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Math. Softw."],"published-print":{"date-parts":[[2019,12,31]]},"abstract":"<jats:p>\n            We present FloatX (Float eXtended), a C\n            <jats:bold>++<\/jats:bold>\n            framework to investigate the effect of leveraging customized floating-point formats in numerical applications. FloatX formats are based on binary IEEE 754 with smaller significand and exponent bit counts specified by the user. Among other properties, FloatX facilitates an incremental transformation of the code, relies on hardware-supported floating-point types as back-end to preserve efficiency, and incurs no storage overhead. The article discusses in detail the design principles, programming interface, and datatype casting rules behind FloatX. Furthermore, it demonstrates FloatX\u2019s usage and benefits via several case studies from well-known numerical dense linear algebra libraries, such as BLAS and LAPACK; the Ginkgo library for sparse linear systems; and two neural network applications related with image processing and text recognition.\n          <\/jats:p>","DOI":"10.1145\/3368086","type":"journal-article","created":{"date-parts":[[2019,12,9]],"date-time":"2019-12-09T13:35:27Z","timestamp":1575898527000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":27,"title":["FloatX"],"prefix":"10.1145","volume":"45","author":[{"given":"Goran","family":"Flegar","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda y Ciencia de Computadores, Universidad Jaime I, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florian","family":"Scheidegger","sequence":"additional","affiliation":[{"name":"IBM* Research-Zurich, R\u00fcschlikon, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vedran","family":"Novakovi\u0107","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda y Ciencia de Computadores, Universidad Jaime I, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giovani","family":"Mariani","sequence":"additional","affiliation":[{"name":"IBM* Research-Zurich, R\u00fcschlikon, Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e9s E.","family":"Tom\u00e1s","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda y Ciencia de Computadores, Universidad Jaime I, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. 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