/* derived from /netlib/fdlibm */ /* @(#)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" static const doubletwo54      =  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; 	double __ieee754_log10(double x){	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;}