4.3BSD - /usr/src/usr.lib/libm/log10.c

   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: }

Defined functions

Defined variables

Defined macros