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Literal Types and constexpr Support

[Note] Note

The features described in this section make heavy use of C++11 language features, currently (as of May 2013) only GCC-4.7 and later, and Clang 3.3 and later have the support required to make these features work.

There is limited support for constexpr and user-defined literals in the library, currently the number front end supports constexpr on default construction and all forwarding constructors, but not on any of the non-member operators. So if some type B is a literal type, then number<B> is also a literal type, and you will be able to compile-time-construct such a type from any literal that B is compile-time-constructible from. However, you will not be able to perform compile-time arithmetic on such types.

Currently the only backend type provided by the library that is also a literal type are instantiations of cpp_int_backend where the Allocator parameter is type void, and the Checked parameter is boost::multiprecision::unchecked.

For example:

using namespace boost::multiprecision;

constexpr int128_t            i = 0;     // OK, fixed precision int128_t has no allocator.
constexpr uint1024_t          j = 0xFFFFFFFF00000000uLL;  // OK, fixed precision uint1024_t has no allocator.

constexpr checked_uint128_t   k = -1; // Error, checked type is not a literal type as we need runtime error checking.
constexpr cpp_int             l = 2;  // Error, type is not a literal as it performs memory management.

There is also limited support for user defined-literals - these are limited to unchecked, fixed precision cpp_int's which are specified in hexadecimal notation. The suffixes supported are:

Suffix

Meaning

_cppi

Specifies a value of type: number<cpp_int_backend<N,N,signed_magnitude,unchecked,void> >, where N is chosen to contain just enough digits to hold the number specified.

_cppui

Specifies a value of type: number<cpp_int_backend<N,N,unsigned_magnitude,unchecked,void> >, where N is chosen to contain just enough digits to hold the number specified.

_cppiN

Specifies a value of type number<cpp_int_backend<N,N,signed_magnitude,unchecked,void> >.

_cppuiN

Specifies a value of type number<cpp_int_backend<N,N,signed_magnitude,unchecked,void> >.

In each case, use of these suffixes with hexadecimal values produces a constexpr result.

Examples:

//
// Any use of user defined literals requires that we import the literal-operators
// into current scope first:
using namespace boost::multiprecision::literals;
//
// To keep things simple in the example, we'll make our types used visible to this scope as well:
using namespace boost::multiprecision;
//
// The value zero as a number<cpp_int_backend<4,4,signed_magnitude,unchecked,void> >:
constexpr auto a = 0x0_cppi;
// The type of each constant has 4 bits per hexadecimal digit,
// so this is of type uint256_t (ie number<cpp_int_backend<256,256,unsigned_magnitude,unchecked,void> >):
constexpr auto b = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF_cppui;
//
// Smaller values can be assigned to larger values:
int256_t c = 0x1234_cppi; // OK
//
// However, this does not currently work in constexpr contexts:
constexpr int256_t d = 0x1_cppi; // Compiler error
//
// Constants can be padded out with leading zeros to generate wider types:
constexpr uint256_t e = 0x0000000000000000000000000000000000000000000FFFFFFFFFFFFFFFFFFFFF_cppui; // OK
//
// However, specific width types are best produced with specific-width suffixes,
// ones supported by default are `_cpp[u]i128`, `_cpp[u]i256`, `_cpp[u]i512`, `_cpp[u]i1024`.
//
constexpr int128_t f = 0x1234_cppi128; // OK, always produces an int128_t as the result.
constexpr uint1024_t g = 0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbccccccccccccccccccccc_cppui1024;
//
// If other specific width types are required, then there is a macro for generating the operators
// for these.  The macro can be used at namespace scope only:
//
BOOST_MP_DEFINE_SIZED_CPP_INT_LITERAL(2048);
//
// Now we can create 2048-bit literals as well:
constexpr auto h = 0xff_cppi2048; // h is of type number<cpp_int_backend<2048,2048,signed_magnitude,unchecked,void> >
//
// Finally negative values are handled via the unary minus operator:
//
constexpr int1024_t i = -0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF_cppui1024;
//
// Which means this also works:
constexpr int1024_t j = -g;   // OK: unary minus operator is constexpr.

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