Here's what I think - firstly lets "Keep It Simple" - and if the digits
are present in the internal representation, then why *shouldn't* they be used for comparisons and printing out?
Nod. I looked at a few possibilities today. But, as usual, I had underestimated the difficulty.
Let me give you an example - if there are guard digits which aren't used for comparisons - could you not get into a situation where two numbers> which compare equal lead to different results after some sequence of arithmetic operations? IMO that would not be good, and at the very least could lead to all kinds of confusions.
Consider what GMP's mpf_t does - there are hidden guard digits that you don't see, which do take part in comparisons and all arithmetic operations, on the other hand they don't provide a way to print those out which makes round tripping impossible - which IMO is very annoying.
On the other hand, MPFR takes a much less loose approach, and rounds everything to *exactly* the requested precision after each step, round tripping is also possible in this case.
The equivalent in cpp_dec_float would be to have no guard digits at all, and round after each operation to exactly Digits10 decimal places. While there may be use cases for that, I think we want to Keep It Simple for now and not go down that road.
This is too costly in base-10. If I (we) ever write another back-end, base-2 might be a better way to go.
So.... the situation we have now seems to be path of least resistance. It's somewhat inelegant having max_digits10 so much larger than digits10, but it seems to me that nothing really bad can happen here - just maybe that serialized numbers will occupy a touch more space on disk than expected? Cheers, John.
You are right again. And if I keep fiddling around with it, then I'm just wasting everyone's time. I designed the e_float back-end (the basis of cpp_dec_float) and tested it for years with its present strategy. I should just stop fiddling around and simply rely on the test suite and adherence to the back-end requirements. And we are getting very close to this, if not already there. I think we're done with the digits10, max_digits10 thing now. Thanks for your help. Best regards, Chris.