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