/* * Copyright (c) 1985 Regents of the University of California. * All rights reserved. * * Redistribution and use in source and binary forms are permitted * provided that the above copyright notice and this paragraph are * duplicated in all such forms and that any documentation, * advertising materials, and other materials related to such * distribution and use acknowledge that the software was developed * by the University of California, Berkeley. The name of the * University may not be used to endorse or promote products derived * from this software without specific prior written permission. * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE. * * All recipients should regard themselves as participants in an ongoing * research project and hence should feel obligated to report their * experiences (good or bad) with these elementary function codes, using * the sendbug(8) program, to the authors. */ #ifndef lint static char sccsid[] = "@(#)log10.c 5.3 (Berkeley) 6/30/88"; #endif /* not lint */ /* LOG10(X) * RETURN THE BASE 10 LOGARITHM OF x * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) * CODED IN C BY K.C. NG, 1/20/85; * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85. * * Required kernel function: * log(x) * * Method : * log(x) * log10(x) = --------- or [1/log(10)]*log(x) * log(10) * * Note: * [log(10)] rounded to 56 bits has error .0895 ulps, * [1/log(10)] rounded to 53 bits has error .198 ulps; * therefore, for better accuracy, in VAX D format, we divide * log(x) by log(10), but in IEEE Double format, we multiply * log(x) by [1/log(10)]. * * Special cases: * log10(x) is NaN with signal if x < 0; * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; * log10(NaN) is that NaN with no signal. * * Accuracy: * log10(X) returns the exact log10(x) nearly rounded. In a test run * with 1,536,000 random arguments on a VAX, the maximum observed * error was 1.74 ulps (units in the last place). * * Constants: * The hexadecimal values are the intended ones for the following constants. * The decimal values may be used, provided that the compiler will convert * from decimal to binary accurately enough to produce the hexadecimal values * shown. */ #if defined(vax)||defined(tahoe) /* VAX D format (56 bits) */ #ifdef vax #define _0x(A,B) 0x/**/A/**/B #else /* vax */ #define _0x(A,B) 0x/**/B/**/A #endif /* vax */ /* static double */ /* ln10hi = 2.3025850929940456790E0 ; Hex 2^ 2 * .935D8DDDAAA8AC */ static long ln10hix[] = { _0x(5d8d,4113), _0x(a8ac,ddaa)}; #define ln10hi (*(double*)ln10hix) #else /* defined(vax)||defined(tahoe) */ static double ivln10 = 4.3429448190325181667E-1 ; /*Hex 2^ -2 * 1.BCB7B1526E50E */ #endif /* defined(vax)||defined(tahoe) */ double log10(x) double x; { double log(); #if defined(vax)||defined(tahoe) return(log(x)/ln10hi); #else /* defined(vax)||defined(tahoe) */ return(ivln10*log(x)); #endif /* defined(vax)||defined(tahoe) */ }