ext-boost/boost/safe_numerics/checked_integer.hpp

820 lines
26 KiB
C++

#ifndef BOOST_NUMERIC_CHECKED_INTEGER_HPP
#define BOOST_NUMERIC_CHECKED_INTEGER_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)
// contains operations for doing checked aritmetic on NATIVE
// C++ types.
#include <limits>
#include <type_traits> // is_integral, make_unsigned, enable_if
#include <algorithm> // std::max
#include "checked_result.hpp"
#include "checked_default.hpp"
#include "safe_compare.hpp"
#include "utility.hpp"
#include "exception.hpp"
namespace boost {
namespace safe_numerics {
// utility
template<bool tf>
using bool_type = typename std::conditional<tf, std::true_type, std::false_type>::type;
////////////////////////////////////////////////////
// layer 0 - implement safe operations for intrinsic integers
// Note presumption of twos complement integer arithmetic
// convert an integral value to some other integral type
template<
typename R,
R Min,
R Max,
typename T,
class F
>
struct heterogeneous_checked_operation<
R,
Min,
Max,
T,
F,
typename std::enable_if<
std::is_integral<R>::value
&& std::is_integral<T>::value
>::type
>{
////////////////////////////////////////////////////
// safe casting on primitive types
struct cast_impl_detail {
constexpr static checked_result<R>
cast_impl(
const T & t,
std::true_type, // R is signed
std::true_type // T is signed
){
// INT32-C Ensure that operations on signed
// integers do not overflow
return
boost::safe_numerics::safe_compare::greater_than(
t,
Max
) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"converted signed value too large"
)
:
boost::safe_numerics::safe_compare::less_than(
t,
Min
) ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"converted signed value too small"
)
:
checked_result<R>(static_cast<R>(t))
;
}
constexpr static checked_result<R>
cast_impl(
const T & t,
std::true_type, // R is signed
std::false_type // T is unsigned
){
// INT30-C Ensure that unsigned integer operations
// do not wrap
return
boost::safe_numerics::safe_compare::greater_than(
t,
Max
) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"converted unsigned value too large"
)
:
checked_result<R>(static_cast<R>(t))
;
}
constexpr static checked_result<R>
cast_impl(
const T & t,
std::false_type, // R is unsigned
std::false_type // T is unsigned
){
// INT32-C Ensure that operations on unsigned
// integers do not overflow
return
boost::safe_numerics::safe_compare::greater_than(
t,
Max
) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"converted unsigned value too large"
)
:
checked_result<R>(static_cast<R>(t))
;
}
constexpr static checked_result<R>
cast_impl(
const T & t,
std::false_type, // R is unsigned
std::true_type // T is signed
){
return
boost::safe_numerics::safe_compare::less_than(t, 0) ?
F::template invoke<safe_numerics_error::domain_error>(
"converted negative value to unsigned"
)
:
boost::safe_numerics::safe_compare::greater_than(
t,
Max
) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"converted signed value too large"
)
:
checked_result<R>(static_cast<R>(t))
;
}
}; // cast_impl_detail
constexpr static checked_result<R>
cast(const T & t){
return
cast_impl_detail::cast_impl(
t,
std::is_signed<R>(),
std::is_signed<T>()
);
}
};
// converting floating point value to integral type
template<
typename R,
R Min,
R Max,
typename T,
class F
>
struct heterogeneous_checked_operation<
R,
Min,
Max,
T,
F,
typename std::enable_if<
std::is_integral<R>::value
&& std::is_floating_point<T>::value
>::type
>{
constexpr static checked_result<R>
cast(const T & t){
return static_cast<R>(t);
}
};
// converting integral value to floating point type
// INT35-C. Use correct integer precisions
template<
typename R,
R Min,
R Max,
typename T,
class F
>
struct heterogeneous_checked_operation<
R,
Min,
Max,
T,
F,
typename std::enable_if<
std::is_floating_point<R>::value
&& std::is_integral<T>::value
>::type
>{
constexpr static checked_result<R>
cast(const T & t){
if(std::numeric_limits<R>::digits < std::numeric_limits<T>::digits){
if(utility::significant_bits(t) > std::numeric_limits<R>::digits){
return F::invoke(
safe_numerics_error::precision_overflow_error,
"keep precision"
);
}
}
return t;
}
};
// binary operations on primitive integer types
template<
typename R,
class F
>
struct checked_operation<R, F,
typename std::enable_if<
std::is_integral<R>::value
>::type
>{
////////////////////////////////////////////////////
// safe addition on primitive types
struct add_impl_detail {
// result unsigned
constexpr static checked_result<R> add(
const R t,
const R u,
std::false_type // R unsigned
){
return
// INT30-C. Ensure that unsigned integer operations do not wrap
std::numeric_limits<R>::max() - u < t ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"addition result too large"
)
:
checked_result<R>(t + u)
;
}
// result signed
constexpr static checked_result<R> add(
const R t,
const R u,
std::true_type // R signed
){
// INT32-C. Ensure that operations on signed integers do not result in overflow
return
// INT32-C. Ensure that operations on signed integers do not result in overflow
((u > 0) && (t > (std::numeric_limits<R>::max() - u))) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"addition result too large"
)
:
((u < 0) && (t < (std::numeric_limits<R>::min() - u))) ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"addition result too low"
)
:
checked_result<R>(t + u)
;
}
}; // add_impl_detail
constexpr static checked_result<R>
add(const R & t, const R & u){
return add_impl_detail::add(t, u, std::is_signed<R>());
}
////////////////////////////////////////////////////
// safe subtraction on primitive types
struct subtract_impl_detail {
// result unsigned
constexpr static checked_result<R> subtract(
const R t,
const R u,
std::false_type // R is unsigned
){
// INT30-C. Ensure that unsigned integer operations do not wrap
return
t < u ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"subtraction result cannot be negative"
)
:
checked_result<R>(t - u)
;
}
// result signed
constexpr static checked_result<R> subtract(
const R t,
const R u,
std::true_type // R is signed
){ // INT32-C
return
// INT32-C. Ensure that operations on signed integers do not result in overflow
((u > 0) && (t < (std::numeric_limits<R>::min() + u))) ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"subtraction result overflows result type"
)
:
((u < 0) && (t > (std::numeric_limits<R>::max() + u))) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"subtraction result overflows result type"
)
:
checked_result<R>(t - u)
;
}
}; // subtract_impl_detail
constexpr static checked_result<R> subtract(const R & t, const R & u){
return subtract_impl_detail::subtract(t, u, std::is_signed<R>());
}
////////////////////////////////////////////////////
// safe minus on primitive types
struct minus_impl_detail {
// result unsigned
constexpr static checked_result<R> minus(
const R t,
std::false_type // R is unsigned
){
return t > 0 ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"minus unsigned would be negative"
)
:
// t == 0
checked_result<R>(0)
;
}
// result signed
constexpr static checked_result<R> minus(
const R t,
std::true_type // R is signed
){ // INT32-C
return t == std::numeric_limits<R>::min() ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"subtraction result overflows result type"
)
:
checked_result<R>(-t)
;
}
}; // minus_impl_detail
constexpr static checked_result<R> minus(const R & t){
return minus_impl_detail::minus(t, std::is_signed<R>());
}
////////////////////////////////////////////////////
// safe multiplication on primitive types
struct multiply_impl_detail {
// result unsigned
constexpr static checked_result<R> multiply(
const R t,
const R u,
std::false_type, // R is unsigned
std::false_type // !(sizeochecked_result<R>R) > sizeochecked_result<R>std::uintmax_t) / 2)
){
// INT30-C
// fast method using intermediate result guaranteed not to overflow
// todo - replace std::uintmax_t with a size double the size of R
using i_type = std::uintmax_t;
return
static_cast<i_type>(t) * static_cast<i_type>(u)
> std::numeric_limits<R>::max() ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"multiplication overflow"
)
:
checked_result<R>(t * u)
;
}
constexpr static checked_result<R> multiply(
const R t,
const R u,
std::false_type, // R is unsigned
std::true_type // (sizeochecked_result<R>R) > sizeochecked_result<R>std::uintmax_t) / 2)
){
// INT30-C
return
u > 0 && t > std::numeric_limits<R>::max() / u ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"multiplication overflow"
)
:
checked_result<R>(t * u)
;
}
// result signed
constexpr static checked_result<R> multiply(
const R t,
const R u,
std::true_type, // R is signed
std::false_type // ! (sizeochecked_result<R>R) > (sizeochecked_result<R>std::intmax_t) / 2))
){
// INT30-C
// fast method using intermediate result guaranteed not to overflow
// todo - replace std::intmax_t with a size double the size of R
using i_type = std::intmax_t;
return
(
static_cast<i_type>(t) * static_cast<i_type>(u)
> static_cast<i_type>(std::numeric_limits<R>::max())
) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"multiplication overflow"
)
:
(
static_cast<i_type>(t) * static_cast<i_type>(u)
< static_cast<i_type>(std::numeric_limits<R>::min())
) ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"multiplication overflow"
)
:
checked_result<R>(t * u)
;
}
constexpr static checked_result<R> multiply(
const R t,
const R u,
std::true_type, // R is signed
std::true_type // (sizeochecked_result<R>R) > (sizeochecked_result<R>std::intmax_t) / 2))
){ // INT32-C
return t > 0 ?
u > 0 ?
t > std::numeric_limits<R>::max() / u ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"multiplication overflow"
)
:
checked_result<R>(t * u)
: // u <= 0
u < std::numeric_limits<R>::min() / t ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"multiplication overflow"
)
:
checked_result<R>(t * u)
: // t <= 0
u > 0 ?
t < std::numeric_limits<R>::min() / u ?
F::template invoke<safe_numerics_error::negative_overflow_error>(
"multiplication overflow"
)
:
checked_result<R>(t * u)
: // u <= 0
t != 0 && u < std::numeric_limits<R>::max() / t ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"multiplication overflow"
)
:
checked_result<R>(t * u)
;
}
}; // multiply_impl_detail
constexpr static checked_result<R> multiply(const R & t, const R & u){
return multiply_impl_detail::multiply(
t,
u,
std::is_signed<R>(),
std::integral_constant<
bool,
(sizeof(R) > sizeof(std::uintmax_t) / 2)
>()
);
}
////////////////////////////////
// safe division on unsafe types
struct divide_impl_detail {
constexpr static checked_result<R> divide(
const R & t,
const R & u,
std::false_type // R is unsigned
){
return t / u;
}
constexpr static checked_result<R> divide(
const R & t,
const R & u,
std::true_type // R is signed
){
return
(u == -1 && t == std::numeric_limits<R>::min()) ?
F::template invoke<safe_numerics_error::positive_overflow_error>(
"result cannot be represented"
)
:
checked_result<R>(t / u)
;
}
}; // divide_impl_detail
// note that we presume that the size of R >= size of T
constexpr static checked_result<R> divide(const R & t, const R & u){
if(u == 0){
return F::template invoke<safe_numerics_error::domain_error>(
"divide by zero"
);
}
return divide_impl_detail::divide(t, u, std::is_signed<R>());
}
////////////////////////////////
// safe modulus on unsafe types
struct modulus_impl_detail {
constexpr static checked_result<R> modulus(
const R & t,
const R & u,
std::false_type // R is unsigned
){
return t % u;
}
constexpr static checked_result<R> modulus(
const R & t,
const R & u,
std::true_type // R is signed
){
if(u >= 0)
return t % u;
checked_result<R> ux = checked::minus(u);
if(ux.exception())
return t;
return t % static_cast<R>(ux);
}
}; // modulus_impl_detail
constexpr static checked_result<R> modulus(const R & t, const R & u){
if(0 == u)
return F::template invoke<safe_numerics_error::domain_error>(
"denominator is zero"
);
// why to we need abs here? the sign of the modulus is the sign of the
// dividend. Consider -128 % -1 The result of this operation should be -1
// but if I use t % u the x86 hardware uses the divide instruction
// capturing the modulus as a side effect. When it does this, it
// invokes the operation -128 / -1 -> 128 which overflows a signed type
// and provokes a hardware exception. We can fix this using abs()
// since -128 % -1 = -128 % 1 = 0
return modulus_impl_detail::modulus(t, u, typename std::is_signed<R>::type());
}
///////////////////////////////////
// shift operations
struct left_shift_integer_detail {
#if 0
// todo - optimize for gcc to exploit builtin
/* for gcc compilers
int __builtin_clz (unsigned int x)
Returns the number of leading 0-bits in x, starting at the
most significant bit position. If x is 0, the result is undefined.
*/
#ifndef __has_feature // Optional of course.
#define __has_feature(x) 0 // Compatibility with non-clang compilers.
#endif
template<typename T>
constexpr unsigned int leading_zeros(const T & t){
if(0 == t)
return 0;
#if __has_feature(builtin_clz)
return __builtin_clz(t);
#else
#endif
}
#endif
// INT34-C C++
// standard paragraph 5.8 / 2
// The value of E1 << E2 is E1 left-shifted E2 bit positions;
// vacated bits are zero-filled.
constexpr static checked_result<R> left_shift(
const R & t,
const R & u,
std::false_type // R is unsigned
){
// the value of the result is E1 x 2^E2, reduced modulo one more than
// the maximum value representable in the result type.
// see 5.8 & 1
// if right operand is
// greater than or equal to the length in bits of the promoted left operand.
if(
safe_compare::greater_than(
u,
std::numeric_limits<R>::digits - utility::significant_bits(t)
)
){
// behavior is undefined
return F::template invoke<safe_numerics_error::shift_too_large>(
"shifting left more bits than available is undefined behavior"
);
}
return t << u;
}
constexpr static checked_result<R> left_shift(
const R & t,
const R & u,
std::true_type // R is signed
){
// and [E1] has a non-negative value
if(t >= 0){
// and E1 x 2^E2 is representable in the corresponding
// unsigned type of the result type,
// see 5.8 & 1
// if right operand is
// greater than or equal to the length in bits of the promoted left operand.
if(
safe_compare::greater_than(
u,
std::numeric_limits<R>::digits - utility::significant_bits(t)
)
){
// behavior is undefined
return F::template invoke<safe_numerics_error::shift_too_large>(
"shifting left more bits than available"
);
}
else{
return t << u;
}
}
// otherwise, the behavior is undefined.
return F::template invoke<safe_numerics_error::negative_shift>(
"shifting a negative value"
);
}
}; // left_shift_integer_detail
constexpr static checked_result<R> left_shift(
const R & t,
const R & u
){
// INT34-C - Do not shift an expression by a negative number of bits
// standard paragraph 5.8 & 1
// if the right operand is negative
if(u == 0){
return t;
}
if(u < 0){
return F::template invoke<safe_numerics_error::negative_shift>(
"shifting negative amount"
);
}
if(u > std::numeric_limits<R>::digits){
// behavior is undefined
return F::template invoke<safe_numerics_error::shift_too_large>(
"shifting more bits than available"
);
}
return left_shift_integer_detail::left_shift(t, u, std::is_signed<R>());
}
// right shift
struct right_shift_integer_detail {
// INT34-C C++
// standard paragraph 5.8 / 3
// The value of E1 << E2 is E1 left-shifted E2 bit positions;
// vacated bits are zero-filled.
constexpr static checked_result<R> right_shift(
const R & t,
const R & u,
std::false_type // T is unsigned
){
// the value of the result is the integral part of the
// quotient of E1/2E2
return t >> u;
}
constexpr static checked_result<R> right_shift(
const R & t,
const R & u,
std::true_type // T is signed;
){
if(t < 0){
// note that the C++ standard considers this case is "implemenation
// defined" rather than "undefined".
return F::template invoke<safe_numerics_error::negative_value_shift>(
"shifting a negative value"
);
}
// the value is the integral part of E1 / 2^E2,
return t >> u;
}
}; // right_shift_integer_detail
constexpr static checked_result<R> right_shift(
const R & t,
const R & u
){
// INT34-C - Do not shift an expression by a negative number of bits
// standard paragraph 5.8 & 1
// if the right operand is negative
if(u < 0){
return F::template invoke<safe_numerics_error::negative_shift>(
"shifting negative amount"
);
}
if(u > std::numeric_limits<R>::digits){
// behavior is undefined
return F::template invoke<safe_numerics_error::shift_too_large>(
"shifting more bits than available"
);
}
return right_shift_integer_detail::right_shift(t, u ,std::is_signed<R>());
}
///////////////////////////////////
// bitwise operations
// INT13-C Note: We don't enforce recommendation as acually written
// as it would break too many programs. Specifically, we permit signed
// integer operands.
constexpr static checked_result<R> bitwise_or(const R & t, const R & u){
using namespace boost::safe_numerics::utility;
const unsigned int result_size
= std::max(significant_bits(t), significant_bits(u));
if(result_size > bits_type<R>::value){
return F::template invoke<safe_numerics_error::positive_overflow_error>(
"result type too small to hold bitwise or"
);
}
return t | u;
}
constexpr static checked_result<R> bitwise_xor(const R & t, const R & u){
using namespace boost::safe_numerics::utility;
const unsigned int result_size
= std::max(significant_bits(t), significant_bits(u));
if(result_size > bits_type<R>::value){
return F::template invoke<safe_numerics_error::positive_overflow_error>(
"result type too small to hold bitwise or"
);
}
return t ^ u;
}
constexpr static checked_result<R> bitwise_and(const R & t, const R & u){
using namespace boost::safe_numerics::utility;
const unsigned int result_size
= std::min(significant_bits(t), significant_bits(u));
if(result_size > bits_type<R>::value){
return F::template invoke<safe_numerics_error::positive_overflow_error>(
"result type too small to hold bitwise and"
);
}
return t & u;
}
constexpr static checked_result<R> bitwise_not(const R & t){
using namespace boost::safe_numerics::utility;
if(significant_bits(t) > bits_type<R>::value){
return F::template invoke<safe_numerics_error::positive_overflow_error>(
"result type too small to hold bitwise inverse"
);
}
return ~t;
}
}; // checked_operation
} // safe_numerics
} // boost
#endif // BOOST_NUMERIC_CHECKED_INTEGER_HPP