dieharder (1) - Linux Manuals
dieharder: A testing and benchmarking tool for random number
NAME
dieharder - A testing and benchmarking tool for random number generators.SYNOPSIS
dieharder [-a] [-d dieharder test number] [-f filename] [-B]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
dieharderWelcome 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:
to see an extremely terse, easy to import report or
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:
(prints the command synopsis like the one above).
(prints the test descriptions only for -a(ll) tests or for the specific
test indicated).
(lists all known tests, including how reliable rgb thinks that they are
as things stand).
(lists all known rngs).
(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!
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.:
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.
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.:
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:
for raw binary input or
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!
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.
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!
To demonstrate all tests, run on the default GSL rng, enter:
To demonstrate a test of an external generator of a raw binary stream of
bits, use the stdin (raw) interface:
To use it with an ascii formatted file:
(testrands.txt should consist of a header such as:
etc.).
To use it with a binary file
or
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:
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:
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:
Since the flags are cumulated from zero (unless no flag is entered and
the default is used) you could accomplish the same display via:
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:
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.
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.
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.
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...
dieharder -g 205 -d diehard_opso -c
dieharder -g 205 -d diehard_opso -c
dieharder -h
dieharder -a -h
dieharder -d 6 -h
dieharder -l
dieharder -g -1
dieharder -F
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.
FILE INPUT
BEST PRACTICE
WARNING!
EXAMPLES
85411969
DISPLAY OPTIONS
PUBLICATION RULES
dieharder
is entirely original code and can be modified and used at will by any
user, provided that:
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.
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.