# 3.5.6 Real Types

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.

## Contents

## Syntax

real_type_definition ::= floating_point_definition | fixed_point_definition

## Static Semantics

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*.

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. 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

The elaboration of a real_type_definition consists of the elaboration of the floating_point_definition or the fixed_point_definition.

## Implementation Requirements

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.

## Implementation Permissions

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).

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.

## Notes

32 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.

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