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Ingy döt Net 2015-02-20 00:35:01 -05:00
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Task/Safe-addition/00DESCRIPTION
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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.
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.