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 polynomial defined by the given
len
coefficients. Requires thatlen
is nonzero.

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¶

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 zerothorder 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.