3.5.6 Real Types


3.5.6 Real Types

1 {real type} Real types provide approximations to the real numbers, with relative bounds on errors for floating point types, and with absolute bounds for fixed point types. 


2 real_type_definition ::= 
   floating_point_definition | fixed_point_definition

Static Semantics

3 {root_real} A type defined by a real_type_definition is implicitly derived from root_real, an anonymous predefined (specific) real type. [Hence, all real types, whether floating point or fixed point, are in the derivation class rooted at root_real.]

3.a Ramification: It is not specified whether the derivation from root_real is direct or indirect, not that it really matters. All we want is for all real types to be descendants of root_real.

3.a.1/1 Note that this derivation does not imply any inheritance of subprograms. Subprograms are inherited only for types derived by a derived_type_definition (see §3.4), or a private_extension_declaration (see §7.3, §7.3.1, and §12.5.1).

4 [{universal_real [partial]} {real literals} Real literals are all of the type universal_real, the universal type (see §3.4.1) for the class rooted at root_real, allowing their use with the operations of any real type. {universal_fixed [partial]} Certain multiplying operators have a result type of universal_fixed (see §4.5.5), the universal type for the class of fixed point types, allowing the result of the multiplication or division to be used where any specific fixed point type is expected.] 

Dynamic Semantics

5 {elaboration (real_type_definition) [partial]} The elaboration of a real_type_definition consists of the elaboration of the floating_point_definition or the fixed_point_definition

Implementation Requirements

6 An implementation shall perform the run-time evaluation of a use of a predefined operator of root_real with an accuracy at least as great as that of any floating point type definable by a floating_point_definition.

6.a Ramification: Static calculations using the operators of root_real are exact, as for all static calculations. See §4.9. 

6.b Implementation Note: The Digits attribute of the type used to represent root_real at run time is at least as great as that of any other floating point type defined by a floating_point_definition, and its safe range includes that of any such floating point type with the same Digits attribute. On some machines, there might be real types with less accuracy but a wider range, and hence run-time calculations with root_real might not be able to accommodate all values that can be represented at run time in such floating point or fixed point types. 

Implementation Permissions

7/2 [For the execution of a predefined operation of a real type, the implementation need not raise Constraint_Error if the result is outside the base range of the type, so long as the correct result is produced, or the Machine_Overflows attribute of the type is False (see §G.2).]

8 {nonstandard real type} An implementation may provide nonstandard real types, descendants of root_real that are declared outside of the specification of package Standard, which need not have all the standard characteristics of a type defined by a real_type_definition. For example, a nonstandard real type might have an asymmetric or unsigned base range, or its predefined operations might wrap around or “saturate” rather than overflow (modular or saturating arithmetic), or it might not conform to the accuracy model (see §G.2). Any type descended from a nonstandard real type is also nonstandard. An implementation may place arbitrary restrictions on the use of such types; it is implementation defined whether operators that are predefined for “any real type” are defined for a particular nonstandard real type. [In any case, such types are not permitted as explicit_generic_actual_parameters for formal scalar types — see §12.5.2.]

8.a Implementation defined: Any nonstandard real types and the operators defined for them.


9 (34)  As stated, real literals are of the anonymous predefined real type universal_real. Other real types have no literals. However, the overload resolution rules (see §8.6) allow expressions of the type universal_real whenever a real type is expected.

Wording Changes from Ada 83

9.a The syntax rule for real_type_definition is modified to use the new syntactic categories floating_point_definition and fixed_point_definition, instead of floating_point_constraint and fixed_point_constraint, because the semantics of a type definition are significantly different than the semantics of a constraint.

9.b All discussion of model numbers, safe ranges, and machine numbers is moved to §3.5.7, §3.5.8, and §G.2. Values of a fixed point type are now described as being multiples of the small of the fixed point type, and we have no need for model numbers, safe ranges, etc. for fixed point types.