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This is not necessary, however, if provision is made for the * The implication of our remarks is that for all values of the subscripts, the subscripted definition holds true; were this the case for definitions appearing in command sequences, an ambiguity of meaning would result, since the more natural meaning is that for the subscript values currently defined, the array element has a particular value. Thus implicit arrays may be used, but not defined, in programs. t Although, on a machine of 12 digit accuracy, it becomes irksome to have to replace constants such as '3*9 sin (π — 2·5)' by their numerical values, and it is convenient to have them evaluated automatically during code construction.

A. Brooker and D. ] has been defined this does not completely resolve the arithmetical operation involved and in the cases A = ^ [ ± ] [ ^ ] a n d A = [ ± ? ] [ ^ ] it is necessary to distinguish the + and — signs. This is done by means of the first half dozen instructions, as a result of which βλ = 1, 2, 3, 4, 5, 6 corresponding respectively to the cases A = A + [F], A = Ax[F], A = A/[F], A = [F], A = A - [F] and A = - [ F ] . We then examine the form of the [F]> distinguishing first whether it is a [Q] or a TS[N], and then if a [Q] whether it is a [Y][K] or [/].

37 35] let [FD] = 1 ? ? , - * 37 36] let [FD] = 1??? ][T] 50 R. A. Brooker and D. ][EOL] Note : This represents only a subset of the index arithmetic instructions. In practice, however, the majority of them are of this form which lends itself to a more efficient treatment than the general case : [/] = [GE] [EOL]. The special case must of course come before the general case in order of preference. ] = [±N or / * ] ßl — number of [±N or / * ] 02 = 1 4] let [±NorI*(ß2)] = [±][iVor/] let [FD] = 0 1 2 4 -+ 3 unless [ ± ] = — let [FD] = 0 1 2 2 3] [FD], 20, 0, [Nor I] ß2 = ß2 + l ->4if/S2 <ßl 2] ßl = category of [/] 0121,01,20,0 END statement defn: [FD], [word], 0, [Nor I] -►1 unless [JV or I] = [N] ßl = 2 X [N] [FD], [word], 0, ßl END 52 R.

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