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Annotation of 43BSDTahoe/usr.lib/libm/asinh.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 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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