/*=============================================================================

    This file is part of FLINT.

    FLINT is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    FLINT is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with FLINT; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2012 Fredrik Johansson

******************************************************************************/

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    Random functions 

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double d_randtest(flint_rand_t state)

    Returns a random number in the interval $[0.5, 1)$.


*******************************************************************************

    Arithmetic

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double d_polyval(const double * poly, int len, double x)

    Uses Horner's rule to evaluate the the polynomial defined by the given
    \code{len} coefficients. Requires that \code{len} is nonzero.


*******************************************************************************

    Special functions

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double d_lambertw(double x)

    Computes the principal branch of the Lambert W function, solving
    the equation $x = W(x) \exp(W(x))$. If $x < -1/e$, the solution is
    complex, and NaN is returned.

    Depending on the magnitude of $x$, we start from a piecewise rational
    approximation or a zeroth-order truncation of the asymptotic expansion
    at infinity, and perform 0, 1 or 2 iterations with Halley's
    method to obtain full accuracy.

    A test of $10^7$ random inputs showed a maximum relative error smaller
    than 0.95 times \code{DBL_EPSILON} ($2^{-52}$) for positive $x$.
    Accuracy for negative $x$ is slightly worse, and can grow to
    about 10 times \code{DBL_EPSILON} close to $-1/e$.
    However, accuracy may be worse depending on compiler flags and
    the accuracy of the system libm functions.