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 #if defined(LIBM_SCCS) && !defined(lint)
14 static char rcsid[] = "$NetBSD: e_sinh.c,v 1.7 1995/05/10 20:46:13 jtc Exp $";
15 #endif
16
17 /* __ieee754_sinh(x)
18 * Method :
19 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
20 * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
21 * 2.
22 * E + E/(E+1)
23 * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
24 * 2
25 *
26 * 22 <= x <= lnovft : sinh(x) := exp(x)/2
27 * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
28 * ln2ovft < x : sinh(x) := x*shuge (overflow)
29 *
30 * Special cases:
31 * sinh(x) is |x| if x is +INF, -INF, or NaN.
32 * only sinh(0)=0 is exact for finite x.
33 */
34
35 #include <float.h>
36 #include <math.h>
37 #include <math-narrow-eval.h>
38 #include <math_private.h>
39 #include <math-underflow.h>
40 #include <libm-alias-finite.h>
41
42 static const double one = 1.0, shuge = 1.0e307;
43
44 double
__ieee754_sinh(double x)45 __ieee754_sinh (double x)
46 {
47 double t, w, h;
48 int32_t ix, jx;
49 uint32_t lx;
50
51 /* High word of |x|. */
52 GET_HIGH_WORD (jx, x);
53 ix = jx & 0x7fffffff;
54
55 /* x is INF or NaN */
56 if (__glibc_unlikely (ix >= 0x7ff00000))
57 return x + x;
58
59 h = 0.5;
60 if (jx < 0)
61 h = -h;
62 /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
63 if (ix < 0x40360000) /* |x|<22 */
64 {
65 if (__glibc_unlikely (ix < 0x3e300000)) { /* |x|<2**-28 */
66 math_check_force_underflow (x);
67 if (shuge + x > one)
68 return x;
69 /* sinh(tiny) = tiny with inexact */
70 }
71 t = __expm1 (fabs (x));
72 if (ix < 0x3ff00000)
73 return h * (2.0 * t - t * t / (t + one));
74 return h * (t + t / (t + one));
75 }
76
77 /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
78 if (ix < 0x40862e42)
79 return h * __ieee754_exp (fabs (x));
80
81 /* |x| in [log(maxdouble), overflowthresold] */
82 GET_LOW_WORD (lx, x);
83 if (ix < 0x408633ce || ((ix == 0x408633ce) && (lx <= (uint32_t) 0x8fb9f87d)))
84 {
85 w = __ieee754_exp (0.5 * fabs (x));
86 t = h * w;
87 return t * w;
88 }
89
90 /* |x| > overflowthresold, sinh(x) overflow */
91 return math_narrow_eval (x * shuge);
92 }
93 libm_alias_finite (__ieee754_sinh, __sinh)
94