The Lucas-Lehmer test for Mersenne primality can be efficiently parallelized for GPU-based computation. The gpuLucas project implements an irrational-base discrete weighted transform approach (IBDWT) using balanced-integers, non-power-of-two transforms, and carry-save radix representations. gpuLucas uses the CUDA programming language and requires the double-precision floating point capabilities of recent GPUs. Results show up to 7x speedups over benchmark averages for optimized sequential code and factor-of-two speedups over CUDALucas, another GPU-based Lucas-Lehmer tester developed independently and with a different optimization strategy. This work demonstrates techniques for implementing GPU-based number theoretic algorithms on very large numbers, including fast multiplication, prefix-sum-based carry-propagation, and the use of carry-save arithmetic with balanced integers. The work presents timing profiles of convolution-based integer multiplication based on the IBDWT, in particular for non-power-of-two transformations, and establishes the usefulness of the software as a GPU benchmarking application and as a platform for large-integer and polynomial experimentation.<\/p>\n","protected":false},"excerpt":{"rendered":"
The Lucas-Lehmer test for Mersenne primality can be efficiently parallelized for GPU-based computation. The gpuLucas project implements an irrational-base discrete weighted transform approach (IBDWT) using balanced-integers, non-power-of-two transforms, and carry-save radix representations. gpuLucas uses the CUDA programming language and requires the double-precision floating point capabilities of recent GPUs. Results show up to 7x speedups over […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[36,89,157,3],"tags":[1787,451,14,597,1796,20,379,298,67,378],"class_list":["post-5578","post","type-post","status-publish","format-standard","hentry","category-algorithms","category-nvidia-cuda","category-mathematics","category-paper","tag-algorithms","tag-benchmarking","tag-cuda","tag-mathematical-software","tag-mathematics","tag-nvidia","tag-nvidia-geforce-gtx-480","tag-optimization","tag-performance","tag-tesla-c2050"],"views":3408,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/5578","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5578"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/5578\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5578"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5578"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5578"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}