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Name: Danlee
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993

Given double precision an IEEE double precision floating point calculation, is there anything thing that can be said in general about round- off error? For example, given N multiplications and N additions, is there some limit on N below which one can expect, say, seven decimal digits of accuracy?

It is hard to say anything useful in general terms, because the effect of round-off error depends very strongly on the relative sizes of the things you are operating on. Here is the nutshell: Floating point numbers are stored as a number and an exponent, so very large and very small numbers can be stored with equal accuracy (up to a point that depends on how many bits are allocated to the exponent). To ADD two numbers, however, they must first be converted so that they have the same exponent. If the exponents differ by N, you lose N bits of precision somewhere. If you have a very large number and a very small one, you can lose ALL of the smaller number in a single addition.


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