This paper presents FloPoCo, a framework for easily designing custom arithmetic datapaths for FPGAs. Its main features are: an important basis of highly optimized arithmetic operators, a unique methodology for frequency-directed pipelining the designed circuits and a flexible test-bench generation suite for numerically validating the designs. The framework was tested for designing several compl...

This paper investigates the usage of floating-point arithmetic on FPGAs for N-Body simulation in natural science. The common aspect of these applications is the simple computing structure where forces between a particle and its surrounding particles are summed up. The role of reduced precision arithmetic is discussed, and our implementation of a floating-point arithmetic library with parameteri...

This paper introduces the smooth operators for arithmetic expressions as an approach to smoothening the search space in Genetic Programming (GP). Smooth operator GP interpolates between arithmetic operators such as ∗ and /, thereby allowing a gradual adaptation to the problem. The suggested approach is compared to traditional GP on a system identification problem.

A summary on the symbolic basic arithmetic operators and aggre-gation operators of linguistic information developed by the authors is presented. In particular, label addition, label diierence, product of a label by a positive real number, and convex combination of labels are shown as the symbolic basic arithmetic operators, and two aggregation operators of linguistic information built using tho...

A summary on the symbolic basic arithmetic operators and aggregation operators of linguistic information developed by the authors is presented. In particular, label addition, label diierence, product of a label by a positive real number, and convex combination of labels are shown as the symbolic basic arithmetic operators, and two aggregation operators of linguistic information built using thos...

Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation o...

units (adders, ALUs, multipliers, dividers) are essential to fault-tolerant computer designs. Some researchers based early design schemes for such units on arithmetic residue codes.1 Others proposed parity prediction schemes for the same purpose.2 These schemes compute the output operand’s parity as a function of the operator’s internal carries and of the input operands’ parities. The basic dra...

We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non-decreasing operators,...

An often overlooked way to increase the efficiency of HPC on FPGA is to tailor, as tightly as possible, the arithmetic to the application. An ideally efficient implementation would, for each of its operations, toggle and transmit just the number of bits required by the application at this point. Conventional microprocessors, with their word-level granularity and fixed memory hierarchy, keep us ...

Redundant operators such as adders and multipliers increase performance (timing and area) of high computational digital circuits. Mixing redundant operators with classical ones is nevertheless complex for circuit designers who might not have necessarily the required arithmetic knowledge. In this context, Computer Aided Design tools considering redundant arithmetic are of interest. In this paper...