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.. _double-extras:
**double_extras.h** -- support functions for double arithmetic
===============================================================================
Random functions
--------------------------------------------------------------------------------
.. function:: double d_randtest(flint_rand_t state)
Returns a random number in the interval `[0.5, 1)`.
.. function:: double d_randtest_signed(flint_rand_t state, slong minexp, slong maxexp)
Returns a random signed number with exponent between ``minexp`` and
``maxexp`` or zero.
.. function:: double d_randtest_special(flint_rand_t state, slong minexp, slong maxexp)
Returns a random signed number with exponent between ``minexp`` and
``maxexp``, zero, ``D_NAN`` or `\pm`\ ``D_INF``.
Arithmetic
--------------------------------------------------------------------------------
.. function:: double d_polyval(const double * poly, int len, double x)
Uses Horner's rule to evaluate the polynomial defined by the given
``len`` coefficients. Requires that ``len`` is nonzero.
.. function:: double d_mul_2exp_inrange(double x, int i)
double d_mul_2exp_inrange2(double x, int i)
double d_mul_2exp(double x, int i)
Returns `x \cdot 2^i`.
The *inrange* version requires that `2^i` is in the normal exponent
range. The *inrange2* version additionally requires that both
`x` and `x \cdot 2^i` are in the normal exponent range,
and in particular also assumes that `x \ne 0`.
Special functions
--------------------------------------------------------------------------------
.. function:: 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 ``DBL_EPSILON`` (`2^{-52}`) for positive `x`.
Accuracy for negative `x` is slightly worse, and can grow to
about 10 times ``DBL_EPSILON`` close to `-1/e`.
However, accuracy may be worse depending on compiler flags and
the accuracy of the system libm functions.
.. function:: int d_is_nan(double x)
Returns a nonzero integral value if ``x`` is ``D_NAN``, and otherwise
returns 0.
.. function:: double d_log2(double x)
Returns the base 2 logarithm of ``x`` provided ``x`` is positive. If
a domain or pole error occurs, the appropriate error value is returned.
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