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Annotation of 43BSD/usr.lib/libm/sinh.c, revision 1.1

1.1     ! root        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
        !            15: static char sccsid[] = "@(#)sinh.c     4.3 (Berkeley) 8/21/85";
        !            16: #endif not lint
        !            17: 
        !            18: /* SINH(X)
        !            19:  * RETURN THE HYPERBOLIC SINE OF X
        !            20:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !            21:  * CODED IN C BY K.C. NG, 1/8/85; 
        !            22:  * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
        !            23:  *
        !            24:  * Required system supported functions :
        !            25:  *     copysign(x,y)
        !            26:  *     scalb(x,N)
        !            27:  *
        !            28:  * Required kernel functions:
        !            29:  *     expm1(x)        ...return exp(x)-1
        !            30:  *
        !            31:  * Method :
        !            32:  *     1. reduce x to non-negative by sinh(-x) = - sinh(x).
        !            33:  *     2. 
        !            34:  *
        !            35:  *                                           expm1(x) + expm1(x)/(expm1(x)+1)
        !            36:  *         0 <= x <= lnovfl     : sinh(x) := --------------------------------
        !            37:  *                                                           2
        !            38:  *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
        !            39:  * lnovfl+ln2 <  x <  INF        :  overflow to INF
        !            40:  *     
        !            41:  *
        !            42:  * Special cases:
        !            43:  *     sinh(x) is x if x is +INF, -INF, or NaN.
        !            44:  *     only sinh(0)=0 is exact for finite argument.
        !            45:  *
        !            46:  * Accuracy:
        !            47:  *     sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
        !            48:  *     a test run with 1,024,000 random arguments on a VAX, the maximum
        !            49:  *     observed error was 1.93 ulps (units in the last place).
        !            50:  *
        !            51:  * Constants:
        !            52:  * The hexadecimal values are the intended ones for the following constants.
        !            53:  * The decimal values may be used, provided that the compiler will convert
        !            54:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            55:  * shown.
        !            56:  */
        !            57: #ifdef VAX
        !            58: /* double static */
        !            59: /* mln2hi =  8.8029691931113054792E1     , Hex  2^  7   *  .B00F33C7E22BDB */
        !            60: /* mln2lo = -4.9650192275318476525E-16   , Hex  2^-50   * -.8F1B60279E582A */
        !            61: /* lnovfl =  8.8029691931113053016E1     ; Hex  2^  7   *  .B00F33C7E22BDA */
        !            62: static long    mln2hix[] = { 0x0f3343b0, 0x2bdbc7e2};
        !            63: static long    mln2lox[] = { 0x1b60a70f, 0x582a279e};
        !            64: static long    lnovflx[] = { 0x0f3343b0, 0x2bdac7e2};
        !            65: #define   mln2hi    (*(double*)mln2hix)
        !            66: #define   mln2lo    (*(double*)mln2lox)
        !            67: #define   lnovfl    (*(double*)lnovflx)
        !            68: #else  /* IEEE double */
        !            69: double static 
        !            70: mln2hi =  7.0978271289338397310E2     , /*Hex  2^ 10   *  1.62E42FEFA39EF */
        !            71: mln2lo =  2.3747039373786107478E-14   , /*Hex  2^-45   *  1.ABC9E3B39803F */
        !            72: lnovfl =  7.0978271289338397310E2     ; /*Hex  2^  9   *  1.62E42FEFA39EF */
        !            73: #endif
        !            74: 
        !            75: #ifdef VAX
        !            76: static max = 126                      ;
        !            77: #else  /* IEEE double */
        !            78: static max = 1023                     ;
        !            79: #endif
        !            80: 
        !            81: 
        !            82: double sinh(x)
        !            83: double x;
        !            84: {
        !            85:        static double  one=1.0, half=1.0/2.0 ;
        !            86:        double expm1(), t, scalb(), copysign(), sign;
        !            87: #ifndef VAX
        !            88:        if(x!=x) return(x);     /* x is NaN */
        !            89: #endif
        !            90:        sign=copysign(one,x);
        !            91:        x=copysign(x,one);
        !            92:        if(x<lnovfl)
        !            93:            {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
        !            94: 
        !            95:        else if(x <= lnovfl+0.7)
        !            96:                /* subtract x by ln(2^(max+1)) and return 2^max*exp(x) 
        !            97:                        to avoid unnecessary overflow */
        !            98:            return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
        !            99: 
        !           100:        else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
        !           101:            return( expm1(x)*sign );
        !           102: }

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