s_log1pf.c

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/* s_log1pf.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 "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 */
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,c,s,z,R,u;
    int32_t k,hx,hu,ax;

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

    k = 1;
    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 (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);
}