//           Copyright Matthew Pulver 2018 - 2019.
// Distributed under the Boost Software License, Version 1.0.
//      (See accompanying file LICENSE_1_0.txt or copy at
//           https://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_MATH_TEST_AUTODIFF_HPP
#define BOOST_MATH_TEST_AUTODIFF_HPP

#ifndef BOOST_TEST_MODULE
#define BOOST_TEST_MODULE test_autodiff
#endif

#ifndef BOOST_ALLOW_DEPRECATED_HEADERS
#define BOOST_ALLOW_DEPRECATED_HEADERS // artifact of sp_typeinfo.hpp inclusion from unit_test.hpp
#endif

#include <boost/math/tools/config.hpp>

#include <boost/math/differentiation/autodiff.hpp>
#include <boost/multiprecision/cpp_bin_float.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/mp11/function.hpp>
#include <boost/mp11/integral.hpp>
#include <boost/mp11/list.hpp>
#include <boost/mp11/utility.hpp>
#include <boost/range/irange.hpp>
#include <boost/test/included/unit_test.hpp>

#include <algorithm>
#include <cfenv>
#include <cstdlib>
#include <random>

namespace mp11 = boost::mp11;
namespace bmp = boost::multiprecision;

#if defined(BOOST_USE_VALGRIND) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS)
using bin_float_types = mp11::mp_list<float>;
#else
using bin_float_types = mp11::mp_list<float, double, long double>;
#endif

// cpp_dec_float_50 cannot be used with close_at_tolerance
/*using multiprecision_float_types =
    mp_list<bmp::cpp_dec_float_50, bmp::cpp_bin_float_50>;*/

#if !defined(BOOST_VERSION) || BOOST_VERSION < 107000 || defined(BOOST_USE_VALGRIND) || defined(BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS) || defined(BOOST_NO_STRESS_TEST)
using multiprecision_float_types = mp11::mp_list<>;
#else
#define BOOST_AUTODIFF_TESTING_INCLUDE_MULTIPRECISION
using multiprecision_float_types = mp11::mp_list<bmp::cpp_bin_float_50>;
#endif

using all_float_types = mp11::mp_append<bin_float_types, multiprecision_float_types>;

using namespace boost::math::differentiation;

namespace test_detail {
template <typename T>
using is_multiprecision_t =
    mp11::mp_or<bmp::is_number<T>, bmp::is_number_expression<T>>;

template<bool IfValue, typename ThenType, typename ElseType>
using if_c = mp11::mp_eval_if_c<IfValue, ThenType, mp11::mp_identity_t, ElseType>;

template<typename IfType, typename ThenType, typename ElseType>
using if_t = if_c<IfType::value, ThenType, ElseType>;

/**
 * Simple struct to hold constants that are used in each test
 * since BOOST_AUTO_TEST_CASE_TEMPLATE doesn't support fixtures.
 */
template <typename T, std::size_t OrderValue>
struct test_constants_t {
  static constexpr auto n_samples = if_t<mp11::mp_or<bmp::is_number<T>, bmp::is_number_expression<T>>, mp11::mp_int<10>, mp11::mp_int<25>>::value;
  static constexpr auto order = OrderValue;
  static constexpr T pct_epsilon() BOOST_NOEXCEPT {
    return (is_multiprecision_t<T>::value ? 2 : 1) * std::numeric_limits<T>::epsilon() * 100;
  }
};

/**
 * struct to emit pseudo-random values from a given interval.
 * Endpoints are closed or open depending on whether or not they're infinite).
 */

template <typename T>
struct RandomSample {
  using numeric_limits_t = std::numeric_limits<T>;
  using is_integer_t = mp11::mp_bool<std::numeric_limits<T>::is_integer>;

  using distribution_param_t = if_t<
      is_multiprecision_t<T>,
      if_t<is_integer_t,
                  if_c<numeric_limits_t::is_signed, int64_t, uint64_t>,
                  long double>,
      T>;
  static_assert((std::numeric_limits<T>::is_integer &&
                 std::numeric_limits<distribution_param_t>::is_integer) ||
                    (!std::numeric_limits<T>::is_integer &&
                     !std::numeric_limits<distribution_param_t>::is_integer),
                "T and distribution_param_t must either both be integral or "
                "both be not integral");

  using dist_t = if_t<is_integer_t,
  std::uniform_int_distribution<distribution_param_t>,
  std::uniform_real_distribution<distribution_param_t>>;

  struct get_integral_endpoint {
    template <typename V>
    constexpr distribution_param_t operator()(V finish) const noexcept {
      return static_cast<distribution_param_t>(finish);
    }
  };

  struct get_real_endpoint {
    template <typename V>
    constexpr distribution_param_t operator()(V finish) const noexcept {
      return std::nextafter(static_cast<distribution_param_t>(finish),
                            (std::numeric_limits<distribution_param_t>::max)());
    }
  };

  using get_endpoint_t = if_t<is_integer_t, get_integral_endpoint, get_real_endpoint>;

  template <typename U, typename V>
  RandomSample(U start, V finish)
      : rng_(std::random_device{}()),
        dist_(static_cast<distribution_param_t>(start),
              get_endpoint_t{}(finish)) {}

  T next() noexcept { return static_cast<T>(dist_(rng_)); }
  T normalize(const T& x) noexcept {
    return x / ((dist_.max)() - (dist_.min)());
  }

  std::mt19937 rng_;
  dist_t dist_;
};
static_assert(std::is_same<RandomSample<float>::dist_t,
                           std::uniform_real_distribution<float>>::value,
              "");
static_assert(std::is_same<RandomSample<int64_t>::dist_t,
                           std::uniform_int_distribution<int64_t>>::value,
              "");
static_assert(std::is_same<RandomSample<bmp::uint512_t>::dist_t,
                           std::uniform_int_distribution<uint64_t>>::value,
              "");
static_assert(std::is_same<RandomSample<bmp::cpp_bin_float_50>::dist_t,
                           std::uniform_real_distribution<long double>>::value,
              "");

}  // namespace test_detail

template<typename T>
auto isNearZero(const T& t) noexcept -> typename std::enable_if<!detail::is_fvar<T>::value, bool>::type
{
  using std::sqrt;
  using bmp::sqrt;
  using detail::sqrt;
  using std::fabs;
  using bmp::fabs;
  using detail::fabs;
  using boost::math::fpclassify;
  using std::sqrt;
  return fpclassify(fabs(t)) == FP_ZERO || fpclassify(fabs(t)) == FP_SUBNORMAL || boost::math::fpc::is_small(fabs(t), sqrt(std::numeric_limits<T>::epsilon()));
}

template<typename T>
auto isNearZero(const T& t) noexcept -> typename std::enable_if<detail::is_fvar<T>::value, bool>::type
{
  using root_type = typename T::root_type;
  return isNearZero(static_cast<root_type>(t));
}

template <typename T, std::size_t Order = 5>
using test_constants_t = test_detail::test_constants_t<T, Order>;

template <typename W, typename X, typename Y, typename Z>
promote<W, X, Y, Z> mixed_partials_f(const W& w, const X& x, const Y& y,
                                     const Z& z) {

  return exp(w * sin(x * log(y) / z) + sqrt(w * z / (x * y))) + w * w / tan(z);
}

// Equations and function/variable names are from
// https://en.wikipedia.org/wiki/Greeks_(finance)#Formulas_for_European_option_Greeks
//
// Standard normal probability density function
template <typename T>
T phi(const T& x) {
  return boost::math::constants::one_div_root_two_pi<T>() * exp(-0.5 * x * x);
}

// Standard normal cumulative distribution function
template <typename T>
T Phi(const T& x) {
  return 0.5 * erfc(-boost::math::constants::one_div_root_two<T>() * x);
}

enum class CP { call, put };

// Assume zero annual dividend yield (q=0).
template <typename Price, typename Sigma, typename Tau, typename Rate>
promote<Price, Sigma, Tau, Rate> black_scholes_option_price(CP cp, double K,
                                                            const Price& S,
                                                            const Sigma& sigma,
                                                            const Tau& tau,
                                                            const Rate& r) {
  const auto d1 =
      (log(S / K) + (r + sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
  const auto d2 =
      (log(S / K) + (r - sigma * sigma / 2) * tau) / (sigma * sqrt(tau));
  if (cp == CP::call) {
    return S * Phi(d1) - exp(-r * tau) * K * Phi(d2);
  }
  return exp(-r * tau) * K * Phi(-d2) - S * Phi(-d1);
}

template <typename T>
T uncast_return(const T& x) {
  return x == 0 ? 0 : 1;
}

#endif  // BOOST_MATH_TEST_AUTODIFF_HPP