math - arithmetic library for tracking worst case error -

(edited)
Is there a library or device to know the maximum deposit Allows an error in arithmetic operations?

For example if I do some iterations ...

  myVars = initialValues; While (not notated) {myVars = updateMyVars (myVars)}   
 ... I want to know only the calculated values ​​at the end, but also the possible error (the limit of posible values If results in the operation of each person take limits on each operand)  
 I have already written a letter called Java Class (EA for Error Accounting) which updates the maximum positive and negative errors with the calculation and updates the value, for some basic operations, But I am afraid that I can revise a square wheel again.  
 Any library / which is in Java / whatever? Any suggestions?  
 
 
 Updated July 11: Added links for existing libraries and sample codes were tested.  
 As is done from Fellow, there is the concept of it, and there was only a few questions about my intention on the topic (past): 
 
 I have upper and lower limitations I pay more attention to the "main" value than, however, it should be straight-forward to add that extra value to the open library.  
 Accounting error as an independent floating point may allow better accuracy (for example, instead of the upper limit, instead of a full ULP, it will grow from only half).  
 I have a library: 
 
 (Only the main value will be added to Java. My favorites  
 (C ++, Very complicated / complete)  
 (Java, account value, and error as standard deviation)    
 Sample code () runs a ballistic simulation And calculates the number E. Although they are not very demanding of the circumstances.    
 
 
 Maybe it's too late, but look at BAIS Rophile: The computer is completely simple, consumes computer error, and if your errors are centered with easy access to your nominal (middle ... ...).   < / Html>