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[] = 16 "@(#)log10.c 1.2 (Berkeley) 8/21/85; 1.2 (ucb.elefunt) 09/11/85"; 17 #endif not lint 18 19 /* LOG10(X) 20 * RETURN THE BASE 10 LOGARITHM OF x 21 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 22 * CODED IN C BY K.C. NG, 1/20/85; 23 * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85. 24 * 25 * Required kernel function: 26 * log(x) 27 * 28 * Method : 29 * log(x) 30 * log10(x) = --------- or [1/log(10)]*log(x) 31 * log(10) 32 * 33 * Note: 34 * [log(10)] rounded to 56 bits has error .0895 ulps, 35 * [1/log(10)] rounded to 53 bits has error .198 ulps; 36 * therefore, for better accuracy, in VAX D format, we divide 37 * log(x) by log(10), but in IEEE Double format, we multiply 38 * log(x) by [1/log(10)]. 39 * 40 * Special cases: 41 * log10(x) is NaN with signal if x < 0; 42 * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; 43 * log10(NaN) is that NaN with no signal. 44 * 45 * Accuracy: 46 * log10(X) returns the exact log10(x) nearly rounded. In a test run 47 * with 1,536,000 random arguments on a VAX, the maximum observed 48 * error was 1.74 ulps (units in the last place). 49 * 50 * Constants: 51 * The hexadecimal values are the intended ones for the following constants. 52 * The decimal values may be used, provided that the compiler will convert 53 * from decimal to binary accurately enough to produce the hexadecimal values 54 * shown. 55 */ 56 57 #ifdef VAX /* VAX D format (56 bits) */ 58 /* static double */ 59 /* ln10hi = 2.3025850929940456790E0 ; Hex 2^ 2 * .935D8DDDAAA8AC */ 60 static long ln10hix[] = { 0x5d8d4113, 0xa8acddaa}; 61 #define ln10hi (*(double*)ln10hix) 62 #else /* IEEE double */ 63 static double 64 ivln10 = 4.3429448190325181667E-1 ; /*Hex 2^ -2 * 1.BCB7B1526E50E */ 65 #endif 66 67 double log10(x) 68 double x; 69 { 70 double log(); 71 72 #ifdef VAX 73 return(log(x)/ln10hi); 74 #else /* IEEE double */ 75 return(ivln10*log(x)); 76 #endif 77 } 78