Rounding of Floating Point Intervals

Correct rounding of the infinitely precise arithmetic as prescribed for the floating point operations is not always attainable with reasonable resource. Many functions return explicit or implicit interval outputs. Yet, the IEEE standard does not allow ecient use of this information. We present how the IEEE rounding mechanisms can be extended to accept interval rounding which is shown to be a first natural step toward non infinitely precise rounding. Along with the proposal of this faithful rounding for non-infinitely precise operation, we present the intrinsic properties of this new rounding mechanism.