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MathGroup Archive 1997

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Unfinished machine arithmatic

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7508] Unfinished machine arithmatic
  • From: Ersek_Ted%PAX1A at mr.nawcad.navy.mil
  • Date: Sat, 7 Jun 1997 03:48:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Consider the following lines involving a mixture of machine numbers
and exact numbers.

In[1]:=  15.0/0.125 +Log[1-Erf[3]]
Out[1]= 109.28

In[2]:=  15.0/0.125 +Log[1-Erf[7]]
In[2]=  120. +Log[1-Erf[7]]

The first line evaluates without any trouble, but
the second line doesn't evaluate to a number even though it
has a numerical value of  68.472 (found using arbitrary precision).


Question:   Was the appropriate value given for Out[2].
Lets look at the next line.

In[3]:=  15.0/0.125+Log[1-Erf[7.0]]     (* all machine numbers *)
Out[3]=  -Infinity


The numerical value of Out[2] is 68.472  and thats a long way from 
(-Infinity).
 I suppose it WRI decided the following:

 -  Arbitrary precision should not be used in the case of In[2]
    for the sake of efficiency.

 -  The result of In[2] will not be (-Infinity), because it is far from 
correct.

 -  The only thing left is to give an incomplete calculation for Out[2].

I think the implementation is very good, but I thought users should be
aware that the arithmatic can end up unfinished.

               Ted Ersek



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