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Annotation of 43BSDReno/lib/libm/common_source/acosh.c, revision 1.1.1.1

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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