source: asp3_tinet_ecnl_rx/trunk/musl-1.1.18/src/math/log1pf.c@ 337

/* origin: FreeBSD /usr/src/lib/msun/src/s_log1pf.c */
/*
 * ====================================================
 * 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 "libm.h"

static const float
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
/* |(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 */

float log1pf(float x)
{
        union {float f; uint32_t i;} u = {x};
        float_t hfsq,f,c,s,z,R,w,t1,t2,dk;
        uint32_t ix,iu;
        int k;

        ix = u.i;
        k = 1;
        if (ix < 0x3ed413d0 || ix>>31) {  /* 1+x < sqrt(2)+  */
                if (ix >= 0xbf800000) {  /* x <= -1.0 */
                        if (x == -1)
                                return x/0.0f; /* log1p(-1)=+inf */
                        return (x-x)/0.0f;     /* log1p(x<-1)=NaN */
                }
                if (ix<<1 < 0x33800000<<1) {   /* |x| < 2**-24 */
                        /* underflow if subnormal */
                        if ((ix&0x7f800000) == 0)
                                FORCE_EVAL(x*x);
                        return x;
                }
                if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */
                        k = 0;
                        c = 0;
                        f = x;
                }
        } else if (ix >= 0x7f800000)
                return x;
        if (k) {
                u.f = 1 + x;
                iu = u.i;
                iu += 0x3f800000 - 0x3f3504f3;
                k = (int)(iu>>23) - 0x7f;
                /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */
                if (k < 25) {
                        c = k >= 2 ? 1-(u.f-x) : x-(u.f-1);
                        c /= u.f;
                } else
                        c = 0;
                /* reduce u into [sqrt(2)/2, sqrt(2)] */
                iu = (iu&0x007fffff) + 0x3f3504f3;
                u.i = iu;
                f = u.f - 1;
        }
        s = f/(2.0f + f);
        z = s*s;
        w = z*z;
        t1= w*(Lg2+w*Lg4);
        t2= z*(Lg1+w*Lg3);
        R = t2 + t1;
        hfsq = 0.5f*f*f;
        dk = k;
        return s*(hfsq+R) + (dk*ln2_lo+c) - hfsq + f + dk*ln2_hi;
}