/* @(#)e_log.c 5.1 93/09/24 */

/*

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

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

 *

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

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

 * software is freely granted, provided that this notice

 * is preserved.

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

 */

#if defined(LIBM_SCCS) && !defined(lint)

static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";

#endif

/* __ieee754_log(x)

 * Return the logrithm of x

 *

 * Method :

 *   1. Argument Reduction: find k and f such that

 *			x = 2^k * (1+f),

 *	   where  sqrt(2)/2 < 1+f < sqrt(2) .

 *

 *   2. Approximation of log(1+f).

 *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)

 *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,

 *	     	 = 2s + s*R

 *      We use a special Reme algorithm on [0,0.1716] to generate

 * 	a polynomial of degree 14 to approximate R The maximum error

 *	of this polynomial approximation is bounded by 2**-58.45. In

 *	other words,

 *		        2      4      6      8      10      12      14

 *	    R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s

 *  	(the values of Lg1 to Lg7 are listed in the program)

 *	and

 *	    |      2          14          |     -58.45

 *	    | Lg1*s +...+Lg7*s    -  R(z) | <= 2

 *	    |                             |

 *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.

 *	In order to guarantee error in log below 1ulp, we compute log

 *	by

 *		log(1+f) = f - s*(f - R)	(if f is not too large)

 *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)

 *

 *	3. Finally,  log(x) = k*ln2 + log(1+f).

 *			    = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))

 *	   Here ln2 is split into two floating point number:

 *			ln2_hi + ln2_lo,

 *	   where n*ln2_hi is always exact for |n| < 2000.

 *

 * Special cases:

 *	log(x) is NaN with signal if x < 0 (including -INF) ;

 *	log(+INF) is +INF; log(0) is -INF with signal;

 *	log(NaN) is that NaN with no signal.

 *

 * Accuracy:

 *	according to an error analysis, the error is always less than

 *	1 ulp (unit in the last place).

 *

 * 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 "math.h"*/

#include "math_private.h"

#ifdef __STDC__

static const double

#else

static double

#endif

#ifdef __STDC__

#else

#endif

{

}