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<H1> 3.5.5 Operations of Discrete Types</H1>
<H4 ALIGN=CENTER>Static Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> For every discrete
subtype S, the following attributes are defined: </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DL Class="Hanging" Style="margin-bottom: 0.4em"><DT> S'Pos<DD Class="Hanging">
<A NAME="I1714"></A><A NAME="I1715"></A>S'Pos denotes a function with
the following specification: </DL>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="IndentedExamples"><TT><B>function</B> S'Pos(<I>Arg</I> : S'Base)<BR>
<B>return</B> <I>universal_integer</I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>4</FONT></DIV>
<DL Class="Hanging"><DD Class ="Hanging">This function returns the position number of the
value of <I>Arg</I>, as a value of type <I>universal_integer</I>.</DL>
<DIV Class="Paranum"><FONT SIZE=-2>5</FONT></DIV>
<DL Class="Hanging" Style="margin-bottom: 0.4em"><DT> S'Val<DD Class="Hanging">
<A NAME="I1716"></A><A NAME="I1717"></A>S'Val denotes a function with
the following specification: </DL>
<DIV Class="Paranum"><FONT SIZE=-2>6</FONT></DIV>
<DIV Class="IndentedExamples"><TT><B>function</B> S'Val(<I>Arg</I> : <I>universal_integer</I>)<BR>
<B>return</B> S'Base</TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>7</FONT></DIV>
<DL Class="Hanging"><DD Class ="Hanging"><A NAME="I1718"></A><A NAME="I1719"></A>This function
returns a value of the type of S whose position number equals the value
of <I>Arg</I>. <A NAME="I1720"></A><A NAME="I1721"></A>For the evaluation
of a call on S'Val, if there is no value in the base range of its type
with the given position number, Constraint_Error is raised. </DL>
<DIV Class="Paranum"><FONT SIZE=-2>7.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Ramification: </B>By the overload
resolution rules, a formal parameter of type <I>universal_integer</I>
allows an actual parameter of any integer type.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>7.b</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Reason: </B>We considered allowing
S'Val for a signed integer subtype S to return an out-of-range value,
but since checks were required for enumeration and modular types anyway,
the allowance didn't seem worth the complexity of the rule.</FONT></DIV>
<H4 ALIGN=CENTER>Implementation Advice</H4>
<DIV Class="Paranum"><FONT SIZE=-2>8</FONT></DIV>
<DIV Class="Normal"> For the evaluation of a call on S'Pos for an enumeration
subtype, if the value of the operand does not correspond to the internal
code for any enumeration literal of its type [(perhaps due to an uninitialized
variable)], then the implementation should raise Program_Error. <A NAME="I1722"></A>This
is particularly important for enumeration types with noncontiguous internal
codes specified by an <FONT FACE="Arial, Helvetica">enumeration_representation_clause</FONT>.
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Reason: </B>We say Program_Error
here, rather than Constraint_Error, because the main reason for such
values is uninitialized variables, and the normal way to indicate such
a use (if detected) is to raise Program_Error. (Other reasons would involve
the misuse of low-level features such as Unchecked_Conversion.) </FONT></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>28 Indexing and loop iteration
use values of discrete types.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>10</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>29 <A NAME="I1723"></A>The
predefined operations of a discrete type include the assignment operation,
qualification, the membership tests, and the relational operators; for
a boolean type they include the short-circuit control forms and the logical
operators; for an integer type they include type conversion to and from
other numeric types, as well as the binary and unary adding operators
- and +, the multiplying operators, the unary operator <B>abs</B>, and
the exponentiation operator. The assignment operation is described in
<A HREF="AA-5-2.html">5.2</A>. The other predefined operations are described
in Section 4.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>11</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>30 As for all types, objects
of a discrete type have Size and Address attributes (see <A HREF="AA-13-3.html">13.3</A>).</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>12</FONT></DIV>
<DIV Class="Notes" Style="margin-bottom: 0.4em"><FONT SIZE=-1>31 For
a subtype of a discrete type, the result delivered by the attribute Val
might not belong to the subtype; similarly, the actual parameter of the
attribute Pos need not belong to the subtype. The following relations
are satisfied (in the absence of an exception) by these attributes: </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>13</FONT></DIV>
<DIV Class="Examples"><TT> S'Val(S'Pos(X)) = X<BR>
S'Pos(S'Val(N)) = N</TT></DIV>
<H4 ALIGN=CENTER>Examples</H4>
<DIV Class="Paranum"><FONT SIZE=-2>14</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <I>Examples of
attributes of discrete subtypes: </I></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>15</FONT></DIV>
<DIV Class="Examples"><TT><I>-- For the types and subtypes declared in subclause <A HREF="AA-3-5-1.html">3.5.1</A> the following hold: </I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>16</FONT></DIV>
<DIV Class="Examples"><TT>-- Color'First = White, Color'Last = Black<BR>
-- Rainbow'First = Red, Rainbow'Last = Blue</TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>17</FONT></DIV>
<DIV Class="Examples"><TT>-- Color'Succ(Blue) = Rainbow'Succ(Blue) = Brown<BR>
-- Color'Pos(Blue) = Rainbow'Pos(Blue) = 4<BR>
-- Color'Val(0) = Rainbow'Val(0) = White</TT></DIV>
<H4 ALIGN=CENTER>Extensions to Ada 83</H4>
<DIV Class="Paranum"><FONT SIZE=-2>17.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><A NAME="I1724"></A>The attributes
S'Succ, S'Pred, S'Width, S'Image, and S'Value have been generalized to
apply to real types as well (see <A HREF="AA-3-5.html">3.5</A>, ``<A HREF="AA-3-5.html">Scalar
Types</A>''). </FONT></DIV>
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