<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=""><div><blockquote type="cite" class=""><div class="">On Feb 19, 2020, at 11:45 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="">Yet another attempt as an attachment.</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="">Please comment soon so I can try to make the next WG14 mailing deadline.</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>2020-02-??<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><div class=""><br class=""></div></div></blockquote>I think there are two problems. As you say, there are a few incorrect, missing, or ambiguous statements. But also there’s the problem of too casual reading of statements that are correct given common mathematical terminology. We’re trying to address both of these problems by fixing the former and by clarifying the specification to be less subject to misreading. I’m not suggesting this be stated in the paper, but consider adding “Implementers have interpreted these terms differently” (assuming of course it’s true). <br class=""><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="">It appears that "magnitude" has no formal definition.</p><div class=""><br class=""></div></div></blockquote><div><br class=""></div>Is there any evidence that “magnitude” has been misunderstood? If not, omit the statement about magnitude.</div><div><br class=""></div><div> <blockquote type="cite" class=""><div class=""><div class=""><br class=""></div><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><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="">Sizes of integer types <limits.h><p class="">Change 5.2.4.2.1#1 to give magnitude a definition</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">... magnitude (absolute value) ...</blockquote>to:<blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">...<span class="Apple-converted-space"> </span><i class="">magnitude</i><span class="Apple-converted-space"> </span>(absolute value) …</blockquote></li></ul></div></blockquote>I don’t think this is needed. What problem is it fixing? Also, just italicizing it doesn’t provide a definition. Parenthetical remarks should not be normative. And, there’s no definition of absolute value in the standard.<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="">Treatment of error conditions<p class="">Change 7.12.1#5</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">... overflows if the magnitude ...</blockquote>to:<blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">... overflows if the magnitude<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">(absolute value)</ins><span class="Apple-converted-space"> </span>...</blockquote></li><li class="">Treatment of error conditions<p class="">Change 7.12.1#6</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">... underflows if the magnitude ...</blockquote>to:<blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">... underflows if the magnitude<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">(absolute value)</ins><span class="Apple-converted-space"> </span>…</blockquote></li></ul></div></blockquote></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=""><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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero y/x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><li class="">The asinpi functions<p class="">Change 7.12.4.9#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 nonzero x is too small.</blockquote>to:<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>nonzero 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 atanpi functions<p class="">Change 7.12.4.10#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 nonzero x is too small.</blockquote>to:<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>nonzero 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 atan2pi functions<p class="">Change 7.12.4.11#2</p><blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if x is positive and the magnitude of nonzero y/x is too small.</blockquote>to:<blockquote style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px;" class="">A range error occurs if x is positive and<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>nonzero y/x is too<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">small</del><span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">close to zero</ins>.</blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero</ins>.</blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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><li class="">The exp10 functions<p class="">Change 7.12.6.2#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 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</del><span class="Apple-converted-space"> </span>nonzero x is too<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 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><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</del>nonzero 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 expm1 functions<p class="">Change 7.12.6.6#2 from</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.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 nonzero x is too close to zero</ins>.252)</blockquote></li><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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs for some finite x, depending on p</ins>.</blockquote></li><li class="">The log10p1 function<p class="">Change 7.12.6.13#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 nonzero x is too small.</blockquote>to:<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</del><span class="Apple-converted-space"> </span>nonzero 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 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 nonzero x is too close to zero.</ins></blockquote></li><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 nonzero x is too close to zero.</ins></blockquote></li><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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs for some finite x, depending on n</ins>.</blockquote></li><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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs</ins><span class="Apple-converted-space"> </span>if<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">positive finite x</ins><span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">n</del><span class="Apple-converted-space"> </span>is too large<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">or if negative x is too near -1</ins>, depending on<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">n</ins><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">x</del>.</blockquote></li></ul></blockquote>I think it should be</div><div><br class=""></div><div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>• A range error occurs if positive finite x is too large or if x is too near but not equal to -1, depending on n.<br class=""></div><div class=""><br class=""></div><blockquote type="cite" class=""><ul style="text-align: start; text-indent: 0px;" 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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs for some finite arguments</ins>.</blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">ocurs if the magnitude of nonzero finite x is too large or too near zero, depending on y</ins>.</blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs if the magnitude of nonzero finite x is too large or too near zero, depending on n</ins>.</blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs if positive nonzero finite x is too large or too near zero, depending on y</ins>.</blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs if the magnitude of nonzero finite x is too large or too near zero and</ins><span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">if</del><span class="Apple-converted-space"> </span>n is -1.</blockquote></li></ul></blockquote>Consider</div><div><br class=""></div><div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>• A range error occurs if n is -1 and the magnitude of nonzero finite x is too large or too near zero.<br class=""></div><br class=""><blockquote type="cite" class=""><ul style="text-align: start; text-indent: 0px;" class=""><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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 nonzero x is too close to zero.</ins></blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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, and</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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><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><span class="Apple-converted-space"> </span>nonzero 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></blockquote>I believe the following would be more consistent with other wording:</div><div><br class=""></div><div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span>• A range error occurs for some negative finite x, and if positive finite x is too large or nonzero x is too close to zero.<br class=""></div><br class=""><blockquote type="cite" class=""><ul style="text-align: start; text-indent: 0px;" class=""><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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 occurs if x is finite, both x and y are nonzero, and either is too close to zero.</ins></blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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 occurs if x is finite, both x and y are nonzero, and either is too close to zero.</ins></blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs if positive finite x-y is too large or too close to zero</ins>.</blockquote></li><li class="" 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-transform: none; white-space: normal; word-spacing: 0px; text-decoration: none; -webkit-text-stroke-width: 0px;">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<span class="Apple-converted-space"> </span><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">may occur</del><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">occurs for some finite arguments</ins>.</blockquote></li></ul><span style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; 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