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Re: Missing functions tanPi, asinPi and acosPi
Michel Hack wrote:
Nobody ever mentioned tanPi, asinPi and acosPi since then, until
now. Could it be that they were thought to be easily-derivable
from the others? Perhaps they are -- except for single-rounding
of the result...
They are not.
Any trig functions using pi violate either correct rounding or
correct range reduction. If 1.0 is the right angle, the input is
0.95 and the possible FP values are either 0.7 or 1.1, the correctly
rounded result would be 1.1, but this gives the wrong sector and
therefore the wrong sign for tan() and cos().
Moreover the normal trig functions made it impossible to exactly
specify fractions of the full angle: half angle, right angle, 45°
etc. This is annoying if you need routines which have a precise
defined number of steps for a full angle.
Best,
Thorsten