// (C) Copyright John Maddock 2006, 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_RELATIVE_ERROR #define BOOST_MATH_RELATIVE_ERROR #include #include #include namespace boost{ namespace math{ template typename boost::math::tools::promote_args::type relative_difference(const T& arg_a, const U& arg_b) { typedef typename boost::math::tools::promote_args::type result_type; result_type a = arg_a; result_type b = arg_b; BOOST_MATH_STD_USING #ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS // // If math.h has no long double support we can't rely // on the math functions generating exponents outside // the range of a double: // result_type min_val = (std::max)( tools::min_value(), static_cast((std::numeric_limits::min)())); result_type max_val = (std::min)( tools::max_value(), static_cast((std::numeric_limits::max)())); #else result_type min_val = tools::min_value(); result_type max_val = tools::max_value(); #endif // Screen out NaN's first, if either value is a NaN then the distance is "infinite": if((boost::math::isnan)(a) || (boost::math::isnan)(b)) return max_val; // Screen out infinites: if(fabs(b) > max_val) { if(fabs(a) > max_val) return (a < 0) == (b < 0) ? 0 : max_val; // one infinity is as good as another! else return max_val; // one infinity and one finite value implies infinite difference } else if(fabs(a) > max_val) return max_val; // one infinity and one finite value implies infinite difference // // If the values have different signs, treat as infinite difference: // if(((a < 0) != (b < 0)) && (a != 0) && (b != 0)) return max_val; a = fabs(a); b = fabs(b); // // Now deal with zero's, if one value is zero (or denorm) then treat it the same as // min_val for the purposes of the calculation that follows: // if(a < min_val) a = min_val; if(b < min_val) b = min_val; return (std::max)(fabs((a - b) / a), fabs((a - b) / b)); } #if defined(macintosh) || defined(__APPLE__) || defined(__APPLE_CC__) template <> inline boost::math::tools::promote_args::type relative_difference(const double& arg_a, const double& arg_b) { BOOST_MATH_STD_USING double a = arg_a; double b = arg_b; // // On Mac OS X we evaluate "double" functions at "long double" precision, // but "long double" actually has a very slightly narrower range than "double"! // Therefore use the range of "long double" as our limits since results outside // that range may have been truncated to 0 or INF: // double min_val = (std::max)((double)tools::min_value(), tools::min_value()); double max_val = (std::min)((double)tools::max_value(), tools::max_value()); // Screen out NaN's first, if either value is a NaN then the distance is "infinite": if((boost::math::isnan)(a) || (boost::math::isnan)(b)) return max_val; // Screen out infinites: if(fabs(b) > max_val) { if(fabs(a) > max_val) return 0; // one infinity is as good as another! else return max_val; // one infinity and one finite value implies infinite difference } else if(fabs(a) > max_val) return max_val; // one infinity and one finite value implies infinite difference // // If the values have different signs, treat as infinite difference: // if(((a < 0) != (b < 0)) && (a != 0) && (b != 0)) return max_val; a = fabs(a); b = fabs(b); // // Now deal with zero's, if one value is zero (or denorm) then treat it the same as // min_val for the purposes of the calculation that follows: // if(a < min_val) a = min_val; if(b < min_val) b = min_val; return (std::max)(fabs((a - b) / a), fabs((a - b) / b)); } #endif template inline typename boost::math::tools::promote_args::type epsilon_difference(const T& arg_a, const U& arg_b) { typedef typename boost::math::tools::promote_args::type result_type; result_type r = relative_difference(arg_a, arg_b); if(tools::max_value() * boost::math::tools::epsilon() < r) return tools::max_value(); return r / boost::math::tools::epsilon(); } } // namespace math } // namespace boost #endif