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Annotation of 43BSDTahoe/usr.lib/libm/acosh.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[] = "@(#)acosh.c    5.3 (Berkeley) 6/30/88";
        !            25: #endif /* not lint */
        !            26: 
        !            27: /* ACOSH(X)
        !            28:  * RETURN THE INVERSE HYPERBOLIC COSINE 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 3/6/85, 3/24/85, 4/16/85, 8/17/85.
        !            32:  *
        !            33:  * Required system supported functions :
        !            34:  *     sqrt(x)
        !            35:  *
        !            36:  * Required kernel function:
        !            37:  *     log1p(x)                ...return log(1+x)
        !            38:  *
        !            39:  * Method :
        !            40:  *     Based on 
        !            41:  *             acosh(x) = log [ x + sqrt(x*x-1) ]
        !            42:  *     we have
        !            43:  *             acosh(x) := log1p(x)+ln2,       if (x > 1.0E20); else           
        !            44:  *             acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
        !            45:  *     These formulae avoid the over/underflow complication.
        !            46:  *
        !            47:  * Special cases:
        !            48:  *     acosh(x) is NaN with signal if x<1.
        !            49:  *     acosh(NaN) is NaN without signal.
        !            50:  *
        !            51:  * Accuracy:
        !            52:  *     acosh(x) returns the exact inverse hyperbolic cosine of x nearly 
        !            53:  *     rounded. In a test run with 512,000 random arguments on a VAX, the
        !            54:  *     maximum observed error was 3.30 ulps (units of the last place) at
        !            55:  *     x=1.0070493753568216 .
        !            56:  *
        !            57:  * Constants:
        !            58:  * The hexadecimal values are the intended ones for the following constants.
        !            59:  * The decimal values may be used, provided that the compiler will convert
        !            60:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            61:  * shown.
        !            62:  */
        !            63: 
        !            64: #if defined(vax)||defined(tahoe)       /* VAX D format */
        !            65: #ifdef vax
        !            66: #define _0x(A,B)       0x/**/A/**/B
        !            67: #else  /* vax */
        !            68: #define _0x(A,B)       0x/**/B/**/A
        !            69: #endif /* vax */
        !            70: /* static double */
        !            71: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
        !            72: /* ln2lo  =  1.6465949582897081279E-12   ; Hex  2^-39   *  .E7BCD5E4F1D9CC */
        !            73: static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
        !            74: static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
        !            75: #define    ln2hi    (*(double*)ln2hix)
        !            76: #define    ln2lo    (*(double*)ln2lox)
        !            77: #else  /* defined(vax)||defined(tahoe) */
        !            78: static double
        !            79: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
        !            80: ln2lo  =  1.9082149292705877000E-10   ; /*Hex  2^-33   *  1.A39EF35793C76 */
        !            81: #endif /* defined(vax)||defined(tahoe) */
        !            82: 
        !            83: double acosh(x)
        !            84: double x;
        !            85: {      
        !            86:        double log1p(),sqrt(),t,big=1.E20; /* big+1==big */
        !            87: 
        !            88: #if !defined(vax)&&!defined(tahoe)
        !            89:        if(x!=x) return(x);     /* x is NaN */
        !            90: #endif /* !defined(vax)&&!defined(tahoe) */
        !            91: 
        !            92:     /* return log1p(x) + log(2) if x is large */
        !            93:        if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 
        !            94: 
        !            95:        t=sqrt(x-1.0);
        !            96:        return(log1p(t*(t+sqrt(x+1.0))));
        !            97: }

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