72 lines
2.7 KiB
Plaintext
72 lines
2.7 KiB
Plaintext
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2012 Fredrik Johansson
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******************************************************************************/
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*******************************************************************************
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Random functions
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*******************************************************************************
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double d_randtest(flint_rand_t state)
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Returns a random number in the interval $[0.5, 1)$.
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*******************************************************************************
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Arithmetic
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*******************************************************************************
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double d_polyval(const double * poly, int len, double x)
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Uses Horner's rule to evaluate the the polynomial defined by the given
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\code{len} coefficients. Requires that \code{len} is nonzero.
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*******************************************************************************
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Special functions
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*******************************************************************************
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double d_lambertw(double x)
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Computes the principal branch of the Lambert W function, solving
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the equation $x = W(x) \exp(W(x))$. If $x < -1/e$, the solution is
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complex, and NaN is returned.
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Depending on the magnitude of $x$, we start from a piecewise rational
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approximation or a zeroth-order truncation of the asymptotic expansion
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at infinity, and perform 0, 1 or 2 iterations with Halley's
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method to obtain full accuracy.
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A test of $10^7$ random inputs showed a maximum relative error smaller
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than 0.95 times \code{DBL_EPSILON} ($2^{-52}$) for positive $x$.
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Accuracy for negative $x$ is slightly worse, and can grow to
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about 10 times \code{DBL_EPSILON} close to $-1/e$.
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However, accuracy may be worse depending on compiler flags and
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the accuracy of the system libm functions.
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