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 |
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(x: fabsl(x: 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: x)); |
70 | |
71 | /* |x| in [log(maxdouble), overflowthresold] */ |
72 | if (ix <= 0x408633ce8fb9f87eLL) { |
73 | w = __ieee754_expl(0.5*fabsl(x: 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 | |