{"id":8497,"date":"2012-11-14T23:55:25","date_gmt":"2012-11-14T21:55:25","guid":{"rendered":"http:\/\/hgpu.org\/?p=8497"},"modified":"2012-11-14T23:55:25","modified_gmt":"2012-11-14T21:55:25","slug":"correctly-rounding-elementary-functions-on-gpu","status":"publish","type":"post","link":"https:\/\/hgpu.org\/?p=8497","title":{"rendered":"Correctly rounding elementary functions on GPU"},"content":{"rendered":"<p>The IEEE 754-2008 standard recommends the correct rounding of elementary functions. This requires to solve the Table Maker&#8217;s Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such computations, namely Lef&#8217;evre algorithm, on Graphics Processing Units (GPU) which are massively parallel architectures with a partial SIMD execution (Single Instruction Multiple Data). We first propose an analysis of the Lef&#8217;evre hard-to-round argument search using the concept of continued fractions. We then propose a new parallel search algorithm much more efficient on GPU thanks to its more regular control flow. We also present an efficient hybrid CPU-GPU deployment of the generation of polynomial approximations required in Lef&#8217;evre algorithm. In the end, we manage to obtain overall speedups up to 53.4x on one GPU over a sequential CPU execution, and up to 7.1x over a multi-core CPU.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The IEEE 754-2008 standard recommends the correct rounding of elementary functions. This requires to solve the Table Maker&#8217;s Dilemma which implies a huge amount of CPU computation time. We consider in this paper accelerating such computations, namely Lef&#8217;evre algorithm, on Graphics Processing Units (GPU) which are massively parallel architectures with a partial SIMD execution (Single [&hellip;]<\/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":[36,11,89,3],"tags":[1787,1782,14,769,20,1006],"class_list":["post-8497","post","type-post","status-publish","format-standard","hentry","category-algorithms","category-computer-science","category-nvidia-cuda","category-paper","tag-algorithms","tag-computer-science","tag-cuda","tag-elementary-functions","tag-nvidia","tag-tesla-c2070"],"views":2337,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8497","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=8497"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/8497\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}