What was "whole-value computation" in early real-time systems?

Question

I've been reading Achieving Accuracy: A Legacy of Computers and Missiles by M. W. McMurran, who helped develop the Autonetics D-17 guidance computer for the Minuteman ICBM in the early 1960s. For all its specialised features, the D-17 has at least a family resemblance to general-purpose magnetic drum computers like the IBM 650 (after the Minuteman I was retired, some surplus D-17s made their way to universities and bitsavers.org has a good collection of documents from them).

However, McMurran suggests that the D-17 was a break from Autonetics tradition, and its design was in part reaction to a competing proposal from TRW Space Technology Laboratories:

The STL "Blue Book" computer was to be a "compulsory-optimum" programmed whole-value machine. [...] Autonetics computer designers had virtually no experience with whole-value general-purpose real-time systems. But [overnight we] blocked out a general-purpose alternative to Blue Book. By then, we had developed very serious concerns about the speed of any emerging serial whole-value computer [but those concerns were addressed by features of the D-17 design]. (p. 276)

The part I'm struggling with here is what is meant by whole-value computation, and why was it a problem for real-time systems?

One possible answer comes from the fact that the first digital guidance systems were modelled after analogue computers, but were built around digital differential analysers (DDAs, not to be confused with the graphics algorithm) which were hard-wired elements for solving discretised differential equations at high speed. McMurran describes two Autonetics DDA guidance computers that preceded the D-17, NATDAN (the North American Transistorized Digital ANalyzer, developed for the Navaho cruise missile), and Verdan (the VERsatile Digital ANalyzer):

[NATDAN] was rate-limited, but could solve an amazing array of complex differential equations one pulse at a time, as long as the solution moved at a rate NATDAN could handle. [...] Since NATDAN had no whole value section, communication with guidance and control systems was a lot easier for it than communicating with people. (pp. 138-139)

The [Verdan] design started with the NADAN (sic) DDA. By 1955, it had become clear that even embedded control computers frequently needed to communicate with whole-value based systems, often with people in the loop. (pp. 142-143)

Because DDAs dealt with rates of change discretised into relatively small increments (e.g. integrating accelerometer output to compute vehicle velocity and hence position), I'm guessing this made them faster in a serial computer than dealing with full-precision variables representing physical quantities across a range of scales. However, I suspect that's too simplistic an answer: is the phrase "whole value" more than just a synonym for "general purpose" computation in this context?

EDIT: Since posting I've found a couple of early papers on DDAs that give insight into the digital techniques used in systems like NATDAN and Verdan:

• R. E. Sprague, Fundamental Concepts of the Digital Differential Analyzer Method of Computation. Mathematical Tables and Other Aids to Computation v6n37 (Jan. 1952), pp. 41-49
• John F. Donan, The Serial-Memory Digital Differential Analyzer. Mathematical Tables and Other Aids to Computation v6n38 (Apr. 1952), pp. 102-112

Answer 1

This is fundamentally talking about how an analog input system (missile inertial guidance, in this case) can be interfaced to a digital computer whose sole purpose is the eventual output to another analog system (missile control surfaces, in this case).

An inertial guidance system consists of a gyroscope on gimbals that will mechanically create an analog output that measures acceleration in each of the 3 planes of 3d space. Summing these 3 output vectors would produced a single vector representing the total instantaneous acceleration. The integral of that acceleration vector over time is the instantaneous velocity of the guidance system, and the second integral would be the guidance system's current position. Hitting a target downrange is just a computation of the path needed to traverse from the initial (launch) position to the target position. Such computations can be done by a digital computer, but those computers must maintain sufficient accuracy while also providing sufficient computational speed.

Since a missile like the Minuteman is intended to be autonomous, it has to leave the launchpad already "programmed" with the flight path, and then it has to constantly guide itself to the target by comparing its current position, derived from gimbal vectors, with the programmed position along the flight path. All of this can be accomplished without digital computers, but using digital computers makes sense for portions of the system that might interface with other computers, like external targeting computers, or databases, or with human operators of such external systems. Also, there may be benefits in size, weight, power consumption, and (given a good enough digital computer) accuracy to using digital computers. Also a recognized first brought about with the use of a digital computer for the Minuteman was the flexibility to run other programs, like on-board status tests, when the missile was in the silo, and improve missile performance with software upgrades.

Since digital computers can only work with digital values, the analog inputs must at some stage be "digitized" into "whole values" which are just binary numbers. Then computation can proceed. If the digitization happens at the gimbal output, then you represent 3 vectors as 3 complex number "whole values" (a + bi) stored digitally. From there the computer can perform the necessary maths. Then, downstream, you need some D-to-A conversion to manipulate the missile control surfaces. This creates the necessary missile acceleration then used to fly back to the pre-determined path.

Given the timeframe of early-1960s development, small transistorized computers obviously would have been limited in their computational power (precision and speed). And those are the issues the engineers would have to overcome. I suspect the book goes into considerably more details on how they did overcome those issues.

Answer 2

The part I'm struggling with here is what is meant by whole-value computation,

It means digital numeric system using integers, instead of analog or digital/analog systems. The D17 used 24 bit integer for all calculation.

and why was it a problem for real-time systems?

It needs a lot of operations to do the job, thus considerable time and all done in a single computer (to reduce weight *1), while previous designs used two analog operating systems.

A digital system has to go through the whole calculation for a new result, while an analog's reaction time is tied to the input difference, thus fast, practically instant, on small chances - which are the usual case - while also offering in-between correction.

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Background

The Minuteman is somewhat of a turning point in US rocket development as it's the first major design that's no longer a variation of German WW2 technology (*2). This is not only due the use of solid fuel for a large scale guided missile, but also the guidance systems. The guidance systems until that point where derived from the basic designs as used in V1/V2 guidance. While much improved, these still consisted of separate modules of an autopilot 'planning' the route to follow and a correction unit comparing this with the flight data delivered by an inertial platform, with the result sent to motor/control surfaces.

While developments previous to the D17 were greatly improved, in parts even digitalized, it was the D17 that replaced it by an integrated, all digital system. The digital nature made it possible to reduce the system in size and weight and also greatly reduce the setup time, as setting a new destination was now merely transferring a new data set onto the hard disk, which could be done in minutes instead of hours (*3)

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*1 - Weight was a major design goal for the Minuteman, beside short reaction time. It grossed only about 1/6th of the competing Soviet designs. Just by sheer size the Soviets hat the luxury to load a full-blown tube computer onto a R-7 - which BTW was effectively the first iteration of today's Soyuz design.

*2 - In contrast the mentioned, in parallel developed Navaho missile is still a direct descendant of the V1 Buzz-Bomb, based on recommendations already made by German scientists during the war for future vehicles. Now beefed up in size and with improved engines and guidance systems, partly digital but still split in two.

*3 - Using air-cushioned gyroscopes further made it possible so save on spin-up time making all the other improvements count, but that's a different story.