class RooMath

 @brief evaluate Faddeeva function for complex argument
   *
   * @author Manuel Schiller <manuel.schiller@nikhef.nl>
   * @date 2013-02-21
   *
   * Calculate the value of the Faddeeva function @f$w(z) = \exp(-z^2)
   * \mathrm{erfc}(-i z)@f$.
   *
   * The method described in
   *
   * S.M. Abrarov, B.M. Quine: "Efficient algotithmic implementation of
   * Voigt/complex error function based on exponential series approximation"
   * published in Applied Mathematics and Computation 218 (2011) 1894-1902
   * doi:10.1016/j.amc.2011.06.072
   *
   * is used. At the heart of the method (equation (14) of the paper) is the
   * following Fourier series based approximation:
   *
   * @f[ w(z) \approx \frac{i}{2\sqrt{\pi}}\left(
   * \sum^N_{n=0} a_n \tau_m\left(
   * \frac{1-e^{i(n\pi+\tau_m z)}}{n\pi + \tau_m z} -
   * \frac{1-e^{i(-n\pi+\tau_m z)}}{n\pi - \tau_m z}
   * \right) - a_0 \frac{1-e^{i \tau_m z}}{z}
   * \right) @f]
   *
   * The coefficients @f$a_b@f$ are given by:
   *
   * @f[ a_n=\frac{2\sqrt{\pi}}{\tau_m}
   * \exp\left(-\frac{n^2\pi^2}{\tau_m^2}\right) @f]
   *
   * To achieve machine accuracy in double precision floating point arithmetic
   * for most of the upper half of the complex plane, chose @f$t_m=12@f$ and
   * @f$N=23@f$ as is done in the paper.
   *
   * There are two complications: For Im(z) negative, the exponent in the
   * equation above becomes so large that the roundoff in the rest of the
   * calculation is amplified enough that the result cannot be trusted.
   * Therefore, for Im(z) < 0, the symmetry of the erfc function under the
   * transformation z --> -z is used to avoid accuracy issues for Im(z) < 0 by
   * formulating the problem such that the calculation can be done for Im(z) > 0
   * where the accuracy of the method is fine, and some postprocessing then
   * yields the desired final result.
   *
   * Second, the denominators in the equation above become singular at
   * @f$z = n * pi / 12@f$ (for 0 <= n < 24). In a tiny disc around these
   * points, Taylor expansions are used to overcome that difficulty.
   *
   * This routine precomputes everything it can, and tries to write out complex
   * operations to minimise subroutine calls, e.g. for the multiplication of
   * complex numbers.
   *
   * In the square -8 <= Re(z) <= 8, -8 <= Im(z) <= 8, the routine is accurate
   * to better than 4e-13 relative, the average relative error is better than
   * 7e-16. On a modern x86_64 machine, the routine is roughly three times as
   * fast than the old CERNLIB implementation and offers better accuracy.
   *
   * For large @f$|z|@f$, the familiar continued fraction approximation
   *
   * @f[ w(z)=\frac{-iz/\sqrt{\pi}}{-z^2+\frac{1/2}{1+\frac{2/2}{-z^2 +
   * \frac{3/2}{1+\frac{4/2}{-z^2+\frac{5/2}{1+\frac{6/2}{-z^2+\frac{7/2
   * }{1+\frac{8/2}{-z^2+\frac{9/2}{1+\ldots}}}}}}}}}} @f]
   *
   * is used, truncated at the ellipsis ("...") in the formula; for @f$|z| >
   * 12@f$, @f$Im(z)>0@f$ it will give full double precision at a smaller
   * computational cost than the method described above. (For @f$|z|>12@f$,
   * @f$Im(z)<0@f$, the symmetry property @f$w(x-iy)=2e^{-(x+iy)^2-w(x+iy)}@f$
   * is used.

 @brief evaluate Faddeeva function for complex argument (fast version)
   *
   * @author Manuel Schiller <manuel.schiller@nikhef.nl>
   * @date 2013-02-21
   *
   * Calculate the value of the Faddeeva function @f$w(z) = \exp(-z^2)
   * \mathrm{erfc}(-i z)@f$.
   *
   * This is the "fast" version of the faddeeva routine above. Fast means that
   * is takes roughly half the amount of CPU of the slow version of the
   * routine, but is a little less accurate.
   *
   * To be fast, chose @f$t_m=8@f$ and @f$N=11@f$ which should give accuracies
   * around 1e-7.
   *
   * In the square -8 <= Re(z) <= 8, -8 <= Im(z) <= 8, the routine is accurate
   * to better than 4e-7 relative, the average relative error is better than
   * 5e-9. On a modern x86_64 machine, the routine is roughly five times as
   * fast than the old CERNLIB implementation, or about 30% faster than the
   * interpolation/lookup table based fast method used previously in RooFit,
   * and offers better accuracy than the latter (the relative error is roughly
   * a factor 280 smaller than the old interpolation/table lookup routine).
   *
   * For large @f$|z|@f$, the familiar continued fraction approximation
   *
   * @f[ w(z)=\frac{-iz/\sqrt{\pi}}{-z^2+\frac{1/2}{1+\frac{2/2}{-z^2 +
   * \frac{3/2}{1+\ldots}}}} @f]
   *
   * is used, truncated at the ellipsis ("...") in the formula; for @f$|z| >
   * 8@f$, @f$Im(z)>0@f$ it will give full float precision at a smaller
   * computational cost than the method described above. (For @f$|z|>8@f$,
   * @f$Im(z)<0@f$, the symmetry property @f$w(x-iy)=2e^{-(x+iy)^2-w(x+iy)}@f$
   * is used.

 @brief complex erf function
   *
   * @author Manuel Schiller <manuel.schiller@nikhef.nl>
   * @date 2013-02-21
   *
   * Calculate erf(z) for complex z.

 @brief complex erf function (fast version)
   *
   * @author Manuel Schiller <manuel.schiller@nikhef.nl>
   * @date 2013-02-21
   *
   * Calculate erf(z) for complex z. Use the code in faddeeva_fast to save some time.

 @brief complex erfc function
   *
   * @author Manuel Schiller <manuel.schiller@nikhef.nl>
   * @date 2013-02-21
   *
   * Calculate erfc(z) for complex z.

 @brief complex erfc function (fast version)
   *
   * @author Manuel Schiller <manuel.schiller@nikhef.nl>
   * @date 2013-02-21
   *
   * Calculate erfc(z) for complex z. Use the code in faddeeva_fast to save some time.

 1-D nth order polynomial interpolation routines

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