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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 /* __ieee754_log10(x)
     15  * Return the base 10 logarithm of x
     16  *
     17  * Method :
     18  *	Let log10_2hi = leading 40 bits of ieee_log10(2) and
     19  *	    log10_2lo = ieee_log10(2) - log10_2hi,
     20  *	    ivln10   = 1/ieee_log(10) rounded.
     21  *	Then
     22  *		n = ieee_ilogb(x),
     23  *		if(n<0)  n = n+1;
     24  *		x = ieee_scalbn(x,-n);
     25  *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*ieee_log(x))
     26  *
     27  * Note 1:
     28  *	To guarantee ieee_log10(10**n)=n, where 10**n is normal, the rounding
     29  *	mode must set to Round-to-Nearest.
     30  * Note 2:
     31  *	[1/ieee_log(10)] rounded to 53 bits has error  .198   ulps;
     32  *	log10 is monotonic at all binary break points.
     33  *
     34  * Special cases:
     35  *	log10(x) is NaN with signal if x < 0;
     36  *	log10(+INF) is +INF with no signal; ieee_log10(0) is -INF with signal;
     37  *	log10(NaN) is that NaN with no signal;
     38  *	log10(10**N) = N  for N=0,1,...,22.
     39  *
     40  * Constants:
     41  * The hexadecimal values are the intended ones for the following constants.
     42  * The decimal values may be used, provided that the compiler will convert
     43  * from decimal to binary accurately enough to produce the hexadecimal values
     44  * shown.
     45  */
     46 
     47 #include "fdlibm.h"
     48 
     49 #ifdef __STDC__
     50 static const double
     51 #else
     52 static double
     53 #endif
     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 double zero   =  0.0;
     60 
     61 #ifdef __STDC__
     62 	double __ieee754_log10(double x)
     63 #else
     64 	double __ieee754_log10(x)
     65 	double x;
     66 #endif
     67 {
     68 	double y,z;
     69 	int i,k,hx;
     70 	unsigned lx;
     71 
     72 	hx = __HI(x);	/* high word of x */
     73 	lx = __LO(x);	/* low word of x */
     74 
     75         k=0;
     76         if (hx < 0x00100000) {                  /* x < 2**-1022  */
     77             if (((hx&0x7fffffff)|lx)==0)
     78                 return -two54/zero;             /* ieee_log(+-0)=-inf */
     79             if (hx<0) return (x-x)/zero;        /* ieee_log(-#) = NaN */
     80             k -= 54; x *= two54; /* subnormal number, scale up x */
     81             hx = __HI(x);                /* high word of x */
     82         }
     83 	if (hx >= 0x7ff00000) return x+x;
     84 	k += (hx>>20)-1023;
     85 	i  = ((unsigned)k&0x80000000)>>31;
     86         hx = (hx&0x000fffff)|((0x3ff-i)<<20);
     87         y  = (double)(k+i);
     88         __HI(x) = hx;
     89 	z  = y*log10_2lo + ivln10*__ieee754_log(x);
     90 	return  z+y*log10_2hi;
     91 }
     92