{"id":33918984,"url":"https://github.com/tuwien-cms/xprec-rs","last_synced_at":"2026-04-01T19:18:30.758Z","repository":{"id":320560694,"uuid":"1079967946","full_name":"tuwien-cms/xprec-rs","owner":"tuwien-cms","description":"Fast emulated quadruple precision in Rust","archived":false,"fork":false,"pushed_at":"2025-12-13T17:19:13.000Z","size":204,"stargazers_count":5,"open_issues_count":5,"forks_count":1,"subscribers_count":0,"default_branch":"mainline","last_synced_at":"2026-03-28T00:58:06.636Z","etag":null,"topics":["accuracy","compensated-sum","double-double","numerics","quad-precision"],"latest_commit_sha":null,"homepage":"https://crates.io/crates/xprec","language":"Rust","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/tuwien-cms.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2025-10-20T17:01:19.000Z","updated_at":"2025-12-13T17:19:19.000Z","dependencies_parsed_at":"2025-10-24T14:34:07.460Z","dependency_job_id":null,"html_url":"https://github.com/tuwien-cms/xprec-rs","commit_stats":null,"previous_names":["tuwien-cms/xprec-rs"],"tags_count":3,"template":false,"template_full_name":null,"purl":"pkg:github/tuwien-cms/xprec-rs","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tuwien-cms%2Fxprec-rs","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tuwien-cms%2Fxprec-rs/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tuwien-cms%2Fxprec-rs/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tuwien-cms%2Fxprec-rs/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/tuwien-cms","download_url":"https://codeload.github.com/tuwien-cms/xprec-rs/tar.gz/refs/heads/mainline","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/tuwien-cms%2Fxprec-rs/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":31291117,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-04-01T13:12:26.723Z","status":"ssl_error","status_checked_at":"2026-04-01T13:12:25.102Z","response_time":53,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["accuracy","compensated-sum","double-double","numerics","quad-precision"],"created_at":"2025-12-12T08:38:35.410Z","updated_at":"2026-04-01T19:18:30.751Z","avatar_url":"https://github.com/tuwien-cms.png","language":"Rust","funding_links":[],"categories":[],"sub_categories":[],"readme":"Fast emulated quadruple precision in Rust\n=========================================\n\nEmulates quadruple precision with a pair of doubles.  This roughly doubles\nthe mantissa bits (and thus squares the precision of double).  The range\nis almost the same as double, with a larger area of denormalized numbers.\nThis is also called double-double arithmetic, compensated arithmetic, or Dekker\narithmetic.\n\nThe rough cost in floating point operations (fl) and relative error as\nmultiples of u² = 1.32e-32 (round-off error or half the machine epsilon) is\nas follows:\n\n  | (op)       | f64 f64 | error | Df64 f64 | error | Df64 Df64 | error |\n  |------------|--------:|------:|--------:|------:|--------:|------:|\n  | add_fast   |    3 fl |   0u² |    7 fl |   2u² |   17 fl |   3u² |\n  | + -        |    6 fl |   0u² |   10 fl |   2u² |   20 fl |   3u² |\n  | *          |    2 fl |   0u² |    6 fl |   2u² |    9 fl |   4u² |\n  | /          |   3* fl |   1u² |   7* fl |   3u² |  28* fl |   6u² |\n  | reciprocal |   3* fl |   1u² |         |       |  19* fl | 2.3u² |\n  | sqrt       |   4* fl |   2u² |         |       |   8* fl |   4u² |\n\nThe error bounds are mostly tight analytical bounds (except for divisions).[^1]\nAn asterisk indicates the need for one or two double divisions, which are about\nan order of magnitude more expensive than regular flops on a modern CPU.\n\nThe table can be distilled into two rules of thumb: double-double arithmetic\nroughly doubles the number of significant digits at the cost of a roughly\n15x slowdown compared to double arithmetic.\n\n[^1]: M. Joldes, et al., ACM Trans. Math. Softw. 44, 1-27 (2018) and\n      J.-M. Muller and L. Rideau, ACM Trans. Math. Softw. 48, 1, 9 (2022).\n      The flop count has been reduced by 3 for divisons/reciprocals.\n      In the case of double-double division, the bound is 10u² but largest\n      observed error is 6u². In double by double division, we expect u². We\n      report the largest observed error.\n\n\nLicense and Copying\n-------------------\nCopyright (C) 2023-2025 Markus Wallerberger and others.\n\nReleased under the MIT license (see LICENSE for details).\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftuwien-cms%2Fxprec-rs","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ftuwien-cms%2Fxprec-rs","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftuwien-cms%2Fxprec-rs/lists"}