1 /* Boost interval/rounded_arith.hpp template implementation file 2 * 3 * Copyright 2002-2003 Hervé Brönnimann, Guillaume Melquiond, Sylvain Pion 4 * 5 * Distributed under the Boost Software License, Version 1.0. 6 * (See accompanying file LICENSE_1_0.txt or 7 * copy at http://www.boost.org/LICENSE_1_0.txt) 8 */ 9 10 #ifndef BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP 11 #define BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP 12 13 #include <boost/numeric/interval/rounding.hpp> 14 #include <boost/numeric/interval/detail/bugs.hpp> 15 #include <boost/config/no_tr1/cmath.hpp> 16 17 namespace boost { 18 namespace numeric { 19 namespace interval_lib { 20 21 /* 22 * Three classes of rounding: exact, std, opp 23 * See documentation for details. 24 */ 25 26 template<class T, class Rounding> 27 struct rounded_arith_exact: Rounding { initboost::numeric::interval_lib::rounded_arith_exact28 void init() { } conv_downboost::numeric::interval_lib::rounded_arith_exact29 template<class U> T conv_down(U const &v) { return v; } conv_upboost::numeric::interval_lib::rounded_arith_exact30 template<class U> T conv_up (U const &v) { return v; } add_downboost::numeric::interval_lib::rounded_arith_exact31 T add_down (const T& x, const T& y) { return x + y; } add_upboost::numeric::interval_lib::rounded_arith_exact32 T add_up (const T& x, const T& y) { return x + y; } sub_downboost::numeric::interval_lib::rounded_arith_exact33 T sub_down (const T& x, const T& y) { return x - y; } sub_upboost::numeric::interval_lib::rounded_arith_exact34 T sub_up (const T& x, const T& y) { return x - y; } mul_downboost::numeric::interval_lib::rounded_arith_exact35 T mul_down (const T& x, const T& y) { return x * y; } mul_upboost::numeric::interval_lib::rounded_arith_exact36 T mul_up (const T& x, const T& y) { return x * y; } div_downboost::numeric::interval_lib::rounded_arith_exact37 T div_down (const T& x, const T& y) { return x / y; } div_upboost::numeric::interval_lib::rounded_arith_exact38 T div_up (const T& x, const T& y) { return x / y; } medianboost::numeric::interval_lib::rounded_arith_exact39 T median (const T& x, const T& y) { return (x + y) / 2; } sqrt_downboost::numeric::interval_lib::rounded_arith_exact40 T sqrt_down(const T& x) 41 { BOOST_NUMERIC_INTERVAL_using_math(sqrt); return sqrt(x); } sqrt_upboost::numeric::interval_lib::rounded_arith_exact42 T sqrt_up (const T& x) 43 { BOOST_NUMERIC_INTERVAL_using_math(sqrt); return sqrt(x); } int_downboost::numeric::interval_lib::rounded_arith_exact44 T int_down (const T& x) 45 { BOOST_NUMERIC_INTERVAL_using_math(floor); return floor(x); } int_upboost::numeric::interval_lib::rounded_arith_exact46 T int_up (const T& x) 47 { BOOST_NUMERIC_INTERVAL_using_math(ceil); return ceil(x); } 48 }; 49 50 template<class T, class Rounding> 51 struct rounded_arith_std: Rounding { 52 # define BOOST_DN(EXPR) this->downward(); return this->force_rounding(EXPR) 53 # define BOOST_NR(EXPR) this->to_nearest(); return this->force_rounding(EXPR) 54 # define BOOST_UP(EXPR) this->upward(); return this->force_rounding(EXPR) initboost::numeric::interval_lib::rounded_arith_std55 void init() { } conv_downboost::numeric::interval_lib::rounded_arith_std56 template<class U> T conv_down(U const &v) { BOOST_DN(v); } conv_upboost::numeric::interval_lib::rounded_arith_std57 template<class U> T conv_up (U const &v) { BOOST_UP(v); } add_downboost::numeric::interval_lib::rounded_arith_std58 T add_down(const T& x, const T& y) { BOOST_DN(x + y); } sub_downboost::numeric::interval_lib::rounded_arith_std59 T sub_down(const T& x, const T& y) { BOOST_DN(x - y); } mul_downboost::numeric::interval_lib::rounded_arith_std60 T mul_down(const T& x, const T& y) { BOOST_DN(x * y); } div_downboost::numeric::interval_lib::rounded_arith_std61 T div_down(const T& x, const T& y) { BOOST_DN(x / y); } add_upboost::numeric::interval_lib::rounded_arith_std62 T add_up (const T& x, const T& y) { BOOST_UP(x + y); } sub_upboost::numeric::interval_lib::rounded_arith_std63 T sub_up (const T& x, const T& y) { BOOST_UP(x - y); } mul_upboost::numeric::interval_lib::rounded_arith_std64 T mul_up (const T& x, const T& y) { BOOST_UP(x * y); } div_upboost::numeric::interval_lib::rounded_arith_std65 T div_up (const T& x, const T& y) { BOOST_UP(x / y); } medianboost::numeric::interval_lib::rounded_arith_std66 T median(const T& x, const T& y) { BOOST_NR((x + y) / 2); } sqrt_downboost::numeric::interval_lib::rounded_arith_std67 T sqrt_down(const T& x) 68 { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_DN(sqrt(x)); } sqrt_upboost::numeric::interval_lib::rounded_arith_std69 T sqrt_up (const T& x) 70 { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_UP(sqrt(x)); } int_downboost::numeric::interval_lib::rounded_arith_std71 T int_down(const T& x) { this->downward(); return this->to_int(x); } int_upboost::numeric::interval_lib::rounded_arith_std72 T int_up (const T& x) { this->upward(); return this->to_int(x); } 73 # undef BOOST_DN 74 # undef BOOST_NR 75 # undef BOOST_UP 76 }; 77 78 template<class T, class Rounding> 79 struct rounded_arith_opp: Rounding { initboost::numeric::interval_lib::rounded_arith_opp80 void init() { this->upward(); } 81 # define BOOST_DN(EXPR) \ 82 this->downward(); \ 83 T r = this->force_rounding(EXPR); \ 84 this->upward(); \ 85 return r 86 # define BOOST_NR(EXPR) \ 87 this->to_nearest(); \ 88 T r = this->force_rounding(EXPR); \ 89 this->upward(); \ 90 return r 91 # define BOOST_UP(EXPR) return this->force_rounding(EXPR) 92 # define BOOST_UP_NEG(EXPR) return -this->force_rounding(EXPR) conv_downboost::numeric::interval_lib::rounded_arith_opp93 template<class U> T conv_down(U const &v) { BOOST_UP_NEG(-v); } conv_upboost::numeric::interval_lib::rounded_arith_opp94 template<class U> T conv_up (U const &v) { BOOST_UP(v); } add_downboost::numeric::interval_lib::rounded_arith_opp95 T add_down(const T& x, const T& y) { BOOST_UP_NEG((-x) - y); } sub_downboost::numeric::interval_lib::rounded_arith_opp96 T sub_down(const T& x, const T& y) { BOOST_UP_NEG(y - x); } mul_downboost::numeric::interval_lib::rounded_arith_opp97 T mul_down(const T& x, const T& y) { BOOST_UP_NEG(x * (-y)); } div_downboost::numeric::interval_lib::rounded_arith_opp98 T div_down(const T& x, const T& y) { BOOST_UP_NEG(x / (-y)); } add_upboost::numeric::interval_lib::rounded_arith_opp99 T add_up (const T& x, const T& y) { BOOST_UP(x + y); } sub_upboost::numeric::interval_lib::rounded_arith_opp100 T sub_up (const T& x, const T& y) { BOOST_UP(x - y); } mul_upboost::numeric::interval_lib::rounded_arith_opp101 T mul_up (const T& x, const T& y) { BOOST_UP(x * y); } div_upboost::numeric::interval_lib::rounded_arith_opp102 T div_up (const T& x, const T& y) { BOOST_UP(x / y); } medianboost::numeric::interval_lib::rounded_arith_opp103 T median (const T& x, const T& y) { BOOST_NR((x + y) / 2); } sqrt_downboost::numeric::interval_lib::rounded_arith_opp104 T sqrt_down(const T& x) 105 { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_DN(sqrt(x)); } sqrt_upboost::numeric::interval_lib::rounded_arith_opp106 T sqrt_up (const T& x) 107 { BOOST_NUMERIC_INTERVAL_using_math(sqrt); BOOST_UP(sqrt(x)); } int_downboost::numeric::interval_lib::rounded_arith_opp108 T int_down(const T& x) { return -this->to_int(-x); } int_upboost::numeric::interval_lib::rounded_arith_opp109 T int_up (const T& x) { return this->to_int(x); } 110 # undef BOOST_DN 111 # undef BOOST_NR 112 # undef BOOST_UP 113 # undef BOOST_UP_NEG 114 }; 115 116 } // namespace interval_lib 117 } // namespace numeric 118 } // namespace boost 119 120 #endif // BOOST_NUMERIC_INTERVAL_ROUNDED_ARITH_HPP 121