xref: /third_party/jerryscript/jerry-libm/log10.c

/* Copyright JS Foundation and other contributors, http://js.foundation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * This file is based on work under the following copyright and permission
 * notice:
 *
 *     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.
 *
 *     @(#)e_log10.c 1.3 95/01/18
 */

#include "jerry-libm-internal.h"

/* 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.
 */

#define zero 0.0
#define two54 1.80143985094819840000e+16     /* 0x43500000, 0x00000000 */
#define ivln10 4.34294481903251816668e-01    /* 0x3FDBCB7B, 0x1526E50E */
#define log10_2hi 3.01029995663611771306e-01 /* 0x3FD34413, 0x509F6000 */
#define log10_2lo 3.69423907715893078616e-13 /* 0x3D59FEF3, 0x11F12B36 */

double
log10 (double x)
{
  double y, z;
  int i, k, hx;
  unsigned lx;
  double_accessor temp;

  hx = __HI (x); /* high word of x */
  lx = __LO (x); /* low word of x */

  k = 0;
  if (hx < 0x00100000)
  {
    /* x < 2**-1022  */
    if (((hx & 0x7fffffff) | lx) == 0)
    {
      /* log(+-0)=-inf */
      return -two54 / zero;
    }
    if (hx < 0)
    {
      /* log(-#) = NaN */
      return (x - x) / zero;
    }
    k -= 54;
    x *= two54;    /* subnormal number, scale up x */
    hx = __HI (x); /* high word of x */
  }
  if (hx >= 0x7ff00000)
  {
    return x + x;
  }
  k += (hx >> 20) - 1023;
  i = ((unsigned) k & 0x80000000) >> 31;
  hx = (hx & 0x000fffff) | ((0x3ff - i) << 20);
  y = (double) (k + i);
  temp.dbl = x;
  temp.as_int.hi = hx;
  z = y * log10_2lo + ivln10 * log (temp.dbl);
  return z + y * log10_2hi;
} /* log10 */

#undef zero
#undef two54
#undef ivln10
#undef log10_2hi
#undef log10_2lo