adtools/clib2

/*
 * $Id: math_expm1.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
one        = 1.0,
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=0.0,t,e,hxs,hfx,r1;
    LONG k,xsb;
    ULONG hx;

    GET_HIGH_WORD(hx,x);
    xsb = hx&0x80000000U;        /* 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) {
            ULONG 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 */
            ULONG 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) {
            ULONG 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 {
            ULONG 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 */