Anunrestricted algorithm is analgorithm for the computation of amathematical function that puts no restrictions on the range of theargument or on the precision that may be demanded in the result.[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.[1][2]
In the problem of developing algorithms for computing, as regards the values of areal-valued function of areal variable (e.g.,g[x] in "restricted" algorithms), the error that can be tolerated in the result is specified in advance. An interval on thereal 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 ofx and also the precision required ing(x) quite arbitrarily. The algorithm should then produce an acceptable result without failure.[1]