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// Copyright 2008 John Maddock
//
// Use, modification and distribution are subject to 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)
#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_QUANTILE_HPP
#define BOOST_MATH_DISTRIBUTIONS_DETAIL_HG_QUANTILE_HPP
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/distributions/detail/hypergeometric_pdf.hpp>
namespace boost{ namespace math{ namespace detail{
template <class T>
inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&)
{
if((p < cum * fudge_factor) && (x != lbound))
{
BOOST_MATH_INSTRUMENT_VARIABLE(x-1);
return --x;
}
return x;
}
template <class T>
inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned /*lbound*/, unsigned ubound, const policies::discrete_quantile<policies::integer_round_up>&)
{
if((cum < p * fudge_factor) && (x != ubound))
{
BOOST_MATH_INSTRUMENT_VARIABLE(x+1);
return ++x;
}
return x;
}
template <class T>
inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_inwards>&)
{
if(p >= 0.5)
return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>());
return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>());
}
template <class T>
inline unsigned round_x_from_p(unsigned x, T p, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_outwards>&)
{
if(p >= 0.5)
return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>());
return round_x_from_p(x, p, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>());
}
template <class T>
inline unsigned round_x_from_p(unsigned x, T /*p*/, T /*cum*/, T /*fudge_factor*/, unsigned /*lbound*/, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&)
{
return x;
}
template <class T>
inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_down>&)
{
if((q * fudge_factor > cum) && (x != lbound))
{
BOOST_MATH_INSTRUMENT_VARIABLE(x-1);
return --x;
}
return x;
}
template <class T>
inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned /*lbound*/, unsigned ubound, const policies::discrete_quantile<policies::integer_round_up>&)
{
if((q < cum * fudge_factor) && (x != ubound))
{
BOOST_MATH_INSTRUMENT_VARIABLE(x+1);
return ++x;
}
return x;
}
template <class T>
inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_inwards>&)
{
if(q < 0.5)
return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>());
return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>());
}
template <class T>
inline unsigned round_x_from_q(unsigned x, T q, T cum, T fudge_factor, unsigned lbound, unsigned ubound, const policies::discrete_quantile<policies::integer_round_outwards>&)
{
if(q >= 0.5)
return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_down>());
return round_x_from_q(x, q, cum, fudge_factor, lbound, ubound, policies::discrete_quantile<policies::integer_round_up>());
}
template <class T>
inline unsigned round_x_from_q(unsigned x, T /*q*/, T /*cum*/, T /*fudge_factor*/, unsigned /*lbound*/, unsigned /*ubound*/, const policies::discrete_quantile<policies::integer_round_nearest>&)
{
return x;
}
template <class T, class Policy>
unsigned hypergeometric_quantile_imp(T p, T q, unsigned r, unsigned n, unsigned N, const Policy& pol)
{
#ifdef BOOST_MSVC
# pragma warning(push)
# pragma warning(disable:4267)
#endif
typedef typename Policy::discrete_quantile_type discrete_quantile_type;
BOOST_MATH_STD_USING
BOOST_FPU_EXCEPTION_GUARD
T result;
T fudge_factor = 1 + tools::epsilon<T>() * ((N <= boost::math::prime(boost::math::max_prime - 1)) ? 50 : 2 * N);
unsigned base = static_cast<unsigned>((std::max)(0, (int)(n + r) - (int)(N)));
unsigned lim = (std::min)(r, n);
BOOST_MATH_INSTRUMENT_VARIABLE(p);
BOOST_MATH_INSTRUMENT_VARIABLE(q);
BOOST_MATH_INSTRUMENT_VARIABLE(r);
BOOST_MATH_INSTRUMENT_VARIABLE(n);
BOOST_MATH_INSTRUMENT_VARIABLE(N);
BOOST_MATH_INSTRUMENT_VARIABLE(fudge_factor);
BOOST_MATH_INSTRUMENT_VARIABLE(base);
BOOST_MATH_INSTRUMENT_VARIABLE(lim);
if(p <= 0.5)
{
unsigned x = base;
result = hypergeometric_pdf<T>(x, r, n, N, pol);
T diff = result;
while(result < p)
{
diff = (diff > tools::min_value<T>() * 8)
? T(n - x) * T(r - x) * diff / (T(x + 1) * T(N + x + 1 - n - r))
: hypergeometric_pdf<T>(x + 1, r, n, N, pol);
if(result + diff / 2 > p)
break;
++x;
result += diff;
#ifdef BOOST_MATH_INSTRUMENT
if(diff != 0)
{
BOOST_MATH_INSTRUMENT_VARIABLE(x);
BOOST_MATH_INSTRUMENT_VARIABLE(diff);
BOOST_MATH_INSTRUMENT_VARIABLE(result);
}
#endif
}
return round_x_from_p(x, p, result, fudge_factor, base, lim, discrete_quantile_type());
}
else
{
unsigned x = lim;
result = 0;
T diff = hypergeometric_pdf<T>(x, r, n, N, pol);
while(result + diff / 2 < q)
{
result += diff;
diff = (diff > tools::min_value<T>() * 8)
? x * T(N + x - n - r) * diff / (T(1 + n - x) * T(1 + r - x))
: hypergeometric_pdf<T>(x - 1, r, n, N, pol);
--x;
#ifdef BOOST_MATH_INSTRUMENT
if(diff != 0)
{
BOOST_MATH_INSTRUMENT_VARIABLE(x);
BOOST_MATH_INSTRUMENT_VARIABLE(diff);
BOOST_MATH_INSTRUMENT_VARIABLE(result);
}
#endif
}
return round_x_from_q(x, q, result, fudge_factor, base, lim, discrete_quantile_type());
}
#ifdef BOOST_MSVC
# pragma warning(pop)
#endif
}
template <class T, class Policy>
inline unsigned hypergeometric_quantile(T p, T q, unsigned r, unsigned n, unsigned N, const Policy&)
{
BOOST_FPU_EXCEPTION_GUARD
typedef typename tools::promote_args<T>::type result_type;
typedef typename policies::evaluation<result_type, Policy>::type value_type;
typedef typename policies::normalise<
Policy,
policies::promote_float<false>,
policies::promote_double<false>,
policies::assert_undefined<> >::type forwarding_policy;
return detail::hypergeometric_quantile_imp<value_type>(p, q, r, n, N, forwarding_policy());
}
}}} // namespaces
#endif
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