We present a fixed point architecture (source VHDL code is provided) for powering computation. The fully customized architecture, based on the expanded hyperbolic CORDIC algorithm, allows for design space exploration to establish tradeoffs among design parameters (numerical format, number of iterations), execution time, resource usage and accuracy. We also generate Pareto-optimal realizations i...

• Forward and Inverse 32-, 64-, 128-, 256-, 512-, 1,024-, and 2,048-Point Complex FFT • Decimation–In-Time (DIT) Radix-2 Implementation Optimized for Actel FPGAs • Selection of Unconditional or Conditional Block Floating-Point Scaling • Embedded RAM-Block-Based Twiddle Factor Generator • 8to 16-Bit Configurable Input/Output Data and Twiddle Coefficients Precision • Naturally Ordered Input and O...

Many inequalities involving the functions ln, exp, sin, cos, etc., can be proved automatically by MetiTarski: a resolution theorem prover (Metis) modified to call a decision procedure (QEPCAD) for the theory of real closed fields. The decision procedure simplifies clauses by deleting literals that are inconsistent with other algebraic facts, while deleting as redundant clauses that follow algeb...

G4LTL-ST automatically synthesizes control code for industrial Programmable Logic Controls (PLC) from timed behavioral specifications of inputoutput signals. These specifications are expressed in a linear temporal logic (LTL) extended with non-linear arithmetic constraints and timing constraints on signals. G4LTL-ST generates code in IEC 61131-3-compatible Structured Text, which is compiled int...

Continuing the work K. C. Das, I. Gutman, B. Furtula, On second geometric-arithmetic index of graphs, Iran. J. Math Chem., 1(2) (2010) 17-28, in this paper we present lower and upper bounds on the third geometric-arithmetic index GA3 and characterize the extremal graphs. Moreover, we give Nordhaus-Gaddum-type result for GA3.

Arithmetic coding is a method for data compression. Although the idea was developed in the 1970’s, it wasn’t until the publication of an “accessible implementation” [14] that it achieved the popularity it has today. Over the past ten years arithmetic coding has been refined and its advantages and disadvantages over rival compression schemes, particularly Huffman [9] and Shannon-Fano [5] coding,...

Sparse Matrix Vector multiplication (SpMV) is one of the most important operation for exact sparse linear algebra. A lot of research has been done by the numerical community to provide efficient sparse matrix formats. However, when computing over finite fields, one need to deal with multi-precision values and more complex operations. In order to provide highly efficient SpMV kernel over finite ...

While the equation above is correct, it is not very useful for incremental updates since the equation above updates the checksum C, rather than the 1’s complement of the checksum, ̃C, which is the value stored in the checksum field. In addition, it suffers because the notation does not clearly specify that all arithmetic, including the unary negation, must be performed one’s complement, and so i...

We show that the theory of D(6 g), where g is a 2-generic or a 1-generic degree below 0′, interprets true first order arithmetic. To this end we show that 1-genericity is sufficient to find the parameters needed to code a set of degrees using Slaman and Woodin’s method of coding in Turing degrees. We also prove that any recursive lattice can be embedded below a 1-generic degree preserving top a...

Fifty years ago, John McCarthy and James Painter (1967) published the first paper on compiler verification, in which they showed how to formally prove the correctness of a compiler that translates arithmetic expressions into code for a register-based machine. In this article, we revisit this example in a modern context, and show how such a compiler can now be calculated directly from a specific...