boost/multiprecision/random.hpp
///////////////////////////////////////////////////////////////
// Copyright Jens Maurer 2006-1011
// Copyright Steven Watanabe 2011
// Copyright 2012 John Maddock. 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_
#ifndef BOOST_MP_RANDOM_HPP
#define BOOST_MP_RANDOM_HPP
#ifdef BOOST_MSVC
#pragma warning(push)
#pragma warning(disable:4127)
#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());
}
} // detail
}} // namespaces
#ifdef BOOST_MSVC
#pragma warning(pop)
#endif
#endif