![]() The GNU MP Library ( GNU, 2016) also includes fast calculation algorithms for arbitrary precision arithmetic. Additionally, IntX ( INT, 2015) is a large precision integer library with fast multiplication based on the Hartley Transform ( Boussakta and Holt, 1988). For example, Microsoft introduced the BigInteger type in.NET 4.0, to compute large integers ( BIG, 2010), and which has no upper or lower bounds. There are some serial libraries and frameworks which perform large integer multiplications. Finally, this work also provides a parallel approach to the carry normalization applied after polynomial multiplication, which is based on a two-level hierarchical adder. This new approach takes advantage of the recent improvements in GPU memory bandwidth and the performance of new atomic operations to provide fast and safe, high-precision integer multiplication with no numerical issues. ![]() ![]() On the other hand, a divide-and-conquer approach of the classical convolution operation on a GPU, which is based on tiling, is also developed. As it works with floating-point numbers, only a certain range of sizes can be multiplied with no numerical issues, which are theoretically demonstrated to ensure that no rounding error can ever occur. (2018), an efficient FFT proposal for large-size problems called the ID-FFT library, the fastest one to the best of our knowledge. In order to provide an efficient FFT operation, this proposal uses the approach presented in Diéguez et al. On the one hand, one approach is based on the Strassen FFT algorithm on current GPUs. Specifically, this work presents two efficient approaches for the polynomial multiplication of large integers on GPU. Our results show the efficiency of our approaches for short, medium, and large sizes. Additionally, most previous studies do not examine the implementation of the carry normalization, but this work describes a parallel implementation for this operation. Previous studies reported that the Strassen algorithm is an effective implementation for “large enough” integers on GPUs. This work develops two approaches for efficient polynomial multiplication: one approach is based on tiling the classical convolution algorithm, but taking advantage of new CUDA architectures, a novelty approach to compute the multiplication using integers without accuracy lossless the other one is based on the Strassen algorithm, an algorithm that multiplies large polynomials using the FFT operation, but adapting the fastest FFT libraries for current GPUs and working on the complex field. The multiplication of large integers, which has many applications in computer science, is an operation that can be expressed as a polynomial multiplication followed by a carry normalization. All subjects Allied Health Cardiology & Cardiovascular Medicine Dentistry Emergency Medicine & Critical Care Endocrinology & Metabolism Environmental Science General Medicine Geriatrics Infectious Diseases Medico-legal Neurology Nursing Nutrition Obstetrics & Gynecology Oncology Orthopaedics & Sports Medicine Otolaryngology Palliative Medicine & Chronic Care Pediatrics Pharmacology & Toxicology Psychiatry & Psychology Public Health Pulmonary & Respiratory Medicine Radiology Research Methods & Evaluation Rheumatology Surgery Tropical Medicine Veterinary Medicine Cell Biology Clinical Biochemistry Environmental Science Life Sciences Neuroscience Pharmacology & Toxicology Biomedical Engineering Engineering & Computing Environmental Engineering Materials Science Anthropology & Archaeology Communication & Media Studies Criminology & Criminal Justice Cultural Studies Economics & Development Education Environmental Studies Ethnic Studies Family Studies Gender Studies Geography Gerontology & Aging Group Studies History Information Science Interpersonal Violence Language & Linguistics Law Management & Organization Studies Marketing & Hospitality Music Peace Studies & Conflict Resolution Philosophy Politics & International Relations Psychoanalysis Psychology & Counseling Public Administration Regional Studies Religion Research Methods & Evaluation Science & Society Studies Social Work & Social Policy Sociology Special Education Urban Studies & Planning BROWSE JOURNALS
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