/*
 * $Id: math_log1p.c,v 1.3 2006-01-08 12:04:23 obarthel Exp $
 *
 * :ts=4
 *
 * Portable ISO 'C' (1994) runtime library for the Amiga computer
 * Copyright (c) 2002-2015 by Olaf Barthel <obarthel (at) gmx.net>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 *   - Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *
 *   - Neither the name of Olaf Barthel nor the names of contributors
 *     may be used to endorse or promote products derived from this
 *     software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
 * POSSIBILITY OF SUCH DAMAGE.
 *
 *
 * PowerPC math library based in part on work by Sun Microsystems
 * 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.
 */

#ifndef _MATH_HEADERS_H
#include "math_headers.h"
#endif /* _MATH_HEADERS_H */

/****************************************************************************/

#if defined(FLOATING_POINT_SUPPORT)

/****************************************************************************/

static const double
ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
two54   =  1.80143985094819840000e+16,  /* 43500000 00000000 */
Lp1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
Lp2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
Lp3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
Lp4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
Lp5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
Lp6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
Lp7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

static const double zero = 0.0;

double
log1p(double x)
{
	double hfsq,f=0.0,c=0.0,s,z,R;
	volatile double u;	/* so GCC never optimizes it away */
	LONG k,hx,hu=0.0,ax;

	GET_HIGH_WORD(hx,x);
	ax = hx&0x7fffffff;

	k = 1;
	if (hx < 0x3FDA827A) {			/* x < 0.41422  */
	    if(ax>=0x3ff00000)			/* x <= -1.0 */
		return log(1+x);		/* log1p(-1) */
	    if(ax<0x3e200000) {			/* |x| < 2**-29 */
		if(two54+x>zero			/* raise inexact */
	            &&ax<0x3c900000) 		/* |x| < 2**-54 */
		    return x;
		else
		    return x - x*x*0.5;
	    }
	    if(hx>0||hx<=((LONG)0xbfd2bec3U)) {
		k=0;f=x;hu=1;}	/* -0.2929<x<0.41422 */
	} 
	if (hx >= 0x7ff00000) return x+x;
	if(k!=0) {
	    if(hx<0x43400000) {
		u  = 1.0+x; 
		GET_HIGH_WORD(hu,u);
	        k  = (hu>>20)-1023;
	        c  = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
		c /= u;
	    } else {
		u  = x;
		GET_HIGH_WORD(hu,u);
	        k  = (hu>>20)-1023;
		c  = 0;
	    }
	    hu &= 0x000fffff;
	    if(hu<0x6a09e) {
	        SET_HIGH_WORD(u,hu|0x3ff00000);	/* normalize u */
	    } else {
	        k += 1; 
		SET_HIGH_WORD(u,hu|0x3fe00000);	/* normalize u/2 */
	        hu = (0x00100000-hu)>>2;
	    }
	    f = u-1.0;
	}
	hfsq=0.5*f*f;
	if(hu==0) {	/* |f| < 2**-20 */
	    if(f==zero) { if(k==0) return zero;  
			  else {c += k*ln2_lo; return k*ln2_hi+c;}
			}
	    R = hfsq*(1.0-0.66666666666666666*f);
	    if(k==0) return f-R; else
	    	     return k*ln2_hi-((R-(k*ln2_lo+c))-f);
	}
 	s = f/(2.0+f); 
	z = s*s;
	R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
	if(k==0) return f-(hfsq-s*(hfsq+R)); else
		 return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}

/****************************************************************************/

#endif /* FLOATING_POINT_SUPPORT */