vx32

Local 9vx git repository for patches.
git clone git://r-36.net/vx32
Log | Files | Refs

e_log10.c (2697B)

      1 /* @(#)e_log10.c 5.1 93/09/24 */
      2 /*
      3  * ====================================================
      4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      5  *
      6  * Developed at SunPro, a Sun Microsystems, Inc. business.
      7  * Permission to use, copy, modify, and distribute this
      8  * software is freely granted, provided that this notice
      9  * is preserved.
     10  * ====================================================
     11  */
     12 
     13 #ifndef lint
     14 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_log10.c,v 1.10 2003/07/23 04:53:46 peter Exp $";
     15 #endif
     16 
     17 /* __ieee754_log10(x)
     18  * Return the base 10 logarithm of x
     19  *
     20  * Method :
     21  *	Let log10_2hi = leading 40 bits of log10(2) and
     22  *	    log10_2lo = log10(2) - log10_2hi,
     23  *	    ivln10   = 1/log(10) rounded.
     24  *	Then
     25  *		n = ilogb(x),
     26  *		if(n<0)  n = n+1;
     27  *		x = scalbn(x,-n);
     28  *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
     29  *
     30  * Note 1:
     31  *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
     32  *	mode must set to Round-to-Nearest.
     33  * Note 2:
     34  *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
     35  *	log10 is monotonic at all binary break points.
     36  *
     37  * Special cases:
     38  *	log10(x) is NaN with signal if x < 0;
     39  *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
     40  *	log10(NaN) is that NaN with no signal;
     41  *	log10(10**N) = N  for N=0,1,...,22.
     42  *
     43  * Constants:
     44  * The hexadecimal values are the intended ones for the following constants.
     45  * The decimal values may be used, provided that the compiler will convert
     46  * from decimal to binary accurately enough to produce the hexadecimal values
     47  * shown.
     48  */
     49 
     50 #include "math.h"
     51 #include "math_private.h"
     52 
     53 static const double
     54 two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
     55 ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */
     56 log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
     57 log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */
     58 
     59 static const double zero   =  0.0;
     60 
     61 double
     62 __ieee754_log10(double x)
     63 {
     64 	double y,z;
     65 	int32_t i,k,hx;
     66 	u_int32_t lx;
     67 
     68 	EXTRACT_WORDS(hx,lx,x);
     69 
     70         k=0;
     71         if (hx < 0x00100000) {                  /* x < 2**-1022  */
     72             if (((hx&0x7fffffff)|lx)==0)
     73                 return -two54/zero;             /* log(+-0)=-inf */
     74             if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */
     75             k -= 54; x *= two54; /* subnormal number, scale up x */
     76 	    GET_HIGH_WORD(hx,x);
     77         }
     78 	if (hx >= 0x7ff00000) return x+x;
     79 	k += (hx>>20)-1023;
     80 	i  = ((u_int32_t)k&0x80000000)>>31;
     81         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
     82         y  = (double)(k+i);
     83 	SET_HIGH_WORD(x,hx);
     84 	z  = y*log10_2lo + ivln10*__ieee754_log(x);
     85 	return  z+y*log10_2hi;
     86 }