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}.

sincerely,

--
William Boyd

```

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