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acos
Inverse circular cosine.SYNOPSIS:
double x, y, acos();
y = acos(x);
DESCRIPTION:
Returns radian angle between 0 and pi whose cosine is x.
Analytically, acos(x) = pi/2 - asin(x). However if |x| is near 1, there is cancellation error in subtracting asin(x) from pi/2. Hence if x < -0.5, acos(x) = pi - 2.0 * asin(sqrt((1+x)/2)); or if x > +0.5, acos(x) = 2.0 * asin(sqrt((1-x)/2)).
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
DEC -1, 1 50000 3.3e-17 8.2e-18
IEEE -1, 1 10^6 2.2e-16 6.5e-17
ERROR MESSAGES:
message condition value returned
domain |x| > 1 NAN