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<a name="Computing-bounds-on-poly_005fints"></a>
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Next: <a href="Converting-poly_005fints.html#Converting-poly_005fints" accesskey="n" rel="next">Converting <code>poly_int</code>s</a>, Previous: <a href="Alignment-of-poly_005fints.html#Alignment-of-poly_005fints" accesskey="p" rel="previous">Alignment of <code>poly_int</code>s</a>, Up: <a href="poly_005fint.html#poly_005fint" accesskey="u" rel="up">poly_int</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Option-Index.html#Option-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Computing-bounds-on-poly_005fints-1"></a>
<h3 class="section">10.6 Computing bounds on <code>poly_int</code>s</h3>
<p><code>poly_int</code> also provides routines for calculating lower and upper bounds:
</p>
<dl compact="compact">
<dt>‘<samp>constant_lower_bound (<var>a</var>)</samp>’</dt>
<dd><p>Assert that <var>a</var> is nonnegative and return the smallest value it can have.
</p>
</dd>
<dt>‘<samp>constant_lower_bound_with_limit (<var>a</var>, <var>b</var>)</samp>’</dt>
<dd><p>Return the least value <var>a</var> can have, given that the context in
which <var>a</var> appears guarantees that the answer is no less than <var>b</var>.
In other words, the caller is asserting that <var>a</var> is greater than or
equal to <var>b</var> even if ‘<samp>known_ge (<var>a</var>, <var>b</var>)</samp>’ doesn’t hold.
</p>
</dd>
<dt>‘<samp>constant_upper_bound_with_limit (<var>a</var>, <var>b</var>)</samp>’</dt>
<dd><p>Return the greatest value <var>a</var> can have, given that the context in
which <var>a</var> appears guarantees that the answer is no greater than <var>b</var>.
In other words, the caller is asserting that <var>a</var> is less than or equal
to <var>b</var> even if ‘<samp>known_le (<var>a</var>, <var>b</var>)</samp>’ doesn’t hold.
</p>
</dd>
<dt>‘<samp>lower_bound (<var>a</var>, <var>b</var>)</samp>’</dt>
<dd><p>Return a value that is always less than or equal to both <var>a</var> and <var>b</var>.
It will be the greatest such value for some indeterminate values
but necessarily for all.
</p>
</dd>
<dt>‘<samp>upper_bound (<var>a</var>, <var>b</var>)</samp>’</dt>
<dd><p>Return a value that is always greater than or equal to both <var>a</var> and
<var>b</var>. It will be the least such value for some indeterminate values
but necessarily for all.
</p></dd>
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