Chris@16: /* boost random/linear_congruential.hpp header file
Chris@16:  *
Chris@16:  * Copyright Jens Maurer 2000-2001
Chris@16:  * Distributed under the Boost Software License, Version 1.0. (See
Chris@16:  * accompanying file LICENSE_1_0.txt or copy at
Chris@16:  * http://www.boost.org/LICENSE_1_0.txt)
Chris@16:  *
Chris@16:  * See http://www.boost.org for most recent version including documentation.
Chris@16:  *
Chris@101:  * $Id$
Chris@16:  *
Chris@16:  * Revision history
Chris@16:  *  2001-02-18  moved to individual header files
Chris@16:  */
Chris@16: 
Chris@16: #ifndef BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
Chris@16: #define BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP
Chris@16: 
Chris@16: #include <iostream>
Chris@16: #include <stdexcept>
Chris@16: #include <boost/assert.hpp>
Chris@16: #include <boost/config.hpp>
Chris@16: #include <boost/cstdint.hpp>
Chris@16: #include <boost/limits.hpp>
Chris@16: #include <boost/static_assert.hpp>
Chris@16: #include <boost/integer/static_log2.hpp>
Chris@16: #include <boost/mpl/if.hpp>
Chris@16: #include <boost/type_traits/is_arithmetic.hpp>
Chris@16: #include <boost/random/detail/config.hpp>
Chris@16: #include <boost/random/detail/const_mod.hpp>
Chris@16: #include <boost/random/detail/seed.hpp>
Chris@16: #include <boost/random/detail/seed_impl.hpp>
Chris@16: #include <boost/detail/workaround.hpp>
Chris@16: 
Chris@16: #include <boost/random/detail/disable_warnings.hpp>
Chris@16: 
Chris@16: namespace boost {
Chris@16: namespace random {
Chris@16: 
Chris@16: /**
Chris@16:  * Instantiations of class template linear_congruential_engine model a
Chris@16:  * \pseudo_random_number_generator. Linear congruential pseudo-random
Chris@16:  * number generators are described in:
Chris@16:  *
Chris@16:  *  @blockquote
Chris@16:  *  "Mathematical methods in large-scale computing units", D. H. Lehmer,
Chris@16:  *  Proc. 2nd Symposium on Large-Scale Digital Calculating Machines,
Chris@16:  *  Harvard University Press, 1951, pp. 141-146
Chris@16:  *  @endblockquote
Chris@16:  *
Chris@16:  * Let x(n) denote the sequence of numbers returned by some pseudo-random
Chris@16:  * number generator. Then for the linear congruential generator,
Chris@16:  * x(n+1) := (a * x(n) + c) mod m. Parameters for the generator are
Chris@16:  * x(0), a, c, m. The template parameter IntType shall denote an integral
Chris@16:  * type. It must be large enough to hold values a, c, and m. The template
Chris@16:  * parameters a and c must be smaller than m.
Chris@16:  *
Chris@16:  * Note: The quality of the generator crucially depends on the choice of
Chris@16:  * the parameters. User code should use one of the sensibly parameterized
Chris@16:  * generators such as minstd_rand instead.
Chris@16:  */
Chris@16: template<class IntType, IntType a, IntType c, IntType m>
Chris@16: class linear_congruential_engine
Chris@16: {
Chris@16: public:
Chris@16:     typedef IntType result_type;
Chris@16: 
Chris@16:     // Required for old Boost.Random concept
Chris@16:     BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
Chris@16: 
Chris@16:     BOOST_STATIC_CONSTANT(IntType, multiplier = a);
Chris@16:     BOOST_STATIC_CONSTANT(IntType, increment = c);
Chris@16:     BOOST_STATIC_CONSTANT(IntType, modulus = m);
Chris@16:     BOOST_STATIC_CONSTANT(IntType, default_seed = 1);
Chris@16:     
Chris@16:     BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer);
Chris@16:     BOOST_STATIC_ASSERT(m == 0 || a < m);
Chris@16:     BOOST_STATIC_ASSERT(m == 0 || c < m);
Chris@16:     
Chris@16:     /**
Chris@16:      * Constructs a @c linear_congruential_engine, using the default seed
Chris@16:      */
Chris@16:     linear_congruential_engine() { seed(); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c linear_congruential_engine, seeding it with @c x0.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(linear_congruential_engine,
Chris@16:                                                IntType, x0)
Chris@16:     { seed(x0); }
Chris@16:     
Chris@16:     /**
Chris@16:      * Constructs a @c linear_congruential_engine, seeding it with values
Chris@16:      * produced by a call to @c seq.generate().
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(linear_congruential_engine,
Chris@16:                                              SeedSeq, seq)
Chris@16:     { seed(seq); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Constructs a @c linear_congruential_engine  and seeds it
Chris@16:      * with values taken from the itrator range [first, last)
Chris@16:      * and adjusts first to point to the element after the last one
Chris@16:      * used.  If there are not enough elements, throws @c std::invalid_argument.
Chris@16:      *
Chris@16:      * first and last must be input iterators.
Chris@16:      */
Chris@16:     template<class It>
Chris@16:     linear_congruential_engine(It& first, It last)
Chris@16:     {
Chris@16:         seed(first, last);
Chris@16:     }
Chris@16: 
Chris@16:     // compiler-generated copy constructor and assignment operator are fine
Chris@16: 
Chris@16:     /**
Chris@16:      * Calls seed(default_seed)
Chris@16:      */
Chris@16:     void seed() { seed(default_seed); }
Chris@16: 
Chris@16:     /**
Chris@16:      * If c mod m is zero and x0 mod m is zero, changes the current value of
Chris@16:      * the generator to 1. Otherwise, changes it to x0 mod m. If c is zero,
Chris@16:      * distinct seeds in the range [1,m) will leave the generator in distinct
Chris@16:      * states. If c is not zero, the range is [0,m).
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(linear_congruential_engine, IntType, x0)
Chris@16:     {
Chris@16:         // wrap _x if it doesn't fit in the destination
Chris@16:         if(modulus == 0) {
Chris@16:             _x = x0;
Chris@16:         } else {
Chris@16:             _x = x0 % modulus;
Chris@16:         }
Chris@16:         // handle negative seeds
Chris@16:         if(_x <= 0 && _x != 0) {
Chris@16:             _x += modulus;
Chris@16:         }
Chris@16:         // adjust to the correct range
Chris@16:         if(increment == 0 && _x == 0) {
Chris@16:             _x = 1;
Chris@16:         }
Chris@16:         BOOST_ASSERT(_x >= (min)());
Chris@16:         BOOST_ASSERT(_x <= (max)());
Chris@16:     }
Chris@16: 
Chris@16:     /**
Chris@16:      * Seeds a @c linear_congruential_engine using values from a SeedSeq.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(linear_congruential_engine, SeedSeq, seq)
Chris@16:     { seed(detail::seed_one_int<IntType, m>(seq)); }
Chris@16: 
Chris@16:     /**
Chris@16:      * seeds a @c linear_congruential_engine with values taken
Chris@16:      * from the itrator range [first, last) and adjusts @c first to
Chris@16:      * point to the element after the last one used.  If there are
Chris@16:      * not enough elements, throws @c std::invalid_argument.
Chris@16:      *
Chris@16:      * @c first and @c last must be input iterators.
Chris@16:      */
Chris@16:     template<class It>
Chris@16:     void seed(It& first, It last)
Chris@16:     { seed(detail::get_one_int<IntType, m>(first, last)); }
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns the smallest value that the @c linear_congruential_engine
Chris@16:      * can produce.
Chris@16:      */
Chris@16:     static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
Chris@16:     { return c == 0 ? 1 : 0; }
Chris@16:     /**
Chris@16:      * Returns the largest value that the @c linear_congruential_engine
Chris@16:      * can produce.
Chris@16:      */
Chris@16:     static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
Chris@16:     { return modulus-1; }
Chris@16: 
Chris@16:     /** Returns the next value of the @c linear_congruential_engine. */
Chris@16:     IntType operator()()
Chris@16:     {
Chris@16:         _x = const_mod<IntType, m>::mult_add(a, _x, c);
Chris@16:         return _x;
Chris@16:     }
Chris@16:   
Chris@16:     /** Fills a range with random values */
Chris@16:     template<class Iter>
Chris@16:     void generate(Iter first, Iter last)
Chris@16:     { detail::generate_from_int(*this, first, last); }
Chris@16: 
Chris@16:     /** Advances the state of the generator by @c z. */
Chris@16:     void discard(boost::uintmax_t z)
Chris@16:     {
Chris@16:         typedef const_mod<IntType, m> mod_type;
Chris@16:         IntType b_inv = mod_type::invert(a-1);
Chris@16:         IntType b_gcd = mod_type::mult(a-1, b_inv);
Chris@16:         if(b_gcd == 1) {
Chris@16:             IntType a_z = mod_type::pow(a, z);
Chris@16:             _x = mod_type::mult_add(a_z, _x, 
Chris@16:                 mod_type::mult(mod_type::mult(c, b_inv), a_z - 1));
Chris@16:         } else {
Chris@16:             // compute (a^z - 1)*c % (b_gcd * m) / (b / b_gcd) * inv(b / b_gcd)
Chris@16:             // we're storing the intermediate result / b_gcd
Chris@16:             IntType a_zm1_over_gcd = 0;
Chris@16:             IntType a_km1_over_gcd = (a - 1) / b_gcd;
Chris@16:             boost::uintmax_t exponent = z;
Chris@16:             while(exponent != 0) {
Chris@16:                 if(exponent % 2 == 1) {
Chris@16:                     a_zm1_over_gcd =
Chris@16:                         mod_type::mult_add(
Chris@16:                             b_gcd,
Chris@16:                             mod_type::mult(a_zm1_over_gcd, a_km1_over_gcd),
Chris@16:                             mod_type::add(a_zm1_over_gcd, a_km1_over_gcd));
Chris@16:                 }
Chris@16:                 a_km1_over_gcd = mod_type::mult_add(
Chris@16:                     b_gcd,
Chris@16:                     mod_type::mult(a_km1_over_gcd, a_km1_over_gcd),
Chris@16:                     mod_type::add(a_km1_over_gcd, a_km1_over_gcd));
Chris@16:                 exponent /= 2;
Chris@16:             }
Chris@16:             
Chris@16:             IntType a_z = mod_type::mult_add(b_gcd, a_zm1_over_gcd, 1);
Chris@16:             IntType num = mod_type::mult(c, a_zm1_over_gcd);
Chris@16:             b_inv = mod_type::invert((a-1)/b_gcd);
Chris@16:             _x = mod_type::mult_add(a_z, _x, mod_type::mult(b_inv, num));
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16:     friend bool operator==(const linear_congruential_engine& x,
Chris@16:                            const linear_congruential_engine& y)
Chris@16:     { return x._x == y._x; }
Chris@16:     friend bool operator!=(const linear_congruential_engine& x,
Chris@16:                            const linear_congruential_engine& y)
Chris@16:     { return !(x == y); }
Chris@16:     
Chris@16: #if !defined(BOOST_RANDOM_NO_STREAM_OPERATORS)
Chris@16:     /** Writes a @c linear_congruential_engine to a @c std::ostream. */
Chris@16:     template<class CharT, class Traits>
Chris@16:     friend std::basic_ostream<CharT,Traits>&
Chris@16:     operator<<(std::basic_ostream<CharT,Traits>& os,
Chris@16:                const linear_congruential_engine& lcg)
Chris@16:     {
Chris@16:         return os << lcg._x;
Chris@16:     }
Chris@16: 
Chris@16:     /** Reads a @c linear_congruential_engine from a @c std::istream. */
Chris@16:     template<class CharT, class Traits>
Chris@16:     friend std::basic_istream<CharT,Traits>&
Chris@16:     operator>>(std::basic_istream<CharT,Traits>& is,
Chris@16:                linear_congruential_engine& lcg)
Chris@16:     {
Chris@16:         lcg.read(is);
Chris@16:         return is;
Chris@16:     }
Chris@16: #endif
Chris@16: 
Chris@16: private:
Chris@16: 
Chris@16:     /// \cond show_private
Chris@16: 
Chris@16:     template<class CharT, class Traits>
Chris@16:     void read(std::basic_istream<CharT, Traits>& is) {
Chris@16:         IntType x;
Chris@16:         if(is >> x) {
Chris@16:             if(x >= (min)() && x <= (max)()) {
Chris@16:                 _x = x;
Chris@16:             } else {
Chris@16:                 is.setstate(std::ios_base::failbit);
Chris@16:             }
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16:     /// \endcond
Chris@16: 
Chris@16:     IntType _x;
Chris@16: };
Chris@16: 
Chris@16: #ifndef BOOST_NO_INCLASS_MEMBER_INITIALIZATION
Chris@16: //  A definition is required even for integral static constants
Chris@16: template<class IntType, IntType a, IntType c, IntType m>
Chris@16: const bool linear_congruential_engine<IntType, a, c, m>::has_fixed_range;
Chris@16: template<class IntType, IntType a, IntType c, IntType m>
Chris@16: const IntType linear_congruential_engine<IntType,a,c,m>::multiplier;
Chris@16: template<class IntType, IntType a, IntType c, IntType m>
Chris@16: const IntType linear_congruential_engine<IntType,a,c,m>::increment;
Chris@16: template<class IntType, IntType a, IntType c, IntType m>
Chris@16: const IntType linear_congruential_engine<IntType,a,c,m>::modulus;
Chris@16: template<class IntType, IntType a, IntType c, IntType m>
Chris@16: const IntType linear_congruential_engine<IntType,a,c,m>::default_seed;
Chris@16: #endif
Chris@16: 
Chris@16: /// \cond show_deprecated
Chris@16: 
Chris@16: // provided for backwards compatibility
Chris@16: template<class IntType, IntType a, IntType c, IntType m, IntType val = 0>
Chris@16: class linear_congruential : public linear_congruential_engine<IntType, a, c, m>
Chris@16: {
Chris@16:     typedef linear_congruential_engine<IntType, a, c, m> base_type;
Chris@16: public:
Chris@16:     linear_congruential(IntType x0 = 1) : base_type(x0) {}
Chris@16:     template<class It>
Chris@16:     linear_congruential(It& first, It last) : base_type(first, last) {}
Chris@16: };
Chris@16: 
Chris@16: /// \endcond
Chris@16: 
Chris@16: /**
Chris@16:  * The specialization \minstd_rand0 was originally suggested in
Chris@16:  *
Chris@16:  *  @blockquote
Chris@16:  *  A pseudo-random number generator for the System/360, P.A. Lewis,
Chris@16:  *  A.S. Goodman, J.M. Miller, IBM Systems Journal, Vol. 8, No. 2,
Chris@16:  *  1969, pp. 136-146
Chris@16:  *  @endblockquote
Chris@16:  *
Chris@16:  * It is examined more closely together with \minstd_rand in
Chris@16:  *
Chris@16:  *  @blockquote
Chris@16:  *  "Random Number Generators: Good ones are hard to find",
Chris@16:  *  Stephen K. Park and Keith W. Miller, Communications of
Chris@16:  *  the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201 
Chris@16:  *  @endblockquote
Chris@16:  */
Chris@16: typedef linear_congruential_engine<uint32_t, 16807, 0, 2147483647> minstd_rand0;
Chris@16: 
Chris@16: /** The specialization \minstd_rand was suggested in
Chris@16:  *
Chris@16:  *  @blockquote
Chris@16:  *  "Random Number Generators: Good ones are hard to find",
Chris@16:  *  Stephen K. Park and Keith W. Miller, Communications of
Chris@16:  *  the ACM, Vol. 31, No. 10, October 1988, pp. 1192-1201
Chris@16:  *  @endblockquote
Chris@16:  */
Chris@16: typedef linear_congruential_engine<uint32_t, 48271, 0, 2147483647> minstd_rand;
Chris@16: 
Chris@16: 
Chris@16: #if !defined(BOOST_NO_INT64_T) && !defined(BOOST_NO_INTEGRAL_INT64_T)
Chris@16: /**
Chris@16:  * Class @c rand48 models a \pseudo_random_number_generator. It uses
Chris@16:  * the linear congruential algorithm with the parameters a = 0x5DEECE66D,
Chris@16:  * c = 0xB, m = 2**48. It delivers identical results to the @c lrand48()
Chris@16:  * function available on some systems (assuming lcong48 has not been called).
Chris@16:  *
Chris@16:  * It is only available on systems where @c uint64_t is provided as an
Chris@16:  * integral type, so that for example static in-class constants and/or
Chris@16:  * enum definitions with large @c uint64_t numbers work.
Chris@16:  */
Chris@16: class rand48 
Chris@16: {
Chris@16: public:
Chris@16:     typedef boost::uint32_t result_type;
Chris@16: 
Chris@16:     BOOST_STATIC_CONSTANT(bool, has_fixed_range = false);
Chris@16:     /**
Chris@16:      * Returns the smallest value that the generator can produce
Chris@16:      */
Chris@16:     static uint32_t min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; }
Chris@16:     /**
Chris@16:      * Returns the largest value that the generator can produce
Chris@16:      */
Chris@16:     static uint32_t max BOOST_PREVENT_MACRO_SUBSTITUTION ()
Chris@16:     { return 0x7FFFFFFF; }
Chris@16:   
Chris@16:     /** Seeds the generator with the default seed. */
Chris@16:     rand48() : lcf(cnv(static_cast<uint32_t>(1))) {}
Chris@16:     /**
Chris@16:      * Constructs a \rand48 generator with x(0) := (x0 << 16) | 0x330e.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(rand48, result_type, x0)
Chris@16:     { seed(x0); }
Chris@16:     /**
Chris@16:      * Seeds the generator with values produced by @c seq.generate().
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(rand48, SeedSeq, seq)
Chris@16:     { seed(seq); }
Chris@16:     /**
Chris@16:      * Seeds the generator using values from an iterator range,
Chris@16:      * and updates first to point one past the last value consumed.
Chris@16:      */
Chris@16:     template<class It> rand48(It& first, It last) : lcf(first, last) { }
Chris@16: 
Chris@16:     // compiler-generated copy ctor and assignment operator are fine
Chris@16: 
Chris@16:     /** Seeds the generator with the default seed. */
Chris@16:     void seed() { seed(static_cast<uint32_t>(1)); }
Chris@16:     /**
Chris@16:      * Changes the current value x(n) of the generator to (x0 << 16) | 0x330e.
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(rand48, result_type, x0)
Chris@16:     { lcf.seed(cnv(x0)); }
Chris@16:     /**
Chris@16:      * Seeds the generator using values from an iterator range,
Chris@16:      * and updates first to point one past the last value consumed.
Chris@16:      */
Chris@16:     template<class It> void seed(It& first, It last) { lcf.seed(first,last); }
Chris@16:     /**
Chris@16:      * Seeds the generator with values produced by @c seq.generate().
Chris@16:      */
Chris@16:     BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(rand48, SeedSeq, seq)
Chris@16:     { lcf.seed(seq); }
Chris@16: 
Chris@16:     /**  Returns the next value of the generator. */
Chris@16:     uint32_t operator()() { return static_cast<uint32_t>(lcf() >> 17); }
Chris@16:     
Chris@16:     /** Advances the state of the generator by @c z. */
Chris@16:     void discard(boost::uintmax_t z) { lcf.discard(z); }
Chris@16:   
Chris@16:     /** Fills a range with random values */
Chris@16:     template<class Iter>
Chris@16:     void generate(Iter first, Iter last)
Chris@16:     {
Chris@16:         for(; first != last; ++first) {
Chris@16:             *first = (*this)();
Chris@16:         }
Chris@16:     }
Chris@16: 
Chris@16: #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS
Chris@16:     /**  Writes a @c rand48 to a @c std::ostream. */
Chris@16:     template<class CharT,class Traits>
Chris@16:     friend std::basic_ostream<CharT,Traits>&
Chris@16:     operator<<(std::basic_ostream<CharT,Traits>& os, const rand48& r)
Chris@16:     { os << r.lcf; return os; }
Chris@16: 
Chris@16:     /** Reads a @c rand48 from a @c std::istream. */
Chris@16:     template<class CharT,class Traits>
Chris@16:     friend std::basic_istream<CharT,Traits>&
Chris@16:     operator>>(std::basic_istream<CharT,Traits>& is, rand48& r)
Chris@16:     { is >> r.lcf; return is; }
Chris@16: #endif
Chris@16: 
Chris@16:     /**
Chris@16:      * Returns true if the two generators will produce identical
Chris@16:      * sequences of values.
Chris@16:      */
Chris@16:     friend bool operator==(const rand48& x, const rand48& y)
Chris@16:     { return x.lcf == y.lcf; }
Chris@16:     /**
Chris@16:      * Returns true if the two generators will produce different
Chris@16:      * sequences of values.
Chris@16:      */
Chris@16:     friend bool operator!=(const rand48& x, const rand48& y)
Chris@16:     { return !(x == y); }
Chris@16: private:
Chris@16:     /// \cond show_private
Chris@16:     typedef random::linear_congruential_engine<uint64_t,
Chris@16:         // xxxxULL is not portable
Chris@16:         uint64_t(0xDEECE66DUL) | (uint64_t(0x5) << 32),
Chris@16:         0xB, uint64_t(1)<<48> lcf_t;
Chris@16:     lcf_t lcf;
Chris@16: 
Chris@16:     static boost::uint64_t cnv(boost::uint32_t x)
Chris@16:     { return (static_cast<uint64_t>(x) << 16) | 0x330e; }
Chris@16:     /// \endcond
Chris@16: };
Chris@16: #endif /* !BOOST_NO_INT64_T && !BOOST_NO_INTEGRAL_INT64_T */
Chris@16: 
Chris@16: } // namespace random
Chris@16: 
Chris@16: using random::minstd_rand0;
Chris@16: using random::minstd_rand;
Chris@16: using random::rand48;
Chris@16: 
Chris@16: } // namespace boost
Chris@16: 
Chris@16: #include <boost/random/detail/enable_warnings.hpp>
Chris@16: 
Chris@16: #endif // BOOST_RANDOM_LINEAR_CONGRUENTIAL_HPP