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<p class="MsoNormal"><span style="font-size:11.0pt">Hi Paul,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">If you are referring to CFP message 3458, the textual change we were referring to was regarding the first part, aka, change the text to read “</span><span style="font-size:11.0pt;color:#212121">A range error
occurs if x is positive and if y/x is nonzero and too close to zero.”.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;color:#212121"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;color:#212121">I believe in the replied to message below, you are referring to the second part of Javier’s message which was already responded to previously and we are not suggesting any change.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;color:#212121"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;color:#212121">If I misunderstood your message, please let me know.</span><span style="font-size:11.0pt"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri",sans-serif;color:#212121">Regards,</span><span style="font-family:"Calibri",sans-serif;color:#212121"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">Paul Zimmermann <Paul.Zimmermann@inria.fr><br>
<b>Date: </b>Thursday, May 15, 2025 at 2:51</span><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:12.0pt;color:black">AM<br>
<b>To: </b>RAJAN BHAKTA <rbhakta@us.ibm.com><br>
<b>Cc: </b>javier@aerotri.es <javier@aerotri.es>, cfp-interest@ucbtest.org <cfp-interest@ucbtest.org><br>
<b>Subject: </b>[EXTERNAL] Re: [cfp-interest 3458] Re: Range error conditions for atan2 and atan2pi<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:11.0pt"> Hi,<br>
<br>
> atan2:<br>
> <br>
> The atan2 functions [...]. A domain error may occur if both arguments are<br>
> zero. A range error occurs if x is positive and nonzero y/x is too close to<br>
> zero.<br>
><br>
> Why "positive"? Considering that atan2 is an odd function, +x and -x should<br>
> give +alpha and -alpha uniformly. The "atan", "sin", "tan", etc. functions<br>
> don't make this distinction. Its presence in atan2 and atan2pi seems<br>
> spurious.<br>
<br>
for y/x close to zero and x > 0, atan2(y,x) is close to zero, since z = x+i*y<br>
is near the right real axis, and atan2(y,x) gives the angle of the complex<br>
number z.<br>
<br>
However, for y/x close to zero and x < 0, the complex number z is close to the<br>
left real axis, and then atan2(y,x) is close to +/-pi according to the sign of<br>
y. In that case there can be no underflow, thus no domain error.<br>
<br>
Thus the current text is fine.<br>
<br>
Paul<o:p></o:p></span></p>
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