4.3BSD - /usr/src/usr.lib/libm/log__L.c

   1: /*
   2:  * Copyright (c) 1985 Regents of the University of California.
   3:  *
   4:  * Use and reproduction of this software are granted  in  accordance  with
   5:  * the terms and conditions specified in  the  Berkeley  Software  License
   6:  * Agreement (in particular, this entails acknowledgement of the programs'
   7:  * source, and inclusion of this notice) with the additional understanding
   8:  * that  all  recipients  should regard themselves as participants  in  an
   9:  * ongoing  research  project and hence should  feel  obligated  to report
  10:  * their  experiences (good or bad) with these elementary function  codes,
  11:  * using "sendbug 4bsd-bugs@BERKELEY", to the authors.
  12:  */
  13: 
  14: #ifndef lint
  15: static char sccsid[] = "@(#)log__L.c	1.2 (Berkeley) 8/21/85";
  16: #endif not lint
  17: 
  18: /* log__L(Z)
  19:  *		LOG(1+X) - 2S			       X
  20:  * RETURN      ---------------  WHERE Z = S*S,  S = ------- , 0 <= Z <= .0294...
  21:  *		      S				     2 + X
  22:  *
  23:  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
  24:  * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
  25:  * CODED IN C BY K.C. NG, 1/19/85;
  26:  * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
  27:  *
  28:  * Method :
  29:  *	1. Polynomial approximation: let s = x/(2+x).
  30:  *	   Based on log(1+x) = log(1+s) - log(1-s)
  31:  *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
  32:  *
  33:  *	   (log(1+x) - 2s)/s is computed by
  34:  *
  35:  *	       z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
  36:  *
  37:  *	   where z=s*s. (See the listing below for Lk's values.) The
  38:  *	   coefficients are obtained by a special Remez algorithm.
  39:  *
  40:  * Accuracy:
  41:  *	Assuming no rounding error, the maximum magnitude of the approximation
  42:  *	error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
  43:  *	for VAX D format.
  44:  *
  45:  * Constants:
  46:  * The hexadecimal values are the intended ones for the following constants.
  47:  * The decimal values may be used, provided that the compiler will convert
  48:  * from decimal to binary accurately enough to produce the hexadecimal values
  49:  * shown.
  50:  */
  51: 
  52: #ifdef VAX  /* VAX D format (56 bits) */
  53: /* static double */
  54: /* L1     =  6.6666666666666703212E-1    , Hex  2^  0   *  .AAAAAAAAAAAAC5 */
  55: /* L2     =  3.9999999999970461961E-1    , Hex  2^ -1   *  .CCCCCCCCCC2684 */
  56: /* L3     =  2.8571428579395698188E-1    , Hex  2^ -1   *  .92492492F85782 */
  57: /* L4     =  2.2222221233634724402E-1    , Hex  2^ -2   *  .E38E3839B7AF2C */
  58: /* L5     =  1.8181879517064680057E-1    , Hex  2^ -2   *  .BA2EB4CC39655E */
  59: /* L6     =  1.5382888777946145467E-1    , Hex  2^ -2   *  .9D8551E8C5781D */
  60: /* L7     =  1.3338356561139403517E-1    , Hex  2^ -2   *  .8895B3907FCD92 */
  61: /* L8     =  1.2500000000000000000E-1    , Hex  2^ -2   *  .80000000000000 */
  62: static long        L1x[] = { 0xaaaa402a, 0xaac5aaaa};
  63: static long        L2x[] = { 0xcccc3fcc, 0x2684cccc};
  64: static long        L3x[] = { 0x49243f92, 0x578292f8};
  65: static long        L4x[] = { 0x8e383f63, 0xaf2c39b7};
  66: static long        L5x[] = { 0x2eb43f3a, 0x655ecc39};
  67: static long        L6x[] = { 0x85513f1d, 0x781de8c5};
  68: static long        L7x[] = { 0x95b33f08, 0xcd92907f};
  69: static long        L8x[] = { 0x00003f00, 0x00000000};
  70: #define       L1    (*(double*)L1x)
  71: #define       L2    (*(double*)L2x)
  72: #define       L3    (*(double*)L3x)
  73: #define       L4    (*(double*)L4x)
  74: #define       L5    (*(double*)L5x)
  75: #define       L6    (*(double*)L6x)
  76: #define       L7    (*(double*)L7x)
  77: #define       L8    (*(double*)L8x)
  78: #else   /* IEEE double */
  79: static double
  80: L1     =  6.6666666666667340202E-1    , /*Hex  2^ -1   *  1.5555555555592 */
  81: L2     =  3.9999999999416702146E-1    , /*Hex  2^ -2   *  1.999999997FF24 */
  82: L3     =  2.8571428742008753154E-1    , /*Hex  2^ -2   *  1.24924941E07B4 */
  83: L4     =  2.2222198607186277597E-1    , /*Hex  2^ -3   *  1.C71C52150BEA6 */
  84: L5     =  1.8183562745289935658E-1    , /*Hex  2^ -3   *  1.74663CC94342F */
  85: L6     =  1.5314087275331442206E-1    , /*Hex  2^ -3   *  1.39A1EC014045B */
  86: L7     =  1.4795612545334174692E-1    ; /*Hex  2^ -3   *  1.2F039F0085122 */
  87: #endif
  88: 
  89: double log__L(z)
  90: double z;
  91: {
  92: #ifdef VAX
  93:     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
  94: #else   /* IEEE double */
  95:     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
  96: #endif
  97: }

Defined functions

Defined variables

Defined macros