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<H1> 4.5.6 Highest Precedence Operators</H1>
<H4 ALIGN=CENTER>Static Semantics</H4>
<DIV Class="Paranum"><FONT SIZE=-2>1</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <A NAME="I2695"></A><A NAME="I2696"></A><A NAME="I2697"></A><A NAME="I2698"></A><A NAME="I2699"></A>The
highest precedence unary operator <B>abs</B> (absolute value) is predefined
for every specific numeric type <I>T</I>, with the following specification:
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>2</FONT></DIV>
<DIV Class="Examples"><TT><B>function</B> "<B>abs</B>"(Right : <I>T</I>) <B>return</B> <I>T</I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>3</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <A NAME="I2700"></A><A NAME="I2701"></A><A NAME="I2702"></A>The
highest precedence unary operator <B>not</B> (logical negation) is predefined
for every boolean type <I>T</I>, every modular type <I>T</I>, and for
every one-dimensional array type <I>T</I> whose components are of a boolean
type, with the following specification: </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>4</FONT></DIV>
<DIV Class="Examples"><TT><B>function</B> "<B>not</B>"(Right : <I>T</I>) <B>return</B> <I>T</I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>5</FONT></DIV>
<DIV Class="Normal"> The result of the operator <B>not</B> for a modular
type is defined as the difference between the high bound of the base
range of the type and the value of the operand. [For a binary modulus,
this corresponds to a bit-wise complement of the binary representation
of the value of the operand.]</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>6</FONT></DIV>
<DIV Class="Normal"> The operator <B>not</B> that applies to a one-dimensional
array of boolean components yields a one-dimensional boolean array with
the same bounds; each component of the result is obtained by logical
negation of the corresponding component of the operand (that is, the
component that has the same index value). <A NAME="I2703"></A><A NAME="I2704"></A><A NAME="I2705"></A>A
check is made that each component of the result belongs to the component
subtype; the exception Constraint_Error is raised if this check fails.
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>6.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Discussion: </B>The check against
the component subtype is per AI83-00535. </FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>7</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> <A NAME="I2706"></A><A NAME="I2707"></A><A NAME="I2708"></A><A NAME="I2709"></A>The
highest precedence <I>exponentiation</I> operator ** is predefined for
every specific integer type <I>T</I> with the following specification:
</DIV>
<DIV Class="Paranum"><FONT SIZE=-2>8</FONT></DIV>
<DIV Class="Examples"><TT><B>function</B> "**"(Left : <I>T</I>; Right : Natural) <B>return</B> <I>T</I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>9</FONT></DIV>
<DIV Class="Normal" Style="margin-bottom: 0.4em"> Exponentiation is
also predefined for every specific floating point type as well as <I>root_real</I>,
with the following specification (where <I>T</I> is <I>root_real</I>
or the floating point type): </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>10</FONT></DIV>
<DIV Class="Examples"><TT><B>function</B> "**"(Left : <I>T</I>; Right : Integer'Base) <B>return</B> <I>T</I></TT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>11</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2710"></A>The right operand of an exponentiation
is the <I>exponent</I>. The expression X**N with the value of the exponent
N positive is equivalent to the expression X*X*...X (with N-1 multiplications)
except that the multiplications are associated in an arbitrary order.
With N equal to zero, the result is one. With the value of N negative
[(only defined for a floating point operand)], the result is the reciprocal
of the result using the absolute value of N as the exponent. </DIV>
<DIV Class="Paranum"><FONT SIZE=-2>11.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1><B>Ramification: </B>The language
does not specify the order of association of the multiplications inherent
in an exponentiation. For a floating point type, the accuracy of the
result might depend on the particular association order chosen. </FONT></DIV>
<H4 ALIGN=CENTER>Implementation Permissions</H4>
<DIV Class="Paranum"><FONT SIZE=-2>12</FONT></DIV>
<DIV Class="Normal"> <A NAME="I2711"></A>The implementation of exponentiation
for the case of a negative exponent is allowed to raise Constraint_Error
if the intermediate result of the repeated multiplications is outside
the safe range of the type, even though the final result (after taking
the reciprocal) would not be. (The best machine approximation to the
final result in this case would generally be 0.0.) </DIV>
<DIV Class="NotesHeader"><FONT SIZE=-1>NOTES</FONT></DIV>
<DIV Class="Paranum"><FONT SIZE=-2>13</FONT></DIV>
<DIV Class="Notes"><FONT SIZE=-1>19 <A NAME="I2712"></A><A NAME="I2713"></A>As
implied by the specification given above for exponentiation of an integer
type, a check is made that the exponent is not negative. <A NAME="I2714"></A>Constraint_Error
is raised if this check fails. </FONT></DIV>
<H4 ALIGN=CENTER>Inconsistencies With Ada 83</H4>
<DIV Class="Paranum"><FONT SIZE=-2>13.a.1/1</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1>{<I><A HREF="defect2.html#8652/0100">8652/0100</A></I>}
<U><A NAME="I2715"></A>The definition of "**" allows arbitrary
association of the multiplications which make up the result. Ada 83 required
left-to-right associations (confirmed by AI83-00137). Thus it is possible
that "**" would provide a slightly different answer in Ada
95 than in the same Ada 83 program.</U> </FONT></DIV>
<H4 ALIGN=CENTER>Wording Changes from Ada 83</H4>
<DIV Class="Paranum"><FONT SIZE=-2>13.a</FONT></DIV>
<DIV Class="Annotations"><FONT SIZE=-1>We now show the specification
for "**" for integer types with a parameter subtype of Natural
rather than Integer for the exponent. This reflects the fact that Constraint_Error
is raised if a negative value is provided for the exponent. </FONT></DIV>
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