10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29 
  30 #pragma weak logl = __logl
  31 
  32 /*
  33  * logl(x)
  34  * Table look-up algorithm
  35  * By K.C. Ng, March 6, 1989
  36  *
  37  * (a). For x in [31/33,33/31], using a special approximation:
  38  *      f = x - 1;
  39  *      s = f/(2.0+f);  ... here |s| <= 0.03125
  40  *      z = s*s;
  41  *      return f-s*(f-z*(B1+z*(B2+z*(B3+z*(B4+...+z*B9)...))));
  42  *
  43  * (b). Otherwise, normalize x = 2^n * 1.f.
  44  *      Use a 6-bit table look-up: find a 6 bit g that match f to 6.5 bits,
  45  *      then
  46  *          log(x) = n*ln2 + log(1.g) + log(1.f/1.g).
  47  *      Here the leading and trailing values of log(1.g) are obtained from
  48  *      a size-64 table.
  49  *      For log(1.f/1.g), let s = (1.f-1.g)/(1.f+1.g), then
  50  *          log(1.f/1.g) = log((1+s)/(1-s)) = 2s + 2/3 s^3 + 2/5 s^5 +...

  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29 
  30 #pragma weak __logl = logl
  31 
  32 /*
  33  * logl(x)
  34  * Table look-up algorithm
  35  * By K.C. Ng, March 6, 1989
  36  *
  37  * (a). For x in [31/33,33/31], using a special approximation:
  38  *      f = x - 1;
  39  *      s = f/(2.0+f);  ... here |s| <= 0.03125
  40  *      z = s*s;
  41  *      return f-s*(f-z*(B1+z*(B2+z*(B3+z*(B4+...+z*B9)...))));
  42  *
  43  * (b). Otherwise, normalize x = 2^n * 1.f.
  44  *      Use a 6-bit table look-up: find a 6 bit g that match f to 6.5 bits,
  45  *      then
  46  *          log(x) = n*ln2 + log(1.g) + log(1.f/1.g).
  47  *      Here the leading and trailing values of log(1.g) are obtained from
  48  *      a size-64 table.
  49  *      For log(1.f/1.g), let s = (1.f-1.g)/(1.f+1.g), then
  50  *          log(1.f/1.g) = log((1+s)/(1-s)) = 2s + 2/3 s^3 + 2/5 s^5 +...