mirror of
https://github.com/boostorg/safe_numerics.git
synced 2026-02-11 12:02:30 +00:00
367 lines
12 KiB
C++
367 lines
12 KiB
C++
#ifndef BOOST_NUMERIC_CHECKED_HPP
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#define BOOST_NUMERIC_CHECKED_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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// contains operations for doing checked aritmetic on native
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// C++ types.
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#include "overflow.hpp"
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#include "safe_compare.hpp"
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#include "safe_cast.hpp"
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// we could have used decltype and auto for C++11 but we've decided
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// to use boost/typeof to be compatible with older compilers
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#include <boost/typeof/typeof.hpp>
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namespace boost {
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namespace numeric {
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namespace checked {
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namespace detail {
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template<bool TS, bool US>
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struct addition;
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// both arguments unsigned
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template<>
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struct addition<false, false> {
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template<class R, class T, class U>
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static constexpr bool overflow(const R & r, const T & t, const U & u){
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return boost::numeric::safe_compare::less_than(r, t)
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|| boost::numeric::safe_compare::less_than(r, u);
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}
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template<class T, class U>
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static constexpr bool addition_overflow(const T & t, const U & u){
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return overflow(t + u, t, u);
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}
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template<class R, class T, class U>
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static R add(const T & t, const U & u) {
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R tmp = t + u;
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if(overflow(tmp, t, u))
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boost::numeric::overflow("safe range addition result overflow");
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return tmp;
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}
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};
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// both arguments signed
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template<>
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struct addition<true, true> {
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template<class R, class T, class U>
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static constexpr bool overflow(const R & r, const T & t, const U & u){
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return boost::numeric::safe_compare::less_than(r, t)
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|| boost::numeric::safe_compare::less_than(r, u);
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}
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template<class T, class U>
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static constexpr bool addition_overflow(const T & t, const U & u){
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return overflow(t + u, t, u);
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}
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template<class R, class T, class U>
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static R add(const T & t, const U & u) {
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if(t > 0 && u > 0){
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R tmp = t + u;
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if(tmp < 0)
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boost::numeric::overflow("safe range addition result overflow");
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return tmp;
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}
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if(t < 0 && u < 0){
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R tmp = t + u;
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if(tmp >= 0)
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boost::numeric::overflow("safe range addition result underflow");
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return tmp;
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}
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return t + u;
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}
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};
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// T unsigned, U signed
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template<>
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struct addition<false, true> {
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template<class R, class T, class U>
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static R add(const T & t, const U & u){
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if(boost::numeric::is_unsigned<R>::value){
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if(u < 0)
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overflow("safe range right operand value altered");
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return addition<false, false>::add<R>(
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t,
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static_cast<typename boost::make_unsigned<T>::type>(u)
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);
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}
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else{
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if(u > 0){
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R tmp = t + u;
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if(tmp <= 0)
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overflow("safe range addition result overflow");
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return t + u;
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}
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}
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return t + u;
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}
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};
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// T signed, U unsigned
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template<>
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struct addition<true, false> {
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template<class R, class T, class U>
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static R add(const T & t, const U & u){
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return addition<false, true>::add<R>(u, t);
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}
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};
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} // detail
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template<class R, class T, class U>
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R add(const T & t, const U & u){
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return detail::addition<
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boost::is_unsigned<T>::value,
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boost::is_unsigned<U>::value
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>::template add<R>(
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t, u
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);
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}
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} // checked
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namespace detail {
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////////////////////////////////////////////////////
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// layer 0 - detect overflows / alteration at the
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// atomic operation level taking care to work around
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// otherwise undetect alterations in integers due
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// to machine architecture. Note presumption of twos
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// complement integer arithmetic
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/////////////////////////////
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// subtraction implementation
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template<bool TS, bool US>
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struct check_subtraction_overflow{};
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// both arguments signed
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template<>
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struct check_subtraction_overflow<true, true> {
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template<class T, class U>
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static BOOST_TYPEOF_TPL(T() + U())
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subtract(const T & t, const U & u){
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BOOST_AUTO_TPL(tmp, t - u);
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if(t > 0 && u < 0){
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if(tmp < 0)
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overflow("safe range subtraction result overflow");
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}
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if(t < 0 && u > 0)
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if(tmp >= 0){
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overflow("safe range subtraction result underflow");
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}
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return tmp;
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}
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};
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// both arguments unsigned
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template<>
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struct check_subtraction_overflow<false, false> {
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template<class T, class U>
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static BOOST_TYPEOF_TPL(T() + U())
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subtract(const T & t, const U & u) {
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if(safe_compare::less_than(t, u))
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overflow("safe range subtraction unsigned difference less than zero");
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return t - u;
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}
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};
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// T unsigned, U signed
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template<>
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struct check_subtraction_overflow<false, true> {
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template<class T, class U>
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static BOOST_TYPEOF_TPL(T() + U())
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subtract(const T & t, const U & u){
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typedef BOOST_TYPEOF_TPL(T() + U()) result_type;
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if(boost::numeric::is_unsigned<result_type>::value){
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if(u < 0)
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overflow("safe range left operand value altered");
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// u >= 0
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if(u > t)
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overflow("unsigned result is negative");
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}
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// result is signed
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return t - u;
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}
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};
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// T signed, U unsigned
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template<>
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struct check_subtraction_overflow<true, false> {
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template<class T, class U>
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static BOOST_TYPEOF_TPL(T() + U())
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subtract(const T & t, const U & u){
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typedef BOOST_TYPEOF_TPL(T() + U()) result_type;
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if(boost::numeric::is_unsigned<result_type>::value){
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return check_subtraction_overflow<false, false>::subtract(
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safe_cast<result_type>(t),
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safe_cast<result_type>(u)
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);
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}
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// result is signed
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return check_subtraction_overflow<true, true>::subtract(
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t,
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safe_cast<result_type>(u)
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);
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}
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};
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////////////////////////////////
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// multiplication implementation
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template<class T, class U>
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BOOST_TYPEOF_TPL(T() * U())
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check_multiplication_overflow(const T & t, const U & u){
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typedef BOOST_TYPEOF_TPL(T() * U()) result_type;
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char const * const msg = "safe range multiplication overflow";
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// presume that size of uintmax_t and intmax_t are the same
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typedef bits<boost::uintmax_t> available_bits;
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if(multiply_result_bits<T, U>::value
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<= boost::numeric::bits<result_type>::value)
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return t * u;
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if(multiply_result_bits<T, U>::value <= available_bits::value){
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typedef typename multiply_result_type<T, U>::type temp_type;
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temp_type tmp = static_cast<temp_type>(t) * temp_type(u);
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// the following works for both positive and negative results
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// and for both signed and unsigned numbers
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if(tmp > boost::integer_traits<result_type>::const_max)
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boost::numeric::overflow(msg);
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if(tmp < boost::integer_traits<result_type>::const_min)
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boost::numeric::overflow(msg);
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return static_cast<result_type>(tmp);
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}
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// when the there is no native type which can hold the product
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// use multible precision
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// t is factored as (a << temp_bits) + b
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// u is factored as (c << temp_bits) + d
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// so we use multi-precision:
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// a + b
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// c + d
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// -----
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// bd
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// ad
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// cb
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// ac
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// -----
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// ..
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if(boost::numeric::is_unsigned<result_type>::value
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&& (t < 0 || u < 0))
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overflow("conversion of negative value to unsigned");
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if(t == 1)
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return u;
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if(u == 1)
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return t;
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result_type rt = t;
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if(rt < 0){
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rt = ~rt + 1;
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// address
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if(rt < 0)
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overflow("overflow of negative value");
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}
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result_type ru = u;
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if(ru < 0){
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ru = ~ru + 1;
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// address
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if(ru < 0)
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overflow("overflow of negative value");
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}
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// check positive values for overflow
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// t is factored as (a << temp_bits) + b
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// u is factored as (c << temp_bits) + d
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// so we use multi-precision:
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// a + b
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// c + d
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// -----
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// bd
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// ad
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// cb
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// ac
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// -----
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// ..
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typedef boost::uintmax_t accumulator_type;
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const int temp_bits = bits<accumulator_type>::value / 2;
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typedef typename boost::uint_t<temp_bits>::least temp_type;
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temp_type a = (static_cast<accumulator_type>(rt) >> temp_bits);
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temp_type c = (static_cast<accumulator_type>(ru) >> temp_bits);
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if(0 != a && 0 != c)
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overflow(msg);
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temp_type b = static_cast<temp_type>(rt);
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if((static_cast<accumulator_type>(b) * static_cast<accumulator_type>(c) >> temp_bits) > 0)
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overflow(msg);
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temp_type d = static_cast<const temp_type>(ru);
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if(0 != (static_cast<accumulator_type>(a) * static_cast<accumulator_type>(d) >> temp_bits))
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overflow(msg);
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return t * u;
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}
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template<class T, class U>
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BOOST_TYPEOF_TPL(T() / U())
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check_division_overflow(const T & t, const U & u){
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if(0 == u)
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overflow("divide by zero");
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if(boost::numeric::is_signed<U>::value){
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// t unsigned, u signed
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if(boost::numeric::is_unsigned<T>::value){
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if(u < 0){
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overflow("conversion of negative value to unsigned");
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}
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}
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else{
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// both signed
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// pathological case: change sign on negative number so it overflows
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if(t == boost::integer_traits<T>::const_min && u == -1)
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overflow("overflow in result");
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}
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}
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// both unsigned
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// t signed, u unsigned
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return t / u;
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}
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template<class T, class U>
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BOOST_TYPEOF_TPL(T() / U())
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check_modulus_overflow(const T & t, const U & u){
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if(0 == u)
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overflow("modulus divide by zero");
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if(boost::numeric::is_signed<U>::value){
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// t unsigned, u signed
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if(boost::numeric::is_unsigned<T>::value){
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if(u < 0){
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overflow("conversion of negative value to unsigned");
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}
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}
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else{
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// both signed
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// pathological case: change sign on negative number so it overflows
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if(t == boost::integer_traits<T>::const_min && u == -1)
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overflow("overflow in result");
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}
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}
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// both unsigned
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// t signed, u unsigned
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return t % u;
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}
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} // detail
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} // numeric
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} // boost
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#endif // BOOST_NUMERIC__HPP
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