Sinking Point: Dynamic Precision Tracking for Floating-Point

We present sinking-point, a floating-point-like number system that tracks precision dynamically though computations. With existing floating-point number systems, such as the venerable IEEE 754 standard, numerical results do not inherently contain any information about their precision or accuracy; to determine if a result is numerically accurate, a separate analysis must be performed. By contrast, sinking-point records the precision of each intermediate value and result computed, so highly imprecise results can be identified immediately. Compared to IEEE 754 floating-point, sinking-point's representation requires only a few additional bits of storage, and computations require only a few additional bitwise operations. Sinking-point is fully generalizable, and can be extended to provide dynamic error tracking for nearly any digital number system, including posits.