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Annotation of 43BSDReno/lib/libm/common_source/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: (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[] = "@(#)acosh.c    5.5 (Berkeley) 6/1/90";
        !            27: #endif /* not lint */
        !            28: 
        !            29: /* ACOSH(X)
        !            30:  * RETURN THE INVERSE HYPERBOLIC COSINE 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 3/6/85, 3/24/85, 4/16/85, 8/17/85.
        !            34:  *
        !            35:  * Required system supported functions :
        !            36:  *     sqrt(x)
        !            37:  *
        !            38:  * Required kernel function:
        !            39:  *     log1p(x)                ...return log(1+x)
        !            40:  *
        !            41:  * Method :
        !            42:  *     Based on 
        !            43:  *             acosh(x) = log [ x + sqrt(x*x-1) ]
        !            44:  *     we have
        !            45:  *             acosh(x) := log1p(x)+ln2,       if (x > 1.0E20); else           
        !            46:  *             acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) .
        !            47:  *     These formulae avoid the over/underflow complication.
        !            48:  *
        !            49:  * Special cases:
        !            50:  *     acosh(x) is NaN with signal if x<1.
        !            51:  *     acosh(NaN) is NaN without signal.
        !            52:  *
        !            53:  * Accuracy:
        !            54:  *     acosh(x) returns the exact inverse hyperbolic cosine of x nearly 
        !            55:  *     rounded. In a test run with 512,000 random arguments on a VAX, the
        !            56:  *     maximum observed error was 3.30 ulps (units of the last place) at
        !            57:  *     x=1.0070493753568216 .
        !            58:  *
        !            59:  * Constants:
        !            60:  * The hexadecimal values are the intended ones for the following constants.
        !            61:  * The decimal values may be used, provided that the compiler will convert
        !            62:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            63:  * shown.
        !            64:  */
        !            65: 
        !            66: #include "mathimpl.h"
        !            67: 
        !            68: vc(ln2hi, 6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
        !            69: vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
        !            70: 
        !            71: ic(ln2hi, 6.9314718036912381649E-1,  -1, 1.62E42FEE00000)
        !            72: ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
        !            73: 
        !            74: #ifdef vccast
        !            75: #define    ln2hi    vccast(ln2hi)
        !            76: #define    ln2lo    vccast(ln2lo)
        !            77: #endif
        !            78: 
        !            79: double acosh(x)
        !            80: double x;
        !            81: {      
        !            82:        double t,big=1.E20; /* big+1==big */
        !            83: 
        !            84: #if !defined(vax)&&!defined(tahoe)
        !            85:        if(x!=x) return(x);     /* x is NaN */
        !            86: #endif /* !defined(vax)&&!defined(tahoe) */
        !            87: 
        !            88:     /* return log1p(x) + log(2) if x is large */
        !            89:        if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} 
        !            90: 
        !            91:        t=sqrt(x-1.0);
        !            92:        return(log1p(t*(t+sqrt(x+1.0))));
        !            93: }

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