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Re: Non-deterministic numerical inaccuracies in Mathematica 7

• To: mathgroup at smc.vnet.net
• Subject: [mg94995] Re: Non-deterministic numerical inaccuracies in Mathematica 7
• From: David Bailey <dave at removedbailey.co.uk>
• Date: Thu, 1 Jan 2009 20:30:57 -0500 (EST)
• References: <gjcuio$cnf$1@smc.vnet.net> <gjicrh$c5s$1@smc.vnet.net>

Luis Rademacher wrote:
> What makes you think that this is a bug? Is there really a guarantee
> that the execution of Mathematica code is deterministic (especially,
> involving machine-precision)? I am no expert in floating point numbers,
> but I am aware that dealing with them can easily become tricky.
> Have a look at the following quotations and their sources:
> 
>> We shall discuss the following myths, among others: [...] Arithmetic
>> operations are deterministic; that is, if I do z=x+y in two places in
>> the same program and my program never touches x and y in the 
>> meantime, then the results should be the same.

First, the bug manifests itself as a variation at the same place in the 
code - the loop goes round and the results vary - so I don't think this 
caveat applies.

Furthermore, I think the reason that z=x+y could generate slightly 
different results at two different points in a C or Fortran program, 
would be as a result of some sort of reordering of the code by an 
optimiser, and would not apply here.

I certainly think this is a bug, and I can even guess what may have 
happened - see my reply to a later post on this issue!

David Bailey
http://www.dbaileyconsultancy.co.uk