Float support on interval arithmetics

[metesynnada]

Is your feature request related to a problem or challenge?

Float32 and Float64 support on interval arithmetics library.

Describe the solution you'd like

In interval arithmetic, we need to ensure that the computed bounds are reliable and accurate, which requires controlling the round-off errors that occur due to finite-precision arithmetic. The IEEE 754 floating-point standard, which is widely used for representing floating-point numbers in computers, specifies several rounding modes that can be used to control how numbers are rounded when they cannot be exactly represented in the available format.

By changing the rounding mode as needed during interval arithmetic operations, we can ensure that the computed intervals accurately enclose the true results, despite round-off errors. When performing operations that should expand the interval (e.g., addition, subtraction, multiplication, and division), we use round down for the lower bound and round up for the upper bound. This approach guarantees that the computed intervals are conservative, and the true results are always enclosed within them.

In summary, the ability to change the rounding mode in floating-point arithmetic, as specified by the IEEE 754 standard, is crucial for ensuring the reliability and accuracy of interval arithmetic computations.

Describe alternatives you've considered

NA

Additional context

NA