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Annotation of 43BSDReno/lib/libm/common_source/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: (1) source distributions retain this entire copyright
        !             7:  * notice and comment, and (2) distributions including binaries display
        !             8:  * the following acknowledgement:  ``This product includes software
        !             9:  * developed by the University of California, Berkeley and its contributors''
        !            10:  * in the documentation or other materials provided with the distribution
        !            11:  * and in all advertising materials mentioning features or use of this
        !            12:  * software. Neither the name of the University nor the names of its
        !            13:  * contributors may be used to endorse or promote products derived
        !            14:  * from this software without specific prior written permission.
        !            15:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            16:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            18:  *
        !            19:  * All recipients should regard themselves as participants in an ongoing
        !            20:  * research project and hence should feel obligated to report their
        !            21:  * experiences (good or bad) with these elementary function codes, using
        !            22:  * the sendbug(8) program, to the authors.
        !            23:  */
        !            24: 
        !            25: #ifndef lint
        !            26: static char sccsid[] = "@(#)asinh.c    5.5 (Berkeley) 6/1/90";
        !            27: #endif /* not lint */
        !            28: 
        !            29: /* ASINH(X)
        !            30:  * RETURN THE INVERSE HYPERBOLIC SINE OF X
        !            31:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
        !            32:  * CODED IN C BY K.C. NG, 2/16/85;
        !            33:  * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85.
        !            34:  *
        !            35:  * Required system supported functions :
        !            36:  *     copysign(x,y)
        !            37:  *     sqrt(x)
        !            38:  *
        !            39:  * Required kernel function:
        !            40:  *     log1p(x)                ...return log(1+x)
        !            41:  *
        !            42:  * Method :
        !            43:  *     Based on 
        !            44:  *             asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
        !            45:  *     we have
        !            46:  *     asinh(x) := x  if  1+x*x=1,
        !            47:  *              := sign(x)*(log1p(x)+ln2))      if sqrt(1+x*x)=x, else
        !            48:  *              := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) )  
        !            49:  *
        !            50:  * Accuracy:
        !            51:  *     asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded.
        !            52:  *     In a test run with 52,000 random arguments on a VAX, the maximum 
        !            53:  *     observed error was 1.58 ulps (units in the last place).
        !            54:  *
        !            55:  * Constants:
        !            56:  * The hexadecimal values are the intended ones for the following constants.
        !            57:  * The decimal values may be used, provided that the compiler will convert
        !            58:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            59:  * shown.
        !            60:  */
        !            61: #include "mathimpl.h"
        !            62: 
        !            63: vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
        !            64: vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
        !            65: 
        !            66: ic(ln2hi, 6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
        !            67: ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
        !            68: 
        !            69: #ifdef vccast
        !            70: #define    ln2hi    vccast(ln2hi)
        !            71: #define    ln2lo    vccast(ln2lo)
        !            72: #endif
        !            73: 
        !            74: double asinh(x)
        !            75: double x;
        !            76: {      
        !            77:        double t,s;
        !            78:        const static double     small=1.0E-10,  /* fl(1+small*small) == 1 */
        !            79:                                big  =1.0E20,   /* fl(1+big) == big */
        !            80:                                one  =1.0   ;   
        !            81: 
        !            82: #if !defined(vax)&&!defined(tahoe)
        !            83:        if(x!=x) return(x);     /* x is NaN */
        !            84: #endif /* !defined(vax)&&!defined(tahoe) */
        !            85:        if((t=copysign(x,one))>small) 
        !            86:            if(t<big) {
        !            87:                s=one/t; return(copysign(log1p(t+t/(s+sqrt(one+s*s))),x)); }
        !            88:            else        /* if |x| > big */
        !            89:                {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));}
        !            90:        else    /* if |x| < small */
        !            91:            return(x);
        !            92: }

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