and 
(that is, 
and 
) are adjacent in the float number system. Subtracting them yields 
, exactly. This situation, in which two nearly equal values are subtracted to produce a (necessarily exact) difference much smaller than either value, is often referred to (with an air of foreboding) as massive cancellation. Be aware that if there's a problem it lies not in the subtraction, which is exact, but in whatever operations lead up to it. For example, in the well known expression 
, for certain values a, b, and c, critical information is lost when the products 
and 
are rounded--before the subtraction and its cancellation occur.
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