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* text=auto !eol svneol=native#text/plain
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# Generated by `boostdep --cmake numeric~conversion`
# Copyright 2020 Peter Dimov
# Distributed under the Boost Software License, Version 1.0.
# https://www.boost.org/LICENSE_1_0.txt
cmake_minimum_required(VERSION 3.5...3.16)
project(boost_numeric_conversion VERSION "${BOOST_SUPERPROJECT_VERSION}" LANGUAGES CXX)
add_library(boost_numeric_conversion INTERFACE)
add_library(Boost::numeric_conversion ALIAS boost_numeric_conversion)
target_include_directories(boost_numeric_conversion INTERFACE include)
target_link_libraries(boost_numeric_conversion
INTERFACE
Boost::config
Boost::conversion
Boost::core
Boost::mpl
Boost::preprocessor
Boost::throw_exception
Boost::type_traits
)
if(BUILD_TESTING AND EXISTS "${CMAKE_CURRENT_SOURCE_DIR}/test/CMakeLists.txt")
add_subdirectory(test)
endif()

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# Boost.NumericConversion
The Boost Numeric Conversion library is a collection of tools to describe and perform conversions between values of different [numeric types][1].
The documentation for the library can be found [here][2]
[1]: http://www.boost.org/doc/libs/release/libs/numeric/conversion/doc/html/boost_numericconversion/definitions.html#boost_numericconversion.definitions.numeric_types
[2]: http://www.boost.org/doc/libs/release/libs/numeric/conversion/doc/html/index.html#numeric_conversion.overview

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# Boost.Numeric/Conversion
#
# Copyright (c) 2004-2007 Fernando Luis Cacciola Carballal
#
# 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)
# Quickbook
# -----------------------------------------------------------------------------
import quickbook ;
path-constant images : html ;
xml conversion
:
conversion.qbk
;
boostbook standalone
:
conversion
:
<xsl:param>boost.root=../../../../..
<xsl:param>html.stylesheet=boostbook.css
<xsl:param>toc.max.depth=2
<xsl:param>toc.section.depth=2
<xsl:param>chunk.section.depth=1
<format>pdf:<xsl:param>img.src.path=$(images)/
<format>pdf:<xsl:param>boost.url.prefix=http://www.boost.org/doc/libs/release/libs/numeric/conversion/doc/html
;

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[/
Boost.Optional
Copyright (c) 2003-2007 Fernando Luis Cacciola Carballal
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)
]
[section bounds<> traits class]
[section Introduction]
To determine the ranges of numeric types with `std::numeric_limits` \[18.2.1\],
different syntax have to be used depending on numeric type. Specifically,
`numeric_limits<T>::min()` for integral types returns the minimum finite value,
whereas for floating point types it returns the minimum positive normalized
value. The difference in semantics makes client code unnecessarily complex
and error prone.
`boost::numeric::bounds<>` provides a consistent interface for retrieving the
maximum finite value, the minimum finite value and the minimum positive normalized
value (0 for integral types) for numeric types. The selection of implementation
is performed at compile time, so there is no runtime overhead.
[endsect]
[section traits class bounds<N>]
template<class N>
struct bounds
{
static N lowest () { return implementation_defined; }
static N highest () { return implementation_defined; }
static N smallest() { return implementation_defined; }
};
[heading Members]
[: `lowest()` ]
Returns the minimum finite value, equivalent to `numeric_limits<T>::min()` when `T`
is an integral type, and to `-numeric_limits<T>::max()` when `T` is a floating point type.
[: `highest()` ]
Returns the maximum finite value, equivalent to `numeric_limits<T>::max()`.
[: `smallest()` ]
Returns the smallest positive normalized value for floating point types with
denormalization, or returns 0 for integral types.
[endsect]
[section Examples]
The following example demonstrates the use of `numeric::bounds<>` and the
equivalent code using `numeric_limits`:
#include <iostream>
#include <boost/numeric/conversion/bounds.hpp>
#include <boost/limits.hpp>
int main() {
std::cout << "numeric::bounds versus numeric_limits example.\n";
std::cout << "The maximum value for float:\n";
std::cout << boost::numeric::bounds<float>::highest() << "\n";
std::cout << std::numeric_limits<float>::max() << "\n";
std::cout << "The minimum value for float:\n";
std::cout << boost::numeric::bounds<float>::lowest() << "\n";
std::cout << -std::numeric_limits<float>::max() << "\n";
std::cout << "The smallest positive value for float:\n";
std::cout << boost::numeric::bounds<float>::smallest() << "\n";
std::cout << std::numeric_limits<float>::min() << "\n";
return 0;
}
[endsect]
[endsect]

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[library Boost.NumericConversion
[quickbook 1.4]
[authors [Cacciola Carballal, Fernando Luis]]
[copyright 2004-2007 Fernando Luis Cacciola Carballal]
[category numerics]
[id numeric_conversion]
[dirname numeric_conversion]
[purpose
Optimized Policy-based Numeric Conversions
]
[source-mode c++]
[license
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])
]
]
[/ Macros will be used for links so we have a central place to change them ]
[/ Cited Boost resources ]
[def __MPL_INTEGRAL_CONSTANT__ [@../../../../mpl/doc/refmanual/integral-constant.html MPL's Integral Constant] ]
[/ Other web resources ]
[def __SGI_UNARY_FUNCTION__ [@http://www.sgi.com/tech/stl/UnaryFunction.html Unary Function Object]]
[/ Icons ]
[def __NOTE__ [$images/note.png]]
[def __ALERT__ [$images/caution.png]]
[def __DETAIL__ [$images/note.png]]
[def __TIP__ [$images/tip.png]]
[def __QUESTION_MARK__ [$images/question.png]]
[def __SPACE__ [$images/space.png]]
[def __GO_TO__ [$images/callouts/R.png]]
[section Overview]
The Boost Numeric Conversion library is a collection of tools to describe and
perform conversions between values of different
[link boost_numericconversion.definitions.numeric_types numeric types].
The library includes a special alternative for a subset of `std::numeric_limits<>`,
the [link boost_numericconversion.bounds___traits_class bounds<>] traits class, which provides
a consistent way to obtain the [link boost_numericconversion.definitions.range_and_precision boundary]
values for the [link boost_numericconversion.definitions.range_and_precision range] of a numeric type.
It also includes a set of [link boost_numericconversion.conversion_traits___traits_class trait classes]
which describes the compile-time
properties of a conversion from a source to a target numeric type.
Both [link boost_numericconversion.definitions.c___arithmetic_types arithmetic] and
[link boost_numericconversion.definitions.numeric_types user-defined numeric types] can be used.
A policy-based [link boost_numericconversion.converter___function_object converter] object which
uses `conversion_traits` to select
an optimized implementation is supplied. Such implementation uses an optimal
range checking code suitable for the source/target combination.
* The converter's out-of-range behavior can be customized via an
[link boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler OverflowHandler] policy.
* For floating-point to integral conversions, the rounding mode can be selected via the
[link boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder Float2IntRounder] policy.
* A custom low-level conversion routine (for UDTs for instance) can be passed via a
[link boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter RawConverter] policy.
* The optimized automatic range-checking logic can be overridden via a
[link boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker UserRangeChecker] policy.
[endsect]
[include definitions.qbk]
[include converter.qbk]
[include requirements.qbk]
[include bounds.qbk]
[include conversion_traits.qbk]
[include converter_policies.qbk]
[include numeric_cast.qbk]
[section History and Acknowledgments]
[heading Pre-formal review]
* Kevlin Henney, with help from David Abrahams and Beman Dawes, originally contributed
the previous version of `numeric_cast<>` which already presented the idea of a runtime
range check.
* Later, Eric Ford, Kevin Lynch and the author spotted some genericity problems with
that `numeric_cast<>` which prevented it from being used in a generic layer of math
functions.
* An improved `numeric_cast<>` which properly handled all combinations of arithmetic
types was presented.
* David Abrahams and Beman Dawes acknowledged the need of an improved version of
`numeric_cast<>` and supported the submission as originally laid out. Daryl Walker and
Darin Adler made some important comments and proposed fixes to the original submission.
* Special thanks go to Björn Karlsoon who helped the author considerably. Having found the
problems with `numeric_cast<>` himself, he revised very carefully the original submission
and spot a subtle bug in the range checking implementation. He also wrote part of
this documentation and proof-read and corrected other parts. And most importantly:
the features now presented here in this library evolved from the original submission as
a result of the useful private communications between Björn and the author.
[heading Post-formal review]
* Guillaume Melquiond spoted some documentation and code issues, particularly about
rounding conversions.
* The following people contributed an important review of the design, documentation and c
ode: Kevin Lynch, Thorsten Ottosen, Paul Bristow, Daryle Walker, Jhon Torjo, Eric Ford,
Gennadiy Rozental.
[endsect]
[section Bibliography]
* Standard Documents:
# ISO/IEC 14882:98 (C++98 Standard)
# ISO/IEC 9899:1999 (C99 Standard)
# ISO/IEC 10967-1 (Language Independent Arithmetic (LIA), Part I, 1994)
# ISO/IEC 2382-1:1993 (Information Technology - Vocabulary - Part I: Fundamental Terms)
# ANSI/IEEE 754-1985 [and IEC 60559:1989] (Binary floating-point)
# ANSI/IEEE 854-1988 (Radix Independent floating-point)
# ANSI X3/TR-1-82 (Dictionary for Information Processing Systems)
# ISO/IEC JTC1/SC22/WG14/N753 C9X Revision Proposal: LIA-1 Binding: Rationale
* Papers:
# David Goldberg What Every Computer Scientist Should Know About Floating-Point Arithmetic
# Prof. William Kahan papers on floating-point.
[endsect]

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[/
Boost.Optional
Copyright (c) 2003-2007 Fernando Luis Cacciola Carballal
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)
]
[section conversion_traits<> traits class]
[section Types]
[section enumeration int_float_mixture_enum]
namespace boost { namespace numeric {
enum int_float_mixture_enum
{
integral_to_integral
,integral_to_float
,float_to_integral
,float_to_float
} ;
} } // namespace boost::numeric
[endsect]
[section enumeration sign_mixture_enum]
namespace boost { namespace numeric {
enum sign_mixture_enum
{
unsigned_to_unsigned
,signed_to_signed
,signed_to_unsigned
,unsigned_to_signed
} ;
} } // namespace boost::numeric
[endsect]
[section enumeration udt_builtin_mixture_enum]
namespace boost { namespace numeric {
enum udt_builtin_mixture_enum
{
builtin_to_builtin
,builtin_to_udt
,udt_to_builtin
,udt_to_udt
} ;
} } // namespace boost::numeric
[endsect]
[section template class int_float_mixture<>]
namespace boost { namespace numeric {
template <class T, class S>
struct int_float_mixture : mpl::integral_c<int_float_mixture_enum, impl-def-value> {} ;
} } // namespace boost::numeric
Classifying `S` and `T` as either integral or float, this __MPL_INTEGRAL_CONSTANT__
indicates the combination of these attributes.
Its `::value` is of enumeration type
[link boost_numericconversion.conversion_traits___traits_class.types.enumeration_int_float_mixture_enum `boost::numeric::int_float_mixture_enum`]
[endsect]
[section template class sign_mixture<>]
namespace boost { namespace numeric {
template <class T, class S>
struct sign_mixture : mpl::integral_c<sign_mixture_enum, impl-def-value> {} ;
} } // namespace boost::numeric
Classifying `S` and `T` as either signed or unsigned, this __MPL_INTEGRAL_CONSTANT__
indicates the combination of these attributes.
Its `::value` is of enumeration type
[link boost_numericconversion.conversion_traits___traits_class.types.enumeration_sign_mixture_enum `boost::numeric::sign_mixture_enum`]
[endsect]
[section template class udt_builtin_mixture<>]
namespace boost { namespace numeric {
template <class T, class S>
struct udt_builtin_mixture : mpl::integral_c<udt_builtin__mixture_enum, impl-def-value> {} ;
} } // namespace boost::numeric
Classifying `S` and `T` as either user-defined or builtin, this __MPL_INTEGRAL_CONSTANT__
indicates the combination of these attributes.
Its `::value` is of enumeration type
[link boost_numericconversion.conversion_traits___traits_class.types.enumeration_udt_builtin_mixture_enum `boost::numeric::udt_builtin_mixture_enum`]
[endsect]
[section template class is_subranged<>]
namespace boost { namespace numeric {
template <class T, class S>
struct is_subranged : mpl::bool_<impl-def-value> {} ;
} } // namespace boost::numeric
Indicates if the range of the target type `T` is a subset of the range of the source
type `S`. That is: if there are some source values which fall out of the
Target type's range.
It is a boolean __MPL_INTEGRAL_CONSTANT__.
It does not indicate if a particular conversion is effectively out of range;
it indicates that some conversion might be out of range because not all the
source values are representable as Target type.
[endsect]
[section template class conversion_traits<>]
namespace boost { namespace numeric {
template <class T, class S>
struct conversion_traits
{
mpl::integral_c<int_float_mixture_enum , ...> int_float_mixture ;
mpl::integral_c<sign_mixture_enum , ...> sign_mixture;
mpl::integral_c<udt_builtin_mixture_enum, ...> udt_builtin_mixture ;
mpl::bool_<...> subranged ;
mpl::bool_<...> trivial ;
typedef T target_type ;
typedef S source_type ;
typedef ... argument_type ;
typedef ... result_type ;
typedef ... supertype ;
typedef ... subtype ;
} ;
} } // namespace numeric, namespace boost
This traits class indicates some properties of a ['numeric conversion] direction:
from a source type `S` to a target type `T`. It does not indicate the properties
of a ['specific] conversion, but of the conversion direction. See
[link boost_numericconversion.definitions.subranged_conversion_direction__subtype_and_supertype Definitions] for details.
The traits class provides the following __MPL_INTEGRAL_CONSTANT__\s of enumeration
type. They express the combination of certain attributes of the Source and
Target types (thus they are call mixture):
[table
[[ ][ ]]
[[[*int_float_mixture ]][
Same as given by the traits class
[link boost_numericconversion.conversion_traits___traits_class.types.template_class_int_float_mixture__ int_float_mixture]
]]
[[[*sign_mixture ]][
Same as given by the traits class
[link boost_numericconversion.conversion_traits___traits_class.types.template_class_sign_mixture__ sign_mixture]
]]
[[[*udt_builtin_mixture ]]
[Same as given by the traits class
[link boost_numericconversion.conversion_traits___traits_class.types.template_class_udt_builtin_mixture__ udt_builtin_mixture]
]]
]
The traits class provides the following __MPL_INTEGRAL_CONSTANT__\s of boolean type
which indicates indirectly the relation between the Source and Target ranges
(see [link boost_numericconversion.definitions.range_and_precision Definitions] for details).
[table
[[ ][ ]]
[[subranged ][
Same as given by [link boost_numericconversion.conversion_traits___traits_class.types.template_class_is_subranged__ is_subranged]
]]
[[trivial][
Indicates if both Source and Target, [_without cv-qualifications], are the same type.
Its `::value` is of boolean type.
]]
]
The traits class provides the following types. They are the Source and Target types classified
and qualified for different purposes.
[table
[[ ][ ]]
[[[*target_type]][
The template parameter `T` without cv-qualifications
]]
[[[*source_type]][
The template parameter `S` without cv-qualifications
]]
[[[*argument_type]][
This type is either source_type or `source_type const&`.
It represents the optimal argument type for the
[link boost_numericconversion.converter___function_object converter] member functions.
If S is a built-in type, this is `source_type`, otherwise, this is `source_type const&`.
]]
[[[*result_type]][
This type is either target_type or target_type const&
It represents the return type of the
[link boost_numericconversion.converter___function_object converter] member functions.
If `T==S`, it is `target_type const&`, otherwise, it is `target_type`.
]]
[[[*supertype]][
If the conversion is subranged, it is `source_type`, otherwise, it is `target_type`
]]
[[[*subtype]][
If the conversion is subranged, it is `target_type`, otherwise, it is `source_type`
]]
]
[endsect]
[endsect]
[section Examples]
#include <cassert>
#include <typeinfo>
#include <boost/numeric/conversion/conversion_traits.hpp>
int main()
{
// A trivial conversion.
typedef boost::numeric::conversion_traits<short,short> Short2Short_Traits ;
assert ( Short2Short_Traits::trivial::value ) ;
// A subranged conversion.
typedef boost::numeric::conversion_traits<double,unsigned int> UInt2Double_Traits ;
assert ( UInt2Double_Traits::int_float_mixture::value == boost::numeric::integral_to_float ) ;
assert ( UInt2Double_Traits::sign_mixture::value == boost::numeric::unsigned_to_signed ) ;
assert ( !UInt2Double_Traits::subranged::value ) ;
assert ( typeid(UInt2Double_Traits::supertype) == typeid(double) ) ;
assert ( typeid(UInt2Double_Traits::subtype) == typeid(unsigned int) ) ;
// A doubly subranged conversion.
assert ( (boost::numeric::conversion_traits<short, unsigned short>::subranged::value) );
assert ( (boost::numeric::conversion_traits<unsigned short, short>::subranged::value) );
return 0;
}
[endsect]
[endsect]

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[/
Boost.Optional
Copyright (c) 2003-2007 Fernando Luis Cacciola Carballal
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)
]
[section converter<> function object]
[section Synopsis]
namespace boost { namespace numeric {
template<class T,
class S,
class Traits, = conversion_traits<T,S>
class OverflowHandler = def_overflow_handler,
class Float2IntRounder = Trunc< typename Traits::source_type >,
class RawConverter = raw_converter<Traits>,
class UserRangeChecker = UseInternalRangeChecker
>
struct converter
{
typedef Traits traits ;
typedef typename Traits::source_type source_type ;
typedef typename Traits::argument_type argument_type ;
typedef typename Traits::result_type result_type ;
static result_type convert ( argument_type s ) ;
result_type operator() ( argument_type s ) const ;
// Internal member functions:
static range_check_result out_of_range ( argument_type s ) ;
static void validate_range ( argument_type s ) ;
static result_type low_level_convert ( argument_type s ) ;
static source_type nearbyint ( argument_type s ) ;
} ;
} } // namespace numeric, boost
`boost::numeric::converter<>` is a __SGI_UNARY_FUNCTION__ encapsulating
the code to perform a numeric conversion with the direction and
properties specified by the Traits template parameter. It can optionally
take some [link boost_numericconversion.numeric_converter_policy_classes policies] which can be used to customize its behavior. The
`Traits` parameter is not a policy but the parameter that defines
the conversion.
[endsect]
[section Template parameters]
[table
[[ ][ ]]
[[`T`][
The [link boost_numericconversion.definitions.numeric_types Numeric Type]
which is the ['Target] of the conversion.
]]
[[`S`][
The [link boost_numericconversion.definitions.numeric_types Numeric Type]
which is the ['Source] of the conversion.
]]
[[`Traits`][
This must be a conversion traits class with the interface of
[link boost_numericconversion.conversion_traits___traits_class `boost::numeric::conversion_traits`]
]]
[[`OverflowHandler`][
[*Stateless Policy] called to administrate the result of the range checking.
It is a [*Function Object] which receives the result of `out_of_range()`
and is called inside the `validate_range()` static member function exposed
by the converter.
]]
[[`Float2IntRounder`][
[*Stateless Policy] which specifies the rounding mode used for float to
integral conversions.
It supplies the `nearbyint()` static member function exposed by the converter.
]]
[[`RawConverter`][
[*Stateless Policy] which is used to perform the actual conversion.
It supplies the `low_level_convert()` static member function exposed
by the converter.
]]
[[`UserRangeChecker`][
['Special and Optional] [*Stateless Policy] which can be used to override
the internal range checking logic.
If given, supplies alternative code for the `out_of_range()` and
`validate_range()` static member functions exposed by the converter.
]]
]
[endsect]
[section Member functions]
[: `static result_type converter<>::convert ( argument_type s ) ; // throw
`]
This static member function converts an rvalue of type `source_type` to
an rvalue of type `target_type`.
If the conversion requires it, it performs a range checking before the conversion
and passes the result of the check to the overflow handler policy (the default
policy throws an exception if out-of-range is detected)
The implementation of this function is actually built from the policies and is
basically as follows:
result_type converter<>::convert ( argument_type s )
{
validate_range(s); // Implemented by the internal range checking logic
// (which also calls the OverflowHandler policy)
// or externally supplied by the UserRangeChecker policy.
s = nearbyint(s); // Externally supplied by the Float2IntRounder policy.
// NOTE: This is actually called only for float to int conversions.
return low_level_convert(s); // Externally supplied by the RawConverter policy.
}
`converter<>::operator() const` just calls `convert()`
__SPACE__
[: `static range_check_result numeric_converter<>::out_of_range ( argument_type s ) ;`]
This [link numeric_conversion_converter_internal internal] static member function
determines if the value `s` can be
represented by the target type without overflow.
It does not determine if the conversion is ['exact]; that is, it does not detect
['inexact] conversions, only ['out-of-range] conversions (see the
[link boost_numericconversion.definitions.exact__correctly_rounded_and_out_of_range_representations Definitions] for further details).
The return value is of enum type
[link boost_numericconversion.numeric_converter_policy_classes.enum_range_check_result `boost::numeric::range_check_result`]
The actual code for the range checking logic is optimized for the combined
properties of the source and target types. For example, a non-subranged
conversion (i.e: `int`->`float`), requires no range checking, so `out_of_range()`
returns `cInRange` directly. See the following
[link boost_numericconversion.converter___function_object.range_checking_logic table] for more details.
If the user supplied a
[link boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker UserRangeChecker] policy,
is this policy which implements this function, so the implementation is user
defined, although it is expected to perform the same conceptual check and
return the appropriate result.
__SPACE__
[: `static void numeric_converter<>::validate_range ( argument_type s ) ; // no throw
`]
This [link numeric_conversion_converter_internal internal] static member function
calls out_of_range(s), and passes the
result to the [link boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler OverflowHandler]
policy class.
For those Target/Source combinations which don't require range checking, this
is an empty inline function.
If the user supplied a
[link boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker UserRangeChecker] policy,
is this policy which implements this function, so the implementation is user
defined, although it is expected to perform the same action as the default.
In particular, it is expected to pass the result of the check to the overflow handler.
__SPACE__
[: `static result_type numeric_converter<>::low_level_convert ( argument_type s ) ;` ]
This [link numeric_conversion_converter_internal internal] static member function
performs the actual conversion.
This function is externally supplied by the
[link boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter RawConverter] policy class.
__SPACE__
[: `static source_type converter<>::nearbyint ( argument_type s ) ;`]
This [link numeric_conversion_converter_internal internal] static member function,
which is [_only used] for
`float` to `int` conversions, returns an ['integer] value of ['[_floating-point
type]] according to some rounding direction.
This function is externally supplied by the
[link boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder Float2IntRounder] policy class
which encapsulates the specific rounding mode.
__SPACE__
[#numeric_conversion_converter_internal]
[heading Internal Member Functions]
These static member functions build the actual conversion code used by `convert()`.
The user does not have to call these if calling `convert()`, since `convert()` calls
them infernally, but they can be called separately for specific needs.
[endsect]
[section Range Checking Logic]
The following table summarizes the internal range checking logic performed for
each combination of the properties of Source and Target.
LowestT/HighestT denotes the highest and lowest values of the Target type, respectively.
`S(n)` is short for `static_cast<S>(n)` (`S` denotes the Source type).
`NONE` indicates that for this case there is no range checking.
[pre
[^
int_to_int |--> sig_to_sig |--> subranged |--> ( s >= S(LowestT) ) && ( s <= S(HighestT) )
| |--> not subranged |--> NONE
|
|--> unsig_to_unsig |--> subranged |--> ( s >= S(LowestT) ) && ( s <= S(HighestT) )
| |--> not subranged |--> NONE
|
|--> sig_to_unsig |--> pos subranged |--> ( s >= S(0) ) && ( s <= S(HighestT) )
| |--> not pos subranged |--> ( s >= S(0) )
|
|--> unsig_to_sig |--> subranged |--> ( s <= S(HighestT) )
| |--> not subranged |--> NONE
]
[^
int_to_float |--> NONE
]
[^
float_to_int |--> round_to_zero |--> ( s > S(LowestT)-S(1) ) && ( s < S(HighestT)+S(1) )
|--> round_to_even_nearest |--> ( s >= S(LowestT)-S(0.5) ) && ( s < S(HighestT)+S(0.5) )
|--> round_to_infinity |--> ( s > S(LowestT)-S(1) ) && ( s <= S(HighestT) )
|--> round_to_neg_infinity |--> ( s >= S(LowestT) ) && ( s < S(HighestT)+S(1) )
]
[^
float_to_float |--> subranged |--> ( s >= S(LowestT) ) && ( s <= S(HighestT) )
|--> not subranged |--> NONE
]
]
[endsect]
[section Examples]
#include <cassert>
#include <boost/numeric/conversion/converter.hpp>
int main() {
typedef boost::numeric::converter<int,double> Double2Int ;
int x = Double2Int::convert(2.0);
assert ( x == 2 );
int y = Double2Int()(3.14); // As a function object.
assert ( y == 3 ) ; // The default rounding is trunc.
try
{
double m = boost::numeric::bounds<double>::highest();
int z = Double2Int::convert(m); // By default throws positive_overflow()
}
catch ( boost::numeric::positive_overflow const& )
{
}
return 0;
}
[endsect]
[endsect]

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[/
Boost.Optional
Copyright (c) 2003-2007 Fernando Luis Cacciola Carballal
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)
]
[section Numeric Converter Policy Classes]
[section enum range_check_result]
namespace boost { namespace numeric {
enum range_check_result
{
cInRange ,
cNegOverflow ,
cPosOverflow
} ;
} }
Defines the values returned by `boost::numeric::converter<>::out_of_range()`
[endsect]
[section Policy OverflowHandler]
This ['stateless] non-template policy class must be a ['function object] and is
called to administrate the result of the range checking. It can throw an exception
if overflow has been detected by the range checking as indicated by its argument.
If it throws, is is recommended that it be `std::bad_cast` or derived.
It must have the following interface (it does not has to be a template class):
struct YourOverflowHandlerPolicy
{
void operator() ( boost::range_check_result ) ; // throw bad_cast or derived
} ;
It is called with the result of the converter's `out_of_range()` inside `validate_range()`.
These are the two overflow handler classes provided by the library:
namespace boost { namespace numeric {
struct def_overflow_handler
{
void operator() ( range_check_result r ) // throw bad_numeric_conversion derived
{
if ( r == cNegOverflow )
throw negative_overflow() ;
else if ( r == cPosOverflow )
throw positive_overflow() ;
}
} ;
struct silent_overflow_handler
{
void operator() ( range_check_result ) // no-throw
{}
} ;
} }
And these are the Exception Classes thrown by the default overflow handler
[link numeric_conversion_policy_overflow_handler_important_note (see IMPORTANT note)]
namespace boost { namespace numeric {
``[#numeric_conversion_bad_numeric_cast]``
class bad_numeric_cast : public std::bad_cast
{
public:
virtual const char *what() const // throw()
{
return "bad numeric conversion: overflow";
}
};
``[#numeric_conversion_negative_overflow]``
class negative_overflow : public bad_numeric_cast
{
public:
virtual const char *what() const // throw()
{
return "bad numeric conversion: negative overflow";
}
};
``[#numeric_conversion_possitive_overflow]``
class positive_overflow : public bad_numeric_cast
{
public:
virtual const char *what() const // throw()
{
return "bad numeric conversion: positive overflow";
}
};
} }
[#numeric_conversion_policy_overflow_handler_important_note]
[important [*RELEASE NOTE for 1.33]
Previous to boost version 1.33, the exception class `bad_numeric_cast` was
named `bad_numeric_conversion`. However, in 1.33, the old function
`numeric_cast<>` from `boost/cast.hpp` was completly replaced by the
new `numeric_cast<>` in `boost/numeric/conversion/cast.hpp`
(and `boost/cast.hpp` is including `boost/numeric/conversion/cast.hpp` now).
That old function which existed in boost for quite some time used the
`bad_numeric_cast` as its exception type so I decided to avoid backward
compatibility problems by adopting it (guessing that the user base for
the old code is wider than for the new code).
]
[endsect]
[section Policy Float2IntRounder]
This ['stateless] template policy class specifies the rounding mode used
for [_float to integral] conversions. It supplies the `nearbyint()`
static member function exposed by the converter, which means that it
[_publicly inherits from this policy].
The policy must have the following interface:
template<class S>
struct YourFloat2IntRounderPolicy
{
typedef S source_type ;
typedef {S or S const&} argument_type ;
static source_type nearbyint ( argument_type s ) { ... }
typedef mpl::integral_c<std::float_round_style,std::round_...> round_style ;
} ;
These are the rounder classes provided by the library (only the specific parts are shown,
see the general policy form above)
[note
These classes are not intended to be general purpose rounding functions
but specific policies for `converter<>`. This is why they are not function objects.
]
namespace boost { namespace numeric {
template<class S>
struct Trunc
{
static source_type nearbyint ( argument_type s )
{
using std::floor ;
using std::ceil ;
return s >= static_cast<S>(0) ? floor(s) : ceil(s) ;
}
typedef mpl::integral_c<std::float_round_style,std::round_toward_zero> round_style ;
} ;
template<class S>
struct RoundEven
{
static source_type nearbyint ( argument_type s )
{
return impl-defined-value ;
}
typedef mpl::integral_c<std::float_round_style,std::round_to_nearest> round_style ;
} ;
template<class S>
struct Ceil
{
static source_type nearbyint ( argument_type s )
{
using std::ceil ;
return ceil(s) ;
}
typedef mpl::integral_c<std::float_round_style,std::round_toward_infinity> round_style ;
} ;
template<class S>
struct Floor
{
static source_type nearbyint ( argument_type s )
{
using std::floor ;
return floor(s) ;
}
typedef mpl::integral_c<std::float_round_style,std::round_toward_neg_infinity> round_style ;
} ;
} } // namespace numeric, namespace boost
[heading Math Functions used by the rounder policies]
The rounder policies supplied by this header use math functions `floor()` and `ceil()`.
The standard versions of these functions are introduced in context by a using directive,
so in normal conditions, the standard functions will be used.
However, if there are other visible corresponding overloads an ambiguity could arise.
In this case, the user can supply her own rounder policy which could, for instance,
use a fully qualified call.
This technique allows the default rounder policies to be used directly with
user defined types. The user only requires that suitable overloads of `floor()` and `ceil()`
be visible. See also [link boost_numericconversion.type_requirements_and_user_defined_types_support User Defined Numeric Types]
support.
[endsect]
[section Policy RawConverter]
This ['stateless] template policy class is used to perform the
actual conversion from Source to Target. It supplies the
`low_level_convert()` static member function exposed by the
converter, which means that it publicly inherits from this policy.
The policy must have the following interface:
template<class Traits>
struct YourRawConverterPolicy
{
typedef typename Traits::result_type result_type ;
typedef typename Traits::argument_type argument_type ;
static result_type low_level_convert ( argument_type s ) { return <impl defined> ; }
} ;
This policy is mostly provided as a hook for user defined types which don't support `static_cast<>` conversions to some types
This is the only raw converter policy class provided by the library:
namespace boost { namespace numeric {
template<class Traits>
struct raw_numeric_converter
{
typedef typename Traits::result_type result_type ;
typedef typename Traits::argument_type argument_type ;
static result_type low_level_convert ( argument_type s )
{
return static_cast<result_type>(s) ;
}
} ;
} }
[endsect]
[section Policy UserRangeChecker]
This ['stateless] template policy class is used [_only if supplied]
to [*override] the internal range checking logic.
It supplies the `validate_range()` static member function
exposed by the converter, which means that it publicly inherits
from this policy.
The policy must have the following interface:
template<class Traits>
struct YourRangeCheckerPolicy
{
typedef typename Traits::argument_type argument_type ;
// Determines if the value 's' fits in the range of the Target type.
static range_check_result out_of_range ( argument_type s ) ;
// Checks whether the value 's' is out_of_range()
// and passes the result of the check to the OverflowHandler policy.
static void validate_range ( argument_type s )
{
OverflowHandler()( out_of_range(s) ) ;
}
} ;
This policy is [*only] provided as a hook for user defined types which require
range checking (which is disabled by default when a UDT is involved).
The library provides a class: `UseInternalRangeChecker{}`; which is a ['fake]
`RangeChecker` policy used to signal the converter to use its internal
range checking implementation.
[endsect]
[endsect]

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[/
Boost.Optional
Copyright (c) 2003-2007 Fernando Luis Cacciola Carballal
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)
]
[section Definitions]
[section Introduction]
This section provides definitions of terms used in the Numeric Conversion library.
[blurb [*Notation]
[_underlined text] denotes terms defined in the C++ standard.
[*bold face] denotes terms defined here but not in the standard.
]
[endsect]
[section Types and Values]
As defined by the [_C++ Object Model] (§1.7) the [_storage] or memory on which a
C++ program runs is a contiguous sequence of [_bytes] where each byte is a
contiguous sequence of bits.
An [_object] is a region of storage (§1.8) and has a type (§3.9).
A [_type] is a discrete set of values.
An object of type `T` has an [_object representation] which is the sequence of
bytes stored in the object (§3.9/4)
An object of type `T` has a [_value representation] which is the set of
bits that determine the ['value] of an object of that type (§3.9/4).
For [_POD] types (§3.9/10), this bitset is given by the object representation,
but not all the bits in the storage need to participate in the value
representation (except for character types): for example, some bits might
be used for padding or there may be trap-bits.
__SPACE__
The [*typed value] that is held by an object is the value which is determined
by its value representation.
An [*abstract value] (untyped) is the conceptual information that is
represented in a type (i.e. the number π).
The [*intrinsic value] of an object is the binary value of the sequence of
unsigned characters which form its object representation.
__SPACE__
['Abstract] values can be [*represented] in a given type.
To [*represent] an abstract value `V` in a type `T` is to obtain a typed value
`v` which corresponds to the abstract value `V`.
The operation is denoted using the `rep()` operator, as in: `v=rep(V)`.
`v` is the [*representation] of `V` in the type `T`.
For example, the abstract value π can be represented in the type
`double` as the `double value M_PI` and in the type `int` as the
`int value 3`
__SPACE__
Conversely, ['typed values] can be [*abstracted].
To [*abstract] a typed value `v` of type `T` is to obtain the abstract value `V`
whose representation in `T` is `v`.
The operation is denoted using the `abt()` operator, as in: `V=abt(v)`.
`V` is the [*abstraction] of `v` of type `T`.
Abstraction is just an abstract operation (you can't do it); but it is
defined nevertheless because it will be used to give the definitions in the
rest of this document.
[endsect]
[section C++ Arithmetic Types]
The C++ language defines [_fundamental types] (§3.9.1). The following subsets of
the fundamental types are intended to represent ['numbers]:
[variablelist
[[[_signed integer types] (§3.9.1/2):][
`{signed char, signed short int, signed int, signed long int}`
Can be used to represent general integer numbers (both negative and positive).
]]
[[[_unsigned integer types] (§3.9.1/3):][
`{unsigned char, unsigned short int, unsigned int, unsigned long int}`
Can be used to represent positive integer numbers with modulo-arithmetic.
]]
[[[_floating-point types] (§3.9.1/8):][
`{float,double,long double}`
Can be used to represent real numbers.
]]
[[[_integral or integer types] (§3.9.1/7):][
`{{signed integers},{unsigned integers}, bool, char and wchar_t}`
]]
[[[_arithmetic types] (§3.9.1/8):][
`{{integer types},{floating types}}`
]]
]
The integer types are required to have a ['binary] value representation.
Additionally, the signed/unsigned integer types of the same base type
(`short`, `int` or `long`) are required to have the same value representation,
that is:
int i = -3 ; // suppose value representation is: 10011 (sign bit + 4 magnitude bits)
unsigned int u = i ; // u is required to have the same 10011 as its value representation.
In other words, the integer types signed/unsigned X use the same value
representation but a different ['interpretation] of it; that is, their
['typed values] might differ.
Another consequence of this is that the range for signed X is always a smaller
subset of the range of unsigned X, as required by §3.9.1/3.
[note
Always remember that unsigned types, unlike signed types, have modulo-arithmetic;
that is, they do not overflow.
This means that:
[*-] Always be extra careful when mixing signed/unsigned types
[*-] Use unsigned types only when you need modulo arithmetic or very very large
numbers. Don't use unsigned types just because you intend to deal with
positive values only (you can do this with signed types as well).
]
[endsect]
[section Numeric Types]
This section introduces the following definitions intended to integrate
arithmetic types with user-defined types which behave like numbers.
Some definitions are purposely broad in order to include a vast variety of
user-defined number types.
Within this library, the term ['number] refers to an abstract numeric value.
A type is [*numeric] if:
* It is an arithmetic type, or,
* It is a user-defined type which
* Represents numeric abstract values (i.e. numbers).
* Can be converted (either implicitly or explicitly) to/from at least one arithmetic type.
* Has [link boost_numericconversion.definitions.range_and_precision range] (possibly unbounded)
and [link boost_numericconversion.definitions.range_and_precision precision] (possibly dynamic or
unlimited).
* Provides an specialization of `std::numeric_limits`.
A numeric type is [*signed] if the abstract values it represent include negative numbers.
A numeric type is [*unsigned] if the abstract values it represent exclude negative numbers.
A numeric type is [*modulo] if it has modulo-arithmetic (does not overflow).
A numeric type is [*integer] if the abstract values it represent are whole numbers.
A numeric type is [*floating] if the abstract values it represent are real numbers.
An [*arithmetic value] is the typed value of an arithmetic type
A [*numeric value] is the typed value of a numeric type
These definitions simply generalize the standard notions of arithmetic types and
values by introducing a superset called [_numeric]. All arithmetic types and values are
numeric types and values, but not vice versa, since user-defined numeric types are not
arithmetic types.
The following examples clarify the differences between arithmetic and numeric
types (and values):
// A numeric type which is not an arithmetic type (is user-defined)
// and which is intended to represent integer numbers (i.e., an 'integer' numeric type)
class MyInt
{
MyInt ( long long v ) ;
long long to_builtin();
} ;
namespace std {
template<> numeric_limits<MyInt> { ... } ;
}
// A 'floating' numeric type (double) which is also an arithmetic type (built-in),
// with a float numeric value.
double pi = M_PI ;
// A 'floating' numeric type with a whole numeric value.
// NOTE: numeric values are typed valued, hence, they are, for instance,
// integer or floating, despite the value itself being whole or including
// a fractional part.
double two = 2.0 ;
// An integer numeric type with an integer numeric value.
MyInt i(1234);
[endsect]
[section Range and Precision]
Given a number set `N`, some of its elements are representable in a numeric type `T`.
The set of representable values of type `T`, or numeric set of `T`, is a set of numeric
values whose elements are the representation of some subset of `N`.
For example, the interval of `int` values `[INT_MIN,INT_MAX]` is the set of representable
values of type `int`, i.e. the `int` numeric set, and corresponds to the representation
of the elements of the interval of abstract values `[abt(INT_MIN),abt(INT_MAX)]` from
the integer numbers.
Similarly, the interval of `double` values `[-DBL_MAX,DBL_MAX]` is the `double`
numeric set, which corresponds to the subset of the real numbers from `abt(-DBL_MAX)` to
`abt(DBL_MAX)`.
__SPACE__
Let [*`next(x)`] denote the lowest numeric value greater than x.
Let [*`prev(x)`] denote the highest numeric value lower then x.
Let [*`v=prev(next(V))`] and [*`v=next(prev(V))`] be identities that relate a numeric
typed value `v` with a number `V`.
An ordered pair of numeric values `x`,`y` s.t. `x<y` are [*consecutive] iff `next(x)==y`.
The abstract distance between consecutive numeric values is usually referred to as a
[_Unit in the Last Place], or [*ulp] for short. A ulp is a quantity whose abstract
magnitude is relative to the numeric values it corresponds to: If the numeric set
is not evenly distributed, that is, if the abstract distance between consecutive
numeric values varies along the set -as is the case with the floating-point types-,
the magnitude of 1ulp after the numeric value `x` might be (usually is) different
from the magnitude of a 1ulp after the numeric value y for `x!=y`.
Since numbers are inherently ordered, a [*numeric set] of type `T` is an ordered sequence
of numeric values (of type `T`) of the form:
REP(T)={l,next(l),next(next(l)),...,prev(prev(h)),prev(h),h}
where `l` and `h` are respectively the lowest and highest values of type `T`, called
the boundary values of type `T`.
__SPACE__
A numeric set is discrete. It has a [*size] which is the number of numeric values in the set,
a [*width] which is the abstract difference between the highest and lowest boundary values:
`[abt(h)-abt(l)]`, and a [*density] which is the relation between its size and width:
`density=size/width`.
The integer types have density 1, which means that there are no unrepresentable integer
numbers between `abt(l)` and `abt(h)` (i.e. there are no gaps). On the other hand,
floating types have density much smaller than 1, which means that there are real numbers
unrepresented between consecutive floating values (i.e. there are gaps).
__SPACE__
The interval of [_abstract values] `[abt(l),abt(h)]` is the range of the type `T`,
denoted `R(T)`.
A range is a set of abstract values and not a set of numeric values. In other
documents, such as the C++ standard, the word `range` is ['sometimes] used as synonym
for `numeric set`, that is, as the ordered sequence of numeric values from `l` to `h`.
In this document, however, a range is an abstract interval which subtends the
numeric set.
For example, the sequence `[-DBL_MAX,DBL_MAX]` is the numeric set of the type
`double`, and the real interval `[abt(-DBL_MAX),abt(DBL_MAX)]` is its range.
Notice, for instance, that the range of a floating-point type is ['continuous]
unlike its numeric set.
This definition was chosen because:
* [*(a)] The discrete set of numeric values is already given by the numeric set.
* [*(b)] Abstract intervals are easier to compare and overlap since only boundary
values need to be considered.
This definition allows for a concise definition of `subranged` as given in the last section.
The width of a numeric set, as defined, is exactly equivalent to the width of a range.
__SPACE__
The [*precision] of a type is given by the width or density of the numeric set.
For integer types, which have density 1, the precision is conceptually equivalent
to the range and is determined by the number of bits used in the value representation:
The higher the number of bits the bigger the size of the numeric set, the wider the
range, and the higher the precision.
For floating types, which have density <<1, the precision is given not by the width
of the range but by the density. In a typical implementation, the range is determined
by the number of bits used in the exponent, and the precision by the number of bits
used in the mantissa (giving the maximum number of significant digits that can be
exactly represented). The higher the number of exponent bits the wider the range,
while the higher the number of mantissa bits, the higher the precision.
[endsect]
[section Exact, Correctly Rounded and Out-Of-Range Representations]
Given an abstract value `V` and a type `T` with its corresponding range `[abt(l),abt(h)]`:
If `V < abt(l)` or `V > abt(h)`, `V` is [*not representable] (cannot be represented) in
the type `T`, or, equivalently, it's representation in the type `T` is [*out of range],
or [*overflows].
* If `V < abt(l)`, the [*overflow is negative].
* If `V > abt(h)`, the [*overflow is positive].
If `V >= abt(l)` and `V <= abt(h)`, `V` is [*representable] (can be represented) in the
type `T`, or, equivalently, its representation in the type `T` is [*in range], or
[*does not overflow].
Notice that a numeric type, such as a C++ unsigned type, can define that any `V` does
not overflow by always representing not `V` itself but the abstract value
`U = [ V % (abt(h)+1) ]`, which is always in range.
Given an abstract value `V` represented in the type `T` as `v`, the [*roundoff] error
of the representation is the abstract difference: `(abt(v)-V)`.
Notice that a representation is an ['operation], hence, the roundoff error corresponds
to the representation operation and not to the numeric value itself
(i.e. numeric values do not have any error themselves)
* If the roundoff is 0, the representation is [*exact], and `V` is exactly representable
in the type `T`.
* If the roundoff is not 0, the representation is [*inexact], and `V` is inexactly
representable in the type `T`.
If a representation `v` in a type `T` -either exact or inexact-, is any of the adjacents
of `V` in that type, that is, if `v==prev` or `v==next`, the representation is
faithfully rounded. If the choice between `prev` and `next` matches a given
[*rounding direction], it is [*correctly rounded].
All exact representations are correctly rounded, but not all inexact representations are.
In particular, C++ requires numeric conversions (described below) and the result of
arithmetic operations (not covered by this document) to be correctly rounded, but
batch operations propagate roundoff, thus final results are usually incorrectly
rounded, that is, the numeric value `r` which is the computed result is neither of
the adjacents of the abstract value `R` which is the theoretical result.
Because a correctly rounded representation is always one of adjacents of the abstract
value being represented, the roundoff is guaranteed to be at most 1ulp.
The following examples summarize the given definitions. Consider:
* A numeric type `Int` representing integer numbers with a
['numeric set]: `{-2,-1,0,1,2}` and
['range]: `[-2,2]`
* A numeric type `Cardinal` representing integer numbers with a
['numeric set]: `{0,1,2,3,4,5,6,7,8,9}` and
['range]: `[0,9]` (no modulo-arithmetic here)
* A numeric type `Real` representing real numbers with a
['numeric set]: `{-2.0,-1.5,-1.0,-0.5,-0.0,+0.0,+0.5,+1.0,+1.5,+2.0}` and
['range]: `[-2.0,+2.0]`
* A numeric type `Whole` representing real numbers with a
['numeric set]: `{-2.0,-1.0,0.0,+1.0,+2.0}` and
['range]: `[-2.0,+2.0]`
First, notice that the types `Real` and `Whole` both represent real numbers,
have the same range, but different precision.
* The integer number `1` (an abstract value) can be exactly represented
in any of these types.
* The integer number `-1` can be exactly represented in `Int`, `Real` and `Whole`,
but cannot be represented in `Cardinal`, yielding negative overflow.
* The real number `1.5` can be exactly represented in `Real`, and inexactly
represented in the other types.
* If `1.5` is represented as either `1` or `2` in any of the types (except `Real`),
the representation is correctly rounded.
* If `0.5` is represented as `+1.5` in the type `Real`, it is incorrectly rounded.
* `(-2.0,-1.5)` are the `Real` adjacents of any real number in the interval
`[-2.0,-1.5]`, yet there are no `Real` adjacents for `x < -2.0`, nor for `x > +2.0`.
[endsect]
[section Standard (numeric) Conversions]
The C++ language defines [_Standard Conversions] (§4) some of which are conversions
between arithmetic types.
These are [_Integral promotions] (§4.5), [_Integral conversions] (§4.7),
[_Floating point promotions] (§4.6), [_Floating point conversions] (§4.8) and
[_Floating-integral conversions] (§4.9).
In the sequel, integral and floating point promotions are called [*arithmetic promotions],
and these plus integral, floating-point and floating-integral conversions are called
[*arithmetic conversions] (i.e, promotions are conversions).
Promotions, both Integral and Floating point, are ['value-preserving], which means that
the typed value is not changed with the conversion.
In the sequel, consider a source typed value `s` of type `S`, the source abstract
value `N=abt(s)`, a destination type `T`; and whenever possible, a result typed value
`t` of type `T`.
Integer to integer conversions are always defined:
* If `T` is unsigned, the abstract value which is effectively represented is not
`N` but `M=[ N % ( abt(h) + 1 ) ]`, where `h` is the highest unsigned typed
value of type `T`.
* If `T` is signed and `N` is not directly representable, the result `t` is
[_implementation-defined], which means that the C++ implementation is required to
produce a value `t` even if it is totally unrelated to `s`.
Floating to Floating conversions are defined only if `N` is representable;
if it is not, the conversion has [_undefined behavior].
* If `N` is exactly representable, `t` is required to be the exact representation.
* If `N` is inexactly representable, `t` is required to be one of the two
adjacents, with an implementation-defined choice of rounding direction;
that is, the conversion is required to be correctly rounded.
Floating to Integer conversions represent not `N` but `M=trunc(N)`, were
`trunc()` is to truncate: i.e. to remove the fractional part, if any.
* If `M` is not representable in `T`, the conversion has [_undefined behavior]
(unless `T` is `bool`, see §4.12).
Integer to Floating conversions are always defined.
* If `N` is exactly representable, `t` is required to be the exact representation.
* If `N` is inexactly representable, `t` is required to be one of the
two adjacents, with an implementation-defined choice of rounding direction;
that is, the conversion is required to be correctly rounded.
[endsect]
[section Subranged Conversion Direction, Subtype and Supertype]
Given a source type `S` and a destination type `T`, there is a
[*conversion direction] denoted: `S->T`.
For any two ranges the following ['range relation] can be defined:
A range `X` can be ['entirely contained] in a range `Y`, in which case
it is said that `X` is enclosed by `Y`.
[: [*Formally:] `R(S)` is enclosed by `R(T)` iif `(R(S) intersection R(T)) == R(S)`.]
If the source type range, `R(S)`, is not enclosed in the target type range,
`R(T)`; that is, if `(R(S) & R(T)) != R(S)`, the conversion direction is said
to be [*subranged], which means that `R(S)` is not entirely contained in `R(T)`
and therefore there is some portion of the source range which falls outside
the target range. In other words, if a conversion direction `S->T` is subranged,
there are values in `S` which cannot be represented in `T` because they are
out of range.
Notice that for `S->T`, the adjective subranged applies to `T`.
Examples:
Given the following numeric types all representing real numbers:
* `X` with numeric set `{-2.0,-1.0,0.0,+1.0,+2.0}` and range `[-2.0,+2.0]`
* `Y` with numeric set `{-2.0,-1.5,-1.0,-0.5,0.0,+0.5,+1.0,+1.5,+2.0}` and range `[-2.0,+2.0]`
* `Z` with numeric set `{-1.0,0.0,+1.0}` and range `[-1.0,+1.0]`
For:
[variablelist
[[(a) X->Y:][
`R(X) & R(Y) == R(X)`, then `X->Y` is not subranged.
Thus, all values of type `X` are representable in the type `Y`.
]]
[[(b) Y->X:][
`R(Y) & R(X) == R(Y)`, then `Y->X` is not subranged.
Thus, all values of type `Y` are representable in the type `X`, but in this case,
some values are ['inexactly] representable (all the halves).
(note: it is to permit this case that a range is an interval of abstract values and
not an interval of typed values)
]]
[[(b) X->Z:][
`R(X) & R(Z) != R(X)`, then `X->Z` is subranged.
Thus, some values of type `X` are not representable in the type `Z`, they fall
out of range `(-2.0 and +2.0)`.
]]
]
It is possible that `R(S)` is not enclosed by `R(T)`, while neither is `R(T)` enclosed
by `R(S)`; for example, `UNSIG=[0,255]` is not enclosed by `SIG=[-128,127]`;
neither is `SIG` enclosed by `UNSIG`.
This implies that is possible that a conversion direction is subranged both ways.
This occurs when a mixture of signed/unsigned types are involved and indicates that
in both directions there are values which can fall out of range.
Given the range relation (subranged or not) of a conversion direction `S->T`, it
is possible to classify `S` and `T` as [*supertype] and [*subtype]:
If the conversion is subranged, which means that `T` cannot represent all possible
values of type `S`, `S` is the supertype and `T` the subtype; otherwise, `T` is the
supertype and `S` the subtype.
For example:
[: `R(float)=[-FLT_MAX,FLT_MAX]` and `R(double)=[-DBL_MAX,DBL_MAX]` ]
If `FLT_MAX < DBL_MAX`:
* `double->float` is subranged and `supertype=double`, `subtype=float`.
* `float->double` is not subranged and `supertype=double`, `subtype=float`.
Notice that while `double->float` is subranged, `float->double` is not,
which yields the same supertype,subtype for both directions.
Now consider:
[: `R(int)=[INT_MIN,INT_MAX]` and `R(unsigned int)=[0,UINT_MAX]` ]
A C++ implementation is required to have `UINT_MAX > INT_MAX` (§3.9/3), so:
* 'int->unsigned' is subranged (negative values fall out of range)
and `supertype=int`, `subtype=unsigned`.
* 'unsigned->int' is ['also] subranged (high positive values fall out of range)
and `supertype=unsigned`, `subtype=int`.
In this case, the conversion is subranged in both directions and the
supertype,subtype pairs are not invariant (under inversion of direction).
This indicates that none of the types can represent all the values of the other.
When the supertype is the same for both `S->T` and `T->S`, it is effectively
indicating a type which can represent all the values of the subtype.
Consequently, if a conversion `X->Y` is not subranged, but the opposite `(Y->X)` is,
so that the supertype is always `Y`, it is said that the direction `X->Y` is [*correctly
rounded value preserving], meaning that all such conversions are guaranteed to
produce results in range and correctly rounded (even if inexact).
For example, all integer to floating conversions are correctly rounded value preserving.
[endsect]
[endsect]

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<div class="toc"><dl class="toc">
<dt><span class="section"><a href="bounds___traits_class.html#boost_numericconversion.bounds___traits_class.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="bounds___traits_class.html#boost_numericconversion.bounds___traits_class.traits_class_bounds_n_">traits
class bounds&lt;N&gt;</a></span></dt>
<dt><span class="section"><a href="bounds___traits_class.html#boost_numericconversion.bounds___traits_class.examples">Examples</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.bounds___traits_class.introduction"></a><a class="link" href="bounds___traits_class.html#boost_numericconversion.bounds___traits_class.introduction" title="Introduction">Introduction</a>
</h3></div></div></div>
<p>
To determine the ranges of numeric types with <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>
[18.2.1], different syntax have to be used depending on numeric type. Specifically,
<code class="computeroutput"><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">min</span><span class="special">()</span></code> for
integral types returns the minimum finite value, whereas for floating point
types it returns the minimum positive normalized value. The difference in
semantics makes client code unnecessarily complex and error prone.
</p>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bounds</span><span class="special">&lt;&gt;</span></code>
provides a consistent interface for retrieving the maximum finite value,
the minimum finite value and the minimum positive normalized value (0 for
integral types) for numeric types. The selection of implementation is performed
at compile time, so there is no runtime overhead.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.bounds___traits_class.traits_class_bounds_n_"></a><a class="link" href="bounds___traits_class.html#boost_numericconversion.bounds___traits_class.traits_class_bounds_n_" title="traits class bounds&lt;N&gt;">traits
class bounds&lt;N&gt;</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">N</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">bounds</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="identifier">N</span> <span class="identifier">lowest</span> <span class="special">()</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">implementation_defined</span><span class="special">;</span> <span class="special">}</span>
<span class="keyword">static</span> <span class="identifier">N</span> <span class="identifier">highest</span> <span class="special">()</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">implementation_defined</span><span class="special">;</span> <span class="special">}</span>
<span class="keyword">static</span> <span class="identifier">N</span> <span class="identifier">smallest</span><span class="special">()</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">implementation_defined</span><span class="special">;</span> <span class="special">}</span>
<span class="special">};</span>
</pre>
<h5>
<a name="boost_numericconversion.bounds___traits_class.traits_class_bounds_n_.h0"></a>
<span class="phrase"><a name="boost_numericconversion.bounds___traits_class.traits_class_bounds_n_.members"></a></span><a class="link" href="bounds___traits_class.html#boost_numericconversion.bounds___traits_class.traits_class_bounds_n_.members">Members</a>
</h5>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="identifier">lowest</span><span class="special">()</span></code>
</p></blockquote></div>
<p>
Returns the minimum finite value, equivalent to <code class="computeroutput"><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">min</span><span class="special">()</span></code> when
<code class="computeroutput"><span class="identifier">T</span></code> is an integral type, and
to <code class="computeroutput"><span class="special">-</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">()</span></code> when
<code class="computeroutput"><span class="identifier">T</span></code> is a floating point type.
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="identifier">highest</span><span class="special">()</span></code>
</p></blockquote></div>
<p>
Returns the maximum finite value, equivalent to <code class="computeroutput"><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">()</span></code>.
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="identifier">smallest</span><span class="special">()</span></code>
</p></blockquote></div>
<p>
Returns the smallest positive normalized value for floating point types with
denormalization, or returns 0 for integral types.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.bounds___traits_class.examples"></a><a class="link" href="bounds___traits_class.html#boost_numericconversion.bounds___traits_class.examples" title="Examples">Examples</a>
</h3></div></div></div>
<p>
The following example demonstrates the use of <code class="computeroutput"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bounds</span><span class="special">&lt;&gt;</span></code> and the equivalent code using <code class="computeroutput"><span class="identifier">numeric_limits</span></code>:
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">conversion</span><span class="special">/</span><span class="identifier">bounds</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">limits</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> <span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"numeric::bounds versus numeric_limits example.\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The maximum value for float:\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bounds</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;::</span><span class="identifier">highest</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The minimum value for float:\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bounds</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;::</span><span class="identifier">lowest</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="special">-</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"The smallest positive value for float:\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bounds</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;::</span><span class="identifier">smallest</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;::</span><span class="identifier">min</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">"\n"</span><span class="special">;</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_numericconversion.conversion_traits___traits_class"></a><a class="link" href="conversion_traits___traits_class.html" title="conversion_traits&lt;&gt; traits class">conversion_traits&lt;&gt;
traits class</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types">Types</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.examples">Examples</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types" title="Types">Types</a>
</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_int_float_mixture_enum">enumeration
int_float_mixture_enum</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_sign_mixture_enum">enumeration
sign_mixture_enum</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_udt_builtin_mixture_enum">enumeration
udt_builtin_mixture_enum</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_int_float_mixture__">template
class int_float_mixture&lt;&gt;</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_sign_mixture__">template
class sign_mixture&lt;&gt;</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_udt_builtin_mixture__">template
class udt_builtin_mixture&lt;&gt;</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_is_subranged__">template
class is_subranged&lt;&gt;</a></span></dt>
<dt><span class="section"><a href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_conversion_traits__">template
class conversion_traits&lt;&gt;</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.enumeration_int_float_mixture_enum"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_int_float_mixture_enum" title="enumeration int_float_mixture_enum">enumeration
int_float_mixture_enum</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">enum</span> <span class="identifier">int_float_mixture_enum</span>
<span class="special">{</span>
<span class="identifier">integral_to_integral</span>
<span class="special">,</span><span class="identifier">integral_to_float</span>
<span class="special">,</span><span class="identifier">float_to_integral</span>
<span class="special">,</span><span class="identifier">float_to_float</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace boost::numeric</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.enumeration_sign_mixture_enum"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_sign_mixture_enum" title="enumeration sign_mixture_enum">enumeration
sign_mixture_enum</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">enum</span> <span class="identifier">sign_mixture_enum</span>
<span class="special">{</span>
<span class="identifier">unsigned_to_unsigned</span>
<span class="special">,</span><span class="identifier">signed_to_signed</span>
<span class="special">,</span><span class="identifier">signed_to_unsigned</span>
<span class="special">,</span><span class="identifier">unsigned_to_signed</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace boost::numeric</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.enumeration_udt_builtin_mixture_enum"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_udt_builtin_mixture_enum" title="enumeration udt_builtin_mixture_enum">enumeration
udt_builtin_mixture_enum</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">enum</span> <span class="identifier">udt_builtin_mixture_enum</span>
<span class="special">{</span>
<span class="identifier">builtin_to_builtin</span>
<span class="special">,</span><span class="identifier">builtin_to_udt</span>
<span class="special">,</span><span class="identifier">udt_to_builtin</span>
<span class="special">,</span><span class="identifier">udt_to_udt</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace boost::numeric</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.template_class_int_float_mixture__"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_int_float_mixture__" title="template class int_float_mixture&lt;&gt;">template
class int_float_mixture&lt;&gt;</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">int_float_mixture</span> <span class="special">:</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">int_float_mixture_enum</span><span class="special">,</span> <span class="identifier">impl</span><span class="special">-</span><span class="identifier">def</span><span class="special">-</span><span class="identifier">value</span><span class="special">&gt;</span> <span class="special">{}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace boost::numeric</span>
</pre>
<p>
Classifying <code class="computeroutput"><span class="identifier">S</span></code> and <code class="computeroutput"><span class="identifier">T</span></code> as either integral or float, this
<a href="../../../../../mpl/doc/refmanual/integral-constant.html" target="_top">MPL's
Integral Constant</a> indicates the combination of these attributes.
</p>
<p>
Its <code class="computeroutput"><span class="special">::</span><span class="identifier">value</span></code>
is of enumeration type <a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_int_float_mixture_enum" title="enumeration int_float_mixture_enum"><code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">int_float_mixture_enum</span></code></a>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.template_class_sign_mixture__"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_sign_mixture__" title="template class sign_mixture&lt;&gt;">template
class sign_mixture&lt;&gt;</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">sign_mixture</span> <span class="special">:</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">sign_mixture_enum</span><span class="special">,</span> <span class="identifier">impl</span><span class="special">-</span><span class="identifier">def</span><span class="special">-</span><span class="identifier">value</span><span class="special">&gt;</span> <span class="special">{}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace boost::numeric</span>
</pre>
<p>
Classifying <code class="computeroutput"><span class="identifier">S</span></code> and <code class="computeroutput"><span class="identifier">T</span></code> as either signed or unsigned, this
<a href="../../../../../mpl/doc/refmanual/integral-constant.html" target="_top">MPL's
Integral Constant</a> indicates the combination of these attributes.
</p>
<p>
Its <code class="computeroutput"><span class="special">::</span><span class="identifier">value</span></code>
is of enumeration type <a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_sign_mixture_enum" title="enumeration sign_mixture_enum"><code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">sign_mixture_enum</span></code></a>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.template_class_udt_builtin_mixture__"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_udt_builtin_mixture__" title="template class udt_builtin_mixture&lt;&gt;">template
class udt_builtin_mixture&lt;&gt;</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">udt_builtin_mixture</span> <span class="special">:</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">udt_builtin__mixture_enum</span><span class="special">,</span> <span class="identifier">impl</span><span class="special">-</span><span class="identifier">def</span><span class="special">-</span><span class="identifier">value</span><span class="special">&gt;</span> <span class="special">{}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace boost::numeric</span>
</pre>
<p>
Classifying <code class="computeroutput"><span class="identifier">S</span></code> and <code class="computeroutput"><span class="identifier">T</span></code> as either user-defined or builtin,
this <a href="../../../../../mpl/doc/refmanual/integral-constant.html" target="_top">MPL's
Integral Constant</a> indicates the combination of these attributes.
</p>
<p>
Its <code class="computeroutput"><span class="special">::</span><span class="identifier">value</span></code>
is of enumeration type <a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.enumeration_udt_builtin_mixture_enum" title="enumeration udt_builtin_mixture_enum"><code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">udt_builtin_mixture_enum</span></code></a>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.template_class_is_subranged__"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_is_subranged__" title="template class is_subranged&lt;&gt;">template
class is_subranged&lt;&gt;</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">is_subranged</span> <span class="special">:</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">bool_</span><span class="special">&lt;</span><span class="identifier">impl</span><span class="special">-</span><span class="identifier">def</span><span class="special">-</span><span class="identifier">value</span><span class="special">&gt;</span> <span class="special">{}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace boost::numeric</span>
</pre>
<p>
Indicates if the range of the target type <code class="computeroutput"><span class="identifier">T</span></code>
is a subset of the range of the source type <code class="computeroutput"><span class="identifier">S</span></code>.
That is: if there are some source values which fall out of the Target type's
range.
</p>
<p>
It is a boolean <a href="../../../../../mpl/doc/refmanual/integral-constant.html" target="_top">MPL's
Integral Constant</a> .
</p>
<p>
It does not indicate if a particular conversion is effectively out of range;
it indicates that some conversion might be out of range because not all
the source values are representable as Target type.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.types.template_class_conversion_traits__"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_conversion_traits__" title="template class conversion_traits&lt;&gt;">template
class conversion_traits&lt;&gt;</a>
</h4></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">conversion_traits</span>
<span class="special">{</span>
<span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">int_float_mixture_enum</span> <span class="special">,</span> <span class="special">...&gt;</span> <span class="identifier">int_float_mixture</span> <span class="special">;</span>
<span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">sign_mixture_enum</span> <span class="special">,</span> <span class="special">...&gt;</span> <span class="identifier">sign_mixture</span><span class="special">;</span>
<span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">udt_builtin_mixture_enum</span><span class="special">,</span> <span class="special">...&gt;</span> <span class="identifier">udt_builtin_mixture</span> <span class="special">;</span>
<span class="identifier">mpl</span><span class="special">::</span><span class="identifier">bool_</span><span class="special">&lt;...&gt;</span> <span class="identifier">subranged</span> <span class="special">;</span>
<span class="identifier">mpl</span><span class="special">::</span><span class="identifier">bool_</span><span class="special">&lt;...&gt;</span> <span class="identifier">trivial</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">target_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">S</span> <span class="identifier">source_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="special">...</span> <span class="identifier">argument_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="special">...</span> <span class="identifier">result_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="special">...</span> <span class="identifier">supertype</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="special">...</span> <span class="identifier">subtype</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace numeric, namespace boost</span>
</pre>
<p>
This traits class indicates some properties of a <span class="emphasis"><em>numeric conversion</em></span>
direction: from a source type <code class="computeroutput"><span class="identifier">S</span></code>
to a target type <code class="computeroutput"><span class="identifier">T</span></code>. It
does not indicate the properties of a <span class="emphasis"><em>specific</em></span> conversion,
but of the conversion direction. See <a class="link" href="definitions.html#boost_numericconversion.definitions.subranged_conversion_direction__subtype_and_supertype" title="Subranged Conversion Direction, Subtype and Supertype">Definitions</a>
for details.
</p>
<p>
The traits class provides the following <a href="../../../../../mpl/doc/refmanual/integral-constant.html" target="_top">MPL's
Integral Constant</a> \s of enumeration type. They express the combination
of certain attributes of the Source and Target types (thus they are call
mixture):
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<span class="bold"><strong>int_float_mixture </strong></span>
</p>
</td>
<td>
<p>
Same as given by the traits class <a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_int_float_mixture__" title="template class int_float_mixture&lt;&gt;">int_float_mixture</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="bold"><strong>sign_mixture </strong></span>
</p>
</td>
<td>
<p>
Same as given by the traits class <a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_sign_mixture__" title="template class sign_mixture&lt;&gt;">sign_mixture</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="bold"><strong>udt_builtin_mixture </strong></span>
</p>
</td>
<td>
<p>
Same as given by the traits class <a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_udt_builtin_mixture__" title="template class udt_builtin_mixture&lt;&gt;">udt_builtin_mixture</a>
</p>
</td>
</tr>
</tbody>
</table></div>
<p>
The traits class provides the following <a href="../../../../../mpl/doc/refmanual/integral-constant.html" target="_top">MPL's
Integral Constant</a> \s of boolean type which indicates indirectly
the relation between the Source and Target ranges (see <a class="link" href="definitions.html#boost_numericconversion.definitions.range_and_precision" title="Range and Precision">Definitions</a>
for details).
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
subranged
</p>
</td>
<td>
<p>
Same as given by <a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types.template_class_is_subranged__" title="template class is_subranged&lt;&gt;">is_subranged</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
trivial
</p>
</td>
<td>
<p>
Indicates if both Source and Target, <span class="underline">without
cv-qualifications</span>, are the same type.
</p>
<p>
Its <code class="computeroutput"><span class="special">::</span><span class="identifier">value</span></code>
is of boolean type.
</p>
</td>
</tr>
</tbody>
</table></div>
<p>
The traits class provides the following types. They are the Source and
Target types classified and qualified for different purposes.
</p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<span class="bold"><strong>target_type</strong></span>
</p>
</td>
<td>
<p>
The template parameter <code class="computeroutput"><span class="identifier">T</span></code>
without cv-qualifications
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="bold"><strong>source_type</strong></span>
</p>
</td>
<td>
<p>
The template parameter <code class="computeroutput"><span class="identifier">S</span></code>
without cv-qualifications
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="bold"><strong>argument_type</strong></span>
</p>
</td>
<td>
<p>
This type is either source_type or <code class="computeroutput"><span class="identifier">source_type</span>
<span class="keyword">const</span><span class="special">&amp;</span></code>.
</p>
<p>
It represents the optimal argument type for the <a class="link" href="converter___function_object.html" title="converter&lt;&gt; function object">converter</a>
member functions.
</p>
<p>
If S is a built-in type, this is <code class="computeroutput"><span class="identifier">source_type</span></code>,
otherwise, this is <code class="computeroutput"><span class="identifier">source_type</span>
<span class="keyword">const</span><span class="special">&amp;</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="bold"><strong>result_type</strong></span>
</p>
</td>
<td>
<p>
This type is either target_type or target_type const&amp;
</p>
<p>
It represents the return type of the <a class="link" href="converter___function_object.html" title="converter&lt;&gt; function object">converter</a>
member functions.
</p>
<p>
If <code class="computeroutput"><span class="identifier">T</span><span class="special">==</span><span class="identifier">S</span></code>, it is <code class="computeroutput"><span class="identifier">target_type</span>
<span class="keyword">const</span><span class="special">&amp;</span></code>,
otherwise, it is <code class="computeroutput"><span class="identifier">target_type</span></code>.
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="bold"><strong>supertype</strong></span>
</p>
</td>
<td>
<p>
If the conversion is subranged, it is <code class="computeroutput"><span class="identifier">source_type</span></code>,
otherwise, it is <code class="computeroutput"><span class="identifier">target_type</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<span class="bold"><strong>subtype</strong></span>
</p>
</td>
<td>
<p>
If the conversion is subranged, it is <code class="computeroutput"><span class="identifier">target_type</span></code>,
otherwise, it is <code class="computeroutput"><span class="identifier">source_type</span></code>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.conversion_traits___traits_class.examples"></a><a class="link" href="conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.examples" title="Examples">Examples</a>
</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">cassert</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">typeinfo</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">conversion</span><span class="special">/</span><span class="identifier">conversion_traits</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="comment">// A trivial conversion.</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="keyword">short</span><span class="special">,</span><span class="keyword">short</span><span class="special">&gt;</span> <span class="identifier">Short2Short_Traits</span> <span class="special">;</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="identifier">Short2Short_Traits</span><span class="special">::</span><span class="identifier">trivial</span><span class="special">::</span><span class="identifier">value</span> <span class="special">)</span> <span class="special">;</span>
<span class="comment">// A subranged conversion.</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span><span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">UInt2Double_Traits</span> <span class="special">;</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="identifier">UInt2Double_Traits</span><span class="special">::</span><span class="identifier">int_float_mixture</span><span class="special">::</span><span class="identifier">value</span> <span class="special">==</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">integral_to_float</span> <span class="special">)</span> <span class="special">;</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="identifier">UInt2Double_Traits</span><span class="special">::</span><span class="identifier">sign_mixture</span><span class="special">::</span><span class="identifier">value</span> <span class="special">==</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">unsigned_to_signed</span> <span class="special">)</span> <span class="special">;</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="special">!</span><span class="identifier">UInt2Double_Traits</span><span class="special">::</span><span class="identifier">subranged</span><span class="special">::</span><span class="identifier">value</span> <span class="special">)</span> <span class="special">;</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">UInt2Double_Traits</span><span class="special">::</span><span class="identifier">supertype</span><span class="special">)</span> <span class="special">==</span> <span class="keyword">typeid</span><span class="special">(</span><span class="keyword">double</span><span class="special">)</span> <span class="special">)</span> <span class="special">;</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="keyword">typeid</span><span class="special">(</span><span class="identifier">UInt2Double_Traits</span><span class="special">::</span><span class="identifier">subtype</span><span class="special">)</span> <span class="special">==</span> <span class="keyword">typeid</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">)</span> <span class="special">)</span> <span class="special">;</span>
<span class="comment">// A doubly subranged conversion.</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="keyword">short</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">short</span><span class="special">&gt;::</span><span class="identifier">subranged</span><span class="special">::</span><span class="identifier">value</span><span class="special">)</span> <span class="special">);</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">short</span><span class="special">,</span> <span class="keyword">short</span><span class="special">&gt;::</span><span class="identifier">subranged</span><span class="special">::</span><span class="identifier">value</span><span class="special">)</span> <span class="special">);</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
</div>
</div>
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<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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<a name="boost_numericconversion.converter___function_object"></a><a class="link" href="converter___function_object.html" title="converter&lt;&gt; function object">converter&lt;&gt;
function object</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="converter___function_object.html#boost_numericconversion.converter___function_object.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="converter___function_object.html#boost_numericconversion.converter___function_object.template_parameters">Template
parameters</a></span></dt>
<dt><span class="section"><a href="converter___function_object.html#boost_numericconversion.converter___function_object.member_functions">Member
functions</a></span></dt>
<dt><span class="section"><a href="converter___function_object.html#boost_numericconversion.converter___function_object.range_checking_logic">Range
Checking Logic</a></span></dt>
<dt><span class="section"><a href="converter___function_object.html#boost_numericconversion.converter___function_object.examples">Examples</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.converter___function_object.synopsis"></a><a class="link" href="converter___function_object.html#boost_numericconversion.converter___function_object.synopsis" title="Synopsis">Synopsis</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span>
<span class="keyword">class</span> <span class="identifier">S</span><span class="special">,</span>
<span class="keyword">class</span> <span class="identifier">Traits</span><span class="special">,</span> <span class="special">=</span> <span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span><span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">OverflowHandler</span> <span class="special">=</span> <span class="identifier">def_overflow_handler</span><span class="special">,</span>
<span class="keyword">class</span> <span class="identifier">Float2IntRounder</span> <span class="special">=</span> <span class="identifier">Trunc</span><span class="special">&lt;</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">source_type</span> <span class="special">&gt;,</span>
<span class="keyword">class</span> <span class="identifier">RawConverter</span> <span class="special">=</span> <span class="identifier">raw_converter</span><span class="special">&lt;</span><span class="identifier">Traits</span><span class="special">&gt;,</span>
<span class="keyword">class</span> <span class="identifier">UserRangeChecker</span> <span class="special">=</span> <span class="identifier">UseInternalRangeChecker</span>
<span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">converter</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">Traits</span> <span class="identifier">traits</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">source_type</span> <span class="identifier">source_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">argument_type</span> <span class="identifier">argument_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">result_type</span> <span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">result_type</span> <span class="identifier">convert</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">;</span>
<span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="keyword">const</span> <span class="special">;</span>
<span class="comment">// Internal member functions:</span>
<span class="keyword">static</span> <span class="identifier">range_check_result</span> <span class="identifier">out_of_range</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">;</span>
<span class="keyword">static</span> <span class="keyword">void</span> <span class="identifier">validate_range</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">result_type</span> <span class="identifier">low_level_convert</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace numeric, boost</span>
</pre>
<p>
<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">converter</span><span class="special">&lt;&gt;</span></code>
is a <a href="http://www.sgi.com/tech/stl/UnaryFunction.html" target="_top">Unary Function
Object</a> encapsulating the code to perform a numeric conversion with
the direction and properties specified by the Traits template parameter.
It can optionally take some <a class="link" href="numeric_converter_policy_classes.html" title="Numeric Converter Policy Classes">policies</a>
which can be used to customize its behavior. The <code class="computeroutput"><span class="identifier">Traits</span></code>
parameter is not a policy but the parameter that defines the conversion.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.converter___function_object.template_parameters"></a><a class="link" href="converter___function_object.html#boost_numericconversion.converter___function_object.template_parameters" title="Template parameters">Template
parameters</a>
</h3></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
</th>
<th>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">T</span></code>
</p>
</td>
<td>
<p>
The <a class="link" href="definitions.html#boost_numericconversion.definitions.numeric_types" title="Numeric Types">Numeric
Type</a> which is the <span class="emphasis"><em>Target</em></span> of the conversion.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">S</span></code>
</p>
</td>
<td>
<p>
The <a class="link" href="definitions.html#boost_numericconversion.definitions.numeric_types" title="Numeric Types">Numeric
Type</a> which is the <span class="emphasis"><em>Source</em></span> of the conversion.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">Traits</span></code>
</p>
</td>
<td>
<p>
This must be a conversion traits class with the interface of <a class="link" href="conversion_traits___traits_class.html" title="conversion_traits&lt;&gt; traits class"><code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">conversion_traits</span></code></a>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">OverflowHandler</span></code>
</p>
</td>
<td>
<p>
<span class="bold"><strong>Stateless Policy</strong></span> called to administrate
the result of the range checking.
</p>
<p>
It is a <span class="bold"><strong>Function Object</strong></span> which
receives the result of <code class="computeroutput"><span class="identifier">out_of_range</span><span class="special">()</span></code> and is called inside the <code class="computeroutput"><span class="identifier">validate_range</span><span class="special">()</span></code>
static member function exposed by the converter.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">Float2IntRounder</span></code>
</p>
</td>
<td>
<p>
<span class="bold"><strong>Stateless Policy</strong></span> which specifies
the rounding mode used for float to integral conversions.
</p>
<p>
It supplies the <code class="computeroutput"><span class="identifier">nearbyint</span><span class="special">()</span></code> static member function exposed
by the converter.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">RawConverter</span></code>
</p>
</td>
<td>
<p>
<span class="bold"><strong>Stateless Policy</strong></span> which is used
to perform the actual conversion.
</p>
<p>
It supplies the <code class="computeroutput"><span class="identifier">low_level_convert</span><span class="special">()</span></code> static member function exposed
by the converter.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">UserRangeChecker</span></code>
</p>
</td>
<td>
<p>
<span class="emphasis"><em>Special and Optional</em></span> <span class="bold"><strong>Stateless
Policy</strong></span> which can be used to override the internal range
checking logic.
</p>
<p>
If given, supplies alternative code for the <code class="computeroutput"><span class="identifier">out_of_range</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">validate_range</span><span class="special">()</span></code> static member functions exposed
by the converter.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.converter___function_object.member_functions"></a><a class="link" href="converter___function_object.html#boost_numericconversion.converter___function_object.member_functions" title="Member functions">Member
functions</a>
</h3></div></div></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="keyword">static</span> <span class="identifier">result_type</span>
<span class="identifier">converter</span><span class="special">&lt;&gt;::</span><span class="identifier">convert</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span>
<span class="special">)</span> <span class="special">;</span> <span class="comment">// throw</span> </code>
</p></blockquote></div>
<p>
This static member function converts an rvalue of type <code class="computeroutput"><span class="identifier">source_type</span></code>
to an rvalue of type <code class="computeroutput"><span class="identifier">target_type</span></code>.
</p>
<p>
If the conversion requires it, it performs a range checking before the conversion
and passes the result of the check to the overflow handler policy (the default
policy throws an exception if out-of-range is detected)
</p>
<p>
The implementation of this function is actually built from the policies and
is basically as follows:
</p>
<pre class="programlisting"><span class="identifier">result_type</span> <span class="identifier">converter</span><span class="special">&lt;&gt;::</span><span class="identifier">convert</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">validate_range</span><span class="special">(</span><span class="identifier">s</span><span class="special">);</span> <span class="comment">// Implemented by the internal range checking logic</span>
<span class="comment">// (which also calls the OverflowHandler policy)</span>
<span class="comment">// or externally supplied by the UserRangeChecker policy.</span>
<span class="identifier">s</span> <span class="special">=</span> <span class="identifier">nearbyint</span><span class="special">(</span><span class="identifier">s</span><span class="special">);</span> <span class="comment">// Externally supplied by the Float2IntRounder policy.</span>
<span class="comment">// NOTE: This is actually called only for float to int conversions.</span>
<span class="keyword">return</span> <span class="identifier">low_level_convert</span><span class="special">(</span><span class="identifier">s</span><span class="special">);</span> <span class="comment">// Externally supplied by the RawConverter policy.</span>
<span class="special">}</span>
</pre>
<p>
<code class="computeroutput"><span class="identifier">converter</span><span class="special">&lt;&gt;::</span><span class="keyword">operator</span><span class="special">()</span> <span class="keyword">const</span></code> just calls <code class="computeroutput"><span class="identifier">convert</span><span class="special">()</span></code>
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="keyword">static</span> <span class="identifier">range_check_result</span>
<span class="identifier">numeric_converter</span><span class="special">&lt;&gt;::</span><span class="identifier">out_of_range</span> <span class="special">(</span>
<span class="identifier">argument_type</span> <span class="identifier">s</span>
<span class="special">)</span> <span class="special">;</span></code>
</p></blockquote></div>
<p>
This <a class="link" href="converter___function_object.html#numeric_conversion_converter_internal">internal</a>
static member function determines if the value <code class="computeroutput"><span class="identifier">s</span></code>
can be represented by the target type without overflow.
</p>
<p>
It does not determine if the conversion is <span class="emphasis"><em>exact</em></span>; that
is, it does not detect <span class="emphasis"><em>inexact</em></span> conversions, only <span class="emphasis"><em>out-of-range</em></span>
conversions (see the <a class="link" href="definitions.html#boost_numericconversion.definitions.exact__correctly_rounded_and_out_of_range_representations" title="Exact, Correctly Rounded and Out-Of-Range Representations">Definitions</a>
for further details).
</p>
<p>
The return value is of enum type <a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.enum_range_check_result" title="enum range_check_result"><code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">range_check_result</span></code></a>
</p>
<p>
The actual code for the range checking logic is optimized for the combined
properties of the source and target types. For example, a non-subranged conversion
(i.e: <code class="computeroutput"><span class="keyword">int</span></code>-&gt;<code class="computeroutput"><span class="keyword">float</span></code>), requires no range checking, so <code class="computeroutput"><span class="identifier">out_of_range</span><span class="special">()</span></code>
returns <code class="computeroutput"><span class="identifier">cInRange</span></code> directly.
See the following <a class="link" href="converter___function_object.html#boost_numericconversion.converter___function_object.range_checking_logic" title="Range Checking Logic">table</a>
for more details.
</p>
<p>
If the user supplied a <a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker" title="Policy UserRangeChecker">UserRangeChecker</a>
policy, is this policy which implements this function, so the implementation
is user defined, although it is expected to perform the same conceptual check
and return the appropriate result.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="keyword">static</span> <span class="keyword">void</span>
<span class="identifier">numeric_converter</span><span class="special">&lt;&gt;::</span><span class="identifier">validate_range</span> <span class="special">(</span>
<span class="identifier">argument_type</span> <span class="identifier">s</span>
<span class="special">)</span> <span class="special">;</span> <span class="comment">// no throw</span> </code>
</p></blockquote></div>
<p>
This <a class="link" href="converter___function_object.html#numeric_conversion_converter_internal">internal</a>
static member function calls out_of_range(s), and passes the result to the
<a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler" title="Policy OverflowHandler">OverflowHandler</a>
policy class.
</p>
<p>
For those Target/Source combinations which don't require range checking,
this is an empty inline function.
</p>
<p>
If the user supplied a <a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker" title="Policy UserRangeChecker">UserRangeChecker</a>
policy, is this policy which implements this function, so the implementation
is user defined, although it is expected to perform the same action as the
default. In particular, it is expected to pass the result of the check to
the overflow handler.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="keyword">static</span> <span class="identifier">result_type</span>
<span class="identifier">numeric_converter</span><span class="special">&lt;&gt;::</span><span class="identifier">low_level_convert</span> <span class="special">(</span>
<span class="identifier">argument_type</span> <span class="identifier">s</span>
<span class="special">)</span> <span class="special">;</span></code>
</p></blockquote></div>
<p>
This <a class="link" href="converter___function_object.html#numeric_conversion_converter_internal">internal</a>
static member function performs the actual conversion.
</p>
<p>
This function is externally supplied by the <a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter" title="Policy RawConverter">RawConverter</a>
policy class.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="keyword">static</span> <span class="identifier">source_type</span>
<span class="identifier">converter</span><span class="special">&lt;&gt;::</span><span class="identifier">nearbyint</span> <span class="special">(</span>
<span class="identifier">argument_type</span> <span class="identifier">s</span>
<span class="special">)</span> <span class="special">;</span></code>
</p></blockquote></div>
<p>
This <a class="link" href="converter___function_object.html#numeric_conversion_converter_internal">internal</a>
static member function, which is <span class="underline">only used</span>
for <code class="computeroutput"><span class="keyword">float</span></code> to <code class="computeroutput"><span class="keyword">int</span></code>
conversions, returns an <span class="emphasis"><em>integer</em></span> value of <span class="emphasis"><em><span class="underline">floating-point type</span></em></span> according to some
rounding direction.
</p>
<p>
This function is externally supplied by the <a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder" title="Policy Float2IntRounder">Float2IntRounder</a>
policy class which encapsulates the specific rounding mode.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<a name="numeric_conversion_converter_internal"></a><h5>
<a name="boost_numericconversion.converter___function_object.member_functions.h0"></a>
<span class="phrase"><a name="boost_numericconversion.converter___function_object.member_functions.internal_member_functions"></a></span><a class="link" href="converter___function_object.html#boost_numericconversion.converter___function_object.member_functions.internal_member_functions">Internal
Member Functions</a>
</h5>
<p>
These static member functions build the actual conversion code used by <code class="computeroutput"><span class="identifier">convert</span><span class="special">()</span></code>.
The user does not have to call these if calling <code class="computeroutput"><span class="identifier">convert</span><span class="special">()</span></code>, since <code class="computeroutput"><span class="identifier">convert</span><span class="special">()</span></code> calls them infernally, but they can be
called separately for specific needs.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.converter___function_object.range_checking_logic"></a><a class="link" href="converter___function_object.html#boost_numericconversion.converter___function_object.range_checking_logic" title="Range Checking Logic">Range
Checking Logic</a>
</h3></div></div></div>
<p>
The following table summarizes the internal range checking logic performed
for each combination of the properties of Source and Target.
</p>
<p>
LowestT/HighestT denotes the highest and lowest values of the Target type,
respectively.
</p>
<p>
<code class="computeroutput"><span class="identifier">S</span><span class="special">(</span><span class="identifier">n</span><span class="special">)</span></code> is short
for <code class="computeroutput"><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">S</span><span class="special">&gt;(</span><span class="identifier">n</span><span class="special">)</span></code> (<code class="computeroutput"><span class="identifier">S</span></code> denotes the Source type).
</p>
<p>
<code class="computeroutput"><span class="identifier">NONE</span></code> indicates that for this
case there is no range checking.
</p>
<pre class="programlisting"><code class="literal">
int_to_int |--&gt; sig_to_sig |--&gt; subranged |--&gt; ( s &gt;= S(LowestT) ) &amp;&amp; ( s &lt;= S(HighestT) )
| |--&gt; not subranged |--&gt; NONE
|
|--&gt; unsig_to_unsig |--&gt; subranged |--&gt; ( s &gt;= S(LowestT) ) &amp;&amp; ( s &lt;= S(HighestT) )
| |--&gt; not subranged |--&gt; NONE
|
|--&gt; sig_to_unsig |--&gt; pos subranged |--&gt; ( s &gt;= S(0) ) &amp;&amp; ( s &lt;= S(HighestT) )
| |--&gt; not pos subranged |--&gt; ( s &gt;= S(0) )
|
|--&gt; unsig_to_sig |--&gt; subranged |--&gt; ( s &lt;= S(HighestT) )
| |--&gt; not subranged |--&gt; NONE
</code>
<code class="literal">
int_to_float |--&gt; NONE
</code>
<code class="literal">
float_to_int |--&gt; round_to_zero |--&gt; ( s &gt; S(LowestT)-S(1) ) &amp;&amp; ( s &lt; S(HighestT)+S(1) )
|--&gt; round_to_even_nearest |--&gt; ( s &gt;= S(LowestT)-S(0.5) ) &amp;&amp; ( s &lt; S(HighestT)+S(0.5) )
|--&gt; round_to_infinity |--&gt; ( s &gt; S(LowestT)-S(1) ) &amp;&amp; ( s &lt;= S(HighestT) )
|--&gt; round_to_neg_infinity |--&gt; ( s &gt;= S(LowestT) ) &amp;&amp; ( s &lt; S(HighestT)+S(1) )
</code>
<code class="literal">
float_to_float |--&gt; subranged |--&gt; ( s &gt;= S(LowestT) ) &amp;&amp; ( s &lt;= S(HighestT) )
|--&gt; not subranged |--&gt; NONE
</code>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.converter___function_object.examples"></a><a class="link" href="converter___function_object.html#boost_numericconversion.converter___function_object.examples" title="Examples">Examples</a>
</h3></div></div></div>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">cassert</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">conversion</span><span class="special">/</span><span class="identifier">converter</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> <span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">converter</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">,</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">Double2Int</span> <span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">Double2Int</span><span class="special">::</span><span class="identifier">convert</span><span class="special">(</span><span class="number">2.0</span><span class="special">);</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="identifier">x</span> <span class="special">==</span> <span class="number">2</span> <span class="special">);</span>
<span class="keyword">int</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">Double2Int</span><span class="special">()(</span><span class="number">3.14</span><span class="special">);</span> <span class="comment">// As a function object.</span>
<span class="identifier">assert</span> <span class="special">(</span> <span class="identifier">y</span> <span class="special">==</span> <span class="number">3</span> <span class="special">)</span> <span class="special">;</span> <span class="comment">// The default rounding is trunc.</span>
<span class="keyword">try</span>
<span class="special">{</span>
<span class="keyword">double</span> <span class="identifier">m</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bounds</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;::</span><span class="identifier">highest</span><span class="special">();</span>
<span class="keyword">int</span> <span class="identifier">z</span> <span class="special">=</span> <span class="identifier">Double2Int</span><span class="special">::</span><span class="identifier">convert</span><span class="special">(</span><span class="identifier">m</span><span class="special">);</span> <span class="comment">// By default throws positive_overflow()</span>
<span class="special">}</span>
<span class="keyword">catch</span> <span class="special">(</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">positive_overflow</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="special">)</span>
<span class="special">{</span>
<span class="special">}</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_numericconversion.definitions"></a><a class="link" href="definitions.html" title="Definitions">Definitions</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.types_and_values">Types
and Values</a></span></dt>
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.c___arithmetic_types">C++
Arithmetic Types</a></span></dt>
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.numeric_types">Numeric
Types</a></span></dt>
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.range_and_precision">Range
and Precision</a></span></dt>
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.exact__correctly_rounded_and_out_of_range_representations">Exact,
Correctly Rounded and Out-Of-Range Representations</a></span></dt>
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.standard__numeric__conversions">Standard
(numeric) Conversions</a></span></dt>
<dt><span class="section"><a href="definitions.html#boost_numericconversion.definitions.subranged_conversion_direction__subtype_and_supertype">Subranged
Conversion Direction, Subtype and Supertype</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.introduction"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.introduction" title="Introduction">Introduction</a>
</h3></div></div></div>
<p>
This section provides definitions of terms used in the Numeric Conversion
library.
</p>
<div class="sidebar">
<div class="titlepage"></div>
<p>
<span class="bold"><strong>Notation</strong></span> <span class="underline">underlined
text</span> denotes terms defined in the C++ standard.
</p>
<p>
<span class="bold"><strong>bold face</strong></span> denotes terms defined here but
not in the standard.
</p>
</div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.types_and_values"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.types_and_values" title="Types and Values">Types
and Values</a>
</h3></div></div></div>
<p>
As defined by the <span class="underline">C++ Object Model</span>
(&#167;1.7) the <span class="underline">storage</span> or memory on which
a C++ program runs is a contiguous sequence of <span class="underline">bytes</span>
where each byte is a contiguous sequence of bits.
</p>
<p>
An <span class="underline">object</span> is a region of storage (&#167;1.8)
and has a type (&#167;3.9).
</p>
<p>
A <span class="underline">type</span> is a discrete set of values.
</p>
<p>
An object of type <code class="computeroutput"><span class="identifier">T</span></code> has an
<span class="underline">object representation</span> which is the
sequence of bytes stored in the object (&#167;3.9/4)
</p>
<p>
An object of type <code class="computeroutput"><span class="identifier">T</span></code> has a
<span class="underline">value representation</span> which is the set
of bits that determine the <span class="emphasis"><em>value</em></span> of an object of that
type (&#167;3.9/4). For <span class="underline">POD</span> types (&#167;3.9/10),
this bitset is given by the object representation, but not all the bits in
the storage need to participate in the value representation (except for character
types): for example, some bits might be used for padding or there may be
trap-bits.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<p>
The <span class="bold"><strong>typed value</strong></span> that is held by an object
is the value which is determined by its value representation.
</p>
<p>
An <span class="bold"><strong>abstract value</strong></span> (untyped) is the conceptual
information that is represented in a type (i.e. the number &#960;).
</p>
<p>
The <span class="bold"><strong>intrinsic value</strong></span> of an object is the
binary value of the sequence of unsigned characters which form its object
representation.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<p>
<span class="emphasis"><em>Abstract</em></span> values can be <span class="bold"><strong>represented</strong></span>
in a given type.
</p>
<p>
To <span class="bold"><strong>represent</strong></span> an abstract value <code class="computeroutput"><span class="identifier">V</span></code> in a type <code class="computeroutput"><span class="identifier">T</span></code>
is to obtain a typed value <code class="computeroutput"><span class="identifier">v</span></code>
which corresponds to the abstract value <code class="computeroutput"><span class="identifier">V</span></code>.
</p>
<p>
The operation is denoted using the <code class="computeroutput"><span class="identifier">rep</span><span class="special">()</span></code> operator, as in: <code class="computeroutput"><span class="identifier">v</span><span class="special">=</span><span class="identifier">rep</span><span class="special">(</span><span class="identifier">V</span><span class="special">)</span></code>. <code class="computeroutput"><span class="identifier">v</span></code> is the <span class="bold"><strong>representation</strong></span>
of <code class="computeroutput"><span class="identifier">V</span></code> in the type <code class="computeroutput"><span class="identifier">T</span></code>.
</p>
<p>
For example, the abstract value &#960; can be represented in the type <code class="computeroutput"><span class="keyword">double</span></code> as the <code class="computeroutput"><span class="keyword">double</span>
<span class="identifier">value</span> <span class="identifier">M_PI</span></code>
and in the type <code class="computeroutput"><span class="keyword">int</span></code> as the
<code class="computeroutput"><span class="keyword">int</span> <span class="identifier">value</span>
<span class="number">3</span></code>
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<p>
Conversely, <span class="emphasis"><em>typed values</em></span> can be <span class="bold"><strong>abstracted</strong></span>.
</p>
<p>
To <span class="bold"><strong>abstract</strong></span> a typed value <code class="computeroutput"><span class="identifier">v</span></code> of type <code class="computeroutput"><span class="identifier">T</span></code>
is to obtain the abstract value <code class="computeroutput"><span class="identifier">V</span></code>
whose representation in <code class="computeroutput"><span class="identifier">T</span></code>
is <code class="computeroutput"><span class="identifier">v</span></code>.
</p>
<p>
The operation is denoted using the <code class="computeroutput"><span class="identifier">abt</span><span class="special">()</span></code> operator, as in: <code class="computeroutput"><span class="identifier">V</span><span class="special">=</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span></code>.
</p>
<p>
<code class="computeroutput"><span class="identifier">V</span></code> is the <span class="bold"><strong>abstraction</strong></span>
of <code class="computeroutput"><span class="identifier">v</span></code> of type <code class="computeroutput"><span class="identifier">T</span></code>.
</p>
<p>
Abstraction is just an abstract operation (you can't do it); but it is defined
nevertheless because it will be used to give the definitions in the rest
of this document.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.c___arithmetic_types"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.c___arithmetic_types" title="C++ Arithmetic Types">C++
Arithmetic Types</a>
</h3></div></div></div>
<p>
The C++ language defines <span class="underline">fundamental types</span>
(&#167;3.9.1). The following subsets of the fundamental types are intended to
represent <span class="emphasis"><em>numbers</em></span>:
</p>
<div class="variablelist">
<p class="title"><b></b></p>
<dl class="variablelist">
<dt><span class="term"><span class="underline">signed integer types</span> (&#167;3.9.1/2):</span></dt>
<dd><p>
<code class="computeroutput"><span class="special">{</span><span class="keyword">signed</span>
<span class="keyword">char</span><span class="special">,</span>
<span class="keyword">signed</span> <span class="keyword">short</span>
<span class="keyword">int</span><span class="special">,</span>
<span class="keyword">signed</span> <span class="keyword">int</span><span class="special">,</span> <span class="keyword">signed</span> <span class="keyword">long</span> <span class="keyword">int</span><span class="special">}</span></code> Can be used to represent general integer
numbers (both negative and positive).
</p></dd>
<dt><span class="term"><span class="underline">unsigned integer types</span> (&#167;3.9.1/3):</span></dt>
<dd><p>
<code class="computeroutput"><span class="special">{</span><span class="keyword">unsigned</span>
<span class="keyword">char</span><span class="special">,</span>
<span class="keyword">unsigned</span> <span class="keyword">short</span>
<span class="keyword">int</span><span class="special">,</span>
<span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">,</span> <span class="keyword">unsigned</span>
<span class="keyword">long</span> <span class="keyword">int</span><span class="special">}</span></code> Can be used to represent positive
integer numbers with modulo-arithmetic.
</p></dd>
<dt><span class="term"><span class="underline">floating-point types</span> (&#167;3.9.1/8):</span></dt>
<dd><p>
<code class="computeroutput"><span class="special">{</span><span class="keyword">float</span><span class="special">,</span><span class="keyword">double</span><span class="special">,</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">}</span></code>
Can be used to represent real numbers.
</p></dd>
<dt><span class="term"><span class="underline">integral or integer types</span> (&#167;3.9.1/7):</span></dt>
<dd><p>
<code class="computeroutput"><span class="special">{{</span><span class="keyword">signed</span>
<span class="identifier">integers</span><span class="special">},{</span><span class="keyword">unsigned</span> <span class="identifier">integers</span><span class="special">},</span> <span class="keyword">bool</span><span class="special">,</span> <span class="keyword">char</span> <span class="keyword">and</span> <span class="keyword">wchar_t</span><span class="special">}</span></code>
</p></dd>
<dt><span class="term"><span class="underline">arithmetic types</span> (&#167;3.9.1/8):</span></dt>
<dd><p>
<code class="computeroutput"><span class="special">{{</span><span class="identifier">integer</span>
<span class="identifier">types</span><span class="special">},{</span><span class="identifier">floating</span> <span class="identifier">types</span><span class="special">}}</span></code>
</p></dd>
</dl>
</div>
<p>
The integer types are required to have a <span class="emphasis"><em>binary</em></span> value
representation.
</p>
<p>
Additionally, the signed/unsigned integer types of the same base type (<code class="computeroutput"><span class="keyword">short</span></code>, <code class="computeroutput"><span class="keyword">int</span></code>
or <code class="computeroutput"><span class="keyword">long</span></code>) are required to have
the same value representation, that is:
</p>
<pre class="programlisting"> <span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="special">-</span><span class="number">3</span> <span class="special">;</span> <span class="comment">// suppose value representation is: 10011 (sign bit + 4 magnitude bits)</span>
<span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">u</span> <span class="special">=</span> <span class="identifier">i</span> <span class="special">;</span> <span class="comment">// u is required to have the same 10011 as its value representation.</span>
</pre>
<p>
In other words, the integer types signed/unsigned X use the same value representation
but a different <span class="emphasis"><em>interpretation</em></span> of it; that is, their
<span class="emphasis"><em>typed values</em></span> might differ.
</p>
<p>
Another consequence of this is that the range for signed X is always a smaller
subset of the range of unsigned X, as required by &#167;3.9.1/3.
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top">
<p>
Always remember that unsigned types, unlike signed types, have modulo-arithmetic;
that is, they do not overflow. This means that:
</p>
<p>
<span class="bold"><strong>-</strong></span> Always be extra careful when mixing
signed/unsigned types
</p>
<p>
<span class="bold"><strong>-</strong></span> Use unsigned types only when you need
modulo arithmetic or very very large numbers. Don't use unsigned types
just because you intend to deal with positive values only (you can do this
with signed types as well).
</p>
</td></tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.numeric_types"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.numeric_types" title="Numeric Types">Numeric
Types</a>
</h3></div></div></div>
<p>
This section introduces the following definitions intended to integrate arithmetic
types with user-defined types which behave like numbers. Some definitions
are purposely broad in order to include a vast variety of user-defined number
types.
</p>
<p>
Within this library, the term <span class="emphasis"><em>number</em></span> refers to an abstract
numeric value.
</p>
<p>
A type is <span class="bold"><strong>numeric</strong></span> if:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
It is an arithmetic type, or,
</li>
<li class="listitem">
It is a user-defined type which
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
<li class="listitem">
Represents numeric abstract values (i.e. numbers).
</li>
<li class="listitem">
Can be converted (either implicitly or explicitly) to/from at least
one arithmetic type.
</li>
<li class="listitem">
Has <a class="link" href="definitions.html#boost_numericconversion.definitions.range_and_precision" title="Range and Precision">range</a>
(possibly unbounded) and <a class="link" href="definitions.html#boost_numericconversion.definitions.range_and_precision" title="Range and Precision">precision</a>
(possibly dynamic or unlimited).
</li>
<li class="listitem">
Provides an specialization of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>.
</li>
</ul></div>
</li>
</ul></div>
<p>
A numeric type is <span class="bold"><strong>signed</strong></span> if the abstract
values it represent include negative numbers.
</p>
<p>
A numeric type is <span class="bold"><strong>unsigned</strong></span> if the abstract
values it represent exclude negative numbers.
</p>
<p>
A numeric type is <span class="bold"><strong>modulo</strong></span> if it has modulo-arithmetic
(does not overflow).
</p>
<p>
A numeric type is <span class="bold"><strong>integer</strong></span> if the abstract
values it represent are whole numbers.
</p>
<p>
A numeric type is <span class="bold"><strong>floating</strong></span> if the abstract
values it represent are real numbers.
</p>
<p>
An <span class="bold"><strong>arithmetic value</strong></span> is the typed value of
an arithmetic type
</p>
<p>
A <span class="bold"><strong>numeric value</strong></span> is the typed value of a
numeric type
</p>
<p>
These definitions simply generalize the standard notions of arithmetic types
and values by introducing a superset called <span class="underline">numeric</span>.
All arithmetic types and values are numeric types and values, but not vice
versa, since user-defined numeric types are not arithmetic types.
</p>
<p>
The following examples clarify the differences between arithmetic and numeric
types (and values):
</p>
<pre class="programlisting"><span class="comment">// A numeric type which is not an arithmetic type (is user-defined)</span>
<span class="comment">// and which is intended to represent integer numbers (i.e., an 'integer' numeric type)</span>
<span class="keyword">class</span> <span class="identifier">MyInt</span>
<span class="special">{</span>
<span class="identifier">MyInt</span> <span class="special">(</span> <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">v</span> <span class="special">)</span> <span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">to_builtin</span><span class="special">();</span>
<span class="special">}</span> <span class="special">;</span>
<span class="keyword">namespace</span> <span class="identifier">std</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">MyInt</span><span class="special">&gt;</span> <span class="special">{</span> <span class="special">...</span> <span class="special">}</span> <span class="special">;</span>
<span class="special">}</span>
<span class="comment">// A 'floating' numeric type (double) which is also an arithmetic type (built-in),</span>
<span class="comment">// with a float numeric value.</span>
<span class="keyword">double</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="identifier">M_PI</span> <span class="special">;</span>
<span class="comment">// A 'floating' numeric type with a whole numeric value.</span>
<span class="comment">// NOTE: numeric values are typed valued, hence, they are, for instance,</span>
<span class="comment">// integer or floating, despite the value itself being whole or including</span>
<span class="comment">// a fractional part.</span>
<span class="keyword">double</span> <span class="identifier">two</span> <span class="special">=</span> <span class="number">2.0</span> <span class="special">;</span>
<span class="comment">// An integer numeric type with an integer numeric value.</span>
<span class="identifier">MyInt</span> <span class="identifier">i</span><span class="special">(</span><span class="number">1234</span><span class="special">);</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.range_and_precision"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.range_and_precision" title="Range and Precision">Range
and Precision</a>
</h3></div></div></div>
<p>
Given a number set <code class="computeroutput"><span class="identifier">N</span></code>, some
of its elements are representable in a numeric type <code class="computeroutput"><span class="identifier">T</span></code>.
</p>
<p>
The set of representable values of type <code class="computeroutput"><span class="identifier">T</span></code>,
or numeric set of <code class="computeroutput"><span class="identifier">T</span></code>, is a
set of numeric values whose elements are the representation of some subset
of <code class="computeroutput"><span class="identifier">N</span></code>.
</p>
<p>
For example, the interval of <code class="computeroutput"><span class="keyword">int</span></code>
values <code class="computeroutput"><span class="special">[</span><span class="identifier">INT_MIN</span><span class="special">,</span><span class="identifier">INT_MAX</span><span class="special">]</span></code> is the set of representable values of type
<code class="computeroutput"><span class="keyword">int</span></code>, i.e. the <code class="computeroutput"><span class="keyword">int</span></code> numeric set, and corresponds to the representation
of the elements of the interval of abstract values <code class="computeroutput"><span class="special">[</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">INT_MIN</span><span class="special">),</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">INT_MAX</span><span class="special">)]</span></code>
from the integer numbers.
</p>
<p>
Similarly, the interval of <code class="computeroutput"><span class="keyword">double</span></code>
values <code class="computeroutput"><span class="special">[-</span><span class="identifier">DBL_MAX</span><span class="special">,</span><span class="identifier">DBL_MAX</span><span class="special">]</span></code> is the <code class="computeroutput"><span class="keyword">double</span></code>
numeric set, which corresponds to the subset of the real numbers from <code class="computeroutput"><span class="identifier">abt</span><span class="special">(-</span><span class="identifier">DBL_MAX</span><span class="special">)</span></code> to <code class="computeroutput"><span class="identifier">abt</span><span class="special">(</span><span class="identifier">DBL_MAX</span><span class="special">)</span></code>.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<p>
Let <span class="bold"><strong><code class="computeroutput"><span class="identifier">next</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code></strong></span>
denote the lowest numeric value greater than x.
</p>
<p>
Let <span class="bold"><strong><code class="computeroutput"><span class="identifier">prev</span><span class="special">(</span><span class="identifier">x</span><span class="special">)</span></code></strong></span>
denote the highest numeric value lower then x.
</p>
<p>
Let <span class="bold"><strong><code class="computeroutput"><span class="identifier">v</span><span class="special">=</span><span class="identifier">prev</span><span class="special">(</span><span class="identifier">next</span><span class="special">(</span><span class="identifier">V</span><span class="special">))</span></code></strong></span> and <span class="bold"><strong><code class="computeroutput"><span class="identifier">v</span><span class="special">=</span><span class="identifier">next</span><span class="special">(</span><span class="identifier">prev</span><span class="special">(</span><span class="identifier">V</span><span class="special">))</span></code></strong></span>
be identities that relate a numeric typed value <code class="computeroutput"><span class="identifier">v</span></code>
with a number <code class="computeroutput"><span class="identifier">V</span></code>.
</p>
<p>
An ordered pair of numeric values <code class="computeroutput"><span class="identifier">x</span></code>,<code class="computeroutput"><span class="identifier">y</span></code> s.t. <code class="computeroutput"><span class="identifier">x</span><span class="special">&lt;</span><span class="identifier">y</span></code> are
<span class="bold"><strong>consecutive</strong></span> iff <code class="computeroutput"><span class="identifier">next</span><span class="special">(</span><span class="identifier">x</span><span class="special">)==</span><span class="identifier">y</span></code>.
</p>
<p>
The abstract distance between consecutive numeric values is usually referred
to as a <span class="underline">Unit in the Last Place</span>, or
<span class="bold"><strong>ulp</strong></span> for short. A ulp is a quantity whose
abstract magnitude is relative to the numeric values it corresponds to: If
the numeric set is not evenly distributed, that is, if the abstract distance
between consecutive numeric values varies along the set -as is the case with
the floating-point types-, the magnitude of 1ulp after the numeric value
<code class="computeroutput"><span class="identifier">x</span></code> might be (usually is) different
from the magnitude of a 1ulp after the numeric value y for <code class="computeroutput"><span class="identifier">x</span><span class="special">!=</span><span class="identifier">y</span></code>.
</p>
<p>
Since numbers are inherently ordered, a <span class="bold"><strong>numeric set</strong></span>
of type <code class="computeroutput"><span class="identifier">T</span></code> is an ordered sequence
of numeric values (of type <code class="computeroutput"><span class="identifier">T</span></code>)
of the form:
</p>
<pre class="programlisting"><span class="identifier">REP</span><span class="special">(</span><span class="identifier">T</span><span class="special">)={</span><span class="identifier">l</span><span class="special">,</span><span class="identifier">next</span><span class="special">(</span><span class="identifier">l</span><span class="special">),</span><span class="identifier">next</span><span class="special">(</span><span class="identifier">next</span><span class="special">(</span><span class="identifier">l</span><span class="special">)),...,</span><span class="identifier">prev</span><span class="special">(</span><span class="identifier">prev</span><span class="special">(</span><span class="identifier">h</span><span class="special">)),</span><span class="identifier">prev</span><span class="special">(</span><span class="identifier">h</span><span class="special">),</span><span class="identifier">h</span><span class="special">}</span>
</pre>
<p>
where <code class="computeroutput"><span class="identifier">l</span></code> and <code class="computeroutput"><span class="identifier">h</span></code> are respectively the lowest and highest
values of type <code class="computeroutput"><span class="identifier">T</span></code>, called
the boundary values of type <code class="computeroutput"><span class="identifier">T</span></code>.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<p>
A numeric set is discrete. It has a <span class="bold"><strong>size</strong></span>
which is the number of numeric values in the set, a <span class="bold"><strong>width</strong></span>
which is the abstract difference between the highest and lowest boundary
values: <code class="computeroutput"><span class="special">[</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)-</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">l</span><span class="special">)]</span></code>, and a <span class="bold"><strong>density</strong></span>
which is the relation between its size and width: <code class="computeroutput"><span class="identifier">density</span><span class="special">=</span><span class="identifier">size</span><span class="special">/</span><span class="identifier">width</span></code>.
</p>
<p>
The integer types have density 1, which means that there are no unrepresentable
integer numbers between <code class="computeroutput"><span class="identifier">abt</span><span class="special">(</span><span class="identifier">l</span><span class="special">)</span></code>
and <code class="computeroutput"><span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)</span></code> (i.e.
there are no gaps). On the other hand, floating types have density much smaller
than 1, which means that there are real numbers unrepresented between consecutive
floating values (i.e. there are gaps).
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<p>
The interval of <span class="underline">abstract values</span> <code class="computeroutput"><span class="special">[</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">l</span><span class="special">),</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)]</span></code>
is the range of the type <code class="computeroutput"><span class="identifier">T</span></code>,
denoted <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">)</span></code>.
</p>
<p>
A range is a set of abstract values and not a set of numeric values. In other
documents, such as the C++ standard, the word <code class="computeroutput"><span class="identifier">range</span></code>
is <span class="emphasis"><em>sometimes</em></span> used as synonym for <code class="computeroutput"><span class="identifier">numeric</span>
<span class="identifier">set</span></code>, that is, as the ordered sequence
of numeric values from <code class="computeroutput"><span class="identifier">l</span></code>
to <code class="computeroutput"><span class="identifier">h</span></code>. In this document, however,
a range is an abstract interval which subtends the numeric set.
</p>
<p>
For example, the sequence <code class="computeroutput"><span class="special">[-</span><span class="identifier">DBL_MAX</span><span class="special">,</span><span class="identifier">DBL_MAX</span><span class="special">]</span></code>
is the numeric set of the type <code class="computeroutput"><span class="keyword">double</span></code>,
and the real interval <code class="computeroutput"><span class="special">[</span><span class="identifier">abt</span><span class="special">(-</span><span class="identifier">DBL_MAX</span><span class="special">),</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">DBL_MAX</span><span class="special">)]</span></code>
is its range.
</p>
<p>
Notice, for instance, that the range of a floating-point type is <span class="emphasis"><em>continuous</em></span>
unlike its numeric set.
</p>
<p>
This definition was chosen because:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<span class="bold"><strong>(a)</strong></span> The discrete set of numeric values
is already given by the numeric set.
</li>
<li class="listitem">
<span class="bold"><strong>(b)</strong></span> Abstract intervals are easier to
compare and overlap since only boundary values need to be considered.
</li>
</ul></div>
<p>
This definition allows for a concise definition of <code class="computeroutput"><span class="identifier">subranged</span></code>
as given in the last section.
</p>
<p>
The width of a numeric set, as defined, is exactly equivalent to the width
of a range.
</p>
<p>
<span class="inlinemediaobject"><img src="../images/space.png" alt="space"></span>
</p>
<p>
The <span class="bold"><strong>precision</strong></span> of a type is given by the
width or density of the numeric set.
</p>
<p>
For integer types, which have density 1, the precision is conceptually equivalent
to the range and is determined by the number of bits used in the value representation:
The higher the number of bits the bigger the size of the numeric set, the
wider the range, and the higher the precision.
</p>
<p>
For floating types, which have density &lt;&lt;1, the precision is given
not by the width of the range but by the density. In a typical implementation,
the range is determined by the number of bits used in the exponent, and the
precision by the number of bits used in the mantissa (giving the maximum
number of significant digits that can be exactly represented). The higher
the number of exponent bits the wider the range, while the higher the number
of mantissa bits, the higher the precision.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.exact__correctly_rounded_and_out_of_range_representations"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.exact__correctly_rounded_and_out_of_range_representations" title="Exact, Correctly Rounded and Out-Of-Range Representations">Exact,
Correctly Rounded and Out-Of-Range Representations</a>
</h3></div></div></div>
<p>
Given an abstract value <code class="computeroutput"><span class="identifier">V</span></code>
and a type <code class="computeroutput"><span class="identifier">T</span></code> with its corresponding
range <code class="computeroutput"><span class="special">[</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">l</span><span class="special">),</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)]</span></code>:
</p>
<p>
If <code class="computeroutput"><span class="identifier">V</span> <span class="special">&lt;</span>
<span class="identifier">abt</span><span class="special">(</span><span class="identifier">l</span><span class="special">)</span></code> or
<code class="computeroutput"><span class="identifier">V</span> <span class="special">&gt;</span>
<span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)</span></code>, <code class="computeroutput"><span class="identifier">V</span></code> is <span class="bold"><strong>not representable</strong></span>
(cannot be represented) in the type <code class="computeroutput"><span class="identifier">T</span></code>,
or, equivalently, it's representation in the type <code class="computeroutput"><span class="identifier">T</span></code>
is <span class="bold"><strong>out of range</strong></span>, or <span class="bold"><strong>overflows</strong></span>.
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
If <code class="computeroutput"><span class="identifier">V</span> <span class="special">&lt;</span>
<span class="identifier">abt</span><span class="special">(</span><span class="identifier">l</span><span class="special">)</span></code>,
the <span class="bold"><strong>overflow is negative</strong></span>.
</li>
<li class="listitem">
If <code class="computeroutput"><span class="identifier">V</span> <span class="special">&gt;</span>
<span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)</span></code>,
the <span class="bold"><strong>overflow is positive</strong></span>.
</li>
</ul></div>
<p>
If <code class="computeroutput"><span class="identifier">V</span> <span class="special">&gt;=</span>
<span class="identifier">abt</span><span class="special">(</span><span class="identifier">l</span><span class="special">)</span></code> and
<code class="computeroutput"><span class="identifier">V</span> <span class="special">&lt;=</span>
<span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)</span></code>, <code class="computeroutput"><span class="identifier">V</span></code> is <span class="bold"><strong>representable</strong></span>
(can be represented) in the type <code class="computeroutput"><span class="identifier">T</span></code>,
or, equivalently, its representation in the type <code class="computeroutput"><span class="identifier">T</span></code>
is <span class="bold"><strong>in range</strong></span>, or <span class="bold"><strong>does
not overflow</strong></span>.
</p>
<p>
Notice that a numeric type, such as a C++ unsigned type, can define that
any <code class="computeroutput"><span class="identifier">V</span></code> does not overflow by
always representing not <code class="computeroutput"><span class="identifier">V</span></code>
itself but the abstract value <code class="computeroutput"><span class="identifier">U</span>
<span class="special">=</span> <span class="special">[</span> <span class="identifier">V</span> <span class="special">%</span> <span class="special">(</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)+</span><span class="number">1</span><span class="special">)</span>
<span class="special">]</span></code>, which is always in range.
</p>
<p>
Given an abstract value <code class="computeroutput"><span class="identifier">V</span></code>
represented in the type <code class="computeroutput"><span class="identifier">T</span></code>
as <code class="computeroutput"><span class="identifier">v</span></code>, the <span class="bold"><strong>roundoff</strong></span>
error of the representation is the abstract difference: <code class="computeroutput"><span class="special">(</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">v</span><span class="special">)-</span><span class="identifier">V</span><span class="special">)</span></code>.
</p>
<p>
Notice that a representation is an <span class="emphasis"><em>operation</em></span>, hence,
the roundoff error corresponds to the representation operation and not to
the numeric value itself (i.e. numeric values do not have any error themselves)
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
If the roundoff is 0, the representation is <span class="bold"><strong>exact</strong></span>,
and <code class="computeroutput"><span class="identifier">V</span></code> is exactly representable
in the type <code class="computeroutput"><span class="identifier">T</span></code>.
</li>
<li class="listitem">
If the roundoff is not 0, the representation is <span class="bold"><strong>inexact</strong></span>,
and <code class="computeroutput"><span class="identifier">V</span></code> is inexactly representable
in the type <code class="computeroutput"><span class="identifier">T</span></code>.
</li>
</ul></div>
<p>
If a representation <code class="computeroutput"><span class="identifier">v</span></code> in
a type <code class="computeroutput"><span class="identifier">T</span></code> -either exact or
inexact-, is any of the adjacents of <code class="computeroutput"><span class="identifier">V</span></code>
in that type, that is, if <code class="computeroutput"><span class="identifier">v</span><span class="special">==</span><span class="identifier">prev</span></code>
or <code class="computeroutput"><span class="identifier">v</span><span class="special">==</span><span class="identifier">next</span></code>, the representation is faithfully
rounded. If the choice between <code class="computeroutput"><span class="identifier">prev</span></code>
and <code class="computeroutput"><span class="identifier">next</span></code> matches a given
<span class="bold"><strong>rounding direction</strong></span>, it is <span class="bold"><strong>correctly
rounded</strong></span>.
</p>
<p>
All exact representations are correctly rounded, but not all inexact representations
are. In particular, C++ requires numeric conversions (described below) and
the result of arithmetic operations (not covered by this document) to be
correctly rounded, but batch operations propagate roundoff, thus final results
are usually incorrectly rounded, that is, the numeric value <code class="computeroutput"><span class="identifier">r</span></code> which is the computed result is neither
of the adjacents of the abstract value <code class="computeroutput"><span class="identifier">R</span></code>
which is the theoretical result.
</p>
<p>
Because a correctly rounded representation is always one of adjacents of
the abstract value being represented, the roundoff is guaranteed to be at
most 1ulp.
</p>
<p>
The following examples summarize the given definitions. Consider:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
A numeric type <code class="computeroutput"><span class="identifier">Int</span></code> representing
integer numbers with a <span class="emphasis"><em>numeric set</em></span>: <code class="computeroutput"><span class="special">{-</span><span class="number">2</span><span class="special">,-</span><span class="number">1</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">}</span></code> and
<span class="emphasis"><em>range</em></span>: <code class="computeroutput"><span class="special">[-</span><span class="number">2</span><span class="special">,</span><span class="number">2</span><span class="special">]</span></code>
</li>
<li class="listitem">
A numeric type <code class="computeroutput"><span class="identifier">Cardinal</span></code>
representing integer numbers with a <span class="emphasis"><em>numeric set</em></span>:
<code class="computeroutput"><span class="special">{</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">,</span><span class="number">5</span><span class="special">,</span><span class="number">6</span><span class="special">,</span><span class="number">7</span><span class="special">,</span><span class="number">8</span><span class="special">,</span><span class="number">9</span><span class="special">}</span></code> and <span class="emphasis"><em>range</em></span>: <code class="computeroutput"><span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">9</span><span class="special">]</span></code> (no
modulo-arithmetic here)
</li>
<li class="listitem">
A numeric type <code class="computeroutput"><span class="identifier">Real</span></code> representing
real numbers with a <span class="emphasis"><em>numeric set</em></span>: <code class="computeroutput"><span class="special">{-</span><span class="number">2.0</span><span class="special">,-</span><span class="number">1.5</span><span class="special">,-</span><span class="number">1.0</span><span class="special">,-</span><span class="number">0.5</span><span class="special">,-</span><span class="number">0.0</span><span class="special">,+</span><span class="number">0.0</span><span class="special">,+</span><span class="number">0.5</span><span class="special">,+</span><span class="number">1.0</span><span class="special">,+</span><span class="number">1.5</span><span class="special">,+</span><span class="number">2.0</span><span class="special">}</span></code> and
<span class="emphasis"><em>range</em></span>: <code class="computeroutput"><span class="special">[-</span><span class="number">2.0</span><span class="special">,+</span><span class="number">2.0</span><span class="special">]</span></code>
</li>
<li class="listitem">
A numeric type <code class="computeroutput"><span class="identifier">Whole</span></code>
representing real numbers with a <span class="emphasis"><em>numeric set</em></span>: <code class="computeroutput"><span class="special">{-</span><span class="number">2.0</span><span class="special">,-</span><span class="number">1.0</span><span class="special">,</span><span class="number">0.0</span><span class="special">,+</span><span class="number">1.0</span><span class="special">,+</span><span class="number">2.0</span><span class="special">}</span></code> and
<span class="emphasis"><em>range</em></span>: <code class="computeroutput"><span class="special">[-</span><span class="number">2.0</span><span class="special">,+</span><span class="number">2.0</span><span class="special">]</span></code>
</li>
</ul></div>
<p>
First, notice that the types <code class="computeroutput"><span class="identifier">Real</span></code>
and <code class="computeroutput"><span class="identifier">Whole</span></code> both represent
real numbers, have the same range, but different precision.
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
The integer number <code class="computeroutput"><span class="number">1</span></code> (an
abstract value) can be exactly represented in any of these types.
</li>
<li class="listitem">
The integer number <code class="computeroutput"><span class="special">-</span><span class="number">1</span></code>
can be exactly represented in <code class="computeroutput"><span class="identifier">Int</span></code>,
<code class="computeroutput"><span class="identifier">Real</span></code> and <code class="computeroutput"><span class="identifier">Whole</span></code>, but cannot be represented in
<code class="computeroutput"><span class="identifier">Cardinal</span></code>, yielding negative
overflow.
</li>
<li class="listitem">
The real number <code class="computeroutput"><span class="number">1.5</span></code> can be
exactly represented in <code class="computeroutput"><span class="identifier">Real</span></code>,
and inexactly represented in the other types.
</li>
<li class="listitem">
If <code class="computeroutput"><span class="number">1.5</span></code> is represented as
either <code class="computeroutput"><span class="number">1</span></code> or <code class="computeroutput"><span class="number">2</span></code> in any of the types (except <code class="computeroutput"><span class="identifier">Real</span></code>), the representation is correctly
rounded.
</li>
<li class="listitem">
If <code class="computeroutput"><span class="number">0.5</span></code> is represented as
<code class="computeroutput"><span class="special">+</span><span class="number">1.5</span></code>
in the type <code class="computeroutput"><span class="identifier">Real</span></code>, it
is incorrectly rounded.
</li>
<li class="listitem">
<code class="computeroutput"><span class="special">(-</span><span class="number">2.0</span><span class="special">,-</span><span class="number">1.5</span><span class="special">)</span></code>
are the <code class="computeroutput"><span class="identifier">Real</span></code> adjacents
of any real number in the interval <code class="computeroutput"><span class="special">[-</span><span class="number">2.0</span><span class="special">,-</span><span class="number">1.5</span><span class="special">]</span></code>, yet there are no <code class="computeroutput"><span class="identifier">Real</span></code>
adjacents for <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
<span class="special">-</span><span class="number">2.0</span></code>,
nor for <code class="computeroutput"><span class="identifier">x</span> <span class="special">&gt;</span>
<span class="special">+</span><span class="number">2.0</span></code>.
</li>
</ul></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.standard__numeric__conversions"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.standard__numeric__conversions" title="Standard (numeric) Conversions">Standard
(numeric) Conversions</a>
</h3></div></div></div>
<p>
The C++ language defines <span class="underline">Standard Conversions</span>
(&#167;4) some of which are conversions between arithmetic types.
</p>
<p>
These are <span class="underline">Integral promotions</span> (&#167;4.5),
<span class="underline">Integral conversions</span> (&#167;4.7), <span class="underline">Floating point promotions</span> (&#167;4.6), <span class="underline">Floating point conversions</span> (&#167;4.8) and <span class="underline">Floating-integral conversions</span> (&#167;4.9).
</p>
<p>
In the sequel, integral and floating point promotions are called <span class="bold"><strong>arithmetic promotions</strong></span>, and these plus integral, floating-point
and floating-integral conversions are called <span class="bold"><strong>arithmetic
conversions</strong></span> (i.e, promotions are conversions).
</p>
<p>
Promotions, both Integral and Floating point, are <span class="emphasis"><em>value-preserving</em></span>,
which means that the typed value is not changed with the conversion.
</p>
<p>
In the sequel, consider a source typed value <code class="computeroutput"><span class="identifier">s</span></code>
of type <code class="computeroutput"><span class="identifier">S</span></code>, the source abstract
value <code class="computeroutput"><span class="identifier">N</span><span class="special">=</span><span class="identifier">abt</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span></code>, a destination type <code class="computeroutput"><span class="identifier">T</span></code>;
and whenever possible, a result typed value <code class="computeroutput"><span class="identifier">t</span></code>
of type <code class="computeroutput"><span class="identifier">T</span></code>.
</p>
<p>
Integer to integer conversions are always defined:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
If <code class="computeroutput"><span class="identifier">T</span></code> is unsigned, the
abstract value which is effectively represented is not <code class="computeroutput"><span class="identifier">N</span></code> but <code class="computeroutput"><span class="identifier">M</span><span class="special">=[</span> <span class="identifier">N</span> <span class="special">%</span> <span class="special">(</span> <span class="identifier">abt</span><span class="special">(</span><span class="identifier">h</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span>
<span class="special">)</span> <span class="special">]</span></code>,
where <code class="computeroutput"><span class="identifier">h</span></code> is the highest
unsigned typed value of type <code class="computeroutput"><span class="identifier">T</span></code>.
</li>
<li class="listitem">
If <code class="computeroutput"><span class="identifier">T</span></code> is signed and <code class="computeroutput"><span class="identifier">N</span></code> is not directly representable, the
result <code class="computeroutput"><span class="identifier">t</span></code> is <span class="underline">implementation-defined</span>, which means that
the C++ implementation is required to produce a value <code class="computeroutput"><span class="identifier">t</span></code>
even if it is totally unrelated to <code class="computeroutput"><span class="identifier">s</span></code>.
</li>
</ul></div>
<p>
Floating to Floating conversions are defined only if <code class="computeroutput"><span class="identifier">N</span></code>
is representable; if it is not, the conversion has <span class="underline">undefined
behavior</span>.
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
If <code class="computeroutput"><span class="identifier">N</span></code> is exactly representable,
<code class="computeroutput"><span class="identifier">t</span></code> is required to be the
exact representation.
</li>
<li class="listitem">
If <code class="computeroutput"><span class="identifier">N</span></code> is inexactly representable,
<code class="computeroutput"><span class="identifier">t</span></code> is required to be one
of the two adjacents, with an implementation-defined choice of rounding
direction; that is, the conversion is required to be correctly rounded.
</li>
</ul></div>
<p>
Floating to Integer conversions represent not <code class="computeroutput"><span class="identifier">N</span></code>
but <code class="computeroutput"><span class="identifier">M</span><span class="special">=</span><span class="identifier">trunc</span><span class="special">(</span><span class="identifier">N</span><span class="special">)</span></code>, were
<code class="computeroutput"><span class="identifier">trunc</span><span class="special">()</span></code>
is to truncate: i.e. to remove the fractional part, if any.
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
If <code class="computeroutput"><span class="identifier">M</span></code> is not representable
in <code class="computeroutput"><span class="identifier">T</span></code>, the conversion
has <span class="underline">undefined behavior</span> (unless
<code class="computeroutput"><span class="identifier">T</span></code> is <code class="computeroutput"><span class="keyword">bool</span></code>,
see &#167;4.12).
</li></ul></div>
<p>
Integer to Floating conversions are always defined.
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
If <code class="computeroutput"><span class="identifier">N</span></code> is exactly representable,
<code class="computeroutput"><span class="identifier">t</span></code> is required to be the
exact representation.
</li>
<li class="listitem">
If <code class="computeroutput"><span class="identifier">N</span></code> is inexactly representable,
<code class="computeroutput"><span class="identifier">t</span></code> is required to be one
of the two adjacents, with an implementation-defined choice of rounding
direction; that is, the conversion is required to be correctly rounded.
</li>
</ul></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.definitions.subranged_conversion_direction__subtype_and_supertype"></a><a class="link" href="definitions.html#boost_numericconversion.definitions.subranged_conversion_direction__subtype_and_supertype" title="Subranged Conversion Direction, Subtype and Supertype">Subranged
Conversion Direction, Subtype and Supertype</a>
</h3></div></div></div>
<p>
Given a source type <code class="computeroutput"><span class="identifier">S</span></code> and
a destination type <code class="computeroutput"><span class="identifier">T</span></code>, there
is a <span class="bold"><strong>conversion direction</strong></span> denoted: <code class="computeroutput"><span class="identifier">S</span><span class="special">-&gt;</span><span class="identifier">T</span></code>.
</p>
<p>
For any two ranges the following <span class="emphasis"><em>range relation</em></span> can
be defined: A range <code class="computeroutput"><span class="identifier">X</span></code> can
be <span class="emphasis"><em>entirely contained</em></span> in a range <code class="computeroutput"><span class="identifier">Y</span></code>,
in which case it is said that <code class="computeroutput"><span class="identifier">X</span></code>
is enclosed by <code class="computeroutput"><span class="identifier">Y</span></code>.
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="bold"><strong>Formally:</strong></span> <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span></code>
is enclosed by <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">)</span></code> iif
<code class="computeroutput"><span class="special">(</span><span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span>
<span class="identifier">intersection</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">))</span>
<span class="special">==</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span></code>.
</p></blockquote></div>
<p>
If the source type range, <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span></code>,
is not enclosed in the target type range, <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">)</span></code>;
that is, if <code class="computeroutput"><span class="special">(</span><span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span>
<span class="special">&amp;</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">))</span>
<span class="special">!=</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span></code>,
the conversion direction is said to be <span class="bold"><strong>subranged</strong></span>,
which means that <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span></code> is not
entirely contained in <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">)</span></code> and
therefore there is some portion of the source range which falls outside the
target range. In other words, if a conversion direction <code class="computeroutput"><span class="identifier">S</span><span class="special">-&gt;</span><span class="identifier">T</span></code>
is subranged, there are values in <code class="computeroutput"><span class="identifier">S</span></code>
which cannot be represented in <code class="computeroutput"><span class="identifier">T</span></code>
because they are out of range. Notice that for <code class="computeroutput"><span class="identifier">S</span><span class="special">-&gt;</span><span class="identifier">T</span></code>,
the adjective subranged applies to <code class="computeroutput"><span class="identifier">T</span></code>.
</p>
<p>
Examples:
</p>
<p>
Given the following numeric types all representing real numbers:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<code class="computeroutput"><span class="identifier">X</span></code> with numeric set <code class="computeroutput"><span class="special">{-</span><span class="number">2.0</span><span class="special">,-</span><span class="number">1.0</span><span class="special">,</span><span class="number">0.0</span><span class="special">,+</span><span class="number">1.0</span><span class="special">,+</span><span class="number">2.0</span><span class="special">}</span></code> and
range <code class="computeroutput"><span class="special">[-</span><span class="number">2.0</span><span class="special">,+</span><span class="number">2.0</span><span class="special">]</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">Y</span></code> with numeric set <code class="computeroutput"><span class="special">{-</span><span class="number">2.0</span><span class="special">,-</span><span class="number">1.5</span><span class="special">,-</span><span class="number">1.0</span><span class="special">,-</span><span class="number">0.5</span><span class="special">,</span><span class="number">0.0</span><span class="special">,+</span><span class="number">0.5</span><span class="special">,+</span><span class="number">1.0</span><span class="special">,+</span><span class="number">1.5</span><span class="special">,+</span><span class="number">2.0</span><span class="special">}</span></code> and range <code class="computeroutput"><span class="special">[-</span><span class="number">2.0</span><span class="special">,+</span><span class="number">2.0</span><span class="special">]</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">Z</span></code> with numeric set <code class="computeroutput"><span class="special">{-</span><span class="number">1.0</span><span class="special">,</span><span class="number">0.0</span><span class="special">,+</span><span class="number">1.0</span><span class="special">}</span></code> and range <code class="computeroutput"><span class="special">[-</span><span class="number">1.0</span><span class="special">,+</span><span class="number">1.0</span><span class="special">]</span></code>
</li>
</ul></div>
<p>
For:
</p>
<div class="variablelist">
<p class="title"><b></b></p>
<dl class="variablelist">
<dt><span class="term">(a) X-&gt;Y:</span></dt>
<dd><p>
<code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">X</span><span class="special">)</span> <span class="special">&amp;</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">Y</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">X</span><span class="special">)</span></code>,
then <code class="computeroutput"><span class="identifier">X</span><span class="special">-&gt;</span><span class="identifier">Y</span></code> is not subranged. Thus, all values
of type <code class="computeroutput"><span class="identifier">X</span></code> are representable
in the type <code class="computeroutput"><span class="identifier">Y</span></code>.
</p></dd>
<dt><span class="term">(b) Y-&gt;X:</span></dt>
<dd><p>
<code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">Y</span><span class="special">)</span> <span class="special">&amp;</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">X</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">Y</span><span class="special">)</span></code>,
then <code class="computeroutput"><span class="identifier">Y</span><span class="special">-&gt;</span><span class="identifier">X</span></code> is not subranged. Thus, all values
of type <code class="computeroutput"><span class="identifier">Y</span></code> are representable
in the type <code class="computeroutput"><span class="identifier">X</span></code>, but
in this case, some values are <span class="emphasis"><em>inexactly</em></span> representable
(all the halves). (note: it is to permit this case that a range is
an interval of abstract values and not an interval of typed values)
</p></dd>
<dt><span class="term">(b) X-&gt;Z:</span></dt>
<dd><p>
<code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">X</span><span class="special">)</span> <span class="special">&amp;</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">Z</span><span class="special">)</span> <span class="special">!=</span> <span class="identifier">R</span><span class="special">(</span><span class="identifier">X</span><span class="special">)</span></code>,
then <code class="computeroutput"><span class="identifier">X</span><span class="special">-&gt;</span><span class="identifier">Z</span></code> is subranged. Thus, some values
of type <code class="computeroutput"><span class="identifier">X</span></code> are not representable
in the type <code class="computeroutput"><span class="identifier">Z</span></code>, they
fall out of range <code class="computeroutput"><span class="special">(-</span><span class="number">2.0</span>
<span class="keyword">and</span> <span class="special">+</span><span class="number">2.0</span><span class="special">)</span></code>.
</p></dd>
</dl>
</div>
<p>
It is possible that <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span></code> is not
enclosed by <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">)</span></code>, while
neither is <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">T</span><span class="special">)</span></code> enclosed
by <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="identifier">S</span><span class="special">)</span></code>; for
example, <code class="computeroutput"><span class="identifier">UNSIG</span><span class="special">=[</span><span class="number">0</span><span class="special">,</span><span class="number">255</span><span class="special">]</span></code> is not enclosed by <code class="computeroutput"><span class="identifier">SIG</span><span class="special">=[-</span><span class="number">128</span><span class="special">,</span><span class="number">127</span><span class="special">]</span></code>; neither
is <code class="computeroutput"><span class="identifier">SIG</span></code> enclosed by <code class="computeroutput"><span class="identifier">UNSIG</span></code>. This implies that is possible that
a conversion direction is subranged both ways. This occurs when a mixture
of signed/unsigned types are involved and indicates that in both directions
there are values which can fall out of range.
</p>
<p>
Given the range relation (subranged or not) of a conversion direction <code class="computeroutput"><span class="identifier">S</span><span class="special">-&gt;</span><span class="identifier">T</span></code>, it is possible to classify <code class="computeroutput"><span class="identifier">S</span></code> and <code class="computeroutput"><span class="identifier">T</span></code>
as <span class="bold"><strong>supertype</strong></span> and <span class="bold"><strong>subtype</strong></span>:
If the conversion is subranged, which means that <code class="computeroutput"><span class="identifier">T</span></code>
cannot represent all possible values of type <code class="computeroutput"><span class="identifier">S</span></code>,
<code class="computeroutput"><span class="identifier">S</span></code> is the supertype and <code class="computeroutput"><span class="identifier">T</span></code> the subtype; otherwise, <code class="computeroutput"><span class="identifier">T</span></code> is the supertype and <code class="computeroutput"><span class="identifier">S</span></code>
the subtype.
</p>
<p>
For example:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="keyword">float</span><span class="special">)=[-</span><span class="identifier">FLT_MAX</span><span class="special">,</span><span class="identifier">FLT_MAX</span><span class="special">]</span></code>
and <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="keyword">double</span><span class="special">)=[-</span><span class="identifier">DBL_MAX</span><span class="special">,</span><span class="identifier">DBL_MAX</span><span class="special">]</span></code>
</p></blockquote></div>
<p>
If <code class="computeroutput"><span class="identifier">FLT_MAX</span> <span class="special">&lt;</span>
<span class="identifier">DBL_MAX</span></code>:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<code class="computeroutput"><span class="keyword">double</span><span class="special">-&gt;</span><span class="keyword">float</span></code> is subranged and <code class="computeroutput"><span class="identifier">supertype</span><span class="special">=</span><span class="keyword">double</span></code>,
<code class="computeroutput"><span class="identifier">subtype</span><span class="special">=</span><span class="keyword">float</span></code>.
</li>
<li class="listitem">
<code class="computeroutput"><span class="keyword">float</span><span class="special">-&gt;</span><span class="keyword">double</span></code> is not subranged and <code class="computeroutput"><span class="identifier">supertype</span><span class="special">=</span><span class="keyword">double</span></code>, <code class="computeroutput"><span class="identifier">subtype</span><span class="special">=</span><span class="keyword">float</span></code>.
</li>
</ul></div>
<p>
Notice that while <code class="computeroutput"><span class="keyword">double</span><span class="special">-&gt;</span><span class="keyword">float</span></code> is subranged, <code class="computeroutput"><span class="keyword">float</span><span class="special">-&gt;</span><span class="keyword">double</span></code>
is not, which yields the same supertype,subtype for both directions.
</p>
<p>
Now consider:
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="keyword">int</span><span class="special">)=[</span><span class="identifier">INT_MIN</span><span class="special">,</span><span class="identifier">INT_MAX</span><span class="special">]</span></code> and <code class="computeroutput"><span class="identifier">R</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">)=[</span><span class="number">0</span><span class="special">,</span><span class="identifier">UINT_MAX</span><span class="special">]</span></code>
</p></blockquote></div>
<p>
A C++ implementation is required to have <code class="computeroutput"><span class="identifier">UINT_MAX</span>
<span class="special">&gt;</span> <span class="identifier">INT_MAX</span></code>
(&#167;3.9/3), so:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
'int-&gt;unsigned' is subranged (negative values fall out of range) and
<code class="computeroutput"><span class="identifier">supertype</span><span class="special">=</span><span class="keyword">int</span></code>, <code class="computeroutput"><span class="identifier">subtype</span><span class="special">=</span><span class="keyword">unsigned</span></code>.
</li>
<li class="listitem">
'unsigned-&gt;int' is <span class="emphasis"><em>also</em></span> subranged (high positive
values fall out of range) and <code class="computeroutput"><span class="identifier">supertype</span><span class="special">=</span><span class="keyword">unsigned</span></code>,
<code class="computeroutput"><span class="identifier">subtype</span><span class="special">=</span><span class="keyword">int</span></code>.
</li>
</ul></div>
<p>
In this case, the conversion is subranged in both directions and the supertype,subtype
pairs are not invariant (under inversion of direction). This indicates that
none of the types can represent all the values of the other.
</p>
<p>
When the supertype is the same for both <code class="computeroutput"><span class="identifier">S</span><span class="special">-&gt;</span><span class="identifier">T</span></code>
and <code class="computeroutput"><span class="identifier">T</span><span class="special">-&gt;</span><span class="identifier">S</span></code>, it is effectively indicating a type
which can represent all the values of the subtype. Consequently, if a conversion
<code class="computeroutput"><span class="identifier">X</span><span class="special">-&gt;</span><span class="identifier">Y</span></code> is not subranged, but the opposite <code class="computeroutput"><span class="special">(</span><span class="identifier">Y</span><span class="special">-&gt;</span><span class="identifier">X</span><span class="special">)</span></code> is,
so that the supertype is always <code class="computeroutput"><span class="identifier">Y</span></code>,
it is said that the direction <code class="computeroutput"><span class="identifier">X</span><span class="special">-&gt;</span><span class="identifier">Y</span></code>
is <span class="bold"><strong>correctly rounded value preserving</strong></span>, meaning
that all such conversions are guaranteed to produce results in range and
correctly rounded (even if inexact). For example, all integer to floating
conversions are correctly rounded value preserving.
</p>
</div>
</div>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_numericconversion.improved_numeric_cast__"></a><a class="link" href="improved_numeric_cast__.html" title="Improved numeric_cast&lt;&gt;">Improved
numeric_cast&lt;&gt;</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.numeric_cast">numeric_cast</a></span></dt>
<dt><span class="section"><a href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.numeric_cast_traits">numeric_cast_traits</a></span></dt>
<dt><span class="section"><a href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.examples">Examples</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.improved_numeric_cast__.introduction"></a><a class="link" href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.introduction" title="Introduction">Introduction</a>
</h3></div></div></div>
<p>
The lack of preservation of range makes conversions between numeric types
error prone. This is true for both implicit conversions and explicit conversions
(through <code class="computeroutput"><span class="keyword">static_cast</span></code>). <a class="link" href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.numeric_cast" title="numeric_cast"><code class="computeroutput"><span class="identifier">numeric_cast</span></code></a> detects loss of range
when a numeric type is converted, and throws an exception if the range cannot
be preserved.
</p>
<p>
There are several situations where conversions are unsafe:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Conversions from an integral type with a wider range than the target
integral type.
</li>
<li class="listitem">
Conversions from unsigned to signed (and vice versa) integral types.
</li>
<li class="listitem">
Conversions from floating point types to integral types.
</li>
</ul></div>
<p>
The C++ Standard does not specify the behavior when a numeric type is assigned
a value that cannot be represented by the type, except for unsigned integral
types [3.9.1.4], which must obey the laws of arithmetic modulo 2n (this implies
that the result will be reduced modulo the number that is one greater than
the largest value that can be represented). The fact that the behavior for
overflow is undefined for all conversions (except the aforementioned unsigned
to unsigned) makes any code that may produce positive or negative overflows
exposed to portability issues.
</p>
<p>
By default <code class="computeroutput"><span class="identifier">numeric_cast</span></code> adheres
to the rules for implicit conversions mandated by the C++ Standard, such
as truncating floating point types when converting to integral types. The
implementation must guarantee that for a conversion to a type that can hold
all possible values of the source type, there will be no runtime overhead.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.improved_numeric_cast__.numeric_cast"></a><a class="link" href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.numeric_cast" title="numeric_cast">numeric_cast</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Target</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Source</span><span class="special">&gt;</span> <span class="keyword">inline</span>
<span class="identifier">Target</span> <span class="identifier">numeric_cast</span><span class="special">(</span> <span class="identifier">Source</span> <span class="identifier">arg</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="identifier">Target</span><span class="special">,</span> <span class="identifier">Source</span><span class="special">&gt;</span> <span class="identifier">conv_traits</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">numeric_cast_traits</span><span class="special">&lt;</span><span class="identifier">Target</span><span class="special">,</span> <span class="identifier">Source</span><span class="special">&gt;</span> <span class="identifier">cast_traits</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">converter</span>
<span class="special">&lt;</span>
<span class="identifier">Target</span><span class="special">,</span>
<span class="identifier">Source</span><span class="special">,</span>
<span class="identifier">conv_traits</span><span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">cast_traits</span><span class="special">::</span><span class="identifier">overflow_policy</span><span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">cast_traits</span><span class="special">::</span><span class="identifier">rounding_policy</span><span class="special">,</span>
<span class="identifier">raw_converter</span><span class="special">&lt;</span><span class="identifier">conv_traits</span><span class="special">&gt;,</span>
<span class="keyword">typename</span> <span class="identifier">cast_traits</span><span class="special">::</span><span class="identifier">range_checking_policy</span>
<span class="special">&gt;</span> <span class="identifier">converter</span><span class="special">;</span>
<span class="keyword">return</span> <span class="identifier">converter</span><span class="special">::</span><span class="identifier">convert</span><span class="special">(</span><span class="identifier">arg</span><span class="special">);</span>
<span class="special">}</span>
</pre>
<p>
<code class="computeroutput"><span class="identifier">numeric_cast</span></code> returns the
result of converting a value of type Source to a value of type Target. If
out-of-range is detected, an overflow policy is executed whose default behavior
is to throw an an exception (see <a class="link" href="numeric_converter_policy_classes.html#numeric_conversion_bad_numeric_cast">bad_numeric_cast</a>,
<a class="link" href="numeric_converter_policy_classes.html#numeric_conversion_negative_overflow">negative_overflow</a>
and <a class="link" href="numeric_converter_policy_classes.html#numeric_conversion_possitive_overflow">positive_overflow</a>
).
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.improved_numeric_cast__.numeric_cast_traits"></a><a class="link" href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.numeric_cast_traits" title="numeric_cast_traits">numeric_cast_traits</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Target</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Source</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">EnableIf</span> <span class="special">=</span> <span class="keyword">void</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">numeric_cast_traits</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">def_overflow_handler</span> <span class="identifier">overflow_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">UseInternalRangeChecker</span> <span class="identifier">range_checking_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Trunc</span><span class="special">&lt;</span><span class="identifier">Source</span><span class="special">&gt;</span> <span class="identifier">rounding_policy</span><span class="special">;</span>
<span class="special">};</span>
</pre>
<p>
The behavior of <code class="computeroutput"><span class="identifier">numeric_cast</span></code>
may be tailored for custom numeric types through the specialization of <code class="computeroutput"><span class="identifier">numeric_cast_traits</span></code>. (see <a class="link" href="type_requirements_and_user_defined_types_support.html" title="Type Requirements and User-defined-types support">User
Defined Types</a> for details. )
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.improved_numeric_cast__.examples"></a><a class="link" href="improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.examples" title="Examples">Examples</a>
</h3></div></div></div>
<p>
The following example performs some typical conversions between numeric types:
</p>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
include &lt;boost/numeric/conversion/cast.hpp&gt;
</li>
<li class="listitem">
include &lt;iostream&gt;
</li>
</ol></div>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric_cast</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bad_numeric_cast</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">positive_overflow</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">negative_overflow</span><span class="special">;</span>
<span class="keyword">try</span>
<span class="special">{</span>
<span class="keyword">int</span> <span class="identifier">i</span><span class="special">=</span><span class="number">42</span><span class="special">;</span>
<span class="keyword">short</span> <span class="identifier">s</span><span class="special">=</span><span class="identifier">numeric_cast</span><span class="special">&lt;</span><span class="keyword">short</span><span class="special">&gt;(</span><span class="identifier">i</span><span class="special">);</span> <span class="comment">// This conversion succeeds (is in range)</span>
<span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="identifier">negative_overflow</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span> <span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">();</span>
<span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="identifier">positive_overflow</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span> <span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">();</span>
<span class="special">}</span>
<span class="keyword">try</span>
<span class="special">{</span>
<span class="keyword">float</span> <span class="identifier">f</span><span class="special">=-</span><span class="number">42.1234</span><span class="special">;</span>
<span class="comment">// This will cause a boost::numeric::negative_overflow exception to be thrown</span>
<span class="keyword">unsigned</span> <span class="keyword">int</span> <span class="identifier">i</span><span class="special">=</span><span class="identifier">numeric_cast</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">int</span><span class="special">&gt;(</span><span class="identifier">f</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="identifier">bad_numeric_cast</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span> <span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">();</span>
<span class="special">}</span>
<span class="keyword">double</span> <span class="identifier">d</span><span class="special">=</span> <span class="identifier">f</span> <span class="special">+</span> <span class="identifier">numeric_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">123</span><span class="special">);</span> <span class="comment">// int -&gt; double</span>
<span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="identifier">l</span><span class="special">=</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">long</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">();</span>
<span class="keyword">try</span>
<span class="special">{</span>
<span class="comment">// This will cause a boost::numeric::positive_overflow exception to be thrown</span>
<span class="comment">// NOTE: *operations* on unsigned integral types cannot cause overflow</span>
<span class="comment">// but *conversions* to a signed type ARE range checked by numeric_cast.</span>
<span class="keyword">unsigned</span> <span class="keyword">char</span> <span class="identifier">c</span><span class="special">=</span><span class="identifier">numeric_cast</span><span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="keyword">char</span><span class="special">&gt;(</span><span class="identifier">l</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">catch</span><span class="special">(</span><span class="identifier">positive_overflow</span><span class="special">&amp;</span> <span class="identifier">e</span><span class="special">)</span> <span class="special">{</span>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span><span class="special">.</span><span class="identifier">what</span><span class="special">();</span>
<span class="special">}</span>
<span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_numericconversion.numeric_converter_policy_classes"></a><a class="link" href="numeric_converter_policy_classes.html" title="Numeric Converter Policy Classes">Numeric
Converter Policy Classes</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.enum_range_check_result">enum
range_check_result</a></span></dt>
<dt><span class="section"><a href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler">Policy
OverflowHandler</a></span></dt>
<dt><span class="section"><a href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder">Policy
Float2IntRounder</a></span></dt>
<dt><span class="section"><a href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter">Policy
RawConverter</a></span></dt>
<dt><span class="section"><a href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker">Policy
UserRangeChecker</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.numeric_converter_policy_classes.enum_range_check_result"></a><a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.enum_range_check_result" title="enum range_check_result">enum
range_check_result</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">enum</span> <span class="identifier">range_check_result</span>
<span class="special">{</span>
<span class="identifier">cInRange</span> <span class="special">,</span>
<span class="identifier">cNegOverflow</span> <span class="special">,</span>
<span class="identifier">cPosOverflow</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span>
</pre>
<p>
Defines the values returned by <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">converter</span><span class="special">&lt;&gt;::</span><span class="identifier">out_of_range</span><span class="special">()</span></code>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler"></a><a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler" title="Policy OverflowHandler">Policy
OverflowHandler</a>
</h3></div></div></div>
<p>
This <span class="emphasis"><em>stateless</em></span> non-template policy class must be a
<span class="emphasis"><em>function object</em></span> and is called to administrate the result
of the range checking. It can throw an exception if overflow has been detected
by the range checking as indicated by its argument. If it throws, is is recommended
that it be <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">bad_cast</span></code> or derived.
</p>
<p>
It must have the following interface (it does not has to be a template class):
</p>
<pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">YourOverflowHandlerPolicy</span>
<span class="special">{</span>
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()</span> <span class="special">(</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">range_check_result</span> <span class="special">)</span> <span class="special">;</span> <span class="comment">// throw bad_cast or derived</span>
<span class="special">}</span> <span class="special">;</span>
</pre>
<p>
It is called with the result of the converter's <code class="computeroutput"><span class="identifier">out_of_range</span><span class="special">()</span></code> inside <code class="computeroutput"><span class="identifier">validate_range</span><span class="special">()</span></code>.
</p>
<p>
These are the two overflow handler classes provided by the library:
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">struct</span> <span class="identifier">def_overflow_handler</span>
<span class="special">{</span>
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()</span> <span class="special">(</span> <span class="identifier">range_check_result</span> <span class="identifier">r</span> <span class="special">)</span> <span class="comment">// throw bad_numeric_conversion derived</span>
<span class="special">{</span>
<span class="keyword">if</span> <span class="special">(</span> <span class="identifier">r</span> <span class="special">==</span> <span class="identifier">cNegOverflow</span> <span class="special">)</span>
<span class="keyword">throw</span> <span class="identifier">negative_overflow</span><span class="special">()</span> <span class="special">;</span>
<span class="keyword">else</span> <span class="keyword">if</span> <span class="special">(</span> <span class="identifier">r</span> <span class="special">==</span> <span class="identifier">cPosOverflow</span> <span class="special">)</span>
<span class="keyword">throw</span> <span class="identifier">positive_overflow</span><span class="special">()</span> <span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span> <span class="special">;</span>
<span class="keyword">struct</span> <span class="identifier">silent_overflow_handler</span>
<span class="special">{</span>
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()</span> <span class="special">(</span> <span class="identifier">range_check_result</span> <span class="special">)</span> <span class="comment">// no-throw</span>
<span class="special">{}</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span>
</pre>
<p>
And these are the Exception Classes thrown by the default overflow handler
<a class="link" href="numeric_converter_policy_classes.html#numeric_conversion_policy_overflow_handler_important_note">(see
IMPORTANT note)</a>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<a name="numeric_conversion_bad_numeric_cast"></a>
<span class="keyword">class</span> <span class="identifier">bad_numeric_cast</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">bad_cast</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">virtual</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">what</span><span class="special">()</span> <span class="keyword">const</span> <span class="comment">// throw()</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="string">"bad numeric conversion: overflow"</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">};</span>
<a name="numeric_conversion_negative_overflow"></a>
<span class="keyword">class</span> <span class="identifier">negative_overflow</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">bad_numeric_cast</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">virtual</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">what</span><span class="special">()</span> <span class="keyword">const</span> <span class="comment">// throw()</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="string">"bad numeric conversion: negative overflow"</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">};</span>
<a name="numeric_conversion_possitive_overflow"></a>
<span class="keyword">class</span> <span class="identifier">positive_overflow</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">bad_numeric_cast</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">virtual</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="special">*</span><span class="identifier">what</span><span class="special">()</span> <span class="keyword">const</span> <span class="comment">// throw()</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="string">"bad numeric conversion: positive overflow"</span><span class="special">;</span>
<span class="special">}</span>
<span class="special">};</span>
<span class="special">}</span> <span class="special">}</span>
</pre>
<a name="numeric_conversion_policy_overflow_handler_important_note"></a><div class="important"><table border="0" summary="Important">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Important]" src="../../../../../../doc/src/images/important.png"></td>
<th align="left">Important</th>
</tr>
<tr><td align="left" valign="top"><p>
<span class="bold"><strong>RELEASE NOTE for 1.33</strong></span> Previous to boost
version 1.33, the exception class <code class="computeroutput"><span class="identifier">bad_numeric_cast</span></code>
was named <code class="computeroutput"><span class="identifier">bad_numeric_conversion</span></code>.
However, in 1.33, the old function <code class="computeroutput"><span class="identifier">numeric_cast</span><span class="special">&lt;&gt;</span></code> from <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cast</span><span class="special">.</span><span class="identifier">hpp</span></code>
was completly replaced by the new <code class="computeroutput"><span class="identifier">numeric_cast</span><span class="special">&lt;&gt;</span></code> in <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">conversion</span><span class="special">/</span><span class="identifier">cast</span><span class="special">.</span><span class="identifier">hpp</span></code>
(and <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cast</span><span class="special">.</span><span class="identifier">hpp</span></code> is including <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">conversion</span><span class="special">/</span><span class="identifier">cast</span><span class="special">.</span><span class="identifier">hpp</span></code>
now). That old function which existed in boost for quite some time used
the <code class="computeroutput"><span class="identifier">bad_numeric_cast</span></code> as
its exception type so I decided to avoid backward compatibility problems
by adopting it (guessing that the user base for the old code is wider than
for the new code).
</p></td></tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder"></a><a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder" title="Policy Float2IntRounder">Policy
Float2IntRounder</a>
</h3></div></div></div>
<p>
This <span class="emphasis"><em>stateless</em></span> template policy class specifies the rounding
mode used for <span class="underline">float to integral</span> conversions.
It supplies the <code class="computeroutput"><span class="identifier">nearbyint</span><span class="special">()</span></code> static member function exposed by the converter,
which means that it <span class="underline">publicly inherits from this
policy</span>.
</p>
<p>
The policy must have the following interface:
</p>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">YourFloat2IntRounderPolicy</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">S</span> <span class="identifier">source_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="special">{</span><span class="identifier">S</span> <span class="keyword">or</span> <span class="identifier">S</span> <span class="keyword">const</span><span class="special">&amp;}</span> <span class="identifier">argument_type</span> <span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">{</span> <span class="special">...</span> <span class="special">}</span>
<span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">float_round_style</span><span class="special">,</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">round_</span><span class="special">...&gt;</span> <span class="identifier">round_style</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">;</span>
</pre>
<p>
These are the rounder classes provided by the library (only the specific
parts are shown, see the general policy form above)
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
These classes are not intended to be general purpose rounding functions
but specific policies for <code class="computeroutput"><span class="identifier">converter</span><span class="special">&lt;&gt;</span></code>. This is why they are not function
objects.
</p></td></tr>
</table></div>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">Trunc</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">floor</span> <span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ceil</span> <span class="special">;</span>
<span class="keyword">return</span> <span class="identifier">s</span> <span class="special">&gt;=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">S</span><span class="special">&gt;(</span><span class="number">0</span><span class="special">)</span> <span class="special">?</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span> <span class="special">;</span>
<span class="special">}</span>
<span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">float_round_style</span><span class="special">,</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">round_toward_zero</span><span class="special">&gt;</span> <span class="identifier">round_style</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">RoundEven</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">impl</span><span class="special">-</span><span class="identifier">defined</span><span class="special">-</span><span class="identifier">value</span> <span class="special">;</span>
<span class="special">}</span>
<span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">float_round_style</span><span class="special">,</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">round_to_nearest</span><span class="special">&gt;</span> <span class="identifier">round_style</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">Ceil</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ceil</span> <span class="special">;</span>
<span class="keyword">return</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span> <span class="special">;</span>
<span class="special">}</span>
<span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">float_round_style</span><span class="special">,</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">round_toward_infinity</span><span class="special">&gt;</span> <span class="identifier">round_style</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">Floor</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">floor</span> <span class="special">;</span>
<span class="keyword">return</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span> <span class="special">;</span>
<span class="special">}</span>
<span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">float_round_style</span><span class="special">,</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">round_toward_neg_infinity</span><span class="special">&gt;</span> <span class="identifier">round_style</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespace numeric, namespace boost</span>
</pre>
<h5>
<a name="boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder.h0"></a>
<span class="phrase"><a name="boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder.math_functions_used_by_the_rounder_policies"></a></span><a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder.math_functions_used_by_the_rounder_policies">Math
Functions used by the rounder policies</a>
</h5>
<p>
The rounder policies supplied by this header use math functions <code class="computeroutput"><span class="identifier">floor</span><span class="special">()</span></code>
and <code class="computeroutput"><span class="identifier">ceil</span><span class="special">()</span></code>.
The standard versions of these functions are introduced in context by a using
directive, so in normal conditions, the standard functions will be used.
</p>
<p>
However, if there are other visible corresponding overloads an ambiguity
could arise. In this case, the user can supply her own rounder policy which
could, for instance, use a fully qualified call.
</p>
<p>
This technique allows the default rounder policies to be used directly with
user defined types. The user only requires that suitable overloads of <code class="computeroutput"><span class="identifier">floor</span><span class="special">()</span></code>
and <code class="computeroutput"><span class="identifier">ceil</span><span class="special">()</span></code>
be visible. See also <a class="link" href="type_requirements_and_user_defined_types_support.html" title="Type Requirements and User-defined-types support">User
Defined Numeric Types</a> support.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter"></a><a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter" title="Policy RawConverter">Policy
RawConverter</a>
</h3></div></div></div>
<p>
This <span class="emphasis"><em>stateless</em></span> template policy class is used to perform
the actual conversion from Source to Target. It supplies the <code class="computeroutput"><span class="identifier">low_level_convert</span><span class="special">()</span></code>
static member function exposed by the converter, which means that it publicly
inherits from this policy.
</p>
<p>
The policy must have the following interface:
</p>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Traits</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">YourRawConverterPolicy</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">result_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">argument_type</span> <span class="identifier">argument_type</span> <span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">result_type</span> <span class="identifier">low_level_convert</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">{</span> <span class="keyword">return</span> <span class="special">&lt;</span><span class="identifier">impl</span> <span class="identifier">defined</span><span class="special">&gt;</span> <span class="special">;</span> <span class="special">}</span>
<span class="special">}</span> <span class="special">;</span>
</pre>
<p>
This policy is mostly provided as a hook for user defined types which don't
support <code class="computeroutput"><span class="keyword">static_cast</span><span class="special">&lt;&gt;</span></code>
conversions to some types
</p>
<p>
This is the only raw converter policy class provided by the library:
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Traits</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">raw_numeric_converter</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">result_type</span> <span class="identifier">result_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">argument_type</span> <span class="identifier">argument_type</span> <span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">result_type</span> <span class="identifier">low_level_convert</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">result_type</span><span class="special">&gt;(</span><span class="identifier">s</span><span class="special">)</span> <span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span> <span class="special">;</span>
<span class="special">}</span> <span class="special">}</span>
</pre>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker"></a><a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker" title="Policy UserRangeChecker">Policy
UserRangeChecker</a>
</h3></div></div></div>
<p>
This <span class="emphasis"><em>stateless</em></span> template policy class is used <span class="underline">only if supplied</span> to <span class="bold"><strong>override</strong></span>
the internal range checking logic.
</p>
<p>
It supplies the <code class="computeroutput"><span class="identifier">validate_range</span><span class="special">()</span></code> static member function exposed by the converter,
which means that it publicly inherits from this policy.
</p>
<p>
The policy must have the following interface:
</p>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Traits</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">YourRangeCheckerPolicy</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">argument_type</span> <span class="identifier">argument_type</span> <span class="special">;</span>
<span class="comment">// Determines if the value 's' fits in the range of the Target type.</span>
<span class="keyword">static</span> <span class="identifier">range_check_result</span> <span class="identifier">out_of_range</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span> <span class="special">;</span>
<span class="comment">// Checks whether the value 's' is out_of_range()</span>
<span class="comment">// and passes the result of the check to the OverflowHandler policy.</span>
<span class="keyword">static</span> <span class="keyword">void</span> <span class="identifier">validate_range</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">OverflowHandler</span><span class="special">()(</span> <span class="identifier">out_of_range</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span> <span class="special">)</span> <span class="special">;</span>
<span class="special">}</span>
<span class="special">}</span> <span class="special">;</span>
</pre>
<p>
This policy is <span class="bold"><strong>only</strong></span> provided as a hook for
user defined types which require range checking (which is disabled by default
when a UDT is involved). The library provides a class: <code class="computeroutput"><span class="identifier">UseInternalRangeChecker</span><span class="special">{}</span></code>; which is a <span class="emphasis"><em>fake</em></span>
<code class="computeroutput"><span class="identifier">RangeChecker</span></code> policy used
to signal the converter to use its internal range checking implementation.
</p>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
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</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_numericconversion.type_requirements_and_user_defined_types_support"></a><a class="link" href="type_requirements_and_user_defined_types_support.html" title="Type Requirements and User-defined-types support">Type
Requirements and User-defined-types support</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.type_requirements">Type
Requirements</a></span></dt>
<dt><span class="section"><a href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics">UDT's
special semantics</a></span></dt>
<dt><span class="section"><a href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.special_policies">Special
Policies</a></span></dt>
<dt><span class="section"><a href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udts_with_numeric_cast">UDTs
with numeric_cast</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.type_requirements_and_user_defined_types_support.type_requirements"></a><a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.type_requirements" title="Type Requirements">Type
Requirements</a>
</h3></div></div></div>
<p>
Both arithmetic (built-in) and user-defined numeric types require proper
specialization of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;&gt;</span></code>
(that is, with (in-class) integral constants).
</p>
<p>
The library uses <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_specialized</span></code> to detect whether the type
is builtin or user defined, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_integer</span></code>, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_signed</span></code> to detect whether the type is
integer or floating point; and whether it is signed/unsigned.
</p>
<p>
The default <code class="computeroutput"><span class="identifier">Float2IntRounder</span></code>
policies uses unqualified calls to functions <code class="computeroutput"><span class="identifier">floor</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">ceil</span><span class="special">()</span></code>; but the standard functions are introduced
in scope by a using directive:
</p>
<pre class="programlisting"><span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">floor</span> <span class="special">;</span> <span class="keyword">return</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">s</span><span class="special">);</span>
</pre>
<p>
Therefore, for builtin arithmetic types, the std functions will be used.
User defined types should provide overloaded versions of these functions
in order to use the default rounder policies. If these overloads are defined
within a user namespace argument dependent lookup (ADL) should find them,
but if your compiler has a weak ADL you might need to put these functions
some place else or write your own rounder policy.
</p>
<p>
The default <code class="computeroutput"><span class="identifier">Trunc</span><span class="special">&lt;&gt;</span></code>
rounder policy needs to determine if the source value is positive or not,
and for this it evaluates the expression <code class="computeroutput"><span class="identifier">s</span>
<span class="special">&lt;</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">S</span><span class="special">&gt;(</span><span class="number">0</span><span class="special">)</span></code>. Therefore,
user defined types require a visible <code class="computeroutput"><span class="keyword">operator</span><span class="special">&lt;</span></code> in order to use the <code class="computeroutput"><span class="identifier">Trunc</span><span class="special">&lt;&gt;</span></code> policy (the default).
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics"></a><a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics" title="UDT's special semantics">UDT's
special semantics</a>
</h3></div></div></div>
<h5>
<a name="boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics.h0"></a>
<span class="phrase"><a name="boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics.conversion_traits"></a></span><a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics.conversion_traits">Conversion
Traits</a>
</h5>
<p>
If a User Defined Type is involved in a conversion, it is <span class="emphasis"><em>assumed</em></span>
that the UDT has <a class="link" href="definitions.html#boost_numericconversion.definitions.range_and_precision" title="Range and Precision">wider
range</a> than any built-in type, and consequently the values of some
<code class="computeroutput"><span class="identifier">converter_traits</span><span class="special">&lt;&gt;</span></code>
members are hardwired regardless of the reality. The following table summarizes
this:
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
<code class="computeroutput"><span class="identifier">Target</span><span class="special">=</span></code><span class="emphasis"><em>UDT</em></span>
and <code class="computeroutput"><span class="identifier">Source</span><span class="special">=</span></code><span class="emphasis"><em>built-in</em></span>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
<li class="listitem">
<code class="computeroutput"><span class="identifier">subranged</span><span class="special">=</span><span class="keyword">false</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">supertype</span><span class="special">=</span><span class="identifier">Target</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">subtype</span><span class="special">=</span><span class="identifier">Source</span></code>
</li>
</ul></div>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">Target</span><span class="special">=</span></code><span class="emphasis"><em>built-in</em></span>
and <code class="computeroutput"><span class="identifier">Source</span><span class="special">=</span></code><span class="emphasis"><em>UDT</em></span>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
<li class="listitem">
<code class="computeroutput"><span class="identifier">subranged</span><span class="special">=</span><span class="keyword">true</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">supertype</span><span class="special">=</span><span class="identifier">Source</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">subtype</span><span class="special">=</span><span class="identifier">Target</span></code>
</li>
</ul></div>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">Target</span><span class="special">=</span></code><span class="emphasis"><em>UDT</em></span>
and <code class="computeroutput"><span class="identifier">Source</span><span class="special">=</span></code><span class="emphasis"><em>UDT</em></span>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
<li class="listitem">
<code class="computeroutput"><span class="identifier">subranged</span><span class="special">=</span><span class="keyword">false</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">supertype</span><span class="special">=</span><span class="identifier">Target</span></code>
</li>
<li class="listitem">
<code class="computeroutput"><span class="identifier">subtype</span><span class="special">=</span><span class="identifier">Source</span></code>
</li>
</ul></div>
</li>
</ul></div>
<p>
The <code class="computeroutput"><span class="identifier">Traits</span></code> member <code class="computeroutput"><span class="identifier">udt_mixture</span></code> can be used to detect whether
a UDT is involved and to infer the validity of the other members as shown
above.
</p>
<h5>
<a name="boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics.h1"></a>
<span class="phrase"><a name="boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics.range_checking"></a></span><a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics.range_checking">Range
Checking</a>
</h5>
<p>
Because User Defined Numeric Types might have peculiar ranges (such as an
unbounded range), this library does not attempt to supply a meaningful range
checking logic when UDTs are involved in a conversion. Therefore, if either
Target or Source are not built-in types, the bundled range checking of the
<code class="computeroutput"><span class="identifier">converter</span><span class="special">&lt;&gt;</span></code>
function object is automatically disabled. However, it is possible to supply
a user-defined range-checker. See <a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.special_policies" title="Special Policies">Special
Policies</a>
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.type_requirements_and_user_defined_types_support.special_policies"></a><a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.special_policies" title="Special Policies">Special
Policies</a>
</h3></div></div></div>
<p>
There are two components of the <code class="computeroutput"><span class="identifier">converter</span><span class="special">&lt;&gt;</span></code> class that might require special
behavior if User Defined Numeric Types are involved: the Range Checking and
the Raw Conversion.
</p>
<p>
When both Target and Source are built-in types, the converter class uses
an internal range checking logic which is optimized and customized for the
combined properties of the types.
</p>
<p>
However, this internal logic is disabled when either type is User Defined.
In this case, the user can specify an <span class="emphasis"><em>external</em></span> range
checking policy which will be used in place of the internal code. See <a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udts_with_numeric_cast" title="UDTs with numeric_cast">numeric_cast_traits</a>
for details on using UDTs with <code class="computeroutput"><span class="identifier">numeric_cast</span></code>.
</p>
<p>
The converter class performs the actual conversion using a Raw Converter
policy. The default raw converter simply performs a <code class="computeroutput"><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">Target</span><span class="special">&gt;(</span><span class="identifier">source</span><span class="special">)</span></code>.
</p>
<p>
However, if the a UDT is involved, the <code class="computeroutput"><span class="keyword">static_cast</span></code>
might not work. In this case, the user can implement and pass a different
raw converter policy. See <a class="link" href="numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter" title="Policy RawConverter">RawConverter</a>
policy for details.
</p>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numericconversion.type_requirements_and_user_defined_types_support.udts_with_numeric_cast"></a><a class="link" href="type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udts_with_numeric_cast" title="UDTs with numeric_cast">UDTs
with numeric_cast</a>
</h3></div></div></div>
<p>
In order to employ UDTs with <code class="computeroutput"><span class="identifier">numeric_cast</span></code>,
the user should define a <code class="computeroutput"><span class="identifier">numeric_cast_traits</span></code>
specialization on the UDT for each conversion. Here is an example of specializations
for converting between the UDT and any other type:
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Source</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">numeric_cast_traits</span><span class="special">&lt;</span><span class="identifier">UDT</span><span class="special">,</span> <span class="identifier">Source</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="identifier">UDT</span><span class="special">,</span> <span class="identifier">Source</span><span class="special">&gt;</span> <span class="identifier">conv_traits</span><span class="special">;</span>
<span class="comment">//! The following are required:</span>
<span class="keyword">typedef</span> <span class="identifier">YourOverflowHandlerPolicy</span> <span class="identifier">overflow_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">YourRangeCheckerPolicy</span><span class="special">&lt;</span><span class="identifier">conv_traits</span><span class="special">&gt;</span> <span class="identifier">range_checking_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">YourFloat2IntRounderPolicy</span><span class="special">&lt;</span><span class="identifier">Source</span><span class="special">&gt;</span> <span class="identifier">rounding_policy</span><span class="special">;</span>
<span class="special">};</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Target</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">numeric_cast_traits</span><span class="special">&lt;</span><span class="identifier">Target</span><span class="special">,</span> <span class="identifier">UDT</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="identifier">Target</span><span class="special">,</span> <span class="identifier">UDT</span><span class="special">&gt;</span> <span class="identifier">conv_traits</span><span class="special">;</span>
<span class="comment">//! The following are required:</span>
<span class="keyword">typedef</span> <span class="identifier">YourOverflowHandlerPolicy</span> <span class="identifier">overflow_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">YourRangeCheckerPolicy</span><span class="special">&lt;</span><span class="identifier">conv_traits</span><span class="special">&gt;</span> <span class="identifier">range_checking_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">YourFloat2IntRounderPolicy</span><span class="special">&lt;</span><span class="identifier">UDT</span><span class="special">&gt;</span> <span class="identifier">rounding_policy</span><span class="special">;</span>
<span class="special">};</span>
<span class="special">}}//</span><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">;</span>
</pre>
<p>
These specializations are already defined with default values for the built-in
numeric types. It is possible to disable the generation of specializations
for built-in types by defining <code class="computeroutput"><span class="identifier">BOOST_NUMERIC_CONVERSION_RELAX_BUILT_IN_CAST_TRAITS</span></code>.
For details on defining custom policies see <a class="link" href="numeric_converter_policy_classes.html" title="Numeric Converter Policy Classes">Converter
Policies</a>.
</p>
<p>
Here is a full example of how to define a custom UDT for use with <code class="computeroutput"><span class="identifier">numeric_cast</span></code>:
</p>
<pre class="programlisting"><span class="comment">//! Define a simple custom number</span>
<span class="keyword">struct</span> <span class="identifier">Double</span>
<span class="special">:</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators</span>
<span class="special">&lt;</span>
<span class="identifier">Double</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">double</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">float</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">int</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">int</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">long</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">long</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">long</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">char</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">char</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">short</span>
<span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">ordered_field_operators2</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="keyword">unsigned</span> <span class="keyword">short</span>
<span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span>
<span class="special">{</span>
<span class="identifier">Double</span><span class="special">()</span>
<span class="special">:</span> <span class="identifier">v</span><span class="special">(</span><span class="number">0</span><span class="special">)</span>
<span class="special">{}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="keyword">explicit</span> <span class="identifier">Double</span><span class="special">(</span> <span class="identifier">T</span> <span class="identifier">v</span> <span class="special">)</span>
<span class="special">:</span> <span class="identifier">v</span><span class="special">(</span><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">v</span><span class="special">))</span>
<span class="special">{}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">=</span> <span class="special">(</span> <span class="identifier">T</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">t</span><span class="special">);</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&lt;</span> <span class="special">(</span> <span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">rhs</span> <span class="special">)</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">v</span> <span class="special">&lt;</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">v</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&lt;</span> <span class="special">(</span> <span class="identifier">T</span> <span class="identifier">rhs</span> <span class="special">)</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">v</span> <span class="special">&lt;</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">rhs</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&gt;</span> <span class="special">(</span> <span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">rhs</span> <span class="special">)</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">v</span> <span class="special">&gt;</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">v</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">&gt;</span> <span class="special">(</span> <span class="identifier">T</span> <span class="identifier">rhs</span> <span class="special">)</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">v</span> <span class="special">&gt;</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">rhs</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==(</span> <span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">rhs</span> <span class="special">)</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">v</span> <span class="special">==</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">v</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span> <span class="identifier">T</span> <span class="identifier">rhs</span> <span class="special">)</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">v</span> <span class="special">==</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">rhs</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!()</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">v</span> <span class="special">==</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">Double</span> <span class="keyword">operator</span> <span class="special">-()</span> <span class="keyword">const</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">Double</span><span class="special">(-</span><span class="identifier">v</span><span class="special">);</span>
<span class="special">}</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=(</span> <span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">+=</span> <span class="identifier">t</span><span class="special">.</span><span class="identifier">v</span><span class="special">;</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=(</span> <span class="identifier">T</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">+=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">t</span><span class="special">);</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=(</span> <span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">-=</span> <span class="identifier">t</span><span class="special">.</span><span class="identifier">v</span><span class="special">;</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=(</span> <span class="identifier">T</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">-=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">t</span><span class="special">);</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span> <span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">factor</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">*=</span> <span class="identifier">factor</span><span class="special">.</span><span class="identifier">v</span><span class="special">;</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">*=(</span> <span class="identifier">T</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">*=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">t</span><span class="special">);</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">divisor</span><span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">/=</span> <span class="identifier">divisor</span><span class="special">.</span><span class="identifier">v</span><span class="special">;</span>
<span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">Double</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">/=(</span> <span class="identifier">T</span> <span class="identifier">t</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">v</span> <span class="special">/=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">t</span><span class="special">);</span>
<span class="keyword">return</span> <span class="special">(*</span><span class="keyword">this</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">double</span> <span class="identifier">v</span><span class="special">;</span>
<span class="special">};</span>
<span class="comment">//! Define numeric_limits for the custom type.</span>
<span class="keyword">namespace</span> <span class="identifier">std</span>
<span class="special">{</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span>
<span class="keyword">class</span> <span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Double</span><span class="special">&gt;</span> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="comment">//! Limit our Double to a range of +/- 100.0</span>
<span class="keyword">static</span> <span class="identifier">Double</span> <span class="special">(</span><span class="identifier">min</span><span class="special">)()</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">Double</span><span class="special">(</span><span class="number">1.e-2</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">static</span> <span class="identifier">Double</span> <span class="special">(</span><span class="identifier">max</span><span class="special">)()</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">Double</span><span class="special">(</span><span class="number">1.e2</span><span class="special">);</span>
<span class="special">}</span>
<span class="keyword">static</span> <span class="identifier">Double</span> <span class="identifier">epsilon</span><span class="special">()</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">Double</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;::</span><span class="identifier">epsilon</span><span class="special">()</span> <span class="special">);</span>
<span class="special">}</span>
<span class="special">};</span>
<span class="special">}</span>
<span class="comment">//! Define range checking and overflow policies.</span>
<span class="keyword">namespace</span> <span class="identifier">custom</span>
<span class="special">{</span>
<span class="comment">//! Define a custom range checker</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">OverFlowHandler</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">range_checker</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">argument_type</span> <span class="identifier">argument_type</span> <span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">source_type</span> <span class="identifier">S</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">Traits</span><span class="special">::</span><span class="identifier">target_type</span> <span class="identifier">T</span><span class="special">;</span>
<span class="comment">//! Check range of integral types.</span>
<span class="keyword">static</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">range_check_result</span> <span class="identifier">out_of_range</span><span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">;</span>
<span class="keyword">if</span><span class="special">(</span> <span class="identifier">s</span> <span class="special">&gt;</span> <span class="identifier">bounds</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">highest</span><span class="special">()</span> <span class="special">)</span>
<span class="keyword">return</span> <span class="identifier">cPosOverflow</span><span class="special">;</span>
<span class="keyword">else</span> <span class="keyword">if</span><span class="special">(</span> <span class="identifier">s</span> <span class="special">&lt;</span> <span class="identifier">bounds</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">lowest</span><span class="special">()</span> <span class="special">)</span>
<span class="keyword">return</span> <span class="identifier">cNegOverflow</span><span class="special">;</span>
<span class="keyword">else</span>
<span class="keyword">return</span> <span class="identifier">cInRange</span><span class="special">;</span>
<span class="special">}</span>
<span class="keyword">static</span> <span class="keyword">void</span> <span class="identifier">validate_range</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="identifier">BOOST_STATIC_ASSERT</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_bounded</span> <span class="special">);</span>
<span class="identifier">OverFlowHandler</span><span class="special">()(</span> <span class="identifier">out_of_range</span><span class="special">(</span><span class="identifier">s</span><span class="special">)</span> <span class="special">);</span>
<span class="special">}</span>
<span class="special">};</span>
<span class="comment">//! Overflow handler</span>
<span class="keyword">struct</span> <span class="identifier">positive_overflow</span><span class="special">{};</span>
<span class="keyword">struct</span> <span class="identifier">negative_overflow</span><span class="special">{};</span>
<span class="keyword">struct</span> <span class="identifier">overflow_handler</span>
<span class="special">{</span>
<span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()</span> <span class="special">(</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">range_check_result</span> <span class="identifier">r</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">;</span>
<span class="keyword">if</span><span class="special">(</span> <span class="identifier">r</span> <span class="special">==</span> <span class="identifier">cNegOverflow</span> <span class="special">)</span>
<span class="keyword">throw</span> <span class="identifier">negative_overflow</span><span class="special">()</span> <span class="special">;</span>
<span class="keyword">else</span> <span class="keyword">if</span><span class="special">(</span> <span class="identifier">r</span> <span class="special">==</span> <span class="identifier">cPosOverflow</span> <span class="special">)</span>
<span class="keyword">throw</span> <span class="identifier">positive_overflow</span><span class="special">()</span> <span class="special">;</span>
<span class="special">}</span>
<span class="special">};</span>
<span class="comment">//! Define a rounding policy and specialize on the custom type.</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">Ceil</span> <span class="special">:</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">Ceil</span><span class="special">&lt;</span><span class="identifier">S</span><span class="special">&gt;{};</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span>
<span class="keyword">struct</span> <span class="identifier">Ceil</span><span class="special">&lt;</span><span class="identifier">Double</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">Double</span> <span class="identifier">source_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Double</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">argument_type</span><span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="preprocessor">#if</span> <span class="special">!</span><span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_NO_STDC_NAMESPACE</span><span class="special">)</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ceil</span> <span class="special">;</span>
<span class="preprocessor">#endif</span>
<span class="keyword">return</span> <span class="identifier">Double</span><span class="special">(</span> <span class="identifier">ceil</span><span class="special">(</span><span class="identifier">s</span><span class="special">.</span><span class="identifier">v</span><span class="special">)</span> <span class="special">);</span>
<span class="special">}</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">float_round_style</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">round_toward_infinity</span><span class="special">&gt;</span> <span class="identifier">round_style</span><span class="special">;</span>
<span class="special">};</span>
<span class="comment">//! Define a rounding policy and specialize on the custom type.</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">Trunc</span><span class="special">:</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">Trunc</span><span class="special">&lt;</span><span class="identifier">S</span><span class="special">&gt;{};</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span>
<span class="keyword">struct</span> <span class="identifier">Trunc</span><span class="special">&lt;</span><span class="identifier">Double</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">Double</span> <span class="identifier">source_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">Double</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">argument_type</span><span class="special">;</span>
<span class="keyword">static</span> <span class="identifier">source_type</span> <span class="identifier">nearbyint</span> <span class="special">(</span> <span class="identifier">argument_type</span> <span class="identifier">s</span> <span class="special">)</span>
<span class="special">{</span>
<span class="preprocessor">#if</span> <span class="special">!</span><span class="identifier">defined</span><span class="special">(</span><span class="identifier">BOOST_NO_STDC_NAMESPACE</span><span class="special">)</span>
<span class="keyword">using</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">floor</span><span class="special">;</span>
<span class="preprocessor">#endif</span>
<span class="keyword">return</span> <span class="identifier">Double</span><span class="special">(</span> <span class="identifier">floor</span><span class="special">(</span><span class="identifier">s</span><span class="special">.</span><span class="identifier">v</span><span class="special">)</span> <span class="special">);</span>
<span class="special">}</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">integral_c</span><span class="special">&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">float_round_style</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">round_toward_zero</span><span class="special">&gt;</span> <span class="identifier">round_style</span><span class="special">;</span>
<span class="special">};</span>
<span class="special">}//</span><span class="keyword">namespace</span> <span class="identifier">custom</span><span class="special">;</span>
<span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span>
<span class="comment">//! Define the numeric_cast_traits specializations on the custom type.</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">numeric_cast_traits</span><span class="special">&lt;</span><span class="identifier">Double</span><span class="special">,</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">custom</span><span class="special">::</span><span class="identifier">overflow_handler</span> <span class="identifier">overflow_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">custom</span><span class="special">::</span><span class="identifier">range_checker</span>
<span class="special">&lt;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="identifier">Double</span><span class="special">,</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="special">,</span> <span class="identifier">overflow_policy</span>
<span class="special">&gt;</span> <span class="identifier">range_checking_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">Trunc</span><span class="special">&lt;</span><span class="identifier">S</span><span class="special">&gt;</span> <span class="identifier">rounding_policy</span><span class="special">;</span>
<span class="special">};</span>
<span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">numeric_cast_traits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Double</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">typedef</span> <span class="identifier">custom</span><span class="special">::</span><span class="identifier">overflow_handler</span> <span class="identifier">overflow_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">custom</span><span class="special">::</span><span class="identifier">range_checker</span>
<span class="special">&lt;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">conversion_traits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Double</span><span class="special">&gt;</span>
<span class="special">,</span> <span class="identifier">overflow_policy</span>
<span class="special">&gt;</span> <span class="identifier">range_checking_policy</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">custom</span><span class="special">::</span><span class="identifier">Trunc</span><span class="special">&lt;</span><span class="identifier">Double</span><span class="special">&gt;</span> <span class="identifier">rounding_policy</span><span class="special">;</span>
<span class="special">};</span>
<span class="comment">//! Define the conversion from the custom type to built-in types and vice-versa.</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">raw_converter</span><span class="special">&lt;</span> <span class="identifier">conversion_traits</span><span class="special">&lt;</span> <span class="identifier">T</span><span class="special">,</span> <span class="identifier">Double</span> <span class="special">&gt;</span> <span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="identifier">T</span> <span class="identifier">low_level_convert</span> <span class="special">(</span> <span class="keyword">const</span> <span class="identifier">Double</span><span class="special">&amp;</span> <span class="identifier">n</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span> <span class="identifier">n</span><span class="special">.</span><span class="identifier">v</span> <span class="special">);</span>
<span class="special">}</span>
<span class="special">};</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">S</span><span class="special">&gt;</span>
<span class="keyword">struct</span> <span class="identifier">raw_converter</span><span class="special">&lt;</span> <span class="identifier">conversion_traits</span><span class="special">&lt;</span> <span class="identifier">Double</span><span class="special">,</span> <span class="identifier">S</span> <span class="special">&gt;</span> <span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">static</span> <span class="identifier">Double</span> <span class="identifier">low_level_convert</span> <span class="special">(</span> <span class="keyword">const</span> <span class="identifier">S</span><span class="special">&amp;</span> <span class="identifier">n</span> <span class="special">)</span>
<span class="special">{</span>
<span class="keyword">return</span> <span class="identifier">Double</span><span class="special">(</span><span class="identifier">n</span><span class="special">);</span>
<span class="special">}</span>
<span class="special">};</span>
<span class="special">}}//</span><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">;</span>
</pre>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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</tr></table>
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/*=============================================================================
Copyright (c) 2004 Joel de Guzman
http://spirit.sourceforge.net/
Use, modification and distribution is subject to the Boost Software
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<div><h2 class="title">
<a name="numeric_conversion"></a>Chapter&#160;1.&#160;Boost.NumericConversion</h2></div>
<div><div class="author"><h3 class="author">
<span class="firstname">Fernando Luis</span> <span class="surname">Cacciola Carballal</span>
</h3></div></div>
<div><p class="copyright">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal</p></div>
<div><div class="legalnotice">
<a name="numeric_conversion.legal"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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</div></div>
<div class="toc">
<p><b>Table of Contents</b></p>
<dl class="toc">
<dt><span class="section"><a href="index.html#numeric_conversion.overview">Overview</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html">Definitions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.types_and_values">Types
and Values</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.c___arithmetic_types">C++
Arithmetic Types</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.numeric_types">Numeric
Types</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.range_and_precision">Range
and Precision</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.exact__correctly_rounded_and_out_of_range_representations">Exact,
Correctly Rounded and Out-Of-Range Representations</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.standard__numeric__conversions">Standard
(numeric) Conversions</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.subranged_conversion_direction__subtype_and_supertype">Subranged
Conversion Direction, Subtype and Supertype</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_numericconversion/converter___function_object.html">converter&lt;&gt;
function object</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_numericconversion/converter___function_object.html#boost_numericconversion.converter___function_object.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/converter___function_object.html#boost_numericconversion.converter___function_object.template_parameters">Template
parameters</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/converter___function_object.html#boost_numericconversion.converter___function_object.member_functions">Member
functions</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/converter___function_object.html#boost_numericconversion.converter___function_object.range_checking_logic">Range
Checking Logic</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/converter___function_object.html#boost_numericconversion.converter___function_object.examples">Examples</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_numericconversion/type_requirements_and_user_defined_types_support.html">Type
Requirements and User-defined-types support</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_numericconversion/type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.type_requirements">Type
Requirements</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udt_s_special_semantics">UDT's
special semantics</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.special_policies">Special
Policies</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/type_requirements_and_user_defined_types_support.html#boost_numericconversion.type_requirements_and_user_defined_types_support.udts_with_numeric_cast">UDTs
with numeric_cast</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_numericconversion/bounds___traits_class.html">bounds&lt;&gt;
traits class</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_numericconversion/bounds___traits_class.html#boost_numericconversion.bounds___traits_class.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/bounds___traits_class.html#boost_numericconversion.bounds___traits_class.traits_class_bounds_n_">traits
class bounds&lt;N&gt;</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/bounds___traits_class.html#boost_numericconversion.bounds___traits_class.examples">Examples</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_numericconversion/conversion_traits___traits_class.html">conversion_traits&lt;&gt;
traits class</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_numericconversion/conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.types">Types</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/conversion_traits___traits_class.html#boost_numericconversion.conversion_traits___traits_class.examples">Examples</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_numericconversion/numeric_converter_policy_classes.html">Numeric
Converter Policy Classes</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.enum_range_check_result">enum
range_check_result</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler">Policy
OverflowHandler</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder">Policy
Float2IntRounder</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter">Policy
RawConverter</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker">Policy
UserRangeChecker</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="boost_numericconversion/improved_numeric_cast__.html">Improved
numeric_cast&lt;&gt;</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="boost_numericconversion/improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.introduction">Introduction</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.numeric_cast">numeric_cast</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.numeric_cast_traits">numeric_cast_traits</a></span></dt>
<dt><span class="section"><a href="boost_numericconversion/improved_numeric_cast__.html#boost_numericconversion.improved_numeric_cast__.examples">Examples</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="numeric_conversion/history_and_acknowledgments.html">History
and Acknowledgments</a></span></dt>
<dt><span class="section"><a href="numeric_conversion/bibliography.html">Bibliography</a></span></dt>
</dl>
</div>
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="numeric_conversion.overview"></a><a class="link" href="index.html#numeric_conversion.overview" title="Overview">Overview</a>
</h2></div></div></div>
<p>
The Boost Numeric Conversion library is a collection of tools to describe and
perform conversions between values of different <a class="link" href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.numeric_types" title="Numeric Types">numeric
types</a>.
</p>
<p>
The library includes a special alternative for a subset of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;&gt;</span></code>, the <a class="link" href="boost_numericconversion/bounds___traits_class.html" title="bounds&lt;&gt; traits class">bounds&lt;&gt;</a>
traits class, which provides a consistent way to obtain the <a class="link" href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.range_and_precision" title="Range and Precision">boundary</a>
values for the <a class="link" href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.range_and_precision" title="Range and Precision">range</a>
of a numeric type.
</p>
<p>
It also includes a set of <a class="link" href="boost_numericconversion/conversion_traits___traits_class.html" title="conversion_traits&lt;&gt; traits class">trait
classes</a> which describes the compile-time properties of a conversion
from a source to a target numeric type. Both <a class="link" href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.c___arithmetic_types" title="C++ Arithmetic Types">arithmetic</a>
and <a class="link" href="boost_numericconversion/definitions.html#boost_numericconversion.definitions.numeric_types" title="Numeric Types">user-defined
numeric types</a> can be used.
</p>
<p>
A policy-based <a class="link" href="boost_numericconversion/converter___function_object.html" title="converter&lt;&gt; function object">converter</a>
object which uses <code class="computeroutput"><span class="identifier">conversion_traits</span></code>
to select an optimized implementation is supplied. Such implementation uses
an optimal range checking code suitable for the source/target combination.
</p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
The converter's out-of-range behavior can be customized via an <a class="link" href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_overflowhandler" title="Policy OverflowHandler">OverflowHandler</a>
policy.
</li>
<li class="listitem">
For floating-point to integral conversions, the rounding mode can be selected
via the <a class="link" href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_float2introunder" title="Policy Float2IntRounder">Float2IntRounder</a>
policy.
</li>
<li class="listitem">
A custom low-level conversion routine (for UDTs for instance) can be passed
via a <a class="link" href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter" title="Policy RawConverter">RawConverter</a>
policy.
</li>
<li class="listitem">
The optimized automatic range-checking logic can be overridden via a <a class="link" href="boost_numericconversion/numeric_converter_policy_classes.html#boost_numericconversion.numeric_converter_policy_classes.policy_userrangechecker" title="Policy UserRangeChecker">UserRangeChecker</a>
policy.
</li>
</ul></div>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: June 02, 2014 at 09:10:01 GMT</small></p></td>
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<a name="numeric_conversion.bibliography"></a><a class="link" href="bibliography.html" title="Bibliography">Bibliography</a>
</h2></div></div></div>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Standard Documents:
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
ISO/IEC 14882:98 (C++98 Standard)
</li>
<li class="listitem">
ISO/IEC 9899:1999 (C99 Standard)
</li>
<li class="listitem">
ISO/IEC 10967-1 (Language Independent Arithmetic (LIA), Part I, 1994)
</li>
<li class="listitem">
ISO/IEC 2382-1:1993 (Information Technology - Vocabulary - Part I:
Fundamental Terms)
</li>
<li class="listitem">
ANSI/IEEE 754-1985 [and IEC 60559:1989] (Binary floating-point)
</li>
<li class="listitem">
ANSI/IEEE 854-1988 (Radix Independent floating-point)
</li>
<li class="listitem">
ANSI X3/TR-1-82 (Dictionary for Information Processing Systems)
</li>
<li class="listitem">
ISO/IEC JTC1/SC22/WG14/N753 C9X Revision Proposal: LIA-1 Binding:
Rationale
</li>
</ol></div>
</li>
<li class="listitem">
Papers:
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
David Goldberg What Every Computer Scientist Should Know About Floating-Point
Arithmetic
</li>
<li class="listitem">
Prof. William Kahan papers on floating-point.
</li>
</ol></div>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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<a name="numeric_conversion.history_and_acknowledgments"></a><a class="link" href="history_and_acknowledgments.html" title="History and Acknowledgments">History
and Acknowledgments</a>
</h2></div></div></div>
<h4>
<a name="numeric_conversion.history_and_acknowledgments.h0"></a>
<span class="phrase"><a name="numeric_conversion.history_and_acknowledgments.pre_formal_review"></a></span><a class="link" href="history_and_acknowledgments.html#numeric_conversion.history_and_acknowledgments.pre_formal_review">Pre-formal
review</a>
</h4>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Kevlin Henney, with help from David Abrahams and Beman Dawes, originally
contributed the previous version of <code class="computeroutput"><span class="identifier">numeric_cast</span><span class="special">&lt;&gt;</span></code> which already presented the idea
of a runtime range check.
</li>
<li class="listitem">
Later, Eric Ford, Kevin Lynch and the author spotted some genericity problems
with that <code class="computeroutput"><span class="identifier">numeric_cast</span><span class="special">&lt;&gt;</span></code> which prevented it from being used
in a generic layer of math functions.
</li>
<li class="listitem">
An improved <code class="computeroutput"><span class="identifier">numeric_cast</span><span class="special">&lt;&gt;</span></code> which properly handled all combinations
of arithmetic types was presented.
</li>
<li class="listitem">
David Abrahams and Beman Dawes acknowledged the need of an improved version
of <code class="computeroutput"><span class="identifier">numeric_cast</span><span class="special">&lt;&gt;</span></code>
and supported the submission as originally laid out. Daryl Walker and Darin
Adler made some important comments and proposed fixes to the original submission.
</li>
<li class="listitem">
Special thanks go to Bj&#246;rn Karlsoon who helped the author considerably.
Having found the problems with <code class="computeroutput"><span class="identifier">numeric_cast</span><span class="special">&lt;&gt;</span></code> himself, he revised very carefully
the original submission and spot a subtle bug in the range checking implementation.
He also wrote part of this documentation and proof-read and corrected other
parts. And most importantly: the features now presented here in this library
evolved from the original submission as a result of the useful private
communications between Bj&#246;rn and the author.
</li>
</ul></div>
<h4>
<a name="numeric_conversion.history_and_acknowledgments.h1"></a>
<span class="phrase"><a name="numeric_conversion.history_and_acknowledgments.post_formal_review"></a></span><a class="link" href="history_and_acknowledgments.html#numeric_conversion.history_and_acknowledgments.post_formal_review">Post-formal
review</a>
</h4>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
Guillaume Melquiond spoted some documentation and code issues, particularly
about rounding conversions.
</li>
<li class="listitem">
The following people contributed an important review of the design, documentation
and c ode: Kevin Lynch, Thorsten Ottosen, Paul Bristow, Daryle Walker,
Jhon Torjo, Eric Ford, Gennadiy Rozental.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2004-2007 Fernando
Luis Cacciola Carballal<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
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[/
Boost.Optional
Copyright (c) 2003-2007 Fernando Luis Cacciola Carballal
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)
]
[section Improved numeric_cast<>]
[section Introduction]
The lack of preservation of range makes conversions between numeric types
error prone. This is true for both implicit conversions and explicit
conversions (through `static_cast`).
[link boost_numericconversion.improved_numeric_cast__.numeric_cast `numeric_cast`]
detects loss of range when a numeric type is converted, and throws an
exception if the range cannot be preserved.
There are several situations where conversions are unsafe:
* Conversions from an integral type with a wider range than the target integral type.
* Conversions from unsigned to signed (and vice versa) integral types.
* Conversions from floating point types to integral types.
The C++ Standard does not specify the behavior when a numeric type is
assigned a value that cannot be represented by the type, except for unsigned
integral types \[3.9.1.4\], which must obey the laws of arithmetic modulo 2n
(this implies that the result will be reduced modulo the number that is one
greater than the largest value that can be represented). The fact that the
behavior for overflow is undefined for all conversions (except the
aforementioned unsigned to unsigned) makes any code that may produce
positive or negative overflows exposed to portability issues.
By default `numeric_cast` adheres to the rules for implicit conversions mandated by
the C++ Standard, such as truncating floating point types when converting
to integral types. The implementation must guarantee that for a conversion
to a type that can hold all possible values of the source type, there will
be no runtime overhead.
[endsect]
[section numeric_cast]
template <typename Target, typename Source> inline
Target numeric_cast( Source arg )
{
typedef conversion_traits<Target, Source> conv_traits;
typedef numeric_cast_traits<Target, Source> cast_traits;
typedef converter
<
Target,
Source,
conv_traits,
typename cast_traits::overflow_policy,
typename cast_traits::rounding_policy,
raw_converter<conv_traits>,
typename cast_traits::range_checking_policy
> converter;
return converter::convert(arg);
}
`numeric_cast` returns the result of converting a value of type Source
to a value of type Target. If out-of-range is detected, an overflow policy
is executed whose default behavior is to throw an an exception (see
[link numeric_conversion_bad_numeric_cast bad_numeric_cast],
[link numeric_conversion_negative_overflow negative_overflow] and
[link numeric_conversion_possitive_overflow positive_overflow]
).
[endsect]
[section numeric_cast_traits]
template <typename Target, typename Source, typename EnableIf = void>
struct numeric_cast_traits
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<Source> rounding_policy;
};
The behavior of `numeric_cast` may be tailored for custom numeric types through
the specialization of `numeric_cast_traits`. (see
[link boost_numericconversion.type_requirements_and_user_defined_types_support User Defined Types]
for details.
)
[endsect]
[section Examples]
The following example performs some typical conversions between numeric types:
#include <boost/numeric/conversion/cast.hpp>
#include <iostream>
int main()
{
using boost::numeric_cast;
using boost::numeric::bad_numeric_cast;
using boost::numeric::positive_overflow;
using boost::numeric::negative_overflow;
try
{
int i=42;
short s=numeric_cast<short>(i); // This conversion succeeds (is in range)
}
catch(negative_overflow& e) {
std::cout << e.what();
}
catch(positive_overflow& e) {
std::cout << e.what();
}
try
{
float f=-42.1234;
// This will cause a boost::numeric::negative_overflow exception to be thrown
unsigned int i=numeric_cast<unsigned int>(f);
}
catch(bad_numeric_cast& e) {
std::cout << e.what();
}
double d= f + numeric_cast<double>(123); // int -> double
unsigned long l=std::numeric_limits<unsigned long>::max();
try
{
// This will cause a boost::numeric::positive_overflow exception to be thrown
// NOTE: *operations* on unsigned integral types cannot cause overflow
// but *conversions* to a signed type ARE range checked by numeric_cast.
unsigned char c=numeric_cast<unsigned char>(l);
}
catch(positive_overflow& e) {
std::cout << e.what();
}
return 0;
}
[endsect]
[endsect]

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[/
Boost.Optional
Copyright (c) 2003-2007 Fernando Luis Cacciola Carballal
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)
]
[section Type Requirements and User-defined-types support]
[section Type Requirements]
Both arithmetic (built-in) and user-defined numeric types require proper
specialization of `std::numeric_limits<>` (that is, with (in-class) integral
constants).
The library uses `std::numeric_limits<T>::is_specialized` to detect whether
the type is builtin or user defined, and `std::numeric_limits<T>::is_integer`,
`std::numeric_limits<T>::is_signed` to detect whether the type is integer
or floating point; and whether it is signed/unsigned.
The default `Float2IntRounder` policies uses unqualified calls to functions
`floor()` and `ceil()`; but the standard functions are introduced in scope
by a using directive:
using std::floor ; return floor(s);
Therefore, for builtin arithmetic types, the std functions will be used.
User defined types should provide overloaded versions of these functions in
order to use the default rounder policies. If these overloads are defined
within a user namespace argument dependent lookup (ADL) should find them,
but if your compiler has a weak ADL you might need to put these functions
some place else or write your own rounder policy.
The default `Trunc<>` rounder policy needs to determine if the source value
is positive or not, and for this it evaluates the expression
`s < static_cast<S>(0)`. Therefore, user defined types require a visible
`operator<` in order to use the `Trunc<>` policy (the default).
[endsect]
[section UDT's special semantics]
[heading Conversion Traits]
If a User Defined Type is involved in a conversion, it is ['assumed] that
the UDT has [link boost_numericconversion.definitions.range_and_precision wider range]
than any built-in type, and consequently the values
of some `converter_traits<>` members are hardwired regardless of the reality.
The following table summarizes this:
* `Target=`['UDT] and `Source=`['built-in]
* `subranged=false`
* `supertype=Target`
* `subtype=Source`
* `Target=`['built-in] and `Source=`['UDT]
* `subranged=true`
* `supertype=Source`
* `subtype=Target`
* `Target=`['UDT] and `Source=`['UDT]
* `subranged=false`
* `supertype=Target`
* `subtype=Source`
The `Traits` member `udt_mixture` can be used to detect whether a UDT is involved
and to infer the validity of the other members as shown above.
[heading Range Checking]
Because User Defined Numeric Types might have peculiar ranges (such as an
unbounded range), this library does not attempt to supply a meaningful range
checking logic when UDTs are involved in a conversion. Therefore, if either
Target or Source are not built-in types, the bundled range checking of the
`converter<>` function object is automatically disabled. However, it is possible
to supply a user-defined range-checker. See
[link boost_numericconversion.type_requirements_and_user_defined_types_support.special_policies Special Policies]
[endsect]
[section Special Policies]
There are two components of the `converter<>` class that might require special
behavior if User Defined Numeric Types are involved: the Range Checking and the
Raw Conversion.
When both Target and Source are built-in types, the converter class uses an internal
range checking logic which is optimized and customized for the combined properties
of the types.
However, this internal logic is disabled when either type is User Defined.
In this case, the user can specify an ['external] range checking policy which will be
used in place of the internal code. See
[link boost_numericconversion.type_requirements_and_user_defined_types_support.udts_with_numeric_cast numeric_cast_traits]
for details on using UDTs with `numeric_cast`.
The converter class performs the actual conversion using a Raw Converter policy.
The default raw converter simply performs a `static_cast<Target>(source)`.
However, if the a UDT is involved, the `static_cast` might not work. In this case,
the user can implement and pass a different raw converter policy.
See [link boost_numericconversion.numeric_converter_policy_classes.policy_rawconverter RawConverter] policy for details.
[endsect]
[section UDTs with numeric_cast]
In order to employ UDTs with `numeric_cast`, the user should define
a `numeric_cast_traits` specialization on the UDT for each conversion.
Here is an example of specializations for converting between the UDT
and any other type:
namespace boost { namespace numeric {
template <typename Source>
struct numeric_cast_traits<UDT, Source>
{
typedef conversion_traits<UDT, Source> conv_traits;
//! The following are required:
typedef YourOverflowHandlerPolicy overflow_policy;
typedef YourRangeCheckerPolicy<conv_traits> range_checking_policy;
typedef YourFloat2IntRounderPolicy<Source> rounding_policy;
};
template <typename Target>
struct numeric_cast_traits<Target, UDT>
{
typedef conversion_traits<Target, UDT> conv_traits;
//! The following are required:
typedef YourOverflowHandlerPolicy overflow_policy;
typedef YourRangeCheckerPolicy<conv_traits> range_checking_policy;
typedef YourFloat2IntRounderPolicy<UDT> rounding_policy;
};
}}//namespace boost::numeric;
These specializations are already defined with default values for the built-in
numeric types. It is possible to disable the generation of specializations for
built-in types by defining `BOOST_NUMERIC_CONVERSION_RELAX_BUILT_IN_CAST_TRAITS`.
For details on defining custom policies see [link boost_numericconversion.numeric_converter_policy_classes Converter Policies].
Here is a full example of how to define a custom UDT for use with `numeric_cast`:
//! Define a simple custom number
struct Double
: boost::ordered_field_operators
<
Double
, boost::ordered_field_operators2< Double, long double
, boost::ordered_field_operators2< Double, double
, boost::ordered_field_operators2< Double, float
, boost::ordered_field_operators2< Double, int
, boost::ordered_field_operators2< Double, unsigned int
, boost::ordered_field_operators2< Double, long
, boost::ordered_field_operators2< Double, unsigned long
, boost::ordered_field_operators2< Double, long long
, boost::ordered_field_operators2< Double, unsigned long long
, boost::ordered_field_operators2< Double, char
, boost::ordered_field_operators2< Double, unsigned char
, boost::ordered_field_operators2< Double, short
, boost::ordered_field_operators2< Double, unsigned short
> > > > > > > > > > > > > >
{
Double()
: v(0)
{}
template <typename T>
explicit Double( T v )
: v(static_cast<double>(v))
{}
template <typename T>
Double& operator= ( T t )
{
v = static_cast<double>(t);
return *this;
}
bool operator < ( const Double& rhs ) const
{
return v < rhs.v;
}
template <typename T>
bool operator < ( T rhs ) const
{
return v < static_cast<double>(rhs);
}
bool operator > ( const Double& rhs ) const
{
return v > rhs.v;
}
template <typename T>
bool operator > ( T rhs ) const
{
return v > static_cast<double>(rhs);
}
bool operator ==( const Double& rhs ) const
{
return v == rhs.v;
}
template <typename T>
bool operator == ( T rhs ) const
{
return v == static_cast<double>(rhs);
}
bool operator !() const
{
return v == 0;
}
Double operator -() const
{
return Double(-v);
}
Double& operator +=( const Double& t )
{
v += t.v;
return *this;
}
template <typename T>
Double& operator +=( T t )
{
v += static_cast<double>(t);
return *this;
}
Double& operator -=( const Double& t )
{
v -= t.v;
return *this;
}
template <typename T>
Double& operator -=( T t )
{
v -= static_cast<double>(t);
return *this;
}
Double& operator *= ( const Double& factor )
{
v *= factor.v;
return *this;
}
template <typename T>
Double& operator *=( T t )
{
v *= static_cast<double>(t);
return *this;
}
Double& operator /= (const Double& divisor)
{
v /= divisor.v;
return *this;
}
template <typename T>
Double& operator /=( T t )
{
v /= static_cast<double>(t);
return (*this);
}
double v;
};
//! Define numeric_limits for the custom type.
namespace std
{
template<>
class numeric_limits<Double> : public numeric_limits<double>
{
public:
//! Limit our Double to a range of +/- 100.0
static Double (min)()
{
return Double(1.e-2);
}
static Double (max)()
{
return Double(1.e2);
}
static Double epsilon()
{
return Double( std::numeric_limits<double>::epsilon() );
}
};
}
//! Define range checking and overflow policies.
namespace custom
{
//! Define a custom range checker
template<typename Traits, typename OverFlowHandler>
struct range_checker
{
typedef typename Traits::argument_type argument_type ;
typedef typename Traits::source_type S;
typedef typename Traits::target_type T;
//! Check range of integral types.
static boost::numeric::range_check_result out_of_range( argument_type s )
{
using namespace boost::numeric;
if( s > bounds<T>::highest() )
return cPosOverflow;
else if( s < bounds<T>::lowest() )
return cNegOverflow;
else
return cInRange;
}
static void validate_range ( argument_type s )
{
BOOST_STATIC_ASSERT( std::numeric_limits<T>::is_bounded );
OverFlowHandler()( out_of_range(s) );
}
};
//! Overflow handler
struct positive_overflow{};
struct negative_overflow{};
struct overflow_handler
{
void operator() ( boost::numeric::range_check_result r )
{
using namespace boost::numeric;
if( r == cNegOverflow )
throw negative_overflow() ;
else if( r == cPosOverflow )
throw positive_overflow() ;
}
};
//! Define a rounding policy and specialize on the custom type.
template<class S>
struct Ceil : boost::numeric::Ceil<S>{};
template<>
struct Ceil<Double>
{
typedef Double source_type;
typedef Double const& argument_type;
static source_type nearbyint ( argument_type s )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::ceil ;
#endif
return Double( ceil(s.v) );
}
typedef boost::mpl::integral_c< std::float_round_style, std::round_toward_infinity> round_style;
};
//! Define a rounding policy and specialize on the custom type.
template<class S>
struct Trunc: boost::numeric::Trunc<S>{};
template<>
struct Trunc<Double>
{
typedef Double source_type;
typedef Double const& argument_type;
static source_type nearbyint ( argument_type s )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::floor;
#endif
return Double( floor(s.v) );
}
typedef boost::mpl::integral_c< std::float_round_style, std::round_toward_zero> round_style;
};
}//namespace custom;
namespace boost { namespace numeric {
//! Define the numeric_cast_traits specializations on the custom type.
template <typename S>
struct numeric_cast_traits<Double, S>
{
typedef custom::overflow_handler overflow_policy;
typedef custom::range_checker
<
boost::numeric::conversion_traits<Double, S>
, overflow_policy
> range_checking_policy;
typedef boost::numeric::Trunc<S> rounding_policy;
};
template <typename T>
struct numeric_cast_traits<T, Double>
{
typedef custom::overflow_handler overflow_policy;
typedef custom::range_checker
<
boost::numeric::conversion_traits<T, Double>
, overflow_policy
> range_checking_policy;
typedef custom::Trunc<Double> rounding_policy;
};
//! Define the conversion from the custom type to built-in types and vice-versa.
template<typename T>
struct raw_converter< conversion_traits< T, Double > >
{
static T low_level_convert ( const Double& n )
{
return static_cast<T>( n.v );
}
};
template<typename S>
struct raw_converter< conversion_traits< Double, S > >
{
static Double low_level_convert ( const S& n )
{
return Double(n);
}
};
}}//namespace boost::numeric;
[endsect]
[endsect]

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// boost cast.hpp header file
//
// (C) Copyright Antony Polukhin 2014.
//
// 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)
//
// See http://www.boost.org/libs/conversion for Documentation.
// This is a DEPRECATED header file!
// Use <boost/polymorphic_cast.hpp> or <boost/numeric/conversion/cast.hpp> instead
#ifndef BOOST_CAST_HPP
#define BOOST_CAST_HPP
# include <boost/polymorphic_cast.hpp>
# include <boost/numeric/conversion/cast.hpp>
#endif // BOOST_CAST_HPP

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_BOUNDS_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_BOUNDS_12NOV2002_HPP
#include "boost/numeric/conversion/detail/bounds.hpp"
namespace boost { namespace numeric
{
template<class N>
struct bounds : boundsdetail::get_impl<N>::type
{} ;
} } // namespace boost::numeric
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
//
// Revision History
//
// 19 Nov 2001 Syntatic changes as suggested by Darin Adler (Fernando Cacciola)
// 08 Nov 2001 Fixes to accommodate MSVC (Fernando Cacciola)
// 04 Nov 2001 Fixes to accommodate gcc2.92 (Fernando Cacciola)
// 30 Oct 2001 Some fixes suggested by Daryle Walker (Fernando Cacciola)
// 25 Oct 2001 Initial boostification (Fernando Cacciola)
// 23 Jan 2004 Inital add to cvs (post review)s
// 22 Jun 2011 Added support for specializing cast policies via numeric_cast_traits (Brandon Kohn).
//
#ifndef BOOST_NUMERIC_CONVERSION_CAST_25OCT2001_HPP
#define BOOST_NUMERIC_CONVERSION_CAST_25OCT2001_HPP
#include <boost/detail/workaround.hpp>
#if BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT(0x582))
# include<boost/numeric/conversion/detail/old_numeric_cast.hpp>
#else
#include <boost/type.hpp>
#include <boost/numeric/conversion/converter.hpp>
#include <boost/numeric/conversion/numeric_cast_traits.hpp>
namespace boost
{
template <typename Target, typename Source>
inline Target numeric_cast( Source arg )
{
typedef numeric::conversion_traits<Target, Source> conv_traits;
typedef numeric::numeric_cast_traits<Target, Source> cast_traits;
typedef boost::numeric::converter
<
Target,
Source,
conv_traits,
typename cast_traits::overflow_policy,
typename cast_traits::rounding_policy,
boost::numeric::raw_converter< conv_traits >,
typename cast_traits::range_checking_policy
> converter;
return converter::convert(arg);
}
using numeric::bad_numeric_cast;
} // namespace boost
#endif
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_CONVERSION_TRAITS_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_CONVERSION_TRAITS_FLC_12NOV2002_HPP
#include "boost/numeric/conversion/detail/conversion_traits.hpp"
#include "boost/detail/workaround.hpp"
#include "boost/config.hpp"
namespace boost { namespace numeric
{
template<class T, class S>
struct conversion_traits
: convdetail::get_conversion_traits<T,S>::type
{
} ;
} } // namespace boost::numeric
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_CONVERTER_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_CONVERTER_FLC_12NOV2002_HPP
#include "boost/numeric/conversion/conversion_traits.hpp"
#include "boost/numeric/conversion/converter_policies.hpp"
#include "boost/numeric/conversion/detail/converter.hpp"
namespace boost { namespace numeric
{
template<class T,
class S,
class Traits = conversion_traits<T,S>,
class OverflowHandler = def_overflow_handler,
class Float2IntRounder = Trunc< BOOST_DEDUCED_TYPENAME Traits::source_type> ,
class RawConverter = raw_converter<Traits>,
class UserRangeChecker = UseInternalRangeChecker
>
struct converter : convdetail::get_converter_impl<Traits,
OverflowHandler,
Float2IntRounder,
RawConverter,
UserRangeChecker
>::type
{
typedef Traits traits ;
typedef typename Traits::argument_type argument_type ;
typedef typename Traits::result_type result_type ;
result_type operator() ( argument_type s ) const { return this->convert(s) ; }
} ;
template<class S,
class OverflowHandler = def_overflow_handler,
class Float2IntRounder = Trunc<S> ,
class UserRangeChecker = UseInternalRangeChecker
>
struct make_converter_from
{
template<class T,
class Traits = conversion_traits<T,S>,
class RawConverter = raw_converter<Traits>
>
struct to
{
typedef converter<T,S,Traits,OverflowHandler,Float2IntRounder,RawConverter,UserRangeChecker> type ;
} ;
} ;
} } // namespace boost::numeric
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_CONVERTER_POLICIES_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_CONVERTER_POLICIES_FLC_12NOV2002_HPP
#include <functional>
#include <typeinfo> // for std::bad_cast
#include <boost/config.hpp>
#include <boost/config/no_tr1/cmath.hpp> // for std::floor and std::ceil
#include <boost/throw_exception.hpp>
#include "boost/type_traits/is_arithmetic.hpp"
#include "boost/mpl/if.hpp"
#include "boost/mpl/integral_c.hpp"
namespace boost { namespace numeric
{
template<class S>
struct Trunc
{
typedef S source_type ;
typedef typename mpl::if_< is_arithmetic<S>,S,S const&>::type argument_type ;
static source_type nearbyint ( argument_type s )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::floor ;
using std::ceil ;
#endif
return s < static_cast<S>(0) ? ceil(s) : floor(s) ;
}
typedef mpl::integral_c< std::float_round_style, std::round_toward_zero> round_style ;
} ;
template<class S>
struct Floor
{
typedef S source_type ;
typedef typename mpl::if_< is_arithmetic<S>,S,S const&>::type argument_type ;
static source_type nearbyint ( argument_type s )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::floor ;
#endif
return floor(s) ;
}
typedef mpl::integral_c< std::float_round_style, std::round_toward_neg_infinity> round_style ;
} ;
template<class S>
struct Ceil
{
typedef S source_type ;
typedef typename mpl::if_< is_arithmetic<S>,S,S const&>::type argument_type ;
static source_type nearbyint ( argument_type s )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::ceil ;
#endif
return ceil(s) ;
}
typedef mpl::integral_c< std::float_round_style, std::round_toward_infinity> round_style ;
} ;
template<class S>
struct RoundEven
{
typedef S source_type ;
typedef typename mpl::if_< is_arithmetic<S>,S,S const&>::type argument_type ;
static source_type nearbyint ( argument_type s )
{
// Algorithm contributed by Guillaume Melquiond
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::floor ;
using std::ceil ;
#endif
// only works inside the range not at the boundaries
S prev = floor(s);
S next = ceil(s);
S rt = (s - prev) - (next - s); // remainder type
S const zero(0.0);
S const two(2.0);
if ( rt < zero )
return prev;
else if ( rt > zero )
return next;
else
{
bool is_prev_even = two * floor(prev / two) == prev ;
return ( is_prev_even ? prev : next ) ;
}
}
typedef mpl::integral_c< std::float_round_style, std::round_to_nearest> round_style ;
} ;
enum range_check_result
{
cInRange = 0 ,
cNegOverflow = 1 ,
cPosOverflow = 2
} ;
class bad_numeric_cast : public std::bad_cast
{
public:
const char * what() const BOOST_NOEXCEPT_OR_NOTHROW BOOST_OVERRIDE
{ return "bad numeric conversion: overflow"; }
};
class negative_overflow : public bad_numeric_cast
{
public:
const char * what() const BOOST_NOEXCEPT_OR_NOTHROW BOOST_OVERRIDE
{ return "bad numeric conversion: negative overflow"; }
};
class positive_overflow : public bad_numeric_cast
{
public:
const char * what() const BOOST_NOEXCEPT_OR_NOTHROW BOOST_OVERRIDE
{ return "bad numeric conversion: positive overflow"; }
};
struct def_overflow_handler
{
void operator() ( range_check_result r ) // throw(negative_overflow,positive_overflow)
{
#ifndef BOOST_NO_EXCEPTIONS
if ( r == cNegOverflow )
throw negative_overflow() ;
else if ( r == cPosOverflow )
throw positive_overflow() ;
#else
if ( r == cNegOverflow )
::boost::throw_exception(negative_overflow()) ;
else if ( r == cPosOverflow )
::boost::throw_exception(positive_overflow()) ;
#endif
}
} ;
struct silent_overflow_handler
{
void operator() ( range_check_result ) {} // throw()
} ;
template<class Traits>
struct raw_converter
{
typedef typename Traits::result_type result_type ;
typedef typename Traits::argument_type argument_type ;
static result_type low_level_convert ( argument_type s ) { return static_cast<result_type>(s) ; }
} ;
struct UseInternalRangeChecker {} ;
} } // namespace boost::numeric
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_BOUNDS_DETAIL_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_BOUNDS_DETAIL_FLC_12NOV2002_HPP
#include "boost/limits.hpp"
#include "boost/config.hpp"
#include "boost/mpl/if.hpp"
namespace boost { namespace numeric { namespace boundsdetail
{
template<class N>
class Integral
{
typedef std::numeric_limits<N> limits ;
public :
static N lowest () { return limits::min BOOST_PREVENT_MACRO_SUBSTITUTION (); }
static N highest () { return limits::max BOOST_PREVENT_MACRO_SUBSTITUTION (); }
static N smallest() { return static_cast<N>(1); }
} ;
template<class N>
class Float
{
typedef std::numeric_limits<N> limits ;
public :
static N lowest () { return static_cast<N>(-limits::max BOOST_PREVENT_MACRO_SUBSTITUTION ()) ; }
static N highest () { return limits::max BOOST_PREVENT_MACRO_SUBSTITUTION (); }
static N smallest() { return limits::min BOOST_PREVENT_MACRO_SUBSTITUTION (); }
} ;
template<class N>
struct get_impl
{
typedef mpl::bool_< ::std::numeric_limits<N>::is_integer > is_int ;
typedef Integral<N> impl_int ;
typedef Float <N> impl_float ;
typedef typename mpl::if_<is_int,impl_int,impl_float>::type type ;
} ;
} } } // namespace boost::numeric::boundsdetail.
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_DETAIL_CONVERSION_TRAITS_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_DETAIL_CONVERSION_TRAITS_FLC_12NOV2002_HPP
#include "boost/type_traits/is_arithmetic.hpp"
#include "boost/type_traits/is_same.hpp"
#include "boost/type_traits/remove_cv.hpp"
#include "boost/numeric/conversion/detail/meta.hpp"
#include "boost/numeric/conversion/detail/int_float_mixture.hpp"
#include "boost/numeric/conversion/detail/sign_mixture.hpp"
#include "boost/numeric/conversion/detail/udt_builtin_mixture.hpp"
#include "boost/numeric/conversion/detail/is_subranged.hpp"
namespace boost { namespace numeric { namespace convdetail
{
//-------------------------------------------------------------------
// Implementation of the Conversion Traits for T != S
//
// This is a VISIBLE base class of the user-level conversion_traits<> class.
//-------------------------------------------------------------------
template<class T,class S>
struct non_trivial_traits_impl
{
typedef typename get_int_float_mixture <T,S>::type int_float_mixture ;
typedef typename get_sign_mixture <T,S>::type sign_mixture ;
typedef typename get_udt_builtin_mixture <T,S>::type udt_builtin_mixture ;
typedef typename get_is_subranged<T,S>::type subranged ;
typedef mpl::false_ trivial ;
typedef T target_type ;
typedef S source_type ;
typedef T result_type ;
typedef typename mpl::if_< is_arithmetic<S>, S, S const&>::type argument_type ;
typedef typename mpl::if_<subranged,S,T>::type supertype ;
typedef typename mpl::if_<subranged,T,S>::type subtype ;
} ;
//-------------------------------------------------------------------
// Implementation of the Conversion Traits for T == S
//
// This is a VISIBLE base class of the user-level conversion_traits<> class.
//-------------------------------------------------------------------
template<class N>
struct trivial_traits_impl
{
typedef typename get_int_float_mixture <N,N>::type int_float_mixture ;
typedef typename get_sign_mixture <N,N>::type sign_mixture ;
typedef typename get_udt_builtin_mixture<N,N>::type udt_builtin_mixture ;
typedef mpl::false_ subranged ;
typedef mpl::true_ trivial ;
typedef N target_type ;
typedef N source_type ;
typedef N const& result_type ;
typedef N const& argument_type ;
typedef N supertype ;
typedef N subtype ;
} ;
//-------------------------------------------------------------------
// Top level implementation selector.
//-------------------------------------------------------------------
template<class T, class S>
struct get_conversion_traits
{
typedef typename remove_cv<T>::type target_type ;
typedef typename remove_cv<S>::type source_type ;
typedef typename is_same<target_type,source_type>::type is_trivial ;
typedef trivial_traits_impl <target_type> trivial_imp ;
typedef non_trivial_traits_impl<target_type,source_type> non_trivial_imp ;
typedef typename mpl::if_<is_trivial,trivial_imp,non_trivial_imp>::type type ;
} ;
} } } // namespace boost::numeric::convdetail
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_DETAIL_CONVERTER_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_DETAIL_CONVERTER_FLC_12NOV2002_HPP
#include <functional>
#include "boost/numeric/conversion/detail/meta.hpp"
#include "boost/numeric/conversion/detail/conversion_traits.hpp"
#include "boost/numeric/conversion/bounds.hpp"
#include "boost/type_traits/is_same.hpp"
#include "boost/mpl/integral_c.hpp"
namespace boost { namespace numeric { namespace convdetail
{
// Integral Constants representing rounding modes
typedef mpl::integral_c<std::float_round_style, std::round_toward_zero> round2zero_c ;
typedef mpl::integral_c<std::float_round_style, std::round_to_nearest> round2nearest_c ;
typedef mpl::integral_c<std::float_round_style, std::round_toward_infinity> round2inf_c ;
typedef mpl::integral_c<std::float_round_style, std::round_toward_neg_infinity> round2neg_inf_c ;
// Metafunction:
//
// for_round_style<RoundStyle,RoundToZero,RoundToNearest,RoundToInf,RoundToNegInf>::type
//
// {RoundStyle} Integral Constant specifying a round style as declared above.
// {RoundToZero,RoundToNearest,RoundToInf,RoundToNegInf} arbitrary types.
//
// Selects one of the 4 types according to the value of RoundStyle.
//
template<class RoundStyle,class RoundToZero,class RoundToNearest,class RoundToInf,class RoundToNegInf>
struct for_round_style
{
typedef ct_switch4<RoundStyle
, round2zero_c, round2nearest_c, round2inf_c // round2neg_inf_c
, RoundToZero , RoundToNearest , RoundToInf , RoundToNegInf
> selector ;
typedef typename selector::type type ;
} ;
//--------------------------------------------------------------------------
// Range Checking Logic.
//
// The range checking logic is built up by combining 1 or 2 predicates.
// Each predicate is encapsulated in a template class and exposes
// the static member function 'apply'.
//
//--------------------------------------------------------------------------
// Because a particular logic can combine either 1 or two predicates, the following
// tags are used to allow the predicate applier to receive 2 preds, but optimize away
// one of them if it is 'non-applicable'
struct non_applicable { typedef mpl::false_ do_apply ; } ;
struct applicable { typedef mpl::true_ do_apply ; } ;
//--------------------------------------------------------------------------
//
// Range Checking Logic implementations.
//
// The following classes, collectivelly named 'Predicates', are instantiated within
// the corresponding range checkers.
// Their static member function 'apply' is called to perform the actual range checking logic.
//--------------------------------------------------------------------------
// s < Lowest(T) ? cNegOverflow : cInRange
//
template<class Traits>
struct LT_LoT : applicable
{
typedef typename Traits::target_type T ;
typedef typename Traits::source_type S ;
typedef typename Traits::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
return s < static_cast<S>(bounds<T>::lowest()) ? cNegOverflow : cInRange ;
}
} ;
// s < 0 ? cNegOverflow : cInRange
//
template<class Traits>
struct LT_Zero : applicable
{
typedef typename Traits::source_type S ;
typedef typename Traits::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
return s < static_cast<S>(0) ? cNegOverflow : cInRange ;
}
} ;
// s <= Lowest(T)-1 ? cNegOverflow : cInRange
//
template<class Traits>
struct LE_PrevLoT : applicable
{
typedef typename Traits::target_type T ;
typedef typename Traits::source_type S ;
typedef typename Traits::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
return s <= static_cast<S>(bounds<T>::lowest()) - static_cast<S>(1.0)
? cNegOverflow : cInRange ;
}
} ;
// s < Lowest(T)-0.5 ? cNegOverflow : cInRange
//
template<class Traits>
struct LT_HalfPrevLoT : applicable
{
typedef typename Traits::target_type T ;
typedef typename Traits::source_type S ;
typedef typename Traits::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
return s < static_cast<S>(bounds<T>::lowest()) - static_cast<S>(0.5)
? cNegOverflow : cInRange ;
}
} ;
// s > Highest(T) ? cPosOverflow : cInRange
//
template<class Traits>
struct GT_HiT : applicable
{
typedef typename Traits::target_type T ;
typedef typename Traits::source_type S ;
typedef typename Traits::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
return s > static_cast<S>(bounds<T>::highest())
? cPosOverflow : cInRange ;
}
} ;
// s >= Lowest(T) + 1 ? cPosOverflow : cInRange
//
template<class Traits>
struct GE_SuccHiT : applicable
{
typedef typename Traits::target_type T ;
typedef typename Traits::source_type S ;
typedef typename Traits::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
return s >= static_cast<S>(bounds<T>::highest()) + static_cast<S>(1.0)
? cPosOverflow : cInRange ;
}
} ;
// s >= Lowest(T) + 0.5 ? cPosgOverflow : cInRange
//
template<class Traits>
struct GT_HalfSuccHiT : applicable
{
typedef typename Traits::target_type T ;
typedef typename Traits::source_type S ;
typedef typename Traits::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
return s >= static_cast<S>(bounds<T>::highest()) + static_cast<S>(0.5)
? cPosOverflow : cInRange ;
}
} ;
//--------------------------------------------------------------------------
//
// Predicate Combiner.
//
// This helper classes are used to possibly combine the range checking logic
// individually performed by the predicates
//
//--------------------------------------------------------------------------
// Applies both predicates: first 'PredA', and if it equals 'cInRange', 'PredB'
template<class PredA, class PredB>
struct applyBoth
{
typedef typename PredA::argument_type argument_type ;
static range_check_result apply ( argument_type s )
{
range_check_result r = PredA::apply(s) ;
if ( r == cInRange )
r = PredB::apply(s);
return r ;
}
} ;
template<class PredA, class PredB>
struct combine
{
typedef applyBoth<PredA,PredB> Both ;
typedef void NNone ; // 'None' is defined as a macro in (/usr/X11R6/include/X11/X.h)
typedef typename PredA::do_apply do_applyA ;
typedef typename PredB::do_apply do_applyB ;
typedef typename for_both<do_applyA, do_applyB, Both, PredA, PredB, NNone>::type type ;
} ;
//--------------------------------------------------------------------------
// Range Checker classes.
//
// The following classes are VISIBLE base classes of the user-level converter<> class.
// They supply the optimized 'out_of_range()' and 'validate_range()' static member functions
// visible in the user interface.
//
//--------------------------------------------------------------------------
// Dummy range checker.
template<class Traits>
struct dummy_range_checker
{
typedef typename Traits::argument_type argument_type ;
static range_check_result out_of_range ( argument_type ) { return cInRange ; }
static void validate_range ( argument_type ) {}
} ;
// Generic range checker.
//
// All the range checking logic for all possible combinations of source and target
// can be arranged in terms of one or two predicates, which test overflow on both neg/pos 'sides'
// of the ranges.
//
// These predicates are given here as IsNegOverflow and IsPosOverflow.
//
template<class Traits, class IsNegOverflow, class IsPosOverflow, class OverflowHandler>
struct generic_range_checker
{
typedef OverflowHandler overflow_handler ;
typedef typename Traits::argument_type argument_type ;
static range_check_result out_of_range ( argument_type s )
{
typedef typename combine<IsNegOverflow,IsPosOverflow>::type Predicate ;
return Predicate::apply(s);
}
static void validate_range ( argument_type s )
{ OverflowHandler()( out_of_range(s) ) ; }
} ;
//--------------------------------------------------------------------------
//
// Selectors for the optimized Range Checker class.
//
//--------------------------------------------------------------------------
template<class Traits,class OverflowHandler>
struct GetRC_Sig2Sig_or_Unsig2Unsig
{
typedef dummy_range_checker<Traits> Dummy ;
typedef LT_LoT<Traits> Pred1 ;
typedef GT_HiT<Traits> Pred2 ;
typedef generic_range_checker<Traits,Pred1,Pred2,OverflowHandler> Normal ;
typedef typename Traits::subranged subranged ;
typedef typename mpl::if_<subranged,Normal,Dummy>::type type ;
} ;
template<class Traits, class OverflowHandler>
struct GetRC_Sig2Unsig
{
typedef LT_Zero<Traits> Pred1 ;
typedef GT_HiT <Traits> Pred2 ;
typedef generic_range_checker<Traits,Pred1,Pred2,OverflowHandler> ChoiceA ;
typedef generic_range_checker<Traits,Pred1,non_applicable,OverflowHandler> ChoiceB ;
typedef typename Traits::target_type T ;
typedef typename Traits::source_type S ;
typedef typename subranged_Unsig2Sig<S,T>::type oposite_subranged ;
typedef typename mpl::not_<oposite_subranged>::type positively_subranged ;
typedef typename mpl::if_<positively_subranged,ChoiceA,ChoiceB>::type type ;
} ;
template<class Traits, class OverflowHandler>
struct GetRC_Unsig2Sig
{
typedef GT_HiT<Traits> Pred1 ;
typedef generic_range_checker<Traits,non_applicable,Pred1,OverflowHandler> type ;
} ;
template<class Traits,class OverflowHandler>
struct GetRC_Int2Int
{
typedef GetRC_Sig2Sig_or_Unsig2Unsig<Traits,OverflowHandler> Sig2SigQ ;
typedef GetRC_Sig2Unsig <Traits,OverflowHandler> Sig2UnsigQ ;
typedef GetRC_Unsig2Sig <Traits,OverflowHandler> Unsig2SigQ ;
typedef Sig2SigQ Unsig2UnsigQ ;
typedef typename Traits::sign_mixture sign_mixture ;
typedef typename
for_sign_mixture<sign_mixture,Sig2SigQ,Sig2UnsigQ,Unsig2SigQ,Unsig2UnsigQ>::type
selector ;
typedef typename selector::type type ;
} ;
template<class Traits>
struct GetRC_Int2Float
{
typedef dummy_range_checker<Traits> type ;
} ;
template<class Traits, class OverflowHandler, class Float2IntRounder>
struct GetRC_Float2Int
{
typedef LE_PrevLoT <Traits> Pred1 ;
typedef GE_SuccHiT <Traits> Pred2 ;
typedef LT_HalfPrevLoT<Traits> Pred3 ;
typedef GT_HalfSuccHiT<Traits> Pred4 ;
typedef GT_HiT <Traits> Pred5 ;
typedef LT_LoT <Traits> Pred6 ;
typedef generic_range_checker<Traits,Pred1,Pred2,OverflowHandler> ToZero ;
typedef generic_range_checker<Traits,Pred3,Pred4,OverflowHandler> ToNearest ;
typedef generic_range_checker<Traits,Pred1,Pred5,OverflowHandler> ToInf ;
typedef generic_range_checker<Traits,Pred6,Pred2,OverflowHandler> ToNegInf ;
typedef typename Float2IntRounder::round_style round_style ;
typedef typename for_round_style<round_style,ToZero,ToNearest,ToInf,ToNegInf>::type type ;
} ;
template<class Traits, class OverflowHandler>
struct GetRC_Float2Float
{
typedef dummy_range_checker<Traits> Dummy ;
typedef LT_LoT<Traits> Pred1 ;
typedef GT_HiT<Traits> Pred2 ;
typedef generic_range_checker<Traits,Pred1,Pred2,OverflowHandler> Normal ;
typedef typename Traits::subranged subranged ;
typedef typename mpl::if_<subranged,Normal,Dummy>::type type ;
} ;
template<class Traits, class OverflowHandler, class Float2IntRounder>
struct GetRC_BuiltIn2BuiltIn
{
typedef GetRC_Int2Int<Traits,OverflowHandler> Int2IntQ ;
typedef GetRC_Int2Float<Traits> Int2FloatQ ;
typedef GetRC_Float2Int<Traits,OverflowHandler,Float2IntRounder> Float2IntQ ;
typedef GetRC_Float2Float<Traits,OverflowHandler> Float2FloatQ ;
typedef typename Traits::int_float_mixture int_float_mixture ;
typedef typename for_int_float_mixture<int_float_mixture, Int2IntQ, Int2FloatQ, Float2IntQ, Float2FloatQ>::type selector ;
typedef typename selector::type type ;
} ;
template<class Traits, class OverflowHandler, class Float2IntRounder>
struct GetRC
{
typedef GetRC_BuiltIn2BuiltIn<Traits,OverflowHandler,Float2IntRounder> BuiltIn2BuiltInQ ;
typedef dummy_range_checker<Traits> Dummy ;
typedef mpl::identity<Dummy> DummyQ ;
typedef typename Traits::udt_builtin_mixture udt_builtin_mixture ;
typedef typename for_udt_builtin_mixture<udt_builtin_mixture,BuiltIn2BuiltInQ,DummyQ,DummyQ,DummyQ>::type selector ;
typedef typename selector::type type ;
} ;
//--------------------------------------------------------------------------
// Converter classes.
//
// The following classes are VISIBLE base classes of the user-level converter<> class.
// They supply the optimized 'nearbyint()' and 'convert()' static member functions
// visible in the user interface.
//
//--------------------------------------------------------------------------
//
// Trivial Converter : used when (cv-unqualified) T == (cv-unqualified) S
//
template<class Traits>
struct trivial_converter_impl : public dummy_range_checker<Traits>
{
typedef Traits traits ;
typedef typename Traits::source_type source_type ;
typedef typename Traits::argument_type argument_type ;
typedef typename Traits::result_type result_type ;
static result_type low_level_convert ( argument_type s ) { return s ; }
static source_type nearbyint ( argument_type s ) { return s ; }
static result_type convert ( argument_type s ) { return s ; }
} ;
//
// Rounding Converter : used for float to integral conversions.
//
template<class Traits,class RangeChecker,class RawConverter,class Float2IntRounder>
struct rounding_converter : public RangeChecker
,public Float2IntRounder
,public RawConverter
{
typedef RangeChecker RangeCheckerBase ;
typedef Float2IntRounder Float2IntRounderBase ;
typedef RawConverter RawConverterBase ;
typedef Traits traits ;
typedef typename Traits::source_type source_type ;
typedef typename Traits::argument_type argument_type ;
typedef typename Traits::result_type result_type ;
static result_type convert ( argument_type s )
{
RangeCheckerBase::validate_range(s);
source_type s1 = Float2IntRounderBase::nearbyint(s);
return RawConverterBase::low_level_convert(s1);
}
} ;
//
// Non-Rounding Converter : used for all other conversions.
//
template<class Traits,class RangeChecker,class RawConverter>
struct non_rounding_converter : public RangeChecker
,public RawConverter
{
typedef RangeChecker RangeCheckerBase ;
typedef RawConverter RawConverterBase ;
typedef Traits traits ;
typedef typename Traits::source_type source_type ;
typedef typename Traits::argument_type argument_type ;
typedef typename Traits::result_type result_type ;
static source_type nearbyint ( argument_type s ) { return s ; }
static result_type convert ( argument_type s )
{
RangeCheckerBase::validate_range(s);
return RawConverterBase::low_level_convert(s);
}
} ;
//--------------------------------------------------------------------------
//
// Selectors for the optimized Converter class.
//
//--------------------------------------------------------------------------
template<class Traits,class OverflowHandler,class Float2IntRounder,class RawConverter, class UserRangeChecker>
struct get_non_trivial_converter
{
typedef GetRC<Traits,OverflowHandler,Float2IntRounder> InternalRangeCheckerQ ;
typedef is_same<UserRangeChecker,UseInternalRangeChecker> use_internal_RC ;
typedef mpl::identity<UserRangeChecker> UserRangeCheckerQ ;
typedef typename
mpl::eval_if<use_internal_RC,InternalRangeCheckerQ,UserRangeCheckerQ>::type
RangeChecker ;
typedef non_rounding_converter<Traits,RangeChecker,RawConverter> NonRounding ;
typedef rounding_converter<Traits,RangeChecker,RawConverter,Float2IntRounder> Rounding ;
typedef mpl::identity<NonRounding> NonRoundingQ ;
typedef mpl::identity<Rounding> RoundingQ ;
typedef typename Traits::int_float_mixture int_float_mixture ;
typedef typename
for_int_float_mixture<int_float_mixture, NonRoundingQ, NonRoundingQ, RoundingQ, NonRoundingQ>::type
selector ;
typedef typename selector::type type ;
} ;
template< class Traits
,class OverflowHandler
,class Float2IntRounder
,class RawConverter
,class UserRangeChecker
>
struct get_converter_impl
{
#if BOOST_WORKAROUND(BOOST_BORLANDC, BOOST_TESTED_AT( 0x0561 ) )
// bcc55 prefers sometimes template parameters to be explicit local types.
// (notice that is is illegal to reuse the names like this)
typedef Traits Traits ;
typedef OverflowHandler OverflowHandler ;
typedef Float2IntRounder Float2IntRounder ;
typedef RawConverter RawConverter ;
typedef UserRangeChecker UserRangeChecker ;
#endif
typedef trivial_converter_impl<Traits> Trivial ;
typedef mpl::identity <Trivial> TrivialQ ;
typedef get_non_trivial_converter< Traits
,OverflowHandler
,Float2IntRounder
,RawConverter
,UserRangeChecker
> NonTrivialQ ;
typedef typename Traits::trivial trivial ;
typedef typename mpl::eval_if<trivial,TrivialQ,NonTrivialQ>::type type ;
} ;
} } } // namespace boost::numeric::convdetail
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_DETAIL_INT_FLOAT_MIXTURE_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_DETAIL_INT_FLOAT_MIXTURE_FLC_12NOV2002_HPP
#include "boost/config.hpp"
#include "boost/limits.hpp"
#include "boost/numeric/conversion/int_float_mixture_enum.hpp"
#include "boost/numeric/conversion/detail/meta.hpp"
#include "boost/mpl/integral_c.hpp"
namespace boost { namespace numeric { namespace convdetail
{
// Integral Constants for 'IntFloatMixture'
typedef mpl::integral_c<int_float_mixture_enum, integral_to_integral> int2int_c ;
typedef mpl::integral_c<int_float_mixture_enum, integral_to_float> int2float_c ;
typedef mpl::integral_c<int_float_mixture_enum, float_to_integral> float2int_c ;
typedef mpl::integral_c<int_float_mixture_enum, float_to_float> float2float_c ;
// Metafunction:
//
// get_int_float_mixture<T,S>::type
//
// Selects the appropriate Int-Float Mixture Integral Constant for the combination T,S.
//
template<class T,class S>
struct get_int_float_mixture
{
typedef mpl::bool_< ::std::numeric_limits<S>::is_integer > S_int ;
typedef mpl::bool_< ::std::numeric_limits<T>::is_integer > T_int ;
typedef typename
for_both<S_int, T_int, int2int_c, int2float_c, float2int_c, float2float_c>::type
type ;
} ;
// Metafunction:
//
// for_int_float_mixture<Mixture,int_int,int_float,float_int,float_float>::type
//
// {Mixture} is one of the Integral Constants for Mixture, declared above.
// {int_int,int_float,float_int,float_float} are aribtrary types. (not metafunctions)
//
// According to the value of 'IntFloatMixture', selects the corresponding type.
//
template<class IntFloatMixture, class Int2Int, class Int2Float, class Float2Int, class Float2Float>
struct for_int_float_mixture
{
typedef typename
ct_switch4<IntFloatMixture
,int2int_c, int2float_c, float2int_c // default
,Int2Int , Int2Float , Float2Int , Float2Float
>::type
type ;
} ;
} } } // namespace boost::numeric::convdetail
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_DETAIL_IS_SUBRANGED_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_DETAIL_IS_SUBRANGED_FLC_12NOV2002_HPP
#include "boost/config.hpp"
#include "boost/limits.hpp"
#include "boost/mpl/int.hpp"
#include "boost/mpl/multiplies.hpp"
#include "boost/mpl/less.hpp"
#include "boost/mpl/equal_to.hpp"
#include "boost/type_traits/is_same.hpp"
#include "boost/numeric/conversion/detail/meta.hpp"
#include "boost/numeric/conversion/detail/int_float_mixture.hpp"
#include "boost/numeric/conversion/detail/sign_mixture.hpp"
#include "boost/numeric/conversion/detail/udt_builtin_mixture.hpp"
namespace boost { namespace numeric { namespace convdetail
{
//---------------------------------------------------------------
// Implementations of the compile time predicate "T is subranged"
//---------------------------------------------------------------
// for integral to integral conversions
template<class T,class S>
struct subranged_Sig2Unsig
{
// Signed to unsigned conversions are 'subranged' because of possible loose
// of negative values.
typedef mpl::true_ type ;
} ;
// for unsigned integral to signed integral conversions
template<class T,class S>
struct subranged_Unsig2Sig
{
// IMPORTANT NOTE:
//
// This code assumes that signed/unsigned integral values are represented
// such that:
//
// numeric_limits<signed T>::digits + 1 == numeric_limits<unsigned T>::digits
//
// The '+1' is required since numeric_limits<>::digits gives 1 bit less for signed integral types.
//
// This fact is used by the following logic:
//
// if ( (numeric_limits<T>::digits+1) < (2*numeric_limits<S>::digits) )
// then the conversion is subranged.
//
typedef mpl::int_< ::std::numeric_limits<S>::digits > S_digits ;
typedef mpl::int_< ::std::numeric_limits<T>::digits > T_digits ;
// T is signed, so take digits+1
typedef typename T_digits::next u_T_digits ;
typedef mpl::int_<2> Two ;
typedef typename mpl::multiplies<S_digits,Two>::type S_digits_times_2 ;
typedef typename mpl::less<u_T_digits,S_digits_times_2>::type type ;
} ;
// for integral to integral conversions of the same sign.
template<class T,class S>
struct subranged_SameSign
{
// An integral conversion of the same sign is subranged if digits(T) < digits(S).
typedef mpl::int_< ::std::numeric_limits<S>::digits > S_digits ;
typedef mpl::int_< ::std::numeric_limits<T>::digits > T_digits ;
typedef typename mpl::less<T_digits,S_digits>::type type ;
} ;
// for integral to float conversions
template<class T,class S>
struct subranged_Int2Float
{
typedef mpl::false_ type ;
} ;
// for float to integral conversions
template<class T,class S>
struct subranged_Float2Int
{
typedef mpl::true_ type ;
} ;
// for float to float conversions
template<class T,class S>
struct subranged_Float2Float
{
// If both T and S are floats,
// compare exponent bits and if they match, mantisa bits.
typedef mpl::int_< ::std::numeric_limits<S>::digits > S_mantisa ;
typedef mpl::int_< ::std::numeric_limits<T>::digits > T_mantisa ;
typedef mpl::int_< ::std::numeric_limits<S>::max_exponent > S_exponent ;
typedef mpl::int_< ::std::numeric_limits<T>::max_exponent > T_exponent ;
typedef typename mpl::less<T_exponent,S_exponent>::type T_smaller_exponent ;
typedef typename mpl::equal_to<T_exponent,S_exponent>::type equal_exponents ;
typedef mpl::less<T_mantisa,S_mantisa> T_smaller_mantisa ;
typedef mpl::eval_if<equal_exponents,T_smaller_mantisa,mpl::false_> not_bigger_exponent_case ;
typedef typename
mpl::eval_if<T_smaller_exponent,mpl::true_,not_bigger_exponent_case>::type
type ;
} ;
// for Udt to built-in conversions
template<class T,class S>
struct subranged_Udt2BuiltIn
{
typedef mpl::true_ type ;
} ;
// for built-in to Udt conversions
template<class T,class S>
struct subranged_BuiltIn2Udt
{
typedef mpl::false_ type ;
} ;
// for Udt to Udt conversions
template<class T,class S>
struct subranged_Udt2Udt
{
typedef mpl::false_ type ;
} ;
//-------------------------------------------------------------------
// Selectors for the implementations of the subranged predicate
//-------------------------------------------------------------------
template<class T,class S>
struct get_subranged_Int2Int
{
typedef subranged_SameSign<T,S> Sig2Sig ;
typedef subranged_Sig2Unsig<T,S> Sig2Unsig ;
typedef subranged_Unsig2Sig<T,S> Unsig2Sig ;
typedef Sig2Sig Unsig2Unsig ;
typedef typename get_sign_mixture<T,S>::type sign_mixture ;
typedef typename
for_sign_mixture<sign_mixture, Sig2Sig, Sig2Unsig, Unsig2Sig, Unsig2Unsig>::type
type ;
} ;
template<class T,class S>
struct get_subranged_BuiltIn2BuiltIn
{
typedef get_subranged_Int2Int<T,S> Int2IntQ ;
typedef subranged_Int2Float <T,S> Int2Float ;
typedef subranged_Float2Int <T,S> Float2Int ;
typedef subranged_Float2Float<T,S> Float2Float ;
typedef mpl::identity<Int2Float > Int2FloatQ ;
typedef mpl::identity<Float2Int > Float2IntQ ;
typedef mpl::identity<Float2Float> Float2FloatQ ;
typedef typename get_int_float_mixture<T,S>::type int_float_mixture ;
typedef for_int_float_mixture<int_float_mixture, Int2IntQ, Int2FloatQ, Float2IntQ, Float2FloatQ> for_ ;
typedef typename for_::type selected ;
typedef typename selected::type type ;
} ;
template<class T,class S>
struct get_subranged
{
typedef get_subranged_BuiltIn2BuiltIn<T,S> BuiltIn2BuiltInQ ;
typedef subranged_BuiltIn2Udt<T,S> BuiltIn2Udt ;
typedef subranged_Udt2BuiltIn<T,S> Udt2BuiltIn ;
typedef subranged_Udt2Udt<T,S> Udt2Udt ;
typedef mpl::identity<BuiltIn2Udt> BuiltIn2UdtQ ;
typedef mpl::identity<Udt2BuiltIn> Udt2BuiltInQ ;
typedef mpl::identity<Udt2Udt > Udt2UdtQ ;
typedef typename get_udt_builtin_mixture<T,S>::type udt_builtin_mixture ;
typedef typename
for_udt_builtin_mixture<udt_builtin_mixture, BuiltIn2BuiltInQ, BuiltIn2UdtQ, Udt2BuiltInQ, Udt2UdtQ>::type
selected ;
typedef typename selected::type selected2 ;
typedef typename selected2::type type ;
} ;
//-------------------------------------------------------------------
// Top level implementation selector.
//-------------------------------------------------------------------
template<class T, class S>
struct get_is_subranged
{
typedef get_subranged<T,S> non_trivial_case ;
typedef mpl::identity<mpl::false_> trivial_case ;
typedef is_same<T,S> is_trivial ;
typedef typename mpl::if_<is_trivial,trivial_case,non_trivial_case>::type selected ;
typedef typename selected::type type ;
} ;
} } } // namespace boost::numeric::convdetail
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_DETAIL_META_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_DETAIL_META_FLC_12NOV2002_HPP
#include "boost/type_traits/remove_cv.hpp"
#include "boost/mpl/if.hpp"
#include "boost/mpl/eval_if.hpp"
#include "boost/mpl/equal_to.hpp"
#include "boost/mpl/not.hpp"
#include "boost/mpl/and.hpp"
#include "boost/mpl/bool.hpp"
#include "boost/mpl/identity.hpp"
namespace boost { namespace numeric { namespace convdetail
{
template< class T1, class T2>
struct equal_to
{
#if !defined(BOOST_BORLANDC)
enum { x = ( BOOST_MPL_AUX_VALUE_WKND(T1)::value == BOOST_MPL_AUX_VALUE_WKND(T2)::value ) };
BOOST_STATIC_CONSTANT(bool, value = x);
typedef mpl::bool_<value> type;
#else
BOOST_STATIC_CONSTANT(bool, value = (
BOOST_MPL_AUX_VALUE_WKND(T1)::value
== BOOST_MPL_AUX_VALUE_WKND(T2)::value
));
typedef mpl::bool_<(
BOOST_MPL_AUX_VALUE_WKND(T1)::value
== BOOST_MPL_AUX_VALUE_WKND(T2)::value
)> type;
#endif
};
// Metafunction:
//
// ct_switch4<Value,Case0Val,Case1Val,Case2Val,Case0Type,Case1Type,Case2Type,DefaultType>::type
//
// {Value,Case(X)Val} are Integral Constants (such as: mpl::int_<>)
// {Case(X)Type,DefaultType} are arbitrary types. (not metafunctions)
//
// Returns Case(X)Type if Val==Case(X)Val; DefaultType otherwise.
//
template<class Value,
class Case0Val,
class Case1Val,
class Case2Val,
class Case0Type,
class Case1Type,
class Case2Type,
class DefaultType
>
struct ct_switch4
{
typedef mpl::identity<Case0Type> Case0TypeQ ;
typedef mpl::identity<Case1Type> Case1TypeQ ;
typedef equal_to<Value,Case0Val> is_case0 ;
typedef equal_to<Value,Case1Val> is_case1 ;
typedef equal_to<Value,Case2Val> is_case2 ;
typedef mpl::if_<is_case2,Case2Type,DefaultType> choose_2_3Q ;
typedef mpl::eval_if<is_case1,Case1TypeQ,choose_2_3Q> choose_1_2_3Q ;
typedef typename
mpl::eval_if<is_case0,Case0TypeQ,choose_1_2_3Q>::type
type ;
} ;
// Metafunction:
//
// for_both<expr0,expr1,TT,TF,FT,FF>::type
//
// {exp0,expr1} are Boolean Integral Constants
// {TT,TF,FT,FF} are aribtrary types. (not metafunctions)
//
// According to the combined boolean value of 'expr0 && expr1', selects the corresponding type.
//
template<class expr0, class expr1, class TT, class TF, class FT, class FF>
struct for_both
{
typedef mpl::identity<TF> TF_Q ;
typedef mpl::identity<TT> TT_Q ;
typedef typename mpl::not_<expr0>::type not_expr0 ;
typedef typename mpl::not_<expr1>::type not_expr1 ;
typedef typename mpl::and_<expr0,expr1>::type caseTT ;
typedef typename mpl::and_<expr0,not_expr1>::type caseTF ;
typedef typename mpl::and_<not_expr0,expr1>::type caseFT ;
typedef mpl::if_<caseFT,FT,FF> choose_FT_FF_Q ;
typedef mpl::eval_if<caseTF,TF_Q,choose_FT_FF_Q> choose_TF_FT_FF_Q ;
typedef typename mpl::eval_if<caseTT,TT_Q,choose_TF_FT_FF_Q>::type type ;
} ;
} } } // namespace boost::numeric::convdetail
#endif

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//
//! Copyright (c) 2011-2012
//! Brandon Kohn
//
// 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)
//
#if !defined(BOOST_NUMERIC_CONVERSION_DONT_USE_PREPROCESSED_FILES)
#include <boost/numeric/conversion/detail/preprocessed/numeric_cast_traits_common.hpp>
#if !defined(BOOST_NO_LONG_LONG)
#include <boost/numeric/conversion/detail/preprocessed/numeric_cast_traits_long_long.hpp>
#endif
#else
#if !BOOST_PP_IS_ITERATING
#include <boost/preprocessor/seq/elem.hpp>
#include <boost/preprocessor/seq/size.hpp>
#include <boost/preprocessor/iteration/iterate.hpp>
#if defined(__WAVE__) && defined(BOOST_NUMERIC_CONVERSION_CREATE_PREPROCESSED_FILES)
#pragma wave option(preserve: 2, line: 0, output: "preprocessed/numeric_cast_traits_common.hpp")
#endif
//
//! Copyright (c) 2011-2012
//! Brandon Kohn
//
// 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)
//
#if defined(__WAVE__) && defined(BOOST_NUMERIC_CONVERSION_CREATE_PREPROCESSED_FILES)
#pragma wave option(preserve: 1)
#endif
//! These are the assumed common built in fundamental types (not typedefs/macros.)
#define BOOST_NUMERIC_CONVERSION_BASE_BUILTIN_TYPES() \
(char) \
(signed char) \
(unsigned char) \
(short) \
(unsigned short) \
(int) \
(unsigned int) \
(long) \
(unsigned long) \
(float) \
(double) \
(long double) \
/***/
#define BOOST_NUMERIC_CONVERSION_SEQ_A() BOOST_NUMERIC_CONVERSION_BASE_BUILTIN_TYPES()
#define BOOST_NUMERIC_CONVERSION_SEQ_B() BOOST_NUMERIC_CONVERSION_BASE_BUILTIN_TYPES()
namespace boost { namespace numeric {
#define BOOST_PP_ITERATION_PARAMS_1 (3, (0, BOOST_PP_DEC(BOOST_PP_SEQ_SIZE(BOOST_NUMERIC_CONVERSION_SEQ_A())), <boost/numeric/conversion/detail/numeric_cast_traits.hpp>))
#include BOOST_PP_ITERATE()
}}//namespace boost::numeric;
#if defined(__WAVE__) && defined(BOOST_NUMERIC_CONVERSION_CREATE_PREPROCESSED_FILES)
#pragma wave option(output: null)
#endif
#if ( defined(__WAVE__) && defined(BOOST_NUMERIC_CONVERSION_CREATE_PREPROCESSED_FILES) ) || !defined(BOOST_NO_LONG_LONG)
#undef BOOST_NUMERIC_CONVERSION_SEQ_A
#undef BOOST_NUMERIC_CONVERSION_SEQ_B
#if defined(__WAVE__) && defined(BOOST_NUMERIC_CONVERSION_CREATE_PREPROCESSED_FILES)
#pragma wave option(preserve: 2, line: 0, output: "preprocessed/numeric_cast_traits_long_long.hpp")
#endif
//
//! Copyright (c) 2011-2012
//! Brandon Kohn
//
// 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)
//
#if defined(__WAVE__) && defined(BOOST_NUMERIC_CONVERSION_CREATE_PREPROCESSED_FILES)
#pragma wave option(preserve: 1)
#endif
namespace boost { namespace numeric {
#define BOOST_NUMERIC_CONVERSION_SEQ_A() BOOST_NUMERIC_CONVERSION_BASE_BUILTIN_TYPES()(boost::long_long_type)(boost::ulong_long_type)
#define BOOST_NUMERIC_CONVERSION_SEQ_B() (boost::long_long_type)(boost::ulong_long_type)
#define BOOST_PP_ITERATION_PARAMS_1 (3, (0, BOOST_PP_DEC(BOOST_PP_SEQ_SIZE(BOOST_NUMERIC_CONVERSION_SEQ_A())), <boost/numeric/conversion/detail/numeric_cast_traits.hpp>))
#include BOOST_PP_ITERATE()
}}//namespace boost::numeric;
#if defined(__WAVE__) && defined(BOOST_NUMERIC_CONVERSION_CREATE_PREPROCESSED_FILES)
#pragma wave option(output: null)
#endif
#endif
#undef BOOST_NUMERIC_CONVERSION_BASE_BUILTIN_TYPES
#undef BOOST_NUMERIC_CONVERSION_SEQ_A
#undef BOOST_NUMERIC_CONVERSION_SEQ_B
#elif BOOST_PP_ITERATION_DEPTH() == 1
#define BOOST_PP_ITERATION_PARAMS_2 (3, (0, BOOST_PP_DEC(BOOST_PP_SEQ_SIZE(BOOST_NUMERIC_CONVERSION_SEQ_B())), <boost/numeric/conversion/detail/numeric_cast_traits.hpp>))
#include BOOST_PP_ITERATE()
#elif BOOST_PP_ITERATION_DEPTH() == 2
//! Generate default traits for the specified source and target.
#define BOOST_NUMERIC_CONVERSION_A BOOST_PP_FRAME_ITERATION(1)
#define BOOST_NUMERIC_CONVERSION_B BOOST_PP_FRAME_ITERATION(2)
template <>
struct numeric_cast_traits
<
BOOST_PP_SEQ_ELEM(BOOST_NUMERIC_CONVERSION_A, BOOST_NUMERIC_CONVERSION_SEQ_A())
, BOOST_PP_SEQ_ELEM(BOOST_NUMERIC_CONVERSION_B, BOOST_NUMERIC_CONVERSION_SEQ_B())
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<BOOST_PP_SEQ_ELEM(BOOST_NUMERIC_CONVERSION_B, BOOST_NUMERIC_CONVERSION_SEQ_B())> rounding_policy;
};
#undef BOOST_NUMERIC_CONVERSION_A
#undef BOOST_NUMERIC_CONVERSION_B
#endif//! Depth 2.
#endif// BOOST_NUMERIC_CONVERSION_DONT_USE_PREPROCESSED_FILES

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// boost cast.hpp header file ----------------------------------------------//
// (C) Copyright Kevlin Henney and Dave Abrahams 1999.
// 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)
// See http://www.boost.org/libs/conversion for Documentation.
// Revision History
// 02 Jun 14 Remove VC6 workarounds.
// 16 Jul 11 Bugfixes for VC6.
// 23 JUN 05 Code extracted from /boost/cast.hpp into this new header.
// Keeps this legacy version of numeric_cast<> for old compilers
// wich can't compile the new version in /boost/numeric/conversion/cast.hpp
// (Fernando Cacciola)
// 02 Apr 01 Removed BOOST_NO_LIMITS workarounds and included
// <boost/limits.hpp> instead (the workaround did not
// actually compile when BOOST_NO_LIMITS was defined in
// any case, so we loose nothing). (John Maddock)
// 21 Jan 01 Undid a bug I introduced yesterday. numeric_cast<> never
// worked with stock GCC; trying to get it to do that broke
// vc-stlport.
// 20 Jan 01 Moved BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS to config.hpp.
// Removed unused BOOST_EXPLICIT_TARGET macro. Moved
// boost::detail::type to boost/type.hpp. Made it compile with
// stock gcc again (Dave Abrahams)
// 29 Nov 00 Remove nested namespace cast, cleanup spacing before Formal
// Review (Beman Dawes)
// 19 Oct 00 Fix numeric_cast for floating-point types (Dave Abrahams)
// 15 Jul 00 Suppress numeric_cast warnings for GCC, Borland and MSVC
// (Dave Abrahams)
// 30 Jun 00 More MSVC6 wordarounds. See comments below. (Dave Abrahams)
// 28 Jun 00 Removed implicit_cast<>. See comment below. (Beman Dawes)
// 27 Jun 00 More MSVC6 workarounds
// 15 Jun 00 Add workarounds for MSVC6
// 2 Feb 00 Remove bad_numeric_cast ";" syntax error (Doncho Angelov)
// 26 Jan 00 Add missing throw() to bad_numeric_cast::what(0 (Adam Levar)
// 29 Dec 99 Change using declarations so usages in other namespaces work
// correctly (Dave Abrahams)
// 23 Sep 99 Change polymorphic_downcast assert to also detect M.I. errors
// as suggested Darin Adler and improved by Valentin Bonnard.
// 2 Sep 99 Remove controversial asserts, simplify, rename.
// 30 Aug 99 Move to cast.hpp, replace value_cast with numeric_cast,
// place in nested namespace.
// 3 Aug 99 Initial version
#ifndef BOOST_OLD_NUMERIC_CAST_HPP
#define BOOST_OLD_NUMERIC_CAST_HPP
# include <boost/config.hpp>
# include <cassert>
# include <typeinfo>
# include <boost/type.hpp>
# include <boost/limits.hpp>
# include <boost/numeric/conversion/converter_policies.hpp>
namespace boost
{
using numeric::bad_numeric_cast;
// LEGACY numeric_cast [only for some old broken compilers] --------------------------------------//
// Contributed by Kevlin Henney
// numeric_cast ------------------------------------------------------------//
#if !defined(BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS) || defined(BOOST_SGI_CPP_LIMITS)
namespace detail
{
template <class T>
struct signed_numeric_limits : std::numeric_limits<T>
{
static inline T min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{
return (std::numeric_limits<T>::min)() >= 0
// unary minus causes integral promotion, thus the static_cast<>
? static_cast<T>(-(std::numeric_limits<T>::max)())
: (std::numeric_limits<T>::min)();
};
};
// Move to namespace boost in utility.hpp?
template <class T, bool specialized>
struct fixed_numeric_limits_base
: public if_true< std::numeric_limits<T>::is_signed >
::BOOST_NESTED_TEMPLATE then< signed_numeric_limits<T>,
std::numeric_limits<T>
>::type
{};
template <class T>
struct fixed_numeric_limits
: fixed_numeric_limits_base<T,(std::numeric_limits<T>::is_specialized)>
{};
# ifdef BOOST_HAS_LONG_LONG
// cover implementations which supply no specialization for long
// long / unsigned long long. Not intended to be full
// numeric_limits replacements, but good enough for numeric_cast<>
template <>
struct fixed_numeric_limits_base< ::boost::long_long_type, false>
{
BOOST_STATIC_CONSTANT(bool, is_specialized = true);
BOOST_STATIC_CONSTANT(bool, is_signed = true);
static ::boost::long_long_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{
# ifdef LONGLONG_MAX
return LONGLONG_MAX;
# else
return 9223372036854775807LL; // hope this is portable
# endif
}
static ::boost::long_long_type min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{
# ifdef LONGLONG_MIN
return LONGLONG_MIN;
# else
return -( 9223372036854775807LL )-1; // hope this is portable
# endif
}
};
template <>
struct fixed_numeric_limits_base< ::boost::ulong_long_type, false>
{
BOOST_STATIC_CONSTANT(bool, is_specialized = true);
BOOST_STATIC_CONSTANT(bool, is_signed = false);
static ::boost::ulong_long_type max BOOST_PREVENT_MACRO_SUBSTITUTION ()
{
# ifdef ULONGLONG_MAX
return ULONGLONG_MAX;
# else
return 0xffffffffffffffffULL; // hope this is portable
# endif
}
static ::boost::ulong_long_type min BOOST_PREVENT_MACRO_SUBSTITUTION () { return 0; }
};
# endif
} // namespace detail
// less_than_type_min -
// x_is_signed should be numeric_limits<X>::is_signed
// y_is_signed should be numeric_limits<Y>::is_signed
// y_min should be numeric_limits<Y>::min()
//
// check(x, y_min) returns true iff x < y_min without invoking comparisons
// between signed and unsigned values.
//
// "poor man's partial specialization" is in use here.
template <bool x_is_signed, bool y_is_signed>
struct less_than_type_min
{
template <class X, class Y>
static bool check(X x, Y y_min)
{ return x < y_min; }
};
template <>
struct less_than_type_min<false, true>
{
template <class X, class Y>
static bool check(X, Y)
{ return false; }
};
template <>
struct less_than_type_min<true, false>
{
template <class X, class Y>
static bool check(X x, Y)
{ return x < 0; }
};
// greater_than_type_max -
// same_sign should be:
// numeric_limits<X>::is_signed == numeric_limits<Y>::is_signed
// y_max should be numeric_limits<Y>::max()
//
// check(x, y_max) returns true iff x > y_max without invoking comparisons
// between signed and unsigned values.
//
// "poor man's partial specialization" is in use here.
template <bool same_sign, bool x_is_signed>
struct greater_than_type_max;
template<>
struct greater_than_type_max<true, true>
{
template <class X, class Y>
static inline bool check(X x, Y y_max)
{ return x > y_max; }
};
template <>
struct greater_than_type_max<false, true>
{
// What does the standard say about this? I think it's right, and it
// will work with every compiler I know of.
template <class X, class Y>
static inline bool check(X x, Y)
{ return x >= 0 && static_cast<X>(static_cast<Y>(x)) != x; }
};
template<>
struct greater_than_type_max<true, false>
{
template <class X, class Y>
static inline bool check(X x, Y y_max)
{ return x > y_max; }
};
template <>
struct greater_than_type_max<false, false>
{
// What does the standard say about this? I think it's right, and it
// will work with every compiler I know of.
template <class X, class Y>
static inline bool check(X x, Y)
{ return static_cast<X>(static_cast<Y>(x)) != x; }
};
#else // use #pragma hacks if available
namespace detail
{
# if BOOST_MSVC
# pragma warning(push)
# pragma warning(disable : 4018)
# pragma warning(disable : 4146)
#elif defined(BOOST_BORLANDC)
# pragma option push -w-8041
# endif
// Move to namespace boost in utility.hpp?
template <class T>
struct fixed_numeric_limits : public std::numeric_limits<T>
{
static inline T min BOOST_PREVENT_MACRO_SUBSTITUTION ()
{
return std::numeric_limits<T>::is_signed && (std::numeric_limits<T>::min)() >= 0
? T(-(std::numeric_limits<T>::max)()) : (std::numeric_limits<T>::min)();
}
};
# if BOOST_MSVC
# pragma warning(pop)
#elif defined(BOOST_BORLANDC)
# pragma option pop
# endif
} // namespace detail
#endif
template<typename Target, typename Source>
inline Target numeric_cast(Source arg)
{
// typedefs abbreviating respective trait classes
typedef detail::fixed_numeric_limits<Source> arg_traits;
typedef detail::fixed_numeric_limits<Target> result_traits;
#if defined(BOOST_STRICT_CONFIG) \
|| (!defined(__HP_aCC) || __HP_aCC > 33900) \
&& (!defined(BOOST_NO_LIMITS_COMPILE_TIME_CONSTANTS) \
|| defined(BOOST_SGI_CPP_LIMITS))
// typedefs that act as compile time assertions
// (to be replaced by boost compile time assertions
// as and when they become available and are stable)
typedef bool argument_must_be_numeric[arg_traits::is_specialized];
typedef bool result_must_be_numeric[result_traits::is_specialized];
const bool arg_is_signed = arg_traits::is_signed;
const bool result_is_signed = result_traits::is_signed;
const bool same_sign = arg_is_signed == result_is_signed;
if (less_than_type_min<arg_is_signed, result_is_signed>::check(arg, (result_traits::min)())
|| greater_than_type_max<same_sign, arg_is_signed>::check(arg, (result_traits::max)())
)
#else // We need to use #pragma hacks if available
# if BOOST_MSVC
# pragma warning(push)
# pragma warning(disable : 4018)
#elif defined(BOOST_BORLANDC)
#pragma option push -w-8012
# endif
if ((arg < 0 && !result_traits::is_signed) // loss of negative range
|| (arg_traits::is_signed && arg < (result_traits::min)()) // underflow
|| arg > (result_traits::max)()) // overflow
# if BOOST_MSVC
# pragma warning(pop)
#elif defined(BOOST_BORLANDC)
#pragma option pop
# endif
#endif
{
throw bad_numeric_cast();
}
return static_cast<Target>(arg);
} // numeric_cast
} // namespace boost
#endif // BOOST_OLD_NUMERIC_CAST_HPP

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//
//! Copyright (c) 2011-2012
//! Brandon Kohn
//
// 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)
//
namespace boost { namespace numeric {
template <>
struct numeric_cast_traits
<
char
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
char
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
signed char
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
signed char
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned char
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned char
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
short
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
short
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned short
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned short
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
int
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
int
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned int
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned int
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
long
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
long
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned long
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
unsigned long
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
float
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
float
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
double
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
double
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
long double
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
long double
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
boost::long_long_type
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
boost::long_long_type
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
boost::ulong_long_type
, boost::long_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::long_long_type> rounding_policy;
};
template <>
struct numeric_cast_traits
<
boost::ulong_long_type
, boost::ulong_long_type
>
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<boost::ulong_long_type> rounding_policy;
};
}}

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_DETAIL_SIGN_MIXTURE_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_DETAIL_SIGN_MIXTURE_FLC_12NOV2002_HPP
#include "boost/config.hpp"
#include "boost/limits.hpp"
#include "boost/numeric/conversion/sign_mixture_enum.hpp"
#include "boost/numeric/conversion/detail/meta.hpp"
#include "boost/mpl/integral_c.hpp"
namespace boost { namespace numeric { namespace convdetail
{
// Integral Constants for 'SignMixture'
typedef mpl::integral_c<sign_mixture_enum, unsigned_to_unsigned> unsig2unsig_c ;
typedef mpl::integral_c<sign_mixture_enum, signed_to_signed> sig2sig_c ;
typedef mpl::integral_c<sign_mixture_enum, signed_to_unsigned> sig2unsig_c ;
typedef mpl::integral_c<sign_mixture_enum, unsigned_to_signed> unsig2sig_c ;
// Metafunction:
//
// get_sign_mixture<T,S>::type
//
// Selects the appropriate SignMixture Integral Constant for the combination T,S.
//
template<class T,class S>
struct get_sign_mixture
{
typedef mpl::bool_< ::std::numeric_limits<S>::is_signed > S_signed ;
typedef mpl::bool_< ::std::numeric_limits<T>::is_signed > T_signed ;
typedef typename
for_both<S_signed, T_signed, sig2sig_c, sig2unsig_c, unsig2sig_c, unsig2unsig_c>::type
type ;
} ;
// Metafunction:
//
// for_sign_mixture<SignMixture,Sig2Sig,Sig2Unsig,Unsig2Sig,Unsig2Unsig>::type
//
// {SignMixture} is one of the Integral Constants for SignMixture, declared above.
// {Sig2Sig,Sig2Unsig,Unsig2Sig,Unsig2Unsig} are aribtrary types. (not metafunctions)
//
// According to the value of 'SignMixture', selects the corresponding type.
//
template<class SignMixture, class Sig2Sig, class Sig2Unsig, class Unsig2Sig, class Unsig2Unsig>
struct for_sign_mixture
{
typedef typename
ct_switch4<SignMixture
, sig2sig_c, sig2unsig_c, unsig2sig_c // default
, Sig2Sig , Sig2Unsig , Unsig2Sig , Unsig2Unsig
>::type
type ;
} ;
} } } // namespace boost::numeric::convdetail
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_DETAIL_UDT_BUILTIN_MIXTURE_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_DETAIL_UDT_BUILTIN_MIXTURE_FLC_12NOV2002_HPP
#include "boost/type_traits/is_arithmetic.hpp"
#include "boost/numeric/conversion/udt_builtin_mixture_enum.hpp"
#include "boost/numeric/conversion/detail/meta.hpp"
#include "boost/mpl/integral_c.hpp"
namespace boost { namespace numeric { namespace convdetail
{
// Integral Constants for 'UdtMixture'
typedef mpl::integral_c<udt_builtin_mixture_enum, builtin_to_builtin> builtin2builtin_c ;
typedef mpl::integral_c<udt_builtin_mixture_enum, builtin_to_udt> builtin2udt_c ;
typedef mpl::integral_c<udt_builtin_mixture_enum, udt_to_builtin> udt2builtin_c ;
typedef mpl::integral_c<udt_builtin_mixture_enum, udt_to_udt> udt2udt_c ;
// Metafunction:
//
// for_udt_mixture<UdtMixture,BuiltIn2BuiltIn,BuiltIn2Udt,Udt2BuiltIn,Udt2Udt>::type
//
// {UdtMixture} is one of the Integral Constants for UdMixture, declared above.
// {BuiltIn2BuiltIn,BuiltIn2Udt,Udt2BuiltIn,Udt2Udt} are aribtrary types. (not metafunctions)
//
// According to the value of 'UdtMixture', selects the corresponding type.
//
template<class UdtMixture, class BuiltIn2BuiltIn, class BuiltIn2Udt, class Udt2BuiltIn, class Udt2Udt>
struct for_udt_builtin_mixture
{
typedef typename
ct_switch4<UdtMixture
, builtin2builtin_c, builtin2udt_c, udt2builtin_c // default
, BuiltIn2BuiltIn , BuiltIn2Udt , Udt2BuiltIn , Udt2Udt
>::type
type ;
} ;
// Metafunction:
//
// get_udt_mixture<T,S>::type
//
// Selects the appropriate UdtMixture Integral Constant for the combination T,S.
//
template<class T,class S>
struct get_udt_builtin_mixture
{
typedef is_arithmetic<S> S_builtin ;
typedef is_arithmetic<T> T_builtin ;
typedef typename
for_both<S_builtin, T_builtin, builtin2builtin_c, builtin2udt_c, udt2builtin_c, udt2udt_c>::type
type ;
} ;
} } } // namespace boost::numeric::convdetail
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_INT_FLOAT_MIXTURE_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_INT_FLOAT_MIXTURE_FLC_12NOV2002_HPP
#include "boost/numeric/conversion/detail/int_float_mixture.hpp"
namespace boost { namespace numeric
{
template<class T, class S>
struct int_float_mixture
: convdetail::get_int_float_mixture< BOOST_DEDUCED_TYPENAME remove_cv<T>::type
,BOOST_DEDUCED_TYPENAME remove_cv<S>::type
>::type {} ;
} } // namespace boost::numeric
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_INT_FLOAT_MIXTURE_ENUM_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_INT_FLOAT_MIXTURE_ENUM_FLC_12NOV2002_HPP
namespace boost { namespace numeric
{
enum int_float_mixture_enum
{
integral_to_integral
,integral_to_float
,float_to_integral
,float_to_float
} ;
} } // namespace boost::numeric
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_IS_SUBRANGED_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_IS_SUBRANGED_FLC_12NOV2002_HPP
#include "boost/numeric/conversion/detail/is_subranged.hpp"
namespace boost { namespace numeric {
template<class T, class S>
struct is_subranged
: convdetail::get_is_subranged< BOOST_DEDUCED_TYPENAME remove_cv<T>::type
,BOOST_DEDUCED_TYPENAME remove_cv<S>::type
>::type {} ;
} } // namespace boost::numeric
#endif

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//
//! Copyright (c) 2011
//! Brandon Kohn
//
// 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)
//
#ifndef BOOST_NUMERIC_CAST_TRAITS_HPP
#define BOOST_NUMERIC_CAST_TRAITS_HPP
#include <boost/numeric/conversion/converter_policies.hpp>
namespace boost { namespace numeric {
template <typename Target, typename Source, typename EnableIf = void>
struct numeric_cast_traits
{
typedef def_overflow_handler overflow_policy;
typedef UseInternalRangeChecker range_checking_policy;
typedef Trunc<Source> rounding_policy;
};
}}//namespace boost::numeric;
#if !defined( BOOST_NUMERIC_CONVERSION_RELAX_BUILT_IN_CAST_TRAITS )
#include <boost/cstdint.hpp>
#include <boost/numeric/conversion/detail/numeric_cast_traits.hpp>
#endif//!defined BOOST_NUMERIC_CONVERSION_RELAX_BUILT_IN_CAST_TRAITS
#endif//BOOST_NUMERIC_CAST_TRAITS_HPP

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_SIGN_MIXTURE_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_SIGN_MIXTURE_FLC_12NOV2002_HPP
#include "boost/numeric/conversion/detail/sign_mixture.hpp"
namespace boost { namespace numeric
{
template<class T, class S>
struct sign_mixture
: convdetail::get_sign_mixture< BOOST_DEDUCED_TYPENAME remove_cv<T>::type
,BOOST_DEDUCED_TYPENAME remove_cv<S>::type
>::type {} ;
} } // namespace boost::numeric
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_SIGN_MIXTURE_ENUM_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_SIGN_MIXTURE_ENUM_FLC_12NOV2002_HPP
namespace boost { namespace numeric
{
enum sign_mixture_enum
{
unsigned_to_unsigned
,signed_to_signed
,signed_to_unsigned
,unsigned_to_signed
} ;
} } // namespace boost::numeric
#endif
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_UDT_BUILTIN_MIXTURE_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_UDT_BUILTIN_MIXTURE_FLC_12NOV2002_HPP
#include "boost/numeric/conversion/detail/udt_builtin_mixture.hpp"
namespace boost { namespace numeric
{
template<class T, class S>
struct udt_builtin_mixture
: convdetail::get_udt_builtin_mixture< BOOST_DEDUCED_TYPENAME remove_cv<T>::type
,BOOST_DEDUCED_TYPENAME remove_cv<S>::type
>::type {} ;
} } // namespace boost::numeric
#endif

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#ifndef BOOST_NUMERIC_CONVERSION_UDT_BUILTIN_MIXTURE_ENUM_FLC_12NOV2002_HPP
#define BOOST_NUMERIC_CONVERSION_UDT_BUILTIN_MIXTURE_ENUM_FLC_12NOV2002_HPP
namespace boost { namespace numeric
{
enum udt_builtin_mixture_enum
{
builtin_to_builtin
,builtin_to_udt
,udt_to_builtin
,udt_to_udt
} ;
} } // namespace boost::numeric
#endif

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<html>
<head>
<meta http-equiv="refresh" content="0; URL=doc/html/index.html">
</head>
<body>
Automatic redirection failed, please go to
<a href="doc/html/index.html">doc/index.html</a>.&nbsp;<hr>
<p><EFBFBD> Copyright Beman Dawes, 2001</p>
<p>Distributed under the Boost Software License, Version 1.0. (See accompanying
file <a href="../../../LICENSE_1_0.txt">LICENSE_1_0.txt</a> or copy
at <a href="http://www.boost.org/LICENSE_1_0.txt">www.boost.org/LICENSE_1_0.txt</a>)</p>
</body>
</html>

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{
"key": "numeric/conversion",
"name": "Numeric Conversion",
"authors": [
"Fernando Cacciola"
],
"description": "Optimized Policy-based Numeric Conversions.",
"category": [
"Math",
"Miscellaneous"
],
"maintainers": [
"Fernando Cacciola <fernando_cacciola -at- ciudad.com.ar>",
"Brandon Kohn <blkohn -at- hotmail.com>"
],
"cxxstd": "03"
}

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# Boost Numeric Conversion Library test Jamfile
#
# Copyright (C) 2003, Fernando Luis Cacciola Carballal.
#
# 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)
#
# import testing ;
project numeric_conversion_unit_tests
:
requirements
<include>.
<toolset>gcc:<cxxflags>"-ftemplate-depth-300 -g0"
<toolset>darwin:<cxxflags>"-ftemplate-depth-300 -g0"
;
test-suite minimal
:
[ run bounds_test.cpp ]
[ run traits_test.cpp : : : <toolset>msvc:<cxxflags>/bigobj ]
[ run converter_test.cpp ]
[ run udt_support_test.cpp ]
[ run numeric_cast_test.cpp ]
[ run udt_example_0.cpp ]
[ run numeric_cast_traits_test.cpp ]
;
test-suite full
:
minimal
[ compile-fail compile_fail/built_in_numeric_cast_traits.cpp ]
;
test-suite extra ;
explicit minimal ;
explicit extra ;
# support the old test target
test-suite numeric/conversion : full ;

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#include<typeinfo>
#include<iostream>
#include<iomanip>
#include "boost/numeric/conversion/bounds.hpp"
#ifdef BOOST_BORLANDC
#pragma hdrstop
#endif
#include "test_helpers.cpp"
using namespace std ;
using namespace boost ;
using namespace numeric ;
// Test the fields of boost::numeric::bounds<> against the expected values.
//
template<class T>
void test_bounds( T expected_lowest, T expected_highest, T expected_smallest )
{
T lowest = bounds<T>::lowest () ;
T highest = bounds<T>::highest () ;
T smallest = bounds<T>::smallest() ;
BOOST_TEST_EQ(lowest, expected_lowest);
BOOST_TEST_EQ(highest, expected_highest);
BOOST_TEST_EQ(smallest, expected_smallest);
}
template<class T>
void test_bounds_integer( MATCH_FNTPL_ARG(T) )
{
test_bounds( numeric_limits<T>::min BOOST_PREVENT_MACRO_SUBSTITUTION()
, numeric_limits<T>::max BOOST_PREVENT_MACRO_SUBSTITUTION()
, static_cast<T>(1)
) ;
}
template<class T>
void test_bounds_float( MATCH_FNTPL_ARG(T))
{
test_bounds( -numeric_limits<T>::max BOOST_PREVENT_MACRO_SUBSTITUTION ()
, numeric_limits<T>::max BOOST_PREVENT_MACRO_SUBSTITUTION ()
, numeric_limits<T>::min BOOST_PREVENT_MACRO_SUBSTITUTION ()
) ;
}
void test_bounds_integers()
{
test_bounds_integer( SET_FNTPL_ARG(unsigned char) ) ;
test_bounds_integer( SET_FNTPL_ARG(signed char) ) ;
test_bounds_integer( SET_FNTPL_ARG(char) ) ;
test_bounds_integer( SET_FNTPL_ARG(unsigned short) ) ;
test_bounds_integer( SET_FNTPL_ARG(short) ) ;
test_bounds_integer( SET_FNTPL_ARG(unsigned int) ) ;
test_bounds_integer( SET_FNTPL_ARG(int) ) ;
test_bounds_integer( SET_FNTPL_ARG(unsigned long) ) ;
test_bounds_integer( SET_FNTPL_ARG(long) ) ;
}
void test_bounds_floats()
{
test_bounds_float( SET_FNTPL_ARG(float) );
test_bounds_float( SET_FNTPL_ARG(double) );
test_bounds_float( SET_FNTPL_ARG(long double) );
}
void test_bounds()
{
test_bounds_integers() ;
test_bounds_floats () ;
}
int main( )
{
cout << setprecision( std::numeric_limits<long double>::digits10 ) ;
test_bounds();
return boost::report_errors();
}

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//
//! Copyright (c) 2011
//! Brandon Kohn
//
// 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)
//
#include <boost/operators.hpp>
#include <boost/numeric/conversion/cast.hpp>
#include <boost/preprocessor/control/iif.hpp>
#include <boost/preprocessor/comparison/less.hpp>
#include <boost/preprocessor/comparison/not_equal.hpp>
#include <boost/preprocessor/repetition/for.hpp>
#include <boost/preprocessor/tuple/elem.hpp>
#include <boost/preprocessor/seq/elem.hpp>
#include <boost/preprocessor/seq/size.hpp>
//! Generate default traits for the specified source and target.
#define BOOST_NUMERIC_CONVERSION_GENERATE_CAST_TRAITS(r, state) \
template <> \
struct numeric_cast_traits< \
BOOST_PP_SEQ_ELEM( BOOST_PP_TUPLE_ELEM(4,0,state) \
, BOOST_PP_TUPLE_ELEM(4,3,state) ) \
, BOOST_PP_TUPLE_ELEM(4,2,state)> \
{ \
typedef def_overflow_handler overflow_policy; \
typedef UseInternalRangeChecker range_checking_policy; \
typedef Trunc<BOOST_PP_TUPLE_ELEM(4,2,state)> rounding_policy; \
}; \
/***/
#define BOOST_NUMERIC_CONVERSION_TUPLE_SENTINAL(r, state) \
BOOST_PP_LESS \
( \
BOOST_PP_TUPLE_ELEM(4,0,state) \
, BOOST_PP_TUPLE_ELEM(4,1,state) \
) \
/***/
#define BOOST_NUMERIC_CONVERSION_INC_OP(r, state) \
( \
BOOST_PP_INC(BOOST_PP_TUPLE_ELEM(4,0,state)) \
, BOOST_PP_TUPLE_ELEM(4,1,state) \
, BOOST_PP_TUPLE_ELEM(4,2,state) \
, BOOST_PP_TUPLE_ELEM(4,3,state) \
) \
/***/
#define BOOST_NUMERIC_CONVERSION_GENERATE_CAST_TARGET_STEP(r, state) \
BOOST_PP_FOR \
( \
( \
0 \
, BOOST_PP_TUPLE_ELEM(4,1,state) \
, BOOST_PP_SEQ_ELEM(BOOST_PP_TUPLE_ELEM(4,0,state),BOOST_PP_TUPLE_ELEM(4,2,state)) \
, BOOST_PP_TUPLE_ELEM(4,2,state) \
) \
, BOOST_NUMERIC_CONVERSION_TUPLE_SENTINAL \
, BOOST_NUMERIC_CONVERSION_INC_OP \
, BOOST_NUMERIC_CONVERSION_GENERATE_CAST_TRAITS \
) \
/***/
#define BOOST_NUMERIC_CONVERSION_GENERATE_BUILTIN_CAST_TRAITS(types) \
BOOST_PP_FOR \
( \
(0,BOOST_PP_SEQ_SIZE(types),types,_) \
, BOOST_NUMERIC_CONVERSION_TUPLE_SENTINAL \
, BOOST_NUMERIC_CONVERSION_INC_OP \
, BOOST_NUMERIC_CONVERSION_GENERATE_CAST_TARGET_STEP \
) \
/***/
namespace boost { namespace numeric {
#if !defined( BOOST_NO_INT64_T )
//! Generate the specializations for the built-in types.
BOOST_NUMERIC_CONVERSION_GENERATE_BUILTIN_CAST_TRAITS
(
(char)
(boost::int8_t)
(boost::uint8_t)
(boost::int16_t)
(boost::uint16_t)
(boost::int32_t)
(boost::uint32_t)
(boost::int64_t)
(boost::uint64_t)
(float)
(double)
(long double)
)
#else
BOOST_NUMERIC_CONVERSION_GENERATE_BUILTIN_CAST_TRAITS
(
(char)
(boost::int8_t)
(boost::uint8_t)
(boost::int16_t)
(boost::uint16_t)
(boost::int32_t)
(boost::uint32_t)
(float)
(double)
(long double)
)
#endif
}}//namespace boost::numeric;
#undef BOOST_NUMERIC_CONVERSION_GENERATE_BUILTIN_CAST_TRAITS
#undef BOOST_NUMERIC_CONVERSION_GENERATE_CAST_TARGET_STEP
#undef BOOST_NUMERIC_CONVERSION_INC_OP
#undef BOOST_NUMERIC_CONVERSION_TUPLE_SENTINAL
#undef BOOST_NUMERIC_CONVERSION_GENERATE_CAST_TRAITS

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// (c) Copyright Fernando Luis Cacciola Carballal 2000-2004
// Use, modification, and distribution is subject to 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)
// See library home page at http://www.boost.org/libs/numeric/conversion
//
// Contact the author at: fernando_cacciola@hotmail.com
//
#include<cstdlib>
#include<iostream>
#include<iomanip>
#include<string>
#include<typeinfo>
#include<vector>
#include<algorithm>
#include "boost/config.hpp"
#include "boost/cstdint.hpp"
#include "boost/utility.hpp"
//
// Borland 5.5 lacks the following math overloads
//
#if BOOST_WORKAROUND(BOOST_BORLANDC, <= 0x551)
namespace std
{
inline float ceil (float x) { return std::ceil ( static_cast<double>(x)); }
inline float floor (float x) { return std::floor ( static_cast<double>(x)); }
inline long double ceil (long double x) { return std::ceill (x); }
inline long double floor (long double x) { return std::floorl(x); }
} // namespace std
#endif
#include "boost/numeric/conversion/converter.hpp"
#include "boost/numeric/conversion/cast.hpp"
#ifdef BOOST_BORLANDC
#pragma hdrstop
#endif
#include "test_helpers.cpp"
#include "test_helpers2.cpp"
#include "test_helpers3.cpp"
#include "boost/mpl/alias.hpp"
using std::cout ;
// A generic 'abs' function.
template<class N> inline N absG ( N v )
{
return v < static_cast<N>(0) ? static_cast<N>(-v) : v ;
}
template<> inline unsigned char absG<unsigned char> ( unsigned char v ) { return v ; }
template<> inline unsigned short absG<unsigned short> ( unsigned short v ) { return v ; }
template<> inline unsigned int absG<unsigned int> ( unsigned int v ) { return v ; }
template<> inline unsigned long absG<unsigned long> ( unsigned long v ) { return v ; }
template<class T> inline void unused_variable ( T const& ) {}
//
// The following function excersizes specific conversions that cover
// usual and boundary cases for each relevant combination.
//
void test_conversions()
{
using namespace boost ;
using namespace numeric ;
// To help the test found possible bugs a random numbers are used.
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::rand ;
#endif
boost::int16_t v16 ;
boost::uint16_t uv16 ;
boost::int32_t v32 ;
boost::uint32_t uv32 ;
volatile float fv ; // avoid this to be cached internally in some fpu register
volatile double dv ; // avoid this to be cached internally in some fpu register
//
// sample (representative) conversions:
//
cout << "Testing representative conversions\n";
// integral to integral
// signed to signed
// not subranged
v16 = static_cast<boost::int16_t>(rand());
TEST_SUCCEEDING_CONVERSION_DEF(boost::int32_t,boost::int16_t,v16,v16);
// subranged
v16 = static_cast<boost::int16_t>(rand());
TEST_SUCCEEDING_CONVERSION_DEF(boost::int16_t,boost::int32_t,v16,v16);
TEST_POS_OVERFLOW_CONVERSION_DEF(boost::int16_t,boost::int32_t,bounds<boost::int16_t>::highest() + boost::int32_t(1) ) ;
TEST_NEG_OVERFLOW_CONVERSION_DEF(boost::int16_t,boost::int32_t,bounds<boost::int16_t>::lowest() - boost::int32_t(1) ) ;
// signed to unsigned
// subranged
v32 = absG(static_cast<boost::int32_t>(rand()));
v16 = absG(static_cast<boost::int16_t>(rand()));
TEST_SUCCEEDING_CONVERSION_DEF(boost::uint32_t,boost::int32_t,v32,v32);
TEST_SUCCEEDING_CONVERSION_DEF(boost::uint16_t,boost::int32_t,v16,v16);
TEST_POS_OVERFLOW_CONVERSION_DEF(boost::uint16_t,boost::int32_t,bounds<boost::uint16_t>::highest() + boost::int32_t(1) ) ;
TEST_NEG_OVERFLOW_CONVERSION_DEF(boost::uint32_t,boost::int32_t,boost::int32_t(-1) ) ;
// unsigned to signed
// not subranged
v32 = absG(static_cast<boost::int32_t>(rand()));
TEST_SUCCEEDING_CONVERSION_DEF(boost::int32_t,boost::uint32_t,v32,v32);
// subranged
v16 = absG(static_cast<boost::int16_t>(rand()));
TEST_SUCCEEDING_CONVERSION_DEF(boost::int16_t,boost::uint32_t,v16,v16);
TEST_POS_OVERFLOW_CONVERSION_DEF(boost::int32_t,boost::uint32_t,bounds<boost::uint32_t>::highest() ) ;
TEST_POS_OVERFLOW_CONVERSION_DEF(boost::int16_t,boost::uint32_t,bounds<boost::uint32_t>::highest() ) ;
// unsigned to unsigned
// not subranged
uv16 = static_cast<boost::uint16_t>(rand());
TEST_SUCCEEDING_CONVERSION_DEF(boost::uint32_t,boost::uint16_t,uv16,uv16);
// subranged
uv16 = static_cast<boost::uint16_t>(rand());
TEST_SUCCEEDING_CONVERSION_DEF(boost::uint16_t,boost::uint32_t,uv16,uv16);
TEST_POS_OVERFLOW_CONVERSION_DEF(boost::uint16_t,boost::uint32_t,bounds<boost::uint32_t>::highest() ) ;
// integral to float
// from signed integral
v32 = static_cast<boost::int32_t>(rand());
TEST_SUCCEEDING_CONVERSION_DEF(double,boost::int32_t,v32,v32);
// from uint32_tegral
uv32 = static_cast<boost::uint32_t>(rand());
TEST_SUCCEEDING_CONVERSION_DEF(double,boost::uint32_t,uv32,uv32);
// float to integral
// to signed integral
v32 = static_cast<boost::int32_t>(rand());
TEST_SUCCEEDING_CONVERSION_DEF(boost::int32_t,double,v32,v32);
dv = static_cast<double>(bounds<boost::uint32_t>::highest()) + 1.0 ;
TEST_POS_OVERFLOW_CONVERSION_DEF(boost::int32_t,double,dv) ;
TEST_NEG_OVERFLOW_CONVERSION_DEF(boost::int32_t,double,-dv) ;
// float to float
// not subranged
fv = static_cast<float>(rand()) / static_cast<float>(3) ;
TEST_SUCCEEDING_CONVERSION_DEF(double,float,fv,fv);
// subranged
fv = static_cast<float>(rand()) / static_cast<float>(3) ;
TEST_SUCCEEDING_CONVERSION_DEF(float,double,fv,fv);
TEST_POS_OVERFLOW_CONVERSION_DEF(float,double,bounds<double>::highest()) ;
TEST_NEG_OVERFLOW_CONVERSION_DEF(float,double,bounds<double>::lowest ()) ;
}
// Custom OverflowHandler
struct custom_overflow_handler
{
void operator() ( boost::numeric::range_check_result r )
{
if ( r == boost::numeric::cNegOverflow )
cout << "negative_overflow detected!\n" ;
else if ( r == boost::numeric::cPosOverflow )
cout << "positive_overflow detected!\n" ;
}
} ;
template<class T, class S,class OverflowHandler>
void test_overflow_handler( MATCH_FNTPL_ARG(T), MATCH_FNTPL_ARG(S), MATCH_FNTPL_ARG(OverflowHandler),
PostCondition pos,
PostCondition neg
)
{
typedef boost::numeric::conversion_traits<T,S> traits ;
typedef boost::numeric::converter<T,S,traits,OverflowHandler> converter ;
static const S psrc = boost::numeric::bounds<S>::highest();
static const S nsrc = boost::numeric::bounds<S>::lowest ();
static const T pres = static_cast<T>(psrc);
static const T nres = static_cast<T>(nsrc);
test_conv_base ( ConversionInstance<converter>(pres,psrc,pos) ) ;
test_conv_base ( ConversionInstance<converter>(nres,nsrc,neg) ) ;
}
template<class T, class S>
void test_overflow_handlers( MATCH_FNTPL_ARG(T), MATCH_FNTPL_ARG(S) )
{
cout << "Testing Silent Overflow Handler policy\n";
test_overflow_handler( SET_FNTPL_ARG(T),
SET_FNTPL_ARG(S),
SET_FNTPL_ARG(boost::numeric::silent_overflow_handler),
c_converted,
c_converted
) ;
cout << "Testing Default Overflow Handler policy\n";
test_overflow_handler( SET_FNTPL_ARG(T),
SET_FNTPL_ARG(S),
SET_FNTPL_ARG(boost::numeric::def_overflow_handler),
c_pos_overflow,
c_neg_overflow
) ;
cout << "Testing Custom (User-Defined) Overflow Handler policy\n";
test_overflow_handler( SET_FNTPL_ARG(T),
SET_FNTPL_ARG(S),
SET_FNTPL_ARG(custom_overflow_handler),
c_converted,
c_converted
) ;
}
// For a given float-type number 'n' of integer value (n.0), check the conversions
// within the range [n-1,n+1] taking values at: (n-1,n-0.5,n,n+0.5,n+1).
// For each sampled value there is an expected result and a PostCondition according to the
// specified round_style.
//
template<class T, class S, class Float2IntRounder>
void test_rounding_conversion ( MATCH_FNTPL_ARG(T), MATCH_FNTPL_ARG(Float2IntRounder),
S s,
PostCondition resl1,
PostCondition resl0,
PostCondition res,
PostCondition resr0,
PostCondition resr1
)
{
typedef boost::numeric::conversion_traits<T,S> Traits ;
typedef boost::numeric::converter<T,S, Traits, boost::numeric::def_overflow_handler,Float2IntRounder>
Converter ;
S sl1 = s - static_cast<S>(1);
S sl0 = s - static_cast<S>(0.5);
S sr0 = s + static_cast<S>(0.5);
S sr1 = s + static_cast<S>(1);
T tl1 = static_cast<T>( Converter::nearbyint(sl1) );
T tl0 = static_cast<T>( Converter::nearbyint(sl0) );
T t = static_cast<T>( Converter::nearbyint(s) );
T tr0 = static_cast<T>( Converter::nearbyint(sr0) );
T tr1 = static_cast<T>( Converter::nearbyint(sr1) );
test_conv_base ( ConversionInstance<Converter>(tl1,sl1,resl1) ) ;
test_conv_base ( ConversionInstance<Converter>(tl0,sl0,resl0) ) ;
test_conv_base ( ConversionInstance<Converter>(t,s,res) ) ;
test_conv_base ( ConversionInstance<Converter>(tr0,sr0,resr0) ) ;
test_conv_base ( ConversionInstance<Converter>(tr1,sr1,resr1) ) ;
}
template<class T,class S>
void test_round_style( MATCH_FNTPL_ARG(T), MATCH_FNTPL_ARG(S) )
{
S min = boost::numeric::bounds<T>::lowest();
S max = boost::numeric::bounds<T>::highest();
cout << "Testing 'Trunc' Float2IntRounder policy\n";
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::Trunc<S>),
min,
c_neg_overflow,
c_converted,
c_converted,
c_converted,
c_converted
) ;
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::Trunc<S>),
max,
c_converted,
c_converted,
c_converted,
c_converted,
c_pos_overflow
) ;
cout << "Testing 'RoundEven' Float2IntRounder policy\n";
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::RoundEven<S>),
min,
c_neg_overflow,
c_converted,
c_converted,
c_converted,
c_converted
) ;
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::RoundEven<S>),
max,
c_converted,
c_converted,
c_converted,
c_pos_overflow,
c_pos_overflow
) ;
cout << "Testing 'Ceil' Float2IntRounder policy\n";
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::Ceil<S>),
min,
c_neg_overflow,
c_converted,
c_converted,
c_converted,
c_converted
) ;
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::Ceil<S>),
max,
c_converted,
c_converted,
c_converted,
c_pos_overflow,
c_pos_overflow
) ;
cout << "Testing 'Floor' Float2IntRounder policy\n" ;
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::Floor<S>),
min,
c_neg_overflow,
c_neg_overflow,
c_converted,
c_converted,
c_converted
) ;
test_rounding_conversion(SET_FNTPL_ARG(T),
SET_FNTPL_ARG(boost::numeric::Floor<S>),
max,
c_converted,
c_converted,
c_converted,
c_converted,
c_pos_overflow
) ;
}
void test_round_even( double n, double x )
{
double r = boost::numeric::RoundEven<double>::nearbyint(n);
BOOST_TEST( r == x ) ;
}
void test_round_even()
{
cout << "Testing 'RoundEven' tie-breaking\n";
double min = boost::numeric::bounds<double>::lowest();
double max = boost::numeric::bounds<double>::highest();
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::floor ;
using std::ceil ;
#endif
test_round_even(min, floor(min));
test_round_even(max, ceil (max));
test_round_even(2.0, 2.0);
test_round_even(2.3, 2.0);
test_round_even(2.5, 2.0);
test_round_even(2.7, 3.0);
test_round_even(3.0, 3.0);
test_round_even(3.3, 3.0);
test_round_even(3.5, 4.0);
test_round_even(3.7, 4.0);
}
int double_to_int ( double n ) { return static_cast<int>(n) ; }
void test_converter_as_function_object()
{
cout << "Testing converter as function object.\n";
// Create a sample sequence of double values.
std::vector<double> S ;
for ( int i = 0 ; i < 10 ; ++ i )
S.push_back( i * ( 18.0 / 19.0 ) );
// Create a sequence of int values from 's' using the standard conversion.
std::vector<int> W ;
std::transform(S.begin(),S.end(),std::back_inserter(W),double_to_int);
// Create a sequence of int values from s using a default numeric::converter
std::vector<int> I ;
std::transform(S.begin(),
S.end(),
std::back_inserter(I),
boost::numeric::converter<int,double>()
) ;
// Match 'w' and 'i' which should be equal.
bool double_to_int_OK = std::equal(W.begin(),W.end(),I.begin()) ;
BOOST_TEST(double_to_int_OK);
// Create a sequence of double values from s using a default numeric::converter (which should be the trivial conv).
std::vector<double> D ;
std::transform(S.begin(),
S.end(),
std::back_inserter(D),
boost::numeric::converter<double,double>()
) ;
// Match 's' and 'd' which should be equal.
bool double_to_double_OK = std::equal(S.begin(),S.end(),D.begin()) ;
BOOST_TEST(double_to_double_OK);
}
#if BOOST_WORKAROUND(__IBMCPP__, <= 600 ) // VCAPP6
# define UNOPTIMIZED
#else
# define UNOPTIMIZED volatile
#endif
void test_optimizations()
{
using namespace boost;
using namespace numeric;
float fv0 = 18.0f / 19.0f ;
// This code deosn't produce any output.
// It is intended to show the optimization of numeric::converter<> by manual inspection
// of the generated code.
// Each test shows first the equivalent hand-coded version.
// The numeric_cast<> code should be the same if full compiler optimization/inlining is used.
//---------------------------------
// trivial conversion.
//
// equivalent code:
UNOPTIMIZED float fv1a = fv0 ;
float fv1b = numeric_cast<float>(fv0);
unused_variable(fv1a);
unused_variable(fv1b);
//
//---------------------------------
//---------------------------------
// nonsubranged conversion.
//
// equivalent code:
UNOPTIMIZED double dv1a = static_cast<double>(fv0);
double dv1b = numeric_cast<double>(fv0);
unused_variable(dv1a);
unused_variable(dv1b);
//
//---------------------------------
//------------------------------------------------------
// subranged conversion with both-sided range checking.
//
// equivalent code:
{
double const& s = dv1b ;
// range checking
range_check_result r = s < static_cast<double>(bounds<float>::lowest())
? cNegOverflow : cInRange ;
if ( r == cInRange )
{
r = s > static_cast<double>(bounds<float>::highest()) ? cPosOverflow : cInRange ;
}
if ( r == cNegOverflow )
throw negative_overflow() ;
else if ( r == cPosOverflow )
throw positive_overflow() ;
// conversion
UNOPTIMIZED float fv2a = static_cast<float>(s);
unused_variable(fv2a);
}
float fv2b = numeric_cast<float>(dv1b);
unused_variable(fv2b);
//
//---------------------------------
//---------------------------------
// subranged rounding conversion
//
// equivalent code:
{
double const& s = dv1b ;
// range checking
range_check_result r = s <= static_cast<double>(bounds<int>::lowest()) - static_cast<double>(1.0)
? cNegOverflow : cInRange ;
if ( r == cInRange )
{
r = s >= static_cast<double>(bounds<int>::highest()) + static_cast<double>(1.0)
? cPosOverflow : cInRange ;
}
if ( r == cNegOverflow )
throw negative_overflow() ;
else if ( r == cPosOverflow )
throw positive_overflow() ;
// rounding
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::floor ;
#endif
double s1 = floor(dv1b + 0.5);
// conversion
UNOPTIMIZED int iv1a = static_cast<int>(s1);
unused_variable(iv1a);
}
int iv1b = numeric_cast<int>(dv1b);
unused_variable(iv1b);
//
//---------------------------------
}
int main()
{
std::cout << std::setprecision( std::numeric_limits<long double>::digits10 ) ;
test_conversions();
test_overflow_handlers( SET_FNTPL_ARG(boost::int16_t), SET_FNTPL_ARG(boost::int32_t));
test_round_style(SET_FNTPL_ARG(boost::int32_t), SET_FNTPL_ARG(double) ) ;
test_round_even() ;
test_converter_as_function_object();
test_optimizations() ;
return boost::report_errors();
}
//---------------------------------------------------------------------------

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// boost utility cast test program -----------------------------------------//
// (C) Copyright Beman Dawes, Dave Abrahams 1999. 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)
// See http://www.boost.org for most recent version including documentation.
// Revision History
// 28 Set 04 taken from the old cast library (Fernando Cacciola)
#include <iostream>
#include <climits>
#include <cfloat> // for DBL_MAX (Peter Schmid)
#include <boost/numeric/conversion/cast.hpp>
#include <boost/core/lightweight_test.hpp>
# if SCHAR_MAX == LONG_MAX
# error "This test program doesn't work if SCHAR_MAX == LONG_MAX"
# endif
using namespace boost;
using std::cout;
int main()
{
# ifdef NDEBUG
cout << "NDEBUG is defined\n";
# else
cout << "NDEBUG is not defined\n";
# endif
cout << "\nBeginning tests...\n";
// test implicit_cast and numeric_cast -------------------------------------//
// tests which should succeed
long small_value = 1;
long small_negative_value = -1;
long large_value = LONG_MAX;
long large_negative_value = LONG_MIN;
signed char c = 0;
c = large_value; // see if compiler generates warning
c = numeric_cast<signed char>( small_value );
BOOST_TEST( c == 1 );
c = 0;
c = numeric_cast<signed char>( small_value );
BOOST_TEST( c == 1 );
c = 0;
c = numeric_cast<signed char>( small_negative_value );
BOOST_TEST( c == -1 );
// These tests courtesy of Joe R NWP Swatosh<joe.r.swatosh@usace.army.mil>
BOOST_TEST( 0.0f == numeric_cast<float>( 0.0 ) );
BOOST_TEST( 0.0 == numeric_cast<double>( 0.0 ) );
// tests which should result in errors being detected
BOOST_TEST_THROWS( numeric_cast<signed char>(large_value),
numeric::bad_numeric_cast );
BOOST_TEST_THROWS( numeric_cast<signed char>(large_negative_value),
numeric::bad_numeric_cast );
BOOST_TEST_THROWS( numeric_cast<signed char>(large_negative_value),
numeric::bad_numeric_cast );
BOOST_TEST_THROWS( numeric_cast<unsigned long>(small_negative_value),
numeric::bad_numeric_cast );
BOOST_TEST_THROWS( numeric_cast<int>(DBL_MAX), numeric::bad_numeric_cast );
return boost::report_errors() ;
} // main

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//
//! Copyright (c) 2011
//! Brandon Kohn
//
// 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)
//
#include <boost/operators.hpp>
#include <boost/numeric/conversion/cast.hpp>
#include <boost/mpl/for_each.hpp>
#include <boost/mpl/vector.hpp>
#include <boost/cstdint.hpp>
#include <boost/core/lightweight_test.hpp>
#include <boost/static_assert.hpp>
//! Define a simple custom number
struct Double
{
Double()
: v(0)
{}
template <typename T>
explicit Double( T v )
: v(static_cast<double>(v))
{}
template <typename T>
Double& operator= ( T t )
{
v = static_cast<double>(t);
return *this;
}
bool operator < ( const Double& rhs ) const
{
return v < rhs.v;
}
template <typename T>
bool operator < ( T rhs ) const
{
return v < static_cast<double>(rhs);
}
template <typename LHS>
friend bool operator < ( const LHS& lhs, const Double& rhs )
{
return lhs < rhs.v;
}
bool operator > ( const Double& rhs ) const
{
return v > rhs.v;
}
template <typename LHS>
friend bool operator > ( const LHS& lhs, const Double& rhs )
{
return lhs > rhs.v;
}
template <typename T>
bool operator > ( T rhs ) const
{
return v > static_cast<double>(rhs);
}
bool operator == ( const Double& rhs ) const
{
return v == rhs.v;
}
template <typename T>
bool operator == ( T rhs ) const
{
return v == static_cast<double>(rhs);
}
template <typename LHS>
friend bool operator == ( const LHS& lhs, const Double& rhs )
{
return lhs == rhs.v;
}
bool operator !() const
{
return v == 0;
}
Double operator -() const
{
return Double(-v);
}
Double& operator +=( const Double& t )
{
v += t.v;
return *this;
}
template <typename T>
Double& operator +=( T t )
{
v += static_cast<double>(t);
return *this;
}
Double& operator -=( const Double& t )
{
v -= t.v;
return *this;
}
template <typename T>
Double& operator -=( T t )
{
v -= static_cast<double>(t);
return *this;
}
Double& operator *= ( const Double& factor )
{
v *= factor.v;
return *this;
}
template <typename T>
Double& operator *=( T t )
{
v *= static_cast<double>(t);
return *this;
}
Double& operator /= (const Double& divisor)
{
v /= divisor.v;
return *this;
}
template <typename T>
Double& operator /=( T t )
{
v /= static_cast<double>(t);
return (*this);
}
double v;
};
//! Define numeric_limits for the custom type.
namespace std
{
template<>
class numeric_limits< Double > : public numeric_limits<double>
{
public:
//! Limit our Double to a range of +/- 100.0
static Double (min)()
{
return Double(1.e-2);
}
static Double (max)()
{
return Double(1.e2);
}
static Double epsilon()
{
return Double( std::numeric_limits<double>::epsilon() );
}
};
}
//! Define range checking and overflow policies.
namespace custom
{
//! Define a custom range checker
template<typename Traits, typename OverFlowHandler>
struct range_checker
{
typedef typename Traits::argument_type argument_type ;
typedef typename Traits::source_type S;
typedef typename Traits::target_type T;
//! Check range of integral types.
static boost::numeric::range_check_result out_of_range( argument_type s )
{
using namespace boost::numeric;
if( s > bounds<T>::highest() )
return cPosOverflow;
else if( s < bounds<T>::lowest() )
return cNegOverflow;
else
return cInRange;
}
static void validate_range ( argument_type s )
{
BOOST_STATIC_ASSERT( std::numeric_limits<T>::is_bounded );
OverFlowHandler()( out_of_range(s) );
}
};
//! Overflow handler
struct positive_overflow{};
struct negative_overflow{};
struct overflow_handler
{
void operator() ( boost::numeric::range_check_result r )
{
using namespace boost::numeric;
if( r == cNegOverflow )
throw negative_overflow() ;
else if( r == cPosOverflow )
throw positive_overflow() ;
}
};
//! Define a rounding policy and specialize on the custom type.
template<class S>
struct Ceil : boost::numeric::Ceil<S>{};
template<>
struct Ceil<Double>
{
typedef Double source_type;
typedef Double const& argument_type;
static source_type nearbyint ( argument_type s )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::ceil ;
#endif
return Double( ceil(s.v) );
}
typedef boost::mpl::integral_c< std::float_round_style, std::round_toward_infinity> round_style;
};
//! Define a rounding policy and specialize on the custom type.
template<class S>
struct Trunc: boost::numeric::Trunc<S>{};
template<>
struct Trunc<Double>
{
typedef Double source_type;
typedef Double const& argument_type;
static source_type nearbyint ( argument_type s )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
using std::floor;
#endif
return Double( floor(s.v) );
}
typedef boost::mpl::integral_c< std::float_round_style, std::round_toward_zero> round_style;
};
}//namespace custom;
namespace boost { namespace numeric {
//! Define the numeric_cast_traits specializations on the custom type.
template <typename S>
struct numeric_cast_traits<Double, S>
{
typedef custom::overflow_handler overflow_policy;
typedef custom::range_checker
<
boost::numeric::conversion_traits<Double, S>
, overflow_policy
> range_checking_policy;
typedef boost::numeric::Trunc<S> rounding_policy;
};
template <typename T>
struct numeric_cast_traits<T, Double>
{
typedef custom::overflow_handler overflow_policy;
typedef custom::range_checker
<
boost::numeric::conversion_traits<T, Double>
, overflow_policy
> range_checking_policy;
typedef custom::Trunc<Double> rounding_policy;
};
//! Define the conversion from the custom type to built-in types and vice-versa.
template<typename T>
struct raw_converter< conversion_traits< T, Double > >
{
static T low_level_convert ( const Double& n )
{
return static_cast<T>( n.v );
}
};
template<typename S>
struct raw_converter< conversion_traits< Double, S > >
{
static Double low_level_convert ( const S& n )
{
return Double(n);
}
};
}}//namespace boost::numeric;
#define BOOST_TEST_CATCH_CUSTOM_POSITIVE_OVERFLOW( CastCode ) \
BOOST_TEST_THROWS( CastCode, custom::positive_overflow )
/***/
#define BOOST_TEST_CATCH_CUSTOM_NEGATIVE_OVERFLOW( CastCode ) \
BOOST_TEST_THROWS( CastCode, custom::negative_overflow )
/***/
struct test_cast_traits
{
template <typename T>
void operator()(T) const
{
Double d = boost::numeric_cast<Double>( static_cast<T>(50) );
BOOST_TEST( d.v == 50. );
T v = boost::numeric_cast<T>( d );
BOOST_TEST( v == 50 );
}
};
void test_numeric_cast_traits()
{
typedef boost::mpl::vector
<
boost::int8_t
, boost::uint8_t
, boost::int16_t
, boost::uint16_t
, boost::int32_t
, boost::uint32_t
#if !defined( BOOST_NO_INT64_T )
, boost::int64_t
, boost::uint64_t
#endif
, float
, double
, long double
> types;
boost::mpl::for_each<types>( test_cast_traits() );
//! Check overflow handler.
Double d( 56.0 );
BOOST_TEST_CATCH_CUSTOM_POSITIVE_OVERFLOW( d = boost::numeric_cast<Double>( 101 ) );
BOOST_TEST( d.v == 56. );
BOOST_TEST_CATCH_CUSTOM_NEGATIVE_OVERFLOW( d = boost::numeric_cast<Double>( -101 ) );
BOOST_TEST( d.v == 56.);
//! Check custom round policy.
d = 5.9;
int five = boost::numeric_cast<int>( d );
BOOST_TEST( five == 5 );
}
int main()
{
test_numeric_cast_traits();
return boost::report_errors();
}
#undef BOOST_TEST_CATCH_CUSTOM_POSITIVE_OVERFLOW
#undef BOOST_TEST_CATCH_CUSTOM_NEGATIVE_OVERFLOW

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// Copyright (C) 2003, Fernando Luis Cacciola Carballal.
//
// 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)
//
//
// NOTE: This file is intended to be used ONLY by the test files
// from the Numeric Conversions Library
//
//
#include <cmath>
#include "boost/limits.hpp"
#include "boost/utility.hpp"
#include <boost/core/lightweight_test.hpp>
// Convenience macros to help with compilers which don't parse
// explicit template function instantiations (MSVC6)
#define MATCH_FNTPL_ARG(t) t const*
#define SET_FNTPL_ARG(t) (static_cast< t const* >(0))
//
// *Minimal* example of a User Defined Numeric Type
//
//
namespace MyUDT
{
template<class T>
struct UDT
{
typedef T builtin_type ;
UDT ( T v_ ) : v (v_) {}
T to_builtin() const { return v ; }
friend bool operator == ( UDT const& lhs, UDT const& rhs )
{ return lhs.to_builtin() == rhs.to_builtin() ; }
// NOTE: This operator is *required* by the Numeric Conversion Library
// if Turnc<> is used as the Float2IntRounder policy.
friend bool operator < ( UDT const& lhs, UDT const& rhs )
{ return lhs.to_builtin() < rhs.to_builtin() ; }
friend std::ostream& operator << ( std::ostream& os, UDT const& n )
{ return os << n.to_builtin() ; }
T v ;
} ;
typedef UDT<int> MyInt ;
typedef UDT<double> MyFloat ;
//
// The Float2IntRounder policies *require* a visible 'ceil' or 'floor' math function
// with standard semantics.
// In a conformant compiler, ADL can pick these functions even if they are defined
// within a user namespace, as below.
//
inline MyInt ceil ( MyInt const& x ) { return x ; }
inline MyInt floor ( MyInt const& x ) { return x ; }
inline MyFloat floor ( MyFloat const& x )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
return MyFloat ( std::floor(x.to_builtin()) ) ;
#else
return MyFloat ( ::floor(x.to_builtin()) ) ;
#endif
}
inline MyFloat ceil ( MyFloat const& x )
{
#if !defined(BOOST_NO_STDC_NAMESPACE)
return MyFloat ( std::ceil(x.to_builtin()) ) ;
#else
return MyFloat ( ::ceil(x.to_builtin()) ) ;
#endif
}
} // namespace MyUDT
//
// The Numeric Conversion Library *requires* User Defined Numeric Types
// to properly specialize std::numeric_limits<>
//
namespace std
{
template<>
class numeric_limits<MyUDT::MyInt> : public numeric_limits<int>
{
public :
BOOST_STATIC_CONSTANT(bool, is_specialized = false);
} ;
template<>
class numeric_limits<MyUDT::MyFloat> : public numeric_limits<double>
{
public :
BOOST_STATIC_CONSTANT(bool, is_specialized = false);
} ;
} // namespace std
//
// The functions floor and ceil defined within namespace MyUDT
// should be found by koenig loopkup, but some compilers don't do it right
// so we inyect them into namespace std so ordinary overload resolution
// can found them.
#if defined(BOOST_NO_ARGUMENT_DEPENDENT_LOOKUP) || defined(BOOST_BORLANDC) || defined(__GNUC__)
namespace std {
using MyUDT::floor ;
using MyUDT::ceil ;
} // namespace std
#endif
std::string to_string( bool arg )
{
return arg ? "true" : "false" ;
}
std::string to_string( ... ) { throw std::runtime_error("to_string() called with wrong type!") ; }
//
// This is used to print 'char' values as numbers instead of characters.
//
template<class T> struct printable_number_type { typedef T type ; } ;
template<> struct printable_number_type<signed char> { typedef int type ; } ;
template<> struct printable_number_type<unsigned char> { typedef unsigned type ; } ;
template<> struct printable_number_type<char> { typedef int type ; } ;
template<class T>
inline
typename printable_number_type<T>::type
printable( T n ) { return n ; }
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// Copyright (C) 2003, Fernando Luis Cacciola Carballal.
//
// 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)
//
//
// NOTE: This file is intended to be used ONLY by the test files
// from the Numeric Conversions Library
//
//
// The following 'to_string' helpers are provided to give readable names
// to the various enums used by the library.
// NOTE: specializations of boost::lexical_cast<> were not used since some compilers had
// trouble dealing with such specializations for different enumerations.
//
std::string to_string ( boost::numeric::int_float_mixture_enum arg )
{
switch ( arg )
{
case boost::numeric::integral_to_integral : return "integral_to_integral" ;
case boost::numeric::integral_to_float : return "integral_to_float" ;
case boost::numeric::float_to_integral : return "float_to_integral" ;
case boost::numeric::float_to_float : return "float_to_float" ;
}
return "(Unknown result!)" ;
}
std::string to_string ( boost::numeric::sign_mixture_enum arg )
{
switch ( arg )
{
case boost::numeric::unsigned_to_unsigned : return "unsigned_to_unsigned" ;
case boost::numeric::signed_to_signed : return "signed_to_signed" ;
case boost::numeric::signed_to_unsigned : return "signed_to_unsigned" ;
case boost::numeric::unsigned_to_signed : return "unsigned_to_signed" ;
}
return "(Unknown result!)" ;
}
std::string to_string ( boost::numeric::udt_builtin_mixture_enum arg )
{
switch ( arg )
{
case boost::numeric::builtin_to_builtin : return "builtin_to_builtin" ;
case boost::numeric::builtin_to_udt : return "builtin_to_udt" ;
case boost::numeric::udt_to_builtin : return "udt_to_builtin" ;
case boost::numeric::udt_to_udt : return "udt_to_udt" ;
}
return "(Unknown result!)" ;
}
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// Copyright (C) 2003, Fernando Luis Cacciola Carballal.
//
// 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)
//
//
// NOTE: This file is intended to be used ONLY by the test files
// from the Numeric Conversions Library
//
// The conversion test is performed using a class whose instances encapsulate
// a particular specific conversion defnied explicitely.
// A ConversionInstance object includes the source type, the target type,
// the source value and the expected result, including possible exceptions.
//
enum PostCondition { c_converted, c_overflow, c_neg_overflow, c_pos_overflow } ;
template<class Converter>
struct ConversionInstance
{
typedef Converter converter ;
typedef typename Converter::argument_type argument_type ;
typedef typename Converter::result_type result_type ;
typedef typename Converter::traits traits ;
typedef typename traits::target_type target_type ;
typedef typename traits::source_type source_type ;
ConversionInstance ( result_type a_result, argument_type a_source, PostCondition a_post)
:
source(a_source),
result(a_result),
post(a_post)
{}
std::string to_string() const
{
return std::string("converter<")
+ typeid(target_type).name()
+ std::string(",")
+ typeid(source_type).name()
+ std::string(">::convert(") ;
}
argument_type source ;
result_type result ;
PostCondition post ;
} ;
//
// Main conversion test point.
// Exercises a specific conversion described by 'conv'.
//
template<class Instance>
void test_conv_base( Instance const& conv )
{
typedef typename Instance::argument_type argument_type ;
typedef typename Instance::result_type result_type ;
typedef typename Instance::converter converter ;
argument_type source = conv.source ;
try
{
result_type result = converter::convert(source);
if (BOOST_TEST_EQ(conv.post, c_converted))
{
BOOST_TEST_EQ(result, conv.result);
}
}
catch ( boost::numeric::negative_overflow const& )
{
BOOST_TEST_EQ(conv.post, c_neg_overflow);
}
catch ( boost::numeric::positive_overflow const& )
{
BOOST_TEST_EQ(conv.post, c_pos_overflow);
}
catch ( boost::numeric::bad_numeric_cast const& )
{
BOOST_TEST_EQ(conv.post, c_overflow);
}
}
#define TEST_SUCCEEDING_CONVERSION(Conv,typeT,typeS,valueT,valueS) \
test_conv_base( ConversionInstance< Conv >(valueT, valueS, c_converted ) )
#define TEST_POS_OVERFLOW_CONVERSION(Conv,typeT,typeS,valueS) \
test_conv_base( ConversionInstance< Conv >( static_cast< typeT >(0), valueS, c_pos_overflow ) )
#define TEST_NEG_OVERFLOW_CONVERSION(Conv,typeT,typeS,valueS) \
test_conv_base( ConversionInstance< Conv >( static_cast< typeT >(0), valueS, c_neg_overflow ) )
#define DEF_CONVERTER(T,S) boost::numeric::converter< T , S >
#define TEST_SUCCEEDING_CONVERSION_DEF(typeT,typeS,valueT,valueS) \
TEST_SUCCEEDING_CONVERSION( DEF_CONVERTER(typeT,typeS), typeT, typeS, valueT, valueS )
#define TEST_POS_OVERFLOW_CONVERSION_DEF(typeT,typeS,valueS) \
TEST_POS_OVERFLOW_CONVERSION( DEF_CONVERTER(typeT,typeS), typeT, typeS, valueS )
#define TEST_NEG_OVERFLOW_CONVERSION_DEF(typeT,typeS,valueS) \
TEST_NEG_OVERFLOW_CONVERSION( DEF_CONVERTER(typeT,typeS), typeT, typeS, valueS )
//
///////////////////////////////////////////////////////////////////////////////////////////////

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// Copyright (C) 2003, Fernando Luis Cacciola Carballal.
//
// 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)
//
//
#include<iostream>
#include<iomanip>
#include<string>
#include<typeinfo>
#include<vector>
#include<algorithm>
#include <boost/cstdint.hpp>
#include <boost/utility.hpp>
#include <boost/preprocessor/cat.hpp>
#include <boost/numeric/conversion/conversion_traits.hpp>
#include <boost/numeric/conversion/int_float_mixture.hpp>
#include <boost/numeric/conversion/sign_mixture.hpp>
#include <boost/numeric/conversion/udt_builtin_mixture.hpp>
#include <boost/numeric/conversion/is_subranged.hpp>
#ifdef BOOST_BORLANDC
#pragma hdrstop
#endif
#include "test_helpers.cpp"
#include "test_helpers2.cpp"
using namespace std ;
using namespace boost ;
using namespace numeric;
using namespace MyUDT ;
// These helpers are used by generate_expected_traits<T,S>.
// Unlike the similar helpers in the implementation, they are specialized by extension.
//
template<class T, class S> struct my_is_subranged ;
template<class T, class S> struct my_is_trivial ;
template<class T, class S> struct my_int_float_mixture ;
template<class T, class S> struct my_sign_mixture ;
template<class T, class S> struct my_udt_builtin_mixture ;
// This macro is used to define the properties of each conversion between
// the builtin arithmetric types
//
// It defines the specialization of the helper traits used by 'generate_expected_traits'
//
#define DEFINE_CONVERSION(Target,Source,Trivial,Mixture,SignMixture,UdtMixture,SubRanged) \
\
template<> struct my_is_subranged<Target,Source> \
{ typedef mpl::bool_< (SubRanged) > type ; } ; \
\
template<> struct my_is_trivial<Target,Source> \
{ typedef mpl::bool_< (Trivial) > type ; } ; \
\
template<> struct my_int_float_mixture<Target,Source> \
{ typedef mpl::integral_c<boost::numeric::int_float_mixture_enum, (Mixture) > type ; } ; \
\
template<> struct my_sign_mixture<Target,Source> \
{ typedef mpl::integral_c<boost::numeric::sign_mixture_enum, (SignMixture) > type ; } ; \
\
template<> struct my_udt_builtin_mixture<Target,Source> \
{ typedef mpl::integral_c<boost::numeric::udt_builtin_mixture_enum, (UdtMixture) > type ; }
#define cSubRanged true
#define cTrivial true
// The following test assumes a specific relation between the sizes of the types being used;
// therefore, use specific fixed-width types instead built-in types directly.
// NOTE --> TARGET,SOURCE
//
DEFINE_CONVERSION(boost::uint8_t , boost::uint8_t, cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::int8_t , boost::uint8_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , boost::uint8_t, !cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::int16_t , boost::uint8_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , boost::uint8_t, !cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::int32_t , boost::uint8_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(float , boost::uint8_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(double , boost::uint8_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(long double , boost::uint8_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(MyInt , boost::uint8_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , boost::uint8_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , boost::int8_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , boost::int8_t, cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , boost::int8_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int16_t , boost::int8_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , boost::int8_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int32_t , boost::int8_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(float , boost::int8_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(double , boost::int8_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(long double , boost::int8_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(MyInt , boost::int8_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , boost::int8_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , boost::uint16_t, !cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , boost::uint16_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , boost::uint16_t, cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::int16_t , boost::uint16_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , boost::uint16_t, !cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::int32_t , boost::uint16_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(float , boost::uint16_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(double , boost::uint16_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(long double , boost::uint16_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(MyInt , boost::uint16_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , boost::uint16_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , boost::int16_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , boost::int16_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , boost::int16_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int16_t , boost::int16_t, cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , boost::int16_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int32_t , boost::int16_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(float , boost::int16_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(double , boost::int16_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(long double , boost::int16_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(MyInt , boost::int16_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , boost::int16_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , boost::uint32_t, !cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , boost::uint32_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , boost::uint32_t, !cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int16_t , boost::uint32_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , boost::uint32_t, cTrivial, integral_to_integral, unsigned_to_unsigned, builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(boost::int32_t , boost::uint32_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(float , boost::uint32_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(double , boost::uint32_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(long double , boost::uint32_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(MyInt , boost::uint32_t, !cTrivial, integral_to_integral, unsigned_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , boost::uint32_t, !cTrivial, integral_to_float , unsigned_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , boost::int32_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , boost::int32_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , boost::int32_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int16_t , boost::int32_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , boost::int32_t, !cTrivial, integral_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int32_t , boost::int32_t, cTrivial, integral_to_integral, signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(float , boost::int32_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(double , boost::int32_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(long double , boost::int32_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(MyInt , boost::int32_t, !cTrivial, integral_to_integral, signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , boost::int32_t, !cTrivial, integral_to_float , signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , float, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , float, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , float, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int16_t , float, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , float, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int32_t , float, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(float , float, cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(double , float, !cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, ( sizeof(float) > sizeof(double) ) );
DEFINE_CONVERSION(long double , float, !cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, ( sizeof(float) > sizeof(long double) ) );
DEFINE_CONVERSION(MyInt , float, !cTrivial, float_to_integral, signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , float, !cTrivial, float_to_float , signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , double, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , double, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int16_t , double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , double, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int32_t , double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(float , double, !cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, ( sizeof(double) > sizeof(float) ) );
DEFINE_CONVERSION(double , double, cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(long double , double, !cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, ( sizeof(double) > sizeof(long double) ) );
DEFINE_CONVERSION(MyInt , double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , double, !cTrivial, float_to_float , signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , long double, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int8_t , long double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , long double, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int16_t , long double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , long double, !cTrivial, float_to_integral, signed_to_unsigned, builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(boost::int32_t , long double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_builtin, cSubRanged );
DEFINE_CONVERSION(float , long double, !cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, ( sizeof(long double) > sizeof(float) ) );
DEFINE_CONVERSION(double , long double, !cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, ( sizeof(long double) > sizeof(double) ) );
DEFINE_CONVERSION(long double , long double, cTrivial, float_to_float , signed_to_signed , builtin_to_builtin, !cSubRanged );
DEFINE_CONVERSION(MyInt , long double, !cTrivial, float_to_integral, signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(MyFloat , long double, !cTrivial, float_to_float , signed_to_signed , builtin_to_udt , !cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , MyInt, !cTrivial, integral_to_integral, signed_to_unsigned, udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::int8_t , MyInt, !cTrivial, integral_to_integral, signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , MyInt, !cTrivial, integral_to_integral, signed_to_unsigned, udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::int16_t , MyInt, !cTrivial, integral_to_integral, signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , MyInt, !cTrivial, integral_to_integral, signed_to_unsigned, udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::int32_t , MyInt, !cTrivial, integral_to_integral, signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(float , MyInt, !cTrivial, integral_to_float , signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(double , MyInt, !cTrivial, integral_to_float , signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(long double , MyInt, !cTrivial, integral_to_float , signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(MyInt , MyInt, cTrivial, integral_to_integral, signed_to_signed , udt_to_udt ,!cSubRanged );
DEFINE_CONVERSION(MyFloat , MyInt, !cTrivial, integral_to_float , signed_to_signed , udt_to_udt ,!cSubRanged );
DEFINE_CONVERSION(boost::uint8_t , MyFloat, !cTrivial, float_to_integral, signed_to_unsigned, udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::int8_t , MyFloat, !cTrivial, float_to_integral, signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::uint16_t , MyFloat, !cTrivial, float_to_integral, signed_to_unsigned, udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::int16_t , MyFloat, !cTrivial, float_to_integral, signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::uint32_t , MyFloat, !cTrivial, float_to_integral, signed_to_unsigned, udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(boost::int32_t , MyFloat, !cTrivial, float_to_integral, signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(float , MyFloat, !cTrivial, float_to_float , signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(double , MyFloat, !cTrivial, float_to_float , signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(long double , MyFloat, !cTrivial, float_to_float , signed_to_signed , udt_to_builtin , cSubRanged );
DEFINE_CONVERSION(MyInt , MyFloat, !cTrivial, float_to_integral, signed_to_signed , udt_to_udt ,!cSubRanged );
DEFINE_CONVERSION(MyFloat , MyFloat, cTrivial, float_to_float , signed_to_signed , udt_to_udt ,!cSubRanged );
//
// The test is performed by comparing each field of
// boost::numeric::conversion_traits<T,S>
// with the fields of
// expected_traits<T,S>
// which is a traits class constructed explicitely for each combination
// of the built-in arithmetic types.
//
template<class T,
class S,
class Supertype,
class Subtype,
class Subranged,
class Trivial
>
struct expected_traits
{
typedef typename my_int_float_mixture <T,S>::type int_float_mixture ;
typedef typename my_sign_mixture <T,S>::type sign_mixture ;
typedef typename my_udt_builtin_mixture <T,S>::type udt_builtin_mixture ;
typedef Subranged subranged ;
typedef Trivial trivial ;
typedef Supertype supertype ;
typedef Subtype subtype ;
} ;
// This is used by the test engine to generate a expected_traits from T and S.
//
template<class T, class S>
struct generate_expected_traits
{
typedef expected_traits<T, S, T, S, mpl::false_, mpl::true_ > trivial ;
typedef expected_traits<T, S, S, T, mpl::true_ , mpl::false_ > subranged ;
typedef expected_traits<T, S, T, S, mpl::false_, mpl::false_ > non_subranged ;
typedef typename my_is_subranged<T,S>::type IsSubranged ;
typedef typename my_is_trivial <T,S>::type IsTrivial ;
typedef typename mpl::if_<IsSubranged,subranged,non_subranged>::type non_trivial ;
typedef typename mpl::if_<IsTrivial,trivial,non_trivial>::type type ;
} ;
// This macro generates the code that compares a non-type field
// in boost::numeric::conversion_traits<> with its corresponding field
// in expected_traits<>
//
#define TEST_VALUE_FIELD(Name) \
typedef typename traits::Name BOOST_PP_CAT(t,Name) ; \
typedef typename expected::Name BOOST_PP_CAT(x,Name) ; \
BOOST_TEST( ( BOOST_PP_CAT(t,Name)::value == BOOST_PP_CAT(x,Name)::value ) ) ;
// This macro generates the code that compares a type field
// in numeric::conversion_traits<> with its corresponding field
// in expected_traits<>
//
#define TEST_TYPE_FIELD(Name) \
typedef typename traits::Name BOOST_PP_CAT(t,Name) ; \
typedef typename expected::Name BOOST_PP_CAT(x,Name) ; \
BOOST_TEST ( ( typeid(BOOST_PP_CAT(t,Name)) == typeid(BOOST_PP_CAT(x,Name)) ) ) ;
//
// Test core.
// Compares each field of boost::numeric::conversion_traits<T,S>
// with the corresponding field of expected_traits<T,S>
//
template<class T, class S>
void test_traits_base( MATCH_FNTPL_ARG(T), MATCH_FNTPL_ARG(S) )
{
typedef boost::numeric::conversion_traits<T,S> traits ;
typedef typename generate_expected_traits<T,S>::type expected ;
TEST_VALUE_FIELD(int_float_mixture) ;
TEST_VALUE_FIELD(sign_mixture) ;
TEST_VALUE_FIELD(udt_builtin_mixture) ;
TEST_VALUE_FIELD(subranged) ;
TEST_VALUE_FIELD(trivial) ;
TEST_TYPE_FIELD (supertype) ;
TEST_TYPE_FIELD (subtype) ;
}
template<class S>
void test_traits_from( MATCH_FNTPL_ARG(S) )
{
test_traits_base( SET_FNTPL_ARG(boost::uint8_t) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(boost::int8_t) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(boost::uint16_t) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(boost::int16_t) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(boost::uint32_t) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(boost::int32_t) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(float) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(double) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(long double) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(MyInt) ,SET_FNTPL_ARG(S) );
test_traits_base( SET_FNTPL_ARG(MyFloat) ,SET_FNTPL_ARG(S) );
}
void test_traits()
{
test_traits_from( SET_FNTPL_ARG(boost::uint8_t) );
test_traits_from( SET_FNTPL_ARG(boost::int8_t) );
test_traits_from( SET_FNTPL_ARG(boost::uint16_t) );
test_traits_from( SET_FNTPL_ARG(boost::int16_t) );
test_traits_from( SET_FNTPL_ARG(boost::uint32_t) );
test_traits_from( SET_FNTPL_ARG(boost::int32_t) );
test_traits_from( SET_FNTPL_ARG(float) );
test_traits_from( SET_FNTPL_ARG(double) );
test_traits_from( SET_FNTPL_ARG(long double) );
test_traits_from( SET_FNTPL_ARG(MyInt) );
test_traits_from( SET_FNTPL_ARG(MyFloat) );
}
int main()
{
std::cout << std::setprecision( std::numeric_limits<long double>::digits10 ) ;
test_traits();
return boost::report_errors();
}
//---------------------------------------------------------------------------

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@@ -0,0 +1,242 @@
// Copyright (C) 2005, Fernando Luis Cacciola Carballal.
//
// 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)
//
//
#include "boost/config.hpp"
#include "boost/utility.hpp"
#include "boost/limits.hpp"
#include "boost/utility.hpp"
#include<iostream>
#include<iomanip>
#include<string>
#include<cmath>
#include <boost/core/lightweight_test.hpp>
#include "boost/numeric/conversion/cast.hpp"
using namespace std ;
using namespace boost;
using namespace numeric;
//
// This example illustrates how to add support for user defined types (UDTs)
// to the Boost Numeric Conversion Library.
// It is assumed that you are familiar with the following documentation:
//
//
//
// The minimum requirement is that boost::is_arithmetic<UDT> evaluates to false
// (Otherwise the converter code will try to examine the UDT as a built-in type)
//
//
// Let's start with the simpliest case of an UDT which supports standard conversions
//
struct Double
{
Double( double v ) : mV(v) {}
operator double() const { return mV ; }
double mV ;
} ;
double dv = (numeric_limits<double>::max)() ;
double fv = (numeric_limits<float >::max)() ;
Double Dv(dv);
Double Fv(fv);
void simplest_case()
{
//
// conversion_traits<>::udt_builtin_mixture works out of the box as long as boost::is_arithmetic<UDT> yields false
//
BOOST_TEST( (conversion_traits<double,Double>::udt_builtin_mixture::value == udt_to_builtin) ) ;
BOOST_TEST( (conversion_traits<Double,double>::udt_builtin_mixture::value == builtin_to_udt) ) ;
BOOST_TEST( (conversion_traits<Double,Double>::udt_builtin_mixture::value == udt_to_udt ) ) ;
// BY DEFINITION, a conversion from UDT to Builtin is subranged. No attempt is made to actually compare ranges.
BOOST_TEST( (conversion_traits<double,Double>::subranged::value) == true ) ;
BOOST_TEST( (conversion_traits<Double,double>::subranged::value) == false ) ;
//
// Conversions to/from FLOATING types, if already supported by an UDT
// are also supported out-of-the-box by converter<> in its default configuration.
//
BOOST_TEST( numeric_cast<double>(Dv) == static_cast<double>(Dv) ) ;
BOOST_TEST( numeric_cast<Double>(dv) == static_cast<Double>(dv) ) ;
BOOST_TEST( numeric_cast<float> (Dv) == static_cast<float> (Dv) ) ;
BOOST_TEST( numeric_cast<Double>(fv) == static_cast<Double>(fv) ) ;
//
// Range checking is disabled by default if an UDT is either the source or target of the conversion.
//
BOOST_TEST( (converter<float,double>::out_of_range(dv) == cPosOverflow) );
BOOST_TEST( (converter<float,Double>::out_of_range(Dv) == cInRange) );
}
//
// The conversion_traits<> class and therefore the converter<> class looks at
// numeric_limits<UDT>::is_integer/is_signed to generate the proper float_in and sign mixtures.
// In most implementations, is_integer/is_signed are both false for UDTs if there is no explicit specialization for it.
// Therefore, the converter<> will see any UDT for which numeric_limits<> is not specialized as Float AND unsigned.
// Signess is used in the converter<> for range checking, but range checking is disabled by default for UDTs, so,
// normally, signess is mostly irrelevant as far as the library is concerned, except for the numeric_traits<>::sign_mixture
// entry.
// is_integer, however, is relevant in that if the conversion is from a float type to an integer type, the conversion is
// "rounding" and the rounder policies will participate.
// ALL implemented rounder policies require proper definitions for floor(udt) and ceil(udt).
// These names will be searched for using ADL, so, if you need to convert TO integral types from a UDT,
// you need to supply those functions along with the UDT in right namespace (that is, any namespace that allows
// ADL to find them)
// If your UDT doesn't supply floor/ceil, conversions to integer types
// won't compile unless a custom Float2IntRounder is used.
Double floor ( Double v ) { return Double(std::floor(v.mV)) ; }
Double ceil ( Double v ) { return Double(std::ceil (v.mV)) ; }
void rounding()
{
BOOST_TEST( numeric_cast<int>(Dv) == static_cast<int>(Dv) ) ;
}
//
// If your UDT can't or won't provide floor/ceil you can set-up and use your own
// Float2IntRounder policy (though doing this is not always required as shown so far)
//
struct DoubleToInt
{
static Double nearbyint ( Double const& s ) { return Double(static_cast<int>(s)); }
typedef mpl::integral_c< std::float_round_style, std::round_toward_zero> round_style ;
} ;
void custom_rounding()
{
typedef converter<int
,Double
,conversion_traits<int,Double>
,void // By default UDT disable range checking so this won't be used
,DoubleToInt
>
DoubleToIntConverter ;
BOOST_TEST( DoubleToIntConverter::convert(Dv) == static_cast<int>(Dv) ) ;
}
//
// In the next Level of complexity, your UDTs might not support conversion operators
//
struct Float
{
Float( float v ) : mV(v) {}
float mV ;
} ;
struct Int
{
Int( int v ) : mV(v) {}
int mV ;
} ;
typedef conversion_traits<Int,Float> Float2IntTraits ;
typedef conversion_traits<Float,Int> Int2FloatTraits ;
namespace boost { namespace numeric
{
//
// Though static_cast<> won't work with them you can still use numeric_cast<> by specializing
// raw_converter as follows:
//
template<> struct raw_converter<Float2IntTraits>
{
typedef Float2IntTraits::result_type result_type ;
typedef Float2IntTraits::argument_type argument_type ;
static result_type low_level_convert ( argument_type s ) { return Int((int)s.mV); }
} ;
template<> struct raw_converter<Int2FloatTraits>
{
typedef Int2FloatTraits::result_type result_type ;
typedef Int2FloatTraits::argument_type argument_type ;
static result_type low_level_convert ( argument_type s ) { return Float(s.mV); }
} ;
} }
void custom_raw_converter()
{
Float f (12.34);
Int i (12);
Float fi(12);
BOOST_TEST(numeric_cast<Int> (f).mV == i .mV ) ;
BOOST_TEST(numeric_cast<Float>(i).mV == fi.mV ) ;
}
//
// Alterntively, the custom raw_converter classes can be defined non-instrusively
// (not as specializations) and passed along as policies
//
struct Float2IntRawConverter
{
static Int low_level_convert ( Float const& s ) { return Int((int)s.mV); }
} ;
struct Int2FloatRawConverter
{
static Float low_level_convert ( Int const& s ) { return Float(s.mV); }
} ;
void custom_raw_converter2()
{
Float f (12.34);
Int i (12);
Float fi(12);
typedef converter<Int
,Float
,Float2IntTraits
,void // By default UDT disable range checking so this won't be used
,void // Float2Int Rounder won't be used if Int isn't marked as integer via numeric_limits<>
,Float2IntRawConverter
>
Float2IntConverter ;
BOOST_TEST(Float2IntConverter::convert(f).mV == i .mV ) ;
}
int main()
{
cout << setprecision( numeric_limits<long double>::digits10 ) ;
simplest_case();
rounding();
custom_rounding();
custom_raw_converter();
custom_raw_converter2();
return boost::report_errors();
}

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// (C) Copyright 2003, Fernando Luis Cacciola Carballal.
//
// 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)
//
//
#include<iostream>
#include<iomanip>
#include<string>
#include<typeinfo>
#include<vector>
#include<algorithm>
#include "boost/numeric/conversion/converter.hpp"
#ifdef BOOST_BORLANDC
#pragma hdrstop
#endif
#include "test_helpers.cpp"
#include "test_helpers2.cpp"
#include "test_helpers3.cpp"
using namespace std ;
using namespace boost ;
using namespace numeric ;
using namespace MyUDT ;
//-------------------------------------------------------------------------
// These are the typical steps that are required to install support for
// conversions from/to UDT which need special treatment.
//-------------------------------------------------------------------------
//
// (1) Instantiate specific convesions traits.
// This step is only for convenience.
// These traits instances are required in order to define the specializations
// that follow (and which *are required* to make the library work with MyInt and MyFloat)
//
namespace MyUDT {
typedef conversion_traits<double , MyFloat> MyFloat_to_double_Traits;
typedef conversion_traits<int , MyFloat> MyFloat_to_int_Traits;
typedef conversion_traits<MyInt , MyFloat> MyFloat_to_MyInt_Traits;
typedef conversion_traits<int , MyInt > MyInt_to_int_Traits;
typedef conversion_traits<MyFloat, MyInt > MyInt_to_MyFloat_Traits;
typedef conversion_traits<MyInt , double > double_to_MyInt_Traits;
} // namespace MyUDT
//
// (2) Define suitable raw converters.
//
// Our sample UDTs don't support implicit conversions.
// Therefore, the default raw_converter<> doesn't work,
// and we need to define our own.
//
// There are two ways of doing this:
//
// (a) One is to simply specialize boost::numeric::raw_converter<> directly.
// This way, the default converter will work out of the box, which means, for instance,
// that numeric_cast<> can be used with these UDTs.
//
// (b) Define a user class with the appropriate interface and supply it explicitely
// as a policy to a converter instance.
//
// This test uses chice (a).
//
namespace boost {
namespace numeric {
template<>
struct raw_converter<MyUDT::MyFloat_to_double_Traits>
{
static double low_level_convert ( MyUDT::MyFloat const& s )
{ return s.to_builtin() ; }
} ;
template<>
struct raw_converter<MyUDT::MyFloat_to_int_Traits>
{
static int low_level_convert ( MyUDT::MyFloat const& s )
{ return static_cast<int>( s.to_builtin() ) ; }
} ;
template<>
struct raw_converter<MyUDT::MyFloat_to_MyInt_Traits>
{
static MyUDT::MyInt low_level_convert ( MyUDT::MyFloat const& s )
{ return MyUDT::MyInt( static_cast<int>(s.to_builtin()) ) ; }
} ;
template<>
struct raw_converter<MyUDT::MyInt_to_int_Traits>
{
static int low_level_convert ( MyUDT::MyInt const& s ) { return s.to_builtin() ; }
} ;
template<>
struct raw_converter<MyUDT::MyInt_to_MyFloat_Traits>
{
static MyUDT::MyFloat low_level_convert ( MyUDT::MyInt const& s )
{
return MyUDT::MyFloat( static_cast<double>(s.to_builtin()) ) ;
}
} ;
template<>
struct raw_converter<MyUDT::double_to_MyInt_Traits>
{
static MyUDT::MyInt low_level_convert ( double s )
{ return MyUDT::MyInt( static_cast<int>(s) ) ; }
} ;
} // namespace numeric
} // namespace boost
//
// (3) Define suitable range checkers
//
// By default, if a UDT is involved in a conversion, internal range checking is disabled.
// This is so because a UDT type can have any sort of range, even unbounded, thus
// the library doesn't attempt to automatically figure out the appropriate range checking logic.
// (as it does when builtin types are involved)
// However, this situation is a bit unsufficient in practice, specially from doing narrowing (subranged)
// conversions from UDTs.
// The library provides a rudimentary hook to help this out: The user can plug in his own
// range checker to the converter instance.
//
// This test shows how to define and use a custom range checker.
//
namespace MyUDT {
//
// The following are metaprogramming tools to allow us the implement the
// MyCustomRangeChecker generically, for either builtin or UDT types.
//
// get_builtin_type<N>::type extracts the built-in type of our UDT's
//
template<class N> struct get_builtin_type { typedef N type ; } ;
template<> struct get_builtin_type<MyInt> { typedef int type ; } ;
template<> struct get_builtin_type<MyFloat> { typedef double type ; } ;
// U extract_builtin ( T s ) returns 's' converted to the corresponding built-in type U.
//
template<class N>
struct extract_builtin
{
static N apply ( N n ) { return n ; }
} ;
template<>
struct extract_builtin<MyInt>
{
static int apply ( MyInt const& n ) { return n.to_builtin() ; }
} ;
template<>
struct extract_builtin<MyFloat>
{
static double apply ( MyFloat const& n ) { return n.to_builtin() ; }
} ;
template<class Traits>
struct MyCustomRangeChecker
{
typedef typename Traits::argument_type argument_type ;
// This custom range checker uses the fact that our 'fake' UDT are merely wrappers
// around builtin types; so it just forward the logic to the correspoding range
// checkers for the wrapped builtin types.
//
typedef typename Traits::source_type S ;
typedef typename Traits::target_type T ;
// NOTE: S and/or T can be either UDT or builtin types.
typedef typename get_builtin_type<S>::type builtinS ;
typedef typename get_builtin_type<T>::type builtinT ;
// NOTE: The internal range checker used by default is *built* when you instantiate
// a converter<> with a given Traits according to the properties of the involved types.
// Currently, there is no way to instantiate this range checker as a separate class.
// However, you can see it as part of the interface of the converter
// (since the converter inherits from it)
// Therefore, here we instantiate a converter corresponding to the builtin types to access
// their associated builtin range checker.
//
typedef boost::numeric::converter<builtinT,builtinS> InternalConverter ;
static range_check_result out_of_range ( argument_type s )
{
return InternalConverter::out_of_range( extract_builtin<S>::apply(s) );
}
static void validate_range ( argument_type s )
{
return InternalConverter::validate_range( extract_builtin<S>::apply(s) );
}
} ;
} // namespace MyUDT
//
// Test here
//
void test_udt_conversions_with_defaults()
{
cout << "Testing UDT conversion with default policies\n" ;
// MyInt <--> int
int mibv = rand();
MyInt miv(mibv);
TEST_SUCCEEDING_CONVERSION_DEF(MyInt,int,miv,mibv);
TEST_SUCCEEDING_CONVERSION_DEF(int,MyInt,mibv,miv);
// MyFloat <--> double
double mfbv = static_cast<double>(rand()) / 3.0 ;
MyFloat mfv (mfbv);
TEST_SUCCEEDING_CONVERSION_DEF(MyFloat,double,mfv,mfbv);
TEST_SUCCEEDING_CONVERSION_DEF(double,MyFloat,mfbv,mfv);
// MyInt <--> MyFloat
MyInt miv2 ( static_cast<int>(mfbv) );
MyFloat miv2F ( static_cast<int>(mfbv) );
MyFloat mfv2 ( static_cast<double>(mibv) );
MyInt mfv2I ( static_cast<double>(mibv) );
TEST_SUCCEEDING_CONVERSION_DEF(MyFloat,MyInt,miv2F,miv2);
TEST_SUCCEEDING_CONVERSION_DEF(MyInt,MyFloat,mfv2I,mfv2);
}
template<class T, class S>
struct GenerateCustomConverter
{
typedef conversion_traits<T,S> Traits;
typedef def_overflow_handler OverflowHandler ;
typedef Trunc<S> Float2IntRounder ;
typedef raw_converter<Traits> RawConverter ;
typedef MyCustomRangeChecker<Traits> RangeChecker ;
typedef converter<T,S,Traits,OverflowHandler,Float2IntRounder,RawConverter,RangeChecker> type ;
} ;
void test_udt_conversions_with_custom_range_checking()
{
cout << "Testing UDT conversions with custom range checker\n" ;
int mibv = rand();
MyFloat mfv ( static_cast<double>(mibv) );
typedef GenerateCustomConverter<MyFloat,int>::type int_to_MyFloat_Conv ;
TEST_SUCCEEDING_CONVERSION( int_to_MyFloat_Conv, MyFloat, int, mfv, mibv );
int mibv2 = rand();
MyInt miv (mibv2);
MyFloat mfv2 ( static_cast<double>(mibv2) );
typedef GenerateCustomConverter<MyFloat,MyInt>::type MyInt_to_MyFloat_Conv ;
TEST_SUCCEEDING_CONVERSION( MyInt_to_MyFloat_Conv, MyFloat, MyInt, mfv2, miv );
double mfbv = bounds<double>::highest();
typedef GenerateCustomConverter<MyInt,double>::type double_to_MyInt_Conv ;
TEST_POS_OVERFLOW_CONVERSION( double_to_MyInt_Conv, MyInt, double, mfbv );
MyFloat mfv3 ( bounds<double>::lowest() ) ;
typedef GenerateCustomConverter<int,MyFloat>::type MyFloat_to_int_Conv ;
TEST_NEG_OVERFLOW_CONVERSION( MyFloat_to_int_Conv, int, MyFloat, mfv3 );
}
int main()
{
cout << setprecision( numeric_limits<long double>::digits10 ) ;
test_udt_conversions_with_defaults();
test_udt_conversions_with_custom_range_checking();
return boost::report_errors();
}

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-- Downloading https://github.com/boostorg/numeric_conversion/archive/boost-1.79.0.tar.gz -> boostorg-numeric_conversion-boost-1.79.0.tar.gz...
-- Extracting source D:/a/1/s/externals/vcpkg/downloads/boostorg-numeric_conversion-boost-1.79.0.tar.gz
-- Using source at D:/a/1/s/externals/vcpkg/buildtrees/boost-numeric-conversion/src/ost-1.79.0-5892db6ff3.clean
-- Copying headers
-- Copying headers done
-- Installing: D:/a/1/s/externals/vcpkg/packages/boost-numeric-conversion_x64-windows/share/boost-numeric-conversion/usage
-- Installing: D:/a/1/s/externals/vcpkg/packages/boost-numeric-conversion_x64-windows/share/boost-numeric-conversion/copyright

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boost-core 498aea0b6b68bcfe1ec683e76c2f0d32477dfe9ba958f518980ff806b6faba90
boost-mpl 89695bf75ab1fa2b706b2a0c2ef28c6726c3abd61ff51fb0966e3270153a6cd9
boost-preprocessor bf16615c7acc80769793c4f62c492a31cf3d22cd0d8393ccfd77d192da7c41b2
boost-throw-exception 4bb4a0182f0f071c3c1ffd9cbd82fbc3bc7db4a35346f930bbe504e7e3a94e0a
boost-type-traits 74f62124585467fbb6c4fa16015164d11e1a079d6bdb70ec1c3fe7cf65b9a594
boost-vcpkg-helpers c81c7b003df356a1a120a7c0c2f5a2ac95f3c33b006a2a5b4c02dcf0c9f3deaa
cmake 3.23.2
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