Is it possible to set the precision for the subtraction operator?

Question

Hi everyone.
I have two complex double precision numbers that are suppose to be equals. Each one is the result of different sets of equations.
When I subtract one from the other the result is not zero.
I think this can be explain by the fact that they are quite large numbers (about 1E+101), causing the subtraction operator to drop (or round, or do something not legit with) the two numbers. Moreover, if I repeat the subtraction with different large numbers, I obtain about half of the time the expected result (zero) and the rest of the time I obtain a value between 1E+84 and 1E+86.
What I would like is to get the result right everytime, so I thought about setting a precision to the subtraction operator. Is that possible? If it is, how am I suppose to do that and if not, what's wrong with the subtraction operator?
Thanks
tonh

Answer 1

Thought 1: 1e+101 is pretty big!  Do you *need* all your calcs to carry such a big exponent?  For example, can you run all the calcs on values that have been scaled by 1e-100, then at the end of all the calcs scale back by 1e+100? 
Thought 2: If you just need to compare for approximate equality, you could divide the difference by the larger of the two values being subtracted.  If you subtract two virtually equal 1e+101 values, you may get a difference in the order of 1e+85.   The division will give you a ratio of ~1e-16.  Ratios in that realm will mean that the two original values are about as nearly equal as the floating point representation can express.   This type of method scales pretty well to work with both very small and very large floating point numbers.
Thought 3: If the inputs to your calcs are in the order of 1e+85 or less, you may really have your work cut out for you.  You'll need to think carefully about floating point representation error at each step of the calculations to know where you can round, truncate, approximate, etc.  There may be places where rounding will be *necessary* and other places where it is *disastrous*.
To summarize: you need to apply some of your error knowledge to your code.  The 1e+101 calculated values probably don't have more than 6-8 *significant* digits of accuracy, right?  (Most numbers come from some kind of measurement, or a rounded-off value for a scientific constant, etc.)  You'll need to analyze your values and calcs to understand about how many digits of the 1e+101 numbers are truly *significant*.  Then your code will need to treat values which differ by less than that amount as if they are truly equal.
-Kevin P.