The log encoding has been perceived to be unsuited to arithmetic constraints due to its hindrance to propagation. The surprising performance of PicatSAT, which is a pure eager SAT compiler based on the log encoding, in the MiniZinc Challenge 2016 has revived interest in the log encoding. This paper details the optimizations used in PicatSAT for encoding arithmetic constraints. PicatSAT adopts s...

We study the complexity of securely evaluating an arithmetic circuit over a finite field F in the setting of secure two-party computation with semi-honest adversaries. In all existing protocols, the number of arithmetic operations per multiplication gate grows either linearly with log |F| or polylogarithmically with the security parameter. We present the first protocol that only makes a constan...

The role of language in performing numerical computations has been a topic of special interest in cognition. The "Triple Code Model" proposes the existence of a language-dependent verbal code involved in retrieving arithmetic facts related to addition and multiplication, and a language-independent analog magnitude code subserving tasks such as number comparison and estimation. Neuroimaging stud...

Arithmetic Coding is generalized to provide a method for transforming source output se quences into sequences whose probability distribution approaches any desired probability distribution. A further modi cation in which gaps are introduced be tween source intervals allows arithmetic encoders to produce code sequences with any information rate, enabling the encoder to perform joint source-cha...

It’s no fun to program complex arithmetic in a language that doesn’t support it. Worse, the resulting code is cumbersome, opaque, and hard to maintain. In this column I illustrate how complex arithmetic simplifies algorithms in two-dimensional Cartesian vector space. I also show how straying into the complex plane can make difficult numerical integrals tractable. In other words, I am arguing th...

Most cryptographic software relies on arithmetic functions, and these functions must be implemented correctly and efficiently. In practice, they are written by hand directly in assembly and undergo costly testing. Proof-assistants provide a way to avoid testing without sacrificing efficiency, but formal verification of low-level code is technically difficult. We propose a way to address the sca...

This paper presents experiments on using integer arithmetic with the channel representation. Integer arithmetic allows reduction of memory requirements, and allows efficient implementations using machine code vector instructions, integer-only CPUs, or dedicated programmable hardware such as FPGAs possible. We demonstrate the effects of discretisation on a non-iterative robust estimation techniq...

In this paper, adaptive coding schemes for contour line drawings based on chain code representation is presented. In this scheme, the chain code or the chain-difference code of a contour is modeled as an n-order Markov sequence and then coded with arithmetic coding scheme adaptively. Experimental result shows that the proposed approach is better than some other conventional approaches.

Value speculation is currently widely used in processor designs to increase the overall number of instructions executed per cycle (IPC). Current methods use sophisticated prediction techniques to speculate on the outcome of branches and execute code accordingly. Speculation can be extended to the approximation of arithmetic values. As arithmetic operations are slow to complete in pipelined exec...

This document explains background material for the ling of two patents, EEcient interval width update in arithmetic coding, and Design of fast circuits for code point update in arithmetic coding. The aim is to give the reader the necessary technical foundation to understand the ideas in the patents, and appreciate their signiicance.