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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_sinhl.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* sinhl(x)
* Method :
* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
* 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
* 2.
* E + E/(E+1)
* 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
* 2
*
* 25 <= x <= lnovft : sinhl(x) := expl(x)/2
* lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
* ln2ovft < x : sinhl(x) := x*huge (overflow)
*
* Special cases:
* sinhl(x) is |x| if x is +INF, -INF, or NaN.
* only sinhl(0)=0 is exact for finite x.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double sinhl(long double x)
{
return sinh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double huge = 1.0e4931L;
long double sinhl(long double x)
{
long double t,w,h;
uint32_t jx,ix,i0,i1;
/* Words of |x|. */
GET_LDOUBLE_WORDS(jx, i0, i1, x);
ix = jx & 0x7fff;
/* x is INF or NaN */
if (ix == 0x7fff) return x + x;
h = 0.5;
if (jx & 0x8000)
h = -h;
/* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x| < 25 */
if (ix < 0x3fdf) /* |x|<2**-32 */
if (huge + x > 1.0)
return x;/* sinh(tiny) = tiny with inexact */
t = expm1l(fabsl(x));
if (ix < 0x3fff)
return h*(2.0*t - t*t/(t + 1.0));
return h*(t + t/(t + 1.0));
}
/* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
return h*expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthreshold] */
if (ix < 0x400c || (ix == 0x400c && (i0 < 0xb174ddc0 ||
(i0 == 0xb174ddc0 && i1 <= 0x31aec0ea)))) {
w = expl(0.5*fabsl(x));
t = h*w;
return t*w;
}
/* |x| > overflowthreshold, sinhl(x) overflow */
return x*huge;
}
#endif
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