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Annotation of 43BSD/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:  * 
                      4:  * Use and reproduction of this software are granted  in  accordance  with
                      5:  * the terms and conditions specified in  the  Berkeley  Software  License
                      6:  * Agreement (in particular, this entails acknowledgement of the programs'
                      7:  * source, and inclusion of this notice) with the additional understanding
                      8:  * that  all  recipients  should regard themselves as participants  in  an
                      9:  * ongoing  research  project and hence should  feel  obligated  to report
                     10:  * their  experiences (good or bad) with these elementary function  codes,
                     11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
                     12:  */
                     13: 
                     14: #ifndef lint
                     15: static char sccsid[] = "@(#)log10.c    1.2 (Berkeley) 8/21/85";
                     16: #endif not lint
                     17: 
                     18: /* LOG10(X)
                     19:  * RETURN THE BASE 10 LOGARITHM OF x
                     20:  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
                     21:  * CODED IN C BY K.C. NG, 1/20/85; 
                     22:  * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85.
                     23:  * 
                     24:  * Required kernel function:
                     25:  *     log(x)
                     26:  *
                     27:  * Method :
                     28:  *                          log(x)
                     29:  *             log10(x) = ---------  or  [1/log(10)]*log(x)
                     30:  *                         log(10)
                     31:  *
                     32:  *    Note:
                     33:  *       [log(10)]   rounded to 56 bits has error  .0895  ulps,
                     34:  *       [1/log(10)] rounded to 53 bits has error  .198   ulps;
                     35:  *       therefore, for better accuracy, in VAX D format, we divide 
                     36:  *       log(x) by log(10), but in IEEE Double format, we multiply 
                     37:  *       log(x) by [1/log(10)].
                     38:  *
                     39:  * Special cases:
                     40:  *     log10(x) is NaN with signal if x < 0; 
                     41:  *     log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
                     42:  *     log10(NaN) is that NaN with no signal.
                     43:  *
                     44:  * Accuracy:
                     45:  *     log10(X) returns the exact log10(x) nearly rounded. In a test run
                     46:  *     with 1,536,000 random arguments on a VAX, the maximum observed
                     47:  *     error was 1.74 ulps (units in the last place).
                     48:  *
                     49:  * Constants:
                     50:  * The hexadecimal values are the intended ones for the following constants.
                     51:  * The decimal values may be used, provided that the compiler will convert
                     52:  * from decimal to binary accurately enough to produce the hexadecimal values
                     53:  * shown.
                     54:  */
                     55: 
                     56: #ifdef VAX     /* VAX D format (56 bits) */
                     57: /* static double */
                     58: /* ln10hi =  2.3025850929940456790E0     ; Hex   2^  2   *  .935D8DDDAAA8AC */
                     59: static long    ln10hix[] = { 0x5d8d4113, 0xa8acddaa};
                     60: #define   ln10hi    (*(double*)ln10hix)
                     61: #else  /* IEEE double */
                     62: static double
                     63: ivln10 =  4.3429448190325181667E-1    ; /*Hex   2^ -2   *  1.BCB7B1526E50E */
                     64: #endif
                     65: 
                     66: double log10(x)
                     67: double x;
                     68: {
                     69:        double log();
                     70: 
                     71: #ifdef VAX
                     72:        return(log(x)/ln10hi);
                     73: #else  /* IEEE double */
                     74:        return(ivln10*log(x));
                     75: #endif
                     76: }

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