double_extras.h – support functions for double arithmetic¶
Random functions¶
-
double
d_randtest
(flint_rand_t state)¶ Returns a random number in the interval \([0.5, 1)\).
-
double
d_randtest_signed
(flint_rand_t state, slong minexp, slong maxexp)¶ Returns a random signed number with exponent between
minexp
andmaxexp
or zero.
-
double
d_randtest_special
(flint_rand_t state, slong minexp, slong maxexp)¶ Returns a random signed number with exponent between
minexp
andmaxexp
, zero,D_NAN
or pm``D_INF``.
Arithmetic¶
-
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 thatlen
is nonzero.
Special functions¶
-
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 timesDBL_EPSILON
close to \(-1/e\). However, accuracy may be worse depending on compiler flags and the accuracy of the system libm functions.
-
int
d_is_nan
(double x)¶ Returns a nonzero integral value if
x
isD_NAN
, and otherwise returns 0.
-
double
d_log2
(double x)¶ Returns the base 2 logarithm of
x
providedx
is positive. If a domain or pole error occurs, the appropriate error value is returned.