1 /*-
2  * SPDX-License-Identifier: BSD-2-Clause
30  * Hyperbolic tangent of a complex argument z = x + I y.
41  *       beta = 1/cos^2(y)
49  *             sinh(x) cos(y) + I cosh(x) sin(y)
50  *           = ---------------------------------
51  *             cosh(x) cos(y) + I sinh(x) sin(y)
53  *             cosh(x) sinh(x) / cos^2(y) + I tan(y)
54  *           = -------------------------------------
55  *                    1 + sinh^2(x) / cos^2(y)
58  *           = ----------------
76 	double x, y;  in ctanh()  local
81 	y = cimag(z);  in ctanh()
87 	 * ctanh(NaN +- I 0) = d(NaN) +- I 0  in ctanh()
89 	 * ctanh(NaN + I y) = d(NaN,y) + I d(NaN,y)	for y != 0  in ctanh()
91 	 * The imaginary part has the sign of x*sin(2*y), but there's no  in ctanh()
94 	 * ctanh(+-Inf +- I Inf) = +-1 +- I 0  in ctanh()
96 	 * ctanh(+-Inf + I y) = +-1 + I 0 sin(2y)	for y finite  in ctanh()
100 	 * y is infinite.  in ctanh()
104 			return (CMPLX(nan_mix(x, y),  in ctanh()
105 			    y == 0 ? y : nan_mix(x, y)));  in ctanh()
106 		SET_HIGH_WORD(x, hx - 0x40000000);	/* x = copysign(1, x) */  in ctanh()
107 		return (CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))));  in ctanh()
111 	 * ctanh(+-0 + i NAN) = +-0 + i NaN  in ctanh()
112 	 * ctanh(+-0 +- i Inf) = +-0 + i NaN  in ctanh()
114 	 * ctanh(x +- i Inf) = NaN + i NaN  in ctanh()
116 	if (!isfinite(y))  in ctanh()
117 		return (CMPLX(x ? y - y : x, y - y));  in ctanh()
120 	 * ctanh(+-huge +- I y) ~= +-1 +- I 2sin(2y)/exp(2x), using the  in ctanh()
125 		double exp_mx = exp(-fabs(x));  in ctanh()
127 		    4 * sin(y) * cos(y) * exp_mx * exp_mx));  in ctanh()
131 	t = tan(y);  in ctanh()
132 	beta = 1.0 + t * t;	/* = 1 / cos^2(y) */  in ctanh()
143 	/* ctan(z) = -I * ctanh(I * z) = I * conj(ctanh(I * conj(z))) */  in ctan()