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- // 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
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