By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...

This paper addresses the formalization in higher-order logic of fixed-point arithmetic. We encoded the fixed-point number system and specified the different quantization modes in fixed-point arithmetic such as the directed and even quantization modes. We also considered the formalization of exceptions detection and their handling like overflow and invalid operation. An error analysis is then pe...

This paper presents an architecture for running interactive ray tracing applications on portable devices such as cell phones, PDAs, and head mounted displays and discusses the main issues related to the mapping of this graphics algorithm using fixed-point arithmetic. The paper shows that a floatingpoint arithmetic unit, with its associated power and area consumption, can be avoided by using app...

The transreal numbers are a total number system in which every arithmetical operation is well defined everywhere. This has many benefits over the real numbers as a basis for computation and, possibly, for physical theories. We define the topology of the transreal numbers and show that it gives a more coherent interpretation of two’s complement arithmetic than the conventional integer model. Tra...

High speed execution of arithmetic operations and high degree of precision in real time system are of major concern in any digital signal processing (DSP). Speed of DSP depends on speed of multiplier and algorithm used. In this paper we propose Residue Number System method for fast “carry free” floating point arithmetic operations. Floating Point RNS units have obvious advantages over tradition...

Students have difficulty solving arithmetic word problems containing a relational term that is inconsistent with the required arithmetic operation (e.g., containing the term less, yet requiring addition) rather than consistent. To investigate this consistency effect, students' eye fixations were recorded as they read arithmetic word problems on a computer monitor and stated a solution plan for ...

Two experiments explore the role that spatial format has on arithmetic computations. In printed arithmetic expressions containing both multiplications and additions, terms that are multiplied are often placed closer together than terms that are added. These experiments test whether that external tendency plays a role in how reasoners construct interpretations of simple compound arithmetic expre...

A simple Neural Network model is presented for end-to-end visual learning of arithmetic operations from pictures of numbers. The input consists of two pictures, each showing a 7-digit number. The output, also a picture, displays the number showing the result of an arithmetic operation (e.g., addition or subtraction) on the two input numbers. The concepts of a number, or of an operator, are not ...

In this paper we present an overview of the integration of a nonlinear arithmetic reasoning package into ACL2. We provide a brief operational description of the entire arithmetic package and describe how it fits into ACL2’s operation, including what was needed for the successful introduction of such a facility into an existing automated theorem prover. We describe most of the changes we made to...

Multiplication is a basic operation in any signal processing application. Multiplication is the most important one among the four arithmetic operations like addition, subtraction, and division. Multipliers are usually hardware intensive, and the main parameters of concern are high speed, low cost, and less VLSI area. The propagation time and power consumption in the multiplier are always high. ...