/* @(#)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 <stdint.h>

static const double two54 = 1.80143985094819840000e+16;		/* 0x4350000000000000 */

static const double ivln10 = 4.34294481903251816668e-01;	/* 0x3FDBCB7B1526E50E */

static const double log10_2hi = 3.01029995663611771306e-01;	/* 0x3FD34413509F6000 */

static const double log10_2lo = 3.69423907715893078616e-13;	/* 0x3D59FEF311F12B36 */

double

__ieee754_log10 (double x)

{

  double y, z;

  int64_t i, hx;

  int32_t k;

  EXTRACT_WORDS64 (hx, x);

  k = 0;

  if (hx < INT64_C(0x0010000000000000))

    {				/* x < 2**-1022  */

      if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 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 */

      EXTRACT_WORDS64 (hx, x);

    }

  /* scale up resulted in a NaN number  */

  if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000)))

    return x + x;

  k += (hx >> 52) - 1023;

  i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63;

  hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52);

  y = (double) (k + i);

  INSERT_WORDS64 (x, hx);

  z = y * log10_2lo + ivln10 * __ieee754_log (x);

  return z + y * log10_2hi;

}

strong_alias (__ieee754_log10, __log10_finite)