Re: A Simplified Number System

From: Sean O'Leathlobhair (jwlawler_at_yahoo.com)
Date: 11/03/04 

Date: 3 Nov 2004 01:42:27 -0800

Tak To <takto@alum.mit.edu.-> wrote in message news:<lpadnSCueY3LjhXcRVn-sQ@comcast.com>...
> Sean wrote:
> > What are your "fixed point numbers"? The ones most familiar
> > to me are BCD.
>
> Lee Sau Dan wrote:
> > Fixed point is as opposed to floating point. Recall that a floating
> > point number consists of 2 (signed) parts: mantissa and exponent.
> > With fixed point, I mean the exponent is always fixed. So, you only
> > need to store the mantissa. The exponent is implicit. You would of
> > course use exponents that are (negative) powers of 10 for financial
> > applications. A reasonable way to represent the mantissa in binary is
> > to use 2's complement form.
>
> Wiktor S. wrote:
> > It's like keeping all prices in cents instead of dollars and it's
> > fractions (or whatever currencies you use). I think it's the best
> > solution. Normal integers and normal arithmetics. You only need to
> > display them correctly. No weird BCD, no special structures.
>
> In some programming languages such as PL/1, one can declare fixed
> point numbers as, for example, FIXED(5,2), meaning a precision of
> 5 (decimal) digits for the integral part, 2 digits for the fraction
> part. The compiler would then do all the converion for you.
>
> Tak

An even more important example is SQL which is the dominant database
language. In a similar way you may declare types such as
DECIMAL(11,2).

The implementer of a particular database is free to choose any
technique provided it functions correctly. A compliant product could
be built using scaled integers but I am unaware of one. But when the
hardware has BCD support then this is a good choice and this is very
popular.

What's wrong with BCD? Those familiar with it think it is the obvious
easy solution and most like the way humans do arithmetic (*). When
introducing people with a Cobol background to a language such as C++,
I have to spend quite a bit of time explaining the weird types int and
double.

(*) This is very important in financial applications. Auditors do
things in a particular human way and will call anything else "wrong".
It is no good explaining the intricacies of computer arithmetic to
them.

What you are used to seems normal and sensible and what you are unused
to seems weird and unnecessary. It works both ways around.

Seán O'Leathlóbhair

Relevant Pages

  • Re: A Simplified Number System
    ... > Fixed point is as opposed to floating point. ... Normal integers and normal arithmetics. ... No weird BCD, no special structures. ... digits for the integral part, ...
    (sci.lang)
  • Re: A Simplified Number System
    ... > Fixed point is as opposed to floating point. ... The exponent is implicit. ... integers and normal arithmetics. ... weird BCD, no special structures. ...
    (sci.lang)
  • Re: Math errors in python
    ... Why would BCD floating point have any less range than ... To get the same range and precision as a 32-bit IEEE, ... binary floating point with about a 50% penalty in storage ...
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