Safe addition: Difference between revisions

m
the example is the addition so the multiplication sign is probably a mistake here
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m (the example is the addition so the multiplication sign is probably a mistake here)
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{{Task|Arithmetic operations}}
Implementation of [[wp:Interval_arithmetic|interval arithmetic]] and more generally fuzzy number arithmetic require operations that yield safe upper and lower bounds of the exact result. For example, for an addition, it is the operations *+↑ and *+↓ defined as: ''a'' +↓ ''b'' ≤ ''a'' + ''b'' ≤ ''a'' +↑ ''b''. Additionally it is desired that the width of the interval (''a'' +↑ ''b'') - (''a'' +↓ ''b'') would be about the machine epsilon after removing the exponent part.
 
Differently to the standard floating-point arithmetic, safe interval arithmetic is '''accurate''' (but still imprecise). I.e. the result of each defined operation contains (though does not identify) the exact mathematical outcome.
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