IBM 610 Manual Of Operation

Also see for 610: Technical overview and introduction

PROGRAMMING THE 610 63A similar example arises in evaluating the exponen-tial e''. Suppose we wish to calculate e^ for a valueof X between and 1 and that we wish to leave theresult accurate to four decimal places. We could usethe seriese'^=l+x + x^+^^ +2! 3!To cause the machine to stop evaluating terms of theseries after the desired accuracy had been reached, onewould say something like, "After calculating eachterm, x°, test to see whether it is greater or less thann.00005. If it is greater, add or subtract the term asappropriate; if it is less, stop calculating."These examples are not intended to show in detailhow to program these problems. They are merelymeant to indicate that, before performing a calcu-lation on the 610, a plan must be made, which canroughly be broken down into the following stages:1. Analyze the problem into a sequence of basicoperations that can be expressed in 610 language onthe program tape or can be wired on the control panel.2. Decide what input data and what results are tobe typed or otherwise recorded and in what format.3. Decide what storage locations are to be used toaccommodate the various constants and variables thatenter the problem.4. Write out, sentence by sentence, the precise in-structions that will get input data into the 610'smemory and will cause the 610 to carry out the nec-essary operations. If the control panel is to be used,this last stage will also include a plan for wiring thecontrol panel.It should be emphasized that these plans need not,or should not, be perfectly rigid. The operator shouldallow himself the freedom of watching the develop-ment of the calculation as it is performed and ofchanging his plans in mid-calculation.Most-Frequent Types of CalculationsStatistical studies of numerical computations showthat about 85% of the basic arithmetic operationsperformed by computers (human, mechanical or elec-tronic) are of two simple types.Type I: A product of two numbers is added to anumber previously obtained.Brieflyprev. + a bFor example, in evaluating a sum of products (inmathematical notation Sj ai bi) , all the operations areof this type.Type II: A number is added to a number previ-ously obtained, and the sum is multiplied by a thirdnumber. Briefly,(prev. + a)bFor example, a polynomial may be evaluated insuch a way that all operations are of this type. Inmathematical notation, a polynomial of the third de-gree may be written as[(ax+b) x+c]x+dThe IBM 610 performs both of these operationswith equal ability.Example of First Type of CalculationSuppose we consider a small problem of Type I.Given six input numbers, P, Q, R, S, T, U, the oper-ator wishes to evaluate the sum of the three productsPQ + RS + TU. In thinking about the problem, hedecides to enter the input data into six storage regis-ters; so, he notes on his planning sheet:p 01Q 02R 03S 04T 05U 06Further, he decides he will use register 07 as thesummation register to accumulate the sum of productsas they are formed. At the end of the computation,he will be able to read out the required answer fromregister 07. From this point on, the amount of de-tailed note-making the operator does will depend onthe complexity of the problem. It is recommendedthat the beginning programmer write out in full de-

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