1 /* e_asinhl.c -- long double version of e_asinh.c.
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
12 * ====================================================
15 #if defined(LIBM_SCCS) && !defined(lint)
16 static char rcsid
[] = "$NetBSD: $";
21 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
22 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
25 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
28 * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
29 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
30 * ln2ovft < x : sinhl(x) := x*shuge (overflow)
33 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
34 * only sinhl(0)=0 is exact for finite x.
39 #include <math_private.h>
40 #include <math-underflow.h>
41 #include <libm-alias-finite.h>
43 static const long double one
= 1.0, shuge
= 1.0e4931L
;
46 __ieee754_sinhl(long double x
)
52 GET_LDOUBLE_WORDS(jx
,i0
,i1
,x
);
56 if(__builtin_expect(ix
==0x7fff, 0)) return x
+x
;
59 if (jx
& 0x8000) h
= -h
;
60 /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
61 if (ix
< 0x4003 || (ix
== 0x4003 && i0
<= 0xc8000000)) { /* |x|<25 */
62 if (ix
<0x3fdf) { /* |x|<2**-32 */
63 math_check_force_underflow (x
);
64 if(shuge
+x
>one
) return x
;/* sinh(tiny) = tiny with inexact */
66 t
= __expm1l(fabsl(x
));
67 if(ix
<0x3fff) return h
*(2.0*t
-t
*t
/(t
+one
));
68 return h
*(t
+t
/(t
+one
));
71 /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
72 if (ix
< 0x400c || (ix
== 0x400c && i0
< 0xb17217f7))
73 return h
*__ieee754_expl(fabsl(x
));
75 /* |x| in [log(maxdouble), overflowthreshold] */
76 if (ix
<0x400c || (ix
== 0x400c && (i0
< 0xb174ddc0
78 && i1
<= 0x31aec0ea)))) {
79 w
= __ieee754_expl(0.5*fabsl(x
));
84 /* |x| > overflowthreshold, sinhl(x) overflow */
87 libm_alias_finite (__ieee754_sinhl
, __sinhl
)