<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 Jul 19, 2019, at 9:10 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="">On Wed, 17 Jul 2019 12:09:58 -0500 Rajan Bhakta wrote:</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=""><blockquote type="cite" style="display: block; font-family: "Times New Roman"; background-color: lightgray; margin: 1em 40px; 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; text-decoration: none;" class=""><br class=""> Fred: Write a paper to make the range error for small nonzero x<br class="">consistent for expm1, logp1, log10p1's other base functions.<br class=""></blockquote><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="">Attached is a first pass.</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=""><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>2019-07-??<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 or missing statements about range errors in some of the math functions. Also, f(infinity) is infinity NOT being a range error is covered by 7.12.1#5 about overflows; therefore, "finite" is not needed in some places.</p><p 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 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 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 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 finite 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><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">finite</del><span class="Apple-converted-space"> </span>x is too large.</blockquote></li></ul></div></blockquote><div><br class=""></div>I don’t think saying “finite” hurts. It's true, and the reader might think this statement has precedence over 7.12.1#5, or view them as contradictory.<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 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><del style="font-weight: bold; background-color: rgb(255, 160, 160);" class="">finite</del><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>See above regarding “finite”. This says x, not the magnitude of x, is too large. We refer to the magnitude of x when the sign is to be ignored. No need to say “positive”. -2 is not larger than 1, and we should assume the reader understands that.<span style="font-family: "Times New Roman"; background-color: lightgray;" class=""> </span><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</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>No need for positive.<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 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></li></ul></div></blockquote>Remove “positive". Same problem in erfc and lgamma.</div><div><br class=""></div><div>- Jim<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=""><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 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 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 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 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></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; 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; 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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://mailman.oakapple.net/mailman/listinfo/cfp-interest</a></div></blockquote></div><br class=""></body></html>