459 lines
14 KiB
C++
459 lines
14 KiB
C++
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// (C) Copyright John Maddock 2008 - 2022.
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// (C) Copyright Matt Borland 2022.
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// Use, modification and distribution are subject to the
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// Boost Software License, Version 1.0. (See accompanying file
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// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
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#ifndef BOOST_MATH_CCMATH_NEXT_HPP
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#define BOOST_MATH_CCMATH_NEXT_HPP
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#include <boost/math/ccmath/detail/config.hpp>
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#ifdef BOOST_MATH_NO_CCMATH
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#error "The header <boost/math/next.hpp> can only be used in C++17 and later."
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#endif
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#include <stdexcept>
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#include <cfloat>
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#include <cstdint>
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#include <boost/math/policies/policy.hpp>
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#include <boost/math/policies/error_handling.hpp>
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#include <boost/math/tools/assert.hpp>
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#include <boost/math/tools/config.hpp>
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#include <boost/math/tools/precision.hpp>
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#include <boost/math/tools/traits.hpp>
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#include <boost/math/tools/promotion.hpp>
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#include <boost/math/ccmath/ilogb.hpp>
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#include <boost/math/ccmath/ldexp.hpp>
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#include <boost/math/ccmath/scalbln.hpp>
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#include <boost/math/ccmath/round.hpp>
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#include <boost/math/ccmath/fabs.hpp>
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#include <boost/math/ccmath/fpclassify.hpp>
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#include <boost/math/ccmath/isfinite.hpp>
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#include <boost/math/ccmath/fmod.hpp>
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namespace boost::math::ccmath {
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namespace detail {
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// Forward Declarations
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template <typename T, typename result_type = tools::promote_args_t<T>>
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constexpr result_type float_prior(const T& val);
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template <typename T, typename result_type = tools::promote_args_t<T>>
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constexpr result_type float_next(const T& val);
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template <typename T>
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struct has_hidden_guard_digits;
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template <>
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struct has_hidden_guard_digits<float> : public std::false_type {};
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template <>
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struct has_hidden_guard_digits<double> : public std::false_type {};
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template <>
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struct has_hidden_guard_digits<long double> : public std::false_type {};
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#ifdef BOOST_HAS_FLOAT128
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template <>
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struct has_hidden_guard_digits<__float128> : public std::false_type {};
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#endif
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template <typename T, bool b>
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struct has_hidden_guard_digits_10 : public std::false_type {};
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template <typename T>
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struct has_hidden_guard_digits_10<T, true> : public std::integral_constant<bool, (std::numeric_limits<T>::digits10 != std::numeric_limits<T>::max_digits10)> {};
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template <typename T>
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struct has_hidden_guard_digits
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: public has_hidden_guard_digits_10<T,
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std::numeric_limits<T>::is_specialized
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&& (std::numeric_limits<T>::radix == 10) >
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{};
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template <typename T>
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constexpr T normalize_value(const T& val, const std::false_type&) { return val; }
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template <typename T>
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constexpr T normalize_value(const T& val, const std::true_type&)
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{
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static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
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static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
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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;
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T result = boost::math::ccmath::scalbn(val, shift);
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result = boost::math::ccmath::round(result);
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return boost::math::ccmath::scalbn(result, -shift);
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}
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template <typename T>
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constexpr T get_smallest_value(const std::true_type&)
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{
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//
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// numeric_limits lies about denorms being present - particularly
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// when this can be turned on or off at runtime, as is the case
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// when using the SSE2 registers in DAZ or FTZ mode.
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//
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constexpr T m = std::numeric_limits<T>::denorm_min();
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return ((tools::min_value<T>() / 2) == 0) ? tools::min_value<T>() : m;
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}
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template <typename T>
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constexpr T get_smallest_value(const std::false_type&)
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{
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return tools::min_value<T>();
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}
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template <typename T>
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constexpr T get_smallest_value()
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{
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return get_smallest_value<T>(std::integral_constant<bool, std::numeric_limits<T>::is_specialized>());
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}
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template <typename T>
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constexpr T calc_min_shifted(const std::true_type&)
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{
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return boost::math::ccmath::ldexp(tools::min_value<T>(), tools::digits<T>() + 1);
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}
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template <typename T>
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constexpr T calc_min_shifted(const std::false_type&)
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{
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static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
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static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
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return boost::math::ccmath::scalbn(tools::min_value<T>(), std::numeric_limits<T>::digits + 1);
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}
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template <typename T>
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constexpr T get_min_shift_value()
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{
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const T val = calc_min_shifted<T>(std::integral_constant<bool, !std::numeric_limits<T>::is_specialized || std::numeric_limits<T>::radix == 2>());
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return val;
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}
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template <typename T, bool b = boost::math::tools::detail::has_backend_type_v<T>>
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struct exponent_type
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{
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using type = int;
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};
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template <typename T>
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struct exponent_type<T, true>
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{
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using type = typename T::backend_type::exponent_type;
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};
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template <typename T, bool b = boost::math::tools::detail::has_backend_type_v<T>>
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using exponent_type_t = typename exponent_type<T>::type;
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template <typename T>
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constexpr T float_next_imp(const T& val, const std::true_type&)
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{
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using exponent_type = exponent_type_t<T>;
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exponent_type expon {};
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int fpclass = boost::math::ccmath::fpclassify(val);
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if (fpclass == FP_NAN)
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{
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return val;
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}
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else if (fpclass == FP_INFINITE)
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{
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return val;
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}
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else if (val <= -tools::max_value<T>())
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{
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return val;
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}
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if (val == 0)
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{
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return detail::get_smallest_value<T>();
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}
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if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO)
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&& (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>())
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&& (val != -tools::min_value<T>()))
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{
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//
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// Special case: if the value of the least significant bit is a denorm, and the result
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// would not be a denorm, then shift the input, increment, and shift back.
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// This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
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//
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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>());
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}
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if (-0.5f == boost::math::ccmath::frexp(val, &expon))
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{
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--expon; // reduce exponent when val is a power of two, and negative.
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}
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T diff = boost::math::ccmath::ldexp(static_cast<T>(1), expon - tools::digits<T>());
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if(diff == 0)
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{
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diff = detail::get_smallest_value<T>();
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}
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return val + diff;
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}
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//
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// Special version for some base other than 2:
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//
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template <typename T>
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constexpr T float_next_imp(const T& val, const std::false_type&)
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{
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using exponent_type = exponent_type_t<T>;
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static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
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static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
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exponent_type expon {};
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int fpclass = boost::math::ccmath::fpclassify(val);
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if (fpclass == FP_NAN)
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{
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return val;
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}
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else if (fpclass == FP_INFINITE)
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{
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return val;
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}
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else if (val <= -tools::max_value<T>())
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{
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return val;
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}
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if (val == 0)
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{
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return detail::get_smallest_value<T>();
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}
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if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO)
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&& (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>())
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&& (val != -tools::min_value<T>()))
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{
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//
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// Special case: if the value of the least significant bit is a denorm, and the result
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// would not be a denorm, then shift the input, increment, and shift back.
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// This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
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//
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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);
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}
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expon = 1 + boost::math::ccmath::ilogb(val);
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if(-1 == boost::math::ccmath::scalbn(val, -expon) * std::numeric_limits<T>::radix)
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{
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--expon; // reduce exponent when val is a power of base, and negative.
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}
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T diff = boost::math::ccmath::scalbn(static_cast<T>(1), expon - std::numeric_limits<T>::digits);
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if(diff == 0)
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{
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diff = detail::get_smallest_value<T>();
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}
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return val + diff;
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}
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template <typename T, typename result_type>
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constexpr result_type float_next(const T& val)
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{
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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)>());
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}
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template <typename T>
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constexpr T float_prior_imp(const T& val, const std::true_type&)
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{
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using exponent_type = exponent_type_t<T>;
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exponent_type expon {};
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int fpclass = boost::math::ccmath::fpclassify(val);
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if (fpclass == FP_NAN)
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{
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return val;
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}
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else if (fpclass == FP_INFINITE)
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{
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return val;
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}
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else if (val <= -tools::max_value<T>())
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{
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return val;
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}
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if (val == 0)
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{
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return -detail::get_smallest_value<T>();
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}
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if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO)
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&& (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>())
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&& (val != tools::min_value<T>()))
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{
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//
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// Special case: if the value of the least significant bit is a denorm, and the result
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// would not be a denorm, then shift the input, increment, and shift back.
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// This avoids issues with the Intel SSE2 registers when the FTZ or DAZ flags are set.
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//
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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>());
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}
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if(T remain = boost::math::ccmath::frexp(val, &expon); remain == 0.5f)
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{
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--expon; // when val is a power of two we must reduce the exponent
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}
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T diff = boost::math::ccmath::ldexp(static_cast<T>(1), expon - tools::digits<T>());
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if(diff == 0)
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{
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diff = detail::get_smallest_value<T>();
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}
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return val - diff;
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}
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//
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// Special version for bases other than 2:
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//
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template <typename T>
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constexpr T float_prior_imp(const T& val, const std::false_type&)
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{
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using exponent_type = exponent_type_t<T>;
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static_assert(std::numeric_limits<T>::is_specialized, "Type T must be specialized.");
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static_assert(std::numeric_limits<T>::radix != 2, "Type T must be specialized.");
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exponent_type expon {};
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int fpclass = boost::math::ccmath::fpclassify(val);
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if (fpclass == FP_NAN)
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{
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return val;
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}
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else if (fpclass == FP_INFINITE)
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{
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return val;
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}
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else if (val <= -tools::max_value<T>())
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{
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return val;
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}
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if (val == 0)
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{
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return -detail::get_smallest_value<T>();
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}
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if ((fpclass != FP_SUBNORMAL) && (fpclass != FP_ZERO)
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&& (boost::math::ccmath::fabs(val) < detail::get_min_shift_value<T>())
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&& (val != tools::min_value<T>()))
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{
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//
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// Special case: if the value of the least significant bit is a denorm, and the result
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// would not be a denorm, then shift the input, increment, and shift back.
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// 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
|