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c77add16 ZAL |
1 | /* |
2 | * Copyright (c) 1985 Regents of the University of California. | |
3 | * | |
4 | * Use and reproduction of this software are granted in accordance with | |
5 | * the terms and conditions specified in the Berkeley Software License | |
6 | * Agreement (in particular, this entails acknowledgement of the programs' | |
7 | * source, and inclusion of this notice) with the additional understanding | |
8 | * that all recipients should regard themselves as participants in an | |
9 | * ongoing research project and hence should feel obligated to report | |
10 | * their experiences (good or bad) with these elementary function codes, | |
11 | * using "sendbug 4bsd-bugs@BERKELEY", to the authors. | |
12 | */ | |
13 | ||
14 | #ifndef lint | |
a62df508 | 15 | static char sccsid[] = |
2893dfdc | 16 | "@(#)cosh.c 1.2 (Berkeley) 8/21/85; 5.1 (ucb.elefunt) %G%"; |
859dc438 | 17 | #endif /* not lint */ |
c77add16 ZAL |
18 | |
19 | /* COSH(X) | |
20 | * RETURN THE HYPERBOLIC COSINE OF X | |
21 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
22 | * CODED IN C BY K.C. NG, 1/8/85; | |
23 | * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. | |
24 | * | |
25 | * Required system supported functions : | |
26 | * copysign(x,y) | |
27 | * scalb(x,N) | |
28 | * | |
29 | * Required kernel function: | |
30 | * exp(x) | |
31 | * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 | |
32 | * | |
33 | * Method : | |
34 | * 1. Replace x by |x|. | |
35 | * 2. | |
36 | * [ exp(x) - 1 ]^2 | |
37 | * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- | |
38 | * 2*exp(x) | |
39 | * | |
40 | * exp(x) + 1/exp(x) | |
41 | * 0.3465 <= x <= 22 : cosh(x) := ------------------- | |
42 | * 2 | |
43 | * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 | |
44 | * lnovfl <= x <= lnovfl+log(2) | |
45 | * : cosh(x) := exp(x)/2 (avoid overflow) | |
46 | * log(2)+lnovfl < x < INF: overflow to INF | |
47 | * | |
48 | * Note: .3465 is a number near one half of ln2. | |
49 | * | |
50 | * Special cases: | |
51 | * cosh(x) is x if x is +INF, -INF, or NaN. | |
52 | * only cosh(0)=1 is exact for finite x. | |
53 | * | |
54 | * Accuracy: | |
55 | * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. | |
56 | * In a test run with 768,000 random arguments on a VAX, the maximum | |
57 | * observed error was 1.23 ulps (units in the last place). | |
58 | * | |
59 | * Constants: | |
60 | * The hexadecimal values are the intended ones for the following constants. | |
61 | * The decimal values may be used, provided that the compiler will convert | |
62 | * from decimal to binary accurately enough to produce the hexadecimal values | |
63 | * shown. | |
64 | */ | |
65 | ||
859dc438 ZAL |
66 | #if defined(vax)||defined(tahoe) |
67 | #ifdef vax | |
0e01cbea | 68 | #define _0x(A,B) 0x/**/A/**/B |
859dc438 | 69 | #else /* vax */ |
0e01cbea | 70 | #define _0x(A,B) 0x/**/B/**/A |
859dc438 | 71 | #endif /* vax */ |
62b65e15 | 72 | /* static double */ |
c77add16 ZAL |
73 | /* mln2hi = 8.8029691931113054792E1 , Hex 2^ 7 * .B00F33C7E22BDB */ |
74 | /* mln2lo = -4.9650192275318476525E-16 , Hex 2^-50 * -.8F1B60279E582A */ | |
75 | /* lnovfl = 8.8029691931113053016E1 ; Hex 2^ 7 * .B00F33C7E22BDA */ | |
0e01cbea ZAL |
76 | static long mln2hix[] = { _0x(0f33,43b0), _0x(2bdb,c7e2)}; |
77 | static long mln2lox[] = { _0x(1b60,a70f), _0x(582a,279e)}; | |
78 | static long lnovflx[] = { _0x(0f33,43b0), _0x(2bda,c7e2)}; | |
c77add16 ZAL |
79 | #define mln2hi (*(double*)mln2hix) |
80 | #define mln2lo (*(double*)mln2lox) | |
81 | #define lnovfl (*(double*)lnovflx) | |
859dc438 | 82 | #else /* defined(vax)||defined(tahoe) */ |
62b65e15 | 83 | static double |
c77add16 ZAL |
84 | mln2hi = 7.0978271289338397310E2 , /*Hex 2^ 10 * 1.62E42FEFA39EF */ |
85 | mln2lo = 2.3747039373786107478E-14 , /*Hex 2^-45 * 1.ABC9E3B39803F */ | |
86 | lnovfl = 7.0978271289338397310E2 ; /*Hex 2^ 9 * 1.62E42FEFA39EF */ | |
859dc438 | 87 | #endif /* defined(vax)||defined(tahoe) */ |
c77add16 | 88 | |
859dc438 | 89 | #if defined(vax)||defined(tahoe) |
c77add16 | 90 | static max = 126 ; |
859dc438 | 91 | #else /* defined(vax)||defined(tahoe) */ |
c77add16 | 92 | static max = 1023 ; |
859dc438 | 93 | #endif /* defined(vax)||defined(tahoe) */ |
c77add16 ZAL |
94 | |
95 | double cosh(x) | |
96 | double x; | |
97 | { | |
98 | static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */ | |
99 | double scalb(),copysign(),exp(),exp__E(),t; | |
100 | ||
859dc438 | 101 | #if !defined(vax)&&!defined(tahoe) |
c77add16 | 102 | if(x!=x) return(x); /* x is NaN */ |
859dc438 | 103 | #endif /* !defined(vax)&&!defined(tahoe) */ |
c77add16 ZAL |
104 | if((x=copysign(x,one)) <= 22) |
105 | if(x<0.3465) | |
106 | if(x<small) return(one+x); | |
107 | else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } | |
108 | ||
109 | else /* for x lies in [0.3465,22] */ | |
110 | { t=exp(x); return((t+one/t)*half); } | |
111 | ||
112 | if( lnovfl <= x && x <= (lnovfl+0.7)) | |
113 | /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) | |
114 | * and return 2^max*exp(x) to avoid unnecessary overflow | |
115 | */ | |
116 | return(scalb(exp((x-mln2hi)-mln2lo), max)); | |
117 | ||
118 | else | |
119 | return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ | |
120 | } |