text: /* @(#)e_log10.c 5.1 93/09/24 */
  /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  /* __ieee754_log10(x)
   * Return the base 10 logarithm of x
   *
   * Method :
   *	Let log10_2hi = leading 40 bits of log10(2) and
   *	    log10_2lo = log10(2) - log10_2hi,
   *	    ivln10   = 1/log(10) rounded.
   *	Then
   *		n = ilogb(x),
   *		if(n<0)  n = n+1;
   *		x = scalbn(x,-n);
   *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
   *
   * Note 1:
   *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
   *	mode must set to Round-to-Nearest.
   * Note 2:
   *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
   *	log10 is monotonic at all binary break points.
   *
   * Special cases:
   *	log10(x) is NaN with signal if x < 0;
   *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
   *	log10(NaN) is that NaN with no signal;
   *	log10(10**N) = N  for N=0,1,...,22.
   *
   * Constants:
   * The hexadecimal values are the intended ones for the following constants.
   * The decimal values may be used, provided that the compiler will convert
   * from decimal to binary accurately enough to produce the hexadecimal values
   * shown.
   */
  
  #include <math.h>
  #include <math_private.h>
  #include <fix-int-fp-convert-zero.h>
  #include <libm-alias-finite.h>
  
  static const double two54 = 1.80143985094819840000e+16;         /* 0x43500000, 0x00000000 */
  static const double ivln10 = 4.34294481903251816668e-01;        /* 0x3FDBCB7B, 0x1526E50E */
  static const double log10_2hi = 3.01029995663611771306e-01;     /* 0x3FD34413, 0x509F6000 */
  static const double log10_2lo = 3.69423907715893078616e-13;     /* 0x3D59FEF3, 0x11F12B36 */
  
  double
  __ieee754_log10 (double x)
  {
    double y, z;
    int32_t i, k, hx;
    uint32_t lx;
  
    EXTRACT_WORDS (hx, lx, x);
  
    k = 0;
    if (hx < 0x00100000)
      {                           /* x < 2**-1022  */
        if (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0))
  	return -two54 / fabs (x);	/* log(+-0)=-inf  */
        if (__glibc_unlikely (hx < 0))
  	return (x - x) / (x - x);       /* log(-#) = NaN */
        k -= 54;
        x *= two54;               /* subnormal number, scale up x */
        GET_HIGH_WORD (hx, x);
      }
    if (__glibc_unlikely (hx >= 0x7ff00000))
      return x + x;
    k += (hx >> 20) - 1023;
    i = ((uint32_t) k & 0x80000000) >> 31;
    hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
    y = (double) (k + i);
    if (FIX_INT_FP_CONVERT_ZERO && y == 0.0)
      y = 0.0;
    SET_HIGH_WORD (x, hx);
    z = y * log10_2lo + ivln10 * __ieee754_log (x);
    return z + y * log10_2hi;
  }
  libm_alias_finite (__ieee754_log10, __log10)
  