| /* boost random/uniform_int.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: uniform_int.hpp 60755 2010-03-22 00:45:06Z steven_watanabe $ | |
| * | |
| * Revision history | |
| * 2001-04-08 added min<max assertion (N. Becker) | |
| * 2001-02-18 moved to individual header files | |
| */ | |
| #ifndef BOOST_RANDOM_UNIFORM_INT_HPP | |
| #define BOOST_RANDOM_UNIFORM_INT_HPP | |
| #include <cassert> | |
| #include <iostream> | |
| #include <boost/config.hpp> | |
| #include <boost/limits.hpp> | |
| #include <boost/static_assert.hpp> | |
| #include <boost/detail/workaround.hpp> | |
| #include <boost/random/detail/config.hpp> | |
| #include <boost/random/detail/signed_unsigned_tools.hpp> | |
| #include <boost/type_traits/make_unsigned.hpp> | |
| namespace boost { | |
| /** | |
| * The distribution function uniform_int models a \random_distribution. | |
| * On each invocation, it returns a random integer value uniformly | |
| * distributed in the set of integer numbers {min, min+1, min+2, ..., max}. | |
| * | |
| * The template parameter IntType shall denote an integer-like value type. | |
| */ | |
| template<class IntType = int> | |
| class uniform_int | |
| { | |
| public: | |
| typedef IntType input_type; | |
| typedef IntType result_type; | |
| /// \cond hide_private_members | |
| typedef typename make_unsigned<result_type>::type range_type; | |
| /// \endcond | |
| /** | |
| * Constructs a uniform_int object. @c min and @c max are | |
| * the parameters of the distribution. | |
| * | |
| * Requires: min <= max | |
| */ | |
| explicit uniform_int(IntType min_arg = 0, IntType max_arg = 9) | |
| : _min(min_arg), _max(max_arg) | |
| { | |
| #ifndef BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS | |
| // MSVC fails BOOST_STATIC_ASSERT with std::numeric_limits at class scope | |
| BOOST_STATIC_ASSERT(std::numeric_limits<IntType>::is_integer); | |
| #endif | |
| assert(min_arg <= max_arg); | |
| init(); | |
| } | |
| /** | |
| * Returns: The "min" parameter of the distribution | |
| */ | |
| result_type min BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _min; } | |
| /** | |
| * Returns: The "max" parameter of the distribution | |
| */ | |
| result_type max BOOST_PREVENT_MACRO_SUBSTITUTION () const { return _max; } | |
| void reset() { } | |
| // can't have member function templates out-of-line due to MSVC bugs | |
| template<class Engine> | |
| result_type operator()(Engine& eng) | |
| { | |
| return generate(eng, _min, _max, _range); | |
| } | |
| template<class Engine> | |
| result_type operator()(Engine& eng, result_type n) | |
| { | |
| assert(n > 0); | |
| if (n == 1) | |
| { | |
| return 0; | |
| } | |
| return generate(eng, 0, n - 1, n - 1); | |
| } | |
| #ifndef BOOST_RANDOM_NO_STREAM_OPERATORS | |
| template<class CharT, class Traits> | |
| friend std::basic_ostream<CharT,Traits>& | |
| operator<<(std::basic_ostream<CharT,Traits>& os, const uniform_int& ud) | |
| { | |
| os << ud._min << " " << ud._max; | |
| return os; | |
| } | |
| template<class CharT, class Traits> | |
| friend std::basic_istream<CharT,Traits>& | |
| operator>>(std::basic_istream<CharT,Traits>& is, uniform_int& ud) | |
| { | |
| is >> std::ws >> ud._min >> std::ws >> ud._max; | |
| ud.init(); | |
| return is; | |
| } | |
| #endif | |
| private: | |
| #ifdef BOOST_MSVC | |
| #pragma warning(push) | |
| // disable division by zero warning, since we can't | |
| // actually divide by zero. | |
| #pragma warning(disable:4723) | |
| #endif | |
| /// \cond hide_private_members | |
| template<class Engine> | |
| static result_type generate(Engine& eng, result_type min_value, result_type /*max_value*/, range_type range) | |
| { | |
| typedef typename Engine::result_type base_result; | |
| // ranges are always unsigned | |
| typedef typename make_unsigned<base_result>::type base_unsigned; | |
| 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(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 = uniform_int<range_type>(0, range/mult)(eng); | |
| if((std::numeric_limits<range_type>::max)() / mult < result_increment) { | |
| // The multiplcation 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 | |
| base_unsigned 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(brange == (std::numeric_limits<base_unsigned>::max)()) { | |
| bucket_size = brange / (static_cast<base_unsigned>(range)+1); | |
| if(brange % (static_cast<base_unsigned>(range)+1) == static_cast<base_unsigned>(range)) { | |
| ++bucket_size; | |
| } | |
| } else { | |
| bucket_size = (brange+1) / (static_cast<base_unsigned>(range)+1); | |
| } | |
| for(;;) { | |
| base_unsigned 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 <= static_cast<base_unsigned>(range)) | |
| return random::detail::add<base_unsigned, result_type>()(result, min_value); | |
| } | |
| } | |
| } | |
| #ifdef BOOST_MSVC | |
| #pragma warning(pop) | |
| #endif | |
| void init() | |
| { | |
| _range = random::detail::subtract<result_type>()(_max, _min); | |
| } | |
| /// \endcond | |
| // The result_type may be signed or unsigned, but the _range is always | |
| // unsigned. | |
| result_type _min, _max; | |
| range_type _range; | |
| }; | |
| } // namespace boost | |
| #endif // BOOST_RANDOM_UNIFORM_INT_HPP |