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 this notice is preserved and that due credit is given 7 * to the University of California at Berkeley. The name of the University 8 * may not be used to endorse or promote products derived from this 9 * software without specific prior written permission. This software 10 * is provided ``as is'' without express or implied warranty. 11 * 12 * All recipients should regard themselves as participants in an ongoing 13 * research project and hence should feel obligated to report their 14 * experiences (good or bad) with these elementary function codes, using 15 * the sendbug(8) program, to the authors. 16 */ 17 18 #ifndef lint 19 static char sccsid[] = "@(#)log10.c 5.2 (Berkeley) 04/29/88"; 20 #endif /* not lint */ 21 22 /* LOG10(X) 23 * RETURN THE BASE 10 LOGARITHM OF x 24 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 25 * CODED IN C BY K.C. NG, 1/20/85; 26 * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85. 27 * 28 * Required kernel function: 29 * log(x) 30 * 31 * Method : 32 * log(x) 33 * log10(x) = --------- or [1/log(10)]*log(x) 34 * log(10) 35 * 36 * Note: 37 * [log(10)] rounded to 56 bits has error .0895 ulps, 38 * [1/log(10)] rounded to 53 bits has error .198 ulps; 39 * therefore, for better accuracy, in VAX D format, we divide 40 * log(x) by log(10), but in IEEE Double format, we multiply 41 * log(x) by [1/log(10)]. 42 * 43 * Special cases: 44 * log10(x) is NaN with signal if x < 0; 45 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 46 * log10(NaN) is that NaN with no signal. 47 * 48 * Accuracy: 49 * log10(X) returns the exact log10(x) nearly rounded. In a test run 50 * with 1,536,000 random arguments on a VAX, the maximum observed 51 * error was 1.74 ulps (units in the last place). 52 * 53 * Constants: 54 * The hexadecimal values are the intended ones for the following constants. 55 * The decimal values may be used, provided that the compiler will convert 56 * from decimal to binary accurately enough to produce the hexadecimal values 57 * shown. 58 */ 59 60 #if defined(vax)||defined(tahoe) /* VAX D format (56 bits) */ 61 #ifdef vax 62 #define _0x(A,B) 0x/**/A/**/B 63 #else /* vax */ 64 #define _0x(A,B) 0x/**/B/**/A 65 #endif /* vax */ 66 /* static double */ 67 /* ln10hi = 2.3025850929940456790E0 ; Hex 2^ 2 * .935D8DDDAAA8AC */ 68 static long ln10hix[] = { _0x(5d8d,4113), _0x(a8ac,ddaa)}; 69 #define ln10hi (*(double*)ln10hix) 70 #else /* defined(vax)||defined(tahoe) */ 71 static double 72 ivln10 = 4.3429448190325181667E-1 ; /*Hex 2^ -2 * 1.BCB7B1526E50E */ 73 #endif /* defined(vax)||defined(tahoe) */ 74 75 double log10(x) 76 double x; 77 { 78 double log(); 79 80 #if defined(vax)||defined(tahoe) 81 return(log(x)/ln10hi); 82 #else /* defined(vax)||defined(tahoe) */ 83 return(ivln10*log(x)); 84 #endif /* defined(vax)||defined(tahoe) */ 85 } 86