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/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
#pragma weak __ctanh = ctanh
/* INDENT OFF */
/*
* dcomplex ctanh(dcomplex z);
*
* tanh x + i tan y sinh 2x + i sin 2y
* ctanh z = --------------------- = --------------------
* 1 + i tanh(x)tan(y) cosh 2x + cos 2y
*
* For |x| >= prec/2 (14,28,34,60 for single, double, double extended, quad),
* we use
*
* 1 2x 2 sin 2y
* cosh 2x = sinh 2x = --- e and hence ctanh z = 1 + i -----------;
* 2 2x
* e
*
* otherwise, to avoid cancellation, for |x| < prec/2,
* 2x 2
* (e - 1) 2 2
* cosh 2x + cos 2y = 1 + ------------ + cos y - sin y
* 2x
* 2 e
*
* 1 2x 2 -2x 2
* = --- (e - 1) e + 2 cos y
* 2
* and
*
* [ 2x ]
* 1 [ 2x e - 1 ]
* sinh 2x = --- [ e - 1 + --------- ]
* 2 [ 2x ]
* [ e ]
* 2x
* Implementation notes: let t = expm1(2x) = e - 1, then
*
* 1 [ t*t 2 ] 1 [ t ]
* cosh 2x + cos 2y = --- * [ ----- + 4 cos y ]; sinh 2x = --- * [ t + --- ]
* 2 [ t+1 ] 2 [ t+1 ]
*
* Hence,
*
*
* t*t+2t [4(t+1)(cos y)]*(sin y)
* ctanh z = --------------------------- + i --------------------------
* t*t+[4(t+1)(cos y)](cos y) t*t+[4(t+1)(cos y)](cos y)
*
* EXCEPTION (conform to ISO/IEC 9899:1999(E)):
* ctanh(0,0)=(0,0)
* ctanh(x,inf) = (NaN,NaN) for finite x
* ctanh(x,NaN) = (NaN,NaN) for finite x
* ctanh(inf,y) = 1+ i*0*sin(2y) for positive-signed finite y
* ctanh(inf,inf) = (1, +-0)
* ctanh(inf,NaN) = (1, +-0)
* ctanh(NaN,0) = (NaN,0)
* ctanh(NaN,y) = (NaN,NaN) for non-zero y
* ctanh(NaN,NaN) = (NaN,NaN)
*/
/* INDENT ON */
#include "libm.h" /* exp/expm1/fabs/sin/tanh/sincos */
#include "complex_wrapper.h"
static const double four = 4.0, two = 2.0, one = 1.0, zero = 0.0;
dcomplex
ctanh(dcomplex z) {
double t, r, v, u, x, y, S, C;
int hx, ix, lx, hy, iy, ly;
dcomplex ans;
x = D_RE(z);
y = D_IM(z);
hx = HI_WORD(x);
lx = LO_WORD(x);
ix = hx & 0x7fffffff;
hy = HI_WORD(y);
ly = LO_WORD(y);
iy = hy & 0x7fffffff;
x = fabs(x);
y = fabs(y);
if ((iy | ly) == 0) { /* ctanh(x,0) = (x,0) for x = 0 or NaN */
D_RE(ans) = tanh(x);
D_IM(ans) = zero;
} else if (iy >= 0x7ff00000) { /* y is inf or NaN */
if (ix < 0x7ff00000) /* catanh(finite x,inf/nan) is nan */
D_RE(ans) = D_IM(ans) = y - y;
else if (((ix - 0x7ff00000) | lx) == 0) { /* x is inf */
D_RE(ans) = one;
D_IM(ans) = zero;
} else {
D_RE(ans) = x + y;
D_IM(ans) = y - y;
}
} else if (ix >= 0x403c0000) {
/*
* |x| > 28 = prec/2 (14,28,34,60)
* ctanh z ~ 1 + i (sin2y)/(exp(2x))
*/
D_RE(ans) = one;
if (iy < 0x7fe00000) /* t = sin(2y) */
S = sin(y + y);
else {
(void) sincos(y, &S, &C);
S = (S + S) * C;
}
if (ix >= 0x7fe00000) { /* |x| > max/2 */
if (ix >= 0x7ff00000) { /* |x| is inf or NaN */
if (((ix - 0x7ff00000) | lx) != 0)
D_RE(ans) = D_IM(ans) = x + y;
/* x is NaN */
else
D_IM(ans) = zero * S; /* x is inf */
} else
D_IM(ans) = S * exp(-x); /* underflow */
} else
D_IM(ans) = (S + S) * exp(-(x + x));
/* 2 sin 2y / exp(2x) */
} else {
/* INDENT OFF */
/*
* t*t+2t
* ctanh z = --------------------------- +
* t*t+[4(t+1)(cos y)](cos y)
*
* [4(t+1)(cos y)]*(sin y)
* i --------------------------
* t*t+[4(t+1)(cos y)](cos y)
*/
/* INDENT ON */
(void) sincos(y, &S, &C);
t = expm1(x + x);
r = (four * C) * (t + one);
u = t * t;
v = one / (u + r * C);
D_RE(ans) = (u + two * t) * v;
D_IM(ans) = (r * S) * v;
}
if (hx < 0)
D_RE(ans) = -D_RE(ans);
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}
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