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Annotation of 43BSDTahoe/usr.lib/libm/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 the above copyright notice and this paragraph are
        !             7:  * duplicated in all such forms and that any documentation,
        !             8:  * advertising materials, and other materials related to such
        !             9:  * distribution and use acknowledge that the software was developed
        !            10:  * by the University of California, Berkeley.  The name of the
        !            11:  * University may not be used to endorse or promote products derived
        !            12:  * from this software without specific prior written permission.
        !            13:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            14:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            15:  * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            16:  *
        !            17:  * All recipients should regard themselves as participants in an ongoing
        !            18:  * research project and hence should feel obligated to report their
        !            19:  * experiences (good or bad) with these elementary function codes, using
        !            20:  * the sendbug(8) program, to the authors.
        !            21:  */
        !            22: 
        !            23: #ifndef lint
        !            24: static char sccsid[] = "@(#)cosh.c     5.3 (Berkeley) 6/30/88";
        !            25: #endif /* not lint */
        !            26: 
        !            27: /* COSH(X)
        !            28:  * RETURN THE HYPERBOLIC COSINE OF X
        !            29:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !            30:  * CODED IN C BY K.C. NG, 1/8/85; 
        !            31:  * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85.
        !            32:  *
        !            33:  * Required system supported functions :
        !            34:  *     copysign(x,y)
        !            35:  *     scalb(x,N)
        !            36:  *
        !            37:  * Required kernel function:
        !            38:  *     exp(x) 
        !            39:  *     exp__E(x,c)     ...return exp(x+c)-1-x for |x|<0.3465
        !            40:  *
        !            41:  * Method :
        !            42:  *     1. Replace x by |x|. 
        !            43:  *     2. 
        !            44:  *                                                     [ exp(x) - 1 ]^2 
        !            45:  *         0        <= x <= 0.3465  :  cosh(x) := 1 + -------------------
        !            46:  *                                                        2*exp(x)
        !            47:  *
        !            48:  *                                                exp(x) +  1/exp(x)
        !            49:  *         0.3465   <= x <= 22      :  cosh(x) := -------------------
        !            50:  *                                                        2
        !            51:  *         22       <= x <= lnovfl  :  cosh(x) := exp(x)/2 
        !            52:  *         lnovfl   <= x <= lnovfl+log(2)
        !            53:  *                                  :  cosh(x) := exp(x)/2 (avoid overflow)
        !            54:  *         log(2)+lnovfl <  x <  INF:  overflow to INF
        !            55:  *
        !            56:  *     Note: .3465 is a number near one half of ln2.
        !            57:  *
        !            58:  * Special cases:
        !            59:  *     cosh(x) is x if x is +INF, -INF, or NaN.
        !            60:  *     only cosh(0)=1 is exact for finite x.
        !            61:  *
        !            62:  * Accuracy:
        !            63:  *     cosh(x) returns the exact hyperbolic cosine of x nearly rounded.
        !            64:  *     In a test run with 768,000 random arguments on a VAX, the maximum
        !            65:  *     observed error was 1.23 ulps (units in the last place).
        !            66:  *
        !            67:  * Constants:
        !            68:  * The hexadecimal values are the intended ones for the following constants.
        !            69:  * The decimal values may be used, provided that the compiler will convert
        !            70:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            71:  * shown.
        !            72:  */
        !            73: 
        !            74: #if defined(vax)||defined(tahoe)
        !            75: #ifdef vax
        !            76: #define _0x(A,B)       0x/**/A/**/B
        !            77: #else  /* vax */
        !            78: #define _0x(A,B)       0x/**/B/**/A
        !            79: #endif /* vax */
        !            80: /* static double  */
        !            81: /* mln2hi =  8.8029691931113054792E1     , Hex  2^  7   *  .B00F33C7E22BDB */
        !            82: /* mln2lo = -4.9650192275318476525E-16   , Hex  2^-50   * -.8F1B60279E582A */
        !            83: /* lnovfl =  8.8029691931113053016E1     ; Hex  2^  7   *  .B00F33C7E22BDA */
        !            84: static long    mln2hix[] = { _0x(0f33,43b0), _0x(2bdb,c7e2)};
        !            85: static long    mln2lox[] = { _0x(1b60,a70f), _0x(582a,279e)};
        !            86: static long    lnovflx[] = { _0x(0f33,43b0), _0x(2bda,c7e2)};
        !            87: #define   mln2hi    (*(double*)mln2hix)
        !            88: #define   mln2lo    (*(double*)mln2lox)
        !            89: #define   lnovfl    (*(double*)lnovflx)
        !            90: #else  /* defined(vax)||defined(tahoe) */
        !            91: static double
        !            92: mln2hi =  7.0978271289338397310E2     , /*Hex  2^ 10   *  1.62E42FEFA39EF */
        !            93: mln2lo =  2.3747039373786107478E-14   , /*Hex  2^-45   *  1.ABC9E3B39803F */
        !            94: lnovfl =  7.0978271289338397310E2     ; /*Hex  2^  9   *  1.62E42FEFA39EF */
        !            95: #endif /* defined(vax)||defined(tahoe) */
        !            96: 
        !            97: #if defined(vax)||defined(tahoe)
        !            98: static max = 126                      ;
        !            99: #else  /* defined(vax)||defined(tahoe) */
        !           100: static max = 1023                     ;
        !           101: #endif /* defined(vax)||defined(tahoe) */
        !           102: 
        !           103: double cosh(x)
        !           104: double x;
        !           105: {      
        !           106:        static double half=1.0/2.0,one=1.0, small=1.0E-18; /* fl(1+small)==1 */
        !           107:        double scalb(),copysign(),exp(),exp__E(),t;
        !           108: 
        !           109: #if !defined(vax)&&!defined(tahoe)
        !           110:        if(x!=x) return(x);     /* x is NaN */
        !           111: #endif /* !defined(vax)&&!defined(tahoe) */
        !           112:        if((x=copysign(x,one)) <= 22)
        !           113:            if(x<0.3465) 
        !           114:                if(x<small) return(one+x);
        !           115:                else {t=x+exp__E(x,0.0);x=t+t; return(one+t*t/(2.0+x)); }
        !           116: 
        !           117:            else /* for x lies in [0.3465,22] */
        !           118:                { t=exp(x); return((t+one/t)*half); }
        !           119: 
        !           120:        if( lnovfl <= x && x <= (lnovfl+0.7)) 
        !           121:         /* for x lies in [lnovfl, lnovfl+ln2], decrease x by ln(2^(max+1)) 
        !           122:          * and return 2^max*exp(x) to avoid unnecessary overflow 
        !           123:          */
        !           124:            return(scalb(exp((x-mln2hi)-mln2lo), max)); 
        !           125: 
        !           126:        else 
        !           127:            return(exp(x)*half);        /* for large x,  cosh(x)=exp(x)/2 */
        !           128: }

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