<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 Aug 23, 2019, at 1:59 PM, 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="">Here is an updated (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=""><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>2019-08-??<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 consider f(infinity) as a range error based upon the text: A range error occurs if [the magnitude of] x is too </p></div></blockquote>Consider changing to: “Some implementations incorrectly treat …”.<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="">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="">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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero y/x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 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 finite<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>x is too large or if the magnitude of nonzero x is too small.</blockquote></li></ul></div></blockquote>I recall David suggesting this be “A range error occurs if the magnitude of finite positive x is too large ….” but am not sure what we agreed to. With that change we’d be saying “magnitude” wherever talking about too large or too small. Without that change we’d be saying “magnitude” just where needed for correctness.<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 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="">finite positive</ins><span class="Apple-converted-space"> </span>x is too large or if the magnitude of nonzero x is too small.</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<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>positive x is too large<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">or if the magnitude of nonzero x is too small</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 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><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 the magnitude of nonzero x is too small.</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 the magnitude of nonzero x is too small.</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 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><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 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></div></blockquote>Do we mean if the magnitude of n 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 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><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><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><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><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><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 the magnitude of nonzero x is too small.</ins></blockquote></li><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<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>positive x is too large.</blockquote></li><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<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>positive x is too large.</blockquote></li><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 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 and may occur if the magnitude of<span class="Apple-converted-space"> </span><ins style="font-weight: bold; background-color: rgb(160, 255, 160);" class="">non-zero</ins><span class="Apple-converted-space"> </span>x is too small.</blockquote></li></ul></div></blockquote>How is there a range error if the magnitude of negative x is too large? Can't there be range errors for moderate magnitude negative x?<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 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 the magnitude of either is too small.</ins></blockquote></li><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 the magnitude of either is too small.</ins></blockquote></li><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><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></div></blockquote><div><br class=""></div>A general question: What does “may occur” mean?</div><div><br class=""></div><div><br class=""></div><div>- Jim Thomas</div><div><br class=""></div><div><blockquote type="cite" class=""><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="">_______________________________________________</span><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; 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