![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to cosh.c CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [CSRG BSD Unix] / 43BSDTahoe / usr.lib / libm|
Return to cosh.c CVS log | Up to [CSRG BSD Unix] / 43BSDTahoe / usr.lib / libm |
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 the above copyright notice and this paragraph are
7: * duplicated in all such forms and that any documentation,
8: * advertising materials, and other materials related to such
9: * distribution and use acknowledge that the software was developed
10: * by the University of California, Berkeley. The name of the
11: * University may not be used to endorse or promote products derived
12: * from this software without specific prior written permission.
13: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
14: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
15: * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
16: *
17: * All recipients should regard themselves as participants in an ongoing
18: * research project and hence should feel obligated to report their
19: * experiences (good or bad) with these elementary function codes, using
20: * the sendbug(8) program, to the authors.
21: */
22:
23: #ifndef lint
24: static char sccsid[] = "@(#)cosh.c 5.3 (Berkeley) 6/30/88";
25: #endif /* not lint */
26:
27: /* COSH(X)
28: * RETURN THE HYPERBOLIC COSINE OF X
29: * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
30: * CODED IN C BY K.C. NG, 1/8/85;
31: * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
32: *
33: * Required system supported functions :
34: * copysign(x,y)
35: * scalb(x,N)
36: *
37: * Required kernel function:
38: * exp(x)
39: * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465
40: *
41: * Method :
42: * 1. Replace x by |x|.
43: * 2.
44: * [ exp(x) - 1 ]^2
45: * 0 <= x <= 0.3465 : cosh(x) := 1 + -------------------
46: * 2*exp(x)
47: *
48: * exp(x) + 1/exp(x)
49: * 0.3465 <= x <= 22 : cosh(x) := -------------------
50: * 2
51: * 22 <= x <= lnovfl : cosh(x) := exp(x)/2
52: * lnovfl <= x <= lnovfl+log(2)
53: * : cosh(x) := exp(x)/2 (avoid overflow)
54: * log(2)+lnovfl < x < INF: overflow to INF
55: *
56: * Note: .3465 is a number near one half of ln2.
57: *
58: * Special cases:
59: * cosh(x) is x if x is +INF, -INF, or NaN.
60: * only cosh(0)=1 is exact for finite x.
61: *
62: * Accuracy:
63: * cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
64: * In a test run with 768,000 random arguments on a VAX, the maximum
65: * observed error was 1.23 ulps (units in the last place).
66: *
67: * Constants:
68: * The hexadecimal values are the intended ones for the following constants.
69: * The decimal values may be used, provided that the compiler will convert
70: * from decimal to binary accurately enough to produce the hexadecimal values
71: * shown.
72: */
73:
74: #if defined(vax)||defined(tahoe)
75: #ifdef vax
76: #define _0x(A,B) 0x/**/A/**/B
77: #else /* vax */
78: #define _0x(A,B) 0x/**/B/**/A
79: #endif /* vax */
80: /* static double */
81: /* mln2hi = 8.8029691931113054792E1 , Hex 2^ 7 * .B00F33C7E22BDB */
82: /* mln2lo = -4.9650192275318476525E-16 , Hex 2^-50 * -.8F1B60279E582A */
83: /* lnovfl = 8.8029691931113053016E1 ; Hex 2^ 7 * .B00F33C7E22BDA */
84: static long mln2hix[] = { _0x(0f33,43b0), _0x(2bdb,c7e2)};
85: static long mln2lox[] = { _0x(1b60,a70f), _0x(582a,279e)};
86: static long lnovflx[] = { _0x(0f33,43b0), _0x(2bda,c7e2)};
87: #define mln2hi (*(double*)mln2hix)
88: #define mln2lo (*(double*)mln2lox)
89: #define lnovfl (*(double*)lnovflx)
90: #else /* defined(vax)||defined(tahoe) */
91: static double
92: mln2hi = 7.0978271289338397310E2 , /*Hex 2^ 10 * 1.62E42FEFA39EF */
93: mln2lo = 2.3747039373786107478E-14 , /*Hex 2^-45 * 1.ABC9E3B39803F */
94: lnovfl = 7.0978271289338397310E2 ; /*Hex 2^ 9 * 1.62E42FEFA39EF */
95: #endif /* defined(vax)||defined(tahoe) */
96:
97: #if defined(vax)||defined(tahoe)
98: static max = 126 ;
99: #else /* defined(vax)||defined(tahoe) */
100: static max = 1023 ;
101: #endif /* defined(vax)||defined(tahoe) */
102:
103: double cosh(x)
104: double x;
105: {
106: static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */
107: double scalb(),copysign(),exp(),exp__E(),t;
108:
109: #if !defined(vax)&&!defined(tahoe)
110: if(x!=x) return(x); /* x is NaN */
111: #endif /* !defined(vax)&&!defined(tahoe) */
112: if((x=copysign(x,one)) <= 22)
113: if(x<0.3465)
114: if(x<small) return(one+x);
115: else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
116:
117: else /* for x lies in [0.3465,22] */
118: { t=exp(x); return((t+one/t)*half); }
119:
120: if( lnovfl <= x && x <= (lnovfl+0.7))
121: /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1))
122: * and return 2^max*exp(x) to avoid unnecessary overflow
123: */
124: return(scalb(exp((x-mln2hi)-mln2lo), max));
125:
126: else
127: return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */
128: }
This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.