A subroutine method for calculating logarithms
Robert W. Bemer · Communications of the ACM · 1958
to x, that the process will not yield reliable values of J.(x).Indeed this is just the situation and this fact provides a means of determining a lower bound (fimi,) for fi relative to x.An upper bound (nma~) for fl will be forced on the generation of J.(x) by the restrictions on the size of numbers that may be used.In the experimental work carried out for the determination of these bounds, the IBM 650 with the automatic floating point device was used.Using this system, all numbers must fall within (10 -~1, 1049).It was found that the maximum number size was attained, not from generation of the Y.(x), but from calculation of the normalizing constant K in equation ( 3).In addition, of course, fi will be limited by the amount of storage space available in the particular machine, but this limitation is not considered here.Proceeding as suggested above, experimental values have been determined for time, and tin relative to x.In presenting the results graphically it was found convenient to consider separately the two ranges 101 _< x < 500 and 10 -bl < x < 101, which may be found in figures 1 and 2 respectively.A useful set of approximating curves for titan, and tim= are also illustrated in figures 1 and 2. The time necessary to calculate both J,(x) and Y,(x) for n =0, 1, • •., fi is approximately linear with ft.For the IBM 650, time in sec ~ .13ft.