amiga-clib2/library/math_kernel_expm1.c

/*
 * $Id: math_kernel_expm1.c,v 1.4 2006-09-22 07:54:24 obarthel Exp $
 *
 * :ts=4
 *
 * Portable ISO 'C' (1994) runtime library for the Amiga computer
 * Copyright (c) 2002-2006 by Olaf Barthel <olsen (at) sourcery.han.de>
 * 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) && defined(PPC_FLOATING_POINT_SUPPORT)

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

static const double
one         = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
huge		= 1.0e+300,
tiny		= 1.0e-300,
o_threshold	= 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
ln2_hi		= 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
ln2_lo		= 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
invln2		= 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
	/* scaled coefficients related to __expm1 */
Q1  =  -3.33333333333331316428e-02, /* BFA11111 111110F4 */
Q2  =   1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
Q3  =  -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
Q4  =   4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
Q5  =  -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */

double __expm1(double x)
{
	double y,hi,lo,c=0,t,e,hxs,hfx,r1;
	int k,xsb;
	unsigned int hx;

	GET_HIGH_WORD(hx,x);
	xsb = hx&0x80000000;		/* sign bit of x */
	if(xsb==0) y=x; else y= -x;	/* y = |x| */
	hx &= 0x7fffffff;		/* high word of |x| */

    /* filter out huge and non-finite argument */
	if(hx >= 0x4043687A) {			/* if |x|>=56*ln2 */
	    if(hx >= 0x40862E42) {		/* if |x|>=709.78... */
                if(hx>=0x7ff00000) {
		    unsigned int low;
		    GET_LOW_WORD(low,x);
		    if(((hx&0xfffff)|low)!=0) 
		         return x+x; 	 /* NaN */
		    else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
	        }
	        if(x > o_threshold) return huge*huge; /* overflow */
	    }
	    if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
		if(x+tiny<0.0)		/* raise inexact */
		return tiny-one;	/* return -1 */
	    }
	}

    /* argument reduction */
	if(hx > 0x3fd62e42) {		/* if  |x| > 0.5 ln2 */ 
	    if(hx < 0x3FF0A2B2) {	/* and |x| < 1.5 ln2 */
		if(xsb==0)
		    {hi = x - ln2_hi; lo =  ln2_lo;  k =  1;}
		else
		    {hi = x + ln2_hi; lo = -ln2_lo;  k = -1;}
	    } else {
		k  = invln2*x+((xsb==0)?0.5:-0.5);
		t  = k;
		hi = x - t*ln2_hi;	/* t*ln2_hi is exact here */
		lo = t*ln2_lo;
	    }
	    x  = hi - lo;
	    c  = (hi-x)-lo;
	} 
	else if(hx < 0x3c900000) {  	/* when |x|<2**-54, return x */
	    t = huge+x;	/* return x with inexact flags when x!=0 */
	    return x - (t-(huge+x));	
	}
	else k = 0;

    /* x is now in primary range */
	hfx = 0.5*x;
	hxs = x*hfx;
	r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
	t  = 3.0-r1*hfx;
	e  = hxs*((r1-t)/(6.0 - x*t));
	if(k==0) return x - (x*e-hxs);		/* c is 0 */
	else {
	    e  = (x*(e-c)-c);
	    e -= hxs;
	    if(k== -1) return 0.5*(x-e)-0.5;
          if(k==1) {
	       	if(x < -0.25) return -2.0*(e-(x+0.5));
	       	else 	      return  one+2.0*(x-e);
          }
	    if (k <= -2 || k>56) {   /* suffice to return exp(x)-1 */
	        unsigned int high;
	        y = one-(e-x);
		GET_HIGH_WORD(high,y);
		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */
	        return y-one;
	    }
	    t = one;
	    if(k<20) {
	        unsigned int high;
	        SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k));  /* t=1-2^-k */
	       	y = t-(e-x);
		GET_HIGH_WORD(high,y);
		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */
	   } else {
	        unsigned int high;
		SET_HIGH_WORD(t,((0x3ff-k)<<20));	/* 2^-k */
	       	y = x-(e+t);
	       	y += one;
		GET_HIGH_WORD(high,y);
		SET_HIGH_WORD(y,high+(k<<20));	/* add k to y's exponent */
	    }
	}
	return y;
}

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

#endif /* FLOATING_POINT_SUPPORT && PPC_FLOATING_POINT_SUPPORT */