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// (C) Copyright John Maddock 2015. // 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_SPECIAL_ULP_HPP #define BOOST_MATH_SPECIAL_ULP_HPP #ifdef _MSC_VER #pragma once #endif #include #include #include #include #include namespace boost{ namespace math{ namespace detail{ template T ulp_imp(const T& val, const std::true_type&, const Policy& pol) { BOOST_MATH_STD_USING int expon; static const char* function = "ulp<%1%>(%1%)"; int fpclass = (boost::math::fpclassify)(val); if(fpclass == FP_NAN) { return policies::raise_domain_error(function, "Argument must be finite, but got %1%", val, pol); } else if((fpclass == (int)FP_INFINITE) || (fabs(val) >= tools::max_value())) { return (val < 0 ? -1 : 1) * policies::raise_overflow_error(function, nullptr, pol); } else if(fpclass == FP_ZERO) return detail::get_smallest_value(); // // This code is almost the same as that for float_next, except for negative integers, // where we preserve the relation ulp(x) == ulp(-x) as does Java: // frexp(fabs(val), &expon); T diff = ldexp(T(1), expon - tools::digits()); if(diff == 0) diff = detail::get_smallest_value(); return diff; } // non-binary version: template T ulp_imp(const T& val, const std::false_type&, const Policy& pol) { static_assert(std::numeric_limits::is_specialized, "Type T must be specialized."); static_assert(std::numeric_limits::radix != 2, "Type T must be specialized."); BOOST_MATH_STD_USING int expon; static const char* function = "ulp<%1%>(%1%)"; int fpclass = (boost::math::fpclassify)(val); if(fpclass == FP_NAN) { return policies::raise_domain_error(function,"Argument must be finite, but got %1%", val, pol); } else if((fpclass == FP_INFINITE) || (fabs(val) >= tools::max_value())) { return (val < 0 ? -1 : 1) * policies::raise_overflow_error(function, nullptr, pol); } else if(fpclass == FP_ZERO) return detail::get_smallest_value(); // // This code is almost the same as that for float_next, except for negative integers, // where we preserve the relation ulp(x) == ulp(-x) as does Java: // expon = 1 + ilogb(fabs(val)); T diff = scalbn(T(1), expon - std::numeric_limits::digits); if(diff == 0) diff = detail::get_smallest_value(); return diff; // LCOV_EXCL_LINE previous lines are covered so this one must be too. } } template inline typename tools::promote_args::type ulp(const T& val, const Policy& pol) { typedef typename tools::promote_args::type result_type; return detail::ulp_imp(static_cast(val), std::integral_constant::is_specialized || (std::numeric_limits::radix == 2)>(), pol); } template inline typename tools::promote_args::type ulp(const T& val) { return ulp(val, policies::policy<>()); } }} // namespaces #endif // BOOST_MATH_SPECIAL_ULP_HPP