Hammering 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...

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...

New directions in floating-point arithmetic

o Konrad Zuse’s Z1, Z3, and Z4 (1936–1945): 22-bit (Z1 and Z3) and 32-bit Z4 with exponent range of 2±63 ≈ 10±19 o Burks, Goldstine, and von Neumann (1946) argued against floating-point arithmetic o It is difficult today to appreciate that probably the biggest problem facing programmers in the early 1950s was scaling numbers so as to achieve acceptable precision from a fixed-point machine, Mart...