Contact : http://craig.mcqueen.id.au
Copyright : 2010 Craig McQueen
Simple pseudo-random number generators for C and Python.
This project provides simplerandom, simple pseudo-random number
generators.
Features:
- Main API functions:
- Seed
- Generate "next" random value
- "Discard" also known as "jumpahead" to skip the generator ahead by 'n' samples.
- Mix real random data into the generator state
- Simple algorithms that are easily ported to different languages.
- Safe seeding. Many generators have some "bad" state values that must be avoided. The seed functions for all generators ensure that any "bad" state values are avoided, and replaced by a suitable alternative initial state.
- Currently supported languages are:
- C
- Python
- Same numeric output in each supported language. It can be useful to be able to implement the identical algorithm on muliple platforms and/or languages.
- Simple algorithms and state size appropriate for limited RAM and ROM (e.g. in embedded systems).
- Decent cross-platform support.
- Various OS.
- Various processors, 8- to 64-bit.
- Implement target language's API idioms and/or existing random number generator API.
- Reasonable statistical properties of pseudo-random output (though not for all generators provided).
Most algorithms were obtained from two newsgroup posts by George Marsaglia [mars1] [mars2]. However, some modifications have been made. From [rose1], it seems that the SHR3 algorithm defined in [mars1] is flawed and should not be used. It doesn't actually have a period of 232-1 as expected, but has 64 different cycles, some with very short periods. The SHR3 in the 2003 post is very similar, but with two shift values swapped. It has a period of 232-1 as expected.
We still find KISS from [mars1] useful mainly because it uses 32-bit calculations for MWC, which can be more suitable for small embedded systems. So we define KISS that uses a MWC based on [mars1], but the Cong and SHR3 from [mars2].
From Pierre L'Ecuyer [lecuyer1] [lecuyer2], the Combined LFSR (Tausworthe) LFSR113 algorithm [lecuyer3] and LFSR88 (aka Taus88) have been implemented.
The following pseudo-random number generators are provided:
| Generator | Notes |
|---|---|
MWC1 |
Two 32-bit MWCs combined. From [mars1]. |
MWC2 |
Very similar to MWC1, but slightly modified to improve its statistical properties. |
Cong |
From [mars2]. |
SHR3 |
From [mars2]. |
MWC64 |
A single 64-bit multiply-with-carry calculation. From [mars2]. |
KISS |
Combination of MWC2, Cong and SHR3. Based on [mars1] but using Cong and SHR3 from [mars2], and the modified MWC. |
KISS2 |
Combination of MWC64, Cong and SHR3. From [mars2]. |
LFSR113 |
Combined LFSR (Tausworthe) random number generator by L'Ecuyer. From [lecuyer1] [lecuyer3]. |
LFSR88 |
Combined LFSR (Tausworthe) random number generator by L'Ecuyer. From [lecuyer2]. |
A C implementation of simplerandom is provided. It should compile on a wide range of platforms and OS.
Note that simplerandom uses stdint.h for integer types such as
uint32_t, so that must be available. The generator MWC64, and
KISS2 which uses it, use 64-bit calculations with uint64_t. For
platforms which do not support 64-bit integers, these generators are
not included in the build. This is done via checking for the macro
define UINT64_C.
Note that C++ compilers may not define the constant macros UINT32_C
and UINT64_C unless the following line is used before the stdint.h
include:
#define __STDC_CONSTANT_MACROS
For Unix-style platforms the library can be built via autotools in the normal method. E.g.:
./configure
make
sudo make install
To run very basic unit tests:
make check
Optional cxxtest unit tests are provided. To run these:
./configure --with-cxxteset
make check
For other platforms, it should not be difficult to add the source files to a project.
Include file:
#include <simplerandom.h>
A C++ simplerandom library is planned in future. C++ code should be able to use the C library, but should use a different include to use the C library instead of a C++ library:
#include <simplerandom-c.h>
First define a variable to contain the simplerandom generator state. E.g.:
static SimpleRandomCong_t rng_cong;
static SimpleRandomKISS_t rng_kiss;
By encapsulating generator state in a variable, multiple independent
generators can be used at the same time. Independent output can be
achieved by seeding them with different seeds, or by calling the
generator's discard function to "jump-ahead" by a certain number of
samples.
Seed the generator once with a suitable number of uint32_t seed
values. The number of seeds depends on the generator.
simplerandom_cong_seed(&rng_cong, 2051391225u);
simplerandom_kiss_seed(&rng_kiss, 2247183469u, 99545079u, 3269400377u, 3950144837u);
Alternatively, there are seed functions which take seed data from an
array of uint32_t.
uint32_t seed_array[8] = { 1, 2, 3, 4, 5, 6, 7, 8 };
simplerandom_kiss_seed_array(&rng_kiss, seed_array, 8, false);
If the last parameter mix_extras is false, then any "extra"
seed values are simply ignored. So the above is equivalent to:
simplerandom_kiss_seed(&rng_kiss, 1, 2, 3, 4);
If the last parameter mix_extras is true, then any "extra"
seed values are mixed into the state in the same was as is done by the
mix function (see below). So:
uint32_t seed_array[8] = { 1, 2, 3, 4, 5, 6, 7, 8 };
simplerandom_kiss_seed_array(&rng_kiss, seed_array, 8, true);
is equivalent to:
simplerandom_kiss_seed(&rng_kiss, 1, 2, 3, 4);
simplerandom_kiss_mix(&rng_kiss, &seed_array[4], 4);
Call the generator's next function multiple times to generate random
values. All generators output uniformly distributed uint32_t values
in the full range (except for the SHR3 generator which excludes 0 as an
output value).
uint32_t rng_value;
uint32_t rng_values_array[8];
...
rng_value = simplerandom_cong_next(&rng_cong);
...
for (i = 0; i < 8; ++i) {
rng_values_array[i] = simplerandom_kiss_next(&rng_kiss);
}
Each generator has a discard function, which is equivalent to the
jumpahead function in the Python package. It is named discard in
the C library, to be consistent with the naming of the function in the
C++11/Boost random API.
The discard function allows for a generator to be moved ahead by n
samples.
simplerandom_kiss_discard(&rng_kiss, 1000000000000uLL);
Note that n is of type uintmax_t, which would probably be 64-bit
on most platforms, but might be 32-bit on some small embedded
platforms.
The calculation is done with time complexity O(log n), so n can be
very large and jumpahead will still calculate quickly.
In some systems, there might be some source of random data available,
although the quality may not be statistically ideal. The simplerandom
library provides mix functions, to mix random data in to the
generator state.
Incorporating truly random data decreases the predictability of the generator's output, which might be useful in some applications. Even if the statistical properties of the random data isn't that great, once it is mixed into the generator's state, the generator's output should still be statistically good.
uint32_t real_random_data[8];
...
get_real_random_data_from_somewhere(&real_random_data, 8);
simplerandom_kiss_mix(&rng_kiss, real_random_data, 8);
The simplerandom package is provided, which contains modules
containing classes for various simple pseudo-random number generators.
One module provides Python iterators, which generate simple unsigned 32-bit integers identical to their C counterparts.
Another module provides random classes that are sub-classed from the
class Random in the random module of the standard Python library.
| Module | Description |
|---|---|
simplerandom.iterators |
Iterator classes, which generate unsigned 32-bit integers. |
simplerandom.random |
Classes that conform to standard Python random.Random API. |
In simplerandom.iterators, the generators are provided as Python
iterators, of infinite length (they never raise StopIteration). They
implement the __next__() function to generate the next random integer.
All the generators output 32-bit unsigned values, and take one or more
32-bit seed values during initialisation/seeding.
In simplerandom.random, pseudo-random number generators are provided
which have the same names as those in simplerandom.iterators, but
these generators implement the standard Python random.Random API.
The jumpahead() function (in the style of the Python 2.x API) is
implemented for all the generators, even though jumpahead() has
officially been removed from the Python 3.x random API. Each generator
uses the iterator of the same name in simplerandom.iterators to
generate the random bits used to produce the random floats.
>>> import simplerandom.iterators as sri
>>> rng = sri.KISS(123958, 34987243, 3495825239, 2398172431)
>>> next(rng)
702862187
>>> next(rng)
13888114
>>> next(rng)
699722976
It is possible to "jump ahead" by n values at any time. The
calculation is done with time complexity O(log n), so n can be very
large and jumpahead will still calculate quickly.
>>> rng.jumpahead(1000000000000000000)
>>> next(rng)
709328996L
>>> import simplerandom.random as srr
>>> rng = srr.KISS(258725234)
>>> rng.random()
0.0925917826051541
>>> rng.random()
0.02901686453730415
>>> rng.random()
0.9024972981686489
The jumpahead function is supported for all generators in both
Python 2.x and 3.x.
>>> rng.jumpahead(1000000000000000000)
>>> rng.random()
0.1423603103150949
Python 3.6 through 3.9 is supported. It may or may not run on earlier Python 3.x versions, but these versions are no longer being tested.
Cython is used to make a fast implementation of
simplerandom.iterators. Cython creates a .c file that can be
compiled into a Python binary extension module.
The simplerandom source distribution package includes a .c file that
was created with Cython, so it is not necessary to have Cython installed
to install simplerandom.
The Cython .pyx file is also included, if you want to modify the
Cython source code, in which case you do need to have Cython installed.
But by default, setup.py builds the extension from the .c file (to
ensure that the build doesn't fail due to particular Cython version
issues). If you wish to build using Cython from the included .pyx
file, you must set USE_CYTHON=True in setup.py.
The simplerandom package is installed using distutils. If you have the
tools installed to build a Python extension module, run the following
command:
python setup.py install
If you cannot build the C extension, you may install just the pure Python implementation, using the following command:
python setup.py build_py install --skip-build
Unit testing of the iterators is in simplerandom.iterators.test.
It duplicates the tests of the C algorithms given in the original
newsgroup post [mars1], as well as other unit tests.
To run unit tests:
python -m simplerandom.iterators.test
A more thorough unit test suite is needed. A unit test suite for
simplerandom.random is needed.
The code is released under the MIT license. See LICENSE.txt for details.
[mars1]
Random Numbers for C: End, at last?
George Marsaglia
Newsgroup post, sci.stat.math and others, Thu, 21 Jan 1999
[mars2]
RNGs
George Marsaglia
Newsgroup post, sci.math, 26 Feb 2003
[rose1]
KISS: A Bit Too Simple
Greg Rose
Qualcomm Inc.
[lecuyer1]
Tables of Maximally-Equidistributed Combined LFSR Generators
Pierre L'Ecuyer
Mathematics of Computation, 68, 225 (1999), 261–269.
[lecuyer2]
Maximally Equidistributed Combined Tausworthe Generators
P. L'Ecuyer
Mathematics of Computation, 65, 213 (1996), 203–213.
[lecuyer3]
LFSR113 C double implementation
Pierre L'Ecuyer