 (1)
 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)
 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.
 (4)
 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
 (5)
 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 runtime 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
 (7)
 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)
 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.

 (9)
(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.
 Email comments, additions, corrections, gripes, kudos, etc. to:
Magnus Kempe  Magnus.Kempe@di.epfl.ch
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