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/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_sinh(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 40 : sinh(x) := --------------, E=expm1(x)
* 2
*
* 40 <= x <= lnovft : sinh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : sinh(x) := x*shuge (overflow)
*
* Special cases:
* sinh(x) is |x| if x is +INF, -INF, or NaN.
* only sinh(0)=0 is exact for finite x.
*/
#include <float.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-finite.h>
static const long double one = 1.0, shuge = 1.0e307;
long double
__ieee754_sinhl(long double x)
{
long double t,w,h;
int64_t ix,jx;
double xhi;
/* High word of |x|. */
xhi = ldbl_high (x);
EXTRACT_WORDS64 (jx, xhi);
ix = jx&0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) return x+x;
h = 0.5;
if (jx<0) h = -h;
/* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x4044000000000000LL) { /* |x|<40 */
if (ix<0x3c90000000000000LL) { /* |x|<2**-54 */
math_check_force_underflow (x);
if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
}
t = __expm1l(fabsl(x));
if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
w = t/(t+one);
return h*(t+w);
}
/* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix <= 0x408633ce8fb9f87eLL) {
w = __ieee754_expl(0.5*fabsl(x));
t = h*w;
return t*w;
}
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
libm_alias_finite (__ieee754_sinhl, __sinhl)
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