projects / unix-history / blame
| Commit | Line | Data |
|---|---|---|
| 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[] = |
| 859dc438 ZAL |
16 | "@(#)cosh.c 1.2 (Berkeley) 8/21/85; 1.6 (ucb.elefunt) %G%"; |
| 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 | } |