/* e_logf.c -- float version of e_log.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 "math.h"
#include "math_private.h"

static const float
ln2_hi =   6.9313812256e-01,    /* 0x3f317180 */
ln2_lo =   9.0580006145e-06,    /* 0x3717f7d1 */
two25 =    3.355443200e+07,     /* 0x4c000000 */
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
Lg1 =      0xaaaaaa.0p-24,      /* 0.66666662693 */
Lg2 =      0xccce13.0p-25,      /* 0.40000972152 */
Lg3 =      0x91e9ee.0p-25,      /* 0.28498786688 */
Lg4 =      0xf89e26.0p-26;      /* 0.24279078841 */

static const float zero   =  0.0;
static volatile float vzero = 0.0;

float
logf(float x)
{
        float hfsq,f,s,z,R,w,t1,t2,dk;
        int32_t k,ix,i,j;

        GET_FLOAT_WORD(ix,x);

        k=0;
        if (ix < 0x00800000) {                  /* x < 2**-126  */
            if ((ix&0x7fffffff)==0)
                return -two25/vzero;            /* log(+-0)=-inf */
            if (ix<0) return (x-x)/zero;        /* log(-#) = NaN */
            k -= 25; x *= two25; /* subnormal number, scale up x */
            GET_FLOAT_WORD(ix,x);
        }
        if (ix >= 0x7f800000) return x+x;
        k += (ix>>23)-127;
        ix &= 0x007fffff;
        i = (ix+(0x95f64<<3))&0x800000;
        SET_FLOAT_WORD(x,ix|(i^0x3f800000));    /* normalize x or x/2 */
        k += (i>>23);
        f = x-(float)1.0;
        if((0x007fffff&(0x8000+ix))<0xc000) {   /* -2**-9 <= f < 2**-9 */
            if(f==zero) {
                if(k==0) {
                    return zero;
                } else {
                    dk=(float)k;
                    return dk*ln2_hi+dk*ln2_lo;
                }
            }
            R = f*f*((float)0.5-(float)0.33333333333333333*f);
            if(k==0) return f-R; else {dk=(float)k;
                     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
        }
        s = f/((float)2.0+f);
        dk = (float)k;
        z = s*s;
        i = ix-(0x6147a<<3);
        w = z*z;
        j = (0x6b851<<3)-ix;
        t1= w*(Lg2+w*Lg4);
        t2= z*(Lg1+w*Lg3);
        i |= j;
        R = t2+t1;
        if(i>0) {
            hfsq=(float)0.5*f*f;
            if(k==0) return f-(hfsq-s*(hfsq+R)); else
                     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
        } else {
            if(k==0) return f-s*(f-R); else
                     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
        }
}