[boost] Re: Formal Review: fixed-point decimal library

From: Bill Seymour (bill-at-the-office_at_[hidden])
Date: 2003-07-15 11:10:04

Fernando Cacciola wrote:
>
> OK.
> So, correct me if I'm wrong:
> For any given decimal with some int_type, a 'digits' constant is
> associated with it which comes from numeric_limits<int_type>::digits10.
> This constant identifies the maxium number of digits (in both the
> whole and fractional parts) that any such decimal can represent.
>

Right, it's the /precision/ (the total number of representable
digits).  Consider, for example, numeric_limits<int>::digits10
on an implementation with 32-bit ints.  This value will be 9
because all 9-digit values are representable.  There will also
be some some 10-digit values that are representable (if the MSD
is in [-2,2]).

>
> Thus numeric_limits<decimal>::digits and digits10 are equal to
> this constant.
>

Yes, and the two values are equal to each other because
numeric_limits<decimal>::radix is 10.

>
> The scale 's' given by the user specifies the desired number of
> decimal digits.
>

I would say "digits to the right of the decimal point".  (Digits
to the left of the point I would also call "decimal" because
they're base-10.)

>
> It cannot be > '(digits-1'), ...
>

Yes, the scale can be equal to the precision (which I believe is
what you're calling "digits"); but then, in general, there won't be
any digits to the left of the point.  (As with the example above
with numeric_limits<int>::digits10, there could be one valid digit
to the left of the point if it's not too large.)

>
> I'd put a description like the one above in the docs so that the
> limit on total number of digits and its relation with the scale
> is well documented.
>

Agreed.

> >
> > Why? [can't decimal be unbounded]
> >
> Because it has a constant max_scale.
>

Ah, so.  Yes, I see that now.  Good catch.

> >
> > I don't see this.  If int_type just wraps around on overflow,
> > then why wouldn't the decimal type itself do the same?
>
> Because decimal has its own arithmetic.
> For instance, would decimal::add/mul wrap around even if
> int_type would?

Yes, I think you're right about that.  OK, is_bounded should be true
and is_modulo should be false.  I'll fix that.

Re the max_val, min_val and max_scale constants:  there was some
reason that I wanted them to be constant expressions.  I'll reconsider
that; but I don't want to promise a change right now.

Re construction from unsigned int:  I think you gave a good reason
to allow it.  I'm pretty busy at my day job right now, so I can't
promise a quick change; but I agree with you.

>
> If the concept of 'digits' is formalized, alon with its relation
> to 'scale', then this statement could simply say that "The conversion
> will be exact if the string contains no more than 'digits()' digits
> (whole and/or decimal)"
>

I don't think that's right.  I can assign 123.45 to a decimal with
a scale of 2 without rounding.  Do I misunderstand what you're
saying?

--Bill Seymour