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      1 
      2 /* @(#)e_log10.c 1.3 95/01/18 */
      3 /*
      4  * ====================================================
      5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      6  *
      7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
      8  * Permission to use, copy, modify, and distribute this
      9  * software is freely granted, provided that this notice
     10  * is preserved.
     11  * ====================================================
     12  */
     13 
     14 #ifndef lint
     15 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.11 2005/02/04 18:26:06 das Exp $";
     16 #endif
     17 
     18 /* __ieee754_log10(x)
     19  * Return the base 10 logarithm of x
     20  *
     21  * Method :
     22  *	Let log10_2hi = leading 40 bits of log10(2) and
     23  *	    log10_2lo = log10(2) - log10_2hi,
     24  *	    ivln10   = 1/log(10) rounded.
     25  *	Then
     26  *		n = ilogb(x),
     27  *		if(n<0)  n = n+1;
     28  *		x = scalbn(x,-n);
     29  *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
     30  *
     31  * Note 1:
     32  *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
     33  *	mode must set to Round-to-Nearest.
     34  * Note 2:
     35  *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
     36  *	log10 is monotonic at all binary break points.
     37  *
     38  * Special cases:
     39  *	log10(x) is NaN with signal if x < 0;
     40  *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
     41  *	log10(NaN) is that NaN with no signal;
     42  *	log10(10**N) = N  for N=0,1,...,22.
     43  *
     44  * Constants:
     45  * The hexadecimal values are the intended ones for the following constants.
     46  * The decimal values may be used, provided that the compiler will convert
     47  * from decimal to binary accurately enough to produce the hexadecimal values
     48  * shown.
     49  */
     50 
     51 #include "math.h"
     52 #include "math_private.h"
     53 
     54 static const double
     55 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
     56 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
     57 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
     58 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
     59 
     60 static const double zero   =  0.0;
     61 
     62 double
     63 __ieee754_log10(double x)
     64 {
     65 	double y,z;
     66 	int32_t i,k,hx;
     67 	u_int32_t lx;
     68 
     69 	EXTRACT_WORDS(hx,lx,x);
     70 
     71         k=0;
     72         if (hx < 0x00100000) {                  /* x < 2**-1022  */
     73             if (((hx&0x7fffffff)|lx)==0)
     74                 return -two54/zero;             /* log(+-0)=-inf */
     75             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
     76             k -= 54; x *= two54; /* subnormal number, scale up x */
     77 	    GET_HIGH_WORD(hx,x);
     78         }
     79 	if (hx >= 0x7ff00000) return x+x;
     80 	k += (hx>>20)-1023;
     81 	i  = ((u_int32_t)k&0x80000000)>>31;
     82         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
     83         y  = (double)(k+i);
     84 	SET_HIGH_WORD(x,hx);
     85 	z  = y*log10_2lo + ivln10*__ieee754_log(x);
     86 	return  z+y*log10_2hi;
     87 }
     88