Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!wuarchive!uunet!mcsun!hp4nl!cwi.nl!jurjen From: jurjen@cwi.nl (Jurjen NE Bos) Newsgroups: comp.sys.handhelds Subject: Re: Accuracy w/ ln and log Message-ID: <3630@charon.cwi.nl> Date: 4 Jun 91 09:10:59 GMT References: <1991May30.120658.3590@panix.uucp> Sender: news@cwi.nl Lines: 34 marek@ifi.uio.no (Marek Vokac) writes: >Re John Hawkinson's question about n-base logarithms on the '48 - >I compared the results from LOG/LOG and LN/LN calculations with those >produced by Mathematica, and it seems LN is _marginally_ more >accurate, the results differed +/- 1 in the last decimal digit >calculated. >The difference is small enough to be insignificant in most >applications; but it does seem to indicate the LN is used for LOG and >not the other way round. This is unfortunately not true: As I said in my previous posting, both LN and LOG are based on a 15 digit logarithm function. Roundoff from the conversion is not visible at all on the user level; both functions are almost always correctly rounded to the last decimal. (I think the answers are even *always* correct, but I am not sure; Bill?) My guess is that you used numbers in the range 10..22026 to test your hypothesis. In this range, the precision of the decimal representation of the LOG is slightly less than that of the LN; this effect is known as "wobbling precision". To be exact, numbers that start with a low decimal digit in their mantissa have a smaller relative precision than numbers that start with a high digit. To see this, note that the interval 1.00000000000 .. 1.00000000001 is ten times as big as .999999999999 .. 1.00000000000 (all numbers being twelve digits). I hope this is clear. Remember: The HP48 is much, much more precise than you think; almost all "inaccuracies" are because of its number system, not because of "internal roundoff".