projects / unix-history / blame
| Commit | Line | Data |
|---|---|---|
| 4c182be8 | 1 | /* |
| c77add16 | 2 | * Copyright (c) 1985 Regents of the University of California. |
| 4c182be8 KB |
3 | * All rights reserved. |
| 4 | * | |
| 7e3eac84 | 5 | * %sccs.include.redist.c% |
| c77add16 ZAL |
6 | */ |
| 7 | ||
| 8 | #ifndef lint | |
| 2bc65d90 | 9 | static char sccsid[] = "@(#)cosh.c 5.6 (Berkeley) %G%"; |
| 4c182be8 | 10 | #endif /* not lint */ |
| c77add16 ZAL |
11 | |
| 12 | /* COSH(X) | |
| 13 | * RETURN THE HYPERBOLIC COSINE OF X | |
| 14 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
| 15 | * CODED IN C BY K.C. NG, 1/8/85; | |
| 16 | * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. | |
| 17 | * | |
| 18 | * Required system supported functions : | |
| 19 | * copysign(x,y) | |
| 20 | * scalb(x,N) | |
| 21 | * | |
| 22 | * Required kernel function: | |
| 23 | * exp(x) | |
| 24 | * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 | |
| 25 | * | |
| 26 | * Method : | |
| 27 | * 1. Replace x by |x|. | |
| 28 | * 2. | |
| 29 | * [ exp(x) - 1 ]^2 | |
| 30 | * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- | |
| 31 | * 2*exp(x) | |
| 32 | * | |
| 33 | * exp(x) + 1/exp(x) | |
| 34 | * 0.3465 <= x <= 22 : cosh(x) := ------------------- | |
| 35 | * 2 | |
| 36 | * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 | |
| 37 | * lnovfl <= x <= lnovfl+log(2) | |
| 38 | * : cosh(x) := exp(x)/2 (avoid overflow) | |
| 39 | * log(2)+lnovfl < x < INF: overflow to INF | |
| 40 | * | |
| 41 | * Note: .3465 is a number near one half of ln2. | |
| 42 | * | |
| 43 | * Special cases: | |
| 44 | * cosh(x) is x if x is +INF, -INF, or NaN. | |
| 45 | * only cosh(0)=1 is exact for finite x. | |
| 46 | * | |
| 47 | * Accuracy: | |
| 48 | * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. | |
| 49 | * In a test run with 768,000 random arguments on a VAX, the maximum | |
| 50 | * observed error was 1.23 ulps (units in the last place). | |
| 51 | * | |
| 52 | * Constants: | |
| 53 | * The hexadecimal values are the intended ones for the following constants. | |
| 54 | * The decimal values may be used, provided that the compiler will convert | |
| 55 | * from decimal to binary accurately enough to produce the hexadecimal values | |
| 56 | * shown. | |
| 57 | */ | |
| 58 | ||
| 9eda3584 KB |
59 | #include "mathimpl.h" |
| 60 | ||
| 61 | vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) | |
| 62 | vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) | |
| 63 | vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) | |
| 64 | ||
| 65 | ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) | |
| 66 | ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) | |
| 67 | ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) | |
| 68 | ||
| 69 | #ifdef vccast | |
| 70 | #define mln2hi vccast(mln2hi) | |
| 71 | #define mln2lo vccast(mln2lo) | |
| 72 | #define lnovfl vccast(lnovfl) | |
| 73 | #endif | |
| c77add16 | 74 | |
| 859dc438 | 75 | #if defined(vax)||defined(tahoe) |
| c77add16 | 76 | static max = 126 ; |
| 859dc438 | 77 | #else /* defined(vax)||defined(tahoe) */ |
| c77add16 | 78 | static max = 1023 ; |
| 859dc438 | 79 | #endif /* defined(vax)||defined(tahoe) */ |
| c77add16 ZAL |
80 | |
| 81 | double cosh(x) | |
| 82 | double x; | |
| 83 | { | |
| 9eda3584 KB |
84 | static const double half=1.0/2.0, |
| 85 | one=1.0, small=1.0E-18; /* fl(1+small)==1 */ | |
| 86 | double t; | |
| c77add16 | 87 | |
| 859dc438 | 88 | #if !defined(vax)&&!defined(tahoe) |
| c77add16 | 89 | if(x!=x) return(x); /* x is NaN */ |
| 859dc438 | 90 | #endif /* !defined(vax)&&!defined(tahoe) */ |
| c77add16 ZAL |
91 | if((x=copysign(x,one)) <= 22) |
| 92 | if(x<0.3465) | |
| 93 | if(x<small) return(one+x); | |
| 94 | else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } | |
| 95 | ||
| 96 | else /* for x lies in [0.3465,22] */ | |
| 97 | { t=exp(x); return((t+one/t)*half); } | |
| 98 | ||
| 99 | if( lnovfl <= x && x <= (lnovfl+0.7)) | |
| 100 | /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) | |
| 101 | * and return 2^max*exp(x) to avoid unnecessary overflow | |
| 102 | */ | |
| 103 | return(scalb(exp((x-mln2hi)-mln2lo), max)); | |
| 104 | ||
| 105 | else | |
| 106 | return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ | |
| 107 | } |