Interval Arithmetic
The data type interval provides a clean and efficient way to compute
approximately with reals by inexact interval arithmetic.
Each input number xi is converted into an interval {xi} and all real
operations are replaced by interval operations. If z is the result of
the exact real calculation and I is the interval computed by interval,
then I contains z, i.e., I is a more or less accurate approximation of
z. In many cases I is small enough to be useful, e.g., to know the sign
of the computation.
Example of Floating Point
Filter, Interval, and Integer Computation
Strengths
- computes an error bound for the result of a computation
- more efficient than exact real arithmetic
- member function
I.sign_is_known() returns true if and
only if all numbers in I have the same sign.
Disadvantages
- slower than corresponding operations on doubles
Tips
Use Interval Arithmetic to speed up your computations with reals, and recompute
with real if the result is not unique. |
See also:
Floating Point Filters
Integers of Arbitrary Length
Algebraic Real Numbers
Rational Numbers
Big Floatingpoint Numbers
Vectors and Matrices with Integer Entries
Vectors and Matrices with Double Entries
Rational Vectors
Functions of numerical analysis
Manual Page Interval Arithmetic
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