Various other functions required for the solution of problems are introduced on tapes fed to the interpolating units. These tapes are punched in code representing successive values of the function at equidistant values of the argument, together with the interpolation coefficients necessary to obtain the desired accuracy. Any order of interpolation may be employed up to and including the 12th.
When a problem is delivered to the interpolation device, the tape-positioning mechanisms position the tape and control the interpolative process. In order to accomplish the tape-positioning in the shortest possible time, the functional tapes are made endless, and suitable sensing circuits direct the tape in the direction of shortest travel.
Once a function has been coded in tape form the tape is preserved and added to the tape library for use in connection with future problems. Thus the value of the machine will increase with its use.
The operator of the machine does not have to be a trained mathematician, but a mathematician must prepare the problem using a code book, so that the operator may punch code holes in a tape to feed the problem to the machine. The code book, which covers every known type of mathematical problem, was written by Commander [Howard H.] Aiken, assisted by Ensign R. V. D. Campbell.
Both the sequence control tapes, and the functional value tapes are prepared on a punch especially designed for this purpose.
All computations of the sequence control tape can be designed to give a series of checks such that an error is called to the attention of the operator by stopping the machine. The control tapes are independent of the values of the parameters involved in the computation. Hence, every control tape represents the general solution of a problem or a system of equations. Such a tape, once punched, is filed for future use.