Re: [boost] Fixed-Point Decimal Type

From: Gabriel Dos Reis (Gabriel.Dos-Reis_at_[hidden])
Date: 2001-05-25 05:51:20

John Max Skaller <skaller_at_[hidden]> writes:

| Gabriel Dos Reis wrote:
| 
| > | I don't see that the rounding mode is a property of the data,
| > | it is property of each individual operation.
| > 
| > No.  Rounding is the act of taking an exact result and producing an
| > approximation within the range of numerical datatype; that is a
| > function defined on a superset of the actual datatype, with values in
| > the set of values of the datatype.  It is independent of individual
| > operations.
| 
| 	I don't think this works. Just consider
| 
| 	decimal<n> * decimal<m>
| 
| There is no 'universal' way to round the results. 

That is why I didn't propose something to that effect. As, I
mentionned, rounding is part of the datatype manipulated. 
My proposal is about

   decimal<n, nearest> * decimal<n, nearest>

You can make nearest the default rounding mode, in which case, it
reads

        deciaml<n> * decimal<n>;

If you want to multiply two numbers with different precision, you need
to make it explicit which precision you want.

| ... The scale
| of the result depends on the arguments AND the operation.
| What you seem to be suggesting is a pair of maps:
| 
| 	LIFT: decimal<n> -> exact decimal
| 	ROUND: exact decimal -> decimal<n>
| 
| But actually, there is a family of maps:
| 
| 	ROUND<n>: exact decimal -> decimal<n>
| 
| and the choice of which ROUND map to use 
| _depends on the operation_ being performed.
| It will differ for addition and multiplication.

I think you misunderstand how the LIA model works.

Let's take mul : decimal<n> * decimal<n> -> decimal<n>.
The result is computed as if:

  1) an exact multiplication is performed, yielding an -exact- result
  (decimal<2*n>). 
  2) and the rounding function is invoked to project the result in 
     decimal<n>.

That is no more different than the conceptual model of IEEE-754.

And no, the model doesn't fail for division and al..

-- Gaby