boost/random/linear_congruential.hpp
/* 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