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Interval package: Difference between revisions
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→Arithmetic operations
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Arithmetic functions in a set-based interval arithmetic follow these rules: Intervals are sets. They are subsets of the set of real numbers. The interval version of an elementary function such as sin(''x'') is essentially the natural extension to sets of the corresponding point-wise function on real numbers. That is, the functions are evaluated for each number in the interval where the function is defined and the result must be an enclosure of all possible values that may occur. | Arithmetic functions in a set-based interval arithmetic follow these rules: Intervals are sets. They are subsets of the set of real numbers. The interval version of an elementary function such as sin(''x'') is essentially the natural extension to sets of the corresponding point-wise function on real numbers. That is, the functions are evaluated for each number in the interval where the function is defined and the result must be an enclosure of all possible values that may occur. | ||
One operation that should be noted is the <code>fma</code> function. It computes '''''x''''' * '''''y''''' + '''''z''''' in a single step and is much slower than multiplication followed by addition. However, it is more accurate and therefore preferred in some situations. | One operation that should be noted is the <code>fma</code> function (fused multiply and add). It computes '''''x''''' * '''''y''''' + '''''z''''' in a single step and is much slower than multiplication followed by addition. However, it is more accurate and therefore preferred in some situations. | ||
=== Reverse arithmetic operations === | === Reverse arithmetic operations === | ||