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 |
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 (x: fabs (x: 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: 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: 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 | |