Although floating point computations are simple and efficient, rounding can cause a stream of floating point computations to quietly diverge from the envisioned stream of real computations. Interval arithmetic guarantees rigorous results yet is built from floating point arithmetic. Interval arithmetic will not prevent a series of computations from wandering but it will inform the user how much the computed result could deviate from the real result (the result using real numbers for the computations). The presentation given here differs somewhat from conventional introductions [4, 56, 57], due to the impending generalizations.
The set of intervals is denoted by 
. An interval
is specified by two floating point numbers, a lower
and upper bound.
represents any particular real number
between a and b.
Rather than returning a single floating point number
each operation will return a range of numbers
which the real result is guaranteed to be in.
For example, 
can be represented as the interval
are not ``aware'' that
represents . The operations only
assume that represents some fixed real
number between 
and 
.
| Jeff Tupper | March 1996 |