ext-boost/boost/safe_numerics/automatic.hpp

480 lines
17 KiB
C++

#ifndef BOOST_NUMERIC_AUTOMATIC_HPP
#define BOOST_NUMERIC_AUTOMATIC_HPP
// Copyright (c) 2012 Robert Ramey
//
// 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)
// policy which creates expanded results types designed
// to avoid overflows.
#include <limits>
#include <cstdint> // (u)intmax_t,
#include <type_traits> // conditional
#include <boost/integer.hpp>
#include "safe_common.hpp"
#include "checked_result.hpp"
#include "checked_default.hpp"
#include "checked_integer.hpp"
#include "checked_result_operations.hpp"
#include "interval.hpp"
#include "utility.hpp"
namespace boost {
namespace safe_numerics {
struct automatic {
private:
// the following returns the "true" type. After calculating the new max and min
// these return the minimum size type which can hold the expected result.
struct defer_stored_signed_lazily {
template<std::intmax_t Min, std::intmax_t Max>
using type = utility::signed_stored_type<Min, Max>;
};
struct defer_stored_unsigned_lazily {
template<std::uintmax_t Min, std::uintmax_t Max>
using type = utility::unsigned_stored_type<Min, Max>;
};
template<typename T, T Min, T Max>
struct result_type {
using type = typename std::conditional<
std::numeric_limits<T>::is_signed,
defer_stored_signed_lazily,
defer_stored_unsigned_lazily
>::type::template type<Min, Max>;
};
public:
///////////////////////////////////////////////////////////////////////
template<typename T, typename U>
struct addition_result {
using temp_base_type = typename std::conditional<
// if both arguments are unsigned
! std::numeric_limits<T>::is_signed
&& ! std::numeric_limits<U>::is_signed,
// result is unsigned
std::uintmax_t,
// otherwise result is signed
std::intmax_t
>::type;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_interval_type u_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
constexpr static const r_interval_type r_interval = t_interval + u_interval;
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
template<typename T, typename U>
struct subtraction_result {
// result of subtraction are always signed.
using temp_base_type = intmax_t;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_interval_type u_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
constexpr static const r_interval_type r_interval = t_interval - u_interval;
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
template<typename T, typename U>
struct multiplication_result {
using temp_base_type = typename std::conditional<
// if both arguments are unsigned
! std::numeric_limits<T>::is_signed
&& ! std::numeric_limits<U>::is_signed,
// result is unsigned
std::uintmax_t,
// otherwise result is signed
std::intmax_t
>::type;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_interval_type u_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
constexpr static const r_interval_type r_interval = t_interval * u_interval;
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
template<typename T, typename U>
struct division_result {
using temp_base_type = typename std::conditional<
// if both arguments are unsigned
! std::numeric_limits<T>::is_signed
&& ! std::numeric_limits<U>::is_signed,
// result is unsigned
std::uintmax_t,
// otherwise result is signed
std::intmax_t
>::type;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_interval_type u_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
constexpr static const r_interval_type rx(){
if(u_interval.u < r_type(0)
|| u_interval.l > r_type(0))
return t_interval / u_interval;
return utility::minmax(
std::initializer_list<r_type> {
t_interval.l / u_interval.l,
t_interval.l / r_type(-1),
t_interval.l / r_type(1),
t_interval.l / u_interval.u,
t_interval.u / u_interval.l,
t_interval.u / r_type(-1),
t_interval.u / r_type(1),
t_interval.u / u_interval.u,
}
);
}
constexpr static const r_interval_type r_interval = rx();
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
template<typename T, typename U>
struct modulus_result {
using temp_base_type = typename std::conditional<
// if both arguments are unsigned
! std::numeric_limits<T>::is_signed
&& ! std::numeric_limits<U>::is_signed,
// result is unsigned
std::uintmax_t,
// otherwise result is signed
std::intmax_t
>::type;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_interval_type u_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
constexpr static const r_interval_type rx(){
if(u_interval.u < r_type(0)
|| u_interval.l > r_type(0))
return t_interval / u_interval;
return utility::minmax(
std::initializer_list<r_type> {
t_interval.l % u_interval.l,
t_interval.l % r_type(-1),
t_interval.l % r_type(1),
t_interval.l % u_interval.u,
t_interval.u % u_interval.l,
t_interval.u % r_type(-1),
t_interval.u % r_type(1),
t_interval.u % u_interval.u,
}
);
}
constexpr static const r_interval_type r_interval = rx();
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
// note: comparison_result (<, >, ...) is special.
// The return value is always a bool. The type returned here is
// the intermediate type applied to make the values comparable.
template<typename T, typename U>
struct comparison_result {
using temp_base_type = typename std::conditional<
// if both arguments are unsigned
! std::numeric_limits<T>::is_signed
&& ! std::numeric_limits<U>::is_signed,
// result is unsigned
std::uintmax_t,
// otherwise result is signed
std::intmax_t
>::type;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_interval_type u_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
// workaround some microsoft problem
#if 0
constexpr static r_type min(const r_type & t, const r_type & u){
// assert(! u.exception());
// assert(! t.exception());
return static_cast<bool>(t < u) ? t : u;
}
constexpr static r_type max(const r_type & t, const r_type & u){
// assert(! u.exception());
// assert(! t.exception());
return static_cast<bool>(t < u) ? u : t;
}
#endif
// union of two intervals
// note: we can't use t_interval | u_interval because it
// depends on max and min which in turn depend on < which in turn
// depends on implicit conversion of tribool to bool
constexpr static r_interval_type union_interval(
const r_interval_type & t,
const r_interval_type & u
){
//const r_type & rl = min(t.l, u.l);
const r_type & rmin = static_cast<bool>(t.l < u.l) ? t.l : u.l;
//const r_type & ru = max(t.u, u.u);
const r_type & rmax = static_cast<bool>(t.u < u.u) ? u.u : t.u;
return r_interval_type(rmin, rmax);
}
constexpr static const r_interval_type r_interval =
union_interval(t_interval, u_interval);
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
// shift operations
template<typename T, typename U>
struct left_shift_result {
using temp_base_type = typename std::conditional<
std::numeric_limits<T>::is_signed,
std::intmax_t,
std::uintmax_t
>::type;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_interval_type u_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
constexpr static const r_interval_type r_interval =
t_interval << u_interval;
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
template<typename T, typename U>
struct right_shift_result {
using temp_base_type = typename std::conditional<
std::numeric_limits<T>::is_signed,
std::intmax_t,
std::uintmax_t
>::type;
using r_type = checked_result<temp_base_type>;
using r_interval_type = interval<r_type>;
constexpr static const r_interval_type t_interval{
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::min())),
checked::cast<temp_base_type>(base_value(std::numeric_limits<T>::max()))
};
constexpr static const r_type u_min
= checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::min()));
constexpr static const r_interval_type u_interval{
u_min.exception()
? r_type(0)
: u_min,
checked::cast<temp_base_type>(base_value(std::numeric_limits<U>::max()))
};
constexpr static const r_interval_type r_interval = t_interval >> u_interval;
constexpr static auto rl = r_interval.l;
constexpr static auto ru = r_interval.u;
using type = typename result_type<
temp_base_type,
rl.exception()
? std::numeric_limits<temp_base_type>::min()
: static_cast<temp_base_type>(rl),
ru.exception()
? std::numeric_limits<temp_base_type>::max()
: static_cast<temp_base_type>(ru)
>::type;
};
///////////////////////////////////////////////////////////////////////
template<typename T, typename U>
struct bitwise_and_result {
using type = decltype(
typename base_type<T>::type()
& typename base_type<U>::type()
);
};
template<typename T, typename U>
struct bitwise_or_result {
using type = decltype(
typename base_type<T>::type()
| typename base_type<U>::type()
);
};
template<typename T, typename U>
struct bitwise_xor_result {
using type = decltype(
typename base_type<T>::type()
^ typename base_type<U>::type()
);
};
};
} // safe_numerics
} // boost
#endif // BOOST_NUMERIC_AUTOMATIC_HPP