d_randtest state

Returns a random number in the interval \([0.5, 1)\).

d_randtest_signed state minexp maxexp

Returns a random signed number with exponent between minexp and maxexp or zero.

d_randtest_special state minexp maxexp

Returns a random signed number with exponent between minexp and maxexp, zero, D_NAN or \(\pm\)D_INF.

d_polyval poly len x

Uses Horner's rule to evaluate the polynomial defined by the given len coefficients. Requires that len is nonzero.

d_lambertw 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.

d_is_nan x

Returns a nonzero integral value if x is D_NAN, and otherwise returns 0.

d_log2 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.