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91 lines
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91 lines
3.7 KiB
Plaintext
[section:issues Known Issues, and Todo List]
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This section lists those issues that are known about.
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Predominantly this is a TODO list, or a list of possible
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future enhancements. Items labled "High Priority" effect
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the proper functioning of the component, and should be fixed
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as soon as possible. Items labled "Medium Priority" are
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desirable enhancements, often pertaining to the performance
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of the component, but do not effect it's accuracy or functionality.
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Items labled "Low Priority" should probably be investigated at
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some point. Such classifications are obviously highly subjective.
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If you don't see a component listed here, then we don't have any known
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issues with it.
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[h4 tgamma]
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* Can the __lanczos be optimized any further? (low priority)
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[h4 Incomplete Beta]
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* Investigate Didonato and Morris' asymptotic expansion for large a and b
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(medium priority).
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[h4 Inverse Gamma]
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* Investigate whether we can skip iteration altogether if the first approximation
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is good enough (Medium Priority).
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[h4 Polynomials]
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* The Legendre and Laguerre Polynomials have surprisingly different error
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rates on different platforms, considering they are evaluated with only
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basic arithmetic operations. Maybe this is telling us something, or maybe not
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(Low Priority).
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[h4 Elliptic Integrals]
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* Carlson's algorithms are essentially unchanged from Xiaogang Zhang's
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Google Summer of Code student project, and are based on Carlson's
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original papers. However, Carlson has revised his algorithms since then
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(refer to the references in the elliptic integral docs for a list), to
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improve performance and accuracy, we may be able to take advantage
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of these improvements too (Low Priority).
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* [para Carlson's algorithms (mainly R[sub J]) are somewhat prone to
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internal overflow/underflow when the arguments are very large or small.
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The homogeneity relations:]
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[para R[sub F](ka, kb, kc) = k[super -1/2] R[sub F](a, b, c)]
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[para and]
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[para R[sub J](ka, kb, kc, kr) = k[super -3/2] R[sub J](a, b, c, r)]
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[para could be used to sidestep trouble here: provided the problem domains
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can be accurately identified. (Medium Priority).]
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* Carlson's R[sub C] can be reduced to elementary funtions (asin and log),
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would it be more efficient evaluated this way, rather than by Carlson's
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algorithms? (Low Priority).
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* Should we add an implementation of Carlson's R[sub G]? It's not
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required for the Legendre form integrals, but some people may find it
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useful (Low Priority).
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* There are a several other integrals: D([phi], k), Z([beta], k),
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[Lambda][sub 0]([beta], k) and Bulirsch's ['el] functions that could
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be implemented using Carlson's integrals (Low Priority).
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* The integrals K(k) and E(k) could be implemented using rational
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approximations (both for efficiency and accuracy),
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assuming we can find them. (Medium Priority).
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* There is a sub-domain of __ellint_3 that is unimplemented (see the docs
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for details), currently
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it's not clear how to solve this issue, or if it's ever likely
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to be an real problem in practice - especially as most other implementations
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don't support this domain either (Medium Priority).
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[h4 Inverse Hyperbolic Functions]
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* These functions are inherited from previous Boost versions,
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before __log1p became widely available. Would they be better expressed
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in terms of this function? This is probably only an issue
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for very high precision types (Low Priority).
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[h4 Statistical distributions]
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* Student's t Perhaps switch to normal distribution as a better approximation for very large degrees of freedom?
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[endsect][/section:issues Known Issues, and Todo List]
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[/
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Copyright 2006 John Maddock and Paul A. Bristow.
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt).
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]
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