Results for “coded source” — Page 19

DOE OSTI2019

Cosmic Microwave Background Anisotropy Numerical Solution (CMBAns) I: An Introduction to $C_l$ Calculation

Cosmological Boltzmann codes are often used by researchers for calculating the CMB angular power spectra from different theoretical models, for cosmological parameter estimation, etc. Therefore, the accuracy of a Boltzmann code is of utmost importance. Different Markov Chain Monte Carlo based parameter estimation algorithms typically require 10^3 - 10^4 iterations of Boltzmann code. This makes the time complexity of such codes another critical factor. In the last two decades, several Boltzmann packages, such as CMBFAST, CAMB, CMBEasy, CLASS etc., have been developed. In this paper, we present a new cosmological Boltzmann code, CMBAns, that can be used for accurate calculation of the CMB power spectrum. At present, CMBAns is developed for a flat background matrix. It is mostly written in the C language. However, we borrowed the concept of class from C++. This gives researchers the flexibility to develop their own independent package based on CMBAns, without an in-depth understanding of the source code. We also develop multiple stand-alone facilities which can be directly compiled and run on a given parameter set. In this paper, we discuss all the mathematical formulation, approximation schemes, integration methods etc., that are used in CMBAns. The package will be made available through github for public use in the near future.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Enhancing ChatPORT with CUDA-to-SYCL Kernel Translation Capability

Large Language Models (LLMs) have shown strong capabilities in general code translation. However, code translation involving parallel programming models remains largely unexplored. This work enhances the capabilities of code LLMs in CUDA-to-SYCL kernel translation with parameter-efficient fine-tuning. The resultant fine-tuned LLM, called ChatPORT, is an effort to provide high-fidelity translations from one programming model to another. We describe the preparation of datasets from heterogeneous computing benchmarks for model fine-tuning and testing, the parameter-efficient fine-tuning of 19 open-source code models ranging in size from 0.5 to 34 billion parameters and evaluate the correctness rates of the SYCL kernels by the fine-tuned models. The experimental results show that most code models fail to translate CUDA codes to SYCL correctly. However, fine-tuning these models using a small set of CUDA and SYCL kernels can enhance the capabilities of these models in kernel translation. Depending on the sizes of the models, the correctness rate ranges from 19.9% to 81.7% for a test dataset of 62 CUDA kernels.

Jin, Zheming [ORNL] (ORCID:000000027197780X)↗

DOE OSTI2025

Code Coverage Status of the ARC Code RCT

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. REBUS plays a pivotal role in the ARC system as the primary fuel cycle analysis capability for fast reactor problems. Over its 60 year history, ARC software usage with REBUS has been applied to numerous fast and thermal spectrum reactor analysis projects with good to excellent comparison against experiments. The RCT code is a later addition and uses the REBUS restart files to define its input. The RCT code was built to provide pin depletion details on EBR-II models and thus many features of RCT were specifically tailored to the needs of EBR-II models. Additional approximations were invoked which are likely only valid for the EBR-II reactor and the particular fuel management that was done for it. The purpose of the present work is to identify a set of test problems for RCT and assess the code coverage for those test problems. The goal is to document what parts of the existing RCT code are touched by the set of test problems and which are not. Because no detailed verification work has been done on RCT, the existing regression testing suite was chosen for the code coverage assessment. The code coverage analysis of RCT was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of RCT. The detailed coverage tables are given for each part of RCT. As will be discussed and shown, some parts of the RCT capability that are known to be used by the EBR-II analysis work are not tested by the regression testing suite. These aspects should be resolved before major source code changes are taken for the RCT software. Because REBUS and DIF3D are not subroutines of RCT, the coverage changes in both of those codes is not altered by RCT. The same is true for all of the modules of DIF3D that are used by RCT such as SYSLIB and SEGLIB.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Fiscal Year 2025 Software Quality Assurance Activities for the ARC Software

The continued goal of the ARC SQA project in the Advanced Reactor Technologies program of DOE is to resolve the QA gaps for the ARC software that limit, or prevent, commercialization of the software for industry users. This project started in earnest in fiscal year 2023 which saw the entire code system moved from a SVN repository to a GitLab repository and an associated software quality assurance plan (SQAP) developed and ratified. Most of the QA gaps in the ARC software were identified in collaboration with industry partners and work begin in fiscal year 2023 and continued through 2024 and 2025. The continuous integration testing was extended to RCT, DASSH, and SE2ANL. Minor changes were required to the original continuous integration methodology to make this happen. When full confidence in the methodology is complete, a report will be created to detail the automated regression testing methodology and minor reports will be created to detail the tolerance settings that have been applied to the output for each ARC code. The primary documentation that is missing includes user manuals, user guides, software verification reports, and code coverage assessments. The DASSH, SE2ANL, and SE2RCT manuals were completed this fiscal year. A review of the SE2ANL software identified that it is unrealistic to include updated correlations or different geometry models and it was scheduled for deprecation in favor of DASSH. The SE2ANL manual is essential for SE2RCT as they are similar but quite different in purpose. The only piece of software missing a manual consistent with the source code is NUBOW-3D which is a focus of the coming year. The code coverage report for DIF3D was updated and code coverage reports were created for REBUS, RCT, PERSENT, GAMSRC, and DASSH. Minor coverage issues were identified for all of these pieces of software which did not prevent the work done to transition them to the OneAPI compiler. Because SE2ANL was scheduled for deprecation, it was not transitioned, but it was successfully tested with the OneAPI compiler. This leaves SE2RCT and NUBOW-3D as the only pieces of software not transitioned to OneAPI and further work is required to get SE2RCT to work properly. The SE2RCT software transition will begin early next year while the NUBOW-3D software requires a manual before it can begin. Software verification work has been completed for DIF3D, REBUS, GAMSOR, GAMSRC, VARPOW, EvaluateFlux, and SUMMAR. The PERSENT software verification work was completed this year which was somewhat delayed because of unexpected bugs in the software. The PERSENT manual was updated to detail some of the issues and discuss the bowing reactivity worth feature added in the previous fiscal year. The RCT, DASSH, SE2RCT, and NUBOW-3D software are the only maintained pieces of software without verification reports. The software verification work for DASSH will be a focus in the upcoming fiscal year and it is hoped that some of the test cases created can serve as verification tests for SE2RCT. The NUBOW-3D work will begin when the manual and requirements report are completed. Only minor industry partner software development funds were provided this year. The DASSH software was updated to handle general axial geometry for each assembly and the NUBOW-3D software was updated to incorporate a new input format and better output. Overall progress on resolving the QA gaps has been good this year.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Fiscal Year 2025 Software Quality Assurance Activities for the ARC Software

The continued goal of the ARC SQA project in the Advanced Reactor Technologies program of DOE is to resolve the QA gaps for the ARC software that limit, or prevent, commercialization of the software for industry users. This project started in earnest in fiscal year 2023 which saw the entire code system moved from a SVN repository to a GitLab repository and an associated software quality assurance plan (SQAP) developed and ratified. Most of the QA gaps in the ARC software were identified in collaboration with industry partners and work begin in fiscal year 2023 and continued through 2024 and 2025. The continuous integration testing was extended to RCT, DASSH, and SE2ANL. Minor changes were required to the original continuous integration methodology to make this happen. When full confidence in the methodology is complete, a report will be created to detail the automated regression testing methodology and minor reports will be created to detail the tolerance settings that have been applied to the output for each ARC code. The primary documentation that is missing includes user manuals, user guides, software verification reports, and code coverage assessments. The DASSH, SE2ANL, and SE2RCT manuals were completed this fiscal year. A review of the SE2ANL software identified that it is unrealistic to include updated correlations or different geometry models and it was scheduled for deprecation in favor of DASSH. The SE2ANL manual is essential for SE2RCT as they are similar but quite different in purpose. The only piece of software missing a manual consistent with the source code is NUBOW-3D which is a focus of the coming year. The code coverage report for DIF3D was updated and code coverage reports were created for REBUS, RCT, PERSENT, GAMSRC, and DASSH. Minor coverage issues were identified for all of these pieces of software which did not prevent the work done to transition them to the OneAPI compiler. Because SE2ANL was scheduled for deprecation, it was not transitioned, but it was successfully tested with the OneAPI compiler. This leaves SE2RCT and NUBOW-3D as the only pieces of software not transitioned to OneAPI and further work is required to get SE2RCT to work properly. The SE2RCT software transition will begin early next year while the NUBOW-3D software requires a manual before it can begin. Software verification work has been completed for DIF3D, REBUS, GAMSOR, GAMSRC, VARPOW, EvaluateFlux, and SUMMAR. The PERSENT software verification work was completed this year which was somewhat delayed because of unexpected bugs in the software. The PERSENT manual was updated to detail some of the issues and discuss the bowing reactivity worth feature added in the previous fiscal year. The RCT, DASSH, SE2RCT, and NUBOW-3D software are the only maintained pieces of software without verification reports. The software verification work for DASSH will be a focus in the upcoming fiscal year and it is hoped that some of the test cases created can serve as verification tests for SE2RCT. The NUBOW-3D work will begin when the manual and requirements report are completed. Only minor industry partner software development funds were provided this year. The DASSH software was updated to handle general axial geometry for each assembly and the NUBOW-3D software was updated to incorporate a new input format and better output. Overall progress on resolving the QA gaps has been good this year.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

ORCHA: A performance portability system for extreme heterogeneity

Heterogeneity is the prevalent trend in the rapidly evolving high-performance computing (HPC) landscape in both hardware and application software. The diversity in hardware platforms, currently comprising various accelerators and a future possibility of specializable chiplets, poses a significant challenge for scientific software developers aiming to harness optimal performance across different computing platforms while maintaining the quality of solutions when their applications are simultaneously growing more complex. Code synthesis and code generation can provide mechanisms to mitigate this challenge. We have developed a divide and conquer approach where different aspects of performance are handled by different stand-alone tools that are interfaced with the application through generated code. This portability system, ORCHA, enables users to configure and orchestrate their computations among available resources on a platform by specifying a high-level recipe, thereby permitting a many-to-many paradigm where each recipe results in a different variant of the application. The core design goal is to let users decide the application’s hardware mapping and orchestration by editing only the high-level recipe—without modifying the maintained source code or binding the application to a particular runtime system. Tools in ORCHA distribution are: CG-Kit for translating the recipe into an execution graph; Milhoja to execute the graph by orchestrating data and task movement among hardware resources; and Macroprocessor that enables users to define their own code-shorthand for higher composability and easier management of code variants. Additionally, the design of ORCHA permits tools to work in a plug-and-play mode where the application can build and run without CG-Kit and Milhoja, and either tool can be swapped out for other tools with similar capabilities by modifying the code generation portion of ORCHA. In this paper, we describe the design of ORCHA and the role that code-generation plays in isolating applications from tools. We demonstrate the breadth of configurations ORCHA enables with a case study in which an application configuration is realized on three distinct hardware mappings—a GPU-centric, a CPU/GPU balanced, and a CPU/GPU concurrent layouts by using different recipes.

Lee, Youngjun↗

DOE OSTI2014

Gyrokinetic Particle Simulation of Compressible Electromagnetic Turbulence in High-β Plasmas

Supported by this award, the PI and his research group at the University of California, Irvine (UCI) have carried out computational and theoretical studies of instability, turbulence, and transport in laboratory and space plasmas. Several massively parallel, gyrokinetic particle simulation codes have been developed to study electromagnetic turbulence in space and laboratory plasmas. In space plasma projects, the simulation codes have been successfully applied to study the spectral cascade and plasma heating in kinetic Alfven wave turbulence, the linear and nonlinear properties of compressible modes including mirror instability and drift compressional mode, and the stability of the current sheet instabilities with finite guide field in the context of collisionless magnetic reconnection. The research results have been published in 25 journal papers and presented at many national and international conferences. Reprints of publications, source codes, and other research-related information are also available to general public on the PI’s webpage (http://phoenix.ps.uci.edu/zlin/). Two PhD theses in space plasma physics are highlighted in this report.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

RNAcentral: an international database of ncRNA sequences

The field of non-coding RNA biology has been hampered by the lack of availability of a comprehensive, up-to-date collection of accessioned RNA sequences. Here we present the first release of RNAcentral, a database that collates and integrates information from an international consortium of established RNA sequence databases. The initial release contains over 8.1 million sequences, including representatives of all major functional classes. A web portal (http://rnacentral.org) provides free access to data, search functionality, cross-references, source code and an integrated genome browser for selected species.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Coupling TRACE with nodal neutronics code Ants using the Exterior Communications Interface and VTT's multi-physics driver Cerberus

In this paper a recently developed coupling between system code TRACE and nodal neutronics code Ants is presented. The TRAC/RELAP Advanced Computational Engine (TRACE) is a reactor system code developed by U.S. Nuclear Regulatory Commission (NRC). The code has been designed to analyse loss-of-coolant accidents (LOCAs), operational transients and other accident scenarios in light water reactors. Ants is the reduced order nodal neutronics code of the Kraken framework. The diffusion solution method in Ants is based on the Analytic Function Expansion Nodal method (AFEN) and Flux Expansion Nodal Method (FENM). Rectangular, hexagonal and triangular geometries are supported. Both steady state and burnup problems including micro-depletion can be simulated. The coupling is implemented using VTT's multi-physics driver Cerberus and the Exterior Communications Interface (ECI) which is supplied with TRACE and enables the coupling of TRACE without source code modifications. The main focus in the paper is on describing the TRACE-Ants coupling in detail in order to share to other code developers what we have learned from the ECI based coupling process. The coupled code system is briefly tested by simulating a simple transient in a SMR core initiated by control rod movement. The results of the test calculation look reasonable and more complicated test cases will be modelled in the near future.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

HiPACE++: A portable, 3D quasi-static particle-in-cell code

Modeling plasma accelerators is a computationally challenging task and the quasi-static particle-in-cell algorithm is a method of choice in a wide range of situations. In this work, we present the first performance-portable, quasi-static, three-dimensional particle-in-cell code HiPACE++. By decomposing all the computation of a 3D domain in successive 2D transverse operations and choosing appropriate memory management, HiPACE++ demonstrates orders-of-magnitude speedups on modern scientific GPUs over CPU-only implementations. The 2D transverse operations are performed on a single GPU, avoiding time-consuming communications. The longitudinal parallelization is done through temporal domain decomposition, enabling near-optimal strong scaling from 1 to 512 GPUs. HiPACE++ is a modular, open-source code enabling efficient modeling of plasma accelerators from laptops to state-of-the-art supercomputers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. Here, in this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Automated Crystal Orientation Mapping in py4DSTEM using Sparse Correlation Matching

Crystalline materials used in technological applications are often complex assemblies composed of multiple phases and differently oriented grains. Robust identification of the phases and orientation relationships from these samples is crucial, but the information extracted from the diffraction condition probed by an electron beam is often incomplete. We have developed an automated crystal orientation mapping (ACOM) procedure which uses a converged electron probe to collect diffraction patterns from multiple locations across a complex sample. We provide an algorithm to determine the orientation of each diffraction pattern based on a fast sparse correlation method. We demonstrate the speed and accuracy of our method by indexing diffraction patterns generated using both kinematical and dynamical simulations. We have also measured orientation maps from an experimental dataset consisting of a complex polycrystalline twisted helical AuAgPd nanowire. From these maps we identify twin planes between adjacent grains, which may be responsible for the twisted helical structure. All of our methods are made freely available as open source code, including tutorials which can be easily adapted to perform ACOM measurements on diffraction pattern datasets.

36 MATERIALS SCIENCE↗

DOE OSTI2016

SU-G-BRB-02: An Open-Source Software Analysis Library for Linear Accelerator Quality Assurance

Purpose: Routine linac quality assurance (QA) tests have become complex enough to require automation of most test analyses. A new data analysis software library was built that allows physicists to automate routine linear accelerator quality assurance tests. The package is open source, code tested, and benchmarked. Methods: Images and data were generated on a TrueBeam linac for the following routine QA tests: VMAT, starshot, CBCT, machine logs, Winston Lutz, and picket fence. The analysis library was built using the general programming language Python. Each test was analyzed with the library algorithms and compared to manual measurements taken at the time of acquisition. Results: VMAT QA results agreed within 0.1% between the library and manual measurements. Machine logs (dynalogs & trajectory logs) were successfully parsed; mechanical axis positions were verified for accuracy and MLC fluence agreed well with EPID measurements. CBCT QA measurements were within 10 HU and 0.2mm where applicable. Winston Lutz isocenter size measurements were within 0.2mm of TrueBeam’s Machine Performance Check. Starshot analysis was within 0.2mm of the Winston Lutz results for the same conditions. Picket fence images with and without a known error showed that the library was capable of detecting MLC offsets within 0.02mm. Conclusion: A new routine QA software library has been benchmarked and is available for use by the community. The library is open-source and extensible for use in larger systems.

43 PARTICLE ACCELERATORS↗

DOE OSTI2012

Development of Internal Non-Contacting Profilomerty Superconducting RF Cavities

Under the scope of this CRADA Microdynamics contributed only by transferring to JLab the control source code (on non-disclosure basis) for the CYCLOPS system that we purchased from them earlier. They invested no additional design or engineering time. They made the business decision that there was no market for this system as a product. We at JLab budgeted in-house funds to work on on continued improvements. Per Costpoint, we spent a total of $21,699 loaded on this project. Additional funds were available to hire a contract programmer to make needed program changes, however, the source language used is an older one, no longer taught or in use. I was unable to find any capable programmer. So, the work came to a halt. The CRADA expired. The system is not presently functional. We estimate that a meaningful redesign would require $250,000 in labor and materials. So, while the promised function of the system would be unique and very helpful for some of our technical trouble-shooting needs, it is presently dead in the water and very, very far down on our unfunded priorities list.

Reece, Charles↗

DOE OSTI2022

Shifting Left for Machine Learning: An Empirical Study of Security Weaknesses in Supervised Learning-based Projects

Context: Supervised learning-based projects (SLPs), i.e., software projects that use supervised learning algorithms, such as decision trees are useful for performing classification-related tasks. Yet, security weaknesses, such as the use of hard-coded passwords in SLPs, can make SLPs susceptible to security attacks. A characterization of security weaknesses in SLPs can help practitioners understand the security weaknesses that are frequent in SLPs and adopt adequate mitigation strategies. Objective: The goal of this paper is to help practitioners se-curely develop supervised learning-based projects by conducting an empirical study of security weaknesses in supervised learning-based projects. Methodology: We conduct an empirical study by quantifying the frequency of security weaknesses in 278 open source SLPs. Results: We identify 22 types of security weaknesses that occur in SLPs. We observe ‘use of potentially dangerous function’ to be the most frequently occurring security weakness in SLPs. Of the identified 3,964 security weaknesses, 23.79 % and 40.49 % respectively, appear for source code files used to train and test models. We also observe evidence of co-location, e.g., instances of command injection co-locates with instances of potentially dangerous function. Conclusion: Based on our findings, we advocate for a shift left approach for SLP development with security-focused code reviews, and application of security static analysis.

Bhuiyan, Farzana Ahamed↗

DOE OSTI2023

CLC: A cross-level program characterization method

Characterization of program execution plays a key role in performance improvement. There are numerous transformations applied to each step that a program takes on its lowering from source code to a compiler intermediate representation to machine language to microarchitecture-specific execution. The unpredictable benefit of each transformation step could lead a notionally superior algorithm to exhibit inferior performance once actually run, and it can be hard to discern which step in the transformation path contradicted the code developer’s assumptions. Conventional approaches to program-execution characterization consider the behavior after only a single one of those steps, which limits the information that can be provided to the user. To help address the issue of myopic views of program execution, this paper presents a novel cross-level characterization approach for understanding the behavior of program execution at different levels in the process of writing, compiling, and running a program. We show that this approach provides a richer view of the sources of performance gains and losses and helps identify program execution in a more accurate manner.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

ITS Version 6.7: The Integrated TIGER Series of Coupled Electron/Photon Monte Carlo Transport Codes User's Manual

ITS is a powerful software package permitting state-of-the-art Monte Carlo solution of linear time-independent coupled electron/photon radiation transport problems, with or without the presence of macroscopic electric and magnetic fields of arbitrary spatial dependence. Our goal has been to simultaneously maximize operational simplicity and physical accuracy. Through a set of preprocessor directives, the user selects one of the many ITS codes. The ease with which the make system is applied combines with an input scheme based on order-independent descriptive keywords that makes maximum use of defaults and internal error checking to provide experimentalists and theorists alike with a method for the routine but rigorous solution of sophisticated radiation transport problems. Physical rigor is provided by employing accurate cross sections, sampling distributions, and physical models for describing the production and transport of the electron/photon cascade from 1.0 GeV down to 1.0 keV. The availability of source code permits the more sophisticated user to tailor the codes to specific applications and to extend the capabilities of the codes to more complex applications. Version 6, the latest version of ITS, contains (1) improvements to the ITS 5.0 codes, and (2) conversion to Fortran 95. The general user friendliness of the software has been enhanced through memory allocation to reduce the need for users to modify and recompile the code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2018

pysrim: Automation, Analysis, and Plotting of SRIM Calculations

The behavior of ions traveling through a material is of great interest to many fields. For instance, radiation damage in nuclear materials and ion beam modification of materials are most concerned with understanding the formation and evolution of defects along the ion path (Was 2016). Some of the important properties that can be gleaned from investigating the initial damage from the ion include: numbers of interstitials and vacancies produced, energy deposited per unit length to electrons and atomic nuclei, track diameter, and implanted ion profile. These properties enable further simulations and allow computing a common unit of radiation damage dose, displacements per atom (dpa), which can be used to compare irradiation experiments with different ions (Backman et al. 2013) (Stoller et al. 2013). Additionally, the ejection of materials near the surface due to incident ions is important to sputtering and ion-beam analysis techniques, such as elastic recoil detection analysis (ERDA) and secondary ion mass spectrometry (SIMS) (Vickerman and Gilmore 2011). The interaction of ions within a material can be broken into two parts: electronic and nuclear stopping. Electronic stopping is the energy lost from the ion due to inelastic collisions with electrons along its path. Nuclear stopping is the energy lost due to elastic collisions between the ion and atomic nuclei within the material. The Stopping and Range of Ions in Matter (SRIM) code is a well known software in the radiation damage and ion-beam communities that allows the simulation, via Monte Carlo, of ions through a material by modeling the energy transfer through electronic and nuclear stopping (J. F. Ziegler, Ziegler, and Biersack 2010). SRIM was originally developed in 1985 and has had numerous updates on the electronic stopping powers since then, with the nuclear stopping well explained by the ZBL potential (J. F. Ziegler 1988). The executable SRIM is free to use for non-commercial use but the source code is not available to the community despite requests. While SRIM is a scientifically accurate code it does not get updated frequently and has many bugs from a usability standpoint.

97 MATHEMATICS AND COMPUTING↗