adtools/clib2

/*
 * $Id: math_log1pf.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.
 *
 *
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

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

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

#if defined(FLOATING_POINT_SUPPORT)

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

static const float
ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
two25 =    3.355443200e+07,    /* 0x4c000000 */
Lp1 = 6.6666668653e-01,    /* 3F2AAAAB */
Lp2 = 4.0000000596e-01,    /* 3ECCCCCD */
Lp3 = 2.8571429849e-01, /* 3E924925 */
Lp4 = 2.2222198546e-01, /* 3E638E29 */
Lp5 = 1.8183572590e-01, /* 3E3A3325 */
Lp6 = 1.5313838422e-01, /* 3E1CD04F */
Lp7 = 1.4798198640e-01; /* 3E178897 */

static const float zero = 0.0;

float
log1pf(float x)
{
    float hfsq,f=0.0,c=0.0,s,z,R;
    volatile float u;    /* so GCC doesn't optimize it away */
    LONG k,hx,hu=0.0,ax;

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

    k = 1;
    if (hx < 0x3ed413d7) {            /* x < 0.41422  */
        if(ax>=0x3f800000)            /* x <= -1.0     */
        return logf(1+x);        /* log1p(x<=-1) */
        if(ax<0x31000000) {            /* |x| < 2**-29 */
        if(two25+x>zero            /* raise inexact */
                &&ax<0x24800000)         /* |x| < 2**-54 */
            return x;
        else
            return x - x*x*(float)0.5;
        }
        if(hx>0||hx<=((LONG)0xbe95f61fU)) {
        k=0;f=x;hu=1;}    /* -0.2929<x<0.41422 */
    } 
    if (hx >= 0x7f800000) return x+x;
    if(k!=0) {
        if(hx<0x5a000000) {
        u  = (float)1.0+x; 
        GET_FLOAT_WORD(hu,u);
            k  = (hu>>23)-127;
        /* correction term */
            c  = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
        c /= u;
        } else {
        u  = x;
        GET_FLOAT_WORD(hu,u);
            k  = (hu>>23)-127;
        c  = 0;
        }
        hu &= 0x007fffff;
        if(hu<0x3504f7) {
            SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
        } else {
            k += 1; 
        SET_FLOAT_WORD(u,hu|0x3f000000);    /* normalize u/2 */
            hu = (0x00800000-hu)>>2;
        }
        f = u-(float)1.0;
    }
    hfsq=(float)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*((float)1.0-(float)0.66666666666666666*f);
        if(k==0) return f-R; else
                 return k*ln2_hi-((R-(k*ln2_lo+c))-f);
    }
     s = f/((float)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 */