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| Implementation and Accuracy</a> |
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| <p> |
| Although there are deceptively simple formulae available for all of these |
| functions, a naive implementation that used these formulae would fail catastrophically |
| for some input values. The Boost versions of these functions have been implemented |
| using the methodology described in "Implementing the Complex Arcsine |
| and Arccosine Functions Using Exception Handling" by T. E. Hull Thomas |
| F. Fairgrieve and Ping Tak Peter Tang, ACM Transactions on Mathematical Software, |
| Vol. 23, No. 3, September 1997. This means that the functions are well defined |
| over the entire complex number range, and produce accurate values even at |
| the extremes of that range, where as a naive formula would cause overflow |
| or underflow to occur during the calculation, even though the result is actually |
| a representable value. The maximum theoretical relative error for all of |
| these functions is less than 9.5E for every machine-representable point in |
| the complex plane. Please refer to comments in the header files themselves |
| and to the above mentioned paper for more information on the implementation |
| methodology. |
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| <td align="right"><div class="copyright-footer">Copyright © 2005 John Maddock<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>) |
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