/* Boost interval/rounded_arith.hpp template implementation file * * Copyright 2002-2003 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion * * Distributed under 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_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP #define BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP #include <boost/numeric/interval/rounding.hpp> #include <boost/numeric/interval/detail/bugs.hpp> #include <boost/config/no_tr1/cmath.hpp> namespace boost { namespace numeric { namespace interval_lib { /* * Three classes of rounding: exact, std, opp * See documentation for details. */ template<class T, class Rounding> struct rounded_arith_exact: Rounding { void init() { } template<class U> T conv_down(U const &v) { return v; } template<class U> T conv_up (U const &v) { return v; } T add_down (const T& x, const T& y) { return x + y; } T add_up (const T& x, const T& y) { return x + y; } T sub_down (const T& x, const T& y) { return x - y; } T sub_up (const T& x, const T& y) { return x - y; } T mul_down (const T& x, const T& y) { return x * y; } T mul_up (const T& x, const T& y) { return x * y; } T div_down (const T& x, const T& y) { return x / y; } T div_up (const T& x, const T& y) { return x / y; } T median (const T& x, const T& y) { return (x + y) / 2; } T sqrt_down(const T& x) { BOOST_NUMERIC_INTERVAL_using_math(sqrt); return sqrt(x); } T sqrt_up (const T& x) { BOOST_NUMERIC_INTERVAL_using_math(sqrt); return sqrt(x); } T int_down (const T& x) { BOOST_NUMERIC_INTERVAL_using_math(floor); return floor(x); } T int_up (const T& x) { BOOST_NUMERIC_INTERVAL_using_math(ceil); return ceil(x); } }; template<class T, class Rounding> struct rounded_arith_std: Rounding { # define BOOST_DN(EXPR) this->downward(); return this->force_rounding(EXPR) # define BOOST_NR(EXPR) this->to_nearest(); return this->force_rounding(EXPR) # define BOOST_UP(EXPR) this->upward(); return this->force_rounding(EXPR) void init() { } template<class U> T conv_down(U const &v) { BOOST_DN(v); } template<class U> T conv_up (U const &v) { BOOST_UP(v); } T add_down(const T& x, const T& y) { BOOST_DN(x + y); } T sub_down(const T& x, const T& y) { BOOST_DN(x - y); } T mul_down(const T& x, const T& y) { BOOST_DN(x * y); } T div_down(const T& x, const T& y) { BOOST_DN(x / y); } T add_up (const T& x, const T& y) { BOOST_UP(x + y); } T sub_up (const T& x, const T& y) { BOOST_UP(x - y); } T mul_up (const T& x, const T& y) { BOOST_UP(x * y); } T div_up (const T& x, const T& y) { BOOST_UP(x / y); } T median(const T& x, const T& y) { BOOST_NR((x + y) / 2); } T sqrt_down(const T& x) { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_DN(sqrt(x)); } T sqrt_up (const T& x) { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_UP(sqrt(x)); } T int_down(const T& x) { this->downward(); return this->to_int(x); } T int_up (const T& x) { this->upward(); return this->to_int(x); } # undef BOOST_DN # undef BOOST_NR # undef BOOST_UP }; template<class T, class Rounding> struct rounded_arith_opp: Rounding { void init() { this->upward(); } # define BOOST_DN(EXPR) \ this->downward(); \ T r = this->force_rounding(EXPR); \ this->upward(); \ return r # define BOOST_NR(EXPR) \ this->to_nearest(); \ T r = this->force_rounding(EXPR); \ this->upward(); \ return r # define BOOST_UP(EXPR) return this->force_rounding(EXPR) # define BOOST_UP_NEG(EXPR) return -this->force_rounding(EXPR) template<class U> T conv_down(U const &v) { BOOST_UP_NEG(-v); } template<class U> T conv_up (U const &v) { BOOST_UP(v); } T add_down(const T& x, const T& y) { BOOST_UP_NEG((-x) - y); } T sub_down(const T& x, const T& y) { BOOST_UP_NEG(y - x); } T mul_down(const T& x, const T& y) { BOOST_UP_NEG(x * (-y)); } T div_down(const T& x, const T& y) { BOOST_UP_NEG(x / (-y)); } T add_up (const T& x, const T& y) { BOOST_UP(x + y); } T sub_up (const T& x, const T& y) { BOOST_UP(x - y); } T mul_up (const T& x, const T& y) { BOOST_UP(x * y); } T div_up (const T& x, const T& y) { BOOST_UP(x / y); } T median (const T& x, const T& y) { BOOST_NR((x + y) / 2); } T sqrt_down(const T& x) { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_DN(sqrt(x)); } T sqrt_up (const T& x) { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_UP(sqrt(x)); } T int_down(const T& x) { return -this->to_int(-x); } T int_up (const T& x) { return this->to_int(x); } # undef BOOST_DN # undef BOOST_NR # undef BOOST_UP # undef BOOST_UP_NEG }; } // namespace interval_lib } // namespace numeric } // namespace boost #endif // BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP