134126Sbostic /* 2*61309Sbostic * Copyright (c) 1985, 1993 3*61309Sbostic * The Regents of the University of California. All rights reserved. 434126Sbostic * 542657Sbostic * %sccs.include.redist.c% 624604Szliu */ 724604Szliu 824604Szliu #ifndef lint 9*61309Sbostic static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 06/04/93"; 1034126Sbostic #endif /* not lint */ 1124604Szliu 1224604Szliu /* log__L(Z) 1324604Szliu * LOG(1+X) - 2S X 1424604Szliu * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294... 1524604Szliu * S 2 + X 1624604Szliu * 1724604Szliu * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS) 1824604Szliu * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS 1924604Szliu * CODED IN C BY K.C. NG, 1/19/85; 2024604Szliu * REVISED BY K.C. Ng, 2/3/85, 4/16/85. 2124604Szliu * 2224604Szliu * Method : 2324604Szliu * 1. Polynomial approximation: let s = x/(2+x). 2424604Szliu * Based on log(1+x) = log(1+s) - log(1-s) 2524604Szliu * = 2s + 2/3 s**3 + 2/5 s**5 + ....., 2624604Szliu * 2724604Szliu * (log(1+x) - 2s)/s is computed by 2824604Szliu * 2924604Szliu * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...))) 3024604Szliu * 3124604Szliu * where z=s*s. (See the listing below for Lk's values.) The 3224604Szliu * coefficients are obtained by a special Remez algorithm. 3324604Szliu * 3424604Szliu * Accuracy: 3524604Szliu * Assuming no rounding error, the maximum magnitude of the approximation 3624604Szliu * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63) 3724604Szliu * for VAX D format. 3824604Szliu * 3924604Szliu * Constants: 4024604Szliu * The hexadecimal values are the intended ones for the following constants. 4124604Szliu * The decimal values may be used, provided that the compiler will convert 4224604Szliu * from decimal to binary accurately enough to produce the hexadecimal values 4324604Szliu * shown. 4424604Szliu */ 4524604Szliu 4635679Sbostic #include "mathimpl.h" 4724604Szliu 4835679Sbostic vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5) 4935679Sbostic vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684) 5035679Sbostic vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782) 5135679Sbostic vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C) 5235679Sbostic vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E) 5335679Sbostic vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D) 5435679Sbostic vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92) 5535679Sbostic vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000) 5635679Sbostic 5735679Sbostic ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592) 5835679Sbostic ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24) 5935679Sbostic ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4) 6035679Sbostic ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6) 6135679Sbostic ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F) 6235679Sbostic ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B) 6335679Sbostic ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122) 6435679Sbostic 6535679Sbostic #ifdef vccast 6635679Sbostic #define L1 vccast(L1) 6735679Sbostic #define L2 vccast(L2) 6835679Sbostic #define L3 vccast(L3) 6935679Sbostic #define L4 vccast(L4) 7035679Sbostic #define L5 vccast(L5) 7135679Sbostic #define L6 vccast(L6) 7235679Sbostic #define L7 vccast(L7) 7335679Sbostic #define L8 vccast(L8) 7435679Sbostic #endif 7535679Sbostic 7657452Sbostic double __log__L(z) 7724604Szliu double z; 7824604Szliu { 7931853Szliu #if defined(vax)||defined(tahoe) 8024604Szliu return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8)))))))); 8131853Szliu #else /* defined(vax)||defined(tahoe) */ 8224604Szliu return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7))))))); 8331853Szliu #endif /* defined(vax)||defined(tahoe) */ 8424604Szliu } 85