Maximum network flow with floating point arithmetic

Floating-Point Arithmetic

Precision Arithmetic: A New Floating-Point Arithmetic

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid the excessive rounding error propagation of conventional floating-point arithmetic. Unlike interval arithmetic, its uncertainty tracking is based on statistics and the central limit theorem, with a much tighter bounding r...

Implementing Taylor models arithmetic with floating-point arithmetic

The implementation of Taylor models arithmetic may use floating-point arithmetic to benefit from the speed of the floatingpoint implementation. The issue is then to take into account the roundoff errors. Here, we assume that the floating-point arithmetic is compliant with the IEEE-754 standard. We show how to get tight bounds of the roundoff errors, and more generally how to get high accuracy f...

Elements of Floating-point Arithmetic

Design Exploration for Decimal Floating-Point Arithmetic

Commercial applications and databases typically store numerical data in decimal format. Currently, however, microprocessors do not provide instructions or hardware support for decimal floating-point arithmetic [ 1 ]. Consequently, decimal numbers are often read into computers, converted to binary numbers, and then processed using binary floating-point arithmetic. Results are then converted back...