libm/complex/catrig.c

93  * The code for casinh, casin, cacos, and cacosh comes first.  The code is
103  *			| casinh, casin, cacos, cacosh |
116  * casinh(z) = sign(x)*log(A+sqrt(A*A-1)) + I*asin(B)
122  *   (a) for Re(casinh(z)) when z is close to the line segment [-I, I] (that
123  *       is, Re(casinh(z)) is close to 0);
124  *   (b) for Im(casinh(z)) when z is close to either of the intervals
125  *       [I, I*infinity) or (-I*infinity, -I] (that is, |Im(casinh(z))| is
169  * rx = Re(casinh(z)) = -Im(cacos(y + I*x)).
233 		 * Avoid a possible underflow caused by y/A.  For casinh this
290  * casinh(z) = z + O(z^3)   as z -> 0
292  * casinh(z) = sign(x)*clog(sign(x)*z) + O(1/z^2)   as z -> infinity
294  * Im(casinh(z)) = sign(x)*atan2(sign(x)*y, fabs(x)) + O(y/z^3)
298 casinh(double complex z)
310 		/* casinh(+-Inf + I*NaN) = +-Inf + I*NaN */
313 		/* casinh(NaN + I*+-Inf) = opt(+-)Inf + I*NaN */
316 		/* casinh(NaN + I*0) = NaN + I*0 */
355  * casin(z) = reverse(casinh(reverse(z)))
361 	double complex w = casinh(CMPLX(cimag(z), creal(z)));