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## Fixed-Point toolbox for octave-forge

 From: David Bateman Subject: Fixed-Point toolbox for octave-forge Date: Tue, 25 May 2004 17:37:56 +0200 User-agent: Mutt/1.4.1i

```Dear All,

I've just committed a fixed-point toolbox for octave to octave-forge.
The toolbox, creates numbers with a known number of bits before and
after the decimal point and then allows arbitrary mathematical
operations on them, taking into account the loss of precision at each
stage. This simulates a real limited complexity implementation of an
algorithm in an ASIC, and can be used to optimize the complexity (i.e
number of bits at each stage, and thus number of logic cells) of an
implementation.

What it does is create several new user types for fixed point scalar,
complex scalars, matrices and complex matrices, and the corresponding
operators on these types. As this code was first written against 2.1.50
there is no capabilities at this time for NDArray operations with this
code, however I'm not sure this is a problem.

A typical use of the toolbox might be something like

n = 2;
a = rand (n, n);
b = rand (n, n);

## Create fixed-point version with 1 bit before decimal and 5 after.
af = fixed (1, 5, a);
bf = fixed (1, 5, b);

c = myfunc (a, b);
cf = myfunc (af, bf);

function y = myfunc (a, b)
y = a * b;
endfunction

where as you can see the underlying function myfunc is unchanged, while
it is called with either floating or fixed point types. The case above is
for fixed-point values with 1-bit before the decimal point and 5 after,
and for me gave a result of

octave:8> c
c =

0.98105  0.94436
0.82622  0.30831

octave:9> cf
cf =

0.93750  0.90625
0.78125  0.25000

which clearly shows the loss of precision of a fixed-point algorithm
with only 6-bits of precision in a matrix multiply. One gotcha in
this toolbox is the use of the concatenation operator "[]" which
will implicitly reconverts fixed-point values back to floating-point.
This is due to an internal limitation of octave at this moment.
I hope in the future that this limitation will be removed, with a
reimplementation of the concatenation operator within octave itself.

The code can be found in the octave-forge cvs under main/fixed. Full
documentation is available and will be built as postscript and texinfo
during the build of the package.

Regards
David

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