<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Oct 15, 2019, at 9:31 AM, Fred J. Tydeman <<a href="mailto:tydeman@tybor.com" class="">tydeman@tybor.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Attached is the updated range error file.</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Comments welcome.</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">---</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Fred J. Tydeman Tydeman Consulting</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><a href="mailto:tydeman@tybor.com" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;" class="">tydeman@tybor.com</a><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class=""><span class="Apple-converted-space"> </span> Testing, numerics, programming</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">+1 (702) 608-6093 Vice-chair of PL22.11 (ANSI "C")</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Sample C99+FPCE tests:<span class="Apple-converted-space"> </span></span><a href="http://www.tybor.com/" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;" class="">http://www.tybor.com</a><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;" class="">Savers sleep well, investors eat well, spenders work forever.</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><p style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><br class=""><b class="">Submitter:</b>Fred Tydeman<br class=""><b class="">Submission Date:</b><span class="Apple-converted-space"> </span>2019-10-??<br class=""><b class="">Document:</b><span class="Apple-converted-space"> </span>WG14 Nxxxx<br class=""><b class="">Reference Documents:</b></p><p style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">Summary</p><p style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">The standard has a few incorrect, missing, or ambiguous statements about range errors in some of the math functions.</p><p style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">Does "too large" mean close to +infinity or +/-infinity?</p><p style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">Does "too small" mean close to -infinity or +/-zero?</p><p style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">Some implementations incorrectly treat f(infinity) as a range error based upon the text: A range error occurs if [the magnitude of] x is too large. While this is covered by 7.12.1#5 about overflows, the CFP group believes it is better to be explicit in each math function where it matters.</p></div></blockquote><blockquote type="cite" class=""><div class=""><p style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">Possible Technical Corrigendum:</p><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The asin functions<p class="">Add to 7.12.4.2#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.</div><div><br class=""></div><div>Also for asinpi.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The atan functions<p class="">Add to 7.12.4.3#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.</div><div><br class=""></div><div>Also for atanpi<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The atan2 functions<p class="">Add to 7.12.4.4#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is positive and y/x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero y/x is too close to zero”.</div><div><br class=""></div><div>Also for atan2pi.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The sin functions<p class="">Add to 7.12.4.6#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.</div><div><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The tan functions<p class="">Add to 7.12.4.7#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.</div><div><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The sinpi functions<p class="">Add to 7.12.4.13#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The tanpi functions<p class="">Add to 7.12.4.14#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The asinh functions<p class="">Add to 7.12.5.2#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The atanh functions<p class="">Add to 7.12.5.3#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The cosh functions<p class="">Change 7.12.5.4#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of x is too large.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x is too large.</blockquote></li><li class="">The sinh functions<p class="">Change 7.12.5.5#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of x is too large.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x is too large<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">or if x is too close to zero</ins>.</blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The tanh functions<p class="">Add to 7.12.5.6#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></div></blockquote>Clarify by saying “… if nonzero x is too close to zero”.<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The exp functions<p class="">Change 7.12.6.1#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of x is too large.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x is too large.</blockquote></li></ul></div></blockquote><div>Might suggest there is a magnitude threshold for range errors. But the thresholds for positive and negative x are different. More explicit would be “… If the magnitude of positive finite x is too large or if the magnitude of negative finite x is too large."</div><blockquote type="cite" class=""><ul class=""></ul></blockquote><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The exp10m1 functions<p class="">Change 7.12.6.3#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if finite x is too large or if the magnitude of nonzero x is too small.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">positive</ins><span class="Apple-converted-space"> </span>finite x is too large or if<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">the magnitude of nonzero</del><span class="Apple-converted-space"> </span>x is too<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">small</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">close to zero</ins>.</blockquote></li></ul></div></blockquote>Might suggest there is a magnitude threshold for range errors nears zero. But the thresholds for positive and negative x are different. More explicit would be “… if positive finite x is too large, if positive nonzero x is too close to zero, or if negative nonzero x is too close to zero."</div><div><blockquote type="cite" class=""><ul class=""></ul></blockquote><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The exp2 functions<p class="">Change 7.12.6.4#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of x is too large.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x is too large.</blockquote></li></ul></div></blockquote>More explicit would be “… If the magnitude of positive finite x is too large or if the magnitude of negative finite x is too large."<br class=""><blockquote type="cite" class=""><div class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The exp2m1 functions<p class="">Change 7.12.6.5#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of x is too large or if the magnitude of nonzero x is too small.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">the magnitude of</del><span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">positive finite</ins><span class="Apple-converted-space"> </span>x is too large or if<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">the magnitude of nonzero</del><span class="Apple-converted-space"> </span>x is too<del class="" style="font-weight: bold; background-color: rgb(255, 160, 160);">small</del><ins class="" style="font-weight: bold; background-color: rgb(160, 255, 160);">close to zero</ins>.</blockquote></li></ul></div></blockquote><div>More explicit would be “… if positive finite x is too large, if positive nonzero x is too close to zero, or if negative nonzero x is too close to zero."</div><blockquote type="cite" class=""><ul class=""><li class="">The expm1 functions</li></ul></blockquote><blockquote type="cite" class=""><ul class=""><li class="">Change 7.12.6.6#2 from</li></ul></blockquote><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class=""><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if positive x is too large.252)</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if positive<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x is too large<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">or if x is too close to zero</ins>.252)</blockquote></li></ul></blockquote>More explicit would be “… if positive finite x is too large, if positive nonzero x is too close to zero, or if negative nonzero x is too close to zero."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The ldexp functions<p class="">Change 7.12.6.9#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite x</ins>.</blockquote></li></ul></blockquote><div>This isn’t the way “may” is normally used in C. Better might be "A range error occurs for some finite x.”</div><div><br class=""></div><div>We generally try to be more specific about when range errors occur, which is tricky for this and some other functions. Whether a range error occurs also depends on p. Maybe “A range error occurs if the magnitude of finite (positive or negative) nonzero x is too large or too near zero, depending on p."</div><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The log1p and logp1 functions<p class="">Add to 7.12.6.14#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></blockquote><div>More explicit would be “… if positive nonzero x is too close to zero or if negative nonzero x is too close to zero."</div><div><blockquote type="cite" class=""><ul class=""></ul></blockquote><blockquote type="cite" class=""><ul class=""></ul></blockquote></div><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The log2p1 functions<p class="">Add to 7.12.6.16#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></blockquote><div>More explicit would be “… if positive nonzero x is too close to zero or if negative nonzero x is too close to zero."</div><div><blockquote type="cite" class=""><ul class=""></ul></blockquote><blockquote type="cite" class=""><ul class=""></ul></blockquote></div><blockquote type="cite" class=""><ul class=""></ul></blockquote><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The scalbn and scalbln functions<p class="">Change 7.12.6.19#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite x</ins>.</blockquote></li></ul></blockquote>See ldexp above. Maybe “A range error occurs if the magnitude of finite (positive or negative) nonzero x is too large or too near zero, depending on n."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The compoundn functions<p class="">Change 7.12.7.2#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur if n is too large, depending on x.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur if<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">the magnitude of</ins><span class="Apple-converted-space"> </span>n is too large, depending on<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x.</blockquote></li></ul></blockquote>Maybe “A range error occurs if the magnitude of finite positve x is too large or if negative x is too near -1, each depending on n."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The hypot functions<p class="">Change 7.12.7.4#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite arguments</ins>.</blockquote></li></ul></blockquote>Maybe “A range error occurs for some finite arguments”, to avoid “may”.<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The pow functions<p class="">Change 7.12.7.5#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite x</ins>.</blockquote></li></ul></blockquote>Maybe "A range error occurs if the magnitude of nonzero finite x is too large or too near zero, depending on y."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The pown functions<p class="">Change 7.12.7.6#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite x</ins>.</blockquote></li></ul></blockquote>Maybe "A range error occurs if the magnitude of nonzero finite x is too large or too near zero, depending on n."<br class=""><blockquote type="cite" class=""><ul class=""></ul></blockquote><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The powr functions<p class="">Change 7.12.7.7#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite x</ins>.</blockquote></li></ul></blockquote>Maybe "A range error occurs if the magnitude of nonzero finite (positive) x is too large or too near zero, depending on y."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The rootn functions<p class="">Change 7.12.7.8#2 from</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur if n is -1.</blockquote><p class="">to</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite x</ins><span class="Apple-converted-space"> </span>if n is -1.</blockquote></li></ul></blockquote>Maybe "A range occurs if the magnitude of finite nonzero x is too large or too near zero and n is -1."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The erf functions<p class="">Add to 7.12.8.1#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error occurs if x is too close to zero.</ins></blockquote></li></ul></blockquote>Clarify by saying “… if nonzero x is too close to zero”.<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The erfc functions<p class="">Change 7.12.8.2#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if positive x is too large.</blockquote><p class="">to:</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if positive<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x is too large.</blockquote></li></ul></blockquote>Maybe “… if the magnitude of positive finite x is too large."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The lgamma functions<p class="">Change 7.12.8.3#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if positive x is too large.</blockquote><p class="">to:</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if positive<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">finite</ins><span class="Apple-converted-space"> </span>x is too large.</blockquote></li></ul></blockquote>Maybe “… if the magnitude of positive finite x is too large."<br class=""><blockquote type="cite" class=""><ul class=""></ul></blockquote><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The tgamma functions<p class="">Change 7.12.8.4#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if the magnitude of x is too large and may occur if the magnitude of x is too small.</blockquote><p class="">to:</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for some negative finite x or</ins><span class="Apple-converted-space"> </span>if<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">the magnitude of</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">positive finite</ins><span class="Apple-converted-space"> </span>x is too large<ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">;</ins><span class="Apple-converted-space"> </span>and may occur if<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">the magnitude of</del><span class="Apple-converted-space"> </span>x is too<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">small</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">close to zero</ins>.</blockquote></li><li class="">The fmod functions<p class="">Add to 7.12.10.1#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error may occur if both x and y are nonzero and either is too close to zero.</ins></blockquote></li></ul></blockquote>“A range error occurs if x is finite, both x and y are nonzero, and either is too close to zero."</div><div><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The remainder functions<p class="">Add to 7.12.10.2#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class=""><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">A range error may occur if both x and y are nonzero and either is too close to zero.</ins></blockquote></li></ul></blockquote><div><div>“A range error occurs if x is finite, both x and y are nonzero, and either is too close to zero."</div><div><blockquote type="cite" class=""><ul class=""></ul></blockquote></div></div><div><blockquote type="cite" class=""><ul class=""></ul></blockquote></div><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The fdim functions<p class="">Change 7.12.12.1#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to:</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite arguments</ins>.</blockquote></li></ul></blockquote>Maybe "A range error occurs if the magnitude of positive x - y is too large or too small."<br class=""><blockquote type="cite" class=""><ul style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><li class="">The fma functions<p class="">Change 7.12.13.1#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur.</blockquote><p class="">to:</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error may occur<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">for finite arguments</ins>.</blockquote></li></ul></blockquote>Maybe “A range error occurs for some finite arguments.”</div><div><br class=""></div><div>- Jim Thomas</div><div><br class=""></div><div><blockquote type="cite" class=""><span style="caret-color: rgb(0, 0, 0); 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