text: /* 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;
  }
  