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<title>Nxxxx: Range errors and math functions</title>
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<p><br>
<!-- Who are the authors... -->
<b>Submitter:</b>Fred Tydeman<br>
<!-- What is the date of submission. yyyy-mm-dd -->
<b>Submission Date:</b> 2019-07-??<br>
<b>Document:</b> WG14 Nxxxx<br>
<b>Reference Documents:</b></p>
<p>Summary</p>
<p>The standard has a few incorrect or missing statements about
range errors in some of the math functions. Also, f(infinity) is
infinity NOT being a range error is covered by 7.12.1#5 about
overflows; therefore, "finite" is not needed in some places.</p>
<p>Possible Technical Corrigendum:</p>
<ul>
<li>The asin functions
<p>Add to 7.12.4.2#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The atan functions
<p>Add to 7.12.4.3#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The atan2 functions
<p>Add to 7.12.4.4#2</p>
<blockquote>
<ins>A range error occurs if x is positive and the
magnitude of nonzero y/x is too small.</ins>
</blockquote>
</li>
<li>The sin functions
<p>Add to 7.12.4.6#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The tan functions
<p>Add to 7.12.4.7#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The sinpi functions
<p>Add to 7.12.4.13#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The tanpi functions
<p>Add to 7.12.4.14#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The asinh functions
<p>Add to 7.12.5.2#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The atanh functions
<p>Add to 7.12.5.3#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The sinh functions
<p>Change 7.12.5.5#2 from</p>
<blockquote>
A range error occurs if the magnitude of x is too large.
</blockquote>
<p>to</p>
<blockquote>
A range error occurs if the magnitude of x is too large
<ins>or if the magnitude of nonzero x is too small.</ins>.
</blockquote>
</li>
<li>The tanh functions
<p>Add to 7.12.5.6#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The exp10 functions
<p>Change 7.12.6.2#2 from</p>
<blockquote>
A range error occurs if the magnitude of finite x is too
large.
</blockquote>
<p>to</p>
<blockquote>
A range error occurs if the magnitude of <del>finite</del>
x is too large.
</blockquote>
</li>
<li>The exp10m1 functions
<p>Change 7.12.6.3#2 from</p>
<blockquote>
A range error occurs if finite x is too large or if the
magnitude of nonzero x is too small.
</blockquote>
<p>to</p>
<blockquote>
A range error occurs if <del>finite</del>
<ins>positive</ins> x is too large or if the magnitude of
nonzero x is too small.
</blockquote>
</li>
<li>The exp2m1 functions
<p>Change 7.12.6.5#2 from</p>
<blockquote>
A range error occurs if the magnitude of x is too large or
if the magnitude of nonzero x is too small.
</blockquote>
<p>to</p>
<blockquote>
A range error occurs if <del>the magnitude of</del>
<ins>positive</ins> x is too large or if the magnitude of
nonzero x is too small.
</blockquote>
</li>
<li>The expm1 functions
<p>Change 7.12.6.6#2 from</p>
<blockquote>
A range error occurs if positive x is too large.252)
</blockquote>
<p>to</p>
<blockquote>
A range error occurs if positive x is too large <ins>or if
the magnitude of nonzero x is too small</ins>.252)
</blockquote>
</li>
<li>The log1p and logp1 functions
<p>Add to 7.12.6.14#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The log2p1 functions
<p>Add to 7.12.6.16#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The erf functions
<p>Add to 7.12.8.1#2</p>
<blockquote>
<ins>A range error occurs if the magnitude of nonzero x is
too small.</ins>
</blockquote>
</li>
<li>The fmod functions
<p>Add to 7.12.10.1#2</p>
<blockquote>
<ins>A range error may occur if both x and y are nonzero
and the magnitude of either is too small.</ins>
</blockquote>
</li>
<li>The remainder functions
<p>Add to 7.12.10.2#2</p>
<blockquote>
<ins>A range error may occur if both x and y are nonzero
and the magnitude of either is too small.</ins>
</blockquote>
</li>
</ul>
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