arithmetic library for tracking worst case error

Question

(edited)
Is there any library or tool that allows for knowing the maximum accumulated error in arithmetic operations?

For example if I make some iterative calculation ...

myVars = initialValues;
while (notEnded) {
    myVars = updateMyVars(myVars)
}

... I want to know at the end not only the calculated values, but also the potential error (the range of posible values if results in each individual operations took the range limits for each operand).

I have already written a Java class called EADouble.java (EA for Error Accounting) which holds and updates the maximum positive and negative errors along with the calculated value, for some basic operations, but I'm afraid I might be reinventing an square wheel.

Any libraries/whatever in Java/whatever? Any suggestions?

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• Updated on July 11th: Examined existing libraries and added link to sample code.
• As commented by fellows, there is the concept of Interval Arithmetic, and there was a previous question ( A good uncertainty (interval) arithmetic library? ) on the topic. There just a couple of small issues about my intent:
  • I care more about the "main" value than about the upper and lower bounds. However, to add that extra value to an open library should be straight-forward.
  • Accounting the error as an independent floating point might allow for a finer accuracy (e.g. for addition the upper bound would be incremented just half ULP instead of a whole ULP).
• Libraries I had a look at:
  • ia_math (Java. Just would have to add the main value. My favourite so far)
  • Boost/numeric/Interval (C++, Very complex/complete)
  • ErrorProp (Java, accounts value, and error as standard deviation)
• The sample code (TestEADouble.java) runs ok a ballistic simulation and a calculation of number e. However those are not very demanding scenarios.

Answer 1

probably way too late, but look at BIAS/Profil: http://www.ti3.tuhh.de/keil/profil/index_e.html Pretty complete, simple, account for computer error, and if your errors are centered easy access to your nominal (through Mid(...)).