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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.complex_implementation"></a><a class="link" href="complex_implementation.html" title="Implementation and Accuracy">Implementation and
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Accuracy</a>
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</h2></div></div></div>
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<p>
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Although there are deceptively simple formulae available for all of these functions,
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a naive implementation that used these formulae would fail catastrophically
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for some input values. The Boost versions of these functions have been implemented
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using the methodology described in "Implementing the Complex Arcsine and
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Arccosine Functions Using Exception Handling" by T. E. Hull Thomas F.
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Fairgrieve and Ping Tak Peter Tang, ACM Transactions on Mathematical Software,
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Vol. 23, No. 3, September 1997. This means that the functions are well defined
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over the entire complex number range, and produce accurate values even at the
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extremes of that range, where as a naive formula would cause overflow or underflow
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to occur during the calculation, even though the result is actually a representable
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value. The maximum theoretical relative error for all of these functions is
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less than 9.5ε for every machine-representable point in the complex plane. Please
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refer to comments in the header files themselves and to the above mentioned
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paper for more information on the implementation methodology.
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<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
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Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
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Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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Daryle Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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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