text: /* origin: FreeBSD /usr/src/lib/msun/src/e_log10.c */
  /*
   * ====================================================
   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   *
   * Developed at SunSoft, a Sun Microsystems, Inc. business.
   * Permission to use, copy, modify, and distribute this
   * software is freely granted, provided that this notice
   * is preserved.
   * ====================================================
   */
  /*
   * Return the base 10 logarithm of x.  See log.c for most comments.
   *
   * Reduce x to 2^k (1+f) and calculate r = log(1+f) - f + f*f/2
   * as in log.c, then combine and scale in extra precision:
   *    log10(x) = (f - f*f/2 + r)/log(10) + k*log10(2)
   */
  
  #include <math.h>
  #include <stdint.h>
  
  static const double
  ivln10hi  = 4.34294481878168880939e-01, /* 0x3fdbcb7b, 0x15200000 */
  ivln10lo  = 2.50829467116452752298e-11, /* 0x3dbb9438, 0xca9aadd5 */
  log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */
  log10_2lo = 3.69423907715893078616e-13, /* 0x3D59FEF3, 0x11F12B36 */
  Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
  Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
  Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
  Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
  Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
  Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
  Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */
  
  double log10(double x)
  {
  	union {double f; uint64_t i;} u = {x};
  	double_t hfsq,f,s,z,R,w,t1,t2,dk,y,hi,lo,val_hi,val_lo;
  	uint32_t hx;
  	int k;
  
  	hx = u.i>>32;
  	k = 0;
  	if (hx < 0x00100000 || hx>>31) {
  		if (u.i<<1 == 0)
  			return -1/(x*x);  /* log(+-0)=-inf */
  		if (hx>>31)
  			return (x-x)/0.0; /* log(-#) = NaN */
  		/* subnormal number, scale x up */
  		k -= 54;
  		x *= 0x1p54;
  		u.f = x;
  		hx = u.i>>32;
  	} else if (hx >= 0x7ff00000) {
  		return x;
  	} else if (hx == 0x3ff00000 && u.i<<32 == 0)
  		return 0;
  
  	/* reduce x into [sqrt(2)/2, sqrt(2)] */
  	hx += 0x3ff00000 - 0x3fe6a09e;
  	k += (int)(hx>>20) - 0x3ff;
  	hx = (hx&0x000fffff) + 0x3fe6a09e;
  	u.i = (uint64_t)hx<<32 | (u.i&0xffffffff);
  	x = u.f;
  
  	f = x - 1.0;
  	hfsq = 0.5*f*f;
  	s = f/(2.0+f);
  	z = s*s;
  	w = z*z;
  	t1 = w*(Lg2+w*(Lg4+w*Lg6));
  	t2 = z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
  	R = t2 + t1;
  
  	/* See log2.c for details. */
  	/* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */
  	hi = f - hfsq;
  	u.f = hi;
  	u.i &= (uint64_t)-1<<32;
  	hi = u.f;
  	lo = f - hi - hfsq + s*(hfsq+R);
  
  	/* val_hi+val_lo ~ log10(1+f) + k*log10(2) */
  	val_hi = hi*ivln10hi;
  	dk = k;
  	y = dk*log10_2hi;
  	val_lo = dk*log10_2lo + (lo+hi)*ivln10lo + lo*ivln10hi;
  
  	/*
  	 * Extra precision in for adding y is not strictly needed
  	 * since there is no very large cancellation near x = sqrt(2) or
  	 * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs
  	 * with some parallelism and it reduces the error for many args.
  	 */
  	w = y + val_hi;
  	val_lo += (y - w) + val_hi;
  	val_hi = w;
  
  	return val_lo + val_hi;
  }
  