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    <p>I'd probably check it like this, because my policy is to be paranoid about the accuracy of math functions:</p> <pre><code>double root = sqrt(z); int introot = floor(root + 0.5); // round to nearby integer if ((introot * introot) == z) { // integer arithmetic, so precise cout &lt;&lt; introot &lt;&lt; " == sqrt(" &lt;&lt; z &lt;&lt; ")\n"; } </code></pre> <p><code>double</code> can exactly represent all the integers we care about (for that matter, on most implementations it can exactly represent all the values of <code>int</code>). It also has enough precision to distinguish between <code>sqrt(x)</code> and <code>sqrt(x+1)</code> for all the integers we care about. sqrt(10000) - sqrt(9999) is 0.005, so we only need 5 decimal places of accuracy to avoid false positives, because a non-integer square root can't be any closer than that to an integer. A good <code>sqrt</code> implementation therefore can be accurate enough that <code>(int)root == root</code> on its own would do the job.</p> <p>However, the standard doesn't specify the accuracy of <code>sqrt</code> and other math functions. In C99 this is explicitly stated in 5.2.4.2.2/5: I'm not sure whether C89 or C++ make it explicit. So I'm reluctant to rule out that the result could be out by a ulp or so. <code>int(root) == root</code> would give a false negative if <code>sqrt(7744)</code> came out as 87.9999999999999-ish</p> <p>Also, there are much larger numbers where <code>sqrt</code> can't be exact (around the limit of what <code>double</code> can represent exactly). So I think it's easier to write the extra two lines of code than to write the comment explaining why I think math functions will be exact in the case I care about :-)</p>
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    1. USSteve Jessop
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    1. CO+1 the obvious square root check is to check the produced square
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      1. USMatthieu M.
 

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