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Annotation of 43BSDTahoe/usr.lib/libm/log10.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[] = "@(#)log10.c    5.3 (Berkeley) 6/30/88";
                     25: #endif /* not lint */
                     26: 
                     27: /* LOG10(X)
                     28:  * RETURN THE BASE 10 LOGARITHM OF x
                     29:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
                     30:  * CODED IN C BY K.C. NG, 1/20/85; 
                     31:  * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85.
                     32:  * 
                     33:  * Required kernel function:
                     34:  *     log(x)
                     35:  *
                     36:  * Method :
                     37:  *                          log(x)
                     38:  *             log10(x) = ---------  or  [1/log(10)]*log(x)
                     39:  *                         log(10)
                     40:  *
                     41:  *    Note:
                     42:  *       [log(10)]   rounded to 56 bits has error  .0895  ulps,
                     43:  *       [1/log(10)] rounded to 53 bits has error  .198   ulps;
                     44:  *       therefore, for better accuracy, in VAX D format, we divide 
                     45:  *       log(x) by log(10), but in IEEE Double format, we multiply 
                     46:  *       log(x) by [1/log(10)].
                     47:  *
                     48:  * Special cases:
                     49:  *     log10(x) is NaN with signal if x < 0; 
                     50:  *     log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
                     51:  *     log10(NaN) is that NaN with no signal.
                     52:  *
                     53:  * Accuracy:
                     54:  *     log10(X) returns the exact log10(x) nearly rounded. In a test run
                     55:  *     with 1,536,000 random arguments on a VAX, the maximum observed
                     56:  *     error was 1.74 ulps (units in the last place).
                     57:  *
                     58:  * Constants:
                     59:  * The hexadecimal values are the intended ones for the following constants.
                     60:  * The decimal values may be used, provided that the compiler will convert
                     61:  * from decimal to binary accurately enough to produce the hexadecimal values
                     62:  * shown.
                     63:  */
                     64: 
                     65: #if defined(vax)||defined(tahoe)       /* VAX D format (56 bits) */
                     66: #ifdef vax
                     67: #define _0x(A,B)       0x/**/A/**/B
                     68: #else  /* vax */
                     69: #define _0x(A,B)       0x/**/B/**/A
                     70: #endif /* vax */
                     71: /* static double */
                     72: /* ln10hi =  2.3025850929940456790E0     ; Hex   2^  2   *  .935D8DDDAAA8AC */
                     73: static long    ln10hix[] = { _0x(5d8d,4113), _0x(a8ac,ddaa)};
                     74: #define   ln10hi    (*(double*)ln10hix)
                     75: #else  /* defined(vax)||defined(tahoe) */
                     76: static double
                     77: ivln10 =  4.3429448190325181667E-1    ; /*Hex   2^ -2   *  1.BCB7B1526E50E */
                     78: #endif /* defined(vax)||defined(tahoe) */
                     79: 
                     80: double log10(x)
                     81: double x;
                     82: {
                     83:        double log();
                     84: 
                     85: #if defined(vax)||defined(tahoe)
                     86:        return(log(x)/ln10hi);
                     87: #else  /* defined(vax)||defined(tahoe) */
                     88:        return(ivln10*log(x));
                     89: #endif /* defined(vax)||defined(tahoe) */
                     90: }

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