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Annotation of 43BSDTahoe/usr.lib/libm/sinh.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[] = "@(#)sinh.c     5.3 (Berkeley) 6/30/88";
        !            25: #endif /* not lint */
        !            26: 
        !            27: /* SINH(X)
        !            28:  * RETURN THE HYPERBOLIC SINE 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, 3/7/85, 3/24/85, 4/16/85.
        !            32:  *
        !            33:  * Required system supported functions :
        !            34:  *     copysign(x,y)
        !            35:  *     scalb(x,N)
        !            36:  *
        !            37:  * Required kernel functions:
        !            38:  *     expm1(x)        ...return exp(x)-1
        !            39:  *
        !            40:  * Method :
        !            41:  *     1. reduce x to non-negative by sinh(-x) = - sinh(x).
        !            42:  *     2. 
        !            43:  *
        !            44:  *                                           expm1(x) + expm1(x)/(expm1(x)+1)
        !            45:  *         0 <= x <= lnovfl     : sinh(x) := --------------------------------
        !            46:  *                                                           2
        !            47:  *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
        !            48:  * lnovfl+ln2 <  x <  INF        :  overflow to INF
        !            49:  *     
        !            50:  *
        !            51:  * Special cases:
        !            52:  *     sinh(x) is x if x is +INF, -INF, or NaN.
        !            53:  *     only sinh(0)=0 is exact for finite argument.
        !            54:  *
        !            55:  * Accuracy:
        !            56:  *     sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
        !            57:  *     a test run with 1,024,000 random arguments on a VAX, the maximum
        !            58:  *     observed error was 1.93 ulps (units in the last place).
        !            59:  *
        !            60:  * Constants:
        !            61:  * The hexadecimal values are the intended ones for the following constants.
        !            62:  * The decimal values may be used, provided that the compiler will convert
        !            63:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            64:  * shown.
        !            65:  */
        !            66: #if defined(vax)||defined(tahoe)
        !            67: #ifdef vax
        !            68: #define _0x(A,B)       0x/**/A/**/B
        !            69: #else  /* vax */
        !            70: #define _0x(A,B)       0x/**/B/**/A
        !            71: #endif /* vax */
        !            72: /* static double */
        !            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 */
        !            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)};
        !            79: #define   mln2hi    (*(double*)mln2hix)
        !            80: #define   mln2lo    (*(double*)mln2lox)
        !            81: #define   lnovfl    (*(double*)lnovflx)
        !            82: #else  /* defined(vax)||defined(tahoe) */
        !            83: static double 
        !            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 */
        !            87: #endif /* defined(vax)||defined(tahoe) */
        !            88: 
        !            89: #if defined(vax)||defined(tahoe)
        !            90: static max = 126                      ;
        !            91: #else  /* defined(vax)||defined(tahoe) */
        !            92: static max = 1023                     ;
        !            93: #endif /* defined(vax)||defined(tahoe) */
        !            94: 
        !            95: 
        !            96: double sinh(x)
        !            97: double x;
        !            98: {
        !            99:        static double  one=1.0, half=1.0/2.0 ;
        !           100:        double expm1(), t, scalb(), copysign(), sign;
        !           101: #if !defined(vax)&&!defined(tahoe)
        !           102:        if(x!=x) return(x);     /* x is NaN */
        !           103: #endif /* !defined(vax)&&!defined(tahoe) */
        !           104:        sign=copysign(one,x);
        !           105:        x=copysign(x,one);
        !           106:        if(x<lnovfl)
        !           107:            {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
        !           108: 
        !           109:        else if(x <= lnovfl+0.7)
        !           110:                /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 
        !           111:                        to avoid unnecessary overflow */
        !           112:            return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
        !           113: 
        !           114:        else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
        !           115:            return( expm1(x)*sign );
        !           116: }

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