diff -r 000000000000 -r bde4ae8d615e os/ossrv/ossrv_pub/boost_apis/boost/numeric/interval/arith2.hpp --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/os/ossrv/ossrv_pub/boost_apis/boost/numeric/interval/arith2.hpp Fri Jun 15 03:10:57 2012 +0200 @@ -0,0 +1,227 @@ +/* Boost interval/arith2.hpp template implementation file + * + * This header provides some auxiliary arithmetic + * functions: fmod, sqrt, square, pov, inverse and + * a multi-interval division. + * + * 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_ARITH2_HPP +#define BOOST_NUMERIC_INTERVAL_ARITH2_HPP + +#include +#include +#include +#include +#include +#include +#include +#include +#include + +namespace boost { +namespace numeric { + +template inline +interval fmod(const interval& x, + const interval& y) +{ + if (interval_lib::detail::test_input(x, y)) + return interval::empty(); + typename Policies::rounding rnd; + typedef typename interval_lib::unprotect >::type I; + T const &yb = interval_lib::user::is_neg(x.lower()) ? y.lower() : y.upper(); + T n = rnd.int_down(rnd.div_down(x.lower(), yb)); + return (const I&)x - n * (const I&)y; +} + +template inline +interval fmod(const interval& x, const T& y) +{ + if (interval_lib::detail::test_input(x, y)) + return interval::empty(); + typename Policies::rounding rnd; + typedef typename interval_lib::unprotect >::type I; + T n = rnd.int_down(rnd.div_down(x.lower(), y)); + return (const I&)x - n * I(y); +} + +template inline +interval fmod(const T& x, const interval& y) +{ + if (interval_lib::detail::test_input(x, y)) + return interval::empty(); + typename Policies::rounding rnd; + typedef typename interval_lib::unprotect >::type I; + T const &yb = interval_lib::user::is_neg(x) ? y.lower() : y.upper(); + T n = rnd.int_down(rnd.div_down(x, yb)); + return x - n * (const I&)y; +} + +namespace interval_lib { + +template inline +interval division_part1(const interval& x, + const interval& y, bool& b) +{ + typedef interval I; + b = false; + if (detail::test_input(x, y)) + return I::empty(); + if (zero_in(y)) + if (!user::is_zero(y.lower())) + if (!user::is_zero(y.upper())) + return detail::div_zero_part1(x, y, b); + else + return detail::div_negative(x, y.lower()); + else + if (!user::is_zero(y.upper())) + return detail::div_positive(x, y.upper()); + else + return I::empty(); + else + return detail::div_non_zero(x, y); +} + +template inline +interval division_part2(const interval& x, + const interval& y, bool b = true) +{ + if (!b) return interval::empty(); + return detail::div_zero_part2(x, y); +} + +template inline +interval multiplicative_inverse(const interval& x) +{ + typedef interval I; + if (detail::test_input(x)) + return I::empty(); + T one = static_cast(1); + typename Policies::rounding rnd; + if (zero_in(x)) { + typedef typename Policies::checking checking; + if (!user::is_zero(x.lower())) + if (!user::is_zero(x.upper())) + return I::whole(); + else + return I(checking::neg_inf(), rnd.div_up(one, x.lower()), true); + else + if (!user::is_zero(x.upper())) + return I(rnd.div_down(one, x.upper()), checking::pos_inf(), true); + else + return I::empty(); + } else + return I(rnd.div_down(one, x.upper()), rnd.div_up(one, x.lower()), true); +} + +namespace detail { + +template inline +T pow_dn(const T& x_, int pwr, Rounding& rnd) // x and pwr are positive +{ + T x = x_; + T y = (pwr & 1) ? x_ : static_cast(1); + pwr >>= 1; + while (pwr > 0) { + x = rnd.mul_down(x, x); + if (pwr & 1) y = rnd.mul_down(x, y); + pwr >>= 1; + } + return y; +} + +template inline +T pow_up(const T& x_, int pwr, Rounding& rnd) // x and pwr are positive +{ + T x = x_; + T y = (pwr & 1) ? x_ : static_cast(1); + pwr >>= 1; + while (pwr > 0) { + x = rnd.mul_up(x, x); + if (pwr & 1) y = rnd.mul_up(x, y); + pwr >>= 1; + } + return y; +} + +} // namespace detail +} // namespace interval_lib + +template inline +interval pow(const interval& x, int pwr) +{ + BOOST_USING_STD_MAX(); + using interval_lib::detail::pow_dn; + using interval_lib::detail::pow_up; + typedef interval I; + + if (interval_lib::detail::test_input(x)) + return I::empty(); + + if (pwr == 0) + if (interval_lib::user::is_zero(x.lower()) + && interval_lib::user::is_zero(x.upper())) + return I::empty(); + else + return I(static_cast(1)); + else if (pwr < 0) + return interval_lib::multiplicative_inverse(pow(x, -pwr)); + + typename Policies::rounding rnd; + + if (interval_lib::user::is_neg(x.upper())) { // [-2,-1] + T yl = pow_dn(static_cast(-x.upper()), pwr, rnd); + T yu = pow_up(static_cast(-x.lower()), pwr, rnd); + if (pwr & 1) // [-2,-1]^1 + return I(-yu, -yl, true); + else // [-2,-1]^2 + return I(yl, yu, true); + } else if (interval_lib::user::is_neg(x.lower())) { // [-1,1] + if (pwr & 1) { // [-1,1]^1 + return I(-pow_up(-x.lower(), pwr, rnd), pow_up(x.upper(), pwr, rnd), true); + } else { // [-1,1]^2 + return I(static_cast(0), pow_up(max BOOST_PREVENT_MACRO_SUBSTITUTION(static_cast(-x.lower()), x.upper()), pwr, rnd), true); + } + } else { // [1,2] + return I(pow_dn(x.lower(), pwr, rnd), pow_up(x.upper(), pwr, rnd), true); + } +} + +template inline +interval sqrt(const interval& x) +{ + typedef interval I; + if (interval_lib::detail::test_input(x) || interval_lib::user::is_neg(x.upper())) + return I::empty(); + typename Policies::rounding rnd; + T l = !interval_lib::user::is_pos(x.lower()) ? static_cast(0) : rnd.sqrt_down(x.lower()); + return I(l, rnd.sqrt_up(x.upper()), true); +} + +template inline +interval square(const interval& x) +{ + typedef interval I; + if (interval_lib::detail::test_input(x)) + return I::empty(); + typename Policies::rounding rnd; + const T& xl = x.lower(); + const T& xu = x.upper(); + if (interval_lib::user::is_neg(xu)) + return I(rnd.mul_down(xu, xu), rnd.mul_up(xl, xl), true); + else if (interval_lib::user::is_pos(x.lower())) + return I(rnd.mul_down(xl, xl), rnd.mul_up(xu, xu), true); + else + return I(static_cast(0), (-xl > xu ? rnd.mul_up(xl, xl) : rnd.mul_up(xu, xu)), true); +} + +} // namespace numeric +} // namespace boost + +#endif // BOOST_NUMERIC_INTERVAL_ARITH2_HPP