It has been widely known that complete decoding for binary linear codes can be regarded as an linear integer programming problem with binary arithmetic conditions. Conti and Traverso [8] have proposed an efficient algorithm which uses Gröbner bases to solve integer programming with ordinary integer arithmetic conditions. Ikegami and Kaji [11] extended the Conti-Traverso algorithm to solve integ...

Once in a great while, the programmer has need for floating point arithmetic in greater precision than the hardware provides. This capability is usually not performance critical, since most performance critical code deals with measured quantities in the physical world, where it is hard to imagine a measurement precision that exceeds the sixteen or so decimal digits provided by standard IEEE-754...

We use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects (rooted ordered trees representing hereditarily finite sequences and rooted ordered binary trees representing Gödel’s System T types). This paper focuses on ...

Reconfigurable architectures offer potential for performance enhancement by specializing the implementation of floating-point arithmetic. This paper presents FloatWatch, a dynamic execution profiling tool designed to identify where an application can benefit from reduced precision or reduced range in floating-point computations. FloatWatch operates on x86 binaries, and generates a profile outpu...

This paper describes work undertaken converting the Artificial Stock Market (LeBaron et al., 1999; Johnson, 2002) to using interval arithmetic instead of floating point arithmetic, the latter having been shown in an earlier article to be the cause of changed behaviour in the ASM (Polhill et al., in press). Results of both a naive (potentially automatable) conversion and one involving a more in-...

Reconfigurable architectures offer potential for performance enhancement by specializing the implementation of floating-point arithmetic. This paper presents FloatWatch, a dynamic execution profiling tool designed to identify where an application can benefit from reduced precision or reduced range in floating-point computations. FloatWatch operates on x86 binaries, and generates a profile outpu...

We present three versions of the revised spectral test for the analysis of liner congruential random number generators. One is a Fortran 90 version of the code presented in 6] which extends the range of integer arithmetic operations by performing the arithmetic using oating-point numbers. The range of modulus values which may be analyzed is determined by the length of the mantissa. The other tw...

The paper presents (human-oriented) specification and (penand-paper) verification of the square root function. The function implements Newton method and uses a look-up table for initial approximations. Specification is done in terms of total correctness assertions with use of precise arithmetic and the mathematical square root √ . . ., algorithms are presented in pseudo-code with explicit disti...

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.