| Pré. | Proc. |
log
Natural logarithm.SYNOPSIS:
double x, y, log();
y = log(x);
DESCRIPTION:
Returns the base e (2.718...) logarithm of x.
The argument is separated into its exponent and fractional parts. If the exponent is between -1 and +1, the logarithm of the fraction is approximated by:
log(1+x) = x - 0.5 x**2 + x**3 P(x)/Q(x).
Otherwise, setting z = 2(x-1)/x+1),
log(x) = z + z**3 P(z)/Q(z).
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
IEEE 0.5, 2.0 150000 1.44e-16 5.06e-17
IEEE +-MAXNUM 30000 1.20e-16 4.78e-17
DEC 0, 10 170000 1.8e-17 6.3e-18
In the tests over the interval [+-MAXNUM], the logarithms of the random arguments were uniformly distributed over [0,MAXLOG].
ERROR MESSAGES:
singularity: x = 0; returns -INFINITY
domain: x < 0; returns NAN