Logical or non-mathematical programmes

A large part of any mathematical programme is concerned with operations which are not strictly mathematical at all. Examples of this are the input and output routines, the arrangements for calling in various sub-routines when required and, above all, the general organization of the problem as a whole. It is an interesting fact that these non-mathematical parts of the programme often take many more instructions than the mathematics proper. As an example, in a problem which involved the step by step integration of a simple non-linear differential equation, the actual integration cycle used 70 instructions, the arrangements to print out the results and to stop the integration at the required point used a further 48 instructions and a printing sub-routine of 64 instructions - a total of 112 instructions. The problem required this integration to be performed a large number of times with different parameters; the organization involved in doing this, and in arranging that the parameters should be fed into the machine in the simplest possible form used no fewer than 250 instructions and sub-routines totalling about 150 instructions. This may be a rather extreme case. but it is generally true to say, I think, that the non-mathematical parts of the programme use far more instructions than one would at first sight expect, and that a relatively large part of effort in preparing the programme is spent dealing with these non-mathematical operations.