Re: 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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