{"id":17723784,"url":"https://github.com/ncw/euler_bbp","last_synced_at":"2026-04-26T12:32:59.288Z","repository":{"id":233894000,"uuid":"595066451","full_name":"ncw/euler_bbp","owner":"ncw","description":"Programs and paper to demonstrate Euler's BBP-type formulae for 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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":["euler","go","golang","math","mathematics","python"],"created_at":"2024-10-25T15:44:01.243Z","updated_at":"2026-04-26T12:32:59.273Z","avatar_url":"https://github.com/ncw.png","language":"TeX","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Programs and paper to demonstrate Euler's BBP-type formulae for pi\n\nThis repository contains programs which can be used to compute binary\nor hex digits from pi without calculating the previous digits and\nprograms to calculate pi using them.\n\nThey use two formulae which were discovered by Euler in 1779 and\ncompare them to the original formula used by Bailey, Borwein and\nPlouffe in 1997.\n\nA paper about this was published in [Eulerania Journal, Vol 3, Issue 1](https://scholarlycommons.pacific.edu/euleriana/vol3/iss1/3/)\nin March 2023.\n\n- [euler_bbp.py](euler_bbp.py) - simple program to calculate hex digits of pi\n- [euler_bbp.go](euler_bbp.go) - faster (100x) program to do the same\n- [check_bbp_equations.py](check_bbp_equations.py) - program to check the equations in the paper work\n\nSource for the paper:\n\n- [euler_bbp.tex](euler_bbp.tex)\n- [refs.bib](refs.bib)\n- [Makefile](Makefile)\n\n## Results\n\n```\n$ python euler_bbp.py\nbbp_original         hex digits of pi from digit         10 5a308d31319 in 0.000s\nbbp_euler            hex digits of pi from digit         10 5a308d31319 in 0.000s\nbbp_euler2           hex digits of pi from digit         10 5a308d313198 in 0.000s\nbbp_original         hex digits of pi from digit        100 c29b7c97c50 in 0.000s\nbbp_euler            hex digits of pi from digit        100 c29b7c97c50 in 0.001s\nbbp_euler2           hex digits of pi from digit        100 c29b7c97c50 in 0.000s\nbbp_original         hex digits of pi from digit       1000 349f1c09b0 in 0.004s\nbbp_euler            hex digits of pi from digit       1000 349f1c09b0 in 0.005s\nbbp_euler2           hex digits of pi from digit       1000 349f1c09b0 in 0.002s\nbbp_original         hex digits of pi from digit      10000 68ac8fcfb in 0.030s\nbbp_euler            hex digits of pi from digit      10000 68ac8fcfb in 0.046s\nbbp_euler2           hex digits of pi from digit      10000 68ac8fcfb in 0.019s\nbbp_original         hex digits of pi from digit     100000 535ea16c in 0.340s\nbbp_euler            hex digits of pi from digit     100000 535ea16c in 0.536s\nbbp_euler2           hex digits of pi from digit     100000 535ea16c in 0.222s\nbbp_original         hex digits of pi from digit    1000000 26c65e52 in 3.885s\nbbp_euler            hex digits of pi from digit    1000000 26c65e5 in 6.115s\nbbp_euler2           hex digits of pi from digit    1000000 26c65e52 in 2.627s\nbbp_original         hex digits of pi from digit   10000000 17af586 in 42.293s\nbbp_euler            hex digits of pi from digit   10000000 17af586 in 66.215s\nbbp_euler2           hex digits of pi from digit   10000000 17af586 in 29.003s\nbbp_original         hex digits of pi from digit  100000000 ecb840 in 463.304s\nbbp_euler            hex digits of pi from digit  100000000 ecb840 in 752.472s\nbbp_euler2           hex digits of pi from digit  100000000 ecb840 in 327.756s\nbbp_original         hex digits of pi from digit 1000000000 85895 in 9379.175s\n```\n\n```\n$ go run euler_bbp.go\n  original hex digits of pi from digit           10 5a308d31319 in 26.87µs\n     euler hex digits of pi from digit           10 5a308d31319 in 9.498µs\n    euler2 hex digits of pi from digit           10 5a308d313198 in 18.084µs\n  original hex digits of pi from digit          100 c29b7c97c50 in 19.587µs\n     euler hex digits of pi from digit          100 c29b7c97c50 in 32.26µs\n    euler2 hex digits of pi from digit          100 c29b7c97c50 in 27.682µs\n  original hex digits of pi from digit         1000 349f1c09b0 in 248.003µs\n     euler hex digits of pi from digit         1000 349f1c09b0 in 369.24µs\n    euler2 hex digits of pi from digit         1000 349f1c09b0 in 131.676µs\n  original hex digits of pi from digit        10000 68ac8fcfb in 2.174754ms\n     euler hex digits of pi from digit        10000 68ac8fcfb in 3.45151ms\n    euler2 hex digits of pi from digit        10000 68ac8fcfb in 1.37503ms\n  original hex digits of pi from digit       100000 535ea16c in 26.643839ms\n     euler hex digits of pi from digit       100000 535ea16c in 20.853328ms\n    euler2 hex digits of pi from digit       100000 535ea16c in 16.504332ms\n  original hex digits of pi from digit      1000000 26c65e52 in 55.597885ms\n     euler hex digits of pi from digit      1000000 26c65e5 in 75.05774ms\n    euler2 hex digits of pi from digit      1000000 26c65e52 in 160.25139ms\n  original hex digits of pi from digit     10000000 17af586 in 480.289261ms\n     euler hex digits of pi from digit     10000000 17af586 in 698.296118ms\n    euler2 hex digits of pi from digit     10000000 17af586 in 362.285909ms\n  original hex digits of pi from digit    100000000 ecb840 in 5.287894989s\n     euler hex digits of pi from digit    100000000 ecb840 in 8.886897248s\n    euler2 hex digits of pi from digit    100000000 ecb840 in 4.047852407s\n  original hex digits of pi from digit   1000000000 85895 in 1m6.804017733s\n     euler hex digits of pi from digit   1000000000 85895 in 1m41.747295359s\n    euler2 hex digits of pi from digit   1000000000 85895 in 44.864847315s\n  original hex digits of pi from digit  10000000000 921c in 13m16.405684459s\n     euler hex digits of pi from digit  10000000000 921c in 19m46.698153514s\n    euler2 hex digits of pi from digit  10000000000 921c in 8m36.587514529s\n  original hex digits of pi from digit 100000000000 c9c in 2h28m30.473717759s\n     euler hex digits of pi from digit 100000000000 c9c in 3h43m8.795869344s\n    euler2 hex digits of pi from digit 100000000000 c9c in 1h36m58.833018519s\n```\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fncw%2Feuler_bbp","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fncw%2Feuler_bbp","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fncw%2Feuler_bbp/lists"}