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<a name="mpfr-binary-operators-with-a-natural-operand-1"></a>
<h3 class="subsection">D.14.3 <code>mpfr</code> binary operators with a natural operand</h3>

<p>Functions with these names take an argument of the form
<code>(<var>x</var>,<var>n</var>)</code>, where <var>x</var> is an <code>mpfr</code> number
and <var>n</var> is a natural number.
</p>
<ul>
<li> <code>root</code>
</li><li> <code>pow_ui</code>
</li><li> <code>mul_2ui</code>
</li><li> <code>div_2ui</code>
</li><li> <code>grow</code>
</li><li> <code>shrink</code>
</li></ul>

<p>The last two are specific to the virtual code interface, having no
counterpart in the native API of the <code>mpfr</code> library.  The
<code>grow</code> function returns a copy of <var>x</var> with its precision
increased by <var>n</var> bits, and the <code>shrink</code> function returns a
copy of <var>x</var> with its precision reduced by <var>n</var> bits. 
</p>
<ul>
<li>
The precisions are silently capped at the maximum or floored at the
<a name="index-precision-1"></a>
minimum allowable precisions if necessary.
</li><li>
Increasing the precision by the <code>grow</code> function does not directly
cause a more accurate result to be computed, but only pads an existing
number with zeros.
</li><li>
Decreasing the precision by the <code>shrink</code> function does not prevent
valid bits from being discarded.
</li></ul>

<p>The appropriate way to use <code>grow</code> is to grow the precision of an
operand before applying an operator to it, which will cause the result
to be computed to the full precision. This capability is suitable for
algorithms that iterate over increasing precisions until a stopping
criterion is met.
</p>
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