4.3BSD - /usr/src/usr.lib/libm/log.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[] = "@(#)log.c	4.5 (Berkeley) 8/21/85";
  16: #endif not lint
  17: 
  18: /* LOG(X)
  19:  * RETURN THE LOGARITHM OF x
  20:  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
  21:  * CODED IN C BY K.C. NG, 1/19/85;
  22:  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 3/24/85, 4/16/85.
  23:  *
  24:  * Required system supported functions:
  25:  *	scalb(x,n)
  26:  *	copysign(x,y)
  27:  *	logb(x)
  28:  *	finite(x)
  29:  *
  30:  * Required kernel function:
  31:  *	log__L(z)
  32:  *
  33:  * Method :
  34:  *	1. Argument Reduction: find k and f such that
  35:  *			x = 2^k * (1+f),
  36:  *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
  37:  *
  38:  *	2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
  39:  *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
  40:  *	   log(1+f) is computed by
  41:  *
  42:  *	     		log(1+f) = 2s + s*log__L(s*s)
  43:  *	   where
  44:  *		log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
  45:  *
  46:  *	   See log__L() for the values of the coefficients.
  47:  *
  48:  *	3. Finally,  log(x) = k*ln2 + log(1+f).  (Here n*ln2 will be stored
  49:  *	   in two floating point number: n*ln2hi + n*ln2lo, n*ln2hi is exact
  50:  *	   since the last 20 bits of ln2hi is 0.)
  51:  *
  52:  * Special cases:
  53:  *	log(x) is NaN with signal if x < 0 (including -INF) ;
  54:  *	log(+INF) is +INF; log(0) is -INF with signal;
  55:  *	log(NaN) is that NaN with no signal.
  56:  *
  57:  * Accuracy:
  58:  *	log(x) returns the exact log(x) nearly rounded. In a test run with
  59:  *	1,536,000 random arguments on a VAX, the maximum observed error was
  60:  *	.826 ulps (units in the last place).
  61:  *
  62:  * Constants:
  63:  * The hexadecimal values are the intended ones for the following constants.
  64:  * The decimal values may be used, provided that the compiler will convert
  65:  * from decimal to binary accurately enough to produce the hexadecimal values
  66:  * shown.
  67:  */
  68: 
  69: #ifdef VAX  /* VAX D format */
  70: #include <errno.h>
  71: 
  72: /* double static */
  73: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
  74: /* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
  75: /* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
  76: static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
  77: static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
  78: static long     sqrt2x[] = { 0x04f340b5, 0xde6533f9};
  79: #define    ln2hi    (*(double*)ln2hix)
  80: #define    ln2lo    (*(double*)ln2lox)
  81: #define    sqrt2    (*(double*)sqrt2x)
  82: #else   /* IEEE double */
  83: double static
  84: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
  85: ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
  86: sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
  87: #endif
  88: 
  89: double log(x)
  90: double x;
  91: {
  92:     static double zero=0.0, negone= -1.0, half=1.0/2.0;
  93:     double logb(),scalb(),copysign(),log__L(),s,z,t;
  94:     int k,n,finite();
  95: 
  96: #ifndef VAX
  97:     if(x!=x) return(x); /* x is NaN */
  98: #endif
  99:     if(finite(x)) {
 100:        if( x > zero ) {
 101: 
 102:        /* argument reduction */
 103:           k=logb(x);   x=scalb(x,-k);
 104:           if(k == -1022) /* subnormal no. */
 105:            {n=logb(x); x=scalb(x,-n); k+=n;}
 106:           if(x >= sqrt2 ) {k += 1; x *= half;}
 107:           x += negone ;
 108: 
 109:        /* compute log(1+x)  */
 110:               s=x/(2+x); t=x*x*half;
 111:           z=k*ln2lo+s*(t+log__L(s*s));
 112:           x += (z - t) ;
 113: 
 114:           return(k*ln2hi+x);
 115:        }
 116:     /* end of if (x > zero) */
 117: 
 118:        else {
 119: #ifdef VAX
 120:         extern double infnan();
 121:         if ( x == zero )
 122:             return (infnan(-ERANGE));   /* -INF */
 123:         else
 124:             return (infnan(EDOM));  /* NaN */
 125: #else   /* IEEE double */
 126:         /* zero argument, return -INF with signal */
 127:         if ( x == zero )
 128:             return( negone/zero );
 129: 
 130:         /* negative argument, return NaN with signal */
 131:         else
 132:             return ( zero / zero );
 133: #endif
 134:         }
 135:     }
 136:     /* end of if (finite(x)) */
 137:     /* NOT REACHED ifdef VAX */
 138: 
 139:     /* log(-INF) is NaN with signal */
 140:     else if (x<0)
 141:         return(zero/zero);
 142: 
 143:     /* log(+INF) is +INF */
 144:     else return(x);
 145: 
 146: }

Defined functions

Defined variables

Defined macros