{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T01:40:04Z","timestamp":1750297204717,"version":"3.41.0"},"reference-count":22,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2025,3,31]],"date-time":"2025-03-31T00:00:00Z","timestamp":1743379200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","award":["RGPN-2020-04467"],"award-info":[{"award-number":["RGPN-2020-04467"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>\n            Legendre elliptic integrals and Jacobi elliptic functions arise in multiple applications within the physical sciences, including oscillations, celestial mechanics, and geodynamics. In this study, we describe the Fortran library\n            <jats:monospace>ellipFor<\/jats:monospace>\n            capable of evaluating the following for generalized input values: (1) the complete Legendre elliptic integrals of the first and second kinds, (2) the incomplete Legendre elliptic integrals of the first and second kinds, and (3) the principal Jacobi elliptic functions. Our software builds upon previously developed Fortran routines, which were designed with restrictions on input parameters that may be limiting in applications. Our routines apply multiple transformations to allow for more general input values, such as elliptic moduli greater than unity for points 1\u20133, arbitrary real Jacobi amplitudes for points 1\u20132, and complex first arguments for point 3. In addition, our routines are thread-safe, allowing for parallel computations. Our routines were compared with values from the computer algebra system SageMath over a wide range of input parameters. Values from\n            <jats:monospace>ellipFor<\/jats:monospace>\n            and SageMath agreed to within tolerances commensurate with the limitations of floating-point arithmetic used for the elliptic integrals and Jacobi elliptic functions listed in points 1, 2, and 3 above for generalized input arguments.\n          <\/jats:p>","DOI":"10.1145\/3709136","type":"journal-article","created":{"date-parts":[[2024,12,24]],"date-time":"2024-12-24T12:57:06Z","timestamp":1735045026000},"page":"1-17","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Algorithm 1054:\n            <tt>ellipFor<\/tt>\n            , a Fortran Software Library for Legendre Elliptic Integrals and Jacobi Elliptic Functions with Generalized Input Arguments"],"prefix":"10.1145","volume":"51","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5076-0620","authenticated-orcid":false,"given":"Sean J.","family":"Trim","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3513-6237","authenticated-orcid":false,"given":"Raymond J.","family":"Spiteri","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Saskatchewan, Saskatoon, Saskatchewan, Canada"}]}],"member":"320","published-online":{"date-parts":[[2025,4,4]]},"reference":[{"key":"e_1_3_1_2_2","volume":"55","author":"Abramowitz Milton","year":"1968","unstructured":"Milton Abramowitz and Irene A. Stegun. 1968. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Vol. 55. US Government Printing Office.","journal-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00693093"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02165405"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-65138-0"},{"key":"e_1_3_1_6_2","volume":"67","author":"Byrd Paul F.","year":"2013","unstructured":"Paul F. Byrd and Morris D. Friedman. 2013. Handbook of Elliptic Integrals for Engineers and Physicists, Vol. 67. Springer.","journal-title":"Handbook of Elliptic Integrals for Engineers and Physicists"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396491"},{"key":"e_1_3_1_8_2","unstructured":"Bille C. Carlson. 2024. Chapter 19: Elliptic Integrals. Retrieved from https:\/\/dlmf.nist.gov\/19"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1145\/355958.355970"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1965-0171370-4"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1965-0178563-0"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0501045"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1088\/0004-6256\/138\/1\/210"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2011-02455-5"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2011.11.007"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-012-0498-0"},{"key":"e_1_3_1_17_2","first-page":"189","article-title":"Elliptic functions and elliptic integrals for celestial mechanics and dynamical astronomy","volume":"2","author":"Fukushima Toshio","year":"2014","unstructured":"Toshio Fukushima and S. Kopeikin. 2014. Elliptic functions and elliptic integrals for celestial mechanics and dynamical astronomy. Frontiers in Relativistic Celestial Mechanics 2 (2014), 189\u2013228.","journal-title":"Frontiers in Relativistic Celestial Mechanics"},{"key":"e_1_3_1_18_2","author":"Wolfram Research, Inc","year":"2024","unstructured":"Wolfram Research, Inc. 2024. Mathematica, Version 14.1.","journal-title":"Mathematica, Version 14.1"},{"key":"e_1_3_1_19_2","volume":"80","author":"Lawden Derek F.","year":"2013","unstructured":"Derek F. Lawden. 2013. Elliptic Functions and Applications, Vol. 80. Springer Science & Business Media.","journal-title":"Elliptic Functions and Applications"},{"key":"e_1_3_1_20_2","volume-title":"Maplesoft, a Division of Waterloo Maple Inc.","author":"Maple 2022","year":"2022","unstructured":"Maple 2022. 2022. Maplesoft, a Division of Waterloo Maple Inc. Waterloo Maple Inc."},{"key":"e_1_3_1_21_2","unstructured":"The Sage Developers. 2024. SageMath the Sage Mathematics Software System (Version 10.4). Retrieved from https:\/\/www.sagemath.org"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","unstructured":"Sean Trim. 2024. seantrim\/ellipFor: Release 2.0.3. 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