// (C) Copyright John Maddock 2008 - 2022. // (C) Copyright Matt Borland 2022. // 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_CCMATH_NEXT_HPP #define BOOST_MATH_CCMATH_NEXT_HPP #include <boost/math/ccmath/detail/config.hpp> #ifdef BOOST_MATH_NO_CCMATH #error "The header <boost/math/next.hpp> can only be used in C++17 and later." #endif #include <stdexcept> #include <cfloat> #include <cstdint> #include <boost/math/policies/policy.hpp> #include <boost/math/policies/error_handling.hpp> #include <boost/math/tools/assert.hpp> #include <boost/math/tools/config.hpp> #include <boost/math/tools/precision.hpp> #include <boost/math/tools/traits.hpp> #include <boost/math/tools/promotion.hpp> #include <boost/math/ccmath/ilogb.hpp> #include <boost/math/ccmath/ldexp.hpp> #include <boost/math/ccmath/scalbln.hpp> #include <boost/math/ccmath/round.hpp> #include <boost/math/ccmath/fabs.hpp> #include <boost/math/ccmath/fpclassify.hpp> #include <boost/math/ccmath/isfinite.hpp> #include <boost/math/ccmath/fmod.hpp> namespace boost::math::ccmath { namespace detail { // Forward Declarations template <typename T, typename result_type = tools::promote_args_t<T>> constexpr result_type float_prior(const T& val); template <typename T, typename result_type = tools::promote_args_t<T>> constexpr result_type float_next(const T& val); template <typename T> struct has_hidden_guard_digits; template <> struct has_hidden_guard_digits<float> : public std::false_type {}; template <> struct has_hidden_guard_digits<double> : public std::false_type {}; template <> struct has_hidden_guard_digits<long double> : public std::false_type {}; #ifdef BOOST_HAS_FLOAT128 template <> struct has_hidden_guard_digits<__float128> : public std::false_type {}; #endif template <typename T, bool b> struct has_hidden_guard_digits_10 : public std::false_type {}; template <typename T> struct has_hidden_guard_digits_10<T, true> : public std::integral_constant<bool, (std::numeric_limits<T>::digits10 != std::numeric_limits<T>::max_digits10)> {}; template <typename T> struct has_hidden_guard_digits : public has_hidden_guard_digits_10<T, std::numeric_limits<T>::is_specialized && (std::numeric_limits<T>::radix == 10) > {}; template <typename T> constexpr T normalize_value(const T& val, const std::false_type&) { return val; } template <typename T> constexpr T normalize_value(const T& val, const std::true_type&) { static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized."); static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized."); std::intmax_t shift = static_cast<std::intmax_t>(std::numeric_limits<T>::digits) - static_cast<std::intmax_t>(boost::math::ccmath::ilogb(val)) - 1; T result = boost::math::ccmath::scalbn(val, shift); result = boost::math::ccmath::round(result); return boost::math::ccmath::scalbn(result, -shift); } template <typename T> constexpr T get_smallest_value(const std::true_type&) { // // numeric_limits lies about denorms being present - particularly // when this can be turned on or off at runtime, as is the case // when using the SSE2 registers in DAZ or FTZ mode. // constexpr T m = std::numeric_limits<T>::denorm_min(); return ((tools::min_value<T>() / 2) == 0) ? tools::min_value<T>() : m; } template <typename T> constexpr T get_smallest_value(const std::false_type&) { return tools::min_value<T>(); } template <typename T> constexpr T get_smallest_value() { return get_smallest_value<T>(std::integral_constant<bool, std::numeric_limits<T>::is_specialized>()); } template <typename T> constexpr T calc_min_shifted(const std::true_type&) { return boost::math::ccmath::ldexp(tools::min_value<T>(), tools::digits<T>() + 1); } template <typename T> constexpr T calc_min_shifted(const std::false_type&) { static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized."); static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized."); return boost::math::ccmath::scalbn(tools::min_value<T>(), std::numeric_limits<T>::digits + 1); } template <typename T> constexpr T get_min_shift_value() { const T val = calc_min_shifted<T>(std::integral_constant<bool, !std::numeric_limits<T>::is_specialized || std::numeric_limits<T>::radix == 2>()); return val; } template <typename T, bool b = boost::math::tools::detail::has_backend_type_v<T>> struct exponent_type { using type = int; }; template <typename T> struct exponent_type<T, true> { using type = typename T::backend_type::exponent_type; }; template <typename T, bool b = boost::math::tools::detail::has_backend_type_v<T>> using exponent_type_t = typename exponent_type<T>::type; template <typename T> constexpr T float_next_imp(const T& val, const std::true_type&) { using exponent_type = exponent_type_t<T>; exponent_type expon {}; int fpclass = boost::math::ccmath::fpclassify(val); if (fpclass == FP_NAN) { return val; } else if (fpclass == FP_INFINITE) { return val; } else if (val <= -tools::max_value<T>()) { return val; } if (val == 0) { return detail::get_smallest_value<T>(); } if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>()) && (val != -tools::min_value<T>())) { // // Special case: if the value of the least significant bit is a denorm, and the result // would not be a denorm, then shift the input, increment, and shift back. // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. // return boost::math::ccmath::ldexp(boost::math::ccmath::detail::float_next(static_cast<T>(boost::math::ccmath::ldexp(val, 2 * tools::digits<T>()))), -2 * tools::digits<T>()); } if (-0.5f == boost::math::ccmath::frexp(val, &expon)) { --expon; // reduce exponent when val is a power of two, and negative. } T diff = boost::math::ccmath::ldexp(static_cast<T>(1), expon - tools::digits<T>()); if(diff == 0) { diff = detail::get_smallest_value<T>(); } return val + diff; } // // Special version for some base other than 2: // template <typename T> constexpr T float_next_imp(const T& val, const std::false_type&) { using exponent_type = exponent_type_t<T>; static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized."); static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized."); exponent_type expon {}; int fpclass = boost::math::ccmath::fpclassify(val); if (fpclass == FP_NAN) { return val; } else if (fpclass == FP_INFINITE) { return val; } else if (val <= -tools::max_value<T>()) { return val; } if (val == 0) { return detail::get_smallest_value<T>(); } if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>()) && (val != -tools::min_value<T>())) { // // Special case: if the value of the least significant bit is a denorm, and the result // would not be a denorm, then shift the input, increment, and shift back. // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. // return boost::math::ccmath::scalbn(boost::math::ccmath::detail::float_next(static_cast<T>(boost::math::ccmath::scalbn(val, 2 * std::numeric_limits<T>::digits))), -2 * std::numeric_limits<T>::digits); } expon = 1 + boost::math::ccmath::ilogb(val); if(-1 == boost::math::ccmath::scalbn(val, -expon) * std::numeric_limits<T>::radix) { --expon; // reduce exponent when val is a power of base, and negative. } T diff = boost::math::ccmath::scalbn(static_cast<T>(1), expon - std::numeric_limits<T>::digits); if(diff == 0) { diff = detail::get_smallest_value<T>(); } return val + diff; } template <typename T, typename result_type> constexpr result_type float_next(const T& val) { return detail::float_next_imp(detail::normalize_value(static_cast<result_type>(val), typename detail::has_hidden_guard_digits<result_type>::type()), std::integral_constant<bool, !std::numeric_limits<result_type>::is_specialized || (std::numeric_limits<result_type>::radix == 2)>()); } template <typename T> constexpr T float_prior_imp(const T& val, const std::true_type&) { using exponent_type = exponent_type_t<T>; exponent_type expon {}; int fpclass = boost::math::ccmath::fpclassify(val); if (fpclass == FP_NAN) { return val; } else if (fpclass == FP_INFINITE) { return val; } else if (val <= -tools::max_value<T>()) { return val; } if (val == 0) { return -detail::get_smallest_value<T>(); } if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>()) && (val != tools::min_value<T>())) { // // Special case: if the value of the least significant bit is a denorm, and the result // would not be a denorm, then shift the input, increment, and shift back. // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. // return boost::math::ccmath::ldexp(boost::math::ccmath::detail::float_prior(static_cast<T>(boost::math::ccmath::ldexp(val, 2 * tools::digits<T>()))), -2 * tools::digits<T>()); } if(T remain = boost::math::ccmath::frexp(val, &expon); remain == 0.5f) { --expon; // when val is a power of two we must reduce the exponent } T diff = boost::math::ccmath::ldexp(static_cast<T>(1), expon - tools::digits<T>()); if(diff == 0) { diff = detail::get_smallest_value<T>(); } return val - diff; } // // Special version for bases other than 2: // template <typename T> constexpr T float_prior_imp(const T& val, const std::false_type&) { using exponent_type = exponent_type_t<T>; static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized."); static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized."); exponent_type expon {}; int fpclass = boost::math::ccmath::fpclassify(val); if (fpclass == FP_NAN) { return val; } else if (fpclass == FP_INFINITE) { return val; } else if (val <= -tools::max_value<T>()) { return val; } if (val == 0) { return -detail::get_smallest_value<T>(); } if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO) && (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>()) && (val != tools::min_value<T>())) { // // Special case: if the value of the least significant bit is a denorm, and the result // would not be a denorm, then shift the input, increment, and shift back. // This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set. // return boost::math::ccmath::scalbn(boost::math::ccmath::detail::float_prior(static_cast<T>(boost::math::ccmath::scalbn(val, 2 * std::numeric_limits<T>::digits))), -2 * std::numeric_limits<T>::digits); } expon = 1 + boost::math::ccmath::ilogb(val); if (T remain = boost::math::ccmath::scalbn(val, -expon); remain * std::numeric_limits<T>::radix == 1) { --expon; // when val is a power of two we must reduce the exponent } T diff = boost::math::ccmath::scalbn(static_cast<T>(1), expon - std::numeric_limits<T>::digits); if (diff == 0) { diff = detail::get_smallest_value<T>(); } return val - diff; } // float_prior_imp template <typename T, typename result_type> constexpr result_type float_prior(const T& val) { return detail::float_prior_imp(detail::normalize_value(static_cast<result_type>(val), typename detail::has_hidden_guard_digits<result_type>::type()), std::integral_constant<bool, !std::numeric_limits<result_type>::is_specialized || (std::numeric_limits<result_type>::radix == 2)>()); } } // namespace detail template <typename T, typename U, typename result_type = tools::promote_args_t<T, U>> constexpr result_type nextafter(const T& val, const U& direction) { if (BOOST_MATH_IS_CONSTANT_EVALUATED(val)) { if (boost::math::ccmath::isnan(val)) { return val; } else if (boost::math::ccmath::isnan(direction)) { return direction; } else if (val < direction) { return boost::math::ccmath::detail::float_next(val); } else if (val == direction) { // IEC 60559 recommends that from is returned whenever from == to. These functions return to instead, // which makes the behavior around zero consistent: std::nextafter(-0.0, +0.0) returns +0.0 and // std::nextafter(+0.0, -0.0) returns -0.0. return direction; } return boost::math::ccmath::detail::float_prior(val); } else { using std::nextafter; return nextafter(static_cast<result_type>(val), static_cast<result_type>(direction)); } } constexpr float nextafterf(float val, float direction) { return boost::math::ccmath::nextafter(val, direction); } #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS constexpr long double nextafterl(long double val, long double direction) { return boost::math::ccmath::nextafter(val, direction); } template <typename T, typename result_type = tools::promote_args_t<T, long double>, typename return_type = std::conditional_t<std::is_integral_v<T>, double, T>> constexpr return_type nexttoward(T val, long double direction) { if (BOOST_MATH_IS_CONSTANT_EVALUATED(val)) { return static_cast<return_type>(boost::math::ccmath::nextafter(static_cast<result_type>(val), direction)); } else { using std::nexttoward; return nexttoward(val, direction); } } constexpr float nexttowardf(float val, long double direction) { return boost::math::ccmath::nexttoward(val, direction); } constexpr long double nexttowardl(long double val, long double direction) { return boost::math::ccmath::nexttoward(val, direction); } #endif } // Namespaces #endif // BOOST_MATH_SPECIAL_NEXT_HPP