Abstract
When dealing with floating-point numbers there are several sources of error which can drastically reduce the numerical quality of computed results. Among those errors, the loss of significance, or cancellation, occurs during for example the subtraction of two nearly equal numbers. In this article, we propose a representation format named Floating-Point Adaptive Noise Reduction (FP-ANR). This format embeds cancellation information directly into the floating-point representation format thanks to a dedicated pattern. With this format, unsignificant trailing bit lost during cancellation are removed from every manipulated floating-point number. The immediate consequence is that it increases the numerical confidence of computed values. The proposed representation format corresponds to a simple and efficient implementation of significance arithmetic based and compatible with the IEEE-754 standard.