them to parse (-c ' ') or import into
a spreadsheet (-c ','). Try:
dieharder -g 205 -d diehard_opso -c ',' -D test_name -D pvalues
to see an extremely terse, easy to import report or
dieharder -g 205 -d diehard_opso -c ' ' -D default -D histogram -D description
to see a verbose report good for a "beginner" that includes a full description of each
test itself.
Finally, the dieharder binary is remarkably autodocumenting even if the man page is not
available. All users should try the following commands to see what they do:
dieharder -h
(prints the command synopsis like the one above).
dieharder -a -h
dieharder -d 6 -h
(prints the test descriptions only for -a(ll) tests or for the specific test indicated).
dieharder -l
(lists all known tests, including how reliable rgb thinks that they are as things stand).
dieharder -g -1
(lists all known rngs).
dieharder -F
(lists all the currently known display/output control flags used with -D).
Both beginners and experts should be aware that the assessment provided by dieharder in
its standard report should be regarded with great suspicion. It is entirely possible for
a generator to "pass" all tests as far as their individual p-values are concerned and yet
to fail utterly when considering them all together. Similarly, it is probable that a rng
will at the very least show up as "weak" on 0, 1 or 2 tests in a typical -a(ll) run, and
may even "fail" 1 test one such run in 10 or so. To understand why this is so, it is
necessary to understand something of rng testing, p-values, and the null hypothesis!
P-VALUES AND THE NULL HYPOTHESIS
dieharder returns "p-values". To understand what a p-value is and how to use it, it is
essential to understand the null hypothesis, H0.
The null hypothesis for random number generator testing is "This generator is a perfect
random number generator, and for any choice of seed produces a infinitely long, unique
sequence of numbers that have all the expected statistical properties of random numbers,
to all orders". Note well that we know that this hypothesis is technically false for all
software generators as they are periodic and do not have the correct entropy content for
this statement to ever be true. However, many hardware generators fail a priori as well,
as they contain subtle bias or correlations due to the deterministic physics that
underlies them. Nature is often unpredictable but it is rarely random and the two words
don't (quite) mean the same thing!
The null hypothesis can be practically true, however. Both software and hardware
generators can be "random" enough that their sequences cannot be distinguished from random
ones, at least not easily or with the available tools (including dieharder!) Hence the
null hypothesis is a practical, not a theoretically pure, statement.
To test H0 , one uses the rng in question to generate a sequence of presumably random
numbers. Using these numbers one can generate any one of a wide range of test statistics
-- empirically computed numbers that are considered random samples that may or may not be
covariant subject to H0, depending on whether overlapping sequences of random numbers are
used to generate successive samples while generating the statistic(s), drawn from a known
distribution. From a knowledge of the target distribution of the statistic(s) and the
associated cumulative distribution function (CDF) and the empirical value of the randomly
generated statistic(s), one can read off the probability of obtaining the empirical result
if the sequence was truly random, that is, if the null hypothesis is true and the
generator in question is a "good" random number generator! This probability is the "p-
value" for the particular test run.
For example, to test a coin (or a sequence of bits) we might simply count the number of
heads and tails in a very long string of flips. If we assume that the coin is a "perfect
coin", we expect the number of heads and tails to be binomially distributed and can easily
compute the probability of getting any particular number of heads and tails. If we
compare our recorded number of heads and tails from the test series to this distribution
and find that the probability of getting the count we obtained is very low with, say, way
more heads than tails we'd suspect the coin wasn't a perfect coin. dieharder applies this
very test (made mathematically precise) and many others that operate on this same
principle to the string of random bits produced by the rng being tested to provide a
picture of how "random" the rng is.
Note that the usual dogma is that if the p-value is low -- typically less than 0.05 -- one
"rejects" the null hypothesis. In a word, it is improbable that one would get the result
obtained if the generator is a good one. If it is any other value, one does not "accept"
the generator as good, one "fails to reject" the generator as bad for this particular
test. A "good random number generator" is hence one that we haven't been able to make
fail yet!
This criterion is, of course, naive in the extreme and cannot be used with dieharder! It
makes just as much sense to reject a generator that has p-values of 0.95 or more! Both of
these p-value ranges are equally unlikely on any given test run, and should be returned
for (on average) 5% of all test runs by a perfect random number generator. A generator
that fails to produce p-values less than 0.05 5% of the time it is tested with different
seeds is a bad random number generator, one that fails the test of the null hypothesis.
Since dieharder returns over 100 pvalues by default per test, one would expect any
perfectly good rng to "fail" such a naive test around five times by this criterion in a
single dieharder run!
The p-values themselves, as it turns out, are test statistics! By their nature, p-values
should be uniformly distributed on the range 0-1. In 100+ test runs with independent
seeds, one should not be surprised to obtain 0, 1, 2, or even (rarely) 3 p-values less
than 0.01. On the other hand obtaining 7 p-values in the range 0.24-0.25, or seeing that
70 of the p-values are greater than 0.5 should make the generator highly suspect! How can
a user determine when a test is producing "too many" of any particular value range for p?
Or too few?
Dieharder does it for you, automatically. One can in fact convert a set of p-values into
a p-value by comparing their distribution to the expected one, using a Kolmogorov-Smirnov
test against the expected uniform distribution of p.
These p-values obtained from looking at the distribution of p-values should in turn be
uniformly distributed and could in principle be subjected to still more KS tests in
aggregate. The distribution of p-values for a good generator should be idempotent, even
across different test statistics and multiple runs.
A failure of the distribution of p-values at any level of aggregation signals trouble. In
fact, if the p-values of any given test are subjected to a KS test, and those p-values are
then subjected to a KS test, as we add more p-values to either level we will either
observe idempotence of the resulting distribution of p to uniformity, or we will observe
idempotence to a single p-value of zero! That is, a good generator will produce a roughly
uniform distribution of p-values, in the specific sense that the p-values of the
distributions of p-values are themselves roughly uniform and so on ad infinitum, while a
bad generator will produce a non-uniform distribution of p-values, and as more p-values
drawn from the non-uniform distribution are added to its KS test, at some point the
failure will be absolutely unmistakeable as the resulting p-value approaches 0 in the
limit. Trouble indeed!
The question is, trouble with what? Random number tests are themselves complex
computational objects, and there is a probability that their code is incorrectly framed or
that roundoff or other numerical -- not methodical -- errors are contributing to a
distortion of the distribution of some of the p-values obtained. This is not an idle
observation; when one works on writing random number generator testing programs, one is
always testing the tests themselves with "good" (we hope) random number generators so that
egregious failures of the null hypothesis signal not a bad generator but an error in the
test code. The null hypothesis above is correctly framed from a theoretical point of
view, but from a real and practical point of view it should read: "This generator is a
perfect random number generator, and for any choice of seed produces a infinitely long,
unique sequence of numbers that have all the expected statistical properties of random
numbers, to all orders and this test is a perfect test and returns precisely correct p-
values from the test computation." Observed "failure" of this joint null hypothesis H0'
can come from failure of either or both of these disjoint components, and comes from the
second as often or more often than the first during the test development process. When
one cranks up the "resolution" of the test (discussed next) to where a generator starts to
fail some test one realizes, or should realize, that development never ends and that new
test regimes will always reveal new failures not only of the generators but of the code.
With that said, one of dieharder's most significant advantages is the control that it
gives you over a critical test parameter. From the remarks above, we can see that we
should feel very uncomfortable about "failing" any given random number generator on the
basis of a 5%, or even a 1%, criterion, especially when we apply a test suite like
dieharder that returns over 100 (and climbing) distinct test p-values as of the last
snapshot. We want failure to be unambiguous and reproducible!
To accomplish this, one can simply crank up its resolution. If we ran any given test
against a random number generator and it returned a p-value of (say) 0.007328, we'd be
perfectly justified in wondering if it is really a good generator. However, the
probability of getting this result isn't really all that small -- when one uses dieharder
for hours at a time numbers like this will definitely happen quite frequently and mean
nothing. If one runs the same test again (with a different seed or part of the random
sequence) and gets a p-value of 0.009122, and a third time and gets 0.002669 -- well,
that's three 1% (or less) shots in a row and that should happen only one in a million
times. One way to clearly resolve failures, then, is to increase the number of p-values
generated in a test run. If the actual distribution of p being returned by the test is
not uniform, a KS test will eventually return a p-value that is not some ambiguous
0.035517 but is instead 0.000000, with the latter produced time after time as we rerun.
For this reason, dieharder is extremely conservative about announcing rng "weakness" or
"failure" relative to any given test. It's internal criterion for these things are
currently p < 0.5% or p > 99.5% weakness (at the 1% level total) and a considerably more
stringent criterion for failure: p < 0.05% or p > 99.95%. Note well that the ranges are
symmetric -- too high a value of p is just as bad (and unlikely) as too low, and it is
critical to flag it, because it is quite possible for a rng to be too good, on average,
and not to produce enough low p-values on the full spectrum of dieharder tests. This is
where the final kstest is of paramount importance, and where the "histogram" option can be
very useful to help you visualize the failure in the distribution of p -- run e.g.:
dieharder [whatever] -D default -D histogram
and you will see a crude ascii histogram of the pvalues that failed (or passed) any given
level of test.
Scattered reports of weakness or marginal failure in a preliminary -a(ll) run should
therefore not be immediate cause for alarm. Rather, they are tests to repeat, to watch
out for, to push the rng harder on using the -m option to -a or simply increasing -p for a
specific test. Dieharder permits one to increase the number of p-values generated for any
test, subject only to the availability of enough random numbers (for file based tests) and
time, to make failures unambiguous. A test that is truly weak at -p 100 will almost
always fail egregiously at some larger value of psamples, be it -p 1000 or -p 100000.
However, because dieharder is a research tool and is under perpetual development and
testing, it is strongly suggested that one always consider the alternative null hypothesis
-- that the failure is a failure of the test code in dieharder itself in some limit of
large numbers -- and take at least some steps (such as running the same test at the same
resolution on a "gold standard" generator) to ensure that the failure is indeed probably
in the rng and not the dieharder code.
Lacking a source of perfect random numbers to use as a reference, validating the tests
themselves is not easy and always leaves one with some ambiguity (even aes or threefish).
During development the best one can usually do is to rely heavily on these "presumed good"
random number generators. There are a number of generators that we have theoretical
reasons to expect to be extraordinarily good and to lack correlations out to some known
underlying dimensionality, and that also test out extremely well quite consistently. By
using several such generators and not just one, one can hope that those generators have
(at the very least) different correlations and should not all uniformly fail a test in the
same way and with the same number of p-values. When all of these generators consistently
fail a test at a given level, I tend to suspect that the problem is in the test code, not
the generators, although it is very difficult to be certain, and many errors in
dieharder's code have been discovered and ultimately fixed in just this way by myself or
others.
One advantage of dieharder is that it has a number of these "good generators" immediately
available for comparison runs, courtesy of the Gnu Scientific Library and user
contribution (notably David Bauer, who kindly encapsulated aes and threefish). I use
AES_OFB, Threefish_OFB, mt19937_1999, gfsr4, ranldx2 and taus2 (as well as "true random"
numbers from random.org) for this purpose, and I try to ensure that dieharder will "pass"
in particular the -g 205 -S 1 -s 1 generator at any reasonable p-value resolution out to
-p 1000 or farther.
Tests (such as the diehard operm5 and sums test) that consistently fail at these high
resolutions are flagged as being "suspect" -- possible failures of the alternative null
hypothesis -- and they are strongly deprecated! Their results should not be used to test
random number generators pending agreement in the statistics and random number community
that those tests are in fact valid and correct so that observed failures can indeed safely
be attributed to a failure of the intended null hypothesis.
As I keep emphasizing (for good reason!) dieharder is community supported. I therefore
openly ask that the users of dieharder who are expert in statistics to help me fix the
code or algorithms being implemented. I would like to see this test suite ultimately be
validated by the general statistics community in hard use in an open environment, where
every possible failure of the testing mechanism itself is subject to scrutiny and eventual
correction. In this way we will eventually achieve a very powerful suite of tools indeed,
ones that may well give us very specific information not just about failure but of the
mode of failure as well, just how the sequence tested deviates from randomness.
Thus far, dieharder has benefitted tremendously from the community. Individuals have
openly contributed tests, new generators to be tested, and fixes for existing tests that
were revealed by their own work with the testing instrument. Efforts are underway to make
dieharder more portable so that it will build on more platforms and faster so that more
thorough testing can be done. Please feel free to participate.
FILE INPUT
The simplest way to use dieharder with an external generator that produces raw binary
(presumed random) bits is to pipe the raw binary output from this generator (presumed to
be a binary stream of 32 bit unsigned integers) directly into dieharder, e.g.:
cat /dev/urandom | ./dieharder -a -g 200
Go ahead and try this example. It will run the entire dieharder suite of tests on the
stream produced by the linux built-in generator /dev/urandom (using /dev/random is not
recommended as it is too slow to test in a reasonable amount of time).
Alternatively, dieharder can be used to test files of numbers produced by a candidate
random number generators:
dieharder -a -g 201 -f random.org_bin
for raw binary input or
dieharder -a -g 202 -f random.org.txt
for formatted ascii input.
A formatted ascii input file can accept either uints (integers in the range 0 to 2^31-1,
one per line) or decimal uniform deviates with at least ten significant digits (that can
be multiplied by UINT_MAX = 2^32 to produce a uint without dropping precition), also one
per line. Floats with fewer digits will almost certainly fail bitlevel tests, although
they may pass some of the tests that act on uniform deviates.
Finally, one can fairly easily wrap any generator in the same (GSL) random number harness
used internally by dieharder and simply test it the same way one would any other internal
generator recognized by dieharder. This is strongly recommended where it is possible,
because dieharder needs to use a lot of random numbers to thoroughly test a generator. A
built in generator can simply let dieharder determine how many it needs and generate them
on demand, where a file that is too small will "rewind" and render the test results where
a rewind occurs suspect.
Note well that file input rands are delivered to the tests on demand, but if the test
needs more than are available it simply rewinds the file and cycles through it again, and
again, and again as needed. Obviously this significantly reduces the sample space and can
lead to completely incorrect results for the p-value histograms unless there are enough
rands to run EACH test without repetition (it is harmless to reuse the sequence for
different tests). Let the user beware!
BEST PRACTICE
A frequently asked question from new users wishing to test a generator they are working on
for fun or profit (or both) is "How should I get its output into dieharder?" This is a
nontrivial question, as dieharder consumes enormous numbers of random numbers in a full
test cycle, and then there are features like -m 10 or -m 100 that let one effortlessly
demand 10 or 100 times as many to stress a new generator even more.
Even with large file support in dieharder, it is difficult to provide enough random
numbers in a file to really make dieharder happy. It is therefore strongly suggested that
you either:
a) Edit the output stage of your random number generator and get it to write its
production to stdout as a random bit stream -- basically create 32 bit unsigned random
integers and write them directly to stdout as e.g. char data or raw binary. Note that
this is not the same as writing raw floating point numbers (that will not be random at all
as a bitstream) and that "endianness" of the uints should not matter for the null
hypothesis of a "good" generator, as random bytes are random in any order. Crank the
generator and feed this stream to dieharder in a pipe as described above.
b) Use the samples of GSL-wrapped dieharder rngs to similarly wrap your generator (or
calls to your generator's hardware interface). Follow the examples in the ./dieharder
source directory to add it as a "user" generator in the command line interface, rebuild,
and invoke the generator as a "native" dieharder generator (it should appear in the list
produced by -g -1 when done correctly). The advantage of doing it this way is that you
can then (if your new generator is highly successful) contribute it back to the dieharder
project if you wish! Not to mention the fact that it makes testing it very easy.
Most users will probably go with option a) at least initially, but be aware that b) is
probably easier than you think. The dieharder maintainers may be able to give you a hand
with it if you get into trouble, but no promises.
WARNING!
A warning for those who are testing files of random numbers. dieharder is a tool that
tests random number generators, not files of random numbers! It is extremely
inappropriate to try to "certify" a file of random numbers as being random just because it
fails to "fail" any of the dieharder tests in e.g. a dieharder -a run. To put it bluntly,
if one rejects all such files that fail any test at the 0.05 level (or any other), the one
thing one can be certain of is that the files in question are not random, as a truly
random sequence would fail any given test at the 0.05 level 5% of the time!
To put it another way, any file of numbers produced by a generator that "fails to fail"
the dieharder suite should be considered "random", even if it contains sequences that
might well "fail" any given test at some specific cutoff. One has to presume that passing
the broader tests of the generator itself, it was determined that the p-values for the
test involved was globally correctly distributed, so that e.g. failure at the 0.01 level
occurs neither more nor less than 1% of the time, on average, over many many tests. If
one particular file generates a failure at this level, one can therefore safely presume
that it is a random file pulled from many thousands of similar files the generator might
create that have the correct distribution of p-values at all levels of testing and
aggregation.
To sum up, use dieharder to validate your generator (via input from files or an embedded
stream). Then by all means use your generator to produce files or streams of random
numbers. Do not use dieharder as an accept/reject tool to validate the files themselves!
EXAMPLES
To demonstrate all tests, run on the default GSL rng, enter:
dieharder -a
To demonstrate a test of an external generator of a raw binary stream of bits, use the
stdin (raw) interface:
cat /dev/urandom | dieharder -g 200 -a
To use it with an ascii formatted file:
dieharder -g 202 -f testrands.txt -a
(testrands.txt should consist of a header such as:
#==================================================================
# generator mt19937_1999 seed = 1274511046
#==================================================================
type: d
count: 100000
numbit: 32
3129711816
85411969
2545911541
etc.).
To use it with a binary file
dieharder -g 201 -f testrands.bin -a
or
cat testrands.bin | dieharder -g 200 -a
An example that demonstrates the use of "prefixes" on the output lines that make it
relatively easy to filter off the different parts of the output report and chop them up
into numbers that can be used in other programs or in spreadsheets, try:
dieharder -a -c ',' -D default -D prefix
DISPLAY OPTIONS
As of version 3.x.x, dieharder has a single output interface that produces tabular data
per test, with common information in headers. The display control options and flags can
be used to customize the output to your individual specific needs.
The options are controlled by binary flags. The flags, and their text versions, are
displayed if you enter:
dieharder -F
by itself on a line.
The flags can be entered all at once by adding up all the desired option flags. For
example, a very sparse output could be selected by adding the flags for the test_name (8)
and the associated pvalues (128) to get 136:
dieharder -a -D 136
Since the flags are cumulated from zero (unless no flag is entered and the default is
used) you could accomplish the same display via:
dieharder -a -D 8 -D pvalues
Note that you can enter flags by value or by name, in any combination. Because people use
dieharder to obtain values and then with to export them into spreadsheets (comma separated
values) or into filter scripts, you can chance the field separator character. For
example:
dieharder -a -c ',' -D default -D -1 -D -2
produces output that is ideal for importing into a spreadsheet (note that one can subtract
field values from the base set of fields provided by the default option as long as it is
given first).
An interesting option is the -D prefix flag, which turns on a field identifier prefix to
make it easy to filter out particular kinds of data. However, it is equally easy to turn
on any particular kind of output to the exclusion of others directly by means of the
flags.
Two other flags of interest to novices to random number generator testing are the -D
histogram (turns on a histogram of the underlying pvalues, per test) and -D description
(turns on a complete test description, per test). These flags turn the output table into
more of a series of "reports" of each test.
PUBLICATION RULES
dieharder is entirely original code and can be modified and used at will by any user,
provided that:
a) The original copyright notices are maintained and that the source, including all
modifications, is made publically available at the time of any derived publication. This
is open source software according to the precepts and spirit of the Gnu Public License.
See the accompanying file COPYING, which also must accompany any redistribution.
b) The primary author of the code (Robert G. Brown) is appropriately acknowledged and
referenced in any derived publication. It is strongly suggested that George Marsaglia and
the Diehard suite and the various authors of the Statistical Test Suite be similarly
acknowledged, although this suite shares no actual code with these random number test
suites.
c) Full responsibility for the accuracy, suitability, and effectiveness of the program
rests with the users and/or modifiers. As is clearly stated in the accompanying
copyright.h:
THE COPYRIGHT HOLDERS DISCLAIM ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING ALL
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL THE COPYRIGHT HOLDERS
BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE
OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
THIS SOFTWARE.
ACKNOWLEDGEMENTS
The author of this suite gratefully acknowledges George Marsaglia (the author of the
diehard test suite) and the various authors of NIST Special Publication 800-22 (which
describes the Statistical Test Suite for testing pseudorandom number generators for
cryptographic applications), for excellent descriptions of the tests therein. These
descriptions enabled this suite to be developed with a GPL.
The author also wishes to reiterate that the academic correctness and accuracy of the
implementation of these tests is his sole responsibility and not that of the authors of
the Diehard or STS suites. This is especially true where he has seen fit to modify those
tests from their strict original descriptions.
COPYRIGHT
GPL 2b; see the file COPYING that accompanies the source of this program. This is the
"standard Gnu General Public License version 2 or any later version", with the one minor
(humorous) "Beverage" modification listed below. Note that this modification is probably
not legally defensible and can be followed really pretty much according to the honor rule.
As to my personal preferences in beverages, red wine is great, beer is delightful, and
Coca Cola or coffee or tea or even milk acceptable to those who for religious or personal
reasons wish to avoid stressing my liver.
The Beverage Modification to the GPL:
Any satisfied user of this software shall, upon meeting the primary author(s) of this
software for the first time under the appropriate circumstances, offer to buy him or her
or them a beverage. This beverage may or may not be alcoholic, depending on the personal
ethical and moral views of the offerer. The beverage cost need not exceed one U.S. dollar
(although it certainly may at the whim of the offerer:-) and may be accepted or declined
with no further obligation on the part of the offerer. It is not necessary to repeat the
offer after the first meeting, but it can't hurt...