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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 __csinh = csinh
/* INDENT OFF */
/*
* dcomplex csinh(dcomplex z);
*
* z -z x -x
* e - e e (cos(y)+i*sin(y)) - e (cos(-y)+i*sin(-y))
* sinh z = -------------- = ---------------------------------------------
* 2 2
* x -x x -x
* cos(y) ( e - e ) + i*sin(y) (e + e )
* = --------------------------------------------
* 2
*
* = cos(y) sinh(x) + i sin(y) cosh(x)
*
* Implementation Note
* -------------------
*
* |x| -|x| |x| -2|x| -2|x| -P-4
* Note that e +- e = e ( 1 +- e ). If e < 2 , where
*
* P stands for the number of significant bits of the machine precision,
* |x|
* then the result will be rounded to e . Therefore, we have
*
* z
* e
* sinh z = ----- if |x| >= (P/2 + 2)*ln2
* 2
*
* EXCEPTION (conform to ISO/IEC 9899:1999(E)):
* csinh(0,0)=(0,0)
* csinh(0,inf)=(+-0,NaN)
* csinh(0,NaN)=(+-0,NaN)
* csinh(x,inf) = (NaN,NaN) for finite positive x
* csinh(x,NaN) = (NaN,NaN) for finite non-zero x
* csinh(inf,0) = (inf, 0)
* csinh(inf,y) = (inf*cos(y),inf*sin(y)) for positive finite y
* csinh(inf,inf) = (+-inf,NaN)
* csinh(inf,NaN) = (+-inf,NaN)
* csinh(NaN,0) = (NaN,0)
* csinh(NaN,y) = (NaN,NaN) for non-zero y
* csinh(NaN,NaN) = (NaN,NaN)
*/
/* INDENT ON */
#include "libm.h" /* cosh/exp/fabs/scalbn/sinh/sincos/__k_cexp */
#include "complex_wrapper.h"
dcomplex
csinh(dcomplex z) {
double t, x, y, S, C;
int hx, ix, lx, hy, iy, ly, n;
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);
(void) sincos(y, &S, &C);
if (ix >= 0x403c0000) { /* |x| > 28 = prec/2 (14,28,34,60) */
if (ix >= 0x40862E42) { /* |x| > 709.78... ~ log(2**1024) */
if (ix >= 0x7ff00000) { /* |x| is inf or NaN */
if ((iy | ly) == 0) {
D_RE(ans) = x;
D_IM(ans) = y;
} else if (iy >= 0x7ff00000) {
D_RE(ans) = x;
D_IM(ans) = x - y;
} else {
D_RE(ans) = C * x;
D_IM(ans) = S * x;
}
} else {
/* return exp(x)=t*2**n */
t = __k_cexp(x, &n);
D_RE(ans) = scalbn(C * t, n - 1);
D_IM(ans) = scalbn(S * t, n - 1);
}
} else {
t = exp(x) * 0.5;
D_RE(ans) = C * t;
D_IM(ans) = S * t;
}
} else {
if ((ix | lx) == 0) { /* x = 0, return (0,S) */
D_RE(ans) = 0.0;
D_IM(ans) = S;
} else {
D_RE(ans) = C * sinh(x);
D_IM(ans) = S * cosh(x);
}
}
if (hx < 0)
D_RE(ans) = -D_RE(ans);
if (hy < 0)
D_IM(ans) = -D_IM(ans);
return (ans);
}
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