Dataset Sensitive Autotuning of Multi-versioned Code Based on Monotonic Properties

Functional languages allow rewrite-rule systems that aggressively generate a multitude of semantically-equivalent but differently-optimized code versions. In the context of GPGPU execution, this paper addresses the important question of how to compose these code versions into a single program that (near-)optimally discriminates them across different datasets. Rather than aiming at a general autotuning framework reliant on stochastic search, we argue that in some cases, a more effective solution can be obtained by customizing the tuning strategy for the compiler transformation producing the code versions.We present a simple and highly-composable strategy which requires that the (dynamic) program property used to discriminate between code versions conforms with a certain monotonicity assumption. Assuming the monotonicity assumption holds, our strategy guarantees that if an optimal solution exists it will be found. If an optimal solution doesn’t exist, our strategy produces human tractable and deterministic results that provide insights into what went wrong and how it can be fixed.We apply our tuning strategy to the incremental-flattening transformation supported by the publicly-available Futhark compiler and compare with a previous black-box tuning solution that uses the popular OpenTuner library. We demonstrate the feasibility of our solution on a set of standard datasets of real-world applications and public benchmark suites, such as Rodinia and FinPar. We show that our approach shortens the tuning time by a factor of $$6\times $$ 6 × on average, and more importantly, in five out of eleven cases, it produces programs that are (as high as $$10\times $$ 10 × ) faster than the ones produced by the OpenTuner-based technique.

RNS Number Comparator Based on a Modified Diagonal Function

Number comparison has long been recognized as one of the most fundamental non-modular arithmetic operations to be executed in a non-positional Residue Number System (RNS). In this paper, a new technique for designing comparators of RNS numbers represented in an arbitrary moduli set is presented. It is based on a newly introduced modified diagonal function, whose strictly monotonic properties make it possible to replace the cumbersome operations of finding the remainder of the division by a large and awkward number with significantly simpler computations involving only a power of 2 modulus. Comparators of numbers represented in sample RNSs composed of varying numbers of moduli and offering different dynamic ranges, designed using various methods, were synthesized for the 65 nm technology. The experimental results suggest that the new circuits enjoy a delay reduction ranging from over 11% to over 75% compared to the fastest circuits designed using existing methods. Moreover, it is achieved using less hardware, the reduction of which reaches over 41%, and is accompanied by significantly reduced power-consumption, which in several cases exceeds 100%. Therefore, it seems that the presented method leads to the design of the most efficient current hardware comparators of numbers represented using a general RNS moduli set.

Completely monotonicity of class functions involving the polygamma and related functions

In this paper, the authors prove some inequalities and completely monotonic properties of polygamma functions. As an application, we give lower bound for the zeta function on natural numbers. Partially, we answer the fifth and sixth open problems listed in [F. Qi and R. P. Agarwal, On complete monotonicity for several classes of functions related to ratios of gamma functions, J. Inequalities Appl. 2019(36) (2019) 42]. We propose two open problems on completely monotonic functions related to polygamma functions.

Research on Chemical Leakage Based on Three-dimensional Soluble Contaminant Diffusion Model

The leakage and diffusion of pollutants are important issues affecting waters. This paper studies the diffusion of soluble pollutants in water. Based on the three-dimensional hydrodynamic model, a three-dimensional soluble pollutant diffusion model was established and validated. The validation results show that the discrete form of the transport equation used in this model must maintain monotonic properties, and otherwise the model calculation cannot converge. Taking Tianjin Nangang as a representative river section, the cognitive experiment on methanol leakage was carried out to predict the variation characteristics of chemical leakage and diffusion over time in Nangang. The model can be used for chemical leakage and diffusion prediction simulations of other pollutants, and can be used for calculations in runoff and tidal waters.

Oscillatory criteria via linearization of half-linear second order delay differential equations

In the paper, we study oscillation of the half-linear second order delay differential equations of the form \[\left(r(t)(y'(t))^{\alpha}\right)'+p(t)y^{\alpha}(\tau(t))=0.\] We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.