source: trunk/libs/newlib/src/newlib/libm/common/sf_log1p.c @ 567

/* sf_log1p.c -- float version of s_log1p.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * 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.
 * ====================================================
 */

#include "fdlibm.h"

#ifdef __STDC__
static const float
#else
static float
#endif
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 */

#ifdef __STDC__
static const float zero = 0.0;
#else
static float zero = 0.0;
#endif

#ifdef __STDC__
        float log1pf(float x)
#else
        float log1pf(x)
        float x;
#endif
{
        float hfsq,f,c,s,z,R,u;
        __int32_t k,hx,hu,ax;

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

        k = 1;
        if (!FLT_UWORD_IS_FINITE(hx)) return x+x;
        if (hx < 0x3ed413d7) {                  /* x < 0.41422  */
            if(ax>=0x3f800000) {                /* x <= -1.0 */
                if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */
                else return (x-x)/(x-x);        /* log1p(x<-1)=NaN */
            }
            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<=((__int32_t)0xbe95f61f)) {
                k=0;f=x;hu=1;}  /* -0.2929<x<0.41422 */
        }
        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);
}

#ifdef _DOUBLE_IS_32BITS

#ifdef __STDC__
        double log1p(double x)
#else
        double log1p(x)
        double x;
#endif
{
        return (double) log1pf((float) x);
}

#endif /* defined(_DOUBLE_IS_32BITS) */