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[] = "@(#)log10.c 1.1 (Berkeley) 05/23/85"; 16 #endif not lint 17 18 /* LOG10(X) 19 * RETURN THE BASE 10 LOGARITHM OF x 20 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 21 * CODED IN C BY K.C. NG, 1/20/85; 22 * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85. 23 * 24 * Required kernel function: 25 * log(x) 26 * 27 * Method : 28 * log(x) 29 * log10(x) = --------- or [1/log(10)]*log(x) 30 * log(10) 31 * 32 * Note: 33 * [log(10)] rounded to 56 bits has error .0895 ulps, 34 * [1/log(10)] rounded to 53 bits has error .198 ulps; 35 * therefore, for better accuracy, in VAX D format, we divide 36 * log(x) by log(10), but in IEEE Double format, we multiply 37 * log(x) by [1/log(10)]. 38 * 39 * Special cases: 40 * log10(x) is NAN with signal if x < 0; 41 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 42 * log10(NAN) is that NAN with no signal. 43 * 44 * Accuracy: 45 * log10(X) returns the exact log10(x) nearly rounded. In a test run 46 * with 1,536,000 random arguments on a VAX, the maximum observed 47 * error was 1.74 ulps (units in the last place). 48 * 49 * Constants: 50 * The hexadecimal values are the intended ones for the following constants. 51 * The decimal values may be used, provided that the compiler will convert 52 * from decimal to binary accurately enough to produce the hexadecimal values 53 * shown. 54 */ 55 56 #ifdef VAX /* VAX D format (56 bits) */ 57 /* static double */ 58 /* ln10hi = 2.3025850929940456790E0 ; Hex 2^ 2 * .935D8DDDAAA8AC */ 59 static long ln10hix[] = { 0x5d8d4113, 0xa8acddaa}; 60 #define ln10hi (*(double*)ln10hix) 61 #else /* IEEE double precision (53 bits) */ 62 static double 63 ivln10 = 4.3429448190325181667E-1 ; /*Hex 2^ -2 * 1.BCB7B1526E50E */ 64 #endif 65 66 double log10(x) 67 double x; 68 { 69 double log(); 70 71 #ifdef VAX 72 return(log(x)/ln10hi); 73 #else 74 return(ivln10*log(x)); 75 #endif 76 } 77