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<title>Known Issues, and Todo List</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.status.issues"></a><a href="issues.html" title="Known Issues, and Todo List"> Known Issues, and Todo List</a>
</h3></div></div></div>
<p>
This section lists those issues that are known about.
</p>
<p>
Predominantly this is a TODO list, or a list of possible future enhancements.
Items labled "High Priority" effect the proper functioning of the
component, and should be fixed as soon as possible. Items labled "Medium
Priority" are desirable enhancements, often pertaining to the performance
of the component, but do not effect it's accuracy or functionality. Items
labled "Low Priority" should probably be investigated at some point.
Such classifications are obviously highly subjective.
</p>
<p>
If you don't see a component listed here, then we don't have any known issues
with it.
</p>
<a name="math_toolkit.status.issues.tgamma"></a><h5>
<a name="id790516"></a>
<a href="issues.html#math_toolkit.status.issues.tgamma">tgamma</a>
</h5>
<div class="itemizedlist"><ul type="disc"><li>
Can the <a href="../backgrounders/lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
be optimized any further? (low priority)
</li></ul></div>
<a name="math_toolkit.status.issues.incomplete_beta"></a><h5>
<a name="id790558"></a>
<a href="issues.html#math_toolkit.status.issues.incomplete_beta">Incomplete Beta</a>
</h5>
<div class="itemizedlist"><ul type="disc"><li>
Investigate Didonato and Morris' asymptotic expansion for large a and b
(medium priority).
</li></ul></div>
<a name="math_toolkit.status.issues.inverse_gamma"></a><h5>
<a name="id790591"></a>
<a href="issues.html#math_toolkit.status.issues.inverse_gamma">Inverse Gamma</a>
</h5>
<div class="itemizedlist"><ul type="disc"><li>
Investigate whether we can skip iteration altogether if the first approximation
is good enough (Medium Priority).
</li></ul></div>
<a name="math_toolkit.status.issues.polynomials"></a><h5>
<a name="id790624"></a>
<a href="issues.html#math_toolkit.status.issues.polynomials">Polynomials</a>
</h5>
<div class="itemizedlist"><ul type="disc"><li>
The Legendre and Laguerre Polynomials have surprisingly different error
rates on different platforms, considering they are evaluated with only
basic arithmetic operations. Maybe this is telling us something, or maybe
not (Low Priority).
</li></ul></div>
<a name="math_toolkit.status.issues.elliptic_integrals"></a><h5>
<a name="id790660"></a>
<a href="issues.html#math_toolkit.status.issues.elliptic_integrals">Elliptic Integrals</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li>
Carlson's algorithms are essentially unchanged from Xiaogang Zhang's Google
Summer of Code student project, and are based on Carlson's original papers.
However, Carlson has revised his algorithms since then (refer to the references
in the elliptic integral docs for a list), to improve performance and accuracy,
we may be able to take advantage of these improvements too (Low Priority).
</li>
<li>
<p>Carlson's algorithms (mainly R<sub>J</sub>) are somewhat prone to internal overflow/underflow
when the arguments are very large or small. The homogeneity relations:</p>
<p>R<sub>F</sub>(ka,
kb, kc) = k<sup>-1/2</sup> R<sub>F</sub>(a, b, c)</p>
<p>and</p>
<p>R<sub>J</sub>(ka, kb, kc, kr) = k<sup>-3/2</sup> R<sub>J</sub>(a, b, c, r)</p>
<p>could
be used to sidestep trouble here: provided the problem domains can be accurately
identified. (Medium Priority).</p>
</li>
<li>
Carlson's R<sub>C</sub> can be reduced to elementary funtions (asin and log), would
it be more efficient evaluated this way, rather than by Carlson's algorithms?
(Low Priority).
</li>
<li>
Should we add an implementation of Carlson's R<sub>G</sub>? It's not required for
the Legendre form integrals, but some people may find it useful (Low Priority).
</li>
<li>
There are a several other integrals: D(φ, k), Z(β, k), Λ<sub>0</sub>(β, k) and Bulirsch's
<span class="emphasis"><em>el</em></span> functions that could be implemented using Carlson's
integrals (Low Priority).
</li>
<li>
The integrals K(k) and E(k) could be implemented using rational approximations
(both for efficiency and accuracy), assuming we can find them. (Medium
Priority).
</li>
<li>
There is a sub-domain of <a href="../special/ellint/ellint_3.html" title="Elliptic Integrals of the Third Kind - Legendre Form">ellint_3</a>
that is unimplemented (see the docs for details), currently it's not clear
how to solve this issue, or if it's ever likely to be an real problem in
practice - especially as most other implementations don't support this
domain either (Medium Priority).
</li>
</ul></div>
<a name="math_toolkit.status.issues.inverse_hyperbolic_functions"></a><h5>
<a name="id790811"></a>
<a href="issues.html#math_toolkit.status.issues.inverse_hyperbolic_functions">Inverse
Hyperbolic Functions</a>
</h5>
<div class="itemizedlist"><ul type="disc"><li>
These functions are inherited from previous Boost versions, before <a href="../special/powers/log1p.html" title="log1p">log1p</a> became widely
available. Would they be better expressed in terms of this function? This
is probably only an issue for very high precision types (Low Priority).
</li></ul></div>
<a name="math_toolkit.status.issues.statistical_distributions"></a><h5>
<a name="id790856"></a>
<a href="issues.html#math_toolkit.status.issues.statistical_distributions">Statistical
distributions</a>
</h5>
<div class="itemizedlist"><ul type="disc"><li>
Student's t Perhaps switch to normal distribution as a better approximation
for very large degrees of freedom?
</li></ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
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