Unbiased Rounding for HUB Floating-point Addition

Copyright (c) 2018 IEEE doi:10.1109/TC.2018.2807429Half-Unit-Biased (HUB) is an emerging format based on shifting the represented numbers by half Unit in the Last Place. This format simplifies two’s complement and roundto- nearest operations by preventing any carry propagation. This saves power consumption, time and area. Taking into account that the IEEE floating-point standard uses an unbiased rounding as the default mode, this feature is also desirable for HUB approaches. In this paper, we study the unbiased rounding for HUB floating-point addition in both as standalone operation and within FMA. We show two different alternatives to eliminate the bias when rounding the sum results, either partially or totally. We also present an error analysis and the implementation results of the proposed architectures to help the designers to decide what their best option are.TIN2013-42253-P, TIN2016-80920-R, JA2012P12-TIC-169

A Generic Library for Floating-Point Numbers and Its Application to Exact Computing

International audienceIn this paper we present a general library to reason about floating-point numbers within the Coq system. Most of the results of the library are proved for an arbitrary floating-point format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors

Sound Randomized Smoothing in Floating-Point Arithmetics

Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of $1.26$ around a point, even though there is an adversarial example in the distance $0.8$ and extend this example further to provide false certificates for CIFAR10. We discuss the implicit assumptions of randomized smoothing and show that they do not apply to generic image classification models whose smoothed versions are commonly certified. In order to overcome this problem, we propose a sound approach to randomized smoothing when using floating-point precision with essentially equal speed and matching the certificates of the standard, unsound practice for standard classifiers tested so far. Our only assumption is that we have access to a fair coin.Comment: Submitted NeurIPS 202

Application of Suction-cup-attached VHF Transmitters to the Study of Beluga, Delphinapterus leucas, Surfacing Behavior in Cook Inlet, Alaska

Suction-cup-attached VHF radio transmittes were deployed on belugas, Delphinapterus leucas, in Cook Inlet, Alaska, in 1994 and 1995 to characterize the whales' surfacing behavior. Data from video recordings were also used to characterize behavior of undisturbed whales and whales actively pursued for tagging. Statistics for dive intervals (time between the midpoints of contiguous surfacings) and surfacing intevals (time at the surface per surfacing) were estimated. Operations took place on the tidal delta of the Susitna and Little Susitna Rivers. During the 2-yr study, eight whales were successfully tagged, five tags remained attached for >60 min, and data from these were used in the analyses. Mean dive interval was 24.1 sec (interwhale SD=6.4 sec, n=5). The mean surfacing interval, as determined from the duration of signals received from the radio transmitters, was 1.8 sec (SD=0.3 sec, n=125) for one of the whales. Videotaped behaviors were categorized as "head-lifts" or "slow-rolls." Belugas were more likely to head-lift than to slow-roll during vessel approaches and tagging attempts when compared to undisturbed whales. In undisturbed groups, surfacing intervals determined from video records were significantly different between head-lifting (average = 1.02 sect, SD=0.38 sed, n=28) and slow-rolling whales (average = 2.45 sec, SD=0.37 sec, n=106). Undisturbed juveniles exhibited shorter slow-roll surfacing intervals (average = 2.25 sec, SD=0.32 sec, n=36) than adults (average = 2.55 sec, SD=0.36 sec, n=70). We did not observe strong reactions by the belugas to the suction-cup tags. This tagging method shows promise for obtaining surfacing data for durations of several days

The Flexible Exchange Rate System: Experience and Alternatives

We review ten aspects of how floating exchange rates have worked in practice, contrasted with ten characteristics that the system was supposed to have in theory. We conclude that the foreign exchange market is characterized by high transactions-volume, short-term horizons, and an absence of stabilizing speculation. As a result, the exchange rate at times strays from the equilibrium level dictated by fundamentals, contrary to theory. We then look at ten proposed alternatives to the current system. Four entail decentralized policy rules: new classical macroeconomics, a gold standard, monetarism, and nominal income targeting. Four foresee enhanced international coordination: G-7 "objective indicators," Williamson target zones, McKinnon "world monetarism," and a "Hosomi Fund." Two propose enhanced independence: a "Tobin tax" on transactions, and a dual exchange rate. We conclude that one might build a case for intervention from the observed failure of international financial markets to behave as in the theoretical ideal, but that government intervention in practice is just as likely to fall short of the theoretical ideal