Re: D simulated by H never halts no matter what H does V3 ---

On 5/5/2024 9:42 AM, joes wrote:
Lots of snips here

 Correct. Simulating here means producing the exact same behaviour.
If it is correct up to a point, it might still make a mistake later.
The only way to know is to keep simulating.

That reminds me of something I encountered in the early 1960s while working on Apollo. There was a workmate who wrote a really accurate decent speed numerical integration routine with variations (Adams Moulton (sp?) 6-point predictor corrector). He adopted it on request to help do long-term very accurate simulations of a gyro that was to be part of the guidance package.
He essentially set up the integrator as the main routine of the simulation and used the predictor corrector to oscillate around an induced discontinuity, continually reducing its step size and backing up and going forward in a grad loop. Meanwhile the normal part of the integrator was capturing very accurate simulation data. This would go on for millions of steps in order to predict behavior and stability of the gyro.
As a footnote: The integrator, in some parts, would examine some of the state variable values for relative size and order arithmetic computations accordingly. It did a lot of work to preserve low order bits and of course used double precision while executing on the IBM 7090 computers. There where many other "tricks" in the code and that integration package was used for a wide variety of Apollo applications. The fellow doing all of this was named Bill ? and was a key example of NASA trying to get real capability injected where it was important. The work was done at North American Aviation in Downy, CA - the prime Apollo contractor and integrator.
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Jeff Barnett