>     That is to say, if the Sage
> documentation says:
>
>    sage: foo(bar)
>    1.2345
>
> but in fact in Sage one has
>
>    sage: foo(bar)
>    1.2351
>
> then I would consider this misleading documentation, i.e., a bug.
> Your statement above suggests that you *don't* consider this a bug at
> all.   In Sage, one possible solution (and it depends on context
> whether this it the right solution or not) would be to change the
> documentation to
>
>    sage: foo(bar)     # last few digits numerically unstable
>    1.23...
>

The idea of documentation is that the user can see what to expect
when typing a command. Your result 1.23... achieves this goal.

The idea of regression test is to detect changes in results
that are incorrect. If you do a computation on a system and the
result differs in the trailing bits (due to a real bug) then
your regression test f() = 1,23... will succeed.

So representing the result f() = 1.23....
will not detect a bad computation if the new library has a bug
and is, at best, a weak regression test.

All non-bit floating point output involves a choice of rounding.
You have chosen to do rounding by truncation. This choice is not
obvious nor necessarily the best. See
http://www.diycalculator.com/popup-m-round.shtml

In any case, you're welcome to test any way you prefer.
I just thought I'd give you insights from Axiom's tests.
I'll let it rest.

Tim

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