mirror of
https://github.com/boostorg/safe_numerics.git
synced 2026-02-09 11:22:23 +00:00
452 lines
14 KiB
C++
452 lines
14 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 "safe_common.hpp"
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#include "checked_result.hpp"
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#include "interval.hpp"
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#include "safe_range.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, class P, class E>
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struct defer_signed_lazily {
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using type = boost::numeric::safe_signed_range<Min, Max, P, E>;
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};
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template<typename T, T Min, T Max, class P, class E>
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struct defer_unsigned_lazily {
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using type = boost::numeric::safe_unsigned_range<Min, Max, P, E>;
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};
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template<typename T, T Min, T Max, class P, class E>
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using safe_range =
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typename boost::mpl::if_<
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std::is_signed<T>,
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defer_signed_lazily<T, Min, Max, P, E>,
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defer_unsigned_lazily<T, Min, Max, P, E>
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>::type;
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U, typename P, typename E>
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struct addition_result {
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typedef typename base_type<T>::type base_type_t;
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typedef typename base_type<U>::type base_type_u;
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constexpr static const interval<base_type_t> t = {
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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<base_type_u> u = {
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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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typedef calculate_max_t<T, U> max_t;
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constexpr static const checked_result<interval< max_t>> r
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= add<max_t>(t, u);
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constexpr static const interval< max_t> default_interval{};
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constexpr static const interval<max_t> result_interval =
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r.no_exception() ?
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static_cast<interval<max_t>>(r)
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:
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default_interval
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;
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typedef typename safe_range<
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max_t,
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result_interval.l,
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result_interval.u,
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P,
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E
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>::type type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U, typename P, typename E>
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struct subtraction_result {
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typedef typename base_type<T>::type base_type_t;
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typedef typename base_type<U>::type base_type_u;
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constexpr static const interval<base_type_t> t = {
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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<base_type_u> u = {
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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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typedef calculate_max_t<T, U> max_t;
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constexpr static const checked_result<interval< max_t>> r
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= subtract<max_t>(t, u);
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constexpr static const interval< max_t> default_interval{};
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constexpr static const interval<max_t> result_interval =
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r.no_exception() ?
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static_cast<interval<max_t>>(r)
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:
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default_interval
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;
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typedef typename safe_range<
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max_t,
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result_interval.l,
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result_interval.u,
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P,
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E
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>::type type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U, typename P, typename E>
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struct multiplication_result {
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typedef typename base_type<T>::type base_type_t;
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typedef typename base_type<U>::type base_type_u;
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constexpr static const interval<base_type_t> t = {
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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<base_type_u> u = {
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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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typedef calculate_max_t<T, U> max_t;
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// typedef print<max_t> p_max_t;
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constexpr static const checked_result<interval< max_t>> r
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{multiply<max_t>(t, u)};
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constexpr static const interval<max_t> default_interval{};
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constexpr static const interval<max_t> result_interval =
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r.no_exception() ?
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static_cast<interval<max_t>>(r)
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:
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default_interval
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;
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typedef typename safe_range<
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max_t,
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result_interval.l,
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result_interval.u,
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P,
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E
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>::type type;
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};
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///////////////////////////////////////////////////////////////////////
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template<class T, class U>
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constexpr static int bits(){
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// figure number of bits in quotient
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return std::min(
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std::numeric_limits<T>::digits
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+ 1 // one guard bit to cover u == -1 & t = numeric_limits<T>::min()
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+ 1 // one sign bit
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,
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std::numeric_limits<std::intmax_t>::digits
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+ 1 // one sign bit
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);
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}
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template<typename T, typename U, typename P, typename E>
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struct division_result {
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typedef typename base_type<T>::type base_type_t;
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static_assert(
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std::is_literal_type< interval<base_type_t> >::value,
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"interval<base_type_t> is not literal type"
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);
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typedef typename base_type<U>::type base_type_u;
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static_assert(
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std::is_literal_type< interval<base_type_u> >::value,
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"interval<base_type_u> is not tliteral type"
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);
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constexpr static interval<base_type_t> t {
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interval<base_type_t>(
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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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};
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constexpr static interval<base_type_u> u {
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interval<base_type_u>(
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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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};
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using base_type_r = typename boost::mpl::if_c<
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std::numeric_limits<base_type_t>::is_signed
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|| std::numeric_limits<base_type_u>::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<base_type_r>> r {
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divide_nz<base_type_r>(t, u)
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};
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constexpr static const interval<base_type_r> default_interval{};
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constexpr static const interval<base_type_r> result_interval {
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r.no_exception() ?
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static_cast<interval<base_type_r>>(r)
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:
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default_interval
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};
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typedef typename safe_range<
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base_type_r,
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result_interval.l,
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result_interval.u,
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P,
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E
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>::type 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, typename P, typename E>
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struct modulus_result {
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typedef typename base_type<T>::type base_type_t;
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static_assert(
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std::is_literal_type< interval<base_type_t> >::value,
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"interval<base_type_t> is not literal type"
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);
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typedef typename base_type<U>::type base_type_u;
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static_assert(
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std::is_literal_type< interval<base_type_u> >::value,
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"interval<base_type_u> is not tliteral type"
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);
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constexpr static const interval<base_type_t> t {
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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<base_type_u> u {
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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 base_type_r = std::make_unsigned_t<base_type_u>;
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constexpr static const checked_result<interval<base_type_r>> r
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{ modulus_nz<base_type_r>(t, u) };
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constexpr static const interval<base_type_r> default_interval{};
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constexpr static const interval<base_type_r> result_interval =
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r.no_exception() ?
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static_cast<interval<base_type_r>>(r)
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:
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default_interval
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;
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typedef typename safe_range<
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base_type_r,
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result_interval.l,
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result_interval.u,
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P,
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E
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>::type 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, typename P, typename E>
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struct left_shift_result {
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typedef typename base_type<T>::type t_base_type;
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typedef typename base_type<U>::type u_base_type;
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constexpr static const interval<t_base_type> t = {
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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 = {
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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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typedef calculate_max_t<T, U> max_t;
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constexpr static const checked_result<interval< max_t>> r
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= left_shift<max_t>(t, u);
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constexpr static const interval< max_t> default_interval{};
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constexpr static const interval<max_t> result_interval =
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r.no_exception() ?
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static_cast<interval<max_t>>(r)
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:
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default_interval
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;
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typedef typename safe_range<
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max_t,
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result_interval.l,
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result_interval.u,
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P,
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E
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>::type type;
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};
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///////////////////////////////////////////////////////////////////////
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template<typename T, typename U, typename P, typename E>
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struct right_shift_result {
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typedef typename base_type<T>::type t_base_type;
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typedef typename base_type<U>::type u_base_type;
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constexpr static const interval<t_base_type> t = {
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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 = {
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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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typedef calculate_max_t<T, U> max_t;
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constexpr static const checked_result<interval< max_t>> r
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= right_shift<max_t>(t, u);
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constexpr static const interval< max_t> default_interval{};
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constexpr static const interval<max_t> result_interval =
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r.no_exception() ?
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static_cast<interval<max_t>>(r)
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:
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default_interval
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;
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typedef typename safe_range<
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max_t,
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result_interval.l,
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result_interval.u,
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P,
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E
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>::type 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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