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<a name="math_toolkit.complex_implementation"></a><a class="link" href="complex_implementation.html" title="Implementation and Accuracy">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 9.5ε 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 © 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
Benjamin Sobotta, Thijs van den Berg, Daryle Walker 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>)
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