Abstract
Von Neumann’s manuscript is a substantial technical document written in unfamiliar notation. This chapter provides a guide to the development of the meshing routine that explains the step-by-step process followed by von Neumann. He began with a slightly ‘high-level’ version of the code and by a process of repeated substitution reduced this to a form that could be straightforwardly translated into binary code. The intermediate and final versions of the routine implicit in the manuscript are tabulated for ease of reference. Von Neumann also considered how the routine would be loaded and called as a subroutine in a more general sorting program, and the manuscript concludes with a discussion of the routine’s performance.
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Notes
- 1.
The full story of ENIAC programming is rather more complicated than this, but this captures the basic model that had evolved by the end of 1944. See (Haigh et al. 2016) for fuller details.
- 2.
Von Neumann (1945e) stipulated that numbers should be written with their most significant bits on the right, to reflect the ‘chronological order’ in which they emerged from the delay lines ready for sequential processing by \(\mathcal {A}\). He did not mention this point in the description of the second EDVAC code, and for simplicity it is ignored here.
- 3.
Knuth (1970, 258) pointed out that von Neumann’s reasoning here was fallacious. For example, the jumps in orders \(5_{\alpha _1}\) and \(5_{\alpha _2}\) invoke orders transferring sequences of words between long and short tanks. These take an unpredictable time to execute because they make what Knuth described as ‘essentially random references to long tanks’, meaning that von Neumann’s strategy of leaving four blank words is over-simplistic.
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Priestley, M. (2018). The 1945 Meshing Routine. In: Routines of Substitution. SpringerBriefs in History of Computing. Springer, Cham. https://doi.org/10.1007/978-3-319-91671-2_4
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DOI: https://doi.org/10.1007/978-3-319-91671-2_4
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