diff options
Diffstat (limited to 'boost/multiprecision/random.hpp')
| -rw-r--r-- | boost/multiprecision/random.hpp | 583 |
1 files changed, 2 insertions, 581 deletions
diff --git a/boost/multiprecision/random.hpp b/boost/multiprecision/random.hpp index def97f0582..c6b7d34e03 100644 --- a/boost/multiprecision/random.hpp +++ b/boost/multiprecision/random.hpp @@ -8,590 +8,11 @@ #ifndef BOOST_MP_RANDOM_HPP #define BOOST_MP_RANDOM_HPP -#ifdef BOOST_MSVC -#pragma warning(push) -#pragma warning(disable:4127) +#if defined(__GNUC__) || defined(_MSC_VER) +# pragma message("NOTE: Use of this header (boost/multiprecision/random.hpp) is deprecated: please use the random number library headers directly.") #endif -#include <boost/multiprecision/number.hpp> - -namespace boost{ namespace random{ namespace detail{ -// -// This is a horrible hack: this declaration has to appear before the definition of -// uniform_int_distribution, otherwise it won't be used... -// Need to find a better solution, like make Boost.Random safe to use with -// UDT's and depricate/remove this header altogether. -// -template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -boost::multiprecision::number<Backend, ExpressionTemplates> - generate_uniform_int(Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value); - -}}} #include <boost/random.hpp> -#include <boost/mpl/eval_if.hpp> - -namespace boost{ -namespace random{ -namespace detail{ - -template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -struct subtract<boost::multiprecision::number<Backend, ExpressionTemplates>, true> -{ - typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type; - result_type operator()(result_type const& x, result_type const& y) { return x - y; } -}; - -} - -template<class Engine, std::size_t w, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -class independent_bits_engine<Engine, w, boost::multiprecision::number<Backend, ExpressionTemplates> > -{ -public: - typedef Engine base_type; - typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type; - - static result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () - { return 0; } - // This is the only function we modify compared to the primary template: - static result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () - { - // This expression allows for the possibility that w == std::numeric_limits<result_type>::digits: - return (((result_type(1) << (w - 1)) - 1) << 1) + 1; - } - - independent_bits_engine() { } - - BOOST_RANDOM_DETAIL_ARITHMETIC_CONSTRUCTOR(independent_bits_engine, - result_type, seed_arg) - { - _base.seed(seed_arg); - } - - BOOST_RANDOM_DETAIL_SEED_SEQ_CONSTRUCTOR(independent_bits_engine, - SeedSeq, seq) - { _base.seed(seq); } - - independent_bits_engine(const base_type& base_arg) : _base(base_arg) {} - - template<class It> - independent_bits_engine(It& first, It last) : _base(first, last) { } - - void seed() { _base.seed(); } - - BOOST_RANDOM_DETAIL_ARITHMETIC_SEED(independent_bits_engine, - result_type, seed_arg) - { _base.seed(seed_arg); } - - BOOST_RANDOM_DETAIL_SEED_SEQ_SEED(independent_bits_engine, - SeedSeq, seq) - { _base.seed(seq); } - - template<class It> void seed(It& first, It last) - { _base.seed(first, last); } - - result_type operator()() - { - // While it may seem wasteful to recalculate this - // every time, both msvc and gcc can propagate - // constants, resolving this at compile time. - base_unsigned range = - detail::subtract<base_result>()((_base.max)(), (_base.min)()); - std::size_t m = - (range == (std::numeric_limits<base_unsigned>::max)()) ? - std::numeric_limits<base_unsigned>::digits : - detail::integer_log2(range + 1); - std::size_t n = (w + m - 1) / m; - std::size_t w0, n0; - base_unsigned y0, y1; - base_unsigned y0_mask, y1_mask; - calc_params(n, range, w0, n0, y0, y1, y0_mask, y1_mask); - if(base_unsigned(range - y0 + 1) > y0 / n) { - // increment n and try again. - ++n; - calc_params(n, range, w0, n0, y0, y1, y0_mask, y1_mask); - } - - BOOST_ASSERT(n0*w0 + (n - n0)*(w0 + 1) == w); - - result_type S = 0; - for(std::size_t k = 0; k < n0; ++k) { - base_unsigned u; - do { - u = detail::subtract<base_result>()(_base(), (_base.min)()); - } while(u > base_unsigned(y0 - 1)); - S = (S << w0) + (u & y0_mask); - } - for(std::size_t k = 0; k < (n - n0); ++k) { - base_unsigned u; - do { - u = detail::subtract<base_result>()(_base(), (_base.min)()); - } while(u > base_unsigned(y1 - 1)); - S = (S << (w0 + 1)) + (u & y1_mask); - } - return S; - } - - /** 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) - { - for(boost::uintmax_t i = 0; i < z; ++i) { - (*this)(); - } - } - - const base_type& base() const { return _base; } - - /** - * Writes the textual representation if the generator to a @c std::ostream. - * The textual representation of the engine is the textual representation - * of the base engine. - */ - BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, independent_bits_engine, r) - { - os << r._base; - return os; - } - - /** - * Reads the state of an @c independent_bits_engine from a - * @c std::istream. - */ - BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, independent_bits_engine, r) - { - is >> r._base; - return is; - } - - /** - * Returns: true iff the two @c independent_bits_engines will - * produce the same sequence of values. - */ - BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(independent_bits_engine, x, y) - { return x._base == y._base; } - /** - * Returns: true iff the two @c independent_bits_engines will - * produce different sequences of values. - */ - BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(independent_bits_engine) - -private: - - /// \cond show_private - typedef typename base_type::result_type base_result; - typedef typename make_unsigned<base_result>::type base_unsigned; - - void calc_params( - std::size_t n, base_unsigned range, - std::size_t& w0, std::size_t& n0, - base_unsigned& y0, base_unsigned& y1, - base_unsigned& y0_mask, base_unsigned& y1_mask) - { - BOOST_ASSERT(w >= n); - w0 = w/n; - n0 = n - w % n; - y0_mask = (base_unsigned(2) << (w0 - 1)) - 1; - y1_mask = (y0_mask << 1) | 1; - y0 = (range + 1) & ~y0_mask; - y1 = (range + 1) & ~y1_mask; - BOOST_ASSERT(y0 != 0 || base_unsigned(range + 1) == 0); - } - /// \endcond - - Engine _base; -}; - -template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -class uniform_smallint<boost::multiprecision::number<Backend, ExpressionTemplates> > -{ -public: - typedef boost::multiprecision::number<Backend, ExpressionTemplates> input_type; - typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type; - - class param_type - { - public: - - typedef uniform_smallint distribution_type; - - /** constructs the parameters of a @c uniform_smallint distribution. */ - param_type(result_type const& min_arg = 0, result_type const& max_arg = 9) - : _min(min_arg), _max(max_arg) - { - BOOST_ASSERT(_min <= _max); - } - - /** Returns the minimum value. */ - result_type a() const { return _min; } - /** Returns the maximum value. */ - result_type b() const { return _max; } - - - /** Writes the parameters to a @c std::ostream. */ - BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, param_type, parm) - { - os << parm._min << " " << parm._max; - return os; - } - - /** Reads the parameters from a @c std::istream. */ - BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, param_type, parm) - { - is >> parm._min >> std::ws >> parm._max; - return is; - } - - /** Returns true if the two sets of parameters are equal. */ - BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(param_type, lhs, rhs) - { return lhs._min == rhs._min && lhs._max == rhs._max; } - - /** Returns true if the two sets of parameters are different. */ - BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(param_type) - - private: - result_type _min; - result_type _max; - }; - - /** - * Constructs a @c uniform_smallint. @c min and @c max are the - * lower and upper bounds of the output range, respectively. - */ - explicit uniform_smallint(result_type const& min_arg = 0, result_type const& max_arg = 9) - : _min(min_arg), _max(max_arg) {} - - /** - * Constructs a @c uniform_smallint from its parameters. - */ - explicit uniform_smallint(const param_type& parm) - : _min(parm.a()), _max(parm.b()) {} - - /** Returns the minimum value of the distribution. */ - result_type a() const { return _min; } - /** Returns the maximum value of the distribution. */ - result_type b() const { return _max; } - /** Returns the minimum value of the distribution. */ - result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; } - /** Returns the maximum value of the distribution. */ - result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; } - - /** Returns the parameters of the distribution. */ - param_type param() const { return param_type(_min, _max); } - /** Sets the parameters of the distribution. */ - void param(const param_type& parm) - { - _min = parm.a(); - _max = parm.b(); - } - - /** - * Effects: Subsequent uses of the distribution do not depend - * on values produced by any engine prior to invoking reset. - */ - void reset() { } - - /** Returns a value uniformly distributed in the range [min(), max()]. */ - template<class Engine> - result_type operator()(Engine& eng) const - { - typedef typename Engine::result_type base_result; - return generate(eng, boost::is_integral<base_result>()); - } - - /** Returns a value uniformly distributed in the range [param.a(), param.b()]. */ - template<class Engine> - result_type operator()(Engine& eng, const param_type& parm) const - { return uniform_smallint(parm)(eng); } - - /** Writes the distribution to a @c std::ostream. */ - BOOST_RANDOM_DETAIL_OSTREAM_OPERATOR(os, uniform_smallint, ud) - { - os << ud._min << " " << ud._max; - return os; - } - - /** Reads the distribution from a @c std::istream. */ - BOOST_RANDOM_DETAIL_ISTREAM_OPERATOR(is, uniform_smallint, ud) - { - is >> ud._min >> std::ws >> ud._max; - return is; - } - - /** - * Returns true if the two distributions will produce identical - * sequences of values given equal generators. - */ - BOOST_RANDOM_DETAIL_EQUALITY_OPERATOR(uniform_smallint, lhs, rhs) - { return lhs._min == rhs._min && lhs._max == rhs._max; } - - /** - * Returns true if the two distributions may produce different - * sequences of values given equal generators. - */ - BOOST_RANDOM_DETAIL_INEQUALITY_OPERATOR(uniform_smallint) - -private: - - // \cond show_private - template<class Engine> - result_type generate(Engine& eng, boost::mpl::true_) const - { - // equivalent to (eng() - eng.min()) % (_max - _min + 1) + _min, - // but guarantees no overflow. - typedef typename Engine::result_type base_result; - typedef typename boost::make_unsigned<base_result>::type base_unsigned; - typedef result_type range_type; - range_type range = random::detail::subtract<result_type>()(_max, _min); - base_unsigned base_range = - random::detail::subtract<result_type>()((eng.max)(), (eng.min)()); - base_unsigned val = - random::detail::subtract<base_result>()(eng(), (eng.min)()); - if(range >= base_range) { - return boost::random::detail::add<range_type, result_type>()( - static_cast<range_type>(val), _min); - } else { - base_unsigned modulus = static_cast<base_unsigned>(range) + 1; - return boost::random::detail::add<range_type, result_type>()( - static_cast<range_type>(val % modulus), _min); - } - } - - template<class Engine> - result_type generate(Engine& eng, boost::mpl::false_) const - { - typedef typename Engine::result_type base_result; - typedef result_type range_type; - range_type range = random::detail::subtract<result_type>()(_max, _min); - base_result val = boost::uniform_01<base_result>()(eng); - // what is the worst that can possibly happen here? - // base_result may not be able to represent all the values in [0, range] - // exactly. If this happens, it will cause round off error and we - // won't be able to produce all the values in the range. We don't - // care about this because the user has already told us not to by - // using uniform_smallint. However, we do need to be careful - // to clamp the result, or floating point rounding can produce - // an out of range result. - range_type offset = static_cast<range_type>(val * (range + 1)); - if(offset > range) return _max; - return boost::random::detail::add<range_type, result_type>()(offset , _min); - } - // \endcond - - result_type _min; - result_type _max; -}; - - -namespace detail{ - -template<class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -struct select_uniform_01<boost::multiprecision::number<Backend, ExpressionTemplates> > -{ - template<class RealType> - struct apply - { - typedef new_uniform_01<boost::multiprecision::number<Backend, ExpressionTemplates> > type; - }; -}; - -template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -boost::multiprecision::number<Backend, ExpressionTemplates> - generate_uniform_int( - Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value, - boost::mpl::true_ /** is_integral<Engine::result_type> */) -{ - typedef boost::multiprecision::number<Backend, ExpressionTemplates> result_type; - // Since we're using big-numbers, use the result type for all internal calculations: - typedef result_type range_type; - typedef result_type base_result; - typedef result_type base_unsigned; - const range_type range = random::detail::subtract<result_type>()(max_value, min_value); - const base_result bmin = (eng.min)(); - const base_unsigned brange = - random::detail::subtract<base_result>()((eng.max)(), (eng.min)()); - - if(range == 0) { - return min_value; - } else if(brange == range) { - // this will probably never happen in real life - // basically nothing to do; just take care we don't overflow / underflow - base_unsigned v = random::detail::subtract<base_result>()(eng(), bmin); - return random::detail::add<base_unsigned, result_type>()(v, min_value); - } else if(brange < range) { - // use rejection method to handle things like 0..3 --> 0..4 - for(;;) { - // concatenate several invocations of the base RNG - // take extra care to avoid overflows - - // limit == floor((range+1)/(brange+1)) - // Therefore limit*(brange+1) <= range+1 - range_type limit; - if(std::numeric_limits<range_type>::is_bounded && (range == (std::numeric_limits<range_type>::max)())) { - limit = range/(range_type(brange)+1); - if(range % (range_type(brange)+1) == range_type(brange)) - ++limit; - } else { - limit = (range+1)/(range_type(brange)+1); - } - - // We consider "result" as expressed to base (brange+1): - // For every power of (brange+1), we determine a random factor - range_type result = range_type(0); - range_type mult = range_type(1); - - // loop invariants: - // result < mult - // mult <= range - while(mult <= limit) { - // Postcondition: result <= range, thus no overflow - // - // limit*(brange+1)<=range+1 def. of limit (1) - // eng()-bmin<=brange eng() post. (2) - // and mult<=limit. loop condition (3) - // Therefore mult*(eng()-bmin+1)<=range+1 by (1),(2),(3) (4) - // Therefore mult*(eng()-bmin)+mult<=range+1 rearranging (4) (5) - // result<mult loop invariant (6) - // Therefore result+mult*(eng()-bmin)<range+1 by (5), (6) (7) - // - // Postcondition: result < mult*(brange+1) - // - // result<mult loop invariant (1) - // eng()-bmin<=brange eng() post. (2) - // Therefore result+mult*(eng()-bmin) < - // mult+mult*(eng()-bmin) by (1) (3) - // Therefore result+(eng()-bmin)*mult < - // mult+mult*brange by (2), (3) (4) - // Therefore result+(eng()-bmin)*mult < - // mult*(brange+1) by (4) - result += static_cast<range_type>(random::detail::subtract<base_result>()(eng(), bmin) * mult); - - // equivalent to (mult * (brange+1)) == range+1, but avoids overflow. - if(mult * range_type(brange) == range - mult + 1) { - // The destination range is an integer power of - // the generator's range. - return(result); - } - - // Postcondition: mult <= range - // - // limit*(brange+1)<=range+1 def. of limit (1) - // mult<=limit loop condition (2) - // Therefore mult*(brange+1)<=range+1 by (1), (2) (3) - // mult*(brange+1)!=range+1 preceding if (4) - // Therefore mult*(brange+1)<range+1 by (3), (4) (5) - // - // Postcondition: result < mult - // - // See the second postcondition on the change to result. - mult *= range_type(brange)+range_type(1); - } - // loop postcondition: range/mult < brange+1 - // - // mult > limit loop condition (1) - // Suppose range/mult >= brange+1 Assumption (2) - // range >= mult*(brange+1) by (2) (3) - // range+1 > mult*(brange+1) by (3) (4) - // range+1 > (limit+1)*(brange+1) by (1), (4) (5) - // (range+1)/(brange+1) > limit+1 by (5) (6) - // limit < floor((range+1)/(brange+1)) by (6) (7) - // limit==floor((range+1)/(brange+1)) def. of limit (8) - // not (2) reductio (9) - // - // loop postcondition: (range/mult)*mult+(mult-1) >= range - // - // (range/mult)*mult + range%mult == range identity (1) - // range%mult < mult def. of % (2) - // (range/mult)*mult+mult > range by (1), (2) (3) - // (range/mult)*mult+(mult-1) >= range by (3) (4) - // - // Note that the maximum value of result at this point is (mult-1), - // so after this final step, we generate numbers that can be - // at least as large as range. We have to really careful to avoid - // overflow in this final addition and in the rejection. Anything - // that overflows is larger than range and can thus be rejected. - - // range/mult < brange+1 -> no endless loop - range_type result_increment = - generate_uniform_int( - eng, - static_cast<range_type>(0), - static_cast<range_type>(range/mult), - boost::mpl::true_()); - if(std::numeric_limits<range_type>::is_bounded && ((std::numeric_limits<range_type>::max)() / mult < result_increment)) { - // The multiplication would overflow. Reject immediately. - continue; - } - result_increment *= mult; - // unsigned integers are guaranteed to wrap on overflow. - result += result_increment; - if(result < result_increment) { - // The addition overflowed. Reject. - continue; - } - if(result > range) { - // Too big. Reject. - continue; - } - return random::detail::add<range_type, result_type>()(result, min_value); - } - } else { // brange > range - range_type bucket_size; - // it's safe to add 1 to range, as long as we cast it first, - // because we know that it is less than brange. However, - // we do need to be careful not to cause overflow by adding 1 - // to brange. - if(std::numeric_limits<base_unsigned>::is_bounded && (brange == (std::numeric_limits<base_unsigned>::max)())) { - bucket_size = brange / (range+1); - if(brange % (range+1) == range) { - ++bucket_size; - } - } else { - bucket_size = (brange+1) / (range+1); - } - for(;;) { - range_type result = - random::detail::subtract<base_result>()(eng(), bmin); - result /= bucket_size; - // result and range are non-negative, and result is possibly larger - // than range, so the cast is safe - if(result <= range) - return result + min_value; - } - } -} - -template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -inline boost::multiprecision::number<Backend, ExpressionTemplates> - generate_uniform_int(Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value) -{ - typedef typename Engine::result_type base_result; - typedef typename mpl::or_<boost::is_integral<base_result>, mpl::bool_<boost::multiprecision::number_category<Backend>::value == boost::multiprecision::number_kind_integer> >::type tag_type; - return generate_uniform_int(eng, min_value, max_value, - tag_type()); -} - -template<class Engine, class Backend, boost::multiprecision::expression_template_option ExpressionTemplates> -inline boost::multiprecision::number<Backend, ExpressionTemplates> generate_uniform_real(Engine& eng, const boost::multiprecision::number<Backend, ExpressionTemplates>& min_value, const boost::multiprecision::number<Backend, ExpressionTemplates>& max_value) -{ - if(max_value / 2 - min_value / 2 > (std::numeric_limits<boost::multiprecision::number<Backend, ExpressionTemplates> >::max)() / 2) - return 2 * generate_uniform_real(eng, boost::multiprecision::number<Backend, ExpressionTemplates>(min_value / 2), boost::multiprecision::number<Backend, ExpressionTemplates>(max_value / 2)); - typedef typename Engine::result_type base_result; - return generate_uniform_real(eng, min_value, max_value, - boost::is_integral<base_result>()); -} - -} // detail - - -}} // namespaces - -#ifdef BOOST_MSVC -#pragma warning(pop) -#endif #endif |