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Annotation of 43BSDReno/lib/libm/common_source/cosh.c, revision 1.1

1.1     ! root        1: /*
        !             2:  * Copyright (c) 1985 Regents of the University of California.
        !             3:  * All rights reserved.
        !             4:  *
        !             5:  * Redistribution and use in source and binary forms are permitted
        !             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
        !            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
        !            17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            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.
        !            23:  */
        !            24: 
        !            25: #ifndef lint
        !            26: static char sccsid[] = "@(#)cosh.c     5.5 (Berkeley) 6/1/90";
        !            27: #endif /* not lint */
        !            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: 
        !            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
        !            91: 
        !            92: #if defined(vax)||defined(tahoe)
        !            93: static max = 126                      ;
        !            94: #else  /* defined(vax)||defined(tahoe) */
        !            95: static max = 1023                     ;
        !            96: #endif /* defined(vax)||defined(tahoe) */
        !            97: 
        !            98: double cosh(x)
        !            99: double x;
        !           100: {      
        !           101:        static const double half=1.0/2.0,
        !           102:                one=1.0, small=1.0E-18; /* fl(1+small)==1 */
        !           103:        double t;
        !           104: 
        !           105: #if !defined(vax)&&!defined(tahoe)
        !           106:        if(x!=x) return(x);     /* x is NaN */
        !           107: #endif /* !defined(vax)&&!defined(tahoe) */
        !           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: }

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