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catan
Complex circular arc tangent.SYNOPSIS:
void catan();
cmplx z, w;
catan(&z, &w);
DESCRIPTION:
If
z = x + iy,
then
1 ( 2x )
Re w = - arctan( ----------- ) + k PI
2 ( 2 2 )
( 1 - x - y )
( 2 2 )
1 ( x + (y+1) )
Im w = - log( ------------ )
4 ( 2 2 )
( x + (y-1) )
Where k is an arbitrary integer.
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
DEC -10,+10 5900 1.3e-16 7.8e-18
IEEE -10,+10 30000 2.3e-15 8.5e-17
The check catan(ctan(z)) = z, with |x| and |y| < PI/2, had peak relative error 1.5e-16, rms relative error 2.9e-17. See also clog().