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Annotation of 43BSD/usr.lib/libm/asinh.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[] = "@(#)asinh.c    1.2 (Berkeley) 8/21/85";
        !            16: #endif not lint
        !            17: 
        !            18: /* ASINH(X)
        !            19:  * RETURN THE INVERSE HYPERBOLIC SINE OF X
        !            20:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !            21:  * CODED IN C BY K.C. NG, 2/16/85;
        !            22:  * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
        !            23:  *
        !            24:  * Required system supported functions :
        !            25:  *     copysign(x,y)
        !            26:  *     sqrt(x)
        !            27:  *
        !            28:  * Required kernel function:
        !            29:  *     log1p(x)                ...return log(1+x)
        !            30:  *
        !            31:  * Method :
        !            32:  *     Based on 
        !            33:  *             asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
        !            34:  *     we have
        !            35:  *     asinh(x) := x  if  1+x*x=1,
        !            36:  *              := sign(x)*(log1p(x)+ln2))      if sqrt(1+x*x)=x, else
        !            37:  *              := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )  
        !            38:  *
        !            39:  * Accuracy:
        !            40:  *     asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
        !            41:  *     In a test run with 52,000 random arguments on a VAX, the maximum 
        !            42:  *     observed error was 1.58 ulps (units in the last place).
        !            43:  *
        !            44:  * Constants:
        !            45:  * The hexadecimal values are the intended ones for the following constants.
        !            46:  * The decimal values may be used, provided that the compiler will convert
        !            47:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            48:  * shown.
        !            49:  */
        !            50: 
        !            51: #ifdef VAX     /* VAX D format */
        !            52: /* static double */
        !            53: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
        !            54: /* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
        !            55: static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
        !            56: static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
        !            57: #define    ln2hi    (*(double*)ln2hix)
        !            58: #define    ln2lo    (*(double*)ln2lox)
        !            59: #else  /* IEEE double */
        !            60: static double
        !            61: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
        !            62: ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
        !            63: #endif
        !            64: 
        !            65: double asinh(x)
        !            66: double x;
        !            67: {      
        !            68:        double copysign(),log1p(),sqrt(),t,s;
        !            69:        static double small=1.0E-10,    /* fl(1+small*small) == 1 */
        !            70:                      big  =1.0E20,     /* fl(1+big) == big */
        !            71:                      one  =1.0   ;     
        !            72: 
        !            73: #ifndef VAX
        !            74:        if(x!=x) return(x);     /* x is NaN */
        !            75: #endif
        !            76:        if((t=copysign(x,one))>small) 
        !            77:            if(t<big) {
        !            78:                s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
        !            79:            else        /* if |x| > big */
        !            80:                {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
        !            81:        else    /* if |x| < small */
        !            82:            return(x);
        !            83: }

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