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1.1 root 1: /*
2: * Copyright (c) 1985 Regents of the University of California.
3: * All rights reserved.
4: *
5: * Redistribution and use in source and binary forms are permitted
6: * provided that: (1) source distributions retain this entire copyright
7: * notice and comment, and (2) distributions including binaries display
8: * the following acknowledgement: ``This product includes software
9: * developed by the University of California, Berkeley and its contributors''
10: * in the documentation or other materials provided with the distribution
11: * and in all advertising materials mentioning features or use of this
12: * software. Neither the name of the University nor the names of its
13: * contributors may be used to endorse or promote products derived
14: * from this software without specific prior written permission.
15: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
16: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
17: * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
18: *
19: * All recipients should regard themselves as participants in an ongoing
20: * research project and hence should feel obligated to report their
21: * experiences (good or bad) with these elementary function codes, using
22: * the sendbug(8) program, to the authors.
23: */
24:
25: #ifndef lint
26: static char sccsid[] = "@(#)sinh.c 5.5 (Berkeley) 6/1/90";
27: #endif /* not lint */
28:
29: /* SINH(X)
30: * RETURN THE HYPERBOLIC SINE OF X
31: * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
32: * CODED IN C BY K.C. NG, 1/8/85;
33: * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
34: *
35: * Required system supported functions :
36: * copysign(x,y)
37: * scalb(x,N)
38: *
39: * Required kernel functions:
40: * expm1(x) ...return exp(x)-1
41: *
42: * Method :
43: * 1. reduce x to non-negative by sinh(-x) = - sinh(x).
44: * 2.
45: *
46: * expm1(x) + expm1(x)/(expm1(x)+1)
47: * 0 <= x <= lnovfl : sinh(x) := --------------------------------
48: * 2
49: * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
50: * lnovfl+ln2 < x < INF : overflow to INF
51: *
52: *
53: * Special cases:
54: * sinh(x) is x if x is +INF, -INF, or NaN.
55: * only sinh(0)=0 is exact for finite argument.
56: *
57: * Accuracy:
58: * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
59: * a test run with 1,024,000 random arguments on a VAX, the maximum
60: * observed error was 1.93 ulps (units in the last place).
61: *
62: * Constants:
63: * The hexadecimal values are the intended ones for the following constants.
64: * The decimal values may be used, provided that the compiler will convert
65: * from decimal to binary accurately enough to produce the hexadecimal values
66: * shown.
67: */
68:
69: #include "mathimpl.h"
70:
71: vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB)
72: vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
73: vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA)
74:
75: ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF)
76: ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
77: ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF)
78:
79: #ifdef vccast
80: #define mln2hi vccast(mln2hi)
81: #define mln2lo vccast(mln2lo)
82: #define lnovfl vccast(lnovfl)
83: #endif
84:
85: #if defined(vax)||defined(tahoe)
86: static max = 126 ;
87: #else /* defined(vax)||defined(tahoe) */
88: static max = 1023 ;
89: #endif /* defined(vax)||defined(tahoe) */
90:
91:
92: double sinh(x)
93: double x;
94: {
95: static const double one=1.0, half=1.0/2.0 ;
96: double t, sign;
97: #if !defined(vax)&&!defined(tahoe)
98: if(x!=x) return(x); /* x is NaN */
99: #endif /* !defined(vax)&&!defined(tahoe) */
100: sign=copysign(one,x);
101: x=copysign(x,one);
102: if(x<lnovfl)
103: {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
104:
105: else if(x <= lnovfl+0.7)
106: /* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
107: to avoid unnecessary overflow */
108: return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
109:
110: else /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
111: return( expm1(x)*sign );
112: }
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