lib/libm/noieee_src/n_log__L.c

   1 /*      $NetBSD: n_log__L.c,v 1.5 2002/06/15 00:10:17 matt Exp $ */
   2 /*
   3  * Copyright (c) 1985, 1993
   4  *      The Regents of the University of California.  All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following disclaimer.
  11  * 2. Redistributions in binary form must reproduce the above copyright
  12  *    notice, this list of conditions and the following disclaimer in the
  13  *    documentation and/or other materials provided with the distribution.
  14  * 3. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 #ifndef lint
  32 #if 0
  33 static char sccsid[] = "@(#)log__L.c    8.1 (Berkeley) 6/4/93";
  34 #endif
  35 #endif /* not lint */
  36
  37 /* log__L(Z)
  38  *              LOG(1+X) - 2S                          X
  39  * RETURN      ---------------  WHERE Z = S*S,  S = ------- , 0 <= Z <= .0294...
  40  *                    S                              2 + X
  41  *
  42  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
  43  * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
  44  * CODED IN C BY K.C. NG, 1/19/85;
  45  * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
  46  *
  47  * Method :
  48  *      1. Polynomial approximation: let s = x/(2+x).
  49  *         Based on log(1+x) = log(1+s) - log(1-s)
  50  *               = 2s + 2/3 s**3 + 2/5 s**5 + .....,
  51  *
  52  *         (log(1+x) - 2s)/s is computed by
  53  *
  54  *             z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
  55  *
  56  *         where z=s*s. (See the listing below for Lk's values.) The
  57  *         coefficients are obtained by a special Remez algorithm.
  58  *
  59  * Accuracy:
  60  *      Assuming no rounding error, the maximum magnitude of the approximation
  61  *      error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
  62  *      for VAX D format.
  63  *
  64  * Constants:
  65  * The hexadecimal values are the intended ones for the following constants.
  66  * The decimal values may be used, provided that the compiler will convert
  67  * from decimal to binary accurately enough to produce the hexadecimal values
  68  * shown.
  69  */
  70
  71 #define _LIBM_STATIC
  72 #include "mathimpl.h"
  73
  74 vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa,  0, .AAAAAAAAAAAAC5)
  75 vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
  76 vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
  77 vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
  78 vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
  79 vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
  80 vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
  81 vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
  82
  83 ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
  84 ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
  85 ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
  86 ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
  87 ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
  88 ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
  89 ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
  90
  91 #ifdef vccast
  92 #define L1      vccast(L1)
  93 #define L2      vccast(L2)
  94 #define L3      vccast(L3)
  95 #define L4      vccast(L4)
  96 #define L5      vccast(L5)
  97 #define L6      vccast(L6)
  98 #define L7      vccast(L7)
  99 #define L8      vccast(L8)
 100 #endif
 101
 102 double
 103 __log__L(double z)
 104 {
 105 #if defined(__vax__)||defined(tahoe)
 106     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
 107 #else   /* defined(__vax__)||defined(tahoe) */
 108     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
 109 #endif  /* defined(__vax__)||defined(tahoe) */
 110 }