1 /* @(#)e_sinh.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13 /* sinhl(x)
14 * Method :
15 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
16 * 1. Replace x by |x| (sinhl(-x) = -sinhl(x)).
17 * 2.
18 * E + E/(E+1)
19 * 0 <= x <= 25 : sinhl(x) := --------------, E=expm1l(x)
20 * 2
21 *
22 * 25 <= x <= lnovft : sinhl(x) := expl(x)/2
23 * lnovft <= x <= ln2ovft: sinhl(x) := expl(x/2)/2 * expl(x/2)
24 * ln2ovft < x : sinhl(x) := x*shuge (overflow)
25 *
26 * Special cases:
27 * sinhl(x) is |x| if x is +INF, -INF, or NaN.
28 * only sinhl(0)=0 is exact for finite x.
29 */
30
31
32
33 static const long double one = 1.0l, shuge = 1.0e4931L;
34
35 long double
sinhl(long double x)36 sinhl(long double x)
37 {
38 long double t,w,h;
39 u_int32_t jx,ix,i0,i1;
40
41 /* Words of |x|. */
42 GET_LDOUBLE_WORDS(jx,i0,i1,x);
43 ix = jx&0x7fff;
44
45 /* x is INF or NaN */
46 if(ix==0x7fff) return x+x;
47
48 h = 0.5l;
49 if (jx & 0x8000) h = -h;
50 /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
51 if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
52 if (ix<0x3fdf) /* |x|<2**-32 */
53 if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
54 t = expm1l(fabsl(x));
55 if(ix<0x3fff) return h*(2.0l*t-t*t/(t+one));
56 return h*(t+t/(t+one));
57 }
58
59 /* |x| in [25, log(maxdouble)] return 0.5*exp(|x|) */
60 if (ix < 0x400c || (ix == 0x400c && i0 < 0xb17217f7))
61 return h*expl(fabsl(x));
62
63 /* |x| in [log(maxdouble), overflowthreshold] */
64 if (ix<0x400c || (ix == 0x400c && (i0 < 0xb174ddc0
65 || (i0 == 0xb174ddc0
66 && i1 <= 0x31aec0ea)))) {
67 w = expl(0.5l*fabsl(x));
68 t = h*w;
69 return t*w;
70 }
71
72 /* |x| > overflowthreshold, sinhl(x) overflow */
73 return x*shuge;
74 }
75
