1  /* @(#)e_log10.c 5.1 93/09/24 */
       2  /*
       3   * ====================================================
       4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       5   *
       6   * Developed at SunPro, a Sun Microsystems, Inc. business.
       7   * Permission to use, copy, modify, and distribute this
       8   * software is freely granted, provided that this notice
       9   * is preserved.
      10   * ====================================================
      11   */
      12  
      13  /* __ieee754_log10(x)
      14   * Return the base 10 logarithm of x
      15   *
      16   * Method :
      17   *	Let log10_2hi = leading 40 bits of log10(2) and
      18   *	    log10_2lo = log10(2) - log10_2hi,
      19   *	    ivln10   = 1/log(10) rounded.
      20   *	Then
      21   *		n = ilogb(x),
      22   *		if(n<0)  n = n+1;
      23   *		x = scalbn(x,-n);
      24   *		log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x))
      25   *
      26   * Note 1:
      27   *	To guarantee log10(10**n)=n, where 10**n is normal, the rounding
      28   *	mode must set to Round-to-Nearest.
      29   * Note 2:
      30   *	[1/log(10)] rounded to 53 bits has error  .198   ulps;
      31   *	log10 is monotonic at all binary break points.
      32   *
      33   * Special cases:
      34   *	log10(x) is NaN with signal if x < 0;
      35   *	log10(+INF) is +INF with no signal; log10(0) is -INF with signal;
      36   *	log10(NaN) is that NaN with no signal;
      37   *	log10(10**N) = N  for N=0,1,...,22.
      38   *
      39   * Constants:
      40   * The hexadecimal values are the intended ones for the following constants.
      41   * The decimal values may be used, provided that the compiler will convert
      42   * from decimal to binary accurately enough to produce the hexadecimal values
      43   * shown.
      44   */
      45  
      46  #include <math.h>
      47  #include <fix-int-fp-convert-zero.h>
      48  #include <math_private.h>
      49  #include <stdint.h>
      50  #include <libm-alias-finite.h>
      51  
      52  static const double two54 = 1.80143985094819840000e+16;		/* 0x4350000000000000 */
      53  static const double ivln10 = 4.34294481903251816668e-01;	/* 0x3FDBCB7B1526E50E */
      54  static const double log10_2hi = 3.01029995663611771306e-01;	/* 0x3FD34413509F6000 */
      55  static const double log10_2lo = 3.69423907715893078616e-13;	/* 0x3D59FEF311F12B36 */
      56  
      57  double
      58  __ieee754_log10 (double x)
      59  {
      60    double y, z;
      61    int64_t i, hx;
      62    int32_t k;
      63  
      64    EXTRACT_WORDS64 (hx, x);
      65  
      66    k = 0;
      67    if (hx < INT64_C(0x0010000000000000))
      68      {				/* x < 2**-1022  */
      69        if (__glibc_unlikely ((hx & UINT64_C(0x7fffffffffffffff)) == 0))
      70  	return -two54 / fabs (x);	/* log(+-0)=-inf */
      71        if (__glibc_unlikely (hx < 0))
      72  	return (x - x) / (x - x);	/* log(-#) = NaN */
      73        k -= 54;
      74        x *= two54;		/* subnormal number, scale up x */
      75        EXTRACT_WORDS64 (hx, x);
      76      }
      77    /* scale up resulted in a NaN number  */
      78    if (__glibc_unlikely (hx >= UINT64_C(0x7ff0000000000000)))
      79      return x + x;
      80    k += (hx >> 52) - 1023;
      81    i = ((uint64_t) k & UINT64_C(0x8000000000000000)) >> 63;
      82    hx = (hx & UINT64_C(0x000fffffffffffff)) | ((0x3ff - i) << 52);
      83    y = (double) (k + i);
      84    if (FIX_INT_FP_CONVERT_ZERO && y == 0.0)
      85      y = 0.0;
      86    INSERT_WORDS64 (x, hx);
      87    z = y * log10_2lo + ivln10 * __ieee754_log (x);
      88    return z + y * log10_2hi;
      89  }
      90  libm_alias_finite (__ieee754_log10, __log10)