e_log10.c

/* @(#)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.
 */

#ifndef __FDLIBM_H__
#include "fdlibm.h"
#endif

#ifndef __have_fpu_log10

double __ieee754_log10(double x)
{
	double y, z;
	int32_t i, k, hx;
	uint32_t lx;

	static const double two54 = 1.80143985094819840000e+16;		/* 0x43500000, 0x00000000 */
	static const double ivln10 = 4.34294481903251816668e-01;	/* 0x3FDBCB7B, 0x1526E50E */
	static const double log10_2hi = 3.01029995663611771306e-01;	/* 0x3FD34413, 0x509F6000 */
	static const double log10_2lo = 3.69423907715893078616e-13;	/* 0x3D59FEF3, 0x11F12B36 */

	static const double zero = 0.0;

	GET_DOUBLE_WORDS(hx, lx, x);

	k = 0;
	if (hx < IC(0x00100000))
	{									/* x < 2**-1022  */
		if (((hx & IC(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 */
		GET_HIGH_WORD(hx, x);
	}
	if (hx >= IC(0x7ff00000))
		return x + x;
	k += (hx >> 20) - 1023;
	i = ((uint32_t) k & UC(0x80000000)) >> 31;
	hx = (hx & IC(0x000fffff)) | ((0x3ff - i) << 20);
	y = (double) (k + i);
	SET_HIGH_WORD(x, hx);
	z = y * log10_2lo + ivln10 * __ieee754_log(x);
	return z + y * log10_2hi;
}
#endif


/* wrapper log10(x) */
double __log10(double x)
{
	if (_LIB_VERSION != _IEEE_ && islessequal(x, 0.0))
	{
		if (x == 0.0)
		{
			feraiseexcept(FE_DIVBYZERO);
			return __kernel_standard(x, x, -HUGE_VAL, KMATHERR_LOG10_ZERO);	/* log10(0) */
		} else
		{
			feraiseexcept(FE_INVALID);
			return __kernel_standard(x, x, __builtin_nan(""), KMATHERR_LOG10_MINUS);	/* log10(x<0) */
		}
	}

	return __ieee754_log10(x);
}

__typeof(__log10) log10 __attribute__((weak, alias("__log10")));
#ifdef __NO_LONG_DOUBLE_MATH
long double __log10l(long double x) __attribute__((alias("__log10")));
__typeof(__log10l) log10l __attribute__((weak, alias("__log10")));
#endif