Related papers: Fast Parallel Integer Adder in Binary Representati…
A class of two-bit bit flipping algorithms for decoding low-density parity-check codes over the binary symmetric channel was proposed in [1]. Initial results showed that decoders which employ a group of these algorithms operating in…
Multiplication is one of the most important operation in computer arithmetic. Many integer operations such as squaring, division and computing reciprocal require same order of time as multiplication whereas some other operations such as…
Parallelization techniques have become ubiquitous for accelerating inference and training of deep neural networks. Despite this, several operations are still performed in a sequential manner. For instance, the forward and backward passes…
As quantum computers continue to improve and support larger, more complex computations, smart control hardware and compilers are needed to efficiently leverage the capabilities of these systems. This paper introduces a novel approach to…
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…
Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping…
Sorting algorithms are the deciding factor for the performance of common operations such as removal of duplicates or database sort-merge joins. This work focuses on 32-bit integer keys, optionally paired with a 32-bit value. We present a…
Feedforward computation, such as evaluating a neural network or sampling from an autoregressive model, is ubiquitous in machine learning. The sequential nature of feedforward computation, however, requires a strict order of execution and…
Binary machines are a generalization of Feedback Shift Registers (FSRs) in which both, feedback and feedforward, connections are allowed and no chain connection between the register stages is required. In this paper, we present an algorithm…
There are many representations of planar graphs, but few are as elegant as Tur\'an's (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main…
The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications,…
The computational demands of modern AI have spurred interest in optical neural networks (ONNs) which offer the potential benefits of increased speed and lower power consumption. However, current ONNs face various challenges,most…
A new family of sequences is proposed. An example of sequence of this family is more accurately studied. This sequence is composed by the integers $n$ for which the sum of binary digits is equal to the sum of binary digits of $n^2$. Some…
Multi-scalar multiplication (MSM) is crucial in cryptographic applications and computationally intensive in zero-knowledge proofs. MSM involves accumulating the products of scalars and points on an elliptic curve over a 377-bit modulus, and…
Adaptive indexing is a concept that considers index creation in databases as a by-product of query processing; as opposed to traditional full index creation where the indexing effort is performed up front before answering any queries.…
The division operation is important for many areas of data processing. Especially considering today's demand for hardware accelerators for machine learning algorithms, there is a high demand for an efficient calculation of the division…
Stochastic computing (SC) presents high error tolerance and low hardware cost, and has great potential in applications such as neural networks and image processing. However, the bitstream generator, which converts a binary number to…
This work introduces the notion of unoperation $\mathfrak{Un}(\hat{O})$ of some operation $\hat{O}$. Given a valid output of $\hat{O}$, the corresponding unoperation produces a set of all valid inputs to $\hat{O}$ that produce the given…
In this paper, we present Clifford+T gates based quantum circuit design of integer division having $n$ ancillary qubits. The proposed quantum circuit is based on restoring division algorithm. The proposed quantum circuit of integer division…
Optimization problems are central to many important cross-disciplinary applications.In their conventional implementations, the sequential nature of operations imposes strict limitations on the computational efficiency. Here, we discuss how…