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[DEV] add v1.76.0

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This commit is contained in:
Edouard DUPIN
2021-10-05 21:37:46 +02:00
parent a97e9ae7d4
commit d0115b733d
45133 changed files with 4744437 additions and 1026325 deletions
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2
libs/random/build/Jamfile.v2
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@@ -13,6 +13,6 @@ project /boost/random
: usage-requirements <link>shared:<define>BOOST_RANDOM_DYN_LINK
;
lib boost_random : [ glob *.cpp ] /boost//system ;
lib boost_random : [ glob *.cpp ] ;
boost-install boost_random ;

10
libs/random/doc/Jamfile.v2
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@@ -27,6 +27,7 @@ doxygen_files =
discrete_distribution
exponential_distribution
extreme_value_distribution
faure
fisher_f_distribution
gamma_distribution
generate_canonical
@@ -40,7 +41,9 @@ doxygen_files =
linear_feedback_shift
lognormal_distribution
mersenne_twister
mixmax
negative_binomial_distribution
niederreiter_base2
non_central_chi_squared_distribution
normal_distribution
piecewise_constant_distribution
@@ -52,6 +55,7 @@ doxygen_files =
seed_seq
shuffle_order
# shuffle_output
sobol
student_t_distribution
subtract_with_carry
taus88
@@ -93,6 +97,7 @@ doxygen reference :
boost=\"$(BOOST_ROOT)\" \\
random_distribution=\"@xmlonly <link linkend=\\\"boost_random.reference.concepts.random_distribution\\\">random distribution</link> @endxmlonly\" \\
pseudo_random_number_generator=\"@xmlonly <link linkend=\\\"boost_random.reference.concepts.pseudo_random_number_generator\\\">pseudo-random number generator</link> @endxmlonly\" \\
quasi_random_number_generator=\"@xmlonly <link linkend=\\\"boost_random.reference.concepts.quasi_random_number_generator\\\">quasi-random number generator</link> @endxmlonly\" \\
uniform_random_number_generator=\"@xmlonly <link linkend=\\\"boost_random.reference.concepts.uniform_random_number_generator\\\">uniform random number generator</link> @endxmlonly\" \\
nondeterministic_random_number_generator=\"@xmlonly <link linkend=\\\"boost_random.reference.concepts.non_deterministic_uniform_random_number_generator\\\">non-deterministic random number generator</link> @endxmlonly\" \\
generators=\"@xmlonly <link linkend=\\\"boost_random.reference.generators\\\">generators</link> @endxmlonly\" \\
@@ -107,6 +112,10 @@ doxygen reference :
rand48=\"@xmlonly <classname alt=\\\"boost::random::rand48\\\">rand48</classname> @endxmlonly\" \\
mt11213b=\"@xmlonly <classname alt=\\\"boost::random::mt11213b\\\">mt11213b</classname> @endxmlonly\" \\
mt19937=\"@xmlonly <classname alt=\\\"boost::random::mt19937\\\">mt19937</classname> @endxmlonly\" \\
mixmax=\"@xmlonly <classname alt=\\\"boost::random::mixmax\\\">mixmax</classname> @endxmlonly\" \\
niederreiter_base2_engine=\"@xmlonly <classname alt=\\\"boost::random::niederreiter_base2_engine\\\">niederreiter_base2_engine</classname> @endxmlonly\" \\
sobol_engine=\"@xmlonly <classname alt=\\\"boost::random::sobol_engine\\\">sobol_engine</classname> @endxmlonly\" \\
faure_engine=\"@xmlonly <classname alt=\\\"boost::random::faure_engine\\\">faure_engine</classname> @endxmlonly\" \\
ecuyer1988=\"@xmlonly <classname alt=\\\"boost::random::ecuyer1988\\\">ecuyer1988</classname> @endxmlonly\" \\
lagged_fibonacci607=\"@xmlonly <classname alt=\\\"boost::random::lagged_fibonacci607\\\">lagged_fibonacci607</classname> @endxmlonly\" \\
lagged_fibonacci44497=\"@xmlonly <classname alt=\\\"boost::random::lagged_fibonacci44497\\\">lagged_fibonacci44497</classname> @endxmlonly\" \\
@@ -127,6 +136,7 @@ doxygen reference :
\"BOOST_PREVENT_MACRO_SUBSTITUTION=\" \\
\"BOOST_STATIC_ASSERT(x)=\" \\
\"BOOST_STATIC_CONSTANT(type,value)=static const type value\" \\
\"BOOST_CONSTEXPR=constexpr\" \\
\"UINT64_C(value)=value ## ull\" \\
\"BOOST_RANDOM_DECL=\" \\
\"RealType(x)=x\" \\

96
libs/random/doc/concepts.qbk
View File

@@ -10,26 +10,26 @@
Random numbers are required in a number of different problem domains, such as
* numerics (simulation, Monte-Carlo integration)
* games (non-deterministic enemy behavior)
* security (key generation)
* testing (random coverage in white-box tests)
* numerics (simulation, Monte-Carlo integration)
* games (non-deterministic enemy behavior)
* security (key generation)
* testing (random coverage in white-box tests)
The Boost Random Number Generator Library provides a framework for random
number generators with well-defined properties so that the generators can be
used in the demanding numerics and security domains. For a general
introduction to random numbers in numerics, see
introduction to random numbers in numerics, see
[:"Numerical Recipes in C: The art of scientific computing", William H. Press,
Saul A. Teukolsky, William A. Vetterling, Brian P. Flannery, 2nd ed., 1992,
pp. 274-328]
Depending on the requirements of the problem domain, different variations of
random number generators are appropriate:
* non-deterministic random number generator
* pseudo-random number generator
* quasi-random number generator
Depending on the requirements of the problem domain, different variations of
random number generators are appropriate:
* non-deterministic random number generator
* pseudo-random number generator
* quasi-random number generator
All variations have some properties in common, the concepts (in the STL
sense) is called __UniformRandomNumberGenerator. This
@@ -38,8 +38,8 @@ concept will be defined in a subsequent section.
The goals for this library are the following:
* allow easy integration of third-party random-number generators
* provide easy-to-use front-end classes which model popular distributions
* provide maximum efficiency
* provide easy-to-use front-end classes which model popular distributions
* provide maximum efficiency
[endsect]
@@ -199,6 +199,76 @@ the generator, for example to re-run a test suite at a later time.]
[endsect]
[section Quasi-Random Number Generator]
A quasi-random number generator is a __UniformRandomNumberGenerator which
provides a deterministic sequence of quasi-random numbers, based on some
algorithm and internal state. [classref boost::random::niederreiter_base2_engine
Niederreiter base 2] generator is an example of such a [qrng quasi-random
number generator]. The "quasi" modifier is used to denote more clearly that the
values produced by such a generator are neither random nor pseudo-random, but
they form a low discrepancy sequence. The intuitive idea is that a low discrepancy
sequence is more evenly distributed than a pseudo random sequence would be.
For example, if we generate a low discrepancy sequence of 2D points on a square,
this square would be covered more evenly, and the number of points falling to any
part of the square would be proportional to the number of points in the whole square.
Such sequences share some properties of random variables and in certain applications
such as the quasi-Monte Carlo method their lower discrepancy is an important advantage.
[note The quasi-Monte Carlo method uses a low-discrepancy sequence such as the
Niederreiter base 2 sequence, the Sobol sequence, or the Faure sequence among the others.
The advantage of using low-discrepancy sequences is a probabilistically faster rate of
convergence. Quasi-Monte Carlo has a rate of convergence O(log(N)[sup s]/N),
whereas the rate of convergence for the Monte Carlo method, which uses a pseudo-random sequence,
is O(N[sup -0.5]).]
Harold Niederreiter gives an extensive overview on random number generation
and quasi-Monte Carlo methods in his book "Random number generation and
quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics, 1992".
In addition to the __UniformRandomNumberGenerator requirements,
a quasi-random number generator has some additional requirements. In the
following table, `X` denotes a quasi-random number generator class, `u` is a value of `X`,
`v` is a const value of `X`, and `j` a value of type `unsigned long long`.
[table QuasiRandomNumberGenerator requirements
[[expression] [return type] [pre/post-condition]]
[[`X(s)`] [-] [creates an `s`-dimensional generator with a default seed. Dimension `s` is an integer no less than 1.]]
[[`v.dimension()`] [std::size_t] [the dimension of quasi-random domain.]]
[[`u.seed(i)`] [`void`] [seeds the generator with the integer `i`.]]
[[`u.discard(j)`] [`void`] [Advances the generator by `j` steps as if by
`j` calls to `u()`.]]
]
[note The `operator()` returns a successive element of an `s`-dimensional (`s` = `v.dimension()`) vector
at each invocation. When all elements are exhausted, `operator()` begins anew with the starting
element of a subsequent `s`-dimensional vector.]
Classes which model a quasi-random number generator shall also model
__EqualityComparable, i.e. implement `operator==`. Two quasi-random number
generators are defined to be /equivalent/ if they both return an identical
sequence of numbers starting from a given state.
Classes which model a quasi-random number generator shall also model the
__Streamable concept, i.e. implement `operator<<` and `operator>>`.
`operator<<` writes all current state of the quasi-random number generator
to the given `ostream` so that `operator>>` can restore the state at a later
time. The state shall be written in a platform-independent manner, but it is
assumed that the `locales` used for writing and reading be the same. The
quasi-random number generator with the restored state and the original at
the just-written state shall be equivalent.
Classes which model a quasi-random number generator should also model the
__CopyConstructible and __Assignable concepts. However, note that the
sequences of the original and the copy are strongly correlated (in fact,
they are identical), which may make them unsuitable for some problem domains.
Thus, copying quasi-random number generators is discouraged; they should
always be passed by (non-const) reference.
The classes __niederreiter_base2, __sobol, __faure are models for a quasi-random number generator.
[endsect]
[section Seed Sequence]
A SeedSeq represents a sequence of values that can be used to

12
libs/random/doc/generators.qbk
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@@ -13,6 +13,15 @@ class templates with template value parameters, hidden in
`namespace boost::random`. Any particular choice of parameters is represented
as the appropriately specializing `typedef` in `namespace boost`.
The [prng Pseudo-random number generators] offered in this library have been
chosen from a few families with different underlying principle of operation
based on their performance and quality characteristics. None of the generators
are capable of producing sequences which are indistinguishable from random for
longer than approximately the cubic root of their period. Thus, the generators
with a period of 2[sup 32] or less (most of them are linear congruential
generators) are suitable only for a program or simulation which needs only a
few hundred random numbers.
[prng Pseudo-random number generators] should not be constructed (initialized)
frequently during program execution, for two reasons. First, initialization
requires full initialization of the internal state of the generator. Thus,
@@ -47,13 +56,14 @@ numbers mean faster random number generation.
[[__minstd_rand] [2[sup 31]-2] [`sizeof(int32_t)`] [[minstd_rand_speed]] [-]]
[[__rand48][2[sup 48]-1] [`sizeof(uint64_t)`] [[rand48_speed]] [-]]
[[__ecuyer1988] [approx. 2[sup 61]] [`2*sizeof(int32_t)`] [[ecuyer_combined_speed]] [-]]
[[__knuth_b] [?] [`257*sizeof(uint32_t)`] [[knuth_b_speed]] [-]]
[[__knuth_b] [2[sup 31]-2] [`257*sizeof(uint32_t)`] [[knuth_b_speed]] [-]]
[[__kreutzer1986] [?] [`98*sizeof(uint32_t)`] [[kreutzer1986_speed]] [-]]
[[__taus88] [~2[sup 88]] [`3*sizeof(uint32_t)`] [[taus88_speed]] [-]]
[[__hellekalek1995] [2[sup 31]-1] [`sizeof(int32_t)`] [[hellekalek1995__inversive__speed]] [good uniform distribution in several dimensions]]
[[__mt11213b] [2[sup 11213]-1] [`352*sizeof(uint32_t)`] [[mt11213b_speed]] [good uniform distribution in up to 350 dimensions]]
[[__mt19937] [2[sup 19937]-1] [`625*sizeof(uint32_t)`] [[mt19937_speed]] [good uniform distribution in up to 623 dimensions]]
[[__mt19937_64] [2[sup 19937]-1] [`312*sizeof(uint64_t)`] [[mt19937_64_speed]] [good uniform distribution in up to 311 dimensions]]
[[__mixmax] [~10[sup 294]] [152] [[-]] [unconditionally guaranteed MC convergence in up to 17 dimensions]]
[[__lagged_fibonacci607] [~2[sup 32000]] [`607*sizeof(double)`] [[lagged_fibonacci607_speed]] [-]]
[[__lagged_fibonacci1279] [~2[sup 67000]] [`1279*sizeof(double)`] [[lagged_fibonacci1279_speed]] [-]]
[[__lagged_fibonacci2281] [~2[sup 120000]] [`2281*sizeof(double)`] [[lagged_fibonacci2281_speed]] [-]]

5
libs/random/doc/random.qbk
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@@ -13,6 +13,7 @@
[template sup[text]'''<superscript>'''[text]'''</superscript>''']
[template prng[text] [link boost_random.reference.concepts.pseudo_random_number_generator [text]]]
[template qrng[text] [link boost_random.reference.concepts.quasi_random_number_generator [text]]]
[template concepts[text] [link boost_random.reference.concepts [text]]]
[template generators[text] [link boost_random.reference.generators [text]]]
[template distributions[text] [link boost_random.reference.distributions [text]]]
@@ -20,6 +21,7 @@
[def __NumberGenerator [link boost_random.reference.concepts.number_generator NumberGenerator]]
[def __UniformRandomNumberGenerator [link boost_random.reference.concepts.uniform_random_number_generator UniformRandomNumberGenerator]]
[def __PseudoRandomNumberGenerator [link boost_random.reference.concepts.pseudo_random_number_generator PseudoRandomNumberGenerator]]
[def __QuasiRandomNumberGenerator [link boost_random.reference.concepts.quasi_random_number_generator QuasiRandomNumberGenerator]]
[def __SeedSeq [link boost_random.reference.concepts.seed_sequence SeedSeq]]
[def __CopyConstructible [@boost:/doc/html/CopyConstructible.html CopyConstructible]]
@@ -64,6 +66,9 @@
[def __ranlux64_4_01 [classref boost::random::ranlux64_4_01 ranlux64_4_01]]
[def __ranlux24 [classref boost::random::ranlux24 ranlux24]]
[def __ranlux48 [classref boost::random::ranlux48 ranlux48]]
[def __niederreiter_base2 [classref boost::random::niederreiter_base2 niederreiter_base2]]
[def __sobol [classref boost::random::sobol sobol]]
[def __faure [classref boost::random::faure faure]]
[def __uniform_smallint [classref boost::random::uniform_smallint uniform_smallint]]
[def __uniform_int_distribution [classref boost::random::uniform_int_distribution uniform_int_distribution]]

590
libs/random/doc/reference.xml
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File diff suppressed because one or more lines are too long

7
libs/random/doc/tutorial.qbk
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@@ -26,3 +26,10 @@
[password]
[endsect]
[section Generating quasi-random line-sphere intersections]
[import ../example/intersections.cpp]
[intersections]
[endsect]

1
libs/random/example/Jamfile.v2
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@@ -10,3 +10,4 @@
run die.cpp ;
run weighted_die.cpp ;
run password.cpp /boost//random ;
run intersections.cpp /boost//random ;

78
libs/random/example/intersections.cpp Normal file
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@@ -0,0 +1,78 @@
// intersections.cpp
//
// Copyright (c) 2018
// Justinas V. Daugmaudis
//
// Distributed under the Boost Software License, Version 1.0. (See
// accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
//[intersections
/*`
For the source of this example see
[@boost://libs/random/example/intersections.cpp intersections.cpp].
This example demonstrates generating quasi-randomly distributed chord
entry and exit points on an S[sup 2] sphere.
First we include the headers we need for __niederreiter_base2
and __uniform_01 distribution.
*/
#include <boost/random/niederreiter_base2.hpp>
#include <boost/random/uniform_01.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/tuple/tuple.hpp>
/*`
We use 4-dimensional __niederreiter_base2 as a source of randomness.
*/
boost::random::niederreiter_base2 gen(4);
int main()
{
typedef boost::tuple<double, double, double> point_t;
const std::size_t n_points = 100; // we will generate 100 points
std::vector<point_t> points;
points.reserve(n_points);
/*<< __niederreiter_base2 produces integers in the range [0, 2[sup 64]-1].
However, we want numbers in the range [0, 1). The distribution
__uniform_01 performs this transformation.
>>*/
boost::random::uniform_01<double> dist;
for (std::size_t i = 0; i != n_points; ++i)
{
/*`
Using formula from J. Rovira et al., "Point sampling with uniformly distributed lines", 2005
to compute uniformly distributed chord entry and exit points on the surface of a sphere.
*/
double cos_theta = 1 - 2 * dist(gen);
double sin_theta = std::sqrt(1 - cos_theta * cos_theta);
double phi = boost::math::constants::two_pi<double>() * dist(gen);
double sin_phi = std::sin(phi), cos_phi = std::cos(phi);
point_t point_on_sphere(sin_theta*sin_phi, cos_theta, sin_theta*cos_phi);
/*`
Here we assume that our sphere is a unit sphere at origin. If your sphere was
different then now would be the time to scale and translate the `point_on_sphere`.
*/
points.push_back(point_on_sphere);
}
/*`
Vector `points` now holds generated 3D points on a sphere.
*/
return 0;
}
//]

1
libs/random/example/password.cpp
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@@ -19,6 +19,7 @@
#include <boost/random/random_device.hpp>
#include <boost/random/uniform_int_distribution.hpp>
#include <iostream>
int main() {
/*<< We first define the characters that we're going

3
libs/random/meta/libraries.json
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@@ -13,5 +13,6 @@
],
"maintainers": [
"Steven Watanabe <watanabesj -at- gmail.com>"
]
],
"cxxstd": "03"
}

4
libs/random/performance/random_speed.cpp
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@@ -352,6 +352,8 @@ int main(int argc, char*argv[])
#if !defined(BOOST_NO_INT64_T)
run(iter, "mt19937_64", boost::mt19937_64());
#endif
run(iter, "mixmax", boost::random::mixmax());
run(iter, "lagged_fibonacci607", boost::lagged_fibonacci607());
run(iter, "lagged_fibonacci1279", boost::lagged_fibonacci1279());
@@ -395,5 +397,7 @@ int main(int argc, char*argv[])
distrib(iter, "mt19937", boost::mt19937());
distrib(iter, "mixmax", boost::random::mixmax());
distrib(iter, "lagged_fibonacci607", boost::lagged_fibonacci607());
}

2
libs/random/src/random_device.cpp
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@@ -48,7 +48,7 @@ using namespace Windows::Security::Cryptography;
#endif
#define BOOST_AUTO_LINK_NOMANGLE
#define BOOST_LIB_NAME "Advapi32"
#define BOOST_LIB_NAME Advapi32
#include <boost/config/auto_link.hpp>
#ifdef __MINGW32__

5
libs/random/test/Jamfile.v2
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@@ -23,6 +23,7 @@ run test_rand48.cpp /boost//unit_test_framework ;
run test_mt11213b.cpp /boost//unit_test_framework ;
run test_mt19937.cpp /boost//unit_test_framework ;
run test_mt19937_64.cpp /boost//unit_test_framework ;
run test_mixmax.cpp /boost//unit_test_framework ;
run test_ecuyer1988.cpp /boost//unit_test_framework ;
run test_hellekalek1995.cpp /boost//unit_test_framework ;
run test_linear_feedback_shift.cpp /boost//unit_test_framework ;
@@ -55,6 +56,10 @@ run test_lagged_fibonacci23209.cpp /boost//unit_test_framework ;
run test_lagged_fibonacci44497.cpp /boost//unit_test_framework ;
run test_zero_seed.cpp /boost//unit_test_framework ;
run niederreiter_base2_validate.cpp /boost//unit_test_framework ;
run sobol_validate.cpp /boost//unit_test_framework ;
run faure_validate.cpp /boost//unit_test_framework ;
# Disable by default. These don't add much and the larger
# ones can overflow the stack.
explicit test_lagged_fibonacci1279 test_lagged_fibonacci2281

2
libs/random/test/concepts.hpp
View File

@@ -151,7 +151,7 @@ private:
const E x;
seed_seq_archetype<> q;
typename detail::seed_type<result_type>::type s;
unsigned long long z;
uintmax_t z;
input_iterator_archetype<boost::uint32_t> sb, se;
};

375
libs/random/test/faure_validate.cpp Normal file
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@@ -0,0 +1,375 @@
// Copyright Justinas Vygintas Daugmaudis, 2010.
// Use, modification and distribution is subject to the
// Boost Software License, Version 1.0. (See accompanying
// file LICENSE-1.0 or http://www.boost.org/LICENSE-1.0)
#include <boost/random/faure.hpp>
#include <boost/utility.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include "test_qrng_functions.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the faure quasi-random number generator.
// These tests compare our results with values produced by the original
// version of ACM TOMS Algorithm 647, which is available in the
// TOMS subdirectory in http://www.netlib.org
//
// For independently generated datasets look at http://people.sc.fsu.edu/~jburkardt/datasets/faure/
// Spatial dimension: 2
// N: 100
// Base: 2
// Vectors skipped: 15
static const double faure_02_100[100][2] =
{
{ 0.9375000000, 0.0625000000 },
{ 0.0312500000, 0.5312500000 },
{ 0.5312500000, 0.0312500000 },
{ 0.2812500000, 0.2812500000 },
{ 0.7812500000, 0.7812500000 },
{ 0.1562500000, 0.1562500000 },
{ 0.6562500000, 0.6562500000 },
{ 0.4062500000, 0.9062500000 },
{ 0.9062500000, 0.4062500000 },
{ 0.0937500000, 0.4687500000 },
{ 0.5937500000, 0.9687500000 },
{ 0.3437500000, 0.7187500000 },
{ 0.8437500000, 0.2187500000 },
{ 0.2187500000, 0.8437500000 },
{ 0.7187500000, 0.3437500000 },
{ 0.4687500000, 0.0937500000 },
{ 0.9687500000, 0.5937500000 },
{ 0.0156250000, 0.7968750000 },
{ 0.5156250000, 0.2968750000 },
{ 0.2656250000, 0.0468750000 },
{ 0.7656250000, 0.5468750000 },
{ 0.1406250000, 0.4218750000 },
{ 0.6406250000, 0.9218750000 },
{ 0.3906250000, 0.6718750000 },
{ 0.8906250000, 0.1718750000 },
{ 0.0781250000, 0.2343750000 },
{ 0.5781250000, 0.7343750000 },
{ 0.3281250000, 0.9843750000 },
{ 0.8281250000, 0.4843750000 },
{ 0.2031250000, 0.6093750000 },
{ 0.7031250000, 0.1093750000 },
{ 0.4531250000, 0.3593750000 },
{ 0.9531250000, 0.8593750000 },
{ 0.0468750000, 0.2656250000 },
{ 0.5468750000, 0.7656250000 },
{ 0.2968750000, 0.5156250000 },
{ 0.7968750000, 0.0156250000 },
{ 0.1718750000, 0.8906250000 },
{ 0.6718750000, 0.3906250000 },
{ 0.4218750000, 0.1406250000 },
{ 0.9218750000, 0.6406250000 },
{ 0.1093750000, 0.7031250000 },
{ 0.6093750000, 0.2031250000 },
{ 0.3593750000, 0.4531250000 },
{ 0.8593750000, 0.9531250000 },
{ 0.2343750000, 0.0781250000 },
{ 0.7343750000, 0.5781250000 },
{ 0.4843750000, 0.8281250000 },
{ 0.9843750000, 0.3281250000 },
{ 0.0078125000, 0.6640625000 },
{ 0.5078125000, 0.1640625000 },
{ 0.2578125000, 0.4140625000 },
{ 0.7578125000, 0.9140625000 },
{ 0.1328125000, 0.0390625000 },
{ 0.6328125000, 0.5390625000 },
{ 0.3828125000, 0.7890625000 },
{ 0.8828125000, 0.2890625000 },
{ 0.0703125000, 0.3515625000 },
{ 0.5703125000, 0.8515625000 },
{ 0.3203125000, 0.6015625000 },
{ 0.8203125000, 0.1015625000 },
{ 0.1953125000, 0.9765625000 },
{ 0.6953125000, 0.4765625000 },
{ 0.4453125000, 0.2265625000 },
{ 0.9453125000, 0.7265625000 },
{ 0.0390625000, 0.1328125000 },
{ 0.5390625000, 0.6328125000 },
{ 0.2890625000, 0.8828125000 },
{ 0.7890625000, 0.3828125000 },
{ 0.1640625000, 0.5078125000 },
{ 0.6640625000, 0.0078125000 },
{ 0.4140625000, 0.2578125000 },
{ 0.9140625000, 0.7578125000 },
{ 0.1015625000, 0.8203125000 },
{ 0.6015625000, 0.3203125000 },
{ 0.3515625000, 0.0703125000 },
{ 0.8515625000, 0.5703125000 },
{ 0.2265625000, 0.4453125000 },
{ 0.7265625000, 0.9453125000 },
{ 0.4765625000, 0.6953125000 },
{ 0.9765625000, 0.1953125000 },
{ 0.0234375000, 0.3984375000 },
{ 0.5234375000, 0.8984375000 },
{ 0.2734375000, 0.6484375000 },
{ 0.7734375000, 0.1484375000 },
{ 0.1484375000, 0.7734375000 },
{ 0.6484375000, 0.2734375000 },
{ 0.3984375000, 0.0234375000 },
{ 0.8984375000, 0.5234375000 },
{ 0.0859375000, 0.5859375000 },
{ 0.5859375000, 0.0859375000 },
{ 0.3359375000, 0.3359375000 },
{ 0.8359375000, 0.8359375000 },
{ 0.2109375000, 0.2109375000 },
{ 0.7109375000, 0.7109375000 },
{ 0.4609375000, 0.9609375000 },
{ 0.9609375000, 0.4609375000 },
{ 0.0546875000, 0.9296875000 },
{ 0.5546875000, 0.4296875000 },
{ 0.3046875000, 0.1796875000 }
};
// Spatial dimension: 7
// N: 100
// Base: 7
// Vectors skipped: 2400
static const double faure_07_100[100][7] =
{
{ 0.9995835069, 0.4602249063, 0.9412744690, 0.3202832153, 0.9850062474, 0.8334027489, 0.1103706789 },
{ 0.0000594990, 0.2437079788, 0.3765692866, 0.6493722854, 0.6685309692, 0.3582435890, 0.2228833224 },
{ 0.1429166419, 0.3865651217, 0.5194264295, 0.7922294282, 0.8113881121, 0.5011007318, 0.3657404653 },
{ 0.2857737847, 0.5294222645, 0.6622835723, 0.9350865711, 0.9542452550, 0.6439578747, 0.5085976081 },
{ 0.4286309276, 0.6722794074, 0.8051407152, 0.0779437139, 0.0971023978, 0.7868150176, 0.6514547510 },
{ 0.5714880704, 0.8151365502, 0.9479978580, 0.2208008568, 0.2399595407, 0.9296721604, 0.7943118939 },
{ 0.7143452133, 0.9579936931, 0.0908550009, 0.3636579996, 0.3828166835, 0.0725293033, 0.9371690367 },
{ 0.8572023562, 0.1008508360, 0.2337121437, 0.5065151425, 0.5256738264, 0.2153864461, 0.0800261796 },
{ 0.0204676623, 0.4069732849, 0.6826917356, 0.0983518772, 0.2603677039, 0.0929374665, 0.1004343428 },
{ 0.1633248051, 0.5498304278, 0.8255488784, 0.2412090201, 0.4032248468, 0.2357946094, 0.2432914857 },
{ 0.3061819480, 0.6926875707, 0.9684060213, 0.3840661629, 0.5460819896, 0.3786517522, 0.3861486285 },
{ 0.4490390909, 0.8355447135, 0.1112631642, 0.5269233058, 0.6889391325, 0.5215088951, 0.5290057714 },
{ 0.5918962337, 0.9784018564, 0.2541203070, 0.6697804486, 0.8317962754, 0.6643660380, 0.6718629143 },
{ 0.7347533766, 0.1212589992, 0.3969774499, 0.8126375915, 0.9746534182, 0.8072231808, 0.8147200571 },
{ 0.8776105194, 0.2641161421, 0.5398345927, 0.9554947343, 0.1175105611, 0.9500803237, 0.9575772000 },
{ 0.0408758255, 0.5702385911, 0.9888141846, 0.5473314690, 0.8522044386, 0.8276313441, 0.9779853632 },
{ 0.1837329684, 0.7130957339, 0.1316713274, 0.6901886119, 0.9950615815, 0.9704884869, 0.1208425061 },
{ 0.3265901113, 0.8559528768, 0.2745284703, 0.8330457547, 0.1379187243, 0.1133456298, 0.2636996490 },
{ 0.4694472541, 0.9988100196, 0.4173856131, 0.9759028976, 0.2807758672, 0.2562027727, 0.4065567918 },
{ 0.6123043970, 0.1416671625, 0.5602427560, 0.1187600405, 0.4236330101, 0.3990599155, 0.5494139347 },
{ 0.7551615398, 0.2845243053, 0.7030998989, 0.2616171833, 0.5664901529, 0.5419170584, 0.6922710775 },
{ 0.8980186827, 0.4273814482, 0.8459570417, 0.4044743262, 0.7093472958, 0.6847742012, 0.8351282204 },
{ 0.0612839888, 0.5906467543, 0.1520794907, 0.9963110609, 0.3011840305, 0.5623252216, 0.8555363836 },
{ 0.2041411317, 0.7335038972, 0.2949366335, 0.1391682037, 0.4440411733, 0.7051823645, 0.9983935265 },
{ 0.3469982745, 0.8763610400, 0.4377937764, 0.2820253466, 0.5868983162, 0.8480395073, 0.1412506694 },
{ 0.4898554174, 0.0192181829, 0.5806509193, 0.4248824894, 0.7297554590, 0.9908966502, 0.2841078122 },
{ 0.6327125602, 0.1620753258, 0.7235080621, 0.5677396323, 0.8726126019, 0.1337537931, 0.4269649551 },
{ 0.7755697031, 0.3049324686, 0.8663652050, 0.7105967752, 0.0154697447, 0.2766109359, 0.5698220979 },
{ 0.9184268460, 0.4477896115, 0.0092223478, 0.8534539180, 0.1583268876, 0.4194680788, 0.7126792408 },
{ 0.0816921521, 0.7539120605, 0.4582019397, 0.3024335098, 0.8930207652, 0.1541619563, 0.5902302612 },
{ 0.2245492949, 0.8967692033, 0.6010590825, 0.4452906527, 0.0358779080, 0.2970190992, 0.7330874041 },
{ 0.3674064378, 0.0396263462, 0.7439162254, 0.5881477956, 0.1787350509, 0.4398762420, 0.8759445469 },
{ 0.5102635807, 0.1824834890, 0.8867733682, 0.7310049384, 0.3215921937, 0.5827333849, 0.0188016898 },
{ 0.6531207235, 0.3253406319, 0.0296305111, 0.8738620813, 0.4644493366, 0.7255905278, 0.1616588326 },
{ 0.7959778664, 0.4681977747, 0.1724876540, 0.0167192241, 0.6073064794, 0.8684476706, 0.3045159755 },
{ 0.9388350092, 0.6110549176, 0.3153447968, 0.1595763670, 0.7501636223, 0.0113048135, 0.4473731183 },
{ 0.1021003153, 0.9171773666, 0.7643243886, 0.7514131017, 0.4848574999, 0.8888558339, 0.4677812816 },
{ 0.2449574582, 0.0600345094, 0.9071815315, 0.8942702445, 0.6277146427, 0.0317129767, 0.6106384245 },
{ 0.3878146011, 0.2028916523, 0.0500386744, 0.0371273874, 0.7705717856, 0.1745701196, 0.7534955673 },
{ 0.5306717439, 0.3457487951, 0.1928958172, 0.1799845303, 0.9134289284, 0.3174272625, 0.8963527102 },
{ 0.6735288868, 0.4886059380, 0.3357529601, 0.3228416731, 0.0562860713, 0.4602844053, 0.0392098530 },
{ 0.8163860296, 0.6314630809, 0.4786101029, 0.4656988160, 0.1991432141, 0.6031415482, 0.1820669959 },
{ 0.9592431725, 0.7743202237, 0.6214672458, 0.6085559588, 0.3420003570, 0.7459986910, 0.3249241388 },
{ 0.1225084786, 0.0804426727, 0.0704468376, 0.2003926935, 0.0766942345, 0.6235497114, 0.3453323020 },
{ 0.2653656215, 0.2232998156, 0.2133039805, 0.3432498364, 0.2195513774, 0.7664068543, 0.4881894449 },
{ 0.4082227643, 0.3661569584, 0.3561611233, 0.4861069792, 0.3624085203, 0.9092639971, 0.6310465877 },
{ 0.5510799072, 0.5090141013, 0.4990182662, 0.6289641221, 0.5052656631, 0.0521211400, 0.7739037306 },
{ 0.6939370500, 0.6518712441, 0.6418754091, 0.7718212649, 0.6481228060, 0.1949782829, 0.9167608734 },
{ 0.8367941929, 0.7947283870, 0.7847325519, 0.9146784078, 0.7909799488, 0.3378354257, 0.0596180163 },
{ 0.9796513358, 0.9375855298, 0.9275896948, 0.0575355507, 0.9338370917, 0.4806925686, 0.2024751592 },
{ 0.0029749509, 0.4098887368, 0.8896888201, 0.9175938597, 0.9775688701, 0.9938121021, 0.3074314274 },
{ 0.1458320938, 0.5527458797, 0.0325459630, 0.0604510026, 0.1204260130, 0.1366692450, 0.4502885702 },
{ 0.2886892366, 0.6956030226, 0.1754031058, 0.2033081454, 0.2632831558, 0.2795263878, 0.5931457131 },
{ 0.4315463795, 0.8384601654, 0.3182602487, 0.3461652883, 0.4061402987, 0.4223835307, 0.7360028560 },
{ 0.5744035223, 0.9813173083, 0.4611173916, 0.4890224311, 0.5489974415, 0.5652406735, 0.8788599988 },
{ 0.7172606652, 0.1241744511, 0.6039745344, 0.6318795740, 0.6918545844, 0.7080978164, 0.0217171417 },
{ 0.8601178081, 0.2670315940, 0.7468316773, 0.7747367168, 0.8347117273, 0.8509549592, 0.1645742845 },
{ 0.0233831142, 0.4302969001, 0.1958112691, 0.3665734515, 0.5694056048, 0.5856488368, 0.1849824478 },
{ 0.1662402570, 0.5731540430, 0.3386684120, 0.5094305944, 0.7122627477, 0.7285059797, 0.3278395906 },
{ 0.3090973999, 0.7160111858, 0.4815255548, 0.6522877373, 0.8551198905, 0.8713631225, 0.4706967335 },
{ 0.4519545428, 0.8588683287, 0.6243826977, 0.7951448801, 0.9979770334, 0.0142202654, 0.6135538764 },
{ 0.5948116856, 0.0017254715, 0.7672398405, 0.9380020230, 0.1408341762, 0.1570774082, 0.7564110192 },
{ 0.7376688285, 0.1445826144, 0.9100969834, 0.0808591658, 0.2836913191, 0.2999345511, 0.8992681621 },
{ 0.8805259713, 0.2874397572, 0.0529541263, 0.2237163087, 0.4265484620, 0.4427916939, 0.0421253049 },
{ 0.0437912774, 0.5935622062, 0.5019337181, 0.8155530434, 0.0183851966, 0.3203427143, 0.0625334682 },
{ 0.1866484203, 0.7364193491, 0.6447908610, 0.9584101862, 0.1612423395, 0.4631998572, 0.2053906111 },
{ 0.3295055632, 0.8792764919, 0.7876480038, 0.1012673291, 0.3040994824, 0.6060570001, 0.3482477539 },
{ 0.4723627060, 0.0221336348, 0.9305051467, 0.2441244719, 0.4469566252, 0.7489141429, 0.4911048968 },
{ 0.6152198489, 0.1649907777, 0.0733622895, 0.3869816148, 0.5898137681, 0.8917712858, 0.6339620396 },
{ 0.7580769917, 0.3078479205, 0.2162194324, 0.5298387577, 0.7326709109, 0.0346284286, 0.7768191825 },
{ 0.9009341346, 0.4507050634, 0.3590765752, 0.6726959005, 0.8755280538, 0.1774855715, 0.9196763253 },
{ 0.0641994407, 0.7568275123, 0.8080561671, 0.2645326352, 0.6102219313, 0.0550365919, 0.9400844886 },
{ 0.2070565836, 0.8996846552, 0.9509133099, 0.4073897781, 0.7530790742, 0.1978937348, 0.0829416315 },
{ 0.3499137264, 0.0425417981, 0.0937704528, 0.5502469209, 0.8959362171, 0.3407508776, 0.2257987743 },
{ 0.4927708693, 0.1853989409, 0.2366275956, 0.6931040638, 0.0387933599, 0.4836080205, 0.3686559172 },
{ 0.6356280121, 0.3282560838, 0.3794847385, 0.8359612066, 0.1816505028, 0.6264651633, 0.5115130600 },
{ 0.7784851550, 0.4711132266, 0.5223418814, 0.9788183495, 0.3245076456, 0.7693223062, 0.6543702029 },
{ 0.9213422979, 0.6139703695, 0.6651990242, 0.1216754924, 0.4673647885, 0.9121794490, 0.7972273457 },
{ 0.0846076040, 0.9200928185, 0.1141786161, 0.7135122270, 0.2020586660, 0.7897304694, 0.8176355090 },
{ 0.2274647468, 0.0629499613, 0.2570357589, 0.8563693699, 0.3449158089, 0.9325876123, 0.9604926519 },
{ 0.3703218897, 0.2058071042, 0.3998929018, 0.9992265128, 0.4877729517, 0.0754447552, 0.1033497947 },
{ 0.5131790325, 0.3486642470, 0.5427500446, 0.1420836556, 0.6306300946, 0.2183018980, 0.2462069376 },
{ 0.6560361754, 0.4915213899, 0.6856071875, 0.2849407985, 0.7734872375, 0.3611590409, 0.3890640804 },
{ 0.7988933183, 0.6343785328, 0.8284643303, 0.4277979413, 0.9163443803, 0.5040161837, 0.5319212233 },
{ 0.9417504611, 0.7772356756, 0.9713214732, 0.5706550842, 0.0592015232, 0.6468733266, 0.6747783662 },
{ 0.1050157672, 0.0833581246, 0.4203010650, 0.0196346760, 0.7938954007, 0.5244243470, 0.6951865294 },
{ 0.2478729101, 0.2262152674, 0.5631582079, 0.1624918189, 0.9367525436, 0.6672814899, 0.8380436723 },
{ 0.3907300530, 0.3690724103, 0.7060153507, 0.3053489617, 0.0796096864, 0.8101386327, 0.9809008151 },
{ 0.5335871958, 0.5119295532, 0.8488724936, 0.4482061046, 0.2224668293, 0.9529957756, 0.1237579580 },
{ 0.6764443387, 0.6547866960, 0.9917296365, 0.5910632475, 0.3653239722, 0.0958529184, 0.2666151009 },
{ 0.8193014815, 0.7976438389, 0.1345867793, 0.7339203903, 0.5081811150, 0.2387100613, 0.4094722437 },
{ 0.9621586244, 0.9405009817, 0.2774439222, 0.8767775332, 0.6510382579, 0.3815672041, 0.5523293866 },
{ 0.1254239305, 0.2466234307, 0.5835663712, 0.4686142679, 0.3857321354, 0.2591182245, 0.4298804070 },
{ 0.2682810734, 0.3894805736, 0.7264235140, 0.6114714107, 0.5285892783, 0.4019753674, 0.5727375498 },
{ 0.4111382162, 0.5323377164, 0.8692806569, 0.7543285536, 0.6714464211, 0.5448325103, 0.7155946927 },
{ 0.5539953591, 0.6751948593, 0.0121377997, 0.8971856964, 0.8143035640, 0.6876896531, 0.8584518355 },
{ 0.6968525019, 0.8180520021, 0.1549949426, 0.0400428393, 0.9571607068, 0.8305467960, 0.0013089784 },
{ 0.8397096448, 0.9609091450, 0.2978520854, 0.1828999822, 0.1000178497, 0.9734039388, 0.1441661213 },
{ 0.9825667876, 0.1037662879, 0.4407092283, 0.3257571250, 0.2428749926, 0.1162610817, 0.2870232641 },
{ 0.0058904028, 0.4536205153, 0.5456654965, 0.1654072708, 0.2661986077, 0.4865234724, 0.5552448385 }
};
// Spatial dimension: 16
// N: 100
// Base: 17
// Vectors skipped: 83520
static const double faure_16_100[100][16] =
{
{ 0.9999880270, 0.8056057758, 0.1198740437, 0.6486751835, 0.0390680188, 0.8792878438, 0.8198536895, 0.5009039643, 0.6317812287, 0.8007207768, 0.6547814322, 0.8998455478, 0.1276086254, 0.0370326026, 0.2198129812, 0.3230085847 },
{ 0.0000007043, 0.0739342061, 0.9946008647, 0.7862221336, 0.0647149678, 0.7918135418, 0.2862640393, 0.2779667248, 0.9710738476, 0.9743784057, 0.2536854063, 0.2482376746, 0.8023258680, 0.1164384864, 0.8034393604, 0.9496301388 },
{ 0.0588242337, 0.1327577355, 0.0534243941, 0.8450456630, 0.1235384972, 0.8506370712, 0.3450875687, 0.3367902542, 0.0298973770, 0.0332019351, 0.3125089358, 0.3070612041, 0.8611493974, 0.1752620158, 0.8622628899, 0.0084536682 },
{ 0.1176477631, 0.1915812649, 0.1122479236, 0.9038691925, 0.1823620266, 0.9094606006, 0.4039110981, 0.3956137836, 0.0887209064, 0.0920254645, 0.3713324652, 0.3658847335, 0.9199729269, 0.2340855452, 0.9210864193, 0.0672771976 },
{ 0.1764712925, 0.2504047943, 0.1710714530, 0.9626927219, 0.2411855560, 0.9682841300, 0.4627346275, 0.4544373131, 0.1475444358, 0.1508489939, 0.4301559946, 0.4247082629, 0.9787964563, 0.2929090746, 0.9799099487, 0.1261007270 },
{ 0.2352948219, 0.3092283237, 0.2298949824, 0.0215162513, 0.3000090854, 0.0271076594, 0.5215581569, 0.5132608425, 0.2063679652, 0.2096725234, 0.4889795240, 0.4835317923, 0.0376199857, 0.3517326041, 0.0387334781, 0.1849242565 },
{ 0.2941183514, 0.3680518531, 0.2887185118, 0.0803397807, 0.3588326148, 0.0859311888, 0.5803816863, 0.5720843719, 0.2651914946, 0.2684960528, 0.5478030534, 0.5423553217, 0.0964435151, 0.4105561335, 0.0975570075, 0.2437477859 },
{ 0.3529418808, 0.4268753825, 0.3475420412, 0.1391633101, 0.4176561442, 0.1447547183, 0.6392052157, 0.6309079013, 0.3240150240, 0.3273195822, 0.6066265828, 0.6011788511, 0.1552670445, 0.4693796629, 0.1563805369, 0.3025713153 },
{ 0.4117654102, 0.4856989119, 0.4063655706, 0.1979868395, 0.4764796737, 0.2035782477, 0.6980287451, 0.6897314307, 0.3828385535, 0.3861431116, 0.6654501122, 0.6600023805, 0.2140905739, 0.5282031923, 0.2152040663, 0.3613948447 },
{ 0.4705889396, 0.5445224413, 0.4651891000, 0.2568103689, 0.5353032031, 0.2624017771, 0.7568522746, 0.7485549601, 0.4416620829, 0.4449666410, 0.7242736416, 0.7188259099, 0.2729141033, 0.5870267217, 0.2740275957, 0.4202183741 },
{ 0.5294124690, 0.6033459708, 0.5240126294, 0.3156338983, 0.5941267325, 0.3212253065, 0.8156758040, 0.8073784895, 0.5004856123, 0.5037901704, 0.7830971711, 0.7776494393, 0.3317376327, 0.6458502511, 0.3328511251, 0.4790419035 },
{ 0.5882359984, 0.6621695002, 0.5828361589, 0.3744574278, 0.6529502619, 0.3800488359, 0.8744993334, 0.8662020189, 0.5593091417, 0.5626136998, 0.8419207005, 0.8364729688, 0.3905611621, 0.7046737805, 0.3916746546, 0.5378654329 },
{ 0.6470595278, 0.7209930296, 0.6416596883, 0.4332809572, 0.7117737913, 0.4388723653, 0.9333228628, 0.9250255483, 0.6181326711, 0.6214372292, 0.9007442299, 0.8952964982, 0.4493846916, 0.7634973099, 0.4504981840, 0.5966889623 },
{ 0.7058830572, 0.7798165590, 0.7004832177, 0.4921044866, 0.7705973207, 0.4976958947, 0.9921463922, 0.9838490778, 0.6769562005, 0.6802607587, 0.9595677593, 0.9541200276, 0.5082082210, 0.8223208394, 0.5093217134, 0.6555124918 },
{ 0.7647065866, 0.8386400884, 0.7593067471, 0.5509280160, 0.8294208501, 0.5565194241, 0.0509699216, 0.0426726072, 0.7357797299, 0.7390842881, 0.0183912887, 0.0129435570, 0.5670317504, 0.8811443688, 0.5681452428, 0.7143360212 },
{ 0.8235301161, 0.8974636178, 0.8181302765, 0.6097515454, 0.8882443795, 0.6153429536, 0.1097934510, 0.1014961366, 0.7946032593, 0.7979078175, 0.0772148181, 0.0717670864, 0.6258552798, 0.9399678982, 0.6269687722, 0.7731595506 },
{ 0.8823536455, 0.9562871472, 0.8769538059, 0.6685750748, 0.9470679090, 0.6741664830, 0.1686169804, 0.1603196660, 0.8534267888, 0.8567313469, 0.1360383475, 0.1305906158, 0.6846788092, 0.9987914276, 0.6857923016, 0.8319830800 },
{ 0.9411771749, 0.0151106766, 0.9357773353, 0.7273986042, 0.0058914384, 0.7329900124, 0.2274405099, 0.2191431954, 0.9122503182, 0.9155548763, 0.1948618769, 0.1894141452, 0.7435023386, 0.0576149570, 0.7446158310, 0.8908066094 },
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{ 0.8961944759, 0.2054220953, 0.3025593422, 0.3882982582, 0.9020852100, 0.8644779016, 0.5353989874, 0.8212193200, 0.7496205604, 0.9882192362, 0.5028203544, 0.7326667404, 0.5220490514, 0.0126322580, 0.9937507791, 0.3752356751 },
{ 0.9550180053, 0.2642456247, 0.3613828717, 0.4471217876, 0.9609087394, 0.9233014311, 0.5942225168, 0.8800428494, 0.8084440898, 0.0470427656, 0.5616438839, 0.7914902698, 0.5808725808, 0.0714557874, 0.0525743085, 0.4340592046 },
{ 0.0173017424, 0.3853528912, 0.5413136675, 0.6858761129, 0.2584865941, 0.2797028151, 0.0094474303, 0.2952677629, 0.3413160621, 0.6387382673, 0.2121629150, 0.5008328303, 0.3490386708, 0.8984454068, 0.9383874573, 0.3786958828 },
{ 0.0761252718, 0.4441764206, 0.6001371969, 0.7446996423, 0.3173101235, 0.3385263446, 0.0682709597, 0.3540912923, 0.4001395915, 0.6975617967, 0.2709864444, 0.5596563598, 0.4078622002, 0.9572689362, 0.9972109867, 0.4375194122 },
{ 0.1349488012, 0.5029999500, 0.6589607263, 0.8035231717, 0.3761336529, 0.3973498740, 0.1270944891, 0.4129148217, 0.4589631209, 0.7563853261, 0.3298099738, 0.6184798892, 0.4666857296, 0.0160924656, 0.0560345162, 0.4963429416 },
{ 0.1937723306, 0.5618234794, 0.7177842557, 0.8623467011, 0.4349571823, 0.4561734034, 0.1859180185, 0.4717383511, 0.5177866503, 0.8152088555, 0.3886335032, 0.6773034186, 0.5255092590, 0.0749159951, 0.1148580456, 0.5551664710 },
{ 0.2525958600, 0.6206470088, 0.7766077852, 0.9211702305, 0.4937807117, 0.5149969328, 0.2447415479, 0.5305618805, 0.5766101798, 0.8740323850, 0.4474570326, 0.7361269480, 0.5843327884, 0.1337395245, 0.1736815750, 0.6139900004 },
{ 0.3114193894, 0.6794705382, 0.8354313146, 0.9799937599, 0.5526042411, 0.5738204622, 0.3035650773, 0.5893854099, 0.6354337092, 0.9328559144, 0.5062805621, 0.7949504774, 0.6431563179, 0.1925630539, 0.2325051044, 0.6728135298 },
{ 0.3702429188, 0.7382940676, 0.8942548440, 0.0388172893, 0.6114277705, 0.6326439916, 0.3623886067, 0.6482089394, 0.6942572386, 0.9916794438, 0.5651040915, 0.8537740068, 0.7019798473, 0.2513865833, 0.2913286338, 0.7316370592 },
{ 0.4290664482, 0.7971175971, 0.9530783734, 0.0976408188, 0.6702513000, 0.6914675210, 0.4212121362, 0.7070324688, 0.7530807680, 0.0505029732, 0.6239276209, 0.9125975362, 0.7608033767, 0.3102101127, 0.3501521632, 0.7904605886 },
{ 0.4878899777, 0.8559411265, 0.0119019028, 0.1564643482, 0.7290748294, 0.7502910504, 0.4800356656, 0.7658559982, 0.8119042974, 0.1093265026, 0.6827511503, 0.9714210656, 0.8196269061, 0.3690336421, 0.4089756926, 0.8492841180 },
{ 0.5467135071, 0.9147646559, 0.0707254322, 0.2152878776, 0.7878983588, 0.8091145798, 0.5388591950, 0.8246795276, 0.8707278268, 0.1681500320, 0.7415746797, 0.0302445951, 0.8784504355, 0.4278571715, 0.4677992220, 0.9081076475 },
{ 0.6055370365, 0.9735881853, 0.1295489616, 0.2741114070, 0.8467218882, 0.8679381093, 0.5976827244, 0.8835030570, 0.9295513562, 0.2269735614, 0.8003982091, 0.0890681245, 0.9372739649, 0.4866807009, 0.5266227514, 0.9669311769 },
{ 0.6643605659, 0.0324117147, 0.1883724910, 0.3329349364, 0.9055454176, 0.9267616387, 0.6565062538, 0.9423265864, 0.9883748856, 0.2857970908, 0.8592217385, 0.1478916539, 0.9960974943, 0.5455042304, 0.5854462809, 0.0257547063 },
{ 0.7231840953, 0.0912352441, 0.2471960204, 0.3917584658, 0.9643689470, 0.9855851681, 0.7153297832, 0.0011501158, 0.0471984151, 0.3446206202, 0.9180452679, 0.2067151833, 0.0549210237, 0.6043277598, 0.6442698103, 0.0845782357 },
{ 0.7820076247, 0.1500587735, 0.3060195499, 0.4505819952, 0.0231924764, 0.0444086975, 0.7741533126, 0.0599736452, 0.1060219445, 0.4034441497, 0.9768687974, 0.2655387127, 0.1137445531, 0.6631512892, 0.7030933397, 0.1434017651 }
};
QRNG_VALIDATION_TEST_FUNCTIONS(faure)
BOOST_AUTO_TEST_CASE( validate_faure )
{
test_faure_values(faure_02_100, 15);
test_faure_values(faure_07_100, 2400);
test_faure_values(faure_16_100, 83520);
}
BOOST_AUTO_TEST_CASE( validate_faure_seed )
{
test_faure_seed(faure_02_100, 15);
test_faure_seed(faure_07_100, 2400);
test_faure_seed(faure_16_100, 83520);
}
BOOST_AUTO_TEST_CASE( validate_faure_discard )
{
test_faure_discard(faure_02_100, 15);
test_faure_discard(faure_07_100, 2400);
test_faure_discard(faure_16_100, 83520);
}

3
libs/random/test/multiprecision_float_test.cpp
View File

@@ -14,6 +14,7 @@
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/core/ignore_unused.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/debug_adaptor.hpp>
@@ -83,7 +84,6 @@ typedef boost::mpl::list <
//boost::random::uniform_01<big_float>, // doesn't respect the concept! But gets used internally anyway.
boost::random::uniform_real_distribution<big_float>,
boost::random::uniform_on_sphere<big_float>,
boost::random::uniform_real_distribution<big_float>,
boost::random::weibull_distribution<big_float>
> distributions;
@@ -95,6 +95,7 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(distributions_test, dist_type, distributions)
result_type a = (d.min)();
result_type b = (d.max)();
typename dist_type::param_type p = d.param();
boost::ignore_unused(p);
d.reset();
std::stringstream ss;

2
libs/random/test/multiprecision_int_test.cpp
View File

@@ -20,6 +20,7 @@
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include <boost/core/ignore_unused.hpp>
#include <boost/multiprecision/debug_adaptor.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
@@ -63,6 +64,7 @@ BOOST_AUTO_TEST_CASE_TEMPLATE(generator_test, engine_type, engines)
gen.discard(20);
typename engine_type::base_type base(gen.base());
boost::ignore_unused(base);
std::stringstream ss;
ss << gen;

379
libs/random/test/niederreiter_base2_validate.cpp Normal file
View File

@@ -0,0 +1,379 @@
// Copyright Justinas Vygintas Daugmaudis, 2010-2018.
// Use, modification and distribution is subject to the
// Boost Software License, Version 1.0. (See accompanying
// file LICENSE-1.0 or http://www.boost.org/LICENSE-1.0)
#include <boost/random/niederreiter_base2.hpp>
#include <boost/utility.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include "test_qrng_functions.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the faure quasi-random number generator.
// These tests compare our results with values produced by the original
// version of ACM TOMS Algorithm 738, which is available in the
// TOMS subdirectory in http://www.netlib.org
//
// For independently generated datasets look at http://people.sc.fsu.edu/~jburkardt/datasets/niederreiter2/
// Spatial dimension: 2
// N: 100
// Vectors skipped: 4095
static const double niederreiter_base2_02_100[100][2] =
{
{ 0.0003662109, 0.4705810548 },
{ 0.5003662111, 0.9705810549 },
{ 0.7503662111, 0.2205810547 },
{ 0.2503662110, 0.7205810549 },
{ 0.3753662110, 0.0955810547 },
{ 0.8753662111, 0.5955810548 },
{ 0.6253662111, 0.3455810548 },
{ 0.1253662110, 0.8455810549 },
{ 0.1878662110, 0.1580810547 },
{ 0.6878662111, 0.6580810548 },
{ 0.9378662112, 0.4080810548 },
{ 0.4378662110, 0.9080810549 },
{ 0.3128662110, 0.2830810548 },
{ 0.8128662111, 0.7830810549 },
{ 0.5628662111, 0.0330810547 },
{ 0.0628662110, 0.5330810548 },
{ 0.0941162110, 0.0018310547 },
{ 0.5941162111, 0.5018310548 },
{ 0.8441162111, 0.2518310547 },
{ 0.3441162110, 0.7518310549 },
{ 0.4691162110, 0.3768310548 },
{ 0.9691162112, 0.8768310549 },
{ 0.7191162111, 0.1268310547 },
{ 0.2191162110, 0.6268310548 },
{ 0.1566162110, 0.3143310548 },
{ 0.6566162111, 0.8143310549 },
{ 0.9066162111, 0.0643310547 },
{ 0.4066162110, 0.5643310548 },
{ 0.2816162110, 0.1893310547 },
{ 0.7816162111, 0.6893310548 },
{ 0.5316162111, 0.4393310548 },
{ 0.0316162109, 0.9393310549 },
{ 0.0472412109, 0.2362060547 },
{ 0.5472412111, 0.7362060549 },
{ 0.7972412111, 0.4862060548 },
{ 0.2972412110, 0.9862060549 },
{ 0.4222412110, 0.3612060548 },
{ 0.9222412112, 0.8612060549 },
{ 0.6722412111, 0.1112060547 },
{ 0.1722412110, 0.6112060548 },
{ 0.2347412110, 0.4237060548 },
{ 0.7347412111, 0.9237060549 },
{ 0.9847412112, 0.1737060547 },
{ 0.4847412111, 0.6737060548 },
{ 0.3597412110, 0.0487060547 },
{ 0.8597412111, 0.5487060548 },
{ 0.6097412111, 0.2987060548 },
{ 0.1097412110, 0.7987060549 },
{ 0.0784912110, 0.2674560547 },
{ 0.5784912111, 0.7674560549 },
{ 0.8284912111, 0.0174560547 },
{ 0.3284912110, 0.5174560548 },
{ 0.4534912110, 0.1424560547 },
{ 0.9534912112, 0.6424560548 },
{ 0.7034912111, 0.3924560548 },
{ 0.2034912110, 0.8924560549 },
{ 0.1409912110, 0.0799560547 },
{ 0.6409912111, 0.5799560548 },
{ 0.8909912111, 0.3299560548 },
{ 0.3909912110, 0.8299560549 },
{ 0.2659912110, 0.4549560548 },
{ 0.7659912111, 0.9549560549 },
{ 0.5159912111, 0.2049560547 },
{ 0.0159912109, 0.7049560549 },
{ 0.0238037109, 0.1190185547 },
{ 0.5238037111, 0.6190185548 },
{ 0.7738037111, 0.3690185548 },
{ 0.2738037110, 0.8690185549 },
{ 0.3988037110, 0.4940185548 },
{ 0.8988037111, 0.9940185549 },
{ 0.6488037111, 0.2440185547 },
{ 0.1488037110, 0.7440185549 },
{ 0.2113037110, 0.3065185548 },
{ 0.7113037111, 0.8065185549 },
{ 0.9613037112, 0.0565185547 },
{ 0.4613037110, 0.5565185548 },
{ 0.3363037110, 0.1815185547 },
{ 0.8363037111, 0.6815185548 },
{ 0.5863037111, 0.4315185548 },
{ 0.0863037110, 0.9315185549 },
{ 0.1175537110, 0.4002685548 },
{ 0.6175537111, 0.9002685549 },
{ 0.8675537111, 0.1502685547 },
{ 0.3675537110, 0.6502685548 },
{ 0.4925537111, 0.0252685547 },
{ 0.9925537112, 0.5252685548 },
{ 0.7425537111, 0.2752685548 },
{ 0.2425537110, 0.7752685549 },
{ 0.1800537110, 0.2127685547 },
{ 0.6800537111, 0.7127685549 },
{ 0.9300537112, 0.4627685548 },
{ 0.4300537110, 0.9627685549 },
{ 0.3050537110, 0.3377685548 },
{ 0.8050537111, 0.8377685549 },
{ 0.5550537111, 0.0877685547 },
{ 0.0550537110, 0.5877685548 },
{ 0.0394287109, 0.3533935548 },
{ 0.5394287111, 0.8533935549 },
{ 0.7894287111, 0.1033935547 },
{ 0.2894287110, 0.6033935548 }
};
// Spatial dimension: 7
// N: 100
// Vectors skipped: 4095
static const double niederreiter_base2_07_100[100][7] =
{
{ 0.0003662109, 0.4705810548, 0.6358642580, 0.9561767580, 0.6715087892, 0.9793701174, 0.6053466798 },
{ 0.5003662111, 0.9705810549, 0.3858642579, 0.0811767578, 0.2965087891, 0.0418701172, 0.4178466798 },
{ 0.7503662111, 0.2205810547, 0.9483642580, 0.8155517580, 0.5621337892, 0.9207763674, 0.5467529298 },
{ 0.2503662110, 0.7205810549, 0.1983642579, 0.1905517579, 0.4371337892, 0.1082763672, 0.4842529298 },
{ 0.3753662110, 0.0955810547, 0.2608642579, 0.7374267580, 0.7652587892, 0.8465576174, 0.6600341798 },
{ 0.8753662111, 0.5955810548, 0.5108642579, 0.3624267579, 0.1402587891, 0.1590576172, 0.3475341798 },
{ 0.6253662111, 0.3455810548, 0.0733642578, 0.5968017580, 0.9058837893, 0.7879638674, 0.7264404299 },
{ 0.1253662110, 0.8455810549, 0.8233642580, 0.4718017579, 0.0308837891, 0.2254638672, 0.2889404298 },
{ 0.1878662110, 0.1580810547, 0.1514892578, 0.2686767579, 0.3590087891, 0.7449951174, 0.9334716799 },
{ 0.6878662111, 0.6580810548, 0.9014892580, 0.6436767580, 0.7340087892, 0.3074951173, 0.1209716797 },
{ 0.9378662112, 0.4080810548, 0.4639892579, 0.3780517579, 0.4996337892, 0.6864013673, 0.9998779299 },
{ 0.4378662110, 0.9080810549, 0.7139892580, 0.5030517579, 0.6246337892, 0.3739013673, 0.0623779297 },
{ 0.3128662110, 0.2830810548, 0.7764892580, 0.0499267578, 0.2027587891, 0.6121826173, 0.8631591799 },
{ 0.8128662111, 0.7830810549, 0.0264892578, 0.9249267580, 0.8277587893, 0.4246826173, 0.1756591797 },
{ 0.5628662111, 0.0330810547, 0.5889892579, 0.1593017578, 0.0933837891, 0.5535888673, 0.8045654299 },
{ 0.0628662110, 0.5330810548, 0.3389892579, 0.7843017580, 0.9683837893, 0.4910888673, 0.2420654297 },
{ 0.0941162110, 0.0018310547, 0.9171142580, 0.5635986329, 0.4195556642, 0.3856201173, 0.3865966798 },
{ 0.5941162111, 0.5018310548, 0.1671142579, 0.4385986329, 0.5445556642, 0.5731201173, 0.5740966798 },
{ 0.8441162111, 0.2518310547, 0.7296142580, 0.7042236330, 0.3101806641, 0.4520263673, 0.4530029298 },
{ 0.3441162110, 0.7518310549, 0.4796142579, 0.3292236329, 0.6851806642, 0.5145263673, 0.5155029298 },
{ 0.4691162110, 0.3768310548, 0.0421142578, 0.8448486330, 0.0133056641, 0.2528076172, 0.3162841798 },
{ 0.9691162112, 0.8768310549, 0.7921142580, 0.2198486329, 0.8883056643, 0.6903076173, 0.6287841798 },
{ 0.7191162111, 0.1268310547, 0.3546142579, 0.9854736330, 0.1539306641, 0.3192138673, 0.2576904297 },
{ 0.2191162110, 0.6268310548, 0.6046142580, 0.1104736328, 0.7789306642, 0.6317138673, 0.6951904298 },
{ 0.1566162110, 0.3143310548, 0.4327392579, 0.1260986328, 0.6070556642, 0.1512451172, 0.0897216797 },
{ 0.6566162111, 0.8143310549, 0.6827392580, 0.7510986330, 0.4820556642, 0.8387451174, 0.9022216799 },
{ 0.9066162111, 0.0643310547, 0.2452392579, 0.0167236328, 0.7476806642, 0.2176513672, 0.0311279297 },
{ 0.4066162110, 0.5643310548, 0.9952392580, 0.8917236330, 0.3726806641, 0.7801513674, 0.9686279299 },
{ 0.2816162110, 0.1893310547, 0.5577392579, 0.4073486329, 0.9508056643, 0.0184326172, 0.1444091797 },
{ 0.7816162111, 0.6893310548, 0.3077392579, 0.5323486329, 0.0758056641, 0.9559326174, 0.8319091799 },
{ 0.5316162111, 0.4393310548, 0.8702392580, 0.2979736329, 0.8414306643, 0.0848388672, 0.2108154297 },
{ 0.0316162109, 0.9393310549, 0.1202392578, 0.6729736330, 0.2164306641, 0.8973388674, 0.7733154299 },
{ 0.0472412109, 0.2362060547, 0.4522705079, 0.1007080078, 0.0426025391, 0.7955322267, 0.4801025392 },
{ 0.5472412111, 0.7362060549, 0.7022705080, 0.9757080080, 0.9176025393, 0.2330322266, 0.5426025392 },
{ 0.7972412111, 0.4862060548, 0.1397705078, 0.2413330079, 0.1832275391, 0.8541259768, 0.4215087892 },
{ 0.2972412110, 0.9862060549, 0.8897705080, 0.8663330080, 0.8082275393, 0.1666259766, 0.6090087892 },
{ 0.4222412110, 0.3612060548, 0.5772705079, 0.3194580079, 0.3863525392, 0.9127197268, 0.2847900391 },
{ 0.9222412112, 0.8612060549, 0.3272705079, 0.6944580080, 0.5113525392, 0.1002197266, 0.7222900392 },
{ 0.6722412111, 0.1112060547, 0.7647705080, 0.4600830079, 0.2769775391, 0.9713134768, 0.3511962891 },
{ 0.1722412110, 0.6112060548, 0.0147705078, 0.5850830079, 0.6519775392, 0.0338134766, 0.6636962892 },
{ 0.2347412110, 0.4237060548, 0.9678955080, 0.6632080080, 0.9801025393, 0.5611572267, 0.0582275391 },
{ 0.7347412111, 0.9237060549, 0.2178955079, 0.2882080079, 0.1051025391, 0.4986572267, 0.9957275393 },
{ 0.9847412112, 0.1737060547, 0.6553955080, 0.5538330079, 0.8707275393, 0.6197509767, 0.1246337891 },
{ 0.4847412111, 0.6737060548, 0.4053955079, 0.4288330079, 0.2457275391, 0.4322509767, 0.9371337893 },
{ 0.3597412110, 0.0487060547, 0.0928955078, 0.8819580080, 0.5738525392, 0.6783447267, 0.2379150391 },
{ 0.8597412111, 0.5487060548, 0.8428955080, 0.0069580078, 0.4488525392, 0.3658447266, 0.8004150392 },
{ 0.6097412111, 0.2987060548, 0.2803955079, 0.7725830080, 0.7144775392, 0.7369384767, 0.1793212891 },
{ 0.1097412110, 0.7987060549, 0.5303955079, 0.1475830078, 0.3394775391, 0.2994384766, 0.8668212893 },
{ 0.0784912110, 0.2674560547, 0.2335205079, 0.4893798829, 0.7906494142, 0.3267822266, 0.5113525392 },
{ 0.5784912111, 0.7674560549, 0.9835205080, 0.6143798830, 0.1656494141, 0.6392822267, 0.4488525392 },
{ 0.8284912111, 0.0174560547, 0.4210205079, 0.3487548829, 0.9312744143, 0.2603759766, 0.5777587892 },
{ 0.3284912110, 0.5174560548, 0.6710205080, 0.7237548830, 0.0562744141, 0.6978759767, 0.3902587892 },
{ 0.4534912110, 0.1424560547, 0.8585205080, 0.2081298829, 0.6343994142, 0.4439697267, 0.6910400392 },
{ 0.9534912112, 0.6424560548, 0.1085205078, 0.8331298830, 0.2593994141, 0.5064697267, 0.2535400391 },
{ 0.7034912111, 0.3924560548, 0.5460205079, 0.0675048828, 0.5250244142, 0.3775634767, 0.6324462892 },
{ 0.2034912110, 0.8924560549, 0.2960205079, 0.9425048830, 0.4000244142, 0.5650634767, 0.3199462891 },
{ 0.1409912110, 0.0799560547, 0.7491455080, 0.8018798830, 0.2281494141, 0.0924072266, 0.9644775393 },
{ 0.6409912111, 0.5799560548, 0.4991455079, 0.1768798829, 0.8531494143, 0.9049072268, 0.0269775391 },
{ 0.8909912111, 0.3299560548, 0.9366455080, 0.9112548830, 0.1187744141, 0.0260009766, 0.9058837893 },
{ 0.3909912110, 0.8299560549, 0.1866455079, 0.0362548828, 0.9937744143, 0.9635009768, 0.0933837891 },
{ 0.2659912110, 0.4549560548, 0.3741455079, 0.5206298829, 0.3218994141, 0.2095947266, 0.7691650392 },
{ 0.7659912111, 0.9549560549, 0.6241455080, 0.3956298829, 0.6968994142, 0.7720947267, 0.2066650391 },
{ 0.5159912111, 0.2049560547, 0.0616455078, 0.6300048830, 0.4625244142, 0.1431884766, 0.8355712893 },
{ 0.0159912109, 0.7049560549, 0.8116455080, 0.2550048829, 0.5875244142, 0.8306884768, 0.1480712891 },
{ 0.0238037109, 0.1190185547, 0.0186767578, 0.1827392579, 0.9136962893, 0.5960693361, 0.2923583985 },
{ 0.5238037111, 0.6190185548, 0.7686767580, 0.8077392580, 0.0386962891, 0.4085693360, 0.7298583986 },
{ 0.7738037111, 0.3690185548, 0.3311767579, 0.0421142578, 0.8043212892, 0.5374755861, 0.3587646485 },
{ 0.2738037110, 0.8690185549, 0.5811767579, 0.9171142580, 0.1793212891, 0.4749755860, 0.6712646486 },
{ 0.3988037110, 0.4940185548, 0.8936767580, 0.4014892579, 0.5074462892, 0.7288818361, 0.4720458985 },
{ 0.8988037111, 0.9940185549, 0.1436767578, 0.5264892579, 0.3824462892, 0.2913818360, 0.5345458986 },
{ 0.6488037111, 0.2440185547, 0.7061767580, 0.2608642579, 0.6480712892, 0.6702880861, 0.4134521485 },
{ 0.1488037110, 0.7440185549, 0.4561767579, 0.6358642580, 0.2730712891, 0.3577880860, 0.6009521486 },
{ 0.2113037110, 0.3065185548, 0.5030517579, 0.6202392580, 0.1011962891, 0.8616943361, 0.2454833985 },
{ 0.7113037111, 0.8065185549, 0.2530517579, 0.4952392579, 0.9761962893, 0.1741943360, 0.8079833986 },
{ 0.9613037112, 0.0565185547, 0.8155517580, 0.7296142580, 0.2418212891, 0.8031005861, 0.1868896485 },
{ 0.4613037110, 0.5565185548, 0.0655517578, 0.3546142579, 0.8668212893, 0.2406005860, 0.8743896486 },
{ 0.3363037110, 0.1815185547, 0.3780517579, 0.8389892580, 0.4449462892, 0.9945068362, 0.0501708984 },
{ 0.8363037111, 0.6815185548, 0.6280517580, 0.2139892579, 0.5699462892, 0.0570068360, 0.9876708987 },
{ 0.5863037111, 0.4315185548, 0.1905517579, 0.9483642580, 0.3355712891, 0.9359130862, 0.1165771485 },
{ 0.0863037110, 0.9315185549, 0.9405517580, 0.0733642578, 0.7105712892, 0.1234130860, 0.9290771487 },
{ 0.1175537110, 0.4002685548, 0.2999267579, 0.2901611329, 0.1617431641, 0.0023193359, 0.6986083986 },
{ 0.6175537111, 0.9002685549, 0.5499267579, 0.6651611330, 0.7867431642, 0.9398193362, 0.2611083985 },
{ 0.8675537111, 0.1502685547, 0.1124267578, 0.4307861329, 0.0523681641, 0.0687255860, 0.6400146486 },
{ 0.3675537110, 0.6502685548, 0.8624267580, 0.5557861329, 0.9273681643, 0.8812255861, 0.3275146485 },
{ 0.4925537111, 0.0252685547, 0.6749267580, 0.0089111328, 0.2554931641, 0.1351318360, 0.5032958986 },
{ 0.9925537112, 0.5252685548, 0.4249267579, 0.8839111330, 0.6304931642, 0.8226318361, 0.4407958985 },
{ 0.7425537111, 0.2752685548, 0.9874267580, 0.1495361328, 0.3961181642, 0.2015380860, 0.5697021486 },
{ 0.2425537110, 0.7752685549, 0.2374267579, 0.7745361330, 0.5211181642, 0.7640380861, 0.3822021485 },
{ 0.1800537110, 0.2127685547, 0.7843017580, 0.9776611330, 0.8492431643, 0.2679443360, 0.7767333986 },
{ 0.6800537111, 0.7127685549, 0.0343017578, 0.1026611328, 0.2242431641, 0.7054443361, 0.2142333985 },
{ 0.9300537112, 0.4627685548, 0.5968017580, 0.8682861330, 0.9898681643, 0.3343505860, 0.8431396486 },
{ 0.4300537110, 0.9627685549, 0.3468017579, 0.2432861329, 0.1148681641, 0.6468505861, 0.1556396485 },
{ 0.3050537110, 0.3377685548, 0.1593017578, 0.6964111330, 0.6929931642, 0.4007568360, 0.9564208987 },
{ 0.8050537111, 0.8377685549, 0.9093017580, 0.3214111329, 0.3179931641, 0.5882568361, 0.0189208984 },
{ 0.5550537111, 0.0877685547, 0.4718017579, 0.5870361329, 0.5836181642, 0.4671630860, 0.8978271486 },
{ 0.0550537110, 0.5877685548, 0.7218017580, 0.4620361329, 0.4586181642, 0.5296630861, 0.0853271485 },
{ 0.0394287109, 0.3533935548, 0.8350830080, 0.7647705080, 0.2847900391, 0.6622314455, 0.6671142580 },
{ 0.5394287111, 0.8533935549, 0.0850830078, 0.1397705078, 0.6597900392, 0.3497314454, 0.3546142579 },
{ 0.7894287111, 0.1033935547, 0.5225830079, 0.9053955080, 0.4254150392, 0.7208251955, 0.7335205080 },
{ 0.2894287110, 0.6033935548, 0.2725830079, 0.0303955078, 0.5504150392, 0.2833251954, 0.2960205079 }
};
// Spatial dimension: 16
// N: 100
// Vectors skipped: 4095
static const double niederreiter_base2_16_100[100][16] =
{
{ 0.0003662109, 0.4705810548, 0.6358642580, 0.9561767580, 0.6715087892, 0.9793701174, 0.6053466798, 0.1983642579, 0.2217731476, 0.3769855500, 0.5390644075, 0.4707050325, 0.2744159699, 0.9942340853, 0.5396728517, 0.0626220703 },
{ 0.5003662111, 0.9705810549, 0.3858642579, 0.0811767578, 0.2965087891, 0.0418701172, 0.4178466798, 0.7608642580, 0.7530231478, 0.5957355501, 0.4453144075, 0.5019550325, 0.7431659700, 0.0254840851, 0.4615478517, 0.9219970705 },
{ 0.7503662111, 0.2205810547, 0.9483642580, 0.8155517580, 0.5621337892, 0.9207763674, 0.5467529298, 0.1397705078, 0.1895465851, 0.4092121125, 0.5087909700, 0.4404315950, 0.3046894074, 0.9639606478, 0.5555419923, 0.0784912110 },
{ 0.2503662110, 0.7205810549, 0.1983642579, 0.1905517579, 0.4371337892, 0.1082763672, 0.4842529298, 0.8272705080, 0.7832965853, 0.5654621126, 0.4775409700, 0.5341815950, 0.7109394075, 0.0577106476, 0.4461669923, 0.9066162111 },
{ 0.3753662110, 0.0955810547, 0.2608642579, 0.7374267580, 0.7652587892, 0.8465576174, 0.6600341798, 0.0030517578, 0.1573200226, 0.4375324250, 0.6035175325, 0.3750019074, 0.3701190949, 0.8985309603, 0.5079345704, 0.0943603516 },
{ 0.8753662111, 0.5955810548, 0.5108642579, 0.3624267579, 0.1402587891, 0.1590576172, 0.3475341798, 0.9405517580, 0.8135700228, 0.5312824251, 0.3847675324, 0.5937519075, 0.6513690950, 0.1172809601, 0.4923095704, 0.8912353518 },
{ 0.6253662111, 0.3455810548, 0.0733642578, 0.5968017580, 0.9058837893, 0.7879638674, 0.7264404299, 0.0694580078, 0.1250934601, 0.4697589875, 0.5732440950, 0.4072284699, 0.3378925324, 0.9307575228, 0.5238037111, 0.1102294922 },
{ 0.1253662110, 0.8455810549, 0.8233642580, 0.4718017579, 0.0308837891, 0.2254638672, 0.2889404298, 0.8819580080, 0.8438434603, 0.5010089875, 0.4169940949, 0.5634784700, 0.6816425325, 0.0870075226, 0.4769287110, 0.8758544924 },
{ 0.1878662110, 0.1580810547, 0.1514892578, 0.2686767579, 0.3590087891, 0.7449951174, 0.9334716799, 0.3389892579, 0.1006793976, 0.2871418000, 0.6367206575, 0.2558612824, 0.4658222200, 0.8106403353, 0.6031494142, 0.0010986328 },
{ 0.6878662111, 0.6580810548, 0.9014892580, 0.6436767580, 0.7340087892, 0.3074951173, 0.1209716797, 0.6514892580, 0.8819293978, 0.6933918001, 0.3554706574, 0.7246112825, 0.5595722200, 0.2168903351, 0.4000244142, 0.9854736330 },
{ 0.9378662112, 0.4080810548, 0.4639892579, 0.3780517579, 0.4996337892, 0.6864013673, 0.9998779299, 0.2803955079, 0.0684528351, 0.2568683625, 0.6689472200, 0.2880878449, 0.4960956575, 0.7803668978, 0.6190185548, 0.0169677734 },
{ 0.4378662110, 0.9080810549, 0.7139892580, 0.5030517579, 0.6246337892, 0.3739013673, 0.0623779297, 0.7178955080, 0.9122028353, 0.7256183626, 0.3251972199, 0.6943378450, 0.5273456575, 0.2491168976, 0.3846435548, 0.9700927737 },
{ 0.3128662110, 0.2830810548, 0.7764892580, 0.0499267578, 0.2027587891, 0.6121826173, 0.8631591799, 0.3936767579, 0.0362262726, 0.3476886750, 0.7011737825, 0.3476581574, 0.4365253450, 0.8399372103, 0.5714111329, 0.0328369141 },
{ 0.8128662111, 0.7830810549, 0.0264892578, 0.9249267580, 0.8277587893, 0.4246826173, 0.1756591797, 0.5811767579, 0.9424762728, 0.6289386751, 0.2949237824, 0.6289081575, 0.5927753450, 0.1836872101, 0.4307861329, 0.9547119143 },
{ 0.5628662111, 0.0330810547, 0.5889892579, 0.1593017578, 0.0933837891, 0.5535888673, 0.8045654299, 0.4600830079, 0.0039997101, 0.3174152375, 0.7334003450, 0.3173847199, 0.4042987824, 0.8721637728, 0.5872802736, 0.0487060547 },
{ 0.0628662110, 0.5330810548, 0.3389892579, 0.7843017580, 0.9683837893, 0.4910888673, 0.2420654297, 0.5225830079, 0.9727497103, 0.6611652376, 0.2646503449, 0.6611347200, 0.6230487825, 0.1534137726, 0.4154052735, 0.9393310549 },
{ 0.0941162110, 0.0018310547, 0.9171142580, 0.5635986329, 0.4195556642, 0.3856201173, 0.3865966798, 0.9796142580, 0.4483356477, 0.1972980500, 0.8125019075, 0.0410175324, 0.1728534699, 0.6114215852, 0.6666259767, 0.2052001954 },
{ 0.5941162111, 0.5018310548, 0.1671142579, 0.4385986329, 0.5445556642, 0.5731201173, 0.5740966798, 0.0421142578, 0.5420856477, 0.7910480501, 0.1562519074, 0.9472675326, 0.8291034700, 0.3926715852, 0.3385009766, 0.7833251955 },
{ 0.8441162111, 0.2518310547, 0.7296142580, 0.7042236330, 0.3101806641, 0.4520263673, 0.4530029298, 0.9210205080, 0.4786090852, 0.2295246125, 0.8447284700, 0.0107440949, 0.1406269074, 0.5811481477, 0.6824951173, 0.1898193360 },
{ 0.3441162110, 0.7518310549, 0.4796142579, 0.3292236329, 0.6851806642, 0.5145263673, 0.5155029298, 0.1085205078, 0.5098590852, 0.7607746126, 0.1259784699, 0.9794940951, 0.8593769075, 0.4248981477, 0.3231201173, 0.7991943361 },
{ 0.4691162110, 0.3768310548, 0.0421142578, 0.8448486330, 0.0133056641, 0.2528076172, 0.3162841798, 0.7843017580, 0.3838825227, 0.1328449250, 0.7519550325, 0.0703144074, 0.2060565949, 0.5157184602, 0.6348876955, 0.2369384766 },
{ 0.9691162112, 0.8768310549, 0.7921142580, 0.2198486329, 0.8883056643, 0.6903076173, 0.6287841798, 0.2218017579, 0.6026325227, 0.8515949251, 0.2207050324, 0.9140644076, 0.7998065950, 0.4844684602, 0.3692626954, 0.7525634767 },
{ 0.7191162111, 0.1268310547, 0.3546142579, 0.9854736330, 0.1539306641, 0.3192138673, 0.2576904297, 0.8507080080, 0.4141559602, 0.1650714875, 0.7841815950, 0.1025409699, 0.2363300324, 0.5479450227, 0.6507568361, 0.2215576172 },
{ 0.2191162110, 0.6268310548, 0.6046142580, 0.1104736328, 0.7789306642, 0.6317138673, 0.6951904298, 0.1632080079, 0.5704059602, 0.8213214876, 0.1904315949, 0.8837909701, 0.7675800325, 0.4541950227, 0.3538818360, 0.7684326174 },
{ 0.1566162110, 0.3143310548, 0.4327392579, 0.1260986328, 0.6070556642, 0.1512451172, 0.0897216797, 0.6202392580, 0.3272418977, 0.1074543000, 0.9726581576, 0.2011737824, 0.1142597199, 0.6778278352, 0.7301025392, 0.1436767578 },
{ 0.6566162111, 0.8143310549, 0.6827392580, 0.7510986330, 0.4820556642, 0.8387451174, 0.9022216799, 0.4327392579, 0.6709918977, 0.8887043001, 0.0039081573, 0.7949237825, 0.8955097201, 0.3340778352, 0.2769775391, 0.8468017580 },
{ 0.9066162111, 0.0643310547, 0.2452392579, 0.0167236328, 0.7476806642, 0.2176513672, 0.0311279297, 0.5616455079, 0.3575153352, 0.0771808624, 0.9423847201, 0.2334003449, 0.0820331574, 0.6475543977, 0.7459716799, 0.1282958985 },
{ 0.4066162110, 0.5643310548, 0.9952392580, 0.8917236330, 0.3726806641, 0.7801513674, 0.9686279299, 0.4991455079, 0.6387653352, 0.9209308626, 0.0361347199, 0.7646503450, 0.9257831576, 0.3663043977, 0.2615966797, 0.8626708986 },
{ 0.2816162110, 0.1893310547, 0.5577392579, 0.4073486329, 0.9508056643, 0.0184326172, 0.1444091797, 0.6749267580, 0.2627887726, 0.0430011749, 0.9121112826, 0.1679706574, 0.0224628449, 0.7071247102, 0.6983642580, 0.1754150391 },
{ 0.7816162111, 0.6893310548, 0.3077392579, 0.5323486329, 0.0758056641, 0.9559326174, 0.8319091799, 0.3624267579, 0.7315387728, 0.9492511751, 0.0683612824, 0.8242206575, 0.9912128451, 0.3008747102, 0.3077392579, 0.8160400393 },
{ 0.5316162111, 0.4393310548, 0.8702392580, 0.2979736329, 0.8414306643, 0.0848388672, 0.2108154297, 0.7413330080, 0.2930622102, 0.0127277374, 0.8818378451, 0.1376972199, 0.0527362824, 0.7393512728, 0.7142333986, 0.1600341797 },
{ 0.0316162109, 0.9393310549, 0.1202392578, 0.6729736330, 0.2164306641, 0.8973388674, 0.7733154299, 0.3038330079, 0.6993122102, 0.9814777377, 0.1005878449, 0.8564472200, 0.9589862826, 0.2706012726, 0.2923583985, 0.8319091799 },
{ 0.0472412109, 0.2362060547, 0.4522705079, 0.1007080078, 0.0426025391, 0.7955322267, 0.4801025392, 0.7025146486, 0.6748981477, 0.7988605501, 0.2421894074, 0.6113300325, 0.5712909700, 0.1973590851, 0.7935791017, 0.3477783204 },
{ 0.5472412111, 0.7362060549, 0.7022705080, 0.9757080080, 0.9176025393, 0.2330322266, 0.5426025392, 0.2650146485, 0.3311481477, 0.2051105500, 0.7734394075, 0.3925800324, 0.4150409699, 0.7911090853, 0.2154541016, 0.6446533205 },
{ 0.7972412111, 0.4862060548, 0.1397705078, 0.2413330079, 0.1832275391, 0.8541259768, 0.4215087892, 0.6361083986, 0.6426715852, 0.7685871126, 0.2119159699, 0.5810565950, 0.6015644075, 0.2295856476, 0.8094482424, 0.3636474610 },
{ 0.2972412110, 0.9862060549, 0.8897705080, 0.8663330080, 0.8082275393, 0.1666259766, 0.6090087892, 0.3236083985, 0.3614215852, 0.2373371125, 0.8056659700, 0.4248065949, 0.3828144074, 0.7608356478, 0.2000732422, 0.6292724611 },
{ 0.4222412110, 0.3612060548, 0.5772705079, 0.3194580079, 0.3863525392, 0.9127197268, 0.2847900391, 0.5072021486, 0.7354450228, 0.8594074251, 0.1816425324, 0.5156269075, 0.5419940950, 0.1641559601, 0.7618408205, 0.3170166016 },
{ 0.9222412112, 0.8612060549, 0.3272705079, 0.6944580080, 0.5113525392, 0.1002197266, 0.7222900392, 0.4447021485, 0.2666950226, 0.1406574250, 0.8378925325, 0.4843769075, 0.4482440950, 0.8204059603, 0.2462158204, 0.6763916017 },
{ 0.6722412111, 0.1112060547, 0.7647705080, 0.4600830079, 0.2769775391, 0.9713134768, 0.3511962891, 0.5657958986, 0.7032184602, 0.8291339876, 0.1513690949, 0.5478534700, 0.5097675325, 0.1338825226, 0.7777099611, 0.3328857423 },
{ 0.1722412110, 0.6112060548, 0.0147705078, 0.5850830079, 0.6519775392, 0.0338134766, 0.6636962892, 0.3782958985, 0.2969684602, 0.1728839875, 0.8701190951, 0.4541034700, 0.4785175325, 0.8526325228, 0.2308349610, 0.6610107423 },
{ 0.2347412110, 0.4237060548, 0.9678955080, 0.6632080080, 0.9801025393, 0.5611572267, 0.0582275391, 0.8431396486, 0.5538043977, 0.8965168001, 0.0898456574, 0.6464862825, 0.6376972200, 0.0137653351, 0.8570556643, 0.2862548829 },
{ 0.7347412111, 0.9237060549, 0.2178955079, 0.2882080079, 0.1051025391, 0.4986572267, 0.9957275393, 0.1556396485, 0.4600543977, 0.1152668000, 0.9335956576, 0.3652362824, 0.3564472199, 0.9825153353, 0.1539306641, 0.7081298830 },
{ 0.9847412112, 0.1737060547, 0.6553955080, 0.5538330079, 0.8707275393, 0.6197509767, 0.1246337891, 0.7767333986, 0.5215778352, 0.9287433626, 0.1220722199, 0.6787128450, 0.6679706575, 0.0459918976, 0.8729248049, 0.3021240235 },
{ 0.4847412111, 0.6737060548, 0.4053955079, 0.4288330079, 0.2457275391, 0.4322509767, 0.9371337893, 0.2142333985, 0.4903278352, 0.0849933624, 0.9033222201, 0.3349628449, 0.3242206574, 0.9522418978, 0.1385498047, 0.6927490236 },
{ 0.3597412110, 0.0487060547, 0.0928955078, 0.8819580080, 0.5738525392, 0.6783447267, 0.2379150391, 0.8978271486, 0.6143512727, 0.9570636751, 0.0292987824, 0.7382831575, 0.7334003450, 0.1055622101, 0.8253173830, 0.2554931641 },
{ 0.8597412111, 0.5487060548, 0.8428955080, 0.0069580078, 0.4488525392, 0.3658447266, 0.8004150392, 0.0853271485, 0.3956012727, 0.0508136749, 0.9980487826, 0.2695331574, 0.2646503449, 0.8868122103, 0.1846923829, 0.7398681642 },
{ 0.6097412111, 0.2987060548, 0.2803955079, 0.7725830080, 0.7144775392, 0.7369384767, 0.1793212891, 0.9564208987, 0.5821247102, 0.9892902377, 0.0615253449, 0.7080097200, 0.7011737825, 0.0752887726, 0.8411865236, 0.2713623048 },
{ 0.1097412110, 0.7987060549, 0.5303955079, 0.1475830078, 0.3394775391, 0.2994384766, 0.8668212893, 0.0189208984, 0.4258747102, 0.0205402374, 0.9677753451, 0.3017597199, 0.2949237824, 0.9190387728, 0.1693115235, 0.7244873049 },
{ 0.0784912110, 0.2674560547, 0.2335205079, 0.4893798829, 0.7906494142, 0.3267822266, 0.5113525392, 0.4837646486, 0.9014606478, 0.6191730501, 0.3906269074, 0.9316425326, 0.9697284701, 0.3145465852, 0.9205322268, 0.4903564454 },
{ 0.5784912111, 0.7674560549, 0.9835205080, 0.6143798830, 0.1656494141, 0.6392822267, 0.4488525392, 0.5462646486, 0.1202106476, 0.4004230500, 0.6093769075, 0.0878925324, 0.0009784698, 0.6582965852, 0.0924072266, 0.5059814454 },
{ 0.8284912111, 0.0174560547, 0.4210205079, 0.3487548829, 0.9312744143, 0.2603759766, 0.5777587892, 0.4173583985, 0.9317340853, 0.5888996126, 0.4228534699, 0.9013690951, 0.9375019076, 0.3467731477, 0.9364013674, 0.4749755860 },
{ 0.3284912110, 0.5174560548, 0.6710205080, 0.7237548830, 0.0562744141, 0.6978759767, 0.3902587892, 0.6048583986, 0.0879840851, 0.4326496125, 0.5791034700, 0.1201190949, 0.0312519074, 0.6280231477, 0.0770263672, 0.5218505861 },
{ 0.4534912110, 0.1424560547, 0.8585205080, 0.2081298829, 0.6343994142, 0.4439697267, 0.6910400392, 0.2884521485, 0.9620075228, 0.5547199251, 0.4550800325, 0.9609394076, 0.8779315951, 0.2813434601, 0.8887939455, 0.4595947267 },
{ 0.9534912112, 0.6424560548, 0.1085205078, 0.8331298830, 0.2593994141, 0.5064697267, 0.2535400391, 0.7259521486, 0.0557575226, 0.4609699250, 0.5488300325, 0.0546894074, 0.0966815949, 0.6875934602, 0.1231689453, 0.5377197267 },
{ 0.7034912111, 0.3924560548, 0.5460205079, 0.0675048828, 0.5250244142, 0.3775634767, 0.6324462892, 0.3470458985, 0.9922809603, 0.5244464875, 0.4873065950, 0.9931659701, 0.9082050326, 0.2510700226, 0.9046630861, 0.4442138673 },
{ 0.2034912110, 0.8924560549, 0.2960205079, 0.9425048830, 0.4000244142, 0.5650634767, 0.3199462891, 0.6595458986, 0.0235309601, 0.4931964875, 0.5185565950, 0.0244159699, 0.0644550324, 0.7198200228, 0.1077880860, 0.5535888673 },
{ 0.1409912110, 0.0799560547, 0.7491455080, 0.8018798830, 0.2281494141, 0.0924072266, 0.9644775393, 0.1243896485, 0.7803668978, 0.7168293001, 0.3007831574, 0.8417987825, 0.7861347200, 0.3809528352, 0.9840087893, 0.4288330079 },
{ 0.6409912111, 0.5799560548, 0.4991455079, 0.1768798829, 0.8531494143, 0.9049072268, 0.0269775391, 0.9368896487, 0.2491168976, 0.3105793000, 0.7070331575, 0.1855487824, 0.1923847199, 0.5997028352, 0.0308837891, 0.5694580079 },
{ 0.8909912111, 0.3299560548, 0.9366455080, 0.9112548830, 0.1187744141, 0.0260009766, 0.9058837893, 0.0579833985, 0.8106403353, 0.7490558626, 0.2705097199, 0.8740253451, 0.7539081575, 0.4131793977, 0.9998779299, 0.4134521485 },
{ 0.3909912110, 0.8299560549, 0.1866455079, 0.0362548828, 0.9937744143, 0.9635009768, 0.0933837891, 0.9954833987, 0.2168903351, 0.2803058625, 0.7392597200, 0.1552753449, 0.2226581574, 0.5694293977, 0.0155029297, 0.5853271486 },
{ 0.2659912110, 0.4549560548, 0.3741455079, 0.5206298829, 0.3218994141, 0.2095947266, 0.7691650392, 0.1790771485, 0.8409137728, 0.6523761751, 0.3652362824, 0.8085956575, 0.8193378450, 0.4727497102, 0.9522705080, 0.3980712892 },
{ 0.7659912111, 0.9549560549, 0.6241455080, 0.3956298829, 0.6968994142, 0.7720947267, 0.2066650391, 0.8665771486, 0.1846637726, 0.3711261750, 0.6464862825, 0.2148456574, 0.1630878449, 0.5039997102, 0.0616455078, 0.6011962892 },
{ 0.5159912111, 0.2049560547, 0.0616455078, 0.6300048830, 0.4625244142, 0.1431884766, 0.8355712893, 0.2376708985, 0.8711872103, 0.6846027376, 0.3349628449, 0.7783222200, 0.8496112825, 0.4424762727, 0.9681396487, 0.3826904298 },
{ 0.0159912109, 0.7049560549, 0.8116455080, 0.2550048829, 0.5875244142, 0.8306884768, 0.1480712891, 0.8001708986, 0.1524372101, 0.3408527375, 0.6787128450, 0.2470722199, 0.1308612824, 0.5362262727, 0.0462646484, 0.6170654298 },
{ 0.0238037109, 0.1190185547, 0.0186767578, 0.1827392579, 0.9136962893, 0.5960693361, 0.2923583985, 0.1285400391, 0.0645160675, 0.2207050324, 0.8828449251, 0.6894855501, 0.9297199251, 0.4326801301, 0.0474853516, 0.5079345704 },
{ 0.5238037111, 0.6190185548, 0.7686767580, 0.8077392580, 0.0386962891, 0.4085693360, 0.7298583986, 0.8160400393, 0.9082660677, 0.7519550325, 0.1015949250, 0.2832355500, 0.0859699249, 0.5889301301, 0.9381103518, 0.4923095704 },
{ 0.7738037111, 0.3690185548, 0.3311767579, 0.0421142578, 0.8043212892, 0.5374755861, 0.3587646485, 0.1949462891, 0.0967426300, 0.1904315949, 0.9150714876, 0.7217121126, 0.8994464876, 0.4004535676, 0.0321044922, 0.5238037111 },
{ 0.2738037110, 0.8690185549, 0.5811767579, 0.9171142580, 0.1793212891, 0.4749755860, 0.6712646486, 0.7574462892, 0.8779926302, 0.7841815950, 0.0713214874, 0.2529621125, 0.1181964875, 0.6192035676, 0.9539794924, 0.4769287110 },
{ 0.3988037110, 0.4940185548, 0.8936767580, 0.4014892579, 0.5074462892, 0.7288818361, 0.4720458985, 0.0738525391, 0.0000629425, 0.1562519074, 0.9472980501, 0.6562824251, 0.9629230502, 0.4619770051, 0.0157470703, 0.5396728517 },
{ 0.8988037111, 0.9940185549, 0.1436767578, 0.5264892579, 0.3824462892, 0.2913818360, 0.5345458986, 0.8863525393, 0.9688129427, 0.8125019075, 0.0410480499, 0.3125324250, 0.0566730499, 0.5557270051, 0.9688720705, 0.4615478517 },
{ 0.6488037111, 0.2440185547, 0.7061767580, 0.2608642579, 0.6480712892, 0.6702880861, 0.4134521485, 0.0152587891, 0.0322895050, 0.1259784699, 0.9795246127, 0.6260089876, 0.9951496127, 0.4922504426, 0.0003662109, 0.5555419923 },
{ 0.1488037110, 0.7440185549, 0.4561767579, 0.6358642580, 0.2730712891, 0.3577880860, 0.6009521486, 0.9527587893, 0.9385395052, 0.8447284700, 0.0107746124, 0.3447589875, 0.0263996124, 0.5235004426, 0.9847412112, 0.4461669923 },
{ 0.2113037110, 0.3065185548, 0.5030517579, 0.6202392580, 0.1011962891, 0.8616943361, 0.2454833985, 0.2691650391, 0.1934223175, 0.0683612824, 0.7930011751, 0.5371418001, 0.8711261751, 0.3740863801, 0.1109619141, 0.5714111329 },
{ 0.7113037111, 0.8065185549, 0.2530517579, 0.4952392579, 0.9761962893, 0.1741943360, 0.8079833986, 0.7066650392, 0.7871723177, 0.9121112826, 0.1992511750, 0.4433918000, 0.1523761750, 0.6553363802, 0.8765869143, 0.4307861329 },
{ 0.9613037112, 0.0565185547, 0.8155517580, 0.7296142580, 0.2418212891, 0.8031005861, 0.1868896485, 0.3355712891, 0.2256488801, 0.1005878449, 0.7627277376, 0.5068683625, 0.8408527376, 0.3418598176, 0.0955810547, 0.5872802736 },
{ 0.4613037110, 0.5565185548, 0.0655517578, 0.3546142579, 0.8668212893, 0.2406005860, 0.8743896486, 0.6480712892, 0.7568988802, 0.8818378451, 0.2314777375, 0.4756183625, 0.1846027375, 0.6856098177, 0.8924560549, 0.4154052735 },
{ 0.3363037110, 0.1815185547, 0.3780517579, 0.8389892580, 0.4449462892, 0.9945068362, 0.0501708984, 0.4644775392, 0.1289691925, 0.0039081573, 0.8574543001, 0.5664386751, 0.7793293001, 0.2783832551, 0.0792236328, 0.6031494142 },
{ 0.8363037111, 0.6815185548, 0.6280517580, 0.2139892579, 0.5699462892, 0.0570068360, 0.9876708987, 0.5269775392, 0.8477191927, 0.9726581576, 0.1387043000, 0.4101886750, 0.2480793000, 0.7471332552, 0.9073486330, 0.4000244142 },
{ 0.5863037111, 0.4315185548, 0.1905517579, 0.9483642580, 0.3355712891, 0.9359130862, 0.1165771485, 0.4058837892, 0.1611957550, 0.0361347199, 0.8271808626, 0.5986652376, 0.8115558626, 0.3086566926, 0.0638427735, 0.6190185548 },
{ 0.0863037110, 0.9315185549, 0.9405517580, 0.0733642578, 0.7105712892, 0.1234130860, 0.9290771487, 0.5933837892, 0.8174457552, 0.9423847201, 0.1709308625, 0.3799152375, 0.2178058625, 0.7149066927, 0.9232177737, 0.3846435548 },
{ 0.1175537110, 0.4002685548, 0.2999267579, 0.2901611329, 0.1617431641, 0.0023193359, 0.6986083986, 0.9097900393, 0.3535785676, 0.4160175324, 0.7187824251, 0.7597980501, 0.5156574250, 0.0498676300, 0.1744384766, 0.6505126955 },
{ 0.6175537111, 0.9002685549, 0.5499267579, 0.6651611330, 0.7867431642, 0.9398193362, 0.2611083985, 0.0972900391, 0.6348285677, 0.5722675325, 0.2500324250, 0.2285480500, 0.4844074250, 0.9561176302, 0.8150634768, 0.3536376954 },
{ 0.8675537111, 0.1502685547, 0.1124267578, 0.4307861329, 0.0523681641, 0.0687255860, 0.6400146486, 0.9761962893, 0.3233051301, 0.3857440949, 0.6885089876, 0.7920246126, 0.5478839876, 0.0176410675, 0.1590576172, 0.6351318361 },
{ 0.3675537110, 0.6502685548, 0.8624267580, 0.5557861329, 0.9273681643, 0.8812255861, 0.3275146485, 0.0386962891, 0.6670551302, 0.6044940950, 0.2822589875, 0.1982746125, 0.4541339875, 0.9863910677, 0.8309326174, 0.3695068360 },
{ 0.4925537111, 0.0252685547, 0.6749267580, 0.0089111328, 0.2554931641, 0.1351318360, 0.5032958986, 0.8551025393, 0.2891254426, 0.4765644075, 0.6582355501, 0.8515949251, 0.6113605501, 0.0791645050, 0.1427001953, 0.6822509767 },
{ 0.9925537112, 0.5252685548, 0.4249267579, 0.8839111330, 0.6304931642, 0.8226318361, 0.4407958985, 0.1676025391, 0.6953754427, 0.5078144075, 0.3144855500, 0.1328449250, 0.3926105500, 0.9229145052, 0.8458251955, 0.3228759766 },
{ 0.7425537111, 0.2752685548, 0.9874267580, 0.1495361328, 0.3961181642, 0.2015380860, 0.5697021486, 0.7965087892, 0.2588520051, 0.4462909700, 0.6279621126, 0.8213214876, 0.5810871126, 0.1094379425, 0.1273193360, 0.6668701173 },
{ 0.2425537110, 0.7752685549, 0.2374267579, 0.7745361330, 0.5211181642, 0.7640380861, 0.3822021485, 0.2340087891, 0.7276020052, 0.5400409700, 0.3467121125, 0.1650714875, 0.4248371125, 0.8906879427, 0.8616943361, 0.3387451173 },
{ 0.1800537110, 0.2127685547, 0.7843017580, 0.9776611330, 0.8492431643, 0.2679443360, 0.7767333986, 0.5504150392, 0.4824848176, 0.2636737824, 0.5664386751, 0.9824543002, 0.7070636751, 0.2412738801, 0.2379150391, 0.7139892580 },
{ 0.6800537111, 0.7127685549, 0.0343017578, 0.1026611328, 0.2242431641, 0.7054443361, 0.2142333985, 0.4879150392, 0.5137348176, 0.7324237825, 0.4101886750, 0.0137042999, 0.3008136750, 0.7725238802, 0.7535400392, 0.2921142579 },
{ 0.9300537112, 0.4627685548, 0.5968017580, 0.8682861330, 0.9898681643, 0.3343505860, 0.8431396486, 0.6168212892, 0.4522113801, 0.2959003449, 0.5986652376, 0.9521808626, 0.7392902376, 0.2090473176, 0.2225341797, 0.6986083986 },
{ 0.4300537110, 0.9627685549, 0.3468017579, 0.2432861329, 0.1148681641, 0.6468505861, 0.1556396485, 0.4293212892, 0.5459613801, 0.7021503450, 0.3799152375, 0.0459308624, 0.2705402375, 0.8027973177, 0.7694091799, 0.3079833985 },
{ 0.3050537110, 0.3377685548, 0.1593017578, 0.6964111330, 0.6929931642, 0.4007568360, 0.9564208987, 0.7457275392, 0.4180316926, 0.3242206574, 0.5058918000, 0.8867511751, 0.6777668001, 0.1455707550, 0.2061767579, 0.7457275392 },
{ 0.8050537111, 0.8377685549, 0.9093017580, 0.3214111329, 0.3179931641, 0.5882568361, 0.0189208984, 0.3082275391, 0.5742816926, 0.6679706575, 0.4746418000, 0.1055011750, 0.3340168000, 0.8643207552, 0.7843017580, 0.2613525391 },
{ 0.5550537111, 0.0877685547, 0.4718017579, 0.5870361329, 0.5836181642, 0.4671630860, 0.8978271486, 0.6871337892, 0.3877582551, 0.3564472199, 0.5381183626, 0.9189777376, 0.6474933626, 0.1758441925, 0.1907958985, 0.7303466799 },
{ 0.0550537110, 0.5877685548, 0.7218017580, 0.4620361329, 0.4586181642, 0.5296630861, 0.0853271485, 0.3746337891, 0.6065082551, 0.6376972200, 0.4443683625, 0.0752277374, 0.3662433625, 0.8320941927, 0.8001708986, 0.2772216798 },
{ 0.0394287109, 0.3533935548, 0.8350830080, 0.7647705080, 0.2847900391, 0.6622314455, 0.6671142580, 0.6326904298, 0.5176410676, 0.5800800325, 0.3359699250, 0.3301105500, 0.2265949250, 0.6358051302, 0.3013916016, 0.7930908205 },
{ 0.5394287111, 0.8533935549, 0.0850830078, 0.1397705078, 0.6597900392, 0.3497314454, 0.3546142579, 0.3201904298, 0.4863910676, 0.4238300324, 0.6797199251, 0.6738605501, 0.7578449251, 0.3545551301, 0.6920166017, 0.2149658204 },
{ 0.7894287111, 0.1033935547, 0.5225830079, 0.9053955080, 0.4254150392, 0.7208251955, 0.7335205080, 0.6912841798, 0.5498676301, 0.6123065950, 0.3681964875, 0.3623371125, 0.1963214875, 0.6660785677, 0.2860107423, 0.8089599611 },
{ 0.2894287110, 0.6033935548, 0.2725830079, 0.0303955078, 0.5504150392, 0.2833251954, 0.2960205079, 0.2537841797, 0.4561176301, 0.3935565949, 0.6494464876, 0.6435871126, 0.7900714876, 0.3223285676, 0.7078857424, 0.1995849610 }
};
QRNG_VALIDATION_TEST_FUNCTIONS(niederreiter_base2)
QRNG_VALIDATION_TEST_DISCARD(niederreiter_base2)
BOOST_AUTO_TEST_CASE( check_generator_limits )
{
test_niederreiter_base2_max_seed();
test_niederreiter_base2_max_discard();
test_niederreiter_base2_max_dimension(BOOST_RANDOM_NIEDERREITER_BASE2_MAX_DIMENSION);
}
BOOST_AUTO_TEST_CASE( validate_niederreiter_base2 )
{
test_niederreiter_base2_values(niederreiter_base2_02_100, 4095);
test_niederreiter_base2_values(niederreiter_base2_07_100, 4095);
test_niederreiter_base2_values(niederreiter_base2_16_100, 4095);
}
BOOST_AUTO_TEST_CASE( validate_niederreiter_base2_seed )
{
test_niederreiter_base2_seed(niederreiter_base2_02_100, 4095);
test_niederreiter_base2_seed(niederreiter_base2_07_100, 4095);
test_niederreiter_base2_seed(niederreiter_base2_16_100, 4095);
}
BOOST_AUTO_TEST_CASE( validate_niederreiter_base2_discard )
{
test_niederreiter_base2_discard(niederreiter_base2_02_100, 4095);
test_niederreiter_base2_discard(niederreiter_base2_07_100, 4095);
test_niederreiter_base2_discard(niederreiter_base2_16_100, 4095);
}

380
libs/random/test/sobol_validate.cpp Normal file
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@@ -0,0 +1,380 @@
// Copyright Justinas Vygintas Daugmaudis, 2010-2018.
// Use, modification and distribution is subject to the
// Boost Software License, Version 1.0. (See accompanying
// file LICENSE-1.0 or http://www.boost.org/LICENSE-1.0)
#include <boost/random/sobol.hpp>
#include <boost/utility.hpp>
#define BOOST_TEST_MAIN
#include <boost/test/unit_test.hpp>
#include "test_qrng_functions.hpp"
//
// DESCRIPTION:
// ~~~~~~~~~~~~
//
// This file tests the sobol quasi-random number generator.
// These tests compare our results with values produced by the
// original sobol.cc program http://web.maths.unsw.edu.au/~fkuo/sobol/,
// using the new-joe-kuo-6.21201 direction polynomials and direction vectors.
//
// Generally, the command line used to generate the datasets was
// sobol SKIP+N+1 DIMENSION new-joe-kuo-6.21201 | tail -n N
// Note that we asked to show +1 sample from sobol.cc program, because
// it outputs trivial zeros as the first sample.
// Spatial dimension: 2
// N: 99
// Vectors skipped: 0
static const double sobol_02_99[99][2] =
{
{ 0.5000000002, 0.5000000002 },
{ 0.7500000003, 0.2500000001 },
{ 0.2500000001, 0.7500000003 },
{ 0.3750000002, 0.3750000002 },
{ 0.8750000004, 0.8750000004 },
{ 0.6250000003, 0.1250000001 },
{ 0.1250000001, 0.6250000003 },
{ 0.1875000001, 0.3125000001 },
{ 0.6875000003, 0.8125000004 },
{ 0.9375000004, 0.0625000000 },
{ 0.4375000002, 0.5625000003 },
{ 0.3125000001, 0.1875000001 },
{ 0.8125000004, 0.6875000003 },
{ 0.5625000003, 0.4375000002 },
{ 0.0625000000, 0.9375000004 },
{ 0.0937500000, 0.4687500002 },
{ 0.5937500003, 0.9687500005 },
{ 0.8437500004, 0.2187500001 },
{ 0.3437500002, 0.7187500003 },
{ 0.4687500002, 0.0937500000 },
{ 0.9687500005, 0.5937500003 },
{ 0.7187500003, 0.3437500002 },
{ 0.2187500001, 0.8437500004 },
{ 0.1562500001, 0.1562500001 },
{ 0.6562500003, 0.6562500003 },
{ 0.9062500004, 0.4062500002 },
{ 0.4062500002, 0.9062500004 },
{ 0.2812500001, 0.2812500001 },
{ 0.7812500004, 0.7812500004 },
{ 0.5312500002, 0.0312500000 },
{ 0.0312500000, 0.5312500002 },
{ 0.0468750000, 0.2656250001 },
{ 0.5468750003, 0.7656250004 },
{ 0.7968750004, 0.0156250000 },
{ 0.2968750001, 0.5156250002 },
{ 0.4218750002, 0.1406250001 },
{ 0.9218750004, 0.6406250003 },
{ 0.6718750003, 0.3906250002 },
{ 0.1718750001, 0.8906250004 },
{ 0.2343750001, 0.0781250000 },
{ 0.7343750003, 0.5781250003 },
{ 0.9843750005, 0.3281250002 },
{ 0.4843750002, 0.8281250004 },
{ 0.3593750002, 0.4531250002 },
{ 0.8593750004, 0.9531250004 },
{ 0.6093750003, 0.2031250001 },
{ 0.1093750001, 0.7031250003 },
{ 0.0781250000, 0.2343750001 },
{ 0.5781250003, 0.7343750003 },
{ 0.8281250004, 0.4843750002 },
{ 0.3281250002, 0.9843750005 },
{ 0.4531250002, 0.3593750002 },
{ 0.9531250004, 0.8593750004 },
{ 0.7031250003, 0.1093750001 },
{ 0.2031250001, 0.6093750003 },
{ 0.1406250001, 0.4218750002 },
{ 0.6406250003, 0.9218750004 },
{ 0.8906250004, 0.1718750001 },
{ 0.3906250002, 0.6718750003 },
{ 0.2656250001, 0.0468750000 },
{ 0.7656250004, 0.5468750003 },
{ 0.5156250002, 0.2968750001 },
{ 0.0156250000, 0.7968750004 },
{ 0.0234375000, 0.3984375002 },
{ 0.5234375002, 0.8984375004 },
{ 0.7734375004, 0.1484375001 },
{ 0.2734375001, 0.6484375003 },
{ 0.3984375002, 0.0234375000 },
{ 0.8984375004, 0.5234375002 },
{ 0.6484375003, 0.2734375001 },
{ 0.1484375001, 0.7734375004 },
{ 0.2109375001, 0.2109375001 },
{ 0.7109375003, 0.7109375003 },
{ 0.9609375004, 0.4609375002 },
{ 0.4609375002, 0.9609375004 },
{ 0.3359375002, 0.3359375002 },
{ 0.8359375004, 0.8359375004 },
{ 0.5859375003, 0.0859375000 },
{ 0.0859375000, 0.5859375003 },
{ 0.1171875001, 0.1171875001 },
{ 0.6171875003, 0.6171875003 },
{ 0.8671875004, 0.3671875002 },
{ 0.3671875002, 0.8671875004 },
{ 0.4921875002, 0.4921875002 },
{ 0.9921875005, 0.9921875005 },
{ 0.7421875003, 0.2421875001 },
{ 0.2421875001, 0.7421875003 },
{ 0.1796875001, 0.3046875001 },
{ 0.6796875003, 0.8046875004 },
{ 0.9296875004, 0.0546875000 },
{ 0.4296875002, 0.5546875003 },
{ 0.3046875001, 0.1796875001 },
{ 0.8046875004, 0.6796875003 },
{ 0.5546875003, 0.4296875002 },
{ 0.0546875000, 0.9296875004 },
{ 0.0390625000, 0.1328125001 },
{ 0.5390625003, 0.6328125003 },
{ 0.7890625004, 0.3828125002 },
{ 0.2890625001, 0.8828125004 }
};
// Spatial dimension: 7
// N: 100
// Vectors skipped: 127
static const double sobol_07_100[100][7] =
{
{ 0.0117187500, 0.3320312500, 0.2929687500, 0.1914062500, 0.9023437500, 0.6757812500, 0.8632812500 },
{ 0.5117187500, 0.8320312500, 0.7929687500, 0.6914062500, 0.4023437500, 0.1757812500, 0.3632812500 },
{ 0.7617187500, 0.0820312500, 0.0429687500, 0.4414062500, 0.1523437500, 0.4257812500, 0.6132812500 },
{ 0.2617187500, 0.5820312500, 0.5429687500, 0.9414062500, 0.6523437500, 0.9257812500, 0.1132812500 },
{ 0.3867187500, 0.2070312500, 0.9179687500, 0.8164062500, 0.5273437500, 0.5507812500, 0.7382812500 },
{ 0.8867187500, 0.7070312500, 0.4179687500, 0.3164062500, 0.0273437500, 0.0507812500, 0.2382812500 },
{ 0.6367187500, 0.4570312500, 0.6679687500, 0.5664062500, 0.2773437500, 0.3007812500, 0.9882812500 },
{ 0.1367187500, 0.9570312500, 0.1679687500, 0.0664062500, 0.7773437500, 0.8007812500, 0.4882812500 },
{ 0.1992187500, 0.0195312500, 0.7304687500, 0.2539062500, 0.4648437500, 0.9882812500, 0.6757812500 },
{ 0.6992187500, 0.5195312500, 0.2304687500, 0.7539062500, 0.9648437500, 0.4882812500, 0.1757812500 },
{ 0.9492187500, 0.2695312500, 0.9804687500, 0.0039062500, 0.7148437500, 0.2382812500, 0.9257812500 },
{ 0.4492187500, 0.7695312500, 0.4804687500, 0.5039062500, 0.2148437500, 0.7382812500, 0.4257812500 },
{ 0.3242187500, 0.3945312500, 0.1054687500, 0.6289062500, 0.0898437500, 0.8632812500, 0.8007812500 },
{ 0.8242187500, 0.8945312500, 0.6054687500, 0.1289062500, 0.5898437500, 0.3632812500, 0.3007812500 },
{ 0.5742187500, 0.1445312500, 0.3554687500, 0.8789062500, 0.8398437500, 0.1132812500, 0.5507812500 },
{ 0.0742187500, 0.6445312500, 0.8554687500, 0.3789062500, 0.3398437500, 0.6132812500, 0.0507812500 },
{ 0.1054687500, 0.1757812500, 0.1992187500, 0.5976562500, 0.6835937500, 0.3320312500, 0.3320312500 },
{ 0.6054687500, 0.6757812500, 0.6992187500, 0.0976562500, 0.1835937500, 0.8320312500, 0.8320312500 },
{ 0.8554687500, 0.4257812500, 0.4492187500, 0.8476562500, 0.4335937500, 0.5820312500, 0.0820312500 },
{ 0.3554687500, 0.9257812500, 0.9492187500, 0.3476562500, 0.9335937500, 0.0820312500, 0.5820312500 },
{ 0.4804687500, 0.3007812500, 0.5742187500, 0.4726562500, 0.8085937500, 0.4570312500, 0.2070312500 },
{ 0.9804687500, 0.8007812500, 0.0742187500, 0.9726562500, 0.3085937500, 0.9570312500, 0.7070312500 },
{ 0.7304687500, 0.0507812500, 0.8242187500, 0.2226562500, 0.0585937500, 0.7070312500, 0.4570312500 },
{ 0.2304687500, 0.5507812500, 0.3242187500, 0.7226562500, 0.5585937500, 0.2070312500, 0.9570312500 },
{ 0.1679687500, 0.4882812500, 0.7617187500, 0.9101562500, 0.2460937500, 0.0195312500, 0.1445312500 },
{ 0.6679687500, 0.9882812500, 0.2617187500, 0.4101562500, 0.7460937500, 0.5195312500, 0.6445312500 },
{ 0.9179687500, 0.2382812500, 0.5117187500, 0.6601562500, 0.9960937500, 0.7695312500, 0.3945312500 },
{ 0.4179687500, 0.7382812500, 0.0117187500, 0.1601562500, 0.4960937500, 0.2695312500, 0.8945312500 },
{ 0.2929687500, 0.1132812500, 0.3867187500, 0.0351562500, 0.3710937500, 0.1445312500, 0.2695312500 },
{ 0.7929687500, 0.6132812500, 0.8867187500, 0.5351562500, 0.8710937500, 0.6445312500, 0.7695312500 },
{ 0.5429687500, 0.3632812500, 0.1367187500, 0.2851562500, 0.6210937500, 0.8945312500, 0.0195312500 },
{ 0.0429687500, 0.8632812500, 0.6367187500, 0.7851562500, 0.1210937500, 0.3945312500, 0.5195312500 },
{ 0.0585937500, 0.0664062500, 0.9960937500, 0.7382812500, 0.7617187500, 0.2539062500, 0.0664062500 },
{ 0.5585937500, 0.5664062500, 0.4960937500, 0.2382812500, 0.2617187500, 0.7539062500, 0.5664062500 },
{ 0.8085937500, 0.3164062500, 0.7460937500, 0.9882812500, 0.0117187500, 0.5039062500, 0.3164062500 },
{ 0.3085937500, 0.8164062500, 0.2460937500, 0.4882812500, 0.5117187500, 0.0039062500, 0.8164062500 },
{ 0.4335937500, 0.4414062500, 0.3710937500, 0.3632812500, 0.6367187500, 0.3789062500, 0.4414062500 },
{ 0.9335937500, 0.9414062500, 0.8710937500, 0.8632812500, 0.1367187500, 0.8789062500, 0.9414062500 },
{ 0.6835937500, 0.1914062500, 0.1210937500, 0.1132812500, 0.3867187500, 0.6289062500, 0.1914062500 },
{ 0.1835937500, 0.6914062500, 0.6210937500, 0.6132812500, 0.8867187500, 0.1289062500, 0.6914062500 },
{ 0.2460937500, 0.2539062500, 0.0585937500, 0.8007812500, 0.3242187500, 0.0664062500, 0.3789062500 },
{ 0.7460937500, 0.7539062500, 0.5585937500, 0.3007812500, 0.8242187500, 0.5664062500, 0.8789062500 },
{ 0.9960937500, 0.0039062500, 0.3085937500, 0.5507812500, 0.5742187500, 0.8164062500, 0.1289062500 },
{ 0.4960937500, 0.5039062500, 0.8085937500, 0.0507812500, 0.0742187500, 0.3164062500, 0.6289062500 },
{ 0.3710937500, 0.1289062500, 0.6835937500, 0.1757812500, 0.1992187500, 0.1914062500, 0.0039062500 },
{ 0.8710937500, 0.6289062500, 0.1835937500, 0.6757812500, 0.6992187500, 0.6914062500, 0.5039062500 },
{ 0.6210937500, 0.3789062500, 0.9335937500, 0.4257812500, 0.9492187500, 0.9414062500, 0.2539062500 },
{ 0.1210937500, 0.8789062500, 0.4335937500, 0.9257812500, 0.4492187500, 0.4414062500, 0.7539062500 },
{ 0.0898437500, 0.4101562500, 0.5273437500, 0.0820312500, 0.5429687500, 0.7226562500, 0.5976562500 },
{ 0.5898437500, 0.9101562500, 0.0273437500, 0.5820312500, 0.0429687500, 0.2226562500, 0.0976562500 },
{ 0.8398437500, 0.1601562500, 0.7773437500, 0.3320312500, 0.2929687500, 0.4726562500, 0.8476562500 },
{ 0.3398437500, 0.6601562500, 0.2773437500, 0.8320312500, 0.7929687500, 0.9726562500, 0.3476562500 },
{ 0.4648437500, 0.0351562500, 0.1523437500, 0.9570312500, 0.9179687500, 0.5976562500, 0.9726562500 },
{ 0.9648437500, 0.5351562500, 0.6523437500, 0.4570312500, 0.4179687500, 0.0976562500, 0.4726562500 },
{ 0.7148437500, 0.2851562500, 0.4023437500, 0.7070312500, 0.1679687500, 0.3476562500, 0.7226562500 },
{ 0.2148437500, 0.7851562500, 0.9023437500, 0.2070312500, 0.6679687500, 0.8476562500, 0.2226562500 },
{ 0.1523437500, 0.2226562500, 0.4648437500, 0.3945312500, 0.1054687500, 0.9101562500, 0.9101562500 },
{ 0.6523437500, 0.7226562500, 0.9648437500, 0.8945312500, 0.6054687500, 0.4101562500, 0.4101562500 },
{ 0.9023437500, 0.4726562500, 0.2148437500, 0.1445312500, 0.8554687500, 0.1601562500, 0.6601562500 },
{ 0.4023437500, 0.9726562500, 0.7148437500, 0.6445312500, 0.3554687500, 0.6601562500, 0.1601562500 },
{ 0.2773437500, 0.3476562500, 0.8398437500, 0.5195312500, 0.4804687500, 0.7851562500, 0.5351562500 },
{ 0.7773437500, 0.8476562500, 0.3398437500, 0.0195312500, 0.9804687500, 0.2851562500, 0.0351562500 },
{ 0.5273437500, 0.0976562500, 0.5898437500, 0.7695312500, 0.7304687500, 0.0351562500, 0.7851562500 },
{ 0.0273437500, 0.5976562500, 0.0898437500, 0.2695312500, 0.2304687500, 0.5351562500, 0.2851562500 },
{ 0.0195312500, 0.1992187500, 0.5976562500, 0.9023437500, 0.2539062500, 0.8710937500, 0.4648437500 },
{ 0.5195312500, 0.6992187500, 0.0976562500, 0.4023437500, 0.7539062500, 0.3710937500, 0.9648437500 },
{ 0.7695312500, 0.4492187500, 0.8476562500, 0.6523437500, 0.5039062500, 0.1210937500, 0.2148437500 },
{ 0.2695312500, 0.9492187500, 0.3476562500, 0.1523437500, 0.0039062500, 0.6210937500, 0.7148437500 },
{ 0.3945312500, 0.3242187500, 0.2226562500, 0.0273437500, 0.1289062500, 0.9960937500, 0.0898437500 },
{ 0.8945312500, 0.8242187500, 0.7226562500, 0.5273437500, 0.6289062500, 0.4960937500, 0.5898437500 },
{ 0.6445312500, 0.0742187500, 0.4726562500, 0.2773437500, 0.8789062500, 0.2460937500, 0.3398437500 },
{ 0.1445312500, 0.5742187500, 0.9726562500, 0.7773437500, 0.3789062500, 0.7460937500, 0.8398437500 },
{ 0.2070312500, 0.3867187500, 0.4101562500, 0.5898437500, 0.8164062500, 0.5585937500, 0.0273437500 },
{ 0.7070312500, 0.8867187500, 0.9101562500, 0.0898437500, 0.3164062500, 0.0585937500, 0.5273437500 },
{ 0.9570312500, 0.1367187500, 0.1601562500, 0.8398437500, 0.0664062500, 0.3085937500, 0.2773437500 },
{ 0.4570312500, 0.6367187500, 0.6601562500, 0.3398437500, 0.5664062500, 0.8085937500, 0.7773437500 },
{ 0.3320312500, 0.0117187500, 0.7851562500, 0.4648437500, 0.6914062500, 0.6835937500, 0.4023437500 },
{ 0.8320312500, 0.5117187500, 0.2851562500, 0.9648437500, 0.1914062500, 0.1835937500, 0.9023437500 },
{ 0.5820312500, 0.2617187500, 0.5351562500, 0.2148437500, 0.4414062500, 0.4335937500, 0.1523437500 },
{ 0.0820312500, 0.7617187500, 0.0351562500, 0.7148437500, 0.9414062500, 0.9335937500, 0.6523437500 },
{ 0.1132812500, 0.2929687500, 0.8789062500, 0.3085937500, 0.0351562500, 0.1523437500, 0.9960937500 },
{ 0.6132812500, 0.7929687500, 0.3789062500, 0.8085937500, 0.5351562500, 0.6523437500, 0.4960937500 },
{ 0.8632812500, 0.0429687500, 0.6289062500, 0.0585937500, 0.7851562500, 0.9023437500, 0.7460937500 },
{ 0.3632812500, 0.5429687500, 0.1289062500, 0.5585937500, 0.2851562500, 0.4023437500, 0.2460937500 },
{ 0.4882812500, 0.1679687500, 0.2539062500, 0.6835937500, 0.4101562500, 0.0273437500, 0.6210937500 },
{ 0.9882812500, 0.6679687500, 0.7539062500, 0.1835937500, 0.9101562500, 0.5273437500, 0.1210937500 },
{ 0.7382812500, 0.4179687500, 0.0039062500, 0.9335937500, 0.6601562500, 0.7773437500, 0.8710937500 },
{ 0.2382812500, 0.9179687500, 0.5039062500, 0.4335937500, 0.1601562500, 0.2773437500, 0.3710937500 },
{ 0.1757812500, 0.1054687500, 0.0664062500, 0.2460937500, 0.5976562500, 0.4648437500, 0.5585937500 },
{ 0.6757812500, 0.6054687500, 0.5664062500, 0.7460937500, 0.0976562500, 0.9648437500, 0.0585937500 },
{ 0.9257812500, 0.3554687500, 0.3164062500, 0.4960937500, 0.3476562500, 0.7148437500, 0.8085937500 },
{ 0.4257812500, 0.8554687500, 0.8164062500, 0.9960937500, 0.8476562500, 0.2148437500, 0.3085937500 },
{ 0.3007812500, 0.4804687500, 0.6914062500, 0.8710937500, 0.9726562500, 0.3398437500, 0.9335937500 },
{ 0.8007812500, 0.9804687500, 0.1914062500, 0.3710937500, 0.4726562500, 0.8398437500, 0.4335937500 },
{ 0.5507812500, 0.2304687500, 0.9414062500, 0.6210937500, 0.2226562500, 0.5898437500, 0.6835937500 },
{ 0.0507812500, 0.7304687500, 0.4414062500, 0.1210937500, 0.7226562500, 0.0898437500, 0.1835937500 },
{ 0.0351562500, 0.4648437500, 0.1757812500, 0.4179687500, 0.3945312500, 0.1992187500, 0.7304687500 },
{ 0.5351562500, 0.9648437500, 0.6757812500, 0.9179687500, 0.8945312500, 0.6992187500, 0.2304687500 },
{ 0.7851562500, 0.2148437500, 0.4257812500, 0.1679687500, 0.6445312500, 0.9492187500, 0.9804687500 },
{ 0.2851562500, 0.7148437500, 0.9257812500, 0.6679687500, 0.1445312500, 0.4492187500, 0.4804687500 }
};
// Spatial dimension: 16
// N: 100
// Vectors skipped: 127
static const double sobol_16_100[100][16] =
{
{ 0.0117187500, 0.3320312500, 0.2929687500, 0.1914062500, 0.9023437500, 0.6757812500, 0.8632812500, 0.2460937500, 0.1054687500, 0.8164062500, 0.7382812500, 0.7382812500, 0.8164062500, 0.8789062500, 0.0273437500, 0.7617187500 },
{ 0.5117187500, 0.8320312500, 0.7929687500, 0.6914062500, 0.4023437500, 0.1757812500, 0.3632812500, 0.7460937500, 0.6054687500, 0.3164062500, 0.2382812500, 0.2382812500, 0.3164062500, 0.3789062500, 0.5273437500, 0.2617187500 },
{ 0.7617187500, 0.0820312500, 0.0429687500, 0.4414062500, 0.1523437500, 0.4257812500, 0.6132812500, 0.9960937500, 0.8554687500, 0.0664062500, 0.4882812500, 0.4882812500, 0.5664062500, 0.6289062500, 0.7773437500, 0.5117187500 },
{ 0.2617187500, 0.5820312500, 0.5429687500, 0.9414062500, 0.6523437500, 0.9257812500, 0.1132812500, 0.4960937500, 0.3554687500, 0.5664062500, 0.9882812500, 0.9882812500, 0.0664062500, 0.1289062500, 0.2773437500, 0.0117187500 },
{ 0.3867187500, 0.2070312500, 0.9179687500, 0.8164062500, 0.5273437500, 0.5507812500, 0.7382812500, 0.8710937500, 0.9804687500, 0.4414062500, 0.3632812500, 0.8632812500, 0.6914062500, 0.2539062500, 0.4023437500, 0.1367187500 },
{ 0.8867187500, 0.7070312500, 0.4179687500, 0.3164062500, 0.0273437500, 0.0507812500, 0.2382812500, 0.3710937500, 0.4804687500, 0.9414062500, 0.8632812500, 0.3632812500, 0.1914062500, 0.7539062500, 0.9023437500, 0.6367187500 },
{ 0.6367187500, 0.4570312500, 0.6679687500, 0.5664062500, 0.2773437500, 0.3007812500, 0.9882812500, 0.1210937500, 0.2304687500, 0.6914062500, 0.6132812500, 0.1132812500, 0.9414062500, 0.0039062500, 0.6523437500, 0.3867187500 },
{ 0.1367187500, 0.9570312500, 0.1679687500, 0.0664062500, 0.7773437500, 0.8007812500, 0.4882812500, 0.6210937500, 0.7304687500, 0.1914062500, 0.1132812500, 0.6132812500, 0.4414062500, 0.5039062500, 0.1523437500, 0.8867187500 },
{ 0.1992187500, 0.0195312500, 0.7304687500, 0.2539062500, 0.4648437500, 0.9882812500, 0.6757812500, 0.8085937500, 0.9179687500, 0.5039062500, 0.0507812500, 0.6757812500, 0.1289062500, 0.0664062500, 0.8398437500, 0.1992187500 },
{ 0.6992187500, 0.5195312500, 0.2304687500, 0.7539062500, 0.9648437500, 0.4882812500, 0.1757812500, 0.3085937500, 0.4179687500, 0.0039062500, 0.5507812500, 0.1757812500, 0.6289062500, 0.5664062500, 0.3398437500, 0.6992187500 },
{ 0.9492187500, 0.2695312500, 0.9804687500, 0.0039062500, 0.7148437500, 0.2382812500, 0.9257812500, 0.0585937500, 0.1679687500, 0.2539062500, 0.8007812500, 0.4257812500, 0.3789062500, 0.3164062500, 0.0898437500, 0.4492187500 },
{ 0.4492187500, 0.7695312500, 0.4804687500, 0.5039062500, 0.2148437500, 0.7382812500, 0.4257812500, 0.5585937500, 0.6679687500, 0.7539062500, 0.3007812500, 0.9257812500, 0.8789062500, 0.8164062500, 0.5898437500, 0.9492187500 },
{ 0.3242187500, 0.3945312500, 0.1054687500, 0.6289062500, 0.0898437500, 0.8632812500, 0.8007812500, 0.1835937500, 0.0429687500, 0.1289062500, 0.9257812500, 0.8007812500, 0.2539062500, 0.6914062500, 0.7148437500, 0.8242187500 },
{ 0.8242187500, 0.8945312500, 0.6054687500, 0.1289062500, 0.5898437500, 0.3632812500, 0.3007812500, 0.6835937500, 0.5429687500, 0.6289062500, 0.4257812500, 0.3007812500, 0.7539062500, 0.1914062500, 0.2148437500, 0.3242187500 },
{ 0.5742187500, 0.1445312500, 0.3554687500, 0.8789062500, 0.8398437500, 0.1132812500, 0.5507812500, 0.9335937500, 0.7929687500, 0.8789062500, 0.1757812500, 0.0507812500, 0.0039062500, 0.9414062500, 0.4648437500, 0.5742187500 },
{ 0.0742187500, 0.6445312500, 0.8554687500, 0.3789062500, 0.3398437500, 0.6132812500, 0.0507812500, 0.4335937500, 0.2929687500, 0.3789062500, 0.6757812500, 0.5507812500, 0.5039062500, 0.4414062500, 0.9648437500, 0.0742187500 },
{ 0.1054687500, 0.1757812500, 0.1992187500, 0.5976562500, 0.6835937500, 0.3320312500, 0.3320312500, 0.9023437500, 0.3867187500, 0.9726562500, 0.6445312500, 0.8320312500, 0.4726562500, 0.2851562500, 0.3710937500, 0.7929687500 },
{ 0.6054687500, 0.6757812500, 0.6992187500, 0.0976562500, 0.1835937500, 0.8320312500, 0.8320312500, 0.4023437500, 0.8867187500, 0.4726562500, 0.1445312500, 0.3320312500, 0.9726562500, 0.7851562500, 0.8710937500, 0.2929687500 },
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{ 0.9882812500, 0.6679687500, 0.7539062500, 0.1835937500, 0.9101562500, 0.5273437500, 0.1210937500, 0.6914062500, 0.7382812500, 0.7773437500, 0.2148437500, 0.0585937500, 0.9648437500, 0.9335937500, 0.4414062500, 0.1601562500 },
{ 0.7382812500, 0.4179687500, 0.0039062500, 0.9335937500, 0.6601562500, 0.7773437500, 0.8710937500, 0.9414062500, 0.9882812500, 0.5273437500, 0.4648437500, 0.3085937500, 0.2148437500, 0.1835937500, 0.1914062500, 0.9101562500 },
{ 0.2382812500, 0.9179687500, 0.5039062500, 0.4335937500, 0.1601562500, 0.2773437500, 0.3710937500, 0.4414062500, 0.4882812500, 0.0273437500, 0.9648437500, 0.8085937500, 0.7148437500, 0.6835937500, 0.6914062500, 0.4101562500 },
{ 0.1757812500, 0.1054687500, 0.0664062500, 0.2460937500, 0.5976562500, 0.4648437500, 0.5585937500, 0.1289062500, 0.1757812500, 0.7148437500, 0.9023437500, 0.9960937500, 0.9023437500, 0.2460937500, 0.2539062500, 0.7226562500 },
{ 0.6757812500, 0.6054687500, 0.5664062500, 0.7460937500, 0.0976562500, 0.9648437500, 0.0585937500, 0.6289062500, 0.6757812500, 0.2148437500, 0.4023437500, 0.4960937500, 0.4023437500, 0.7460937500, 0.7539062500, 0.2226562500 },
{ 0.9257812500, 0.3554687500, 0.3164062500, 0.4960937500, 0.3476562500, 0.7148437500, 0.8085937500, 0.8789062500, 0.9257812500, 0.4648437500, 0.1523437500, 0.2460937500, 0.6523437500, 0.4960937500, 0.5039062500, 0.9726562500 },
{ 0.4257812500, 0.8554687500, 0.8164062500, 0.9960937500, 0.8476562500, 0.2148437500, 0.3085937500, 0.3789062500, 0.4257812500, 0.9648437500, 0.6523437500, 0.7460937500, 0.1523437500, 0.9960937500, 0.0039062500, 0.4726562500 },
{ 0.3007812500, 0.4804687500, 0.6914062500, 0.8710937500, 0.9726562500, 0.3398437500, 0.9335937500, 0.7539062500, 0.8007812500, 0.0898437500, 0.0273437500, 0.6210937500, 0.5273437500, 0.6210937500, 0.1289062500, 0.3476562500 },
{ 0.8007812500, 0.9804687500, 0.1914062500, 0.3710937500, 0.4726562500, 0.8398437500, 0.4335937500, 0.2539062500, 0.3007812500, 0.5898437500, 0.5273437500, 0.1210937500, 0.0273437500, 0.1210937500, 0.6289062500, 0.8476562500 },
{ 0.5507812500, 0.2304687500, 0.9414062500, 0.6210937500, 0.2226562500, 0.5898437500, 0.6835937500, 0.0039062500, 0.0507812500, 0.8398437500, 0.7773437500, 0.3710937500, 0.7773437500, 0.8710937500, 0.8789062500, 0.0976562500 },
{ 0.0507812500, 0.7304687500, 0.4414062500, 0.1210937500, 0.7226562500, 0.0898437500, 0.1835937500, 0.5039062500, 0.5507812500, 0.3398437500, 0.2773437500, 0.8710937500, 0.2773437500, 0.3710937500, 0.3789062500, 0.5976562500 },
{ 0.0351562500, 0.4648437500, 0.1757812500, 0.4179687500, 0.3945312500, 0.1992187500, 0.7304687500, 0.6445312500, 0.3476562500, 0.7617187500, 0.1679687500, 0.4492187500, 0.7929687500, 0.6054687500, 0.2070312500, 0.3632812500 },
{ 0.5351562500, 0.9648437500, 0.6757812500, 0.9179687500, 0.8945312500, 0.6992187500, 0.2304687500, 0.1445312500, 0.8476562500, 0.2617187500, 0.6679687500, 0.9492187500, 0.2929687500, 0.1054687500, 0.7070312500, 0.8632812500 },
{ 0.7851562500, 0.2148437500, 0.4257812500, 0.1679687500, 0.6445312500, 0.9492187500, 0.9804687500, 0.3945312500, 0.5976562500, 0.0117187500, 0.9179687500, 0.6992187500, 0.5429687500, 0.8554687500, 0.9570312500, 0.1132812500 },
{ 0.2851562500, 0.7148437500, 0.9257812500, 0.6679687500, 0.1445312500, 0.4492187500, 0.4804687500, 0.8945312500, 0.0976562500, 0.5117187500, 0.4179687500, 0.1992187500, 0.0429687500, 0.3554687500, 0.4570312500, 0.6132812500 }
};
QRNG_VALIDATION_TEST_FUNCTIONS(sobol)
QRNG_VALIDATION_TEST_DISCARD(sobol)
BOOST_AUTO_TEST_CASE( check_generator_limits )
{
test_sobol_max_seed();
test_sobol_max_discard();
test_sobol_max_dimension(BOOST_RANDOM_SOBOL_MAX_DIMENSION);
}
BOOST_AUTO_TEST_CASE( validate_sobol )
{
test_sobol_values(sobol_02_99, 0);
test_sobol_values(sobol_07_100, 127);
test_sobol_values(sobol_16_100, 127);
}
BOOST_AUTO_TEST_CASE( validate_sobol_seed )
{
test_sobol_seed(sobol_02_99, 0);
test_sobol_seed(sobol_07_100, 127);
test_sobol_seed(sobol_16_100, 127);
}
BOOST_AUTO_TEST_CASE( validate_sobol_discard )
{
test_sobol_discard(sobol_02_99, 0);
test_sobol_discard(sobol_07_100, 127);
test_sobol_discard(sobol_16_100, 127);
}

8
libs/random/test/statistic_tests.hpp
View File

@@ -644,8 +644,8 @@ double run_experiment(const Experiment & experiment, Generator & gen, int n)
generic_counter<std::vector<int> > v(experiment.classes());
experiment.run(gen, v, n);
return chi_square_value(v.begin(), v.end(),
std::bind1st(std::mem_fun_ref(&Experiment::probability),
experiment));
boost::bind(&Experiment::probability,
experiment, boost::placeholders::_1));
}
// chi_square test
@@ -655,8 +655,8 @@ double run_experiment(const Experiment & experiment, const Generator & gen, int
generic_counter<std::vector<int> > v(experiment.classes());
experiment.run(gen, v, n);
return chi_square_value(v.begin(), v.end(),
std::bind1st(std::mem_fun_ref(&Experiment::probability),
experiment));
boost::bind(&Experiment::probability,
experiment, boost::placeholders::_1));
}
// number generator with experiment results (for nesting)

5
libs/random/test/test_generator.ipp
View File

@@ -226,6 +226,11 @@ BOOST_AUTO_TEST_CASE(test_min_max)
}
}
#if !defined(BOOST_NO_CXX11_CONSTEXPR)
constexpr result_type const_min = (BOOST_RANDOM_URNG::min)();
constexpr result_type const_max = (BOOST_RANDOM_URNG::max)();
#endif
BOOST_AUTO_TEST_CASE(test_comparison)
{
BOOST_RANDOM_URNG urng;

80
libs/random/test/test_hyperexponential_distribution.cpp
View File

@@ -61,7 +61,7 @@ BOOST_AUTO_TEST_CASE( test_constructors )
BOOST_RANDOM_HYPEREXP_CHECK_CLOSE_COLLECTIONS(double, dist.probabilities(), boost::assign::list_of(1.0), tol);
BOOST_RANDOM_HYPEREXP_CHECK_CLOSE_COLLECTIONS(double, dist.rates(), boost::assign::list_of(1.0), tol);
#ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) && !defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX)
// Test ctor from initializer_list with probabilities and rates
boost::random::hyperexponential_distribution<> dist_il_p_r = {{1, 2, 3, 4 }, {1, 2, 3, 4}};
BOOST_CHECK_EQUAL(dist_il_p_r.num_phases(), 4u);
@@ -150,7 +150,7 @@ BOOST_AUTO_TEST_CASE( test_param )
BOOST_RANDOM_HYPEREXP_CHECK_CLOSE_COLLECTIONS(double, param_default.rates(), boost::assign::list_of(1.0), tol);
BOOST_CHECK(param != param_default);
BOOST_CHECK(!(param == param_default));
#ifndef BOOST_NO_CXX11_HDR_INITIALIZER_LIST
#if !defined(BOOST_NO_CXX11_HDR_INITIALIZER_LIST) && !defined(BOOST_NO_CXX11_UNIFIED_INITIALIZATION_SYNTAX)
boost::random::hyperexponential_distribution<>::param_type param_il = {{1, 2, 3, 4 }, {1, 2, 3, 4}};
BOOST_RANDOM_HYPEREXP_CHECK_CLOSE_COLLECTIONS(double, param_il.probabilities(), boost::assign::list_of(.1)(.2)(.3)(.4), tol);
BOOST_RANDOM_HYPEREXP_CHECK_CLOSE_COLLECTIONS(double, param_il.rates(), boost::assign::list_of(1.)(2.)(3.)(4.), tol);
@@ -265,15 +265,9 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, rates);
boost::random::hyperexponential_distribution<>::param_type param;
ss.exceptions(std::ios_base::failbit);
try
{
ss >> param;
}
catch (...)
{
boost::random::hyperexponential_distribution<>::param_type check_param;
BOOST_CHECK_EQUAL(param, check_param);
}
ss >> param;
boost::random::hyperexponential_distribution<>::param_type check_param(std::vector<double>(rates.size(), 1), rates);
BOOST_CHECK_EQUAL(param, check_param);
}
// - Test with an empty rate vector and ios_base exceptions enabled
@@ -284,15 +278,9 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, empty_vector);
boost::random::hyperexponential_distribution<>::param_type param;
ss.exceptions(std::ios_base::failbit);
try
{
ss >> param;
}
catch (...)
{
boost::random::hyperexponential_distribution<>::param_type check_param;
BOOST_CHECK_EQUAL(param, check_param);
}
ss >> param;
boost::random::hyperexponential_distribution<>::param_type check_param(probs, std::vector<double>(probs.size(), 1));
BOOST_CHECK_EQUAL(param, check_param);
}
// - Test with an empty probability and rate vectors and ios_base exceptions enabled
@@ -303,15 +291,9 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, empty_vector);
boost::random::hyperexponential_distribution<>::param_type param;
ss.exceptions(std::ios_base::failbit);
try
{
ss >> param;
}
catch (...)
{
boost::random::hyperexponential_distribution<>::param_type check_param;
BOOST_CHECK_EQUAL(param, check_param);
}
ss >> param;
boost::random::hyperexponential_distribution<>::param_type check_param;
BOOST_CHECK_EQUAL(param, check_param);
}
// The the reading of hyperexponential_distribution
@@ -334,7 +316,7 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, rates);
boost::random::hyperexponential_distribution<> dist;
ss >> dist;
boost::random::hyperexponential_distribution<> check_dist;
boost::random::hyperexponential_distribution<> check_dist(std::vector<double>(rates.size(), 1), rates);
BOOST_CHECK_EQUAL(dist, check_dist);
}
@@ -346,7 +328,7 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, empty_vector);
boost::random::hyperexponential_distribution<> dist;
ss >> dist;
boost::random::hyperexponential_distribution<> check_dist;
boost::random::hyperexponential_distribution<> check_dist(probs, std::vector<double>(probs.size(), 1));
BOOST_CHECK_EQUAL(dist, check_dist);
}
@@ -370,15 +352,9 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, rates);
boost::random::hyperexponential_distribution<> dist;
ss.exceptions(std::ios_base::failbit);
try
{
ss >> dist;
}
catch (...)
{
boost::random::hyperexponential_distribution<> check_dist;
BOOST_CHECK_EQUAL(dist, check_dist);
}
ss >> dist;
boost::random::hyperexponential_distribution<> check_dist(std::vector<double>(rates.size(), 1), rates);
BOOST_CHECK_EQUAL(dist, check_dist);
}
// - Test with an empty rate vector and ios_base exceptions enabled
@@ -389,15 +365,9 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, empty_vector);
boost::random::hyperexponential_distribution<> dist;
ss.exceptions(std::ios_base::failbit);
try
{
ss >> dist;
}
catch (...)
{
boost::random::hyperexponential_distribution<> check_dist;
BOOST_CHECK_EQUAL(dist, check_dist);
}
ss >> dist;
boost::random::hyperexponential_distribution<> check_dist(probs, std::vector<double>(probs.size(), 1));
BOOST_CHECK_EQUAL(dist, check_dist);
}
// - Test with an empty probability and rate vectors and ios_base exceptions enabled
@@ -408,15 +378,9 @@ BOOST_AUTO_TEST_CASE( test_streaming )
boost::random::detail::print_vector(ss, empty_vector);
boost::random::hyperexponential_distribution<> dist;
ss.exceptions(std::ios_base::failbit);
try
{
ss >> dist;
}
catch (...)
{
boost::random::hyperexponential_distribution<> check_dist;
BOOST_CHECK_EQUAL(dist, check_dist);
}
ss >> dist;
boost::random::hyperexponential_distribution<> check_dist;
BOOST_CHECK_EQUAL(dist, check_dist);
}
}

52
libs/random/test/test_mixmax.cpp Normal file
View File

@@ -0,0 +1,52 @@
/* test_mixmax.cpp
*
* Copyright Kostas Savvidis 2019
* Distributed under the Boost Software License, Version 1.0. (See
* accompanying file LICENSE_1_0.txt or copy at
* http://www.boost.org/LICENSE_1_0.txt)
*
* $Id$
*
*/
#include <boost/random/mixmax.hpp>
#include <cmath>
#define BOOST_RANDOM_URNG boost::random::mixmax
#define BOOST_RANDOM_SEED_WORDS 4
//#define BOOST_RANDOM_VALIDATION_VALUE 1U
#define BOOST_RANDOM_SEED_SEQ_VALIDATION_VALUE 48757672604362303ULL
#define BOOST_RANDOM_ITERATOR_VALIDATION_VALUE 3802490769389764ULL
// 10000th invocation of MIXMAX with N=17, with default constructor should give:
#define BOOST_RANDOM_VALIDATION_VALUE UINT64_C(1842572666014501720)
#define BOOST_RANDOM_GENERATE_VALUES { 3132207748, 2861541672, 3191701354, 4046050275 }
#include "test_generator.ipp"
struct seed_seq_0 {
template<class It>
void generate(It begin, It end) const {
std::fill(begin, end, boost::uint32_t(0xFFFFFFFF));
}
};
BOOST_AUTO_TEST_CASE(test_special_seed) {
{
seed_seq_0 seed;
std::vector<boost::uint32_t> vec(17);
seed.generate(vec.begin(), vec.end()); // fill vec with ones
std::vector<boost::uint32_t>::iterator it = vec.begin();
boost::random::mixmax gen1(it, vec.end()); // init gen1 with vec iterator
BOOST_CHECK_EQUAL(gen1(), 775778250716139533ULL);
BOOST_CHECK_EQUAL(gen1(), 846264592759195742ULL);
boost::random::mixmax gen2(seed); // init gen2 with seeq_seq, should be the same as gen1!
BOOST_CHECK_EQUAL(gen2(), 775778250716139533ULL);
BOOST_CHECK_EQUAL(gen2(), 846264592759195742ULL);
BOOST_CHECK_EQUAL(gen1, gen2);
}
}

12
libs/random/test/test_mt19937.cpp
View File

@@ -53,12 +53,12 @@ BOOST_AUTO_TEST_CASE(test_special_seed) {
std::vector<boost::uint32_t>::iterator it = vec.begin();
boost::mt19937 gen1(it, vec.end());
BOOST_CHECK_EQUAL(gen1(), 0);
BOOST_CHECK_EQUAL(gen1(), 0);
BOOST_CHECK_EQUAL(gen1(), 0u);
BOOST_CHECK_EQUAL(gen1(), 0u);
boost::mt19937 gen2(seed);
BOOST_CHECK_EQUAL(gen2(), 0);
BOOST_CHECK_EQUAL(gen2(), 0);
BOOST_CHECK_EQUAL(gen2(), 0u);
BOOST_CHECK_EQUAL(gen2(), 0u);
BOOST_CHECK_EQUAL(gen1, gen2);
}
@@ -70,11 +70,11 @@ BOOST_AUTO_TEST_CASE(test_special_seed) {
std::vector<boost::uint32_t>::iterator it = vec.begin();
boost::mt19937 gen1(it, vec.end());
BOOST_CHECK_EQUAL(gen1(), 1141379330u);
BOOST_CHECK_EQUAL(gen1(), 0);
BOOST_CHECK_EQUAL(gen1(), 0u);
boost::mt19937 gen2(seed);
BOOST_CHECK_EQUAL(gen2(), 1141379330u);
BOOST_CHECK_EQUAL(gen2(), 0);
BOOST_CHECK_EQUAL(gen2(), 0u);
BOOST_CHECK_EQUAL(gen1, gen2);
}

2
libs/random/test/test_old_uniform_int_distribution.cpp
View File

@@ -48,6 +48,7 @@
// Author: Jos Hickson
BOOST_AUTO_TEST_CASE(test_random_shuffle)
{
#ifndef BOOST_NO_CXX98_RANDOM_SHUFFLE
typedef boost::uniform_int<> distribution_type;
typedef boost::variate_generator<boost::mt19937 &, distribution_type> generator_type;
@@ -73,4 +74,5 @@ BOOST_AUTO_TEST_CASE(test_random_shuffle)
BOOST_CHECK_EQUAL_COLLECTIONS(
testVec.begin(), testVec.end(),
referenceVec.begin(), referenceVec.end());
#endif
}

278
libs/random/test/test_qrng_functions.hpp Normal file
View File

@@ -0,0 +1,278 @@
// Copyright Justinas Vygintas Daugmaudis, 2010-2018.
// Use, modification and distribution is subject to the
// Boost Software License, Version 1.0. (See accompanying
// file LICENSE-1.0 or http://www.boost.org/LICENSE-1.0)
#ifndef TEST_QRNG_FUNCTIONS_HPP_INCLUDED
#define TEST_QRNG_FUNCTIONS_HPP_INCLUDED
#include <boost/random/uniform_real.hpp>
#include <boost/test/floating_point_comparison.hpp>
#include <sstream>
namespace test {
// Invokes operator() precisely n times. This is to check that
// Engine::discard(n) actually has the same effect.
template<typename Engine>
inline void trivial_discard(Engine& eng, boost::uintmax_t n)
{
for( ; n != 0; --n ) eng();
}
template<typename Engine, typename T, std::size_t Dimension>
inline void match_vector(Engine& eng, T (&pt)[Dimension])
{
BOOST_REQUIRE_EQUAL( eng.dimension(), Dimension ); // paranoid check
boost::uniform_real<T> dist;
for( std::size_t i = 0; i != eng.dimension(); ++i )
{
T val = dist(eng);
// We want to check that quasi-random number generator values differ no
// more than 0.0006% of their value.
BOOST_CHECK_CLOSE(pt[i], val, 0.0006);
}
}
template<typename Engine, typename T, std::size_t Dimension, std::size_t N>
inline void expected_values(T (&pt)[N][Dimension], std::size_t skip)
{
Engine eng(Dimension);
eng.seed(skip);
for( std::size_t i = 0; i != N; ++i )
match_vector(eng, pt[i]);
}
template<typename Engine, typename T>
inline void test_zero_seed(std::size_t dimension)
{
Engine eng(dimension);
Engine other(dimension);
other.seed(0);
// Check that states are equal after zero seed.
boost::uniform_real<T> dist;
BOOST_CHECK( eng == other );
for( std:: size_t i = 0; i != dimension; ++i )
{
T q_val = dist(eng);
T t_val = dist(other);
BOOST_CHECK_CLOSE(q_val, t_val, 0.0001);
}
}
template<typename Engine, typename T, std::size_t Dimension, std::size_t N>
inline void seed_function(T (&pt)[N][Dimension], std::size_t skip)
{
// Test zero seed before doing other tests.
test_zero_seed<Engine, T>(Dimension);
Engine eng(Dimension);
for( std::size_t i = 0; i != N; ++i )
{
// For all N seeds an engine
// and checks if the expected values match.
eng.seed(skip + i);
match_vector(eng, pt[i]);
}
}
template<typename Engine, typename T, std::size_t Dimension, std::size_t N>
inline void discard_function(T (&pt)[N][Dimension], std::size_t skip)
{
Engine eng(Dimension), trivial(Dimension), streamed(Dimension), initial_state(Dimension);
boost::uniform_real<T> dist;
const std::size_t element_count = N * Dimension;
const T* pt_array = reinterpret_cast<T *>(boost::addressof(pt));
std::stringstream ss;
initial_state.seed(skip);
for (std::size_t step = 0; step != element_count; ++step)
{
// Init to the same state
eng = initial_state;
trivial = initial_state;
// Discards have to have the same effect
eng.discard(step);
trivial_discard(trivial, step);
// test serialization to stream
ss.str(std::string()); // clear stream
ss << eng;
ss >> streamed;
// Therefore, states are equal
BOOST_CHECK( eng == trivial );
BOOST_CHECK( eng == streamed );
// Now, let's check whether they really produce the same sequence
T q_val = dist(eng);
T t_val = dist(trivial);
T s_val = dist(streamed);
BOOST_CHECK_CLOSE(q_val, t_val, 0.0001);
BOOST_CHECK_CLOSE(q_val, s_val, 0.0001);
// ~ BOOST_CHECK(q_val == t_val), but those are floating point values,
// so strict equality check may fail unnecessarily
// States remain equal!
BOOST_CHECK( eng == trivial );
BOOST_CHECK( eng == streamed );
// We want to check that quasi-random number generator values differ no
// more than 0.0006% of their value.
BOOST_CHECK_CLOSE(pt_array[step], q_val, 0.0006);
}
}
inline bool accept_all_exceptions(const std::exception& e)
{
BOOST_TEST_MESSAGE( e.what() );
return true;
}
template<typename Engine>
void test_max_seed(std::size_t dim)
{
typedef typename Engine::size_type size_type;
static const size_type maxseed = Engine::max();
Engine eng(dim);
eng.seed(maxseed-1); // must succeed
eng(); // skip one element
BOOST_REQUIRE_EXCEPTION( eng.seed(maxseed), std::range_error, accept_all_exceptions );
Engine other(dim);
other.seed(maxseed-1); // must succeed
other(); // skip one element, too
// States remain the same even after unsuccessful seeding for eng.
BOOST_CHECK( eng == other );
BOOST_CHECK( eng() == other() );
}
template<typename Generator>
void test_max_discard(std::size_t dim)
{
typedef typename Generator::type engine_type;
static const boost::uintmax_t maxdiscard = dim * engine_type::max();
// Max discard limit
{
engine_type eng(dim);
eng.discard(maxdiscard-1); // must succeed
eng(); // the very last element
BOOST_REQUIRE_EXCEPTION( eng(), std::range_error, accept_all_exceptions );
engine_type other(dim);
BOOST_CHECK( eng != other ); // test that comparison does not overflow
other(); // the very first element
other.discard(maxdiscard-1); // must succeed
BOOST_CHECK( eng == other );
BOOST_REQUIRE_EXCEPTION( other(), std::range_error, accept_all_exceptions );
}
// Overdiscarding
{
engine_type eng(dim);
eng.discard(maxdiscard); // must succeed, since it's maxdiscard operator() invocations
// must fail because after discarding the whole sequence
// we can't put the eng to any valid sequence producing state
BOOST_REQUIRE_EXCEPTION( eng(), std::range_error, accept_all_exceptions );
// Plain overdiscarding by 1
engine_type other(dim);
BOOST_REQUIRE_EXCEPTION( other.discard(maxdiscard+1), std::range_error, accept_all_exceptions );
}
// Test wraparound
{
engine_type eng(dim);
// must fail either because seq_count overflow check is triggered,
// or because this discard violates seeding bitcount constraint
BOOST_REQUIRE_EXCEPTION( eng.discard(maxdiscard*2), std::range_error, accept_all_exceptions );
}
}
} // namespace test
#define QRNG_VALIDATION_TEST_FUNCTIONS(QRNG) \
\
typedef boost::random::QRNG engine_t; \
\
template<typename T, std::size_t Dimension, std::size_t N> \
inline void test_##QRNG##_values(T (&pt)[N][Dimension], std::size_t skip) \
{ \
test::expected_values<engine_t>(pt, skip); \
} \
\
template<typename T, std::size_t Dimension, std::size_t N> \
inline void test_##QRNG##_seed(T (&pt)[N][Dimension], std::size_t skip) \
{ \
test::seed_function<engine_t>(pt, skip); \
} \
\
template<typename T, std::size_t Dimension, std::size_t N> \
inline void test_##QRNG##_discard(T (&pt)[N][Dimension], std::size_t skip) \
{ \
test::discard_function<engine_t>(pt, skip); \
} \
inline void test_##QRNG##_max_seed() \
{ \
test::test_max_seed<engine_t>(2); \
} \
inline void test_##QRNG##_max_dimension(std::size_t dim) \
{ \
engine_t eng(dim); /*must succeed*/ \
BOOST_REQUIRE_EXCEPTION( engine_t(dim+1), std::invalid_argument, test::accept_all_exceptions ); \
} \
\
BOOST_AUTO_TEST_CASE( test_##QRNG##_zero_dimension_fails ) \
{ \
BOOST_REQUIRE_EXCEPTION( engine_t(0), std::invalid_argument, test::accept_all_exceptions ); \
} \
/**/
#define QRNG_VALIDATION_TEST_DISCARD(QRNG) \
\
template <typename IntType, unsigned w> \
struct gen_engine \
{ \
typedef boost::random::QRNG##_engine<IntType, w> type; \
}; \
\
inline void test_##QRNG##_max_discard() \
{ \
static const std::size_t dim = 2;\
\
/* test full 8 bits */ \
test::test_max_discard<gen_engine<boost::uint8_t, 8u> >(dim); \
\
/* test 7 bits */ \
test::test_max_discard<gen_engine<boost::uint8_t, 7u> >(dim); \
\
/* test 6 bits for a good measure */ \
test::test_max_discard<gen_engine<boost::uint8_t, 6u> >(dim); \
} \
/**/
#endif // TEST_QRNG_FUNCTIONS_HPP_INCLUDED

5
libs/random/test/test_random_device.cpp
View File

@@ -13,6 +13,11 @@
#include <boost/test/test_tools.hpp>
#include <boost/test/included/test_exec_monitor.hpp>
#ifndef BOOST_NO_CXX11_CONSTEXPR
constexpr boost::random_device::result_type const_min = (boost::random_device::min)();
constexpr boost::random_device::result_type const_max = (boost::random_device::max)();
#endif
int test_main(int, char**) {
boost::random_device rng;
double entropy = rng.entropy();

2
libs/random/test/test_random_number_generator.cpp
View File

@@ -20,6 +20,7 @@
BOOST_AUTO_TEST_CASE(test_random_shuffle)
{
#ifndef BOOST_NO_CXX98_RANDOM_SHUFFLE
boost::mt19937 engine(1234);
boost::random::random_number_generator<boost::mt19937> generator(engine);
@@ -30,4 +31,5 @@ BOOST_AUTO_TEST_CASE(test_random_shuffle)
}
std::random_shuffle(testVec.begin(), testVec.end(), generator);
#endif
}

17
libs/random/test/test_seed_seq.cpp
View File

@@ -111,3 +111,20 @@ BOOST_AUTO_TEST_CASE(test_seed_seq) {
&param[0], &param[0] + 4, &expected_param[0], &expected_param[0] + 4);
#endif
}
BOOST_AUTO_TEST_CASE(test_seed_seq_short_output) {
boost::uint32_t store32[2];
boost::uint32_t expected_short[2] = {
4149590228u,
3175758659u
};
std::vector<int> data = list_of(2)(3)(4)(5);
boost::random::seed_seq seq(data);
seq.generate(&store32[0], &store32[0] + 2);
BOOST_CHECK_EQUAL_COLLECTIONS(
&store32[0], &store32[0] + 2, &expected_short[0], &expected_short[0] + 2);
}