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 // boost/math/distributions/arcsine.hpp
 
 // Copyright John Maddock 2014.
 // Copyright Paul A. Bristow 2014.
 // Copyright Matt Borland 2024.
 
 // 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)
 
 // http://en.wikipedia.org/wiki/arcsine_distribution
 
 // The arcsine Distribution is a continuous probability distribution.
 // http://en.wikipedia.org/wiki/Arcsine_distribution
 // http://www.wolframalpha.com/input/?i=ArcSinDistribution
 
 // Standard arcsine distribution is a special case of beta distribution with both a & b = one half,
 // and 0 <= x <= 1.
 
 // It is generalized to include any bounded support a <= x <= b from 0 <= x <= 1
 // by Wolfram and Wikipedia,
 // but using location and scale parameters by
 // Virtual Laboratories in Probability and Statistics http://www.math.uah.edu/stat/index.html
 // http://www.math.uah.edu/stat/special/Arcsine.html
 // The end-point version is simpler and more obvious, so we implement that.
 // TODO Perhaps provide location and scale functions?
 
 
 #ifndef BOOST_MATH_DIST_ARCSINE_HPP
 #define BOOST_MATH_DIST_ARCSINE_HPP
 
 #include <boost/math/tools/config.hpp>
 #include <boost/math/tools/tuple.hpp>
 #include <boost/math/distributions/complement.hpp> // complements.
 #include <boost/math/distributions/detail/common_error_handling.hpp> // error checks.
 #include <boost/math/constants/constants.hpp>
 #include <boost/math/special_functions/fpclassify.hpp> // isnan.
 #include <boost/math/policies/policy.hpp>
 #include <boost/math/policies/error_handling.hpp>
 
 #ifndef BOOST_MATH_HAS_NVRTC
 #include <boost/math/distributions/fwd.hpp>
 #include <cmath>
 #include <utility>
 #include <exception>  // For std::domain_error.
 #endif
 
 #if defined (BOOST_MSVC)
 #  pragma warning(push)
 #  pragma warning(disable: 4702) // Unreachable code,
 // in domain_error_imp in error_handling.
 #endif
 
 namespace boost
 {
   namespace math
   {
     namespace arcsine_detail
     {
       // Common error checking routines for arcsine distribution functions:
       // Duplicating for x_min and x_max provides specific error messages.
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_x_min(const char* function, const RealType& x, RealType* result, const Policy& pol)
       {
         if (!(boost::math::isfinite)(x))
         {
           *result = policies::raise_domain_error<RealType>(
             function,
             "x_min argument is %1%, but must be finite !", x, pol);
           return false;
         }
         return true;
       } // bool check_x_min
 
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_x_max(const char* function, const RealType& x, RealType* result, const Policy& pol)
       {
         if (!(boost::math::isfinite)(x))
         {
           *result = policies::raise_domain_error<RealType>(
             function,
             "x_max argument is %1%, but must be finite !", x, pol);
           return false;
         }
         return true;
       } // bool check_x_max
 
 
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_x_minmax(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol)
       { // Check x_min < x_max
         if (x_min >= x_max)
         {
           constexpr auto msg = "x_max argument is %1%, but must be > x_min";
           *result = policies::raise_domain_error<RealType>(
             function,
             msg, x_max, pol);
             // "x_max argument is %1%, but must be > x_min !", x_max, pol);
             // "x_max argument is %1%, but must be > x_min %2!", x_max, x_min, pol); would be better. 
             // But would require replication of all helpers functions in /policies/error_handling.hpp for two values,
             // as well as two value versions of raise_error, raise_domain_error and do_format
           return false;
         }
         return true;
       } // bool check_x_minmax
 
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_prob(const char* function, const RealType& p, RealType* result, const Policy& pol)
       {
         if ((p < 0) || (p > 1) || !(boost::math::isfinite)(p))
         {
           *result = policies::raise_domain_error<RealType>(
             function,
             "Probability argument is %1%, but must be >= 0 and <= 1 !", p, pol);
           return false;
         }
         return true;
       } // bool check_prob
 
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_x(const char* function, const RealType& x_min, const RealType& x_max, const RealType& x, RealType* result, const Policy& pol)
       { // Check x finite and x_min < x < x_max.
         if (!(boost::math::isfinite)(x))
         {
           *result = policies::raise_domain_error<RealType>(
             function,
             "x argument is %1%, but must be finite !", x, pol);
           return false;
         }
         if ((x < x_min) || (x > x_max))
         {
           // std::cout << x_min << ' ' << x << x_max << std::endl;
           *result = policies::raise_domain_error<RealType>(
             function,
             "x argument is %1%, but must be x_min < x < x_max !", x, pol);
           // For example:
           // Error in function boost::math::pdf(arcsine_distribution<double> const&, double) : x argument is -1.01, but must be x_min < x < x_max !
           // TODO Perhaps show values of x_min and x_max?
           return false;
         }
         return true;
       } // bool check_x
 
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_dist(const char* function, const RealType& x_min, const RealType& x_max, RealType* result, const Policy& pol)
       { // Check both x_min and x_max finite, and x_min  < x_max.
         return check_x_min(function, x_min, result, pol)
             && check_x_max(function, x_max, result, pol)
             && check_x_minmax(function, x_min, x_max, result, pol);
       } // bool check_dist
 
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_dist_and_x(const char* function, const RealType& x_min, const RealType& x_max, RealType x, RealType* result, const Policy& pol)
       {
         return check_dist(function, x_min, x_max, result, pol)
           && arcsine_detail::check_x(function, x_min, x_max, x, result, pol);
       } // bool check_dist_and_x
 
       template <class RealType, class Policy>
       BOOST_MATH_GPU_ENABLED inline bool check_dist_and_prob(const char* function, const RealType& x_min, const RealType& x_max, RealType p, RealType* result, const Policy& pol)
       {
         return check_dist(function, x_min, x_max, result, pol)
           && check_prob(function, p, result, pol);
       } // bool check_dist_and_prob
 
     } // namespace arcsine_detail
 
     template <class RealType = double, class Policy = policies::policy<> >
     class arcsine_distribution
     {
     public:
       typedef RealType value_type;
       typedef Policy policy_type;
 
       BOOST_MATH_GPU_ENABLED arcsine_distribution(RealType x_min = 0, RealType x_max = 1) : m_x_min(x_min), m_x_max(x_max)
       { // Default beta (alpha = beta = 0.5) is standard arcsine with x_min = 0, x_max = 1.
         // Generalized to allow x_min and x_max to be specified.
         RealType result;
         arcsine_detail::check_dist(
           "boost::math::arcsine_distribution<%1%>::arcsine_distribution",
           m_x_min,
           m_x_max,
           &result, Policy());
       } // arcsine_distribution constructor.
       // Accessor functions:
       BOOST_MATH_GPU_ENABLED RealType x_min() const
       {
         return m_x_min;
       }
       BOOST_MATH_GPU_ENABLED RealType x_max() const
       {
         return m_x_max;
       }
 
     private:
       RealType m_x_min; // Two x min and x max parameters of the arcsine distribution.
       RealType m_x_max;
     }; // template <class RealType, class Policy> class arcsine_distribution
 
     // Convenient typedef to construct double version.
     typedef arcsine_distribution<double> arcsine;
 
     #ifdef __cpp_deduction_guides
     template <class RealType>
     arcsine_distribution(RealType)->arcsine_distribution<typename boost::math::tools::promote_args<RealType>::type>;
     template <class RealType>
     arcsine_distribution(RealType, RealType)->arcsine_distribution<typename boost::math::tools::promote_args<RealType>::type>;
     #endif
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline const boost::math::pair<RealType, RealType> range(const arcsine_distribution<RealType, Policy>&  dist)
     { // Range of permissible values for random variable x.
       using boost::math::tools::max_value;
       return boost::math::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max()));
     }
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline const boost::math::pair<RealType, RealType> support(const arcsine_distribution<RealType, Policy>&  dist)
     { // Range of supported values for random variable x.
       // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
       return boost::math::pair<RealType, RealType>(static_cast<RealType>(dist.x_min()), static_cast<RealType>(dist.x_max()));
     }
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType mean(const arcsine_distribution<RealType, Policy>& dist)
     { // Mean of arcsine distribution .
       RealType result;
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
 
       if (false == arcsine_detail::check_dist(
         "boost::math::mean(arcsine_distribution<%1%> const&, %1% )",
         x_min,
         x_max,
         &result, Policy())
         )
       {
         return result;
       }
       return  (x_min + x_max) / 2;
     } // mean
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType variance(const arcsine_distribution<RealType, Policy>& dist)
     { // Variance of standard arcsine distribution = (1-0)/8 = 0.125.
       RealType result;
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
       if (false == arcsine_detail::check_dist(
         "boost::math::variance(arcsine_distribution<%1%> const&, %1% )",
         x_min,
         x_max,
         &result, Policy())
         )
       {
         return result;
       }
       return  (x_max - x_min) * (x_max - x_min) / 8;
     } // variance
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType mode(const arcsine_distribution<RealType, Policy>& /* dist */)
     { //There are always [*two] values for the mode, at ['x_min] and at ['x_max], default 0 and 1,
       // so instead we raise the exception domain_error.
       return policies::raise_domain_error<RealType>(
         "boost::math::mode(arcsine_distribution<%1%>&)",
         "The arcsine distribution has two modes at x_min and x_max: "
         "so the return value is %1%.",
         std::numeric_limits<RealType>::quiet_NaN(), Policy());
     } // mode
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType median(const arcsine_distribution<RealType, Policy>& dist)
     { // Median of arcsine distribution (a + b) / 2 == mean.
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
       RealType result;
       if (false == arcsine_detail::check_dist(
         "boost::math::median(arcsine_distribution<%1%> const&, %1% )",
         x_min,
         x_max,
         &result, Policy())
         )
       {
         return result;
       }
       return  (x_min + x_max) / 2;
     }
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType skewness(const arcsine_distribution<RealType, Policy>& dist)
     {
       RealType result;
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
 
       if (false == arcsine_detail::check_dist(
         "boost::math::skewness(arcsine_distribution<%1%> const&, %1% )",
         x_min,
         x_max,
         &result, Policy())
         )
       {
         return result;
       }
       return 0;
     } // skewness
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const arcsine_distribution<RealType, Policy>& dist)
     {
       RealType result;
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
 
       if (false == arcsine_detail::check_dist(
         "boost::math::kurtosis_excess(arcsine_distribution<%1%> const&, %1% )",
         x_min,
         x_max,
         &result, Policy())
         )
       {
         return result;
       }
       result = -3;
       return  result / 2;
     } // kurtosis_excess
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const arcsine_distribution<RealType, Policy>& dist)
     {
       RealType result;
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
 
       if (false == arcsine_detail::check_dist(
         "boost::math::kurtosis(arcsine_distribution<%1%> const&, %1% )",
         x_min,
         x_max,
         &result, Policy())
         )
       {
         return result;
       }
 
       return 3 + kurtosis_excess(dist);
     } // kurtosis
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType pdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& xx)
     { // Probability Density/Mass Function arcsine.
       BOOST_FPU_EXCEPTION_GUARD
       BOOST_MATH_STD_USING // For ADL of std functions.
 
       constexpr auto function = "boost::math::pdf(arcsine_distribution<%1%> const&, %1%)";
 
       RealType lo = dist.x_min();
       RealType hi = dist.x_max();
       RealType x = xx;
 
       // Argument checks:
       RealType result = 0; 
       if (false == arcsine_detail::check_dist_and_x(
         function,
         lo, hi, x,
         &result, Policy()))
       {
         return result;
       }
       using boost::math::constants::pi;
       result = static_cast<RealType>(1) / (pi<RealType>() * sqrt((x - lo) * (hi - x)));
       return result;
     } // pdf
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType cdf(const arcsine_distribution<RealType, Policy>& dist, const RealType& x)
     { // Cumulative Distribution Function arcsine.
       BOOST_MATH_STD_USING // For ADL of std functions.
 
       constexpr auto function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)";
 
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
 
       // Argument checks:
       RealType result = 0;
       if (false == arcsine_detail::check_dist_and_x(
         function,
         x_min, x_max, x,
         &result, Policy()))
       {
         return result;
       }
       // Special cases:
       if (x == x_min)
       {
         return 0;
       }
       else if (x == x_max)
       {
         return 1;
       }
       using boost::math::constants::pi;
       result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
       return result;
     } // arcsine cdf
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c)
     { // Complemented Cumulative Distribution Function arcsine.
       BOOST_MATH_STD_USING // For ADL of std functions.
       constexpr auto function = "boost::math::cdf(arcsine_distribution<%1%> const&, %1%)";
 
       RealType x = c.param;
       arcsine_distribution<RealType, Policy> const& dist = c.dist;
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
 
       // Argument checks:
       RealType result = 0;
       if (false == arcsine_detail::check_dist_and_x(
         function,
         x_min, x_max, x,
         &result, Policy()))
       {
         return result;
       }
       if (x == x_min)
       {
         return 0;
       }
       else if (x == x_max)
       {
         return 1;
       }
       using boost::math::constants::pi;
       // Naive version x = 1 - x;
       // result = static_cast<RealType>(2) * asin(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
       // is less accurate, so use acos instead of asin for complement.
       result = static_cast<RealType>(2) * acos(sqrt((x - x_min) / (x_max - x_min))) / pi<RealType>();
       return result;
     } // arcsine ccdf
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType quantile(const arcsine_distribution<RealType, Policy>& dist, const RealType& p)
     { 
       // Quantile or Percent Point arcsine function or
       // Inverse Cumulative probability distribution function CDF.
       // Return x (0 <= x <= 1),
       // for a given probability p (0 <= p <= 1).
       // These functions take a probability as an argument
       // and return a value such that the probability that a random variable x
       // will be less than or equal to that value
       // is whatever probability you supplied as an argument.
       BOOST_MATH_STD_USING // For ADL of std functions.
 
       using boost::math::constants::half_pi;
 
       constexpr auto function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)";
 
       RealType result = 0; // of argument checks:
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
       if (false == arcsine_detail::check_dist_and_prob(
         function,
         x_min, x_max, p,
         &result, Policy()))
       {
         return result;
       }
       // Special cases:
       if (p == 0)
       {
         return 0;
       }
       if (p == 1)
       {
         return 1;
       }
 
       RealType sin2hpip = sin(half_pi<RealType>() * p);
       RealType sin2hpip2 = sin2hpip * sin2hpip;
       result = -x_min * sin2hpip2 + x_min + x_max * sin2hpip2;
 
       return result;
     } // quantile
 
     template <class RealType, class Policy>
     BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type<arcsine_distribution<RealType, Policy>, RealType>& c)
     { 
       // Complement Quantile or Percent Point arcsine function.
       // Return the number of expected x for a given
       // complement of the probability q.
       BOOST_MATH_STD_USING // For ADL of std functions.
 
       using boost::math::constants::half_pi;
       constexpr auto function = "boost::math::quantile(arcsine_distribution<%1%> const&, %1%)";
 
       // Error checks:
       RealType q = c.param;
       const arcsine_distribution<RealType, Policy>& dist = c.dist;
       RealType result = 0;
       RealType x_min = dist.x_min();
       RealType x_max = dist.x_max();
       if (false == arcsine_detail::check_dist_and_prob(
         function,
         x_min,
         x_max,
         q,
         &result, Policy()))
       {
         return result;
       }
       // Special cases:
       if (q == 1)
       {
         return 0;
       }
       if (q == 0)
       {
         return 1;
       }
       // Naive RealType p = 1 - q; result = sin(half_pi<RealType>() * p); loses accuracy, so use a cos alternative instead.
       //result = cos(half_pi<RealType>() * q); // for arcsine(0,1)
       //result = result * result;
       // For generalized arcsine:
       RealType cos2hpip = cos(half_pi<RealType>() * q);
       RealType cos2hpip2 = cos2hpip * cos2hpip;
       result = -x_min * cos2hpip2 + x_min + x_max * cos2hpip2;
 
       return result;
     } // Quantile Complement
 
   } // namespace math
 } // namespace boost
 
 // This include must be at the end, *after* the accessors
 // for this distribution have been defined, in order to
 // keep compilers that support two-phase lookup happy.
 #include <boost/math/distributions/detail/derived_accessors.hpp>
 
 #if defined (BOOST_MSVC)
 # pragma warning(pop)
 #endif
 
 #endif // BOOST_MATH_DIST_ARCSINE_HPP

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