/* @(#)e_log10.c 1.3 95/01/18 */

/*

 * ====================================================

 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.

 *

 * Developed at SunSoft, a Sun Microsystems, Inc. business.

 * Permission to use, copy, modify, and distribute this

 * software is freely granted, provided that this notice 

 * is preserved.

 * ====================================================

 */

/* __ieee754_log10(x)

 * Return the base 10 logarithm of x

 * 

 * Method :

 *	Let log10_2hi = leading 40 bits of log10(2) and

 *	    log10_2lo = log10(2) - log10_2hi,

 *	    ivln10   = 1/log(10) rounded.

 *	Then

 *		n = ilogb(x), 

 *		if(n<0)  n = n+1;

 *		x = scalbn(x,-n);

 *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))

 *

 * Note 1:

 *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding 

 *	mode must set to Round-to-Nearest.

 * Note 2:

 *	[1/log(10)] rounded to 53 bits has error  .198   ulps;

 *	log10 is monotonic at all binary break points.

 *

 * Special cases:

 *	log10(x) is NaN with signal if x < 0; 

 *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;

 *	log10(NaN) is that NaN with no signal;

 *	log10(10**N) = N  for N=0,1,...,22.

 *

 * Constants:

 * The hexadecimal values are the intended ones for the following constants.

 * The decimal values may be used, provided that the compiler will convert

 * from decimal to binary accurately enough to produce the hexadecimal values

 * shown.

 */

#include "fdlibm.h"

#ifdef __STDC__

static const double

#else

static double

#endif

two54      =  1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */

ivln10     =  4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */

log10_2hi  =  3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */

log10_2lo  =  3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */

static double zero   =  0.0;

#ifdef __STDC__

	double __ieee754_log10(double x)

#else

	double __ieee754_log10(x)

	double x;

#endif

{

	double y,z;

	int i,k,hx;

	unsigned lx;

	hx = __HI(x);	/* high word of x */

	lx = __LO(x);	/* low word of x */

        k=0;

        if (hx < 0x00100000) {                  /* x < 2**-1022  */

            if (((hx&0x7fffffff)|lx)==0)

                return -two54/zero;             /* log(+-0)=-inf */

            if (hx<0) return (x-x)/zero;        /* log(-#) = NaN */

            k -= 54; x *= two54; /* subnormal number, scale up x */

            hx = __HI(x);                /* high word of x */

        }

	if (hx >= 0x7ff00000) return x+x;

	k += (hx>>20)-1023;

	i  = ((unsigned)k&0x80000000)>>31;

        hx = (hx&0x000fffff)|((0x3ff-i)<<20);

        y  = (double)(k+i);

        __HI(x) = hx;

	z  = y*log10_2lo + ivln10*__ieee754_log(x);

	return  z+y*log10_2hi;

}