Mathematica 3.0: reliability close to LogZero?

*To*: mathgroup at smc.vnet.net*Subject*: [mg24514] Mathematica 3.0: reliability close to LogZero?*From*: William Boyd <william at kamaz.demon.co.uk>*Date*: Thu, 20 Jul 2000 03:01:50 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Could I ask an expert to cast a jaded eye over the following: is there something wrong with Log close to zero in Mathematica 3.0? All I'm doing is calculating the number of terms needed to reach a given sum in the geometric series: following is typical: the values are the first few terms of a denary limit sequence tending to 1/636, bar the last ordinate which is last digit failsafed: I hope I am working to 50 digit precision (I do find The Book hard work at times) - even if I'm not it should surely be better than this?. The first Log you see in 'result' is the one tending to zero. So we are doing LogZero / LogOne, which is a test of course, but not such a hard test. <<start cut and paste of Mathematica 3.0 notebook: formula is slightly different from standard as I am modelling with first term of series n*(1-r) >> result[n_Real,s_Integer,r_Real]:= Floor[SetPrecision[Log[ 1 - r*s/(n*(1 - r))] / Log[1 - r],50]] + 1 result[1.,635,0.001572327044025] 19022 result[1.,635,0.0015723270440251] 19667 result[1.,635,0.00157232704402515] 20971 result[1.,635,0.001572327044025157] 23347 result[1.,635,0.0015723270440251572] 23347 result[1.,635,0.00157232704402515722] \[Infinity] << finish >> On the face of it, this isn't impressive. Compare my results for the same formula with the same ordinates using the Extended type (19/20 sig figs) in Delphi 3, which gives {19022, 19665, 20979, 23163, 24409, 25008}, while a binary divide algorithm in Delphi using a tried and trusted integer power raise of mine (no logs) gives {19022, 19665, 20979, 23163, 24410, 25014}. Comments appreciated. sincerely, -- William Boyd

**Follow-Ups**:**Re: Mathematica 3.0: reliability close to LogZero?***From:*Daniel Lichtblau <danl@wolfram.com>