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...

The rst high performance oating point unit to support both IBM 360 hexadecimal based oating point architecture and the IEEE 754 Standard binary oating point architecture is described. The S/390 G5 oating point unit supports the new S/390 architecture which includes hexadecimal based short, long, and extended precision formats and IEEE 754 standard single, double, and quad formats. This oating p...

The IEEE-754 floating-point standard, used in nearly all floating-point applications, is considered one of the most important standards. Deep datapath and algorithm complexity have made the verification of such floating-point units a very hard task. Most simulation and reachability analysis verification tools fail to verify a circuit with a deep datapath like most industrial floating-point unit...

Yoshitake Shinkai, Tetsutaro Maruyama, Naomi Yoshizawa Fujitsu Laboratories LTD. Kawasaki, Japan {shinkai, tetutaro, yszw}@flab.fujitsu.co.jp tel +81-44-754-2850 fax +81-44-754-2851 Abstract In this paper, we present a new software RAID technology called file RAID targeted at cluster environments where nodes share files through SAN (Storage Area Network). In it the file system manages separate ...

We give a simple and efficient method to simulate interval operations using only rounding to nearest in IEEE 754. The quality in terms of the diameter of the result is significantly improved compared to existing approaches.

Abstract Verification of programs using floating-point arithmetic is challenging on several accounts. One the difficulties reasoning about such due to peculiarities arithmetic: rounding errors, infinities, non-numeric objects (NaNs), signed zeroes, denormal numbers, different modes, etc. possibility reason model a program computation path by means set ternary constraints form "Image missing"<!-...