Re: Newbie question about numbers

On 10/24/07, Scott Hickey <[email protected]> wrote:
> I guess I probably need to understand BigDecimal better. I have used it quite a bit in an application with some very extensive testing where the numbers have to match what would be calc'd if done by hand and they match (so far).

Yes, this will be true if in BigDecimal for most cases because it
expands the amount of storage to represent the number if at all
possible.  Unfortunately, this results in unbounded memory usage to
get ever increasing amounts of accuracy, and slower performance.

>
> > (eqv? #e1.1 (+ #e1.0 #e0.1))
> # t

The reason for the difference in the latter is that SISC uses a more
accurate conversion from inexacts to exacts, but which unfortunately
relies on some calculation, which with inexact numbers can introduce
representational error.

Scott

> Thanks for your replies!
>
>
> Scott Hickey
>
>
> ----- Original Message ----
> From: Scott G. Miller <[email protected]>
> To: Scott Hickey <[email protected]>
> Cc: [email protected]
> Sent: Wednesday, October 24, 2007 11:09:35 AM
> Subject: Re: [Sisc-users] Newbie question about numbers
>
>
> On 10/24/07, Scott Hickey <[email protected]> wrote:
> > Obviously, 1.2 can be represented exactly using the BigDecimal class.
>  So you're saying that #e doesn't force an different underlying data
>  type than floating point double? In sisc or in Scheme in general?
> >
>
> SISC isn't using BigDecimal, and mathematically, 1.2 isn't exact even
> in the BigDecimal class, rather, it allows you to constraint the
> amount of precision.
>
> #e converts from the inexact number you specified, which is
> represented as a double to start, into an exact number.  This yields
> an exact number, but not the one you may expect.  This is true of most
> programming languages, Scheme included.
>
> > And I should alway represent decimal amounts as fractions to retain
>  exactness in all Schemes?
>
> And in mathematics in general.  The financial industry insists on this
> for accuracy.
>
> >
> > Finally, if I'm pulling data out of a database using SISCWeb, do I
>  lose exactness for decimal amounts?
>
> Decimal amounts never have exactness on computers, but for most
> purposes they tend to keep the precision you expect.  Errors usually
> accumulate when you start operating on the numbers.
>
> Scott
>
>
> > ----- Original Message ----
> > From: Scott G. Miller <[email protected]>
> > To: Scott Hickey <[email protected]>
> > Cc: [email protected]
> > Sent: Wednesday, October 24, 2007 2:17:28 AM
> > Subject: Re: [Sisc-users] Newbie question about numbers
> >
> >
> > On 10/23/07, Scott Hickey <[email protected]> wrote:
> > > I'm new to Scheme.
> > >
> > > In Java, for business math, I declare all my numbers that
>  participate
> > >  in calculations as BigDecimal.  In Scheme, I have seen that there
>  is
> >  the
> > >  notion of exactness.
> > >
> > > I understand that this should evaluate to false because the
> >  underlying
> > >  representation is a double.
> > >
> > > #;> (eqv? 1.2 (+ 1.1 0.1))
> > > #f
> > >
> > > It was my impression that putting #e in front of a litteral would
>  for
> > >  an exact representation, but the statement still fails.
> > > #;> (eqv? #e1.2 (+ #e1.1 #e0.1))
> > > #f
> >
> > The problem is that the conversion from an inexact number to an exact
> > number, well, isn't exact.  Since the representation of for example
> > 1.2 isn't a precise one, and the result of adding 1.1 to 0.1 may not
> > also yield precisely 1.2, its likely that that test still fails.  The
> > only sure way to ensure equivalence in the above expressions is to
> > start with exact numbers.  This is why for example financial packages
> > use fractions to represent money.
> >
> > #;> (eqv? 1200/1000 (+ 1100/1000 100/1000))
> > #t
> >
> >    Scott
> >
> >
> >
> >
>
>
>
>

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