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<H1> 4.5 Operators and Expression Evaluation</H1>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal"> [<A NAME="I2559"></A> <A NAME="I2560"></A>The
language defines the following six categories of operators (given in
order of increasing precedence). The corresponding <FONT FACE="Arial, Helvetica">operator_symbol</FONT>s,
and only those, can be used as <FONT FACE="Arial, Helvetica">designator</FONT>s
in declarations of functions for user-defined operators. See <A HREF="AA-6-6.html">6.6</A>,
``<A HREF="AA-6-6.html">Overloading of Operators</A>''.] </DIV>
<H4 ALIGN=CENTER>Syntax</H4>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">logical_operator<A NAME="I2561"></A>
::= </FONT> <B>and</B> | <B>or</B> | <B>xor</B></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">relational_operator<A NAME="I2562"></A>
::= </FONT> = | /= | < | <= | > | >=</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>4</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">binary_adding_operator<A NAME="I2563"></A>
::= </FONT> + | - | &</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>5</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">unary_adding_operator<A NAME="I2564"></A>
::= </FONT> + | -</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>6</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">multiplying_operator<A NAME="I2565"></A>
::= </FONT> * | / | <B>mod</B> | <B>rem</B></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>7</FONT></DIV>
<DIV Class="SyntaxIndented"><FONT FACE="Arial, Helvetica">highest_precedence_operator<A NAME="I2566"></A>
::= </FONT> ** | <B>abs</B> | <B>not</B></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>7.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Discussion: </B>Some of the
above syntactic categories are not used in other syntax rules. They are
just used for classification. The others are used for both classification
and parsing. </FONT></DIV>
<H4 ALIGN=CENTER>Static Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>8</FONT></DIV>
<DIV Class="Normal"> For a sequence of operators of the same precedence
level, the operators are associated with their operands in textual order
from left to right. Parentheses can be used to impose specific associations.
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Discussion: </B>The left-associativity
is not directly inherent in the grammar of <A HREF="AA-4-4.html">4.4</A>,
though in <A HREF="AA-1-1-4.html">1.1.4</A> the definition of the metasymbols
<B>{}</B> implies left associativity. So this could be seen as redundant,
depending on how literally one interprets the definition of the <B>{}</B>
metasymbols.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8.b</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1>See the Implementation Permissions
below regarding flexibility in reassociating operators of the same precedence.
</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>9</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2567"></A><A NAME="I2568"></A>For each
form of type definition, certain of the above operators are <I>predefined</I>;
that is, they are implicitly declared immediately after the type definition.
<A NAME="I2569"></A><A NAME="I2570"></A><A NAME="I2571"></A><A NAME="I2572"></A>For
each such implicit operator declaration, the parameters are called Left
and Right for <I>binary</I> operators; the single parameter is called
Right for <I>unary</I> operators. [An expression of the form X op Y,
where op is a binary operator, is equivalent to a <FONT FACE="Arial, Helvetica">function_call</FONT>
of the form "op"(X, Y). An expression of the form op Y, where
op is a unary operator, is equivalent to a <FONT FACE="Arial, Helvetica">function_call</FONT>
of the form "op"(Y). The predefined operators and their effects
are described in subclauses <A HREF="AA-4-5-1.html">4.5.1</A> through
<A HREF="AA-4-5-6.html">4.5.6</A>.] </DIV>
<H4 ALIGN=CENTER>Dynamic Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>10</FONT></DIV>
<DIV Class="Normal"> [<A NAME="I2573"></A> The predefined operations
on integer types either yield the mathematically correct result or raise
the exception Constraint_Error. For implementations that support the
Numerics Annex, the predefined operations on real types yield results
whose accuracy is defined in <A HREF="AA-G.html">Annex G</A>, or raise
the exception Constraint_Error. ]</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>10.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>To be honest: </B>Predefined
operations on real types can ``silently'' give wrong results when the
Machine_Overflows attribute is false, and the computation overflows.
</FONT></DIV>
<H4 ALIGN=CENTER>Implementation Requirements</H4>
<DIV Class="Paranum"><FONT SIZE=-2>11</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2574"></A>The implementation of a predefined
operator that delivers a result of an integer or fixed point type may
raise Constraint_Error only if the result is outside the base range of
the result type.</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>12</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2575"></A>The implementation of a predefined
operator that delivers a result of a floating point type may raise Constraint_Error
only if the result is outside the safe range of the result type. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>12.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>To be honest: </B>An exception
is made for exponentiation by a negative exponent in <A HREF="AA-4-5-6.html">4.5.6</A>.</FONT></DIV>
<H4 ALIGN=CENTER>Implementation Permissions</H4>
<DIV Class="Paranum"><FONT SIZE=-2>13</FONT></DIV>
<DIV Class="Normal"> For a sequence of predefined operators of the
same precedence level (and in the absence of parentheses imposing a specific
association), an implementation may impose any association of the operators
with operands so long as the result produced is an allowed result for
the left-to-right association, but ignoring the potential for failure
of language-defined checks in either the left-to-right or chosen order
of association. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>13.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Discussion: </B>Note that the
permission to reassociate the operands in any way subject to producing
a result allowed for the left-to-right association is not much help for
most floating point operators, since reassociation may introduce significantly
different round-off errors, delivering a result that is outside the model
interval for the left-to-right association. Similar problems arise for
division with integer or fixed point operands.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>13.b</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1>Note that this permission does
not apply to user-defined operators. </FONT></DIV>
<DIV Class="NotesHeader"><FONT SIZE=-1>NOTES</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>14</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>11 The two operands of an
expression of the form X op Y, where op is a binary operator, are evaluated
in an arbitrary order, as for any <FONT FACE="Arial, Helvetica">function_call</FONT>
(see <A HREF="AA-6-4.html">6.4</A>). </FONT></DIV>
<H4 ALIGN=CENTER>Examples</H4>
<DIV Class="Paranum"><FONT SIZE=-2>15</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <I>Examples of
precedence:</I> </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>16</FONT></DIV>
<DIV Class="Examples"><TT><B>not</B> Sunny <B>or</B> Warm <I>-- same as (not Sunny) or Warm</I><BR>
X > 4.0 <B>and</B> Y > 0.0 <I>-- same as (X > 4.0) and (Y > 0.0)</I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>17</FONT></DIV>
<DIV Class="Examples"><TT>-4.0*A**2 <I>-- same as -(4.0 * (A**2))</I><BR>
<B>abs</B>(1 + A) + B <I>-- same as (abs (1 + A)) + B</I><BR>
Y**(-3) <I>-- parentheses are necessary</I><BR>
A / B * C <I>-- same as (A/B)*C</I><BR>
A + (B + C) <I>-- evaluate B + C before adding it to A </I></TT></DIV>
<H4 ALIGN=CENTER>Wording Changes from Ada 83</H4>
<DIV Class="Paranum"><FONT SIZE=-2>17.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1>We don't give a detailed definition
of precedence, since it is all implicit in the syntax rules anyway.</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>17.b</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1>The permission to reassociate
is moved here from RM83-11.6(5), so it is closer to the rules defining
operator association. </FONT></DIV>
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