1*05a0b428SJohn Marino /* @(#)e_sinh.c 5.1 93/09/24 */
2*05a0b428SJohn Marino /*
3*05a0b428SJohn Marino * ====================================================
4*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*05a0b428SJohn Marino *
6*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
7*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
8*05a0b428SJohn Marino * software is freely granted, provided that this notice
9*05a0b428SJohn Marino * is preserved.
10*05a0b428SJohn Marino * ====================================================
11*05a0b428SJohn Marino */
12*05a0b428SJohn Marino
13*05a0b428SJohn Marino /* sinh(x)
14*05a0b428SJohn Marino * Method :
15*05a0b428SJohn Marino * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
16*05a0b428SJohn Marino * 1. Replace x by |x| (sinh(-x) = -sinh(x)).
17*05a0b428SJohn Marino * 2.
18*05a0b428SJohn Marino * E + E/(E+1)
19*05a0b428SJohn Marino * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
20*05a0b428SJohn Marino * 2
21*05a0b428SJohn Marino *
22*05a0b428SJohn Marino * 22 <= x <= lnovft : sinh(x) := exp(x)/2
23*05a0b428SJohn Marino * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
24*05a0b428SJohn Marino * ln2ovft < x : sinh(x) := x*shuge (overflow)
25*05a0b428SJohn Marino *
26*05a0b428SJohn Marino * Special cases:
27*05a0b428SJohn Marino * sinh(x) is |x| if x is +INF, -INF, or NaN.
28*05a0b428SJohn Marino * only sinh(0)=0 is exact for finite x.
29*05a0b428SJohn Marino */
30*05a0b428SJohn Marino
31*05a0b428SJohn Marino #include <float.h>
32*05a0b428SJohn Marino #include <math.h>
33*05a0b428SJohn Marino
34*05a0b428SJohn Marino #include "math_private.h"
35*05a0b428SJohn Marino
36*05a0b428SJohn Marino static const double one = 1.0, shuge = 1.0e307;
37*05a0b428SJohn Marino
38*05a0b428SJohn Marino double
sinh(double x)39*05a0b428SJohn Marino sinh(double x)
40*05a0b428SJohn Marino {
41*05a0b428SJohn Marino double t,w,h;
42*05a0b428SJohn Marino int32_t ix,jx;
43*05a0b428SJohn Marino u_int32_t lx;
44*05a0b428SJohn Marino
45*05a0b428SJohn Marino /* High word of |x|. */
46*05a0b428SJohn Marino GET_HIGH_WORD(jx,x);
47*05a0b428SJohn Marino ix = jx&0x7fffffff;
48*05a0b428SJohn Marino
49*05a0b428SJohn Marino /* x is INF or NaN */
50*05a0b428SJohn Marino if(ix>=0x7ff00000) return x+x;
51*05a0b428SJohn Marino
52*05a0b428SJohn Marino h = 0.5;
53*05a0b428SJohn Marino if (jx<0) h = -h;
54*05a0b428SJohn Marino /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
55*05a0b428SJohn Marino if (ix < 0x40360000) { /* |x|<22 */
56*05a0b428SJohn Marino if (ix<0x3e300000) /* |x|<2**-28 */
57*05a0b428SJohn Marino if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
58*05a0b428SJohn Marino t = expm1(fabs(x));
59*05a0b428SJohn Marino if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
60*05a0b428SJohn Marino return h*(t+t/(t+one));
61*05a0b428SJohn Marino }
62*05a0b428SJohn Marino
63*05a0b428SJohn Marino /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
64*05a0b428SJohn Marino if (ix < 0x40862E42) return h*exp(fabs(x));
65*05a0b428SJohn Marino
66*05a0b428SJohn Marino /* |x| in [log(maxdouble), overflowthresold] */
67*05a0b428SJohn Marino GET_LOW_WORD(lx,x);
68*05a0b428SJohn Marino if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
69*05a0b428SJohn Marino w = exp(0.5*fabs(x));
70*05a0b428SJohn Marino t = h*w;
71*05a0b428SJohn Marino return t*w;
72*05a0b428SJohn Marino }
73*05a0b428SJohn Marino
74*05a0b428SJohn Marino /* |x| > overflowthresold, sinh(x) overflow */
75*05a0b428SJohn Marino return x*shuge;
76*05a0b428SJohn Marino }
77*05a0b428SJohn Marino
78*05a0b428SJohn Marino #if LDBL_MANT_DIG == DBL_MANT_DIG
79*05a0b428SJohn Marino __strong_alias(sinhl, sinh);
80*05a0b428SJohn Marino #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
81