1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12
13 /* __ieee754_sinh(x)
14 * Method :
15 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
16 * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
17 * 2.
18 * E + E/(E+1)
19 * 0 <= x <= 40 : sinh(x) := --------------, E=expm1(x)
20 * 2
21 *
22 * 40 <= x <= lnovft : sinh(x) := exp(x)/2
23 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
24 * ln2ovft < x : sinh(x) := x*shuge (overflow)
25 *
26 * Special cases:
27 * sinh(x) is |x| if x is +INF, -INF, or NaN.
28 * only sinh(0)=0 is exact for finite x.
29 */
30
31 #include <float.h>
32 #include <math.h>
33 #include <math_private.h>
34 #include <math-underflow.h>
35 #include <libm-alias-finite.h>
36
37 static const long double one = 1.0, shuge = 1.0e307;
38
39 long double
__ieee754_sinhl(long double x)40 __ieee754_sinhl(long double x)
41 {
42 long double t,w,h;
43 int64_t ix,jx;
44 double xhi;
45
46 /* High word of |x|. */
47 xhi = ldbl_high (x);
48 EXTRACT_WORDS64 (jx, xhi);
49 ix = jx&0x7fffffffffffffffLL;
50
51 /* x is INF or NaN */
52 if(ix>=0x7ff0000000000000LL) return x+x;
53
54 h = 0.5;
55 if (jx<0) h = -h;
56 /* |x| in [0,40], return sign(x)*0.5*(E+E/(E+1))) */
57 if (ix < 0x4044000000000000LL) { /* |x|<40 */
58 if (ix<0x3c90000000000000LL) { /* |x|<2**-54 */
59 math_check_force_underflow (x);
60 if(shuge+x>one) return x;/* sinhl(tiny) = tiny with inexact */
61 }
62 t = __expm1l(fabsl(x));
63 if(ix<0x3ff0000000000000LL) return h*(2.0*t-t*t/(t+one));
64 w = t/(t+one);
65 return h*(t+w);
66 }
67
68 /* |x| in [40, log(maxdouble)] return 0.5*exp(|x|) */
69 if (ix < 0x40862e42fefa39efLL) return h*__ieee754_expl(fabsl(x));
70
71 /* |x| in [log(maxdouble), overflowthresold] */
72 if (ix <= 0x408633ce8fb9f87eLL) {
73 w = __ieee754_expl(0.5*fabsl(x));
74 t = h*w;
75 return t*w;
76 }
77
78 /* |x| > overflowthresold, sinh(x) overflow */
79 return x*shuge;
80 }
81 libm_alias_finite (__ieee754_sinhl, __sinhl)
82