.. _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 \pmD_INF. Arithmetic -------------------------------------------------------------------------------- .. function:: double d_polyval(const double * poly, int len, double x) Uses Horner's rule to evaluate the the polynomial defined by the given len coefficients. Requires that len is nonzero. 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.