Thursday, September 29, 2005, 10:12:44 PM, Dennis Cote wrote:
> On 9/29/05, Darren Duncan <[EMAIL PROTECTED]> wrote:
>[...]
>>> 2. DECIMAL(p,s) - An exactly remembered fractional number that is
>> typically stored in a form akin to text, such as one byte per base-10
>> digit. These can effectively store arbitrarily large numbers of any
>> length and precision without loss of detail, although doing math with
>> them may be slower. For example, if you store '2.5' in one, then
>> '2.5' is actually stored.
> This can also be done with fixed point fractions. This type of scaled
> integer with a fractional component are often used by integer DSPs. They
> store a value in an integer with a fixed binary point (rather than a
> floating binary point as implied by the name floating point). [...]
For those still following this thread, and looking for more examples
of the infinite representations of numbers ;-), here is another...
Instead of a binary fixed point, you can use a binary number with an
implicit decimal fixed point. For example, if your implicit decimal
point were 10^2, the number 345 (stored as a binary integer) would
represent the number 3.45. Concretely in C syntax, you'd print numbers
as printf("%d.%02u", x/100, x%100). Addition and subtraction can be
done with the integer operators. Multiplication and division take some
care to avoid loss of range or precision, but abstractly, multiply is
(x * y) / 100 and divide is (x * 100) / y. This is a neat hack to
maintain fixed decimal accuracy with binary integers.
> These values can also be stored as arbitrary precision integers,
> which store multiple integers words to represent the value which can
> again be interpreted as a fixed point fraction, or as BCD (binary
> coded decimal) values which store 2 digits per byte.
Storing numbers as *two* arbitrary precision integers, a numerator and
a denominator, gives you all the exact rationals (at least as big as
your memory allows -- reducing the numbers helps). Common Lisp and Scheme
have rationals as well as real, complex, and arbitrary precision
integer numbers. http://mathworld.wolfram.com/RationalNumber.html
--
Doug Currie
Londonderry, NH
