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Annotation of 43BSDReno/lib/libm/common_source/log__L.c, revision 1.1

1.1     ! root        1: /*
        !             2:  * Copyright (c) 1985 Regents of the University of California.
        !             3:  * All rights reserved.
        !             4:  *
        !             5:  * Redistribution and use in source and binary forms are permitted
        !             6:  * provided that: (1) source distributions retain this entire copyright
        !             7:  * notice and comment, and (2) distributions including binaries display
        !             8:  * the following acknowledgement:  ``This product includes software
        !             9:  * developed by the University of California, Berkeley and its contributors''
        !            10:  * in the documentation or other materials provided with the distribution
        !            11:  * and in all advertising materials mentioning features or use of this
        !            12:  * software. Neither the name of the University nor the names of its
        !            13:  * contributors may be used to endorse or promote products derived
        !            14:  * from this software without specific prior written permission.
        !            15:  * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
        !            16:  * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
        !            17:  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
        !            18:  *
        !            19:  * All recipients should regard themselves as participants in an ongoing
        !            20:  * research project and hence should feel obligated to report their
        !            21:  * experiences (good or bad) with these elementary function codes, using
        !            22:  * the sendbug(8) program, to the authors.
        !            23:  */
        !            24: 
        !            25: #ifndef lint
        !            26: static char sccsid[] = "@(#)log__L.c   5.5 (Berkeley) 6/1/90";
        !            27: #endif /* not lint */
        !            28: 
        !            29: /* log__L(Z)
        !            30:  *             LOG(1+X) - 2S                          X
        !            31:  * RETURN      ---------------  WHERE Z = S*S,  S = ------- , 0 <= Z <= .0294...
        !            32:  *                   S                              2 + X
        !            33:  *                  
        !            34:  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
        !            35:  * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
        !            36:  * CODED IN C BY K.C. NG, 1/19/85; 
        !            37:  * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
        !            38:  *
        !            39:  * Method :
        !            40:  *     1. Polynomial approximation: let s = x/(2+x). 
        !            41:  *        Based on log(1+x) = log(1+s) - log(1-s)
        !            42:  *              = 2s + 2/3 s**3 + 2/5 s**5 + .....,
        !            43:  *
        !            44:  *        (log(1+x) - 2s)/s is computed by
        !            45:  *
        !            46:  *            z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
        !            47:  *
        !            48:  *        where z=s*s. (See the listing below for Lk's values.) The 
        !            49:  *        coefficients are obtained by a special Remez algorithm. 
        !            50:  *
        !            51:  * Accuracy:
        !            52:  *     Assuming no rounding error, the maximum magnitude of the approximation 
        !            53:  *     error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
        !            54:  *     for VAX D format.
        !            55:  *
        !            56:  * Constants:
        !            57:  * The hexadecimal values are the intended ones for the following constants.
        !            58:  * The decimal values may be used, provided that the compiler will convert
        !            59:  * from decimal to binary accurately enough to produce the hexadecimal values
        !            60:  * shown.
        !            61:  */
        !            62: 
        !            63: #include "mathimpl.h"
        !            64: 
        !            65: vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa,  0, .AAAAAAAAAAAAC5)
        !            66: vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
        !            67: vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
        !            68: vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
        !            69: vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
        !            70: vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
        !            71: vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
        !            72: vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
        !            73: 
        !            74: ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
        !            75: ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
        !            76: ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
        !            77: ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
        !            78: ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
        !            79: ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
        !            80: ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
        !            81: 
        !            82: #ifdef vccast
        !            83: #define        L1      vccast(L1)
        !            84: #define        L2      vccast(L2)
        !            85: #define        L3      vccast(L3)
        !            86: #define        L4      vccast(L4)
        !            87: #define        L5      vccast(L5)
        !            88: #define        L6      vccast(L6)
        !            89: #define        L7      vccast(L7)
        !            90: #define        L8      vccast(L8)
        !            91: #endif
        !            92: 
        !            93: double log__L(z)
        !            94: double z;
        !            95: {
        !            96: #if defined(vax)||defined(tahoe)
        !            97:     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
        !            98: #else  /* defined(vax)||defined(tahoe) */
        !            99:     return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
        !           100: #endif /* defined(vax)||defined(tahoe) */
        !           101: }

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