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Diffstat (limited to 'boost/random/linear_congruential.hpp')
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diff --git a/boost/random/linear_congruential.hpp b/boost/random/linear_congruential.hpp new file mode 100644 index 0000000000..5f8fe7a078 --- /dev/null +++ b/boost/random/linear_congruential.hpp @@ -0,0 +1,466 @@ +/* boost random/linear_congruential.hpp header file + * + * Copyright Jens Maurer 2000-2001 + * 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) + * + * See http://www.boost.org for most recent version including documentation. + * + * $Id: linear_congruential.hpp 71018 2011-04-05 21:27:52Z steven_watanabe $ + * + * Revision history + * 2001-02-18 moved to individual header files + */ + +#ifndef BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP +#define BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP + +#include <iostream> +#include <stdexcept> +#include <boost/assert.hpp> +#include <boost/config.hpp> +#include <boost/cstdint.hpp> +#include <boost/limits.hpp> +#include <boost/static_assert.hpp> +#include <boost/integer/static_log2.hpp> +#include <boost/mpl/if.hpp> +#include <boost/type_traits/is_arithmetic.hpp> +#include <boost/random/detail/config.hpp> +#include <boost/random/detail/const_mod.hpp> +#include <boost/random/detail/seed.hpp> +#include <boost/random/detail/seed_impl.hpp> +#include <boost/detail/workaround.hpp> + +#include <boost/random/detail/disable_warnings.hpp> + +namespace boost { +namespace random { + +/** + * Instantiations of class template linear_congruential_engine model a + * \pseudo_random_number_generator. Linear congruential pseudo-random + * number generators are described in: + * + * @blockquote + * "Mathematical methods in large-scale computing units", D. H. Lehmer, + * Proc. 2nd Symposium on Large-Scale Digital Calculating Machines, + * Harvard University Press, 1951, pp. 141-146 + * @endblockquote + * + * Let x(n) denote the sequence of numbers returned by some pseudo-random + * number generator. Then for the linear congruential generator, + * x(n+1) := (a * x(n) + c) mod m. Parameters for the generator are + * x(0), a, c, m. The template parameter IntType shall denote an integral + * type. It must be large enough to hold values a, c, and m. The template + * parameters a and c must be smaller than m. + * + * Note: The quality of the generator crucially depends on the choice of + * the parameters. User code should use one of the sensibly parameterized + * generators such as minstd_rand instead. + */ +template<class IntType, IntType a, IntType c, IntType m> +class linear_congruential_engine +{ +public: + typedef IntType result_type; + + // Required for old Boost.Random concept + BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); + + BOOST_STATIC_CONSTANT(IntType, multiplier = a); + BOOST_STATIC_CONSTANT(IntType, increment = c); + BOOST_STATIC_CONSTANT(IntType, modulus = m); + BOOST_STATIC_CONSTANT(IntType, default_seed = 1); + + BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer); + BOOST_STATIC_ASSERT(m == 0 || a < m); + BOOST_STATIC_ASSERT(m == 0 || c < m); + + /** + * Constructs a @c linear_congruential_engine, using the default seed + */ + linear_congruential_engine() { seed(); } + + /** + * Constructs a @c linear_congruential_engine, seeding it with @c x0. + */ + BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(linear_congruential_engine, + IntType, x0) + { seed(x0); } + + /** + * Constructs a @c linear_congruential_engine, seeding it with values + * produced by a call to @c seq.generate(). + */ + BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(linear_congruential_engine, + SeedSeq, seq) + { seed(seq); } + + /** + * Constructs a @c linear_congruential_engine and seeds it + * with values taken from the itrator range [first, last) + * and adjusts first to point to the element after the last one + * used. If there are not enough elements, throws @c std::invalid_argument. + * + * first and last must be input iterators. + */ + template<class It> + linear_congruential_engine(It& first, It last) + { + seed(first, last); + } + + // compiler-generated copy constructor and assignment operator are fine + + /** + * Calls seed(default_seed) + */ + void seed() { seed(default_seed); } + + /** + * If c mod m is zero and x0 mod m is zero, changes the current value of + * the generator to 1. Otherwise, changes it to x0 mod m. If c is zero, + * distinct seeds in the range [1,m) will leave the generator in distinct + * states. If c is not zero, the range is [0,m). + */ + BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(linear_congruential_engine, IntType, x0) + { + // wrap _x if it doesn't fit in the destination + if(modulus == 0) { + _x = x0; + } else { + _x = x0 % modulus; + } + // handle negative seeds + if(_x <= 0 && _x != 0) { + _x += modulus; + } + // adjust to the correct range + if(increment == 0 && _x == 0) { + _x = 1; + } + BOOST_ASSERT(_x >= (min)()); + BOOST_ASSERT(_x <= (max)()); + } + + /** + * Seeds a @c linear_congruential_engine using values from a SeedSeq. + */ + BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(linear_congruential_engine, SeedSeq, seq) + { seed(detail::seed_one_int<IntType, m>(seq)); } + + /** + * seeds a @c linear_congruential_engine with values taken + * from the itrator range [first, last) and adjusts @c first to + * point to the element after the last one used. If there are + * not enough elements, throws @c std::invalid_argument. + * + * @c first and @c last must be input iterators. + */ + template<class It> + void seed(It& first, It last) + { seed(detail::get_one_int<IntType, m>(first, last)); } + + /** + * Returns the smallest value that the @c linear_congruential_engine + * can produce. + */ + static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () + { return c == 0 ? 1 : 0; } + /** + * Returns the largest value that the @c linear_congruential_engine + * can produce. + */ + static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () + { return modulus-1; } + + /** Returns the next value of the @c linear_congruential_engine. */ + IntType operator()() + { + _x = const_mod<IntType, m>::mult_add(a, _x, c); + return _x; + } + + /** Fills a range with random values */ + template<class Iter> + void generate(Iter first, Iter last) + { detail::generate_from_int(*this, first, last); } + + /** Advances the state of the generator by @c z. */ + void discard(boost::uintmax_t z) + { + typedef const_mod<IntType, m> mod_type; + IntType b_inv = mod_type::invert(a-1); + IntType b_gcd = mod_type::mult(a-1, b_inv); + if(b_gcd == 1) { + IntType a_z = mod_type::pow(a, z); + _x = mod_type::mult_add(a_z, _x, + mod_type::mult(mod_type::mult(c, b_inv), a_z - 1)); + } else { + // compute (a^z - 1)*c % (b_gcd * m) / (b / b_gcd) * inv(b / b_gcd) + // we're storing the intermediate result / b_gcd + IntType a_zm1_over_gcd = 0; + IntType a_km1_over_gcd = (a - 1) / b_gcd; + boost::uintmax_t exponent = z; + while(exponent != 0) { + if(exponent % 2 == 1) { + a_zm1_over_gcd = + mod_type::mult_add( + b_gcd, + mod_type::mult(a_zm1_over_gcd, a_km1_over_gcd), + mod_type::add(a_zm1_over_gcd, a_km1_over_gcd)); + } + a_km1_over_gcd = mod_type::mult_add( + b_gcd, + mod_type::mult(a_km1_over_gcd, a_km1_over_gcd), + mod_type::add(a_km1_over_gcd, a_km1_over_gcd)); + exponent /= 2; + } + + IntType a_z = mod_type::mult_add(b_gcd, a_zm1_over_gcd, 1); + IntType num = mod_type::mult(c, a_zm1_over_gcd); + b_inv = mod_type::invert((a-1)/b_gcd); + _x = mod_type::mult_add(a_z, _x, mod_type::mult(b_inv, num)); + } + } + + friend bool operator==(const linear_congruential_engine& x, + const linear_congruential_engine& y) + { return x._x == y._x; } + friend bool operator!=(const linear_congruential_engine& x, + const linear_congruential_engine& y) + { return !(x == y); } + +#if !defined(BOOST_RANDOM_NO_STREAM_OPERATORS) + /** Writes a @c linear_congruential_engine to a @c std::ostream. */ + template<class CharT, class Traits> + friend std::basic_ostream<CharT,Traits>& + operator<<(std::basic_ostream<CharT,Traits>& os, + const linear_congruential_engine& lcg) + { + return os << lcg._x; + } + + /** Reads a @c linear_congruential_engine from a @c std::istream. */ + template<class CharT, class Traits> + friend std::basic_istream<CharT,Traits>& + operator>>(std::basic_istream<CharT,Traits>& is, + linear_congruential_engine& lcg) + { + lcg.read(is); + return is; + } +#endif + +private: + + /// \cond show_private + + template<class CharT, class Traits> + void read(std::basic_istream<CharT, Traits>& is) { + IntType x; + if(is >> x) { + if(x >= (min)() && x <= (max)()) { + _x = x; + } else { + is.setstate(std::ios_base::failbit); + } + } + } + + /// \endcond + + IntType _x; +}; + +#ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION +// A definition is required even for integral static constants +template<class IntType, IntType a, IntType c, IntType m> +const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range; +template<class IntType, IntType a, IntType c, IntType m> +const IntType linear_congruential_engine<IntType,a,c,m>::multiplier; +template<class IntType, IntType a, IntType c, IntType m> +const IntType linear_congruential_engine<IntType,a,c,m>::increment; +template<class IntType, IntType a, IntType c, IntType m> +const IntType linear_congruential_engine<IntType,a,c,m>::modulus; +template<class IntType, IntType a, IntType c, IntType m> +const IntType linear_congruential_engine<IntType,a,c,m>::default_seed; +#endif + +/// \cond show_deprecated + +// provided for backwards compatibility +template<class IntType, IntType a, IntType c, IntType m, IntType val = 0> +class linear_congruential : public linear_congruential_engine<IntType, a, c, m> +{ + typedef linear_congruential_engine<IntType, a, c, m> base_type; +public: + linear_congruential(IntType x0 = 1) : base_type(x0) {} + template<class It> + linear_congruential(It& first, It last) : base_type(first, last) {} +}; + +/// \endcond + +/** + * The specialization \minstd_rand0 was originally suggested in + * + * @blockquote + * A pseudo-random number generator for the System/360, P.A. Lewis, + * A.S. Goodman, J.M. Miller, IBM Systems Journal, Vol. 8, No. 2, + * 1969, pp. 136-146 + * @endblockquote + * + * It is examined more closely together with \minstd_rand in + * + * @blockquote + * "Random Number Generators: Good ones are hard to find", + * Stephen K. Park and Keith W. Miller, Communications of + * the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 + * @endblockquote + */ +typedef linear_congruential_engine<uint32_t, 16807, 0, 2147483647> minstd_rand0; + +/** The specialization \minstd_rand was suggested in + * + * @blockquote + * "Random Number Generators: Good ones are hard to find", + * Stephen K. Park and Keith W. Miller, Communications of + * the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 + * @endblockquote + */ +typedef linear_congruential_engine<uint32_t, 48271, 0, 2147483647> minstd_rand; + + +#if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T) +/** + * Class @c rand48 models a \pseudo_random_number_generator. It uses + * the linear congruential algorithm with the parameters a = 0x5DEECE66D, + * c = 0xB, m = 2**48. It delivers identical results to the @c lrand48() + * function available on some systems (assuming lcong48 has not been called). + * + * It is only available on systems where @c uint64_t is provided as an + * integral type, so that for example static in-class constants and/or + * enum definitions with large @c uint64_t numbers work. + */ +class rand48 +{ +public: + typedef boost::uint32_t result_type; + + BOOST_STATIC_CONSTANT(bool, has_fixed_range = false); + /** + * Returns the smallest value that the generator can produce + */ + static uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; } + /** + * Returns the largest value that the generator can produce + */ + static uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION () + { return 0x7FFFFFFF; } + + /** Seeds the generator with the default seed. */ + rand48() : lcf(cnv(static_cast<uint32_t>(1))) {} + /** + * Constructs a \rand48 generator with x(0) := (x0 << 16) | 0x330e. + */ + BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(rand48, result_type, x0) + { seed(x0); } + /** + * Seeds the generator with values produced by @c seq.generate(). + */ + BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(rand48, SeedSeq, seq) + { seed(seq); } + /** + * Seeds the generator using values from an iterator range, + * and updates first to point one past the last value consumed. + */ + template<class It> rand48(It& first, It last) : lcf(first, last) { } + + // compiler-generated copy ctor and assignment operator are fine + + /** Seeds the generator with the default seed. */ + void seed() { seed(static_cast<uint32_t>(1)); } + /** + * Changes the current value x(n) of the generator to (x0 << 16) | 0x330e. + */ + BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(rand48, result_type, x0) + { lcf.seed(cnv(x0)); } + /** + * Seeds the generator using values from an iterator range, + * and updates first to point one past the last value consumed. + */ + template<class It> void seed(It& first, It last) { lcf.seed(first,last); } + /** + * Seeds the generator with values produced by @c seq.generate(). + */ + BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(rand48, SeedSeq, seq) + { lcf.seed(seq); } + + /** Returns the next value of the generator. */ + uint32_t operator()() { return static_cast<uint32_t>(lcf() >> 17); } + + /** Advances the state of the generator by @c z. */ + void discard(boost::uintmax_t z) { lcf.discard(z); } + + /** Fills a range with random values */ + template<class Iter> + void generate(Iter first, Iter last) + { + for(; first != last; ++first) { + *first = (*this)(); + } + } + +#ifndef BOOST_RANDOM_NO_STREAM_OPERATORS + /** Writes a @c rand48 to a @c std::ostream. */ + template<class CharT,class Traits> + friend std::basic_ostream<CharT,Traits>& + operator<<(std::basic_ostream<CharT,Traits>& os, const rand48& r) + { os << r.lcf; return os; } + + /** Reads a @c rand48 from a @c std::istream. */ + template<class CharT,class Traits> + friend std::basic_istream<CharT,Traits>& + operator>>(std::basic_istream<CharT,Traits>& is, rand48& r) + { is >> r.lcf; return is; } +#endif + + /** + * Returns true if the two generators will produce identical + * sequences of values. + */ + friend bool operator==(const rand48& x, const rand48& y) + { return x.lcf == y.lcf; } + /** + * Returns true if the two generators will produce different + * sequences of values. + */ + friend bool operator!=(const rand48& x, const rand48& y) + { return !(x == y); } +private: + /// \cond show_private + typedef random::linear_congruential_engine<uint64_t, + // xxxxULL is not portable + uint64_t(0xDEECE66DUL) | (uint64_t(0x5) << 32), + 0xB, uint64_t(1)<<48> lcf_t; + lcf_t lcf; + + static boost::uint64_t cnv(boost::uint32_t x) + { return (static_cast<uint64_t>(x) << 16) | 0x330e; } + /// \endcond +}; +#endif /* !BOOST_NO_INT64_T && !BOOST_NO_INTEGRAL_INT64_T */ + +} // namespace random + +using random::minstd_rand0; +using random::minstd_rand; +using random::rand48; + +} // namespace boost + +#include <boost/random/detail/enable_warnings.hpp> + +#endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP |