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## Type Requirements and User-defined-types support

### 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).

### UDT's special semantics

##### Conversion Traits

If a User Defined Type is involved in a conversion, it is assumed that the UDT has 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.

##### 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 Special Policies

### 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 UserRangeChecker policy for details.

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 RawConverter policy for details