sysdeps/generic/log__L.c

   1 /*
   2  * Copyright (c) 1985, 1993
   3  *      The Regents of the University of California.  All rights reserved.
   4  *
   5  * Redistribution and use in source and binary forms, with or without
   6  * modification, are permitted provided that the following conditions
   7  * are met:
   8  * 1. Redistributions of source code must retain the above copyright
   9  *    notice, this list of conditions and the following disclaimer.
  10  * 2. Redistributions in binary form must reproduce the above copyright
  11  *    notice, this list of conditions and the following disclaimer in the
  12  *    documentation and/or other materials provided with the distribution.
  13  * 3. All advertising materials mentioning features or use of this software
  14  *    must display the following acknowledgement:
  15  *      This product includes software developed by the University of
  16  *      California, Berkeley and its contributors.
  17  * 4. Neither the name of the University nor the names of its contributors
  18  *    may be used to endorse or promote products derived from this software
  19  *    without specific prior written permission.
  20  *
  21  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  22  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  23  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  24  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  25  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  26  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  27  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  28  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  29  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  30  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  31  * SUCH DAMAGE.
  32  */
  33
  34 #ifndef lint
  35 static char sccsid[] = "@(#)log__L.c    8.1 (Berkeley) 6/4/93";
  36 #endif /* not lint */
  37
  38 /* log__L(Z)
  39  *              LOG(1+X) - 2S                          X
  40  * RETURN      ---------------  WHERE Z = S*S,  S = ------- , 0 <= Z <= .0294...
  41  *                    S                              2 + X
  42  *
  43  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
  44  * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
  45  * CODED IN C BY K.C. NG, 1/19/85;
  46  * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
  47  *
  48  * Method :
  49  *      1. Polynomial approximation: let s = x/(2+x).
  50  *         Based on log(1+x) = log(1+s) - log(1-s)
  51  *               = 2s + 2/3 s**3 + 2/5 s**5 + .....,
  52  *
  53  *         (log(1+x) - 2s)/s is computed by
  54  *
  55  *             z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
  56  *
  57  *         where z=s*s. (See the listing below for Lk's values.) The
  58  *         coefficients are obtained by a special Remez algorithm.
  59  *
  60  * Accuracy:
  61  *      Assuming no rounding error, the maximum magnitude of the approximation
  62  *      error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
  63  *      for VAX D format.
  64  *
  65  * Constants:
  66  * The hexadecimal values are the intended ones for the following constants.
  67  * The decimal values may be used, provided that the compiler will convert
  68  * from decimal to binary accurately enough to produce the hexadecimal values
  69  * shown.
  70  */
  71
  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 __log__L(z)
 103 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 }