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log2
Base 2 logarithm.SYNOPSIS:
double x, y, log2();
y = log2(x);
DESCRIPTION:
Returns the base 2 logarithm of x.
The argument is separated into its exponent and fractional parts. If the exponent is between -1 and +1, the base e 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 30000 2.0e-16 5.5e-17
IEEE exp(+-700) 40000 1.3e-16 4.6e-17
In the tests over the interval [exp(+-700)], the logarithms of the random arguments were uniformly distributed.
ERROR MESSAGES:
singularity: x = 0; returns -INFINITY
domain: x < 0; returns NAN