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Initial QRNG commit
This commit is contained in:
Justinas V. Daugmaudis
committed by
Justinas V. Daugmaudis
Justinas V. Daugmaudis
parent
f3a83d0497
commit
3db2d7cb71
@@ -27,6 +27,7 @@ doxygen_files =
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discrete_distribution
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exponential_distribution
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extreme_value_distribution
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faure
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fisher_f_distribution
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gamma_distribution
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generate_canonical
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@@ -42,6 +43,7 @@ doxygen_files =
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mersenne_twister
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negative_binomial_distribution
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non_central_chi_squared_distribution
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niederreiter_base2
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normal_distribution
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piecewise_constant_distribution
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piecewise_linear_distribution
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@@ -52,6 +54,7 @@ doxygen_files =
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seed_seq
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shuffle_order
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# shuffle_output
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sobol
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student_t_distribution
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subtract_with_carry
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taus88
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@@ -107,6 +110,9 @@ doxygen reference :
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rand48=\"@xmlonly <classname alt=\\\"boost::random::rand48\\\">rand48</classname> @endxmlonly\" \\
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mt11213b=\"@xmlonly <classname alt=\\\"boost::random::mt11213b\\\">mt11213b</classname> @endxmlonly\" \\
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mt19937=\"@xmlonly <classname alt=\\\"boost::random::mt19937\\\">mt19937</classname> @endxmlonly\" \\
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niederreiter_base2=\"@xmlonly <classname alt=\\\"boost::random::niederreiter_base2\\\">niederreiter_base2</classname> @endxmlonly\" \\
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sobol=\"@xmlonly <classname alt=\\\"boost::random::sobol\\\">sobol</classname> @endxmlonly\" \\
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faure=\"@xmlonly <classname alt=\\\"boost::random::faure\\\">faure</classname> @endxmlonly\" \\
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ecuyer1988=\"@xmlonly <classname alt=\\\"boost::random::ecuyer1988\\\">ecuyer1988</classname> @endxmlonly\" \\
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lagged_fibonacci607=\"@xmlonly <classname alt=\\\"boost::random::lagged_fibonacci607\\\">lagged_fibonacci607</classname> @endxmlonly\" \\
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lagged_fibonacci44497=\"@xmlonly <classname alt=\\\"boost::random::lagged_fibonacci44497\\\">lagged_fibonacci44497</classname> @endxmlonly\" \\
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@@ -199,6 +199,70 @@ the generator, for example to re-run a test suite at a later time.]
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[endsect]
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[section Quasi-Random Number Generator]
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A quasi-random number generator is a __UniformRandomNumberGenerator which
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provides a deterministic sequence of quasi-random numbers, based on some
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algorithm and internal state. [classref boost::random::niederreiter_base2
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Niederreiter Base 2] generator is an example of such a [qrng quasi-random
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number generator]. The "quasi" modifier is used to denote more clearly that the
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values produced by such a generator are neither random nor pseudo-random, but
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they form a low discrepancy sequence. The intuitive idea is that a low discrepancy
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sequence is more evenly distributed than a pseudo random sequence would be.
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For example, if we generate a low discrepancy sequence of 2D points on a square,
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this square would be covered more evenly, and the number of points falling to any
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part of the square would be proportional to the number of points in the whole square.
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Such sequences share some properties of random variables and in certain applications
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such as the quasi-Monte Carlo method their lower discrepancy is an important advantage.
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[note Quasi-random sequences are known to give efficient numerical integration
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rules in many Bayesian statistical problems where the posterior distribution can be
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transformed into periodic functions on the n-dimensional hypercube.]
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Harold Niederreiter gives an extensive overview on random number generation
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and quasi-Monte Carlo methods in his book "Random number generation and
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quasi-Monte Carlo methods, Society for Industrial and Applied Mathematics, 1992".
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In addition to the __UniformRandomNumberGenerator requirements,
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a quasi-random number generator has some additional requirements. In the
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following table, `X` denotes a quasi-random number generator class, and `v` is
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a const value of `X`.
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[table QuasiRandomNumberGenerator requirements
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[[expression] [return type] [pre/post-condition]]
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[[`X::dimension()`] [std::size_t] [the dimension of quasi-random domain. It must be no less than 1.
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The return value of this function shall not change during the lifetime of the object.]]
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]
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[note The `operator()` returns a successive element of an n-dimensional (n = `X::dimension()`) vector
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at each invocation. When all elements are exhausted, `operator()` begins anew with the starting
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element of a subsequent n-dimensional vector.]
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Classes which model a quasi-random number generator shall also model
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__EqualityComparable, i.e. implement `operator==`. Two quasi-random number
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generators are defined to be /equivalent/ if they both return an identical
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sequence of numbers starting from a given state.
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Classes which model a quasi-random number generator shall also model the
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__Streamable concept, i.e. implement `operator<<` and `operator>>`.
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`operator<<` writes all current state of the quasi-random number generator
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to the given `ostream` so that `operator>>` can restore the state at a later
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time. The state shall be written in a platform-independent manner, but it is
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assumed that the `locales` used for writing and reading be the same. The
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quasi-random number generator with the restored state and the original at
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the just-written state shall be equivalent.
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Classes which model a quasi-random number generator should also model the
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__CopyConstructible and __Assignable concepts. However, note that the
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sequences of the original and the copy are strongly correlated (in fact,
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they are identical), which may make them unsuitable for some problem domains.
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Thus, copying quasi-random number generators is discouraged; they should
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always be passed by (non-const) reference.
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The classes __niederreiter_base2, __sobol, __faure are models for a quasi-random number generator.
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[endsect]
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[section Seed Sequence]
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A SeedSeq represents a sequence of values that can be used to
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@@ -13,6 +13,7 @@
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[template sup[text]'''<superscript>'''[text]'''</superscript>''']
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[template prng[text] [link boost_random.reference.concepts.pseudo_random_number_generator [text]]]
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[template qrng[text] [link boost_random.reference.concepts.quasi_random_number_generator [text]]]
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[template concepts[text] [link boost_random.reference.concepts [text]]]
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[template generators[text] [link boost_random.reference.generators [text]]]
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[template distributions[text] [link boost_random.reference.distributions [text]]]
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@@ -20,6 +21,7 @@
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[def __NumberGenerator [link boost_random.reference.concepts.number_generator NumberGenerator]]
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[def __UniformRandomNumberGenerator [link boost_random.reference.concepts.uniform_random_number_generator UniformRandomNumberGenerator]]
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[def __PseudoRandomNumberGenerator [link boost_random.reference.concepts.pseudo_random_number_generator PseudoRandomNumberGenerator]]
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[def __QuasiRandomNumberGenerator [link boost_random.reference.concepts.quasi_random_number_generator QuasiRandomNumberGenerator]]
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[def __SeedSeq [link boost_random.reference.concepts.seed_sequence SeedSeq]]
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[def __CopyConstructible [@boost:/doc/html/CopyConstructible.html CopyConstructible]]
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@@ -64,6 +66,9 @@
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[def __ranlux64_4_01 [classref boost::random::ranlux64_4_01 ranlux64_4_01]]
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[def __ranlux24 [classref boost::random::ranlux24 ranlux24]]
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[def __ranlux48 [classref boost::random::ranlux48 ranlux48]]
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[def __niederreiter_base2 [classref boost::random::niederreiter_base2 niederreiter_base2]]
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[def __sobol [classref boost::random::sobol sobol]]
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[def __faure [classref boost::random::faure faure]]
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[def __uniform_smallint [classref boost::random::uniform_smallint uniform_smallint]]
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[def __uniform_int_distribution [classref boost::random::uniform_int_distribution uniform_int_distribution]]
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103
include/boost/random/detail/gray_coded_qrng_base.hpp
Normal file
103
include/boost/random/detail/gray_coded_qrng_base.hpp
Normal file
@@ -0,0 +1,103 @@
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/* boost random/detail/gray_coded_qrng_base.hpp header file
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*
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* Copyright Justinas Vygintas Daugmaudis 2010-2017
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_RANDOM_DETAIL_GRAY_CODED_QRNG_BASE_HPP
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#define BOOST_RANDOM_DETAIL_GRAY_CODED_QRNG_BASE_HPP
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#include <boost/random/detail/qrng_base.hpp>
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// Prerequisite headers for bitscan to work
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#include <limits.h>
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#include <boost/mpl/if.hpp>
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#include <boost/type_traits/make_unsigned.hpp>
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#include <boost/multiprecision/detail/bitscan.hpp> // find_lsb
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//!\file
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//!Describes the gray-coded quasi-random number generator base class template.
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namespace boost {
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namespace random {
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namespace detail {
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template<typename DerivedT, typename LatticeT>
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class gray_coded_qrng_base : public qrng_base<DerivedT, LatticeT>
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{
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private:
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typedef gray_coded_qrng_base<DerivedT, LatticeT> self_t;
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typedef qrng_base<DerivedT, LatticeT> base_t;
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// The base needs to access modifying member f-ns, and we
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// don't want these functions to be available for the public use
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friend class qrng_base<DerivedT, LatticeT>;
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public:
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typedef typename LatticeT::value_type result_type;
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explicit gray_coded_qrng_base(std::size_t dimension)
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: base_t(dimension)
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{}
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// default copy c-tor is fine
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// default assignment operator is fine
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protected:
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void seed(std::size_t init, const char *msg)
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{
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this->curr_elem = 0;
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if (init != this->seq_count)
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{
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base_t::derived().seed();
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this->seq_count = init;
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init ^= (init / 2);
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for (int r = 0; init != 0; ++r, init >>= 1)
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{
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if (init & 1)
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update_quasi(r, msg);
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}
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}
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}
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private:
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// Compute next state for this QRNG
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void compute_next()
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{
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compute_seq(this->seq_count++);
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}
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void compute_seq(std::size_t cnt)
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{
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// Find the position of the least-significant zero in sequence count.
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// This is the bit that changes in the Gray-code representation as
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// the count is advanced.
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int r = multiprecision::detail::find_lsb(~cnt);
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update_quasi(r, "compute_seq");
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}
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void update_quasi(int r, const char* msg)
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{
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if (r < LatticeT::bit_count)
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{
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// Calculate the next state.
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for (std::size_t i = 0; i != this->dimension(); ++i)
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this->quasi_state[i] ^= this->lattice(r, i);
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}
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else
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{
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boost::throw_exception( std::overflow_error(msg) );
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}
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}
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};
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}} // namespace detail::random
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} // namespace boost
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#endif // BOOST_RANDOM_DETAIL_GRAY_CODED_QRNG_BASE_HPP
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203
include/boost/random/detail/qrng_base.hpp
Normal file
203
include/boost/random/detail/qrng_base.hpp
Normal file
@@ -0,0 +1,203 @@
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/* boost random/detail/quasi_random_number_generator_base.hpp header file
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*
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* Copyright Justinas Vygintas Daugmaudis 2010-2017
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* Distributed under the Boost Software License, Version 1.0. (See
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* accompanying file LICENSE_1_0.txt or copy at
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* http://www.boost.org/LICENSE_1_0.txt)
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*/
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#ifndef BOOST_RANDOM_DETAIL_QRNG_BASE_HPP
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#define BOOST_RANDOM_DETAIL_QRNG_BASE_HPP
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#include <istream>
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#include <ostream>
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#include <stdexcept>
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#include <vector>
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#include <boost/random/detail/operators.hpp>
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#include <boost/throw_exception.hpp>
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//!\file
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//!Describes the quasi-random number generator base class template.
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namespace boost {
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namespace random {
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namespace detail {
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template<typename DerivedT, typename LatticeT>
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class qrng_base
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{
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public:
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typedef typename LatticeT::value_type result_type;
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explicit qrng_base(std::size_t dimension)
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// Guard against invalid dimensions before creating the lattice
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: lattice(prevent_zero_dimension(dimension))
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, quasi_state(dimension)
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{
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derived().seed();
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}
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// default copy c-tor is fine
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// default assignment operator is fine
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//!Returns: The dimension of of the quasi-random domain.
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//!
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//!Throws: nothing.
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std::size_t dimension() const { return quasi_state.size(); }
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//!Requirements: *this is mutable.
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//!
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//!Returns: Returns a successive element of an s-dimensional
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//!(s = X::dimension()) vector at each invocation. When all elements are
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//!exhausted, X::operator() begins anew with the starting element of a
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//!subsequent s-dimensional vector.
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//!
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//!Throws: overflow_error.
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result_type operator()()
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{
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return curr_elem != dimension() ? load_cached(): next_state();
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}
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//!Fills a range with quasi-random values.
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template<typename Iter> void generate(Iter first, Iter last)
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{
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for (; first != last; ++first)
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*first = this->operator()();
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}
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//!Requirements: *this is mutable.
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//!
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//!Effects: Advances *this state as if z consecutive
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//!X::operator() invocations were executed.
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//!
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//!Throws: overflow_error.
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void discard(std::size_t z)
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{
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const std::size_t dimension_value = dimension();
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std::size_t vec_n = z / dimension_value;
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std::size_t elem_n = z - vec_n * dimension_value; // z % Dimension
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std::size_t vec_offset = vec_n + (curr_elem + elem_n) / dimension_value;
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// Discards vec_offset consecutive s-dimensional vectors
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discard_vector(vec_offset);
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// Sets up the proper position of the element-to-read
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curr_elem += (z - dimension_value * vec_offset);
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}
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//!Writes a @c DerivedT to a @c std::ostream.
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BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, DerivedT, s)
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{
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os << s.dimension() << " " << s.seq_count << " " << s.curr_elem;
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return os;
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}
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//!Reads a @c DerivedT from a @c std::istream.
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BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, DerivedT, s)
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{
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std::size_t dim, seed, z;
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if (is >> dim >> std::ws >> seed >> std::ws >> z) // initialize iff success!
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{
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if (s.dimension() != dim)
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{
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prevent_zero_dimension(dim);
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s.lattice.resize(dim);
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s.quasi_state.resize(dim);
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}
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// Fast-forward to the correct state
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s.seed(seed);
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s.discard(z);
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}
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return is;
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}
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//!Returns true if the two generators will produce identical sequences.
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BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(DerivedT, x, y)
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{
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const std::size_t dimension_value = x.dimension();
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// Note that two generators with different seq_counts and curr_elems can
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// produce the same sequence because the generator triple
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// (D, S, D) is equivalent to (D, S + 1, 0), where D is dimension, S -- seq_count,
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// and the last one is curr_elem.
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return (dimension_value == y.dimension()) &&
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(x.seq_count + (x.curr_elem / dimension_value) == y.seq_count + (y.curr_elem / dimension_value)) &&
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(x.curr_elem % dimension_value == y.curr_elem % dimension_value);
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}
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//!Returns true if the two generators will produce different sequences,
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BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(DerivedT)
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protected:
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DerivedT& derived() throw()
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{
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return *static_cast<DerivedT * const>(this);
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}
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void reset_state()
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{
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curr_elem = 0;
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seq_count = 0;
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std::fill(quasi_state.begin(), quasi_state.end(), result_type /*zero*/());
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}
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private:
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inline static std::size_t prevent_zero_dimension(std::size_t dimension)
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{
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if (dimension == 0)
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boost::throw_exception( std::invalid_argument("qrng_base: zero dimension") );
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return dimension;
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}
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// Load the result from the saved state.
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result_type load_cached()
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{
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return quasi_state[curr_elem++];
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}
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result_type next_state()
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{
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derived().compute_next();
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curr_elem = 0;
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return load_cached();
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}
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// Discards z consecutive s-dimensional vectors,
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// and preserves the position of the element-to-read
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void discard_vector(std::size_t z)
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{
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std::size_t inc_seq_count = seq_count + z;
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// Here we check that no overflow occurs before we
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// begin seeding the new value
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if (inc_seq_count > seq_count)
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{
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std::size_t tmp = curr_elem;
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derived().seed(inc_seq_count);
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curr_elem = tmp;
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}
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else if (inc_seq_count < seq_count) // Increment overflowed?
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{
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boost::throw_exception( std::overflow_error("discard_vector") );
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}
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}
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protected:
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LatticeT lattice;
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std::size_t curr_elem;
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std::size_t seq_count;
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std::vector<result_type> quasi_state;
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};
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}} // namespace detail::random
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} // namespace boost
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#endif // BOOST_RANDOM_DETAIL_QRNG_BASE_HPP
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367
include/boost/random/faure.hpp
Normal file
367
include/boost/random/faure.hpp
Normal file
@@ -0,0 +1,367 @@
|
||||
/* boost random/faure.hpp header file
|
||||
*
|
||||
* Copyright Justinas Vygintas Daugmaudis 2010-2017
|
||||
* 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)
|
||||
*/
|
||||
|
||||
#ifndef BOOST_RANDOM_FAURE_HPP
|
||||
#define BOOST_RANDOM_FAURE_HPP
|
||||
|
||||
#include <boost/random/detail/qrng_base.hpp>
|
||||
|
||||
#include <vector>
|
||||
#include <algorithm>
|
||||
|
||||
#include <cmath>
|
||||
|
||||
#include <boost/assert.hpp>
|
||||
|
||||
#include <sstream>
|
||||
|
||||
//!\file
|
||||
//!Describes the quasi-random number generator class template faure.
|
||||
|
||||
namespace boost {
|
||||
namespace random {
|
||||
|
||||
/** @cond */
|
||||
namespace detail {
|
||||
namespace fr {
|
||||
|
||||
// There is no particular reason why 187 first primes were chosen
|
||||
// to be put into this table. The only reason was, perhaps, that
|
||||
// the number of dimensions for Faure generator would be around
|
||||
// the same number as the number of dimensions supported by the
|
||||
// Sobol qrng.
|
||||
struct prime_table
|
||||
{
|
||||
typedef unsigned short value_type;
|
||||
|
||||
BOOST_STATIC_CONSTANT(int, number_of_primes = 187);
|
||||
|
||||
// A function that returns lower bound prime for a given n
|
||||
static value_type lower_bound(std::size_t n)
|
||||
{
|
||||
static const value_type prim_a[number_of_primes] = {
|
||||
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
|
||||
59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
|
||||
127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
|
||||
191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
|
||||
257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
|
||||
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
|
||||
401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
|
||||
467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
|
||||
563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619,
|
||||
631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
|
||||
709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787,
|
||||
797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
|
||||
877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953,
|
||||
967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031,
|
||||
1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093,
|
||||
1097, 1103, 1109, 1117 };
|
||||
|
||||
if (n > prim_a[number_of_primes - 1])
|
||||
{
|
||||
std::ostringstream os;
|
||||
os << "The Faure quasi-random number generator only supports up to "
|
||||
<< prim_a[number_of_primes - 1] << " dimensions.";
|
||||
throw std::invalid_argument(os.str());
|
||||
}
|
||||
|
||||
return *std::lower_bound(prim_a, prim_a + number_of_primes, n);
|
||||
}
|
||||
};
|
||||
|
||||
// Returns the integer part of the logarithm base Base of arg.
|
||||
// In erroneous situations, e.g., integer_log(base, 0) the function
|
||||
// returns 0 and does not report the error. This is the intended
|
||||
// behavior.
|
||||
inline std::size_t integer_log(std::size_t base, std::size_t arg)
|
||||
{
|
||||
std::size_t ilog = 0;
|
||||
while( base <= arg )
|
||||
{
|
||||
arg /= base; ++ilog;
|
||||
}
|
||||
return ilog;
|
||||
}
|
||||
|
||||
// Perform exponentiation by squaring
|
||||
inline std::size_t integer_pow(std::size_t base, std::size_t exp)
|
||||
{
|
||||
std::size_t result = 1;
|
||||
while (exp)
|
||||
{
|
||||
if (exp & 1)
|
||||
result *= base;
|
||||
exp >>= 1;
|
||||
base *= base;
|
||||
}
|
||||
return result;
|
||||
}
|
||||
|
||||
// Computes a table of binomial coefficients modulo qs.
|
||||
template<typename RealType>
|
||||
struct binomial_coefficients
|
||||
{
|
||||
typedef RealType value_type;
|
||||
|
||||
// Binomial values modulo qs_base will never be bigger than qs_base.
|
||||
// We can choose an appropriate integer type to hold modulo values and
|
||||
// shave off memory footprint.
|
||||
typedef prime_table::value_type packed_uint_t;
|
||||
|
||||
// default copy c-tor is fine
|
||||
|
||||
explicit binomial_coefficients(std::size_t dimension)
|
||||
{
|
||||
resize(dimension);
|
||||
}
|
||||
|
||||
void resize(std::size_t dimension)
|
||||
{
|
||||
qs_base = fr::prime_table::lower_bound(dimension);
|
||||
inv_qs_base = static_cast<RealType>(1) / static_cast<RealType>(qs_base);
|
||||
|
||||
// Throw away previously computed coefficients.
|
||||
// This will trigger recomputation on next update
|
||||
coeff.clear();
|
||||
}
|
||||
|
||||
void update(std::size_t seq, std::vector<RealType>& quasi)
|
||||
{
|
||||
if (!quasi.empty())
|
||||
{
|
||||
const std::size_t hisum = n_elements(seq);
|
||||
if( coeff.size() != size_hint(hisum) )
|
||||
recompute_tables(hisum);
|
||||
|
||||
typename std::vector<RealType>::iterator it = quasi.begin();
|
||||
|
||||
*it = compute_recip(seq, hisum, ytemp.rbegin());
|
||||
|
||||
// Find other components using the Faure method.
|
||||
++it;
|
||||
for ( ; it != quasi.end(); ++it)
|
||||
{
|
||||
*it = RealType();
|
||||
RealType r = inv_qs_base;
|
||||
|
||||
for (std::size_t i = 0; i != hisum; ++i)
|
||||
{
|
||||
RealType ztemp = RealType();
|
||||
for (std::size_t j = i; j != hisum; ++j)
|
||||
ztemp += ytemp[j] * upper_element(i, j, hisum);
|
||||
|
||||
// Sum ( J <= I <= HISUM ) ( old ytemp(i) * binom(i,j) ) mod QS.
|
||||
ytemp[i] = std::fmod(ztemp, static_cast<RealType>(qs_base));
|
||||
*it += ytemp[i] * r;
|
||||
r *= inv_qs_base;
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
private:
|
||||
inline std::size_t n_elements(std::size_t seq) const
|
||||
{
|
||||
return integer_log(qs_base, seq) + 1;
|
||||
}
|
||||
|
||||
inline static std::size_t size_hint(std::size_t n)
|
||||
{
|
||||
return n * (n + 1) / 2;
|
||||
}
|
||||
|
||||
packed_uint_t& upper_element(std::size_t i, std::size_t j, std::size_t dim)
|
||||
{
|
||||
BOOST_ASSERT( i < dim );
|
||||
BOOST_ASSERT( j < dim );
|
||||
BOOST_ASSERT( i <= j );
|
||||
return coeff[(i * (2 * dim - i + 1)) / 2 + j - i];
|
||||
}
|
||||
|
||||
template<typename Iterator>
|
||||
RealType compute_recip(std::size_t seq, std::size_t n, Iterator out) const
|
||||
{
|
||||
// Here we do
|
||||
// Sum ( 0 <= J <= HISUM ) YTEMP(J) * QS**J
|
||||
// Sum ( 0 <= J <= HISUM ) YTEMP(J) / QS**(J+1)
|
||||
// in one go
|
||||
RealType r = RealType();
|
||||
std::size_t m, k = integer_pow(qs_base, n - 1);
|
||||
for( ; n != 0; --n, ++out, seq = m, k /= qs_base )
|
||||
{
|
||||
m = seq % k;
|
||||
RealType v = (seq - m) / k; // RealType <- IntType
|
||||
r += v;
|
||||
r *= inv_qs_base;
|
||||
*out = v; // saves double dereference
|
||||
}
|
||||
return r;
|
||||
}
|
||||
|
||||
void compute_coefficients(const std::size_t n)
|
||||
{
|
||||
// Resize and initialize to zero
|
||||
coeff.resize(size_hint(n));
|
||||
std::fill(coeff.begin(), coeff.end(), packed_uint_t());
|
||||
|
||||
// The first row and the diagonal is assigned to 1
|
||||
upper_element(0, 0, n) = 1;
|
||||
for (std::size_t i = 1; i < n; ++i)
|
||||
{
|
||||
upper_element(0, i, n) = 1;
|
||||
upper_element(i, i, n) = 1;
|
||||
}
|
||||
|
||||
// Computes binomial coefficients MOD qs_base
|
||||
for (std::size_t i = 1; i < n; ++i)
|
||||
{
|
||||
for (std::size_t j = i + 1; j < n; ++j)
|
||||
{
|
||||
upper_element(i, j, n) = ( upper_element(i, j-1, n) +
|
||||
upper_element(i-1, j-1, n) ) % qs_base;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
void recompute_tables(std::size_t n)
|
||||
{
|
||||
ytemp.resize(n);
|
||||
compute_coefficients(n);
|
||||
}
|
||||
|
||||
private:
|
||||
packed_uint_t qs_base;
|
||||
RealType inv_qs_base;
|
||||
|
||||
// here we cache precomputed data; note that binomial coefficients have
|
||||
// to be recomputed iff the integer part of the logarithm of seq changes,
|
||||
// which happens relatively rarely.
|
||||
std::vector<packed_uint_t> coeff; // packed upper (!) triangular matrix
|
||||
std::vector<RealType> ytemp;
|
||||
};
|
||||
|
||||
}} // namespace detail::fr
|
||||
/** @endcond */
|
||||
|
||||
//!class template faure implements a quasi-random number generator as described in
|
||||
//! \blockquote
|
||||
//!Henri Faure,
|
||||
//!Discrepance de suites associees a un systeme de numeration (en dimension s),
|
||||
//!Acta Arithmetica,
|
||||
//!Volume 41, 1982, pages 337-351.
|
||||
//! \endblockquote
|
||||
//
|
||||
//! \blockquote
|
||||
//!Bennett Fox,
|
||||
//!Algorithm 647:
|
||||
//!Implementation and Relative Efficiency of Quasirandom
|
||||
//!Sequence Generators,
|
||||
//!ACM Transactions on Mathematical Software,
|
||||
//!Volume 12, Number 4, December 1986, pages 362-376.
|
||||
//! \endblockquote
|
||||
//!
|
||||
//!\attention\b Important: This implementation supports up to 229 dimensions.
|
||||
//!
|
||||
//!In the following documentation @c X denotes the concrete class of the template
|
||||
//!faure returning objects of type @c RealType, u and v are the values of @c X.
|
||||
//!
|
||||
//!Some member functions may throw exceptions of type @c std::bad_alloc.
|
||||
//!
|
||||
//! \copydoc friendfunctions
|
||||
template<typename RealType>
|
||||
class faure : public detail::qrng_base<
|
||||
faure<RealType>
|
||||
, detail::fr::binomial_coefficients<RealType>
|
||||
>
|
||||
{
|
||||
typedef faure<RealType> self_t;
|
||||
|
||||
typedef detail::fr::binomial_coefficients<RealType> lattice_t;
|
||||
typedef detail::qrng_base<self_t, lattice_t> base_t;
|
||||
|
||||
friend class detail::qrng_base<self_t, lattice_t >;
|
||||
|
||||
public:
|
||||
typedef RealType result_type;
|
||||
|
||||
/** @copydoc boost::random::niederreiter_base2::min() */
|
||||
static result_type min /** @cond */ BOOST_PREVENT_MACRO_SUBSTITUTION /** @endcond */ () { return static_cast<RealType>(0); }
|
||||
|
||||
/** @copydoc boost::random::niederreiter_base2::max() */
|
||||
static result_type max /** @cond */ BOOST_PREVENT_MACRO_SUBSTITUTION /** @endcond */ () { return static_cast<RealType>(1); }
|
||||
|
||||
//!Effects: Constructs the s-dimensional default Faure quasi-random number generator.
|
||||
//!
|
||||
//!Throws: bad_alloc, invalid_argument.
|
||||
explicit faure(std::size_t s)
|
||||
: base_t(s) // initialize the binomial table here
|
||||
{}
|
||||
|
||||
/** @copydetails boost::random::niederreiter_base2::seed()
|
||||
* Throws: bad_alloc.
|
||||
*/
|
||||
void seed()
|
||||
{
|
||||
seed(0);
|
||||
}
|
||||
|
||||
/** @copydetails boost::random::niederreiter_base2::seed(std::size_t)
|
||||
* Throws: bad_alloc.
|
||||
*/
|
||||
void seed(std::size_t init)
|
||||
{
|
||||
compute_seq(init);
|
||||
this->curr_elem = 0;
|
||||
this->seq_count = init;
|
||||
}
|
||||
|
||||
//=========================Doxygen needs this!==============================
|
||||
|
||||
//!Requirements: *this is mutable.
|
||||
//!
|
||||
//!Returns: Returns a successive element of an s-dimensional
|
||||
//!(s = X::dimension()) vector at each invocation. When all elements are
|
||||
//!exhausted, X::operator() begins anew with the starting element of a
|
||||
//!subsequent s-dimensional vector.
|
||||
//!
|
||||
//!Throws: bad_alloc.
|
||||
|
||||
// Fixed in Doxygen 1.7.0 -- id 612458: Fixed problem handling @copydoc for function operators.
|
||||
result_type operator()()
|
||||
{
|
||||
return base_t::operator()();
|
||||
}
|
||||
|
||||
/** @copydoc boost::random::niederreiter_base2::discard(std::size_t)
|
||||
* Throws: bad_alloc.
|
||||
*/
|
||||
void discard(std::size_t z)
|
||||
{
|
||||
base_t::discard(z);
|
||||
}
|
||||
|
||||
private:
|
||||
/** @cond hide_private_members */
|
||||
void compute_seq(std::size_t seq)
|
||||
{
|
||||
this->lattice.update(seq, this->quasi_state);
|
||||
}
|
||||
void compute_next()
|
||||
{
|
||||
compute_seq(++this->seq_count);
|
||||
}
|
||||
/** @endcond */
|
||||
};
|
||||
|
||||
} // namespace random
|
||||
|
||||
typedef random::faure<double> faure;
|
||||
|
||||
} // namespace boost
|
||||
|
||||
#endif // BOOST_RANDOM_FAURE_HPP
|
||||
389
include/boost/random/niederreiter_base2.hpp
Normal file
389
include/boost/random/niederreiter_base2.hpp
Normal file
@@ -0,0 +1,389 @@
|
||||
/* boost random/nierderreiter_base2.hpp header file
|
||||
*
|
||||
* Copyright Justinas Vygintas Daugmaudis 2010-2017
|
||||
* 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)
|
||||
*/
|
||||
|
||||
#ifndef BOOST_RANDOM_NIEDERREITER_BASE2_HPP
|
||||
#define BOOST_RANDOM_NIEDERREITER_BASE2_HPP
|
||||
|
||||
#include <boost/random/detail/gray_coded_qrng_base.hpp>
|
||||
#include <boost/random/detail/config.hpp>
|
||||
#include <boost/random/detail/operators.hpp>
|
||||
|
||||
#include <limits>
|
||||
#include <boost/cstdint.hpp>
|
||||
|
||||
#include <boost/dynamic_bitset.hpp>
|
||||
#include <boost/multi_array.hpp>
|
||||
|
||||
//!\file
|
||||
//!Describes the quasi-random number generator class template niederreiter_base2.
|
||||
//!
|
||||
//!\b Note: it is especially useful in conjunction with class template uniform_real.
|
||||
|
||||
namespace boost {
|
||||
namespace random {
|
||||
|
||||
/** @cond */
|
||||
namespace detail {
|
||||
namespace nb2 {
|
||||
|
||||
/*
|
||||
Primitive polynomials in binary encoding
|
||||
{
|
||||
{ 1, 0, 0, 0, 0, 0 }, 1
|
||||
{ 0, 1, 0, 0, 0, 0 }, x
|
||||
{ 1, 1, 0, 0, 0, 0 }, 1 + x
|
||||
{ 1, 1, 1, 0, 0, 0 }, 1 + x + x^2
|
||||
{ 1, 1, 0, 1, 0, 0 }, 1 + x + x^3
|
||||
{ 1, 0, 1, 1, 0, 0 }, 1 + x^2 + x^3
|
||||
{ 1, 1, 0, 0, 1, 0 }, 1 + x + x^4
|
||||
{ 1, 0, 0, 1, 1, 0 }, 1 + x^3 + x^4
|
||||
{ 1, 1, 1, 1, 1, 0 }, 1 + x + x^2 + x^3 + x^4
|
||||
{ 1, 0, 1, 0, 0, 1 }, 1 + x^2 + x^5
|
||||
{ 1, 0, 0, 1, 0, 1 }, 1 + x^3 + x^5
|
||||
{ 1, 1, 1, 1, 0, 1 }, 1 + x + x^2 + x^3 + x^5
|
||||
{ 1, 1, 1, 0, 1, 1 } 1 + x + x^2 + x^4 + x^5
|
||||
};
|
||||
*/
|
||||
|
||||
// Maximum allowed space dimension
|
||||
#define BOOST_RANDOM_NIEDERREITER_BASE2_MAX_DIMENSION 54
|
||||
|
||||
struct niederreiter_tables
|
||||
{
|
||||
BOOST_STATIC_CONSTANT(int, max_dimension = BOOST_RANDOM_NIEDERREITER_BASE2_MAX_DIMENSION);
|
||||
|
||||
// Binary irreducible polynomials (primes in the ring GF(2)[X]), evaluated at X=2.
|
||||
static unsigned short polynomial(std::size_t n)
|
||||
{
|
||||
static const unsigned short nb2_a[max_dimension] = {
|
||||
2, 3, 7, 11, 13, 19, 25, 31, 37, 41,
|
||||
47, 55, 59, 61, 67, 73, 87, 91, 97, 103,
|
||||
109, 115, 117, 131, 137, 143, 145, 157,
|
||||
167, 171, 185, 191, 193, 203, 211, 213,
|
||||
229, 239, 241, 247, 253, 283, 285, 299,
|
||||
301, 313, 319, 333, 351, 355, 357, 361, 369,
|
||||
375
|
||||
};
|
||||
|
||||
return nb2_a[n];
|
||||
}
|
||||
};
|
||||
|
||||
// Return the base 2 logarithm for a given bitset v
|
||||
template <typename Block, typename Allocator>
|
||||
inline typename boost::dynamic_bitset<Block, Allocator>::size_type
|
||||
bitset_log2(const boost::dynamic_bitset<Block, Allocator>& v)
|
||||
{
|
||||
typedef boost::dynamic_bitset<Block, Allocator> bitset_t;
|
||||
typedef typename bitset_t::size_type size_type;
|
||||
|
||||
if (v.none())
|
||||
throw std::invalid_argument("bitset_log2");
|
||||
|
||||
size_type up = v.size() - 1;
|
||||
size_type low = v.find_next(0);
|
||||
|
||||
// Binary lookup for the most significant set bit
|
||||
while (low < up)
|
||||
{
|
||||
size_type m = low + (up - low) / 2;
|
||||
|
||||
// Check if any bit is present after mid
|
||||
size_type p = v.find_next(m);
|
||||
if (p != bitset_t::npos)
|
||||
low = p;
|
||||
else
|
||||
up = m;
|
||||
}
|
||||
|
||||
return low;
|
||||
}
|
||||
|
||||
|
||||
// Multiply polynomials over Z_2.
|
||||
template <typename Block, typename Allocator>
|
||||
inline boost::dynamic_bitset<Block, Allocator>
|
||||
modulo2_multiply(int P, boost::dynamic_bitset<Block, Allocator> v)
|
||||
{
|
||||
boost::dynamic_bitset<Block, Allocator> pt (v.size());
|
||||
for (; P; P >>= 1, v <<= 1)
|
||||
if (P & 1) pt ^= v;
|
||||
return pt;
|
||||
}
|
||||
|
||||
|
||||
// Calculate the values of the constants V(J,R) as
|
||||
// described in BFN section 3.3.
|
||||
//
|
||||
// px = appropriate irreducible polynomial for current dimension
|
||||
// pb = polynomial defined in section 2.3 of BFN.
|
||||
// pb is modified
|
||||
template <typename Block, typename Allocator, typename T>
|
||||
inline void calculate_v(const boost::dynamic_bitset<Block, Allocator>& pb,
|
||||
int& pb_degree, std::vector<T>& v)
|
||||
{
|
||||
const T arbitrary_element = static_cast<T>(1); // arbitray element of Z_2
|
||||
|
||||
// Now choose a value of Kj as defined in section 3.3.
|
||||
// We must have 0 <= Kj < E*J = M.
|
||||
// The limit condition on Kj does not seem very relevant
|
||||
// in this program.
|
||||
int kj = pb_degree;
|
||||
|
||||
pb_degree = bitset_log2(pb);
|
||||
|
||||
// Now choose values of V in accordance with
|
||||
// the conditions in section 3.3.
|
||||
std::fill(v.begin(), v.begin() + kj, T());
|
||||
|
||||
// Quoting from BFN: "Our program currently sets each K_q
|
||||
// equal to eq. This has the effect of setting all unrestricted
|
||||
// values of v to 1."
|
||||
// Actually, it sets them to the arbitrary chosen value.
|
||||
// Whatever.
|
||||
for (int r = kj; r < pb_degree; ++r)
|
||||
v[r] = arbitrary_element;
|
||||
|
||||
// Calculate the remaining V's using the recursion of section 2.3,
|
||||
// remembering that the B's have the opposite sign.
|
||||
for (int r = pb_degree; r < v.size(); ++r)
|
||||
{
|
||||
T term = T /*zero*/ ();
|
||||
boost::dynamic_bitset<> pb_c = pb;
|
||||
for (int k = -pb_degree; k < 0; ++k, pb_c >>= 1)
|
||||
{
|
||||
if( pb_c.test(0) )
|
||||
term ^= v[r + k];
|
||||
}
|
||||
v[r] = term;
|
||||
}
|
||||
}
|
||||
|
||||
} // namespace nb2
|
||||
|
||||
template<typename IntType>
|
||||
struct niederreiter_base2_lattice
|
||||
{
|
||||
typedef IntType value_type;
|
||||
|
||||
BOOST_STATIC_CONSTANT(int, bit_count = std::numeric_limits<IntType>::digits);
|
||||
|
||||
explicit niederreiter_base2_lattice(std::size_t dimension)
|
||||
{
|
||||
resize(dimension);
|
||||
}
|
||||
|
||||
void resize(std::size_t dimension)
|
||||
{
|
||||
if (dimension > nb2::niederreiter_tables::max_dimension)
|
||||
{
|
||||
throw std::invalid_argument("The Niederreiter base 2 quasi-random number generator only supports up to "
|
||||
BOOST_PP_STRINGIZE(BOOST_RANDOM_NIEDERREITER_BASE2_MAX_DIMENSION) " dimensions.");
|
||||
}
|
||||
|
||||
// Initialize the bit array
|
||||
bits.resize(boost::extents[bit_count][dimension]);
|
||||
|
||||
// Reserve temporary space for lattice computation
|
||||
boost::multi_array<IntType, 2> ci(boost::extents[bit_count][bit_count]);
|
||||
|
||||
std::vector<IntType> v;
|
||||
|
||||
// Compute Niedderreiter base 2 lattice
|
||||
for (std::size_t dim = 0; dim != dimension; ++dim)
|
||||
{
|
||||
const int poly = nb2::niederreiter_tables::polynomial(dim);
|
||||
if (static_cast<std::size_t>(poly) >
|
||||
static_cast<std::size_t>(std::numeric_limits<IntType>::max())) {
|
||||
boost::throw_exception( std::range_error("niederreiter_base2: polynomial value outside the given IntType range") );
|
||||
}
|
||||
|
||||
const int degree = multiprecision::detail::find_msb(poly); // integer log2(poly)
|
||||
const int max_degree = degree * ((bit_count / degree) + 1);
|
||||
|
||||
v.resize(degree + max_degree);
|
||||
|
||||
// For each dimension, we need to calculate powers of an
|
||||
// appropriate irreducible polynomial, see Niederreiter
|
||||
// page 65, just below equation (19).
|
||||
// Copy the appropriate irreducible polynomial into PX,
|
||||
// and its degree into E. Set polynomial B = PX ** 0 = 1.
|
||||
// M is the degree of B. Subsequently B will hold higher
|
||||
// powers of PX.
|
||||
int pb_degree = 0;
|
||||
boost::dynamic_bitset<> pb(max_degree, 1);
|
||||
|
||||
int j = 0;
|
||||
while (j < bit_count)
|
||||
{
|
||||
// Now multiply B by PX so B becomes PX**J.
|
||||
// In section 2.3, the values of Bi are defined with a minus sign :
|
||||
// don't forget this if you use them later!
|
||||
nb2::modulo2_multiply(poly, boost::move(pb)).swap(pb);
|
||||
|
||||
// If U = 0, we need to set B to the next power of PX
|
||||
// and recalculate V.
|
||||
nb2::calculate_v(pb, pb_degree, v);
|
||||
|
||||
// Niederreiter (page 56, after equation (7), defines two
|
||||
// variables Q and U. We do not need Q explicitly, but we
|
||||
// do need U.
|
||||
|
||||
// Advance Niederreiter's state variables.
|
||||
for (int u = 0; u < degree && j < bit_count; ++u, ++j)
|
||||
{
|
||||
// Now C is obtained from V. Niederreiter
|
||||
// obtains A from V (page 65, near the bottom), and then gets
|
||||
// C from A (page 56, equation (7)). However this can be done
|
||||
// in one step. Here CI(J,R) corresponds to
|
||||
// Niederreiter's C(I,J,R).
|
||||
for (int r = 0; r < bit_count; ++r) {
|
||||
ci[r][j] = v[r + u];
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// The array CI now holds the values of C(I,J,R) for this value
|
||||
// of I. We pack them into array CJ so that CJ(I,R) holds all
|
||||
// the values of C(I,J,R) for J from 1 to NBITS.
|
||||
for (int r = 0; r < bit_count; ++r)
|
||||
{
|
||||
IntType term = 0;
|
||||
for (int j = 0; j < bit_count; ++j)
|
||||
term = 2*term + ci[r][j];
|
||||
bits[r][dim] = term;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
value_type operator()(int i, int j) const
|
||||
{
|
||||
return bits[i][j];
|
||||
}
|
||||
|
||||
private:
|
||||
boost::multi_array<IntType, 2> bits;
|
||||
};
|
||||
|
||||
} // namespace detail
|
||||
/** @endcond */
|
||||
|
||||
//!class template niederreiter_base2 implements a quasi-random number generator as described in
|
||||
//! \blockquote
|
||||
//!Bratley, Fox, Niederreiter, ACM Trans. Model. Comp. Sim. 2, 195 (1992).
|
||||
//! \endblockquote
|
||||
//!
|
||||
//!\attention \b Important: This implementation supports up to 20 dimensions.
|
||||
//!
|
||||
//!In the following documentation @c X denotes the concrete class of the template
|
||||
//!niederreiter_base2 returning objects of type @c IntType, u and v are the values of @c X.
|
||||
//!
|
||||
//!Some member functions may throw exceptions of type std::overflow_error. This
|
||||
//!happens when the quasi-random domain is exhausted and the generator cannot produce
|
||||
//!any more values. The length of the low discrepancy sequence is given by
|
||||
//! \f$L=Dimension \times 2^{digits}\f$, where digits = std::numeric_limits<IntType>::digits.
|
||||
template<typename IntType>
|
||||
class niederreiter_base2 : public detail::gray_coded_qrng_base<
|
||||
niederreiter_base2<IntType>,
|
||||
detail::niederreiter_base2_lattice<IntType> >
|
||||
{
|
||||
typedef niederreiter_base2<IntType> self_t;
|
||||
typedef detail::niederreiter_base2_lattice<IntType> lattice_t;
|
||||
typedef detail::gray_coded_qrng_base<self_t, lattice_t> base_t;
|
||||
|
||||
public:
|
||||
typedef IntType result_type;
|
||||
|
||||
//!Returns: Tight lower bound on the set of values returned by operator().
|
||||
//!
|
||||
//!Throws: nothing.
|
||||
static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; }
|
||||
|
||||
//!Returns: Tight upper bound on the set of values returned by operator().
|
||||
//!
|
||||
//!Throws: nothing.
|
||||
static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () { return std::numeric_limits<IntType>::max(); }
|
||||
|
||||
//!Effects: Constructs the default s-dimensional Niederreiter base 2 quasi-random number generator.
|
||||
//!
|
||||
//!Throws: bad_alloc, invalid_argument, range_error.
|
||||
explicit niederreiter_base2(std::size_t s)
|
||||
: base_t(s) // initialize lattice here
|
||||
{}
|
||||
|
||||
//!Requirements: *this is mutable.
|
||||
//!
|
||||
//!Effects: Resets the quasi-random number generator state to
|
||||
//!the one given by the default construction. Equivalent to u.seed(0).
|
||||
//!
|
||||
//!\brief Throws: nothing.
|
||||
void seed()
|
||||
{
|
||||
base_t::reset_state();
|
||||
}
|
||||
|
||||
//!Requirements: *this is mutable.
|
||||
//!
|
||||
//!Effects: Effectively sets the quasi-random number generator state to the init-th
|
||||
//!vector in the s-dimensional quasi-random domain, where s == X::dimension().
|
||||
//!\code
|
||||
//!X u, v;
|
||||
//!for(int i = 0; i < N; ++i)
|
||||
//! for( std::size_t j = 0; j < u.dimension(); ++j )
|
||||
//! u();
|
||||
//!v.seed(N);
|
||||
//!assert(u() == v());
|
||||
//!\endcode
|
||||
//!
|
||||
//!\brief Throws: overflow_error.
|
||||
void seed(std::size_t init)
|
||||
{
|
||||
base_t::seed(init, "niederreiter_base2::seed");
|
||||
}
|
||||
|
||||
//=========================Doxygen needs this!==============================
|
||||
|
||||
//!Requirements: *this is mutable.
|
||||
//!
|
||||
//!Returns: Returns a successive element of an s-dimensional
|
||||
//!(s = X::dimension()) vector at each invocation. When all elements are
|
||||
//!exhausted, X::operator() begins anew with the starting element of a
|
||||
//!subsequent s-dimensional vector.
|
||||
//!
|
||||
//!Throws: overflow_error.
|
||||
result_type operator()()
|
||||
{
|
||||
return base_t::operator()();
|
||||
}
|
||||
|
||||
//!Requirements: *this is mutable.
|
||||
//!
|
||||
//!Effects: Advances *this state as if z consecutive
|
||||
//!X::operator() invocations were executed.
|
||||
//!\code
|
||||
//!X u = v;
|
||||
//!for(int i = 0; i < N; ++i)
|
||||
//! u();
|
||||
//!v.discard(N);
|
||||
//!assert(u() == v());
|
||||
//!\endcode
|
||||
//!
|
||||
//!Throws: overflow_error.
|
||||
void discard(std::size_t z)
|
||||
{
|
||||
base_t::discard(z);
|
||||
}
|
||||
};
|
||||
|
||||
} // namespace random
|
||||
|
||||
typedef random::niederreiter_base2<uint32_t> niederreiter_base2;
|
||||
|
||||
} // namespace boost
|
||||
|
||||
#endif // BOOST_RANDOM_NIEDERREITER_BASE2_HPP
|
||||
1118
include/boost/random/sobol.hpp
Normal file
1118
include/boost/random/sobol.hpp
Normal file
File diff suppressed because it is too large
Load Diff
@@ -55,6 +55,10 @@ 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
|
||||
|
||||
375
test/faure_validate.cpp
Normal file
375
test/faure_validate.cpp
Normal file
@@ -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 },
|
||||
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|
||||
{ 0.4844297700, 0.7936573894, 0.8907946364, 0.9765335523, 0.4903205041, 0.4527131958, 0.1236342815, 0.4094546141, 0.3378558545, 0.5764545303, 0.0910556486, 0.3209020345, 0.1102843455, 0.6008675522, 0.5819860732, 0.9634709693 },
|
||||
{ 0.5432532995, 0.8524809189, 0.9496181658, 0.0353570817, 0.5491440335, 0.5115367252, 0.1824578109, 0.4682781435, 0.3966793839, 0.6352780597, 0.1498791780, 0.3797255639, 0.1691078749, 0.6596910816, 0.6408096027, 0.0222944987 },
|
||||
{ 0.6020768289, 0.9113044483, 0.0084416952, 0.0941806111, 0.6079675629, 0.5703602546, 0.2412813403, 0.5271016729, 0.4555029133, 0.6941015891, 0.2087027074, 0.4385490933, 0.2279314044, 0.7185146110, 0.6996331321, 0.0811180281 },
|
||||
{ 0.6609003583, 0.9701279777, 0.0672652246, 0.1530041406, 0.6667910923, 0.6291837840, 0.3001048697, 0.5859252023, 0.5143264427, 0.7529251185, 0.2675262368, 0.4973726227, 0.2867549338, 0.7773381404, 0.7584566615, 0.1399415575 },
|
||||
{ 0.7197238877, 0.0289515071, 0.1260887540, 0.2118276700, 0.7256146218, 0.6880073134, 0.3589283991, 0.6447487317, 0.5731499721, 0.8117486479, 0.3263497662, 0.5561961521, 0.3455784632, 0.8361616698, 0.8172801909, 0.1987650869 },
|
||||
{ 0.7785474171, 0.0877750365, 0.1849122834, 0.2706511994, 0.7844381512, 0.7468308428, 0.4177519285, 0.7035722612, 0.6319735016, 0.8705721773, 0.3851732956, 0.6150196816, 0.4044019926, 0.8949851992, 0.8761037203, 0.2575886163 },
|
||||
{ 0.8373709465, 0.1465985659, 0.2437358128, 0.3294747288, 0.8432616806, 0.8056543722, 0.4765754580, 0.7623957906, 0.6907970310, 0.9293957068, 0.4439968250, 0.6738432110, 0.4632255220, 0.9538087286, 0.9349272497, 0.3164121457 },
|
||||
{ 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);
|
||||
}
|
||||
372
test/niederreiter_base2_validade.cpp
Normal file
372
test/niederreiter_base2_validade.cpp
Normal file
@@ -0,0 +1,372 @@
|
||||
// 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/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: 4096
|
||||
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: 4096
|
||||
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: 4096
|
||||
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 },
|
||||
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|
||||
{ 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)
|
||||
|
||||
|
||||
BOOST_AUTO_TEST_CASE( validate_niederreiter_base2 )
|
||||
{
|
||||
test_niederreiter_base2_values(niederreiter_base2_02_100, 4096);
|
||||
test_niederreiter_base2_values(niederreiter_base2_07_100, 4096);
|
||||
test_niederreiter_base2_values(niederreiter_base2_16_100, 4096);
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_CASE( validate_niederreiter_base2_seed )
|
||||
{
|
||||
test_niederreiter_base2_seed(niederreiter_base2_02_100, 4096);
|
||||
test_niederreiter_base2_seed(niederreiter_base2_07_100, 4096);
|
||||
test_niederreiter_base2_seed(niederreiter_base2_16_100, 4096);
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_CASE( validate_niederreiter_base2_discard )
|
||||
{
|
||||
test_niederreiter_base2_discard(niederreiter_base2_02_100, 4096);
|
||||
test_niederreiter_base2_discard(niederreiter_base2_07_100, 4096);
|
||||
test_niederreiter_base2_discard(niederreiter_base2_16_100, 4096);
|
||||
}
|
||||
371
test/sobol_validate.cpp
Normal file
371
test/sobol_validate.cpp
Normal file
@@ -0,0 +1,371 @@
|
||||
// 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/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
|
||||
// version of ACM TOMS Algorithm 659, 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/sobol/
|
||||
|
||||
|
||||
// Spatial dimension: 2
|
||||
// N: 100
|
||||
// Vectors skipped: 0
|
||||
static const double sobol_02_100[100][2] =
|
||||
{
|
||||
{ 0.0000000000, 0.0000000000 },
|
||||
{ 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: 128
|
||||
static const double sobol_07_100[100][7] =
|
||||
{
|
||||
{ 0.0117187500, 0.3320312502, 0.7851562504, 0.9414062504, 0.4648437502, 0.4179687502, 0.4648437502 },
|
||||
{ 0.5117187502, 0.8320312504, 0.2851562501, 0.4414062502, 0.9648437504, 0.9179687504, 0.9648437504 },
|
||||
{ 0.7617187504, 0.0820312500, 0.0351562500, 0.6914062503, 0.7148437503, 0.1679687501, 0.7148437503 },
|
||||
{ 0.2617187501, 0.5820312503, 0.5351562502, 0.1914062501, 0.2148437501, 0.6679687503, 0.2148437501 },
|
||||
{ 0.3867187502, 0.2070312501, 0.4101562502, 0.8164062504, 0.5898437503, 0.5429687503, 0.3398437502 },
|
||||
{ 0.8867187504, 0.7070312503, 0.9101562504, 0.3164062501, 0.0898437500, 0.0429687500, 0.8398437504 },
|
||||
{ 0.6367187503, 0.4570312502, 0.6601562503, 0.5664062503, 0.3398437502, 0.7929687504, 0.5898437503 },
|
||||
{ 0.1367187501, 0.9570312504, 0.1601562501, 0.0664062500, 0.8398437504, 0.2929687501, 0.0898437500 },
|
||||
{ 0.1992187501, 0.0195312500, 0.5976562503, 0.2539062501, 0.9023437504, 0.3554687502, 0.4023437502 },
|
||||
{ 0.6992187503, 0.5195312502, 0.0976562500, 0.7539062504, 0.4023437502, 0.8554687504, 0.9023437504 },
|
||||
{ 0.9492187504, 0.2695312501, 0.3476562502, 0.0039062500, 0.1523437501, 0.1054687500, 0.6523437503 },
|
||||
{ 0.4492187502, 0.7695312504, 0.8476562504, 0.5039062502, 0.6523437503, 0.6054687503, 0.1523437501 },
|
||||
{ 0.3242187502, 0.3945312502, 0.2226562501, 0.3789062502, 0.0273437500, 0.7304687503, 0.2773437501 },
|
||||
{ 0.8242187504, 0.8945312504, 0.7226562503, 0.8789062504, 0.5273437502, 0.2304687501, 0.7773437504 },
|
||||
{ 0.5742187503, 0.1445312501, 0.9726562505, 0.1289062501, 0.7773437504, 0.9804687505, 0.5273437502 },
|
||||
{ 0.0742187500, 0.6445312503, 0.4726562502, 0.6289062503, 0.2773437501, 0.4804687502, 0.0273437500 },
|
||||
{ 0.1054687500, 0.1757812501, 0.0664062500, 0.5976562503, 0.2460937501, 0.1992187501, 0.9960937505 },
|
||||
{ 0.6054687503, 0.6757812503, 0.5664062503, 0.0976562500, 0.7460937503, 0.6992187503, 0.4960937502 },
|
||||
{ 0.8554687504, 0.4257812502, 0.8164062504, 0.8476562504, 0.9960937505, 0.4492187502, 0.2460937501 },
|
||||
{ 0.3554687502, 0.9257812504, 0.3164062501, 0.3476562502, 0.4960937502, 0.9492187504, 0.7460937503 },
|
||||
{ 0.4804687502, 0.3007812501, 0.6914062503, 0.7226562503, 0.8710937504, 0.8242187504, 0.8710937504 },
|
||||
{ 0.9804687505, 0.8007812504, 0.1914062501, 0.2226562501, 0.3710937502, 0.3242187502, 0.3710937502 },
|
||||
{ 0.7304687503, 0.0507812500, 0.4414062502, 0.9726562505, 0.1210937501, 0.5742187503, 0.1210937501 },
|
||||
{ 0.2304687501, 0.5507812503, 0.9414062504, 0.4726562502, 0.6210937503, 0.0742187500, 0.6210937503 },
|
||||
{ 0.1679687501, 0.4882812502, 0.2539062501, 0.1601562501, 0.6835937503, 0.0117187500, 0.9335937504 },
|
||||
{ 0.6679687503, 0.9882812505, 0.7539062504, 0.6601562503, 0.1835937501, 0.5117187502, 0.4335937502 },
|
||||
{ 0.9179687504, 0.2382812501, 0.5039062502, 0.4101562502, 0.4335937502, 0.2617187501, 0.1835937501 },
|
||||
{ 0.4179687502, 0.7382812503, 0.0039062500, 0.9101562504, 0.9335937504, 0.7617187504, 0.6835937503 },
|
||||
{ 0.2929687501, 0.1132812501, 0.8789062504, 0.0351562500, 0.3085937501, 0.8867187504, 0.8085937504 },
|
||||
{ 0.7929687504, 0.6132812503, 0.3789062502, 0.5351562502, 0.8085937504, 0.3867187502, 0.3085937501 },
|
||||
{ 0.5429687503, 0.3632812502, 0.1289062501, 0.2851562501, 0.5585937503, 0.6367187503, 0.0585937500 },
|
||||
{ 0.0429687500, 0.8632812504, 0.6289062503, 0.7851562504, 0.0585937500, 0.1367187501, 0.5585937503 },
|
||||
{ 0.0585937500, 0.0664062500, 0.3320312502, 0.3945312502, 0.7617187504, 0.8085937504, 0.1992187501 },
|
||||
{ 0.5585937503, 0.5664062503, 0.8320312504, 0.8945312504, 0.2617187501, 0.3085937501, 0.6992187503 },
|
||||
{ 0.8085937504, 0.3164062501, 0.5820312503, 0.1445312501, 0.0117187500, 0.5585937503, 0.9492187504 },
|
||||
{ 0.3085937501, 0.8164062504, 0.0820312500, 0.6445312503, 0.5117187502, 0.0585937500, 0.4492187502 },
|
||||
{ 0.4335937502, 0.4414062502, 0.9570312504, 0.2695312501, 0.1367187501, 0.1835937501, 0.0742187500 },
|
||||
{ 0.9335937504, 0.9414062504, 0.4570312502, 0.7695312504, 0.6367187503, 0.6835937503, 0.5742187503 },
|
||||
{ 0.6835937503, 0.1914062501, 0.2070312501, 0.0195312500, 0.8867187504, 0.4335937502, 0.8242187504 },
|
||||
{ 0.1835937501, 0.6914062503, 0.7070312503, 0.5195312502, 0.3867187502, 0.9335937504, 0.3242187502 },
|
||||
{ 0.2460937501, 0.2539062501, 0.0195312500, 0.8320312504, 0.3242187502, 0.9960937505, 0.1367187501 },
|
||||
{ 0.7460937503, 0.7539062504, 0.5195312502, 0.3320312502, 0.8242187504, 0.4960937502, 0.6367187503 },
|
||||
{ 0.9960937505, 0.0039062500, 0.7695312504, 0.5820312503, 0.5742187503, 0.7460937503, 0.8867187504 },
|
||||
{ 0.4960937502, 0.5039062502, 0.2695312501, 0.0820312500, 0.0742187500, 0.2460937501, 0.3867187502 },
|
||||
{ 0.3710937502, 0.1289062501, 0.6445312503, 0.9570312504, 0.6992187503, 0.1210937501, 0.0117187500 },
|
||||
{ 0.8710937504, 0.6289062503, 0.1445312501, 0.4570312502, 0.1992187501, 0.6210937503, 0.5117187502 },
|
||||
{ 0.6210937503, 0.3789062502, 0.3945312502, 0.7070312503, 0.4492187502, 0.3710937502, 0.7617187504 },
|
||||
{ 0.1210937501, 0.8789062504, 0.8945312504, 0.2070312501, 0.9492187504, 0.8710937504, 0.2617187501 },
|
||||
{ 0.0898437500, 0.4101562502, 0.5507812503, 0.0507812500, 0.5429687503, 0.5898437503, 0.7304687503 },
|
||||
{ 0.5898437503, 0.9101562504, 0.0507812500, 0.5507812503, 0.0429687500, 0.0898437500, 0.2304687501 },
|
||||
{ 0.8398437504, 0.1601562501, 0.3007812501, 0.3007812501, 0.2929687501, 0.8398437504, 0.4804687502 },
|
||||
{ 0.3398437502, 0.6601562503, 0.8007812504, 0.8007812504, 0.7929687504, 0.3398437502, 0.9804687505 },
|
||||
{ 0.4648437502, 0.0351562500, 0.1757812501, 0.1757812501, 0.4179687502, 0.4648437502, 0.6054687503 },
|
||||
{ 0.9648437504, 0.5351562502, 0.6757812503, 0.6757812503, 0.9179687504, 0.9648437504, 0.1054687500 },
|
||||
{ 0.7148437503, 0.2851562501, 0.9257812504, 0.4257812502, 0.6679687503, 0.2148437501, 0.3554687502 },
|
||||
{ 0.2148437501, 0.7851562504, 0.4257812502, 0.9257812504, 0.1679687501, 0.7148437503, 0.8554687504 },
|
||||
{ 0.1523437501, 0.2226562501, 0.8632812504, 0.7382812503, 0.1054687500, 0.6523437503, 0.6679687503 },
|
||||
{ 0.6523437503, 0.7226562503, 0.3632812502, 0.2382812501, 0.6054687503, 0.1523437501, 0.1679687501 },
|
||||
{ 0.9023437504, 0.4726562502, 0.1132812501, 0.9882812505, 0.8554687504, 0.9023437504, 0.4179687502 },
|
||||
{ 0.4023437502, 0.9726562505, 0.6132812503, 0.4882812502, 0.3554687502, 0.4023437502, 0.9179687504 },
|
||||
{ 0.2773437501, 0.3476562502, 0.4882812502, 0.6132812503, 0.9804687505, 0.2773437501, 0.5429687503 },
|
||||
{ 0.7773437504, 0.8476562504, 0.9882812505, 0.1132812501, 0.4804687502, 0.7773437504, 0.0429687500 },
|
||||
{ 0.5273437502, 0.0976562500, 0.7382812503, 0.8632812504, 0.2304687501, 0.0273437500, 0.2929687501 },
|
||||
{ 0.0273437500, 0.5976562503, 0.2382812501, 0.3632812502, 0.7304687503, 0.5273437502, 0.7929687504 },
|
||||
{ 0.0195312500, 0.1992187501, 0.7304687503, 0.2460937501, 0.2539062501, 0.7070312503, 0.0664062500 },
|
||||
{ 0.5195312502, 0.6992187503, 0.2304687501, 0.7460937503, 0.7539062504, 0.2070312501, 0.5664062503 },
|
||||
{ 0.7695312504, 0.4492187502, 0.4804687502, 0.4960937502, 0.5039062502, 0.9570312504, 0.8164062504 },
|
||||
{ 0.2695312501, 0.9492187504, 0.9804687505, 0.9960937505, 0.0039062500, 0.4570312502, 0.3164062501 },
|
||||
{ 0.3945312502, 0.3242187502, 0.1054687500, 0.1210937501, 0.6289062503, 0.3320312502, 0.1914062501 },
|
||||
{ 0.8945312504, 0.8242187504, 0.6054687503, 0.6210937503, 0.1289062501, 0.8320312504, 0.6914062503 },
|
||||
{ 0.6445312503, 0.0742187500, 0.8554687504, 0.3710937502, 0.3789062502, 0.0820312500, 0.9414062504 },
|
||||
{ 0.1445312501, 0.5742187503, 0.3554687502, 0.8710937504, 0.8789062504, 0.5820312503, 0.4414062502 },
|
||||
{ 0.2070312501, 0.3867187502, 0.9179687504, 0.5585937503, 0.8164062504, 0.5195312502, 0.0039062500 },
|
||||
{ 0.7070312503, 0.8867187504, 0.4179687502, 0.0585937500, 0.3164062501, 0.0195312500, 0.5039062502 },
|
||||
{ 0.9570312504, 0.1367187501, 0.1679687501, 0.8085937504, 0.0664062500, 0.7695312504, 0.7539062504 },
|
||||
{ 0.4570312502, 0.6367187503, 0.6679687503, 0.3085937501, 0.5664062503, 0.2695312501, 0.2539062501 },
|
||||
{ 0.3320312502, 0.0117187500, 0.2929687501, 0.6835937503, 0.1914062501, 0.3945312502, 0.1289062501 },
|
||||
{ 0.8320312504, 0.5117187502, 0.7929687504, 0.1835937501, 0.6914062503, 0.8945312504, 0.6289062503 },
|
||||
{ 0.5820312503, 0.2617187501, 0.5429687503, 0.9335937504, 0.9414062504, 0.1445312501, 0.8789062504 },
|
||||
{ 0.0820312500, 0.7617187504, 0.0429687500, 0.4335937502, 0.4414062502, 0.6445312503, 0.3789062502 },
|
||||
{ 0.1132812501, 0.2929687501, 0.3867187502, 0.3398437502, 0.0351562500, 0.9257812504, 0.5976562503 },
|
||||
{ 0.6132812503, 0.7929687504, 0.8867187504, 0.8398437504, 0.5351562502, 0.4257812502, 0.0976562500 },
|
||||
{ 0.8632812504, 0.0429687500, 0.6367187503, 0.0898437500, 0.7851562504, 0.6757812503, 0.3476562502 },
|
||||
{ 0.3632812502, 0.5429687503, 0.1367187501, 0.5898437503, 0.2851562501, 0.1757812501, 0.8476562504 },
|
||||
{ 0.4882812502, 0.1679687501, 0.7617187504, 0.4648437502, 0.9101562504, 0.0507812500, 0.7226562503 },
|
||||
{ 0.9882812505, 0.6679687503, 0.2617187501, 0.9648437504, 0.4101562502, 0.5507812503, 0.2226562501 },
|
||||
{ 0.7382812503, 0.4179687502, 0.0117187500, 0.2148437501, 0.1601562501, 0.3007812501, 0.4726562502 },
|
||||
{ 0.2382812501, 0.9179687504, 0.5117187502, 0.7148437503, 0.6601562503, 0.8007812504, 0.9726562505 },
|
||||
{ 0.1757812501, 0.1054687500, 0.1992187501, 0.9023437504, 0.5976562503, 0.8632812504, 0.5351562502 },
|
||||
{ 0.6757812503, 0.6054687503, 0.6992187503, 0.4023437502, 0.0976562500, 0.3632812502, 0.0351562500 },
|
||||
{ 0.9257812504, 0.3554687502, 0.9492187504, 0.6523437503, 0.3476562502, 0.6132812503, 0.2851562501 },
|
||||
{ 0.4257812502, 0.8554687504, 0.4492187502, 0.1523437501, 0.8476562504, 0.1132812501, 0.7851562504 },
|
||||
{ 0.3007812501, 0.4804687502, 0.5742187503, 0.7773437504, 0.4726562502, 0.2382812501, 0.6601562503 },
|
||||
{ 0.8007812504, 0.9804687505, 0.0742187500, 0.2773437501, 0.9726562505, 0.7382812503, 0.1601562501 },
|
||||
{ 0.5507812503, 0.2304687501, 0.3242187502, 0.5273437502, 0.7226562503, 0.4882812502, 0.4101562502 },
|
||||
{ 0.0507812500, 0.7304687503, 0.8242187504, 0.0273437500, 0.2226562501, 0.9882812505, 0.9101562504 },
|
||||
{ 0.0351562500, 0.4648437502, 0.1523437501, 0.6679687503, 0.9570312504, 0.0664062500, 0.3320312502 },
|
||||
{ 0.5351562502, 0.9648437504, 0.6523437503, 0.1679687501, 0.4570312502, 0.5664062503, 0.8320312504 },
|
||||
{ 0.7851562504, 0.2148437501, 0.9023437504, 0.9179687504, 0.2070312501, 0.3164062501, 0.5820312503 },
|
||||
{ 0.2851562501, 0.7148437503, 0.4023437502, 0.4179687502, 0.7070312503, 0.8164062504, 0.0820312500 }
|
||||
};
|
||||
|
||||
// Spatial dimension: 16
|
||||
// N: 100
|
||||
// Vectors skipped: 128
|
||||
static const double sobol_16_100[100][16] =
|
||||
{
|
||||
{ 0.0117187500, 0.3320312502, 0.7851562504, 0.9414062504, 0.4648437502, 0.4179687502, 0.4648437502, 0.4882812502, 0.7304687503, 0.5742187503, 0.5664062503, 0.2460937501, 0.4882812502, 0.6367187503, 0.7617187504, 0.1835937501 },
|
||||
{ 0.5117187502, 0.8320312504, 0.2851562501, 0.4414062502, 0.9648437504, 0.9179687504, 0.9648437504, 0.9882812505, 0.2304687501, 0.0742187500, 0.0664062500, 0.7460937503, 0.9882812505, 0.1367187501, 0.2617187501, 0.6835937503 },
|
||||
{ 0.7617187504, 0.0820312500, 0.0351562500, 0.6914062503, 0.7148437503, 0.1679687501, 0.7148437503, 0.2382812501, 0.9804687505, 0.3242187502, 0.8164062504, 0.9960937505, 0.2382812501, 0.3867187502, 0.5117187502, 0.9335937504 },
|
||||
{ 0.2617187501, 0.5820312503, 0.5351562502, 0.1914062501, 0.2148437501, 0.6679687503, 0.2148437501, 0.7382812503, 0.4804687502, 0.8242187504, 0.3164062501, 0.4960937502, 0.7382812503, 0.8867187504, 0.0117187500, 0.4335937502 },
|
||||
{ 0.3867187502, 0.2070312501, 0.4101562502, 0.8164062504, 0.5898437503, 0.5429687503, 0.3398437502, 0.8632812504, 0.6054687503, 0.4492187502, 0.9414062504, 0.6210937503, 0.3632812502, 0.7617187504, 0.3867187502, 0.0585937500 },
|
||||
{ 0.8867187504, 0.7070312503, 0.9101562504, 0.3164062501, 0.0898437500, 0.0429687500, 0.8398437504, 0.3632812502, 0.1054687500, 0.9492187504, 0.4414062502, 0.1210937501, 0.8632812504, 0.2617187501, 0.8867187504, 0.5585937503 },
|
||||
{ 0.6367187503, 0.4570312502, 0.6601562503, 0.5664062503, 0.3398437502, 0.7929687504, 0.5898437503, 0.6132812503, 0.8554687504, 0.6992187503, 0.6914062503, 0.3710937502, 0.1132812501, 0.0117187500, 0.1367187501, 0.8085937504 },
|
||||
{ 0.1367187501, 0.9570312504, 0.1601562501, 0.0664062500, 0.8398437504, 0.2929687501, 0.0898437500, 0.1132812501, 0.3554687502, 0.1992187501, 0.1914062501, 0.8710937504, 0.6132812503, 0.5117187502, 0.6367187503, 0.3085937501 },
|
||||
{ 0.1992187501, 0.0195312500, 0.5976562503, 0.2539062501, 0.9023437504, 0.3554687502, 0.4023437502, 0.5507812503, 0.5429687503, 0.5117187502, 0.1289062501, 0.9335937504, 0.9257812504, 0.0742187500, 0.9492187504, 0.6210937503 },
|
||||
{ 0.6992187503, 0.5195312502, 0.0976562500, 0.7539062504, 0.4023437502, 0.8554687504, 0.9023437504, 0.0507812500, 0.0429687500, 0.0117187500, 0.6289062503, 0.4335937502, 0.4257812502, 0.5742187503, 0.4492187502, 0.1210937501 },
|
||||
{ 0.9492187504, 0.2695312501, 0.3476562502, 0.0039062500, 0.1523437501, 0.1054687500, 0.6523437503, 0.8007812504, 0.7929687504, 0.2617187501, 0.3789062502, 0.1835937501, 0.6757812503, 0.8242187504, 0.6992187503, 0.3710937502 },
|
||||
{ 0.4492187502, 0.7695312504, 0.8476562504, 0.5039062502, 0.6523437503, 0.6054687503, 0.1523437501, 0.3007812501, 0.2929687501, 0.7617187504, 0.8789062504, 0.6835937503, 0.1757812501, 0.3242187502, 0.1992187501, 0.8710937504 },
|
||||
{ 0.3242187502, 0.3945312502, 0.2226562501, 0.3789062502, 0.0273437500, 0.7304687503, 0.2773437501, 0.1757812501, 0.6679687503, 0.3867187502, 0.2539062501, 0.3085937501, 0.8007812504, 0.4492187502, 0.3242187502, 0.7460937503 },
|
||||
{ 0.8242187504, 0.8945312504, 0.7226562503, 0.8789062504, 0.5273437502, 0.2304687501, 0.7773437504, 0.6757812503, 0.1679687501, 0.8867187504, 0.7539062504, 0.8085937504, 0.3007812501, 0.9492187504, 0.8242187504, 0.2460937501 },
|
||||
{ 0.5742187503, 0.1445312501, 0.9726562505, 0.1289062501, 0.7773437504, 0.9804687505, 0.5273437502, 0.4257812502, 0.9179687504, 0.6367187503, 0.0039062500, 0.5585937503, 0.5507812503, 0.6992187503, 0.0742187500, 0.4960937502 },
|
||||
{ 0.0742187500, 0.6445312503, 0.4726562502, 0.6289062503, 0.2773437501, 0.4804687502, 0.0273437500, 0.9257812504, 0.4179687502, 0.1367187501, 0.5039062502, 0.0585937500, 0.0507812500, 0.1992187501, 0.5742187503, 0.9960937505 },
|
||||
{ 0.1054687500, 0.1757812501, 0.0664062500, 0.5976562503, 0.2460937501, 0.1992187501, 0.9960937505, 0.6445312503, 0.4492187502, 0.9804687505, 0.9726562505, 0.9023437504, 0.6445312503, 0.5429687503, 0.0429687500, 0.6523437503 },
|
||||
{ 0.6054687503, 0.6757812503, 0.5664062503, 0.0976562500, 0.7460937503, 0.6992187503, 0.4960937502, 0.1445312501, 0.9492187504, 0.4804687502, 0.4726562502, 0.4023437502, 0.1445312501, 0.0429687500, 0.5429687503, 0.1523437501 },
|
||||
{ 0.8554687504, 0.4257812502, 0.8164062504, 0.8476562504, 0.9960937505, 0.4492187502, 0.2460937501, 0.8945312504, 0.1992187501, 0.2304687501, 0.7226562503, 0.1523437501, 0.8945312504, 0.2929687501, 0.2929687501, 0.4023437502 },
|
||||
{ 0.3554687502, 0.9257812504, 0.3164062501, 0.3476562502, 0.4960937502, 0.9492187504, 0.7460937503, 0.3945312502, 0.6992187503, 0.7304687503, 0.2226562501, 0.6523437503, 0.3945312502, 0.7929687504, 0.7929687504, 0.9023437504 },
|
||||
{ 0.4804687502, 0.3007812501, 0.6914062503, 0.7226562503, 0.8710937504, 0.8242187504, 0.8710937504, 0.0195312500, 0.3242187502, 0.1054687500, 0.5976562503, 0.2773437501, 0.5195312502, 0.9179687504, 0.6679687503, 0.5273437502 },
|
||||
{ 0.9804687505, 0.8007812504, 0.1914062501, 0.2226562501, 0.3710937502, 0.3242187502, 0.3710937502, 0.5195312502, 0.8242187504, 0.6054687503, 0.0976562500, 0.7773437504, 0.0195312500, 0.4179687502, 0.1679687501, 0.0273437500 },
|
||||
{ 0.7304687503, 0.0507812500, 0.4414062502, 0.9726562505, 0.1210937501, 0.5742187503, 0.1210937501, 0.2695312501, 0.0742187500, 0.8554687504, 0.8476562504, 0.5273437502, 0.7695312504, 0.1679687501, 0.9179687504, 0.2773437501 },
|
||||
{ 0.2304687501, 0.5507812503, 0.9414062504, 0.4726562502, 0.6210937503, 0.0742187500, 0.6210937503, 0.7695312504, 0.5742187503, 0.3554687502, 0.3476562502, 0.0273437500, 0.2695312501, 0.6679687503, 0.4179687502, 0.7773437504 },
|
||||
{ 0.1679687501, 0.4882812502, 0.2539062501, 0.1601562501, 0.6835937503, 0.0117187500, 0.9335937504, 0.3320312502, 0.2617187501, 0.9179687504, 0.2851562501, 0.2148437501, 0.2070312501, 0.2304687501, 0.2304687501, 0.0898437500 },
|
||||
{ 0.6679687503, 0.9882812505, 0.7539062504, 0.6601562503, 0.1835937501, 0.5117187502, 0.4335937502, 0.8320312504, 0.7617187504, 0.4179687502, 0.7851562504, 0.7148437503, 0.7070312503, 0.7304687503, 0.7304687503, 0.5898437503 },
|
||||
{ 0.9179687504, 0.2382812501, 0.5039062502, 0.4101562502, 0.4335937502, 0.2617187501, 0.1835937501, 0.0820312500, 0.0117187500, 0.1679687501, 0.0351562500, 0.9648437504, 0.4570312502, 0.9804687505, 0.4804687502, 0.8398437504 },
|
||||
{ 0.4179687502, 0.7382812503, 0.0039062500, 0.9101562504, 0.9335937504, 0.7617187504, 0.6835937503, 0.5820312503, 0.5117187502, 0.6679687503, 0.5351562502, 0.4648437502, 0.9570312504, 0.4804687502, 0.9804687505, 0.3398437502 },
|
||||
{ 0.2929687501, 0.1132812501, 0.8789062504, 0.0351562500, 0.3085937501, 0.8867187504, 0.8085937504, 0.9570312504, 0.3867187502, 0.0429687500, 0.1601562501, 0.5898437503, 0.0820312500, 0.3554687502, 0.6054687503, 0.2148437501 },
|
||||
{ 0.7929687504, 0.6132812503, 0.3789062502, 0.5351562502, 0.8085937504, 0.3867187502, 0.3085937501, 0.4570312502, 0.8867187504, 0.5429687503, 0.6601562503, 0.0898437500, 0.5820312503, 0.8554687504, 0.1054687500, 0.7148437503 },
|
||||
{ 0.5429687503, 0.3632812502, 0.1289062501, 0.2851562501, 0.5585937503, 0.6367187503, 0.0585937500, 0.7070312503, 0.1367187501, 0.7929687504, 0.4101562502, 0.3398437502, 0.3320312502, 0.6054687503, 0.8554687504, 0.9648437504 },
|
||||
{ 0.0429687500, 0.8632812504, 0.6289062503, 0.7851562504, 0.0585937500, 0.1367187501, 0.5585937503, 0.2070312501, 0.6367187503, 0.2929687501, 0.9101562504, 0.8398437504, 0.8320312504, 0.1054687500, 0.3554687502, 0.4648437502 },
|
||||
{ 0.0585937500, 0.0664062500, 0.3320312502, 0.3945312502, 0.7617187504, 0.8085937504, 0.1992187501, 0.8164062504, 0.1835937501, 0.6210937503, 0.6445312503, 0.1054687500, 0.1289062501, 0.5585937503, 0.8710937504, 0.4179687502 },
|
||||
{ 0.5585937503, 0.5664062503, 0.8320312504, 0.8945312504, 0.2617187501, 0.3085937501, 0.6992187503, 0.3164062501, 0.6835937503, 0.1210937501, 0.1445312501, 0.6054687503, 0.6289062503, 0.0585937500, 0.3710937502, 0.9179687504 },
|
||||
{ 0.8085937504, 0.3164062501, 0.5820312503, 0.1445312501, 0.0117187500, 0.5585937503, 0.9492187504, 0.5664062503, 0.4335937502, 0.3710937502, 0.8945312504, 0.8554687504, 0.3789062502, 0.3085937501, 0.6210937503, 0.6679687503 },
|
||||
{ 0.3085937501, 0.8164062504, 0.0820312500, 0.6445312503, 0.5117187502, 0.0585937500, 0.4492187502, 0.0664062500, 0.9335937504, 0.8710937504, 0.3945312502, 0.3554687502, 0.8789062504, 0.8085937504, 0.1210937501, 0.1679687501 },
|
||||
{ 0.4335937502, 0.4414062502, 0.9570312504, 0.2695312501, 0.1367187501, 0.1835937501, 0.0742187500, 0.4414062502, 0.0585937500, 0.4960937502, 0.7695312504, 0.7304687503, 0.0039062500, 0.9335937504, 0.4960937502, 0.2929687501 },
|
||||
{ 0.9335937504, 0.9414062504, 0.4570312502, 0.7695312504, 0.6367187503, 0.6835937503, 0.5742187503, 0.9414062504, 0.5585937503, 0.9960937505, 0.2695312501, 0.2304687501, 0.5039062502, 0.4335937502, 0.9960937505, 0.7929687504 },
|
||||
{ 0.6835937503, 0.1914062501, 0.2070312501, 0.0195312500, 0.8867187504, 0.4335937502, 0.8242187504, 0.1914062501, 0.3085937501, 0.7460937503, 0.5195312502, 0.4804687502, 0.2539062501, 0.1835937501, 0.2460937501, 0.5429687503 },
|
||||
{ 0.1835937501, 0.6914062503, 0.7070312503, 0.5195312502, 0.3867187502, 0.9335937504, 0.3242187502, 0.6914062503, 0.8085937504, 0.2460937501, 0.0195312500, 0.9804687505, 0.7539062504, 0.6835937503, 0.7460937503, 0.0429687500 },
|
||||
{ 0.2460937501, 0.2539062501, 0.0195312500, 0.8320312504, 0.3242187502, 0.9960937505, 0.1367187501, 0.1289062501, 0.1210937501, 0.5585937503, 0.0820312500, 0.7929687504, 0.6914062503, 0.2460937501, 0.9335937504, 0.8554687504 },
|
||||
{ 0.7460937503, 0.7539062504, 0.5195312502, 0.3320312502, 0.8242187504, 0.4960937502, 0.6367187503, 0.6289062503, 0.6210937503, 0.0585937500, 0.5820312503, 0.2929687501, 0.1914062501, 0.7460937503, 0.4335937502, 0.3554687502 },
|
||||
{ 0.9960937505, 0.0039062500, 0.7695312504, 0.5820312503, 0.5742187503, 0.7460937503, 0.8867187504, 0.3789062502, 0.3710937502, 0.3085937501, 0.3320312502, 0.0429687500, 0.9414062504, 0.9960937505, 0.6835937503, 0.1054687500 },
|
||||
{ 0.4960937502, 0.5039062502, 0.2695312501, 0.0820312500, 0.0742187500, 0.2460937501, 0.3867187502, 0.8789062504, 0.8710937504, 0.8085937504, 0.8320312504, 0.5429687503, 0.4414062502, 0.4960937502, 0.1835937501, 0.6054687503 },
|
||||
{ 0.3710937502, 0.1289062501, 0.6445312503, 0.9570312504, 0.6992187503, 0.1210937501, 0.0117187500, 0.5039062502, 0.2460937501, 0.4335937502, 0.4570312502, 0.4179687502, 0.5664062503, 0.3710937502, 0.3085937501, 0.9804687505 },
|
||||
{ 0.8710937504, 0.6289062503, 0.1445312501, 0.4570312502, 0.1992187501, 0.6210937503, 0.5117187502, 0.0039062500, 0.7460937503, 0.9335937504, 0.9570312504, 0.9179687504, 0.0664062500, 0.8710937504, 0.8085937504, 0.4804687502 },
|
||||
{ 0.6210937503, 0.3789062502, 0.3945312502, 0.7070312503, 0.4492187502, 0.3710937502, 0.7617187504, 0.7539062504, 0.4960937502, 0.6835937503, 0.2070312501, 0.6679687503, 0.8164062504, 0.6210937503, 0.0585937500, 0.2304687501 },
|
||||
{ 0.1210937501, 0.8789062504, 0.8945312504, 0.2070312501, 0.9492187504, 0.8710937504, 0.2617187501, 0.2539062501, 0.9960937505, 0.1835937501, 0.7070312503, 0.1679687501, 0.3164062501, 0.1210937501, 0.5585937503, 0.7304687503 },
|
||||
{ 0.0898437500, 0.4101562502, 0.5507812503, 0.0507812500, 0.5429687503, 0.5898437503, 0.7304687503, 0.0351562500, 0.9023437504, 0.9648437504, 0.8007812504, 0.7617187504, 0.9726562505, 0.6523437503, 0.0898437500, 0.8867187504 },
|
||||
{ 0.5898437503, 0.9101562504, 0.0507812500, 0.5507812503, 0.0429687500, 0.0898437500, 0.2304687501, 0.5351562502, 0.4023437502, 0.4648437502, 0.3007812501, 0.2617187501, 0.4726562502, 0.1523437501, 0.5898437503, 0.3867187502 },
|
||||
{ 0.8398437504, 0.1601562501, 0.3007812501, 0.3007812501, 0.2929687501, 0.8398437504, 0.4804687502, 0.2851562501, 0.6523437503, 0.2148437501, 0.5507812503, 0.0117187500, 0.7226562503, 0.4023437502, 0.3398437502, 0.1367187501 },
|
||||
{ 0.3398437502, 0.6601562503, 0.8007812504, 0.8007812504, 0.7929687504, 0.3398437502, 0.9804687505, 0.7851562504, 0.1523437501, 0.7148437503, 0.0507812500, 0.5117187502, 0.2226562501, 0.9023437504, 0.8398437504, 0.6367187503 },
|
||||
{ 0.4648437502, 0.0351562500, 0.1757812501, 0.1757812501, 0.4179687502, 0.4648437502, 0.6054687503, 0.6601562503, 0.7773437504, 0.0898437500, 0.6757812503, 0.3867187502, 0.8476562504, 0.7773437504, 0.7148437503, 0.7617187504 },
|
||||
{ 0.9648437504, 0.5351562502, 0.6757812503, 0.6757812503, 0.9179687504, 0.9648437504, 0.1054687500, 0.1601562501, 0.2773437501, 0.5898437503, 0.1757812501, 0.8867187504, 0.3476562502, 0.2773437501, 0.2148437501, 0.2617187501 },
|
||||
{ 0.7148437503, 0.2851562501, 0.9257812504, 0.4257812502, 0.6679687503, 0.2148437501, 0.3554687502, 0.9101562504, 0.5273437502, 0.8398437504, 0.9257812504, 0.6367187503, 0.5976562503, 0.0273437500, 0.9648437504, 0.0117187500 },
|
||||
{ 0.2148437501, 0.7851562504, 0.4257812502, 0.9257812504, 0.1679687501, 0.7148437503, 0.8554687504, 0.4101562502, 0.0273437500, 0.3398437502, 0.4257812502, 0.1367187501, 0.0976562500, 0.5273437502, 0.4648437502, 0.5117187502 },
|
||||
{ 0.1523437501, 0.2226562501, 0.8632812504, 0.7382812503, 0.1054687500, 0.6523437503, 0.6679687503, 0.9726562505, 0.8398437504, 0.9023437504, 0.4882812502, 0.0742187500, 0.4101562502, 0.0898437500, 0.1523437501, 0.3242187502 },
|
||||
{ 0.6523437503, 0.7226562503, 0.3632812502, 0.2382812501, 0.6054687503, 0.1523437501, 0.1679687501, 0.4726562502, 0.3398437502, 0.4023437502, 0.9882812505, 0.5742187503, 0.9101562504, 0.5898437503, 0.6523437503, 0.8242187504 },
|
||||
{ 0.9023437504, 0.4726562502, 0.1132812501, 0.9882812505, 0.8554687504, 0.9023437504, 0.4179687502, 0.7226562503, 0.5898437503, 0.1523437501, 0.2382812501, 0.8242187504, 0.1601562501, 0.8398437504, 0.4023437502, 0.5742187503 },
|
||||
{ 0.4023437502, 0.9726562505, 0.6132812503, 0.4882812502, 0.3554687502, 0.4023437502, 0.9179687504, 0.2226562501, 0.0898437500, 0.6523437503, 0.7382812503, 0.3242187502, 0.6601562503, 0.3398437502, 0.9023437504, 0.0742187500 },
|
||||
{ 0.2773437501, 0.3476562502, 0.4882812502, 0.6132812503, 0.9804687505, 0.2773437501, 0.5429687503, 0.3476562502, 0.9648437504, 0.0273437500, 0.1132812501, 0.6992187503, 0.2851562501, 0.4648437502, 0.5273437502, 0.4492187502 },
|
||||
{ 0.7773437504, 0.8476562504, 0.9882812505, 0.1132812501, 0.4804687502, 0.7773437504, 0.0429687500, 0.8476562504, 0.4648437502, 0.5273437502, 0.6132812503, 0.1992187501, 0.7851562504, 0.9648437504, 0.0273437500, 0.9492187504 },
|
||||
{ 0.5273437502, 0.0976562500, 0.7382812503, 0.8632812504, 0.2304687501, 0.0273437500, 0.2929687501, 0.0976562500, 0.7148437503, 0.7773437504, 0.3632812502, 0.4492187502, 0.0351562500, 0.7148437503, 0.7773437504, 0.6992187503 },
|
||||
{ 0.0273437500, 0.5976562503, 0.2382812501, 0.3632812502, 0.7304687503, 0.5273437502, 0.7929687504, 0.5976562503, 0.2148437501, 0.2773437501, 0.8632812504, 0.9492187504, 0.5351562502, 0.2148437501, 0.2773437501, 0.1992187501 },
|
||||
{ 0.0195312500, 0.1992187501, 0.7304687503, 0.2460937501, 0.2539062501, 0.7070312503, 0.0664062500, 0.8085937504, 0.5195312502, 0.8007812504, 0.2460937501, 0.6757812503, 0.9023437504, 0.9570312504, 0.2539062501, 0.4726562502 },
|
||||
{ 0.5195312502, 0.6992187503, 0.2304687501, 0.7460937503, 0.7539062504, 0.2070312501, 0.5664062503, 0.3085937501, 0.0195312500, 0.3007812501, 0.7460937503, 0.1757812501, 0.4023437502, 0.4570312502, 0.7539062504, 0.9726562505 },
|
||||
{ 0.7695312504, 0.4492187502, 0.4804687502, 0.4960937502, 0.5039062502, 0.9570312504, 0.8164062504, 0.5585937503, 0.7695312504, 0.0507812500, 0.4960937502, 0.4257812502, 0.6523437503, 0.2070312501, 0.0039062500, 0.7226562503 },
|
||||
{ 0.2695312501, 0.9492187504, 0.9804687505, 0.9960937505, 0.0039062500, 0.4570312502, 0.3164062501, 0.0585937500, 0.2695312501, 0.5507812503, 0.9960937505, 0.9257812504, 0.1523437501, 0.7070312503, 0.5039062502, 0.2226562501 },
|
||||
{ 0.3945312502, 0.3242187502, 0.1054687500, 0.1210937501, 0.6289062503, 0.3320312502, 0.1914062501, 0.4335937502, 0.6445312503, 0.1757812501, 0.3710937502, 0.0507812500, 0.7773437504, 0.5820312503, 0.8789062504, 0.3476562502 },
|
||||
{ 0.8945312504, 0.8242187504, 0.6054687503, 0.6210937503, 0.1289062501, 0.8320312504, 0.6914062503, 0.9335937504, 0.1445312501, 0.6757812503, 0.8710937504, 0.5507812503, 0.2773437501, 0.0820312500, 0.3789062502, 0.8476562504 },
|
||||
{ 0.6445312503, 0.0742187500, 0.8554687504, 0.3710937502, 0.3789062502, 0.0820312500, 0.9414062504, 0.1835937501, 0.8945312504, 0.9257812504, 0.1210937501, 0.8007812504, 0.5273437502, 0.3320312502, 0.6289062503, 0.5976562503 },
|
||||
{ 0.1445312501, 0.5742187503, 0.3554687502, 0.8710937504, 0.8789062504, 0.5820312503, 0.4414062502, 0.6835937503, 0.3945312502, 0.4257812502, 0.6210937503, 0.3007812501, 0.0273437500, 0.8320312504, 0.1289062501, 0.0976562500 },
|
||||
{ 0.2070312501, 0.3867187502, 0.9179687504, 0.5585937503, 0.8164062504, 0.5195312502, 0.0039062500, 0.2460937501, 0.7070312503, 0.8632812504, 0.5585937503, 0.4882812502, 0.4648437502, 0.2695312501, 0.4414062502, 0.7851562504 },
|
||||
{ 0.7070312503, 0.8867187504, 0.4179687502, 0.0585937500, 0.3164062501, 0.0195312500, 0.5039062502, 0.7460937503, 0.2070312501, 0.3632812502, 0.0585937500, 0.9882812505, 0.9648437504, 0.7695312504, 0.9414062504, 0.2851562501 },
|
||||
{ 0.9570312504, 0.1367187501, 0.1679687501, 0.8085937504, 0.0664062500, 0.7695312504, 0.7539062504, 0.4960937502, 0.9570312504, 0.1132812501, 0.8085937504, 0.7382812503, 0.2148437501, 0.5195312502, 0.1914062501, 0.0351562500 },
|
||||
{ 0.4570312502, 0.6367187503, 0.6679687503, 0.3085937501, 0.5664062503, 0.2695312501, 0.2539062501, 0.9960937505, 0.4570312502, 0.6132812503, 0.3085937501, 0.2382812501, 0.7148437503, 0.0195312500, 0.6914062503, 0.5351562502 },
|
||||
{ 0.3320312502, 0.0117187500, 0.2929687501, 0.6835937503, 0.1914062501, 0.3945312502, 0.1289062501, 0.6210937503, 0.5820312503, 0.2382812501, 0.9335937504, 0.8632812504, 0.3398437502, 0.1445312501, 0.8164062504, 0.9101562504 },
|
||||
{ 0.8320312504, 0.5117187502, 0.7929687504, 0.1835937501, 0.6914062503, 0.8945312504, 0.6289062503, 0.1210937501, 0.0820312500, 0.7382812503, 0.4335937502, 0.3632812502, 0.8398437504, 0.6445312503, 0.3164062501, 0.4101562502 },
|
||||
{ 0.5820312503, 0.2617187501, 0.5429687503, 0.9335937504, 0.9414062504, 0.1445312501, 0.8789062504, 0.8710937504, 0.8320312504, 0.9882812505, 0.6835937503, 0.1132812501, 0.0898437500, 0.8945312504, 0.5664062503, 0.1601562501 },
|
||||
{ 0.0820312500, 0.7617187504, 0.0429687500, 0.4335937502, 0.4414062502, 0.6445312503, 0.3789062502, 0.3710937502, 0.3320312502, 0.4882812502, 0.1835937501, 0.6132812503, 0.5898437503, 0.3945312502, 0.0664062500, 0.6601562503 },
|
||||
{ 0.1132812501, 0.2929687501, 0.3867187502, 0.3398437502, 0.0351562500, 0.9257812504, 0.5976562503, 0.0898437500, 0.3007812501, 0.6445312503, 0.3398437502, 0.4570312502, 0.2460937501, 0.8632812504, 0.5351562502, 0.9414062504 },
|
||||
{ 0.6132812503, 0.7929687504, 0.8867187504, 0.8398437504, 0.5351562502, 0.4257812502, 0.0976562500, 0.5898437503, 0.8007812504, 0.1445312501, 0.8398437504, 0.9570312504, 0.7460937503, 0.3632812502, 0.0351562500, 0.4414062502 },
|
||||
{ 0.8632812504, 0.0429687500, 0.6367187503, 0.0898437500, 0.7851562504, 0.6757812503, 0.3476562502, 0.3398437502, 0.0507812500, 0.3945312502, 0.0898437500, 0.7070312503, 0.4960937502, 0.1132812501, 0.7851562504, 0.1914062501 },
|
||||
{ 0.3632812502, 0.5429687503, 0.1367187501, 0.5898437503, 0.2851562501, 0.1757812501, 0.8476562504, 0.8398437504, 0.5507812503, 0.8945312504, 0.5898437503, 0.2070312501, 0.9960937505, 0.6132812503, 0.2851562501, 0.6914062503 },
|
||||
{ 0.4882812502, 0.1679687501, 0.7617187504, 0.4648437502, 0.9101562504, 0.0507812500, 0.7226562503, 0.7148437503, 0.4257812502, 0.2695312501, 0.2148437501, 0.8320312504, 0.1210937501, 0.7382812503, 0.1601562501, 0.8164062504 },
|
||||
{ 0.9882812505, 0.6679687503, 0.2617187501, 0.9648437504, 0.4101562502, 0.5507812503, 0.2226562501, 0.2148437501, 0.9257812504, 0.7695312504, 0.7148437503, 0.3320312502, 0.6210937503, 0.2382812501, 0.6601562503, 0.3164062501 },
|
||||
{ 0.7382812503, 0.4179687502, 0.0117187500, 0.2148437501, 0.1601562501, 0.3007812501, 0.4726562502, 0.9648437504, 0.1757812501, 0.5195312502, 0.4648437502, 0.0820312500, 0.3710937502, 0.4882812502, 0.4101562502, 0.0664062500 },
|
||||
{ 0.2382812501, 0.9179687504, 0.5117187502, 0.7148437503, 0.6601562503, 0.8007812504, 0.9726562505, 0.4648437502, 0.6757812503, 0.0195312500, 0.9648437504, 0.5820312503, 0.8710937504, 0.9882812505, 0.9101562504, 0.5664062503 },
|
||||
{ 0.1757812501, 0.1054687500, 0.1992187501, 0.9023437504, 0.5976562503, 0.8632812504, 0.5351562502, 0.9023437504, 0.4882812502, 0.7070312503, 0.9023437504, 0.6445312503, 0.6835937503, 0.4257812502, 0.7226562503, 0.2539062501 },
|
||||
{ 0.6757812503, 0.6054687503, 0.6992187503, 0.4023437502, 0.0976562500, 0.3632812502, 0.0351562500, 0.4023437502, 0.9882812505, 0.2070312501, 0.4023437502, 0.1445312501, 0.1835937501, 0.9257812504, 0.2226562501, 0.7539062504 },
|
||||
{ 0.9257812504, 0.3554687502, 0.9492187504, 0.6523437503, 0.3476562502, 0.6132812503, 0.2851562501, 0.6523437503, 0.2382812501, 0.4570312502, 0.6523437503, 0.3945312502, 0.9335937504, 0.6757812503, 0.9726562505, 0.5039062502 },
|
||||
{ 0.4257812502, 0.8554687504, 0.4492187502, 0.1523437501, 0.8476562504, 0.1132812501, 0.7851562504, 0.1523437501, 0.7382812503, 0.9570312504, 0.1523437501, 0.8945312504, 0.4335937502, 0.1757812501, 0.4726562502, 0.0039062500 },
|
||||
{ 0.3007812501, 0.4804687502, 0.5742187503, 0.7773437504, 0.4726562502, 0.2382812501, 0.6601562503, 0.2773437501, 0.3632812502, 0.3320312502, 0.5273437502, 0.0195312500, 0.5585937503, 0.0507812500, 0.0976562500, 0.3789062502 },
|
||||
{ 0.8007812504, 0.9804687505, 0.0742187500, 0.2773437501, 0.9726562505, 0.7382812503, 0.1601562501, 0.7773437504, 0.8632812504, 0.8320312504, 0.0273437500, 0.5195312502, 0.0585937500, 0.5507812503, 0.5976562503, 0.8789062504 },
|
||||
{ 0.5507812503, 0.2304687501, 0.3242187502, 0.5273437502, 0.7226562503, 0.4882812502, 0.4101562502, 0.0273437500, 0.1132812501, 0.5820312503, 0.7773437504, 0.7695312504, 0.8085937504, 0.8007812504, 0.3476562502, 0.6289062503 },
|
||||
{ 0.0507812500, 0.7304687503, 0.8242187504, 0.0273437500, 0.2226562501, 0.9882812505, 0.9101562504, 0.5273437502, 0.6132812503, 0.0820312500, 0.2773437501, 0.2695312501, 0.3085937501, 0.3007812501, 0.8476562504, 0.1289062501 },
|
||||
{ 0.0351562500, 0.4648437502, 0.1523437501, 0.6679687503, 0.9570312504, 0.0664062500, 0.3320312502, 0.3867187502, 0.0664062500, 0.7539062504, 0.0429687500, 0.5351562502, 0.7304687503, 0.8476562504, 0.3632812502, 0.2382812501 },
|
||||
{ 0.5351562502, 0.9648437504, 0.6523437503, 0.1679687501, 0.4570312502, 0.5664062503, 0.8320312504, 0.8867187504, 0.5664062503, 0.2539062501, 0.5429687503, 0.0351562500, 0.2304687501, 0.3476562502, 0.8632812504, 0.7382812503 },
|
||||
{ 0.7851562504, 0.2148437501, 0.9023437504, 0.9179687504, 0.2070312501, 0.3164062501, 0.5820312503, 0.1367187501, 0.3164062501, 0.0039062500, 0.2929687501, 0.2851562501, 0.9804687505, 0.0976562500, 0.1132812501, 0.9882812505 },
|
||||
{ 0.2851562501, 0.7148437503, 0.4023437502, 0.4179687502, 0.7070312503, 0.8164062504, 0.0820312500, 0.6367187503, 0.8164062504, 0.5039062502, 0.7929687504, 0.7851562504, 0.4804687502, 0.5976562503, 0.6132812503, 0.4882812502 }
|
||||
};
|
||||
|
||||
|
||||
QRNG_VALIDATION_TEST_FUNCTIONS(sobol)
|
||||
|
||||
BOOST_AUTO_TEST_CASE( validate_sobol )
|
||||
{
|
||||
test_sobol_values(sobol_02_100, 0);
|
||||
test_sobol_values(sobol_07_100, 128);
|
||||
test_sobol_values(sobol_16_100, 128);
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_CASE( validate_sobol_seed )
|
||||
{
|
||||
test_sobol_seed(sobol_02_100, 0);
|
||||
test_sobol_seed(sobol_07_100, 128);
|
||||
test_sobol_seed(sobol_16_100, 128);
|
||||
}
|
||||
|
||||
BOOST_AUTO_TEST_CASE( validate_sobol_discard )
|
||||
{
|
||||
test_sobol_discard(sobol_02_100, 0);
|
||||
test_sobol_discard(sobol_07_100, 128);
|
||||
test_sobol_discard(sobol_16_100, 128);
|
||||
}
|
||||
Reference in New Issue
Block a user