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# Metafunctions

The MPL includes a number of predefined metafunctions that can be roughly classified in two categories: general purpose metafunctions, dealing with conditional type selection and higher-order metafunction invocation, composition, and argument binding, and numeric metafunctions, incapsulating built-in and user-defined arithmetic, comparison, logical, and bitwise operations.

Given that it is possible to perform integer numeric computations at compile time using the conventional operators notation, the need for the second category might be not obvious, but it in fact plays a cental role in making programming with MPL seemingly effortless. In particular, there are at least two contexts where built-in language facilities fall short [3]:

1. Passing a computation to an algorithm.
2. Performing a computation on non-integer data.

The second use case deserves special attention. In contrast to the built-in, strictly integer compile-time arithmetics, the MPL numeric metafunctions are polymorphic, with support for mixed-type arithmetics. This means that they can operate on a variety of numeric types — for instance, rational, fixed-point or complex numbers, — and that, in general, you are allowed to freely intermix these types within a single expression. See Numeric Metafunction concept for more details on the MPL numeric infrastructure.

To reduce a negative syntactical impact of the metafunctions notation over the infix operator notation, all numeric metafunctions allow to pass up to N arguments, where N is defined by the value of `BOOST_MPL_LIMIT_METAFUNCTION_ARITY` configuration macro.

[3] | All other considerations aside, as of the time of this writing (early 2004), using built-in operators on integral constants still often present a portability problem — many compilers cannot handle particular forms of expressions, forcing us to use conditional compilation. Because MPL numeric metafunctions work on types and encapsulate these kind of workarounds internally, they elude these problems, so if you aim for portability, it is generally adviced to use them in the place of the conventional operators, even at the price of slightly decreased readability.