https://svn.boost.org/trac10/ticket/5113 <p> The documentation and the code have different bugs for the approximation of acosh(x) for x near 1. </p> <p> First of all they use different definitions of y. The documentation has y=1-x and the code has y=x-1. They both use the formula <code>(1+(1/12)*y+(3/160)*y^2)*sqrt(2*y)</code>, but neither of them is correct. </p> <p> correct formulas <a class="changeset" href="https://svn.boost.org/trac10/changeset/1" title="Import core sources for SVNmanger 0.38 ">[1]</a> </p> <p> <code>y=1-x -&gt; (1+(1/12)*y+(3/160)*y^2)*sqrt(-2*y)</code> </p> <p> <code>y=x-1 -&gt; (1-(1/12)*y+(3/160)*y^2)*sqrt(2*y)</code> </p> <p> <a class="changeset" href="https://svn.boost.org/trac10/changeset/1" title="Import core sources for SVNmanger 0.38 ">[1]</a> <a class="ext-link" href="http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/"><span class="icon">​</span>http://functions.wolfram.com/ElementaryFunctions/ArcCosh/06/01/04/01/0001/</a> </p> en-us /htdocs/site/boost.png https://svn.boost.org/trac10/ticket/5113 Trac 1.4.3 John Maddock Mon, 24 Jan 2011 16:41:04 GMT https://svn.boost.org/trac10/ticket/5113#comment:1 https://svn.boost.org/trac10/ticket/5113#comment:1 <ul> <li><strong>status</strong> <span class="trac-field-old">new</span> → <span class="trac-field-new">assigned</span> </li> <li><strong>milestone</strong> <span class="trac-field-old">To Be Determined</span> → <span class="trac-field-new">Boost 1.47.0</span> </li> </ul> <p> Confirmed, testing fixes and new tests... </p> Ticket John Maddock Mon, 24 Jan 2011 19:04:44 GMT https://svn.boost.org/trac10/ticket/5113#comment:2 https://svn.boost.org/trac10/ticket/5113#comment:2 <ul> <li><strong>status</strong> <span class="trac-field-old">assigned</span> → <span class="trac-field-new">closed</span> </li> <li><strong>resolution</strong> → <span class="trac-field-new">fixed</span> </li> </ul> <p> (In <a class="changeset" href="https://svn.boost.org/trac10/changeset/68421" title="Fix acosh bug, and update tests and docs accordingly. Fixes #5113.">[68421]</a>) Fix acosh bug, and update tests and docs accordingly. Fixes <a class="closed ticket" href="https://svn.boost.org/trac10/ticket/5113" title="#5113: Bugs: math/special_functions/acosh.hpp wrong approximation for x near 1 (closed: fixed)">#5113</a>. </p> Ticket