Ask A Scientist© Computer Science Archive

Index Key:   CSI006
Author:      Danlee
Subject:     Floating Point Accuracy
Text:        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? 

Response #:  1 of 1
Author:      mooney
Text:        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.