134126Sbostic /* 224602Szliu * Copyright (c) 1985 Regents of the University of California. 334126Sbostic * All rights reserved. 434126Sbostic * 5*42657Sbostic * %sccs.include.redist.c% 634126Sbostic * 734126Sbostic * All recipients should regard themselves as participants in an ongoing 834126Sbostic * research project and hence should feel obligated to report their 934126Sbostic * experiences (good or bad) with these elementary function codes, using 1034126Sbostic * the sendbug(8) program, to the authors. 1124602Szliu */ 1224602Szliu 1324602Szliu #ifndef lint 14*42657Sbostic static char sccsid[] = "@(#)log10.c 5.5 (Berkeley) 06/01/90"; 1534126Sbostic #endif /* not lint */ 1624602Szliu 1724602Szliu /* LOG10(X) 1824602Szliu * RETURN THE BASE 10 LOGARITHM OF x 1924602Szliu * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 2024602Szliu * CODED IN C BY K.C. NG, 1/20/85; 2124602Szliu * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85. 2224602Szliu * 2324602Szliu * Required kernel function: 2424602Szliu * log(x) 2524602Szliu * 2624602Szliu * Method : 2724602Szliu * log(x) 2824602Szliu * log10(x) = --------- or [1/log(10)]*log(x) 2924602Szliu * log(10) 3024602Szliu * 3124602Szliu * Note: 3224602Szliu * [log(10)] rounded to 56 bits has error .0895 ulps, 3324602Szliu * [1/log(10)] rounded to 53 bits has error .198 ulps; 3424602Szliu * therefore, for better accuracy, in VAX D format, we divide 3524602Szliu * log(x) by log(10), but in IEEE Double format, we multiply 3624602Szliu * log(x) by [1/log(10)]. 3724602Szliu * 3824602Szliu * Special cases: 3924602Szliu * log10(x) is NaN with signal if x < 0; 4024602Szliu * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 4124602Szliu * log10(NaN) is that NaN with no signal. 4224602Szliu * 4324602Szliu * Accuracy: 4424602Szliu * log10(X) returns the exact log10(x) nearly rounded. In a test run 4524602Szliu * with 1,536,000 random arguments on a VAX, the maximum observed 4624602Szliu * error was 1.74 ulps (units in the last place). 4724602Szliu * 4824602Szliu * Constants: 4924602Szliu * The hexadecimal values are the intended ones for the following constants. 5024602Szliu * The decimal values may be used, provided that the compiler will convert 5124602Szliu * from decimal to binary accurately enough to produce the hexadecimal values 5224602Szliu * shown. 5324602Szliu */ 5424602Szliu 5535679Sbostic #include "mathimpl.h" 5624602Szliu 5735679Sbostic vc(ln10hi, 2.3025850929940456790E0 ,5d8d,4113,a8ac,ddaa, 2, .935D8DDDAAA8AC) 5835679Sbostic 5935679Sbostic ic(ivln10, 4.3429448190325181667E-1, -2, 1.BCB7B1526E50E) 6035679Sbostic 6135679Sbostic #ifdef vccast 6235679Sbostic #define ln10hi vccast(ln10hi) 6335679Sbostic #endif 6435679Sbostic 6535679Sbostic 6624602Szliu double log10(x) 6724602Szliu double x; 6824602Szliu { 6931853Szliu #if defined(vax)||defined(tahoe) 7024602Szliu return(log(x)/ln10hi); 7131853Szliu #else /* defined(vax)||defined(tahoe) */ 7224602Szliu return(ivln10*log(x)); 7331853Szliu #endif /* defined(vax)||defined(tahoe) */ 7424602Szliu } 75