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<Head>
<Title>Relational Operators</Title>
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<H1>Relational Operators</H1>
<Table CellPadding=0 CellSpacing=0 width=100%>
<TR>
<TD Align=left><Img src = "utilities.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
<TD Align=right><Img src = "function.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD>
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<TR>
<TD Align=left VAlign=top><b>Category</b>: utilities</TD>
<TD Align=right VAlign=top><b>Component type</b>: function</TD>
</TR>
</Table>
<h3>Prototype</h3>
<pre>
template <class T> bool operator!=(const T& x, const T& y);
template <class T> bool operator>(const T& x, const T& y);
template <class T> bool operator<=(const T& x, const T& y);
template <class T> bool operator>=(const T& x, const T& y);
</pre>
<h3>Description</h3>
The <A href="EqualityComparable.html">Equality Comparable</A> requirements specify that it must be
possible to compare objects using <tt>operator!=</tt> as well as <tt>operator==</tt>;
similarly, the <A href="LessThanComparable.html">LessThan Comparable</A> requirements include
<tt>operator></tt>, <tt>operator<=</tt> and <tt>operator>=</tt> as well as <tt>operator<</tt>.
Logically, however, most of these operators are redundant: all of
them can be defined in terms of <tt>operator==</tt> and <tt>operator<</tt>.
<P>
These four templates use <tt>operator==</tt> and <tt>operator<</tt> to define the other
four relational operators. They exist purely for the sake of convenience:
they make it possible to write algorithms in terms of the operators
<tt>!=</tt>, <tt>></tt>, <tt><=</tt>, and <tt>>=</tt>, without requiring that those operators be
explicitly defined for every type.
<P>
As specified in the <A href="EqualityComparable.html">Equality Comparable</A> requirements, <tt>x != y</tt> is
equivalent to <tt>!(x == y)</tt>. As specified in the <A href="LessThanComparable.html">LessThan Comparable</A>
requirements, <tt>x > y</tt> is equivalent to <tt>y < x</tt>, <tt>x >= y</tt> is equivalent
to <tt>!(x < y)</tt>, and <tt>x <= y</tt> is equivalent to <tt>!(y < x)</tt>.
<h3>Definition</h3>
Defined in the standard header <A href="utility">utility</A>, and in the nonstandard
backward-compatibility header <A href="function.h">function.h</A>.
<h3>Requirements on types</h3>
The requirement for <tt>operator!=</tt> is that <tt>x == y</tt> is a valid expression
for objects <tt>x</tt> and <tt>y</tt> of type <tt>T</tt>.
<P>
The requirement for <tt>operator></tt> is that <tt>y < x</tt> is a valid expression
for objects <tt>x</tt> and <tt>y</tt> of type <tt>T</tt>.
<P>
The requirement for <tt>operator<=</tt> is that <tt>y < x</tt> is a valid expression
for objects <tt>x</tt> and <tt>y</tt> of type <tt>T</tt>.
<P>
The requirement for <tt>operator>=</tt> is that <tt>x < y</tt> is a valid expression
for objects <tt>x</tt> and <tt>y</tt> of type <tt>T</tt>.
<h3>Preconditions</h3>
The precondition for <tt>operator!=</tt> is that <tt>x</tt> and <tt>y</tt> are in the
domain of <tt>operator==</tt>.
<P>
The precondition for <tt>operator></tt>, <tt>operator<=</tt>, and <tt>operator>=</tt> is
that <tt>x</tt> and <tt>y</tt> are in the domain of <tt>operator<</tt>.
<h3>Complexity</h3>
<h3>Example</h3>
<pre>
template <class T> void relations(T x, T y)
{
if (x == y) assert(!(x != y));
else assert(x != y);
if (x < y) {
assert(x <= y);
assert(y > x);
assert(y >= x);
}
else if (y < x) {
assert(y <= x);
assert(x < y);
assert(x <= y);
}
else {
assert(x <= y);
assert(x >= y);
}
}
</pre>
<h3>Notes</h3>
<h3>See also</h3>
<A href="EqualityComparable.html">Equality Comparable</A>, <A href="LessThanComparable.html">LessThan Comparable</A>
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