On 2017-06-06 06:09, Henry Baker wrote:

Now you've lost me.

The the video starts by talking about the Minsky algorithm over the integers.

Where did the reals come in?

I am genuinely sorry to say: Gotcha. The talk never said x₀ and y₀ were integers. Regrettably, it doesn't exhibit a case where they're not. But they always change by integers--their fractional parts stay constant. Adding small fractions to x₀ and y₀ typically just shifts the first few values by those offsets, but at some point a Floor will be different and the sequences will veer apart.

Also, if you're calculating with floating point numbers, how can you be so sure that the algorithm is exactly invertible?

Good point. We need x + ⎣y⎦ - ⎣y⎦ to be x. This can fail when |y| > |x| , as when crossing the y axis, or when |δ| or |ε| is large. --rwg

At 01:15 AM 6/6/2017, Bill Gosper wrote:

...

Important:

The algorithm described in the talk and the book is over the reals, not the integers.

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