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<H1> 3.5.6 Real Types</H1>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1660"></A>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. </DIV>
<H4 ALIGN=CENTER>Syntax</H4>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">real_type_definition<A NAME="I1661"></A>
::= </FONT><BR>
<A NAME="I1662"></A><FONT FACE="Arial, Helvetica">floating_point_definition</FONT> | <A NAME="I1663"></A><FONT FACE="Arial, Helvetica">fixed_point_definition</FONT></DIV>
<H4 ALIGN=CENTER>Static Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1664"></A>A type defined by a <FONT FACE="Arial, Helvetica">real_type_definition</FONT>
is implicitly derived from <I>root_real</I>, an anonymous predefined
(specific) real type. Hence, all real types, whether floating point or
fixed point, are in the derivation class rooted at <I>root_real</I>.
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>4</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1665"></A><A NAME="I1666"></A>Real literals
are all of the type <I>universal_real</I>, the universal type (see <A HREF="RM-3-4-1.html">3.4.1</A>)
for the class rooted at <I>root_real</I>, allowing their use with the
operations of any real type. <A NAME="I1667"></A>Certain multiplying
operators have a result type of <I>universal_fixed</I> (see <A HREF="RM-4-5-5.html">4.5.5</A>),
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. </DIV>
<H4 ALIGN=CENTER>Dynamic Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>5</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1668"></A>The elaboration of a <FONT FACE="Arial, Helvetica">real_type_definition</FONT>
consists of the elaboration of the <FONT FACE="Arial, Helvetica">floating_point_definition</FONT>
or the <FONT FACE="Arial, Helvetica">fixed_point_definition</FONT>. </DIV>
<H4 ALIGN=CENTER>Implementation Requirements</H4>
<DIV Class="Paranum"><FONT SIZE=-2>6</FONT></DIV>
<DIV Class="Normal"> An implementation shall perform the run-time evaluation
of a use of a predefined operator of <I>root_real</I> with an accuracy
at least as great as that of any floating point type definable by a <FONT FACE="Arial, Helvetica">floating_point_definition</FONT>.
</DIV>
<H4 ALIGN=CENTER>Implementation Permissions</H4>
<DIV Class="Paranum"><FONT SIZE=-2>7</FONT></DIV>
<DIV Class="Normal"> 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 <A HREF="RM-G-2.html">G.2</A>).</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8</FONT></DIV>
<DIV Class="Normal"> <A NAME="I1669"></A>An implementation may provide
<I>nonstandard real types</I>, descendants of <I>root_real</I> that are
declared outside of the specification of package Standard, which need
not have all the standard characteristics of a type defined by a <FONT FACE="Arial, Helvetica">real_type_definition</FONT>.
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 <A HREF="RM-G-2.html">G.2</A>).
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 <FONT FACE="Arial, Helvetica">explicit_generic_actual_parameter</FONT>s
for formal scalar types -- see <A HREF="RM-12-5-2.html">12.5.2</A>. </DIV>
<DIV Class="NotesHeader"><FONT SIZE=-1>NOTES</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>9</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>32 As stated, real literals
are of the anonymous predefined real type <I>universal_real</I>. Other
real types have no literals. However, the overload resolution rules (see
<A HREF="RM-8-6.html">8.6</A>) allow expressions of the type <I>universal_real</I>
whenever a real type is expected.</FONT></DIV>
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