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Annotation of 43BSDTahoe/usr.lib/libm/asinh.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[] = "@(#)asinh.c    5.3 (Berkeley) 6/30/88";
        !            25: #endif /* not lint */
        !            26: 
        !            27: /* ASINH(X)
        !            28:  * RETURN THE INVERSE HYPERBOLIC SINE OF X
        !            29:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !            30:  * CODED IN C BY K.C. NG, 2/16/85;
        !            31:  * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
        !            32:  *
        !            33:  * Required system supported functions :
        !            34:  *     copysign(x,y)
        !            35:  *     sqrt(x)
        !            36:  *
        !            37:  * Required kernel function:
        !            38:  *     log1p(x)                ...return log(1+x)
        !            39:  *
        !            40:  * Method :
        !            41:  *     Based on 
        !            42:  *             asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
        !            43:  *     we have
        !            44:  *     asinh(x) := x  if  1+x*x=1,
        !            45:  *              := sign(x)*(log1p(x)+ln2))      if sqrt(1+x*x)=x, else
        !            46:  *              := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )  
        !            47:  *
        !            48:  * Accuracy:
        !            49:  *     asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
        !            50:  *     In a test run with 52,000 random arguments on a VAX, the maximum 
        !            51:  *     observed error was 1.58 ulps (units in the last place).
        !            52:  *
        !            53:  * Constants:
        !            54:  * The hexadecimal values are the intended ones for the following constants.
        !            55:  * The decimal values may be used, provided that the compiler will convert
        !            56:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            57:  * shown.
        !            58:  */
        !            59: 
        !            60: #if defined(vax)||defined(tahoe)       /* VAX/TAHOE D format */
        !            61: #ifdef vax
        !            62: #define _0x(A,B)       0x/**/A/**/B
        !            63: #else  /* vax */
        !            64: #define _0x(A,B)       0x/**/B/**/A
        !            65: #endif /* vax */
        !            66: /* static double */
        !            67: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
        !            68: /* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
        !            69: static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
        !            70: static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
        !            71: #define    ln2hi    (*(double*)ln2hix)
        !            72: #define    ln2lo    (*(double*)ln2lox)
        !            73: #else  /* defined(vax)||defined(tahoe) */
        !            74: static double
        !            75: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
        !            76: ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
        !            77: #endif /* defined(vax)||defined(tahoe) */
        !            78: 
        !            79: double asinh(x)
        !            80: double x;
        !            81: {      
        !            82:        double copysign(),log1p(),sqrt(),t,s;
        !            83:        static double small=1.0E-10,    /* fl(1+small*small) == 1 */
        !            84:                      big  =1.0E20,     /* fl(1+big) == big */
        !            85:                      one  =1.0   ;     
        !            86: 
        !            87: #if !defined(vax)&&!defined(tahoe)
        !            88:        if(x!=x) return(x);     /* x is NaN */
        !            89: #endif /* !defined(vax)&&!defined(tahoe) */
        !            90:        if((t=copysign(x,one))>small) 
        !            91:            if(t<big) {
        !            92:                s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
        !            93:            else        /* if |x| > big */
        !            94:                {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
        !            95:        else    /* if |x| < small */
        !            96:            return(x);
        !            97: }

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