I think the idea of iterating from the fixed point at 0.318... + 1.337...i is valid!

Start with a selection of numbers between 0 and 1, and begin taking the natural logarithm over and over. The values will settle on that particular fixed point (depending on which branch of the logarithm your program uses).

Therefore, we should be able to come up with a fixed point hyperbolic solution that yields REAL numbers after enough exponentiations to get us back to the range (0,1).

The question is, will it match the inverse of Andrew's slog?

By the way, this was a quick, off the cuff test with the xnumbers library in Excel, so until someone can confirm it in a more reliable library, I reserve the right to be wrong.

Start with a selection of numbers between 0 and 1, and begin taking the natural logarithm over and over. The values will settle on that particular fixed point (depending on which branch of the logarithm your program uses).

Therefore, we should be able to come up with a fixed point hyperbolic solution that yields REAL numbers after enough exponentiations to get us back to the range (0,1).

The question is, will it match the inverse of Andrew's slog?

By the way, this was a quick, off the cuff test with the xnumbers library in Excel, so until someone can confirm it in a more reliable library, I reserve the right to be wrong.

~ Jay Daniel Fox