Yes. Use 14. (49 bits floating point) Use less if you need exact equality.
Thanks, Dar. So, does that mean we can take numbers of any length, go ahead and perform the operation, and then trust the result to 14 digits,
Well, the usual roundoff error analysis of floating point arithmetic still applies. You can always come up with computations that completely lose your accuracy. For instance, suppose that
a=0.12345678901234 is the result of a computation and is accurate to these 14 digits, and
b=0.12345678901233 is likewise accurate to 14 digits, then a-b is 0.10000000000000 times 10-to-the-minus-fourteen, but it's only accurate to one digit.
or do we first have to first preprocess the operands to a certain number of digits according to the type of operation?
No, you must avoid operations that are inherently inaccurate. For instance, in the formula for the solutions of a quadratic equation only one of the plus/minus possibilities is guaranteed to be accurate. For a stable computation of the second you need to use a different formula completely.
Numerical accuracy is not trivial. Most people don't see it until they take a (graduate?) course in numerical mathematics or computational computer science.
--
Victor Eijkhout <[EMAIL PROTECTED]>
tel: 865 974 9308 (W), 865 673 6998 (H), 865 974 8296 (F)
http://www.cs.utk.edu/~eijkhout/
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