mirror of
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374 lines
13 KiB
C++
374 lines
13 KiB
C++
#ifndef BOOST_NUMERIC_AUTOMATIC_HPP
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#define BOOST_NUMERIC_AUTOMATIC_HPP
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// MS compatible compilers support #pragma once
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#if defined(_MSC_VER) && (_MSC_VER >= 1020)
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# pragma once
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#endif
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// Copyright (c) 2012 Robert Ramey
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//
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// Distributed under the Boost Software License, Version 1.0. (See
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// accompanying file LICENSE_1_0.txt or copy at
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// http://www.boost.org/LICENSE_1_0.txt)
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// policy which creates results types equal to that of C++ promotions.
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// Using the policy will permit the program to build and run in release
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// mode which is identical to that in debug mode except for the fact
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// that errors aren't trapped.
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#include <limits>
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#include <cstdint> // (u)intmax_t,
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#include <type_traits> // true_type, false_type, is_same
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#include <boost/mpl/if.hpp>
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#include "utility.hpp"
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#include "safe_common.hpp"
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#include "checked_result.hpp"
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#include "interval.hpp"
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namespace boost {
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namespace numeric {
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struct automatic {
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// section 4.13 integer conversion rank
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template<class T>
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using rank =
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typename boost::mpl::if_c<
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sizeof(char) == sizeof(T),
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std::integral_constant<int, 1>,
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typename boost::mpl::if_c<
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sizeof(short) == sizeof(T),
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std::integral_constant<int, 2>,
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typename boost::mpl::if_c<
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sizeof(int) == sizeof(T),
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std::integral_constant<int, 3>,
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typename boost::mpl::if_c<
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sizeof(long) == sizeof(T),
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std::integral_constant<int, 4>,
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typename boost::mpl::if_c<
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sizeof(long long) == sizeof(T),
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std::integral_constant<int, 5>,
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void
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>::type >::type >::type >::type >::type;
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// note presumption that T & U don't have he same sign
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// if that's not true, these won't work
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template<class T, class U>
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using select_signed = typename boost::mpl::if_c<
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std::numeric_limits<T>::is_signed,
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T,
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U
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>::type;
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template<class T, class U>
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using select_unsigned = typename boost::mpl::if_c<
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std::numeric_limits<T>::is_signed,
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U,
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T
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>::type;
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template<class T, class U>
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using calculate_max_t =
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typename boost::mpl::if_c<
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// clause 1 - if both operands have the same sign
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std::numeric_limits<T>::is_signed
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== std::numeric_limits<U>::is_signed,
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// use that sign
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typename boost::mpl::if_c<
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std::numeric_limits<T>::is_signed,
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std::intmax_t,
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std::uintmax_t
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>::type,
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// clause 2 - otherwise if the rank of the unsigned type exceeds
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// the rank of the of the maximum signed type
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typename boost::mpl::if_c<
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(rank< select_unsigned<T, U>>::value
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> rank< std::intmax_t >::value),
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// use unsigned type
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std::uintmax_t,
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// clause 3 - otherwise if the type of the signed integer type can
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// represent all the values of the unsigned type
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typename boost::mpl::if_c<
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std::numeric_limits< std::intmax_t >::digits >=
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std::numeric_limits< select_unsigned<T, U> >::digits,
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// use signed type
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std::intmax_t,
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// clause 4 - otherwise use unsigned version of the signed type
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std::uintmax_t
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>::type >::type >::type;
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template<typename T, T Min, T Max>
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struct defer_stored_signed_lazily {
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using type = signed_stored_type<Min, Max>;
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};
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template<typename T, T Min, T Max>
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struct defer_stored_unsigned_lazily {
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using type = unsigned_stored_type<Min, Max>;
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};
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template<typename T, T Min, T Max>
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using result_type =
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typename boost::mpl::if_<
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std::is_signed<T>,
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defer_stored_signed_lazily<T, Min, Max>,
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defer_stored_unsigned_lazily<T, Min, Max>
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>::type;
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct addition_result {
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using result_base_type = calculate_max_t<T, U>;
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using t_base_type = typename base_type<T>::type;
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using u_base_type = typename base_type<U>::type;
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// filter out case were overflow cannot occur
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// note: subtle trickery. Suppose t is safe_range<MIN, ..>. Then
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// std::numeric_limits<T>::min() will be safe_range<MIN with a value of MIN
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// Use base_value(T) ( which equals MIN ) to create a new interval. Same
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// for MAX. Now
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constexpr static const interval<t_base_type> t_interval{
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base_value(std::numeric_limits<T>::min()),
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base_value(std::numeric_limits<T>::max())
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};
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constexpr static const interval<u_base_type> u_interval{
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base_value(std::numeric_limits<U>::min()),
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base_value(std::numeric_limits<U>::max())
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};
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// when we add the temporary intervals above, we'll get a new interval
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// with the correct range for the sum !
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constexpr static const checked_result<interval<result_base_type>> r_interval
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= add<result_base_type>(t_interval, u_interval);
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constexpr static const interval<result_base_type> result_interval =
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r_interval.no_exception() ?
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static_cast<interval<result_base_type>>(r_interval)
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:
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interval<result_base_type>{}
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;
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using type = typename result_type<
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result_base_type,
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result_interval.l,
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result_interval.u
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>::type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct subtraction_result {
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// subtraction can result in negative result regardless of the
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// operand types !
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using result_base_type = std::intmax_t;
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using t_base_type = typename base_type<T>::type;
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using u_base_type = typename base_type<U>::type;
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constexpr static const interval<t_base_type> t_interval{
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base_value(std::numeric_limits<T>::min()),
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base_value(std::numeric_limits<T>::max())
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};
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constexpr static const interval<u_base_type> u_interval{
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base_value(std::numeric_limits<U>::min()),
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base_value(std::numeric_limits<U>::max())
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};
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constexpr static const checked_result<interval<result_base_type>> r_interval
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= subtract<result_base_type>(t_interval, u_interval);
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constexpr static const interval<result_base_type> result_interval =
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r_interval.no_exception() ?
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static_cast<interval<result_base_type>>(r_interval)
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:
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interval<result_base_type>{}
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;
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using type = typename result_type<
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result_base_type,
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result_interval.l,
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result_interval.u
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>::type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct multiplication_result {
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using result_base_type = calculate_max_t<T, U>;
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using t_base_type = typename base_type<T>::type;
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using u_base_type = typename base_type<U>::type;
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constexpr static const interval<t_base_type> t_interval{
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base_value(std::numeric_limits<T>::min()),
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base_value(std::numeric_limits<T>::max())
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};
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constexpr static const interval<u_base_type> u_interval{
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base_value(std::numeric_limits<U>::min()),
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base_value(std::numeric_limits<U>::max())
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};
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constexpr static const checked_result<interval<result_base_type>> r_interval
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= multiply<result_base_type>(t_interval, u_interval);
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constexpr static const interval<result_base_type> result_interval =
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r_interval.no_exception() ?
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static_cast<interval<result_base_type>>(r_interval)
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:
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interval<result_base_type>{}
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;
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using type = typename result_type<
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result_base_type,
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result_interval.l,
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result_interval.u
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>::type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct division_result {
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using t_base_type = typename base_type<T>::type;
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using u_base_type = typename base_type<U>::type;
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constexpr static const interval<t_base_type> t_interval{
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base_value(std::numeric_limits<T>::min()),
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base_value(std::numeric_limits<T>::max())
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};
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constexpr static const interval<u_base_type> u_interval{
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base_value(std::numeric_limits<U>::min()),
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base_value(std::numeric_limits<U>::max())
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};
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using result_base_type = typename boost::mpl::if_c<
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std::numeric_limits<t_base_type>::is_signed
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|| std::numeric_limits<u_base_type>::is_signed,
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std::intmax_t,
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std::uintmax_t
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>::type;
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constexpr static checked_result<interval<result_base_type>> r {
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divide_nz<result_base_type>(t_interval, u_interval)
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};
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constexpr static const interval<result_base_type> result_interval {
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r.no_exception() ?
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static_cast<interval<result_base_type>>(r)
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:
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interval<result_base_type>{}
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};
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using type = typename result_type<
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result_base_type,
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result_interval.l,
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result_interval.u
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>::type;
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};
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// forward to correct divide implementation
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template<class R, class T, class U>
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checked_result<R>
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static constexpr divide(
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const T & t,
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const U & u
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){
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return checked::divide_automatic<R>(t, u);
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}
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct modulus_result {
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using t_base_type = typename base_type<T>::type;
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using u_base_type = typename base_type<U>::type;
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constexpr static const interval<t_base_type> t_interval{
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base_value(std::numeric_limits<T>::min()),
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base_value(std::numeric_limits<T>::max())
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};
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constexpr static const interval<u_base_type> u_interval{
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base_value(std::numeric_limits<U>::min()),
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base_value(std::numeric_limits<U>::max())
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};
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using r_base_type = std::make_unsigned_t<u_base_type>;
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constexpr static const checked_result<interval<r_base_type>> r
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{ modulus_nz<r_base_type>(t_interval, u_interval) };
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constexpr static const interval<r_base_type> result_interval =
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r.no_exception() ?
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static_cast<interval<r_base_type>>(r)
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:
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interval<r_base_type>{}
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;
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using type = typename result_type<
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r_base_type,
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result_interval.l,
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result_interval.u
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>::type;
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};
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// forward to correct modulus implementation
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template<class R, class T, class U>
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checked_result<R>
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static constexpr modulus(
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const T & t,
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const U & u
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){
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return checked::modulus<R>(t, u);
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}
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct left_shift_result {
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using t_base_type = typename base_type<T>::type;
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constexpr static const interval<t_base_type> t_interval{
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base_value(std::numeric_limits<t_base_type>::min()),
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base_value(std::numeric_limits<t_base_type>::max())
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};
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using type = typename result_type<
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T,
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t_interval.l,
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t_interval.u
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>::type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct right_shift_result {
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using t_base_type = typename base_type<T>::type;
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constexpr static const interval<t_base_type> t_interval{
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base_value(std::numeric_limits<t_base_type>::min()),
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base_value(std::numeric_limits<t_base_type>::max())
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};
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using type = typename result_type<
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T,
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t_interval.l,
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t_interval.u
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>::type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U>
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struct bitwise_result {
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using t_base_type = typename base_type<T>::type;
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using u_base_type = typename base_type<U>::type;
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using type = typename boost::mpl::if_c<
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(sizeof(t_base_type) > sizeof(u_base_type)),
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t_base_type,
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u_base_type
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>::type;
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};
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};
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} // numeric
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} // boost
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#endif // BOOST_NUMERIC_AUTOMATIC_HPP
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