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An unrestricted algorithm is an algorithm for the computation of a mathematical function that puts no restrictions on the range of the argument or on the precision that may be demanded in the result.cite-ref-clenshaw-1-0[1] The idea of such an algorithm was put forward by C. W. Clenshaw and F. W. J. Olver in a paper published in 1980.cite-ref-clenshaw-1-1[1]cite-ref-brent-2-0[2]

In the problem of developing algorithms for computing, as regards the values of a real-valued function of a real variable (e.g., g[x] in "restricted" algorithms), the error that can be tolerated in the result is specified in advance. An interval on the real line would also be specified for values when the values of a function are to be evaluated. Different algorithms may have to be applied for evaluating functions outside the interval. An unrestricted algorithm envisages a situation in which a user may stipulate the value of x and also the precision required in g(x) quite arbitrarily. The algorithm should then produce an acceptable result without failure.cite-ref-clenshaw-1-2[1]

cite-note-clenshaw-11. ↑ citerefc-w-clenshaw-and-f-w-j-olver1980C.W. Clenshaw and F. W. J. Olver (April 1980). "An unrestricted algorithm for the exponential function". SIAM Journal on Numerical Analysis. 17 (2): 310–331. Bibcode:1980SJNA...17..310C. doi:10.1137/0717026. JSTOR 2156615.

cite-note-brent-22. ↑ citerefrichard-p-brent1980Richard P Brent (1980). "Unrestricted algorithms for elementary and special functions". In S. H. Lavington (ed.). Information Processing. Vol. 80. North-Holland, Amsterdam. pp. 613–619. arXiv:1004.3621.