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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 | |
15 | static char sccsid[] = "@(#)cosh.c 1.1 (ELEFUNT) %G%"; | |
16 | #endif not lint | |
17 | ||
18 | /* COSH(X) | |
19 | * RETURN THE HYPERBOLIC COSINE OF X | |
20 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
21 | * CODED IN C BY K.C. NG, 1/8/85; | |
22 | * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. | |
23 | * | |
24 | * Required system supported functions : | |
25 | * copysign(x,y) | |
26 | * scalb(x,N) | |
27 | * | |
28 | * Required kernel function: | |
29 | * exp(x) | |
30 | * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 | |
31 | * | |
32 | * Method : | |
33 | * 1. Replace x by |x|. | |
34 | * 2. | |
35 | * [ exp(x) - 1 ]^2 | |
36 | * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- | |
37 | * 2*exp(x) | |
38 | * | |
39 | * exp(x) + 1/exp(x) | |
40 | * 0.3465 <= x <= 22 : cosh(x) := ------------------- | |
41 | * 2 | |
42 | * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 | |
43 | * lnovfl <= x <= lnovfl+log(2) | |
44 | * : cosh(x) := exp(x)/2 (avoid overflow) | |
45 | * log(2)+lnovfl < x < INF: overflow to INF | |
46 | * | |
47 | * Note: .3465 is a number near one half of ln2. | |
48 | * | |
49 | * Special cases: | |
50 | * cosh(x) is x if x is +INF, -INF, or NaN. | |
51 | * only cosh(0)=1 is exact for finite x. | |
52 | * | |
53 | * Accuracy: | |
54 | * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. | |
55 | * In a test run with 768,000 random arguments on a VAX, the maximum | |
56 | * observed error was 1.23 ulps (units in the last place). | |
57 | * | |
58 | * Constants: | |
59 | * The hexadecimal values are the intended ones for the following constants. | |
60 | * The decimal values may be used, provided that the compiler will convert | |
61 | * from decimal to binary accurately enough to produce the hexadecimal values | |
62 | * shown. | |
63 | */ | |
64 | ||
65 | #ifdef VAX | |
66 | /* double static */ | |
67 | /* mln2hi = 8.8029691931113054792E1 , Hex 2^ 7 * .B00F33C7E22BDB */ | |
68 | /* mln2lo = -4.9650192275318476525E-16 , Hex 2^-50 * -.8F1B60279E582A */ | |
69 | /* lnovfl = 8.8029691931113053016E1 ; Hex 2^ 7 * .B00F33C7E22BDA */ | |
70 | static long mln2hix[] = { 0x0f3343b0, 0x2bdbc7e2}; | |
71 | static long mln2lox[] = { 0x1b60a70f, 0x582a279e}; | |
72 | static long lnovflx[] = { 0x0f3343b0, 0x2bdac7e2}; | |
73 | #define mln2hi (*(double*)mln2hix) | |
74 | #define mln2lo (*(double*)mln2lox) | |
75 | #define lnovfl (*(double*)lnovflx) | |
76 | #else /* IEEE double */ | |
77 | double static | |
78 | mln2hi = 7.0978271289338397310E2 , /*Hex 2^ 10 * 1.62E42FEFA39EF */ | |
79 | mln2lo = 2.3747039373786107478E-14 , /*Hex 2^-45 * 1.ABC9E3B39803F */ | |
80 | lnovfl = 7.0978271289338397310E2 ; /*Hex 2^ 9 * 1.62E42FEFA39EF */ | |
81 | #endif | |
82 | ||
83 | #ifdef VAX | |
84 | static max = 126 ; | |
85 | #else /* IEEE double */ | |
86 | static max = 1023 ; | |
87 | #endif | |
88 | ||
89 | double cosh(x) | |
90 | double x; | |
91 | { | |
92 | static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */ | |
93 | double scalb(),copysign(),exp(),exp__E(),t; | |
94 | ||
95 | #ifndef VAX | |
96 | if(x!=x) return(x); /* x is NaN */ | |
97 | #endif | |
98 | if((x=copysign(x,one)) <= 22) | |
99 | if(x<0.3465) | |
100 | if(x<small) return(one+x); | |
101 | else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } | |
102 | ||
103 | else /* for x lies in [0.3465,22] */ | |
104 | { t=exp(x); return((t+one/t)*half); } | |
105 | ||
106 | if( lnovfl <= x && x <= (lnovfl+0.7)) | |
107 | /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) | |
108 | * and return 2^max*exp(x) to avoid unnecessary overflow | |
109 | */ | |
110 | return(scalb(exp((x-mln2hi)-mln2lo), max)); | |
111 | ||
112 | else | |
113 | return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ | |
114 | } |