projects / unix-history / blame
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| 4c182be8 | 1 | /* |
| c77add16 | 2 | * Copyright (c) 1985 Regents of the University of California. |
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3 | * All rights reserved. |
| 4 | * | |
| 5 | * Redistribution and use in source and binary forms are permitted | |
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6 | * provided that: (1) source distributions retain this entire copyright |
| 7 | * notice and comment, and (2) distributions including binaries display | |
| 8 | * the following acknowledgement: ``This product includes software | |
| 9 | * developed by the University of California, Berkeley and its contributors'' | |
| 10 | * in the documentation or other materials provided with the distribution | |
| 11 | * and in all advertising materials mentioning features or use of this | |
| 12 | * software. Neither the name of the University nor the names of its | |
| 13 | * contributors may be used to endorse or promote products derived | |
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14 | * from this software without specific prior written permission. |
| 15 | * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR | |
| 16 | * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED | |
| 1c15e888 | 17 | * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. |
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18 | * |
| 19 | * All recipients should regard themselves as participants in an ongoing | |
| 20 | * research project and hence should feel obligated to report their | |
| 21 | * experiences (good or bad) with these elementary function codes, using | |
| 22 | * the sendbug(8) program, to the authors. | |
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23 | */ |
| 24 | ||
| 25 | #ifndef lint | |
| 1c15e888 | 26 | static char sccsid[] = "@(#)cosh.c 5.5 (Berkeley) 6/1/90"; |
| 4c182be8 | 27 | #endif /* not lint */ |
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28 | |
| 29 | /* COSH(X) | |
| 30 | * RETURN THE HYPERBOLIC COSINE OF X | |
| 31 | * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) | |
| 32 | * CODED IN C BY K.C. NG, 1/8/85; | |
| 33 | * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. | |
| 34 | * | |
| 35 | * Required system supported functions : | |
| 36 | * copysign(x,y) | |
| 37 | * scalb(x,N) | |
| 38 | * | |
| 39 | * Required kernel function: | |
| 40 | * exp(x) | |
| 41 | * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 | |
| 42 | * | |
| 43 | * Method : | |
| 44 | * 1. Replace x by |x|. | |
| 45 | * 2. | |
| 46 | * [ exp(x) - 1 ]^2 | |
| 47 | * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- | |
| 48 | * 2*exp(x) | |
| 49 | * | |
| 50 | * exp(x) + 1/exp(x) | |
| 51 | * 0.3465 <= x <= 22 : cosh(x) := ------------------- | |
| 52 | * 2 | |
| 53 | * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 | |
| 54 | * lnovfl <= x <= lnovfl+log(2) | |
| 55 | * : cosh(x) := exp(x)/2 (avoid overflow) | |
| 56 | * log(2)+lnovfl < x < INF: overflow to INF | |
| 57 | * | |
| 58 | * Note: .3465 is a number near one half of ln2. | |
| 59 | * | |
| 60 | * Special cases: | |
| 61 | * cosh(x) is x if x is +INF, -INF, or NaN. | |
| 62 | * only cosh(0)=1 is exact for finite x. | |
| 63 | * | |
| 64 | * Accuracy: | |
| 65 | * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. | |
| 66 | * In a test run with 768,000 random arguments on a VAX, the maximum | |
| 67 | * observed error was 1.23 ulps (units in the last place). | |
| 68 | * | |
| 69 | * Constants: | |
| 70 | * The hexadecimal values are the intended ones for the following constants. | |
| 71 | * The decimal values may be used, provided that the compiler will convert | |
| 72 | * from decimal to binary accurately enough to produce the hexadecimal values | |
| 73 | * shown. | |
| 74 | */ | |
| 75 | ||
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76 | #include "mathimpl.h" |
| 77 | ||
| 78 | vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) | |
| 79 | vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) | |
| 80 | vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) | |
| 81 | ||
| 82 | ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) | |
| 83 | ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) | |
| 84 | ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) | |
| 85 | ||
| 86 | #ifdef vccast | |
| 87 | #define mln2hi vccast(mln2hi) | |
| 88 | #define mln2lo vccast(mln2lo) | |
| 89 | #define lnovfl vccast(lnovfl) | |
| 90 | #endif | |
| c77add16 | 91 | |
| 859dc438 | 92 | #if defined(vax)||defined(tahoe) |
| c77add16 | 93 | static max = 126 ; |
| 859dc438 | 94 | #else /* defined(vax)||defined(tahoe) */ |
| c77add16 | 95 | static max = 1023 ; |
| 859dc438 | 96 | #endif /* defined(vax)||defined(tahoe) */ |
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97 | |
| 98 | double cosh(x) | |
| 99 | double x; | |
| 100 | { | |
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101 | static const double half=1.0/2.0, |
| 102 | one=1.0, small=1.0E-18; /* fl(1+small)==1 */ | |
| 103 | double t; | |
| c77add16 | 104 | |
| 859dc438 | 105 | #if !defined(vax)&&!defined(tahoe) |
| c77add16 | 106 | if(x!=x) return(x); /* x is NaN */ |
| 859dc438 | 107 | #endif /* !defined(vax)&&!defined(tahoe) */ |
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108 | if((x=copysign(x,one)) <= 22) |
| 109 | if(x<0.3465) | |
| 110 | if(x<small) return(one+x); | |
| 111 | else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); } | |
| 112 | ||
| 113 | else /* for x lies in [0.3465,22] */ | |
| 114 | { t=exp(x); return((t+one/t)*half); } | |
| 115 | ||
| 116 | if( lnovfl <= x && x <= (lnovfl+0.7)) | |
| 117 | /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) | |
| 118 | * and return 2^max*exp(x) to avoid unnecessary overflow | |
| 119 | */ | |
| 120 | return(scalb(exp((x-mln2hi)-mln2lo), max)); | |
| 121 | ||
| 122 | else | |
| 123 | return(exp(x)*half); /* for large x, cosh(x)=exp(x)/2 */ | |
| 124 | } |