Re: [boost] Is there any Interest in a Fixed Point Library?

From: Stephen Nutt (snutt_at_[hidden])
Date: 2003-02-28 19:48:16

Kevin,

I started on this must be close to a year ago, and I got wrapped up with
other stuff and never got back to it.

A couple of interesting design ideas.  Someone (sorry I forget who) pointed
me towards a great pdf file describing a fixed point arithmetic enhancement
for embedded compilers.  It was very cool, and had some great ideas.

One nifty option was to specify what would happen on overflow.  There were
two choices.  Either the number would not overflow but go to its limit, or
it would overflow in the 'expected' way.  (Did that make sense?)

So if I had a class
fixed<unsigned char, 3> a = 3.0;    // 8 bit fixed point number with three
significant bits

a * 3 would either give me 7.96875 or 1.0  A possible third choice would be
to raise an exception on overflow/underflow.

My personal interest in the template was for a highly efficient 64 bit fixed
point number.  As it turned out, there was no 64 bit support in Boost at the
time, and getting it turned out to be more of a pain than I had time for!
It may be there now as I think I've seen others look for this also since.

I put together some great templates so I could do arithmetic like

fixed <int, 6> a = val1;
fixed <char, 3> b = val2;
fixed <long, 9> = a + b;

without loss of precision.

I also have templates to do 64 bit arbitary fractional multiplication and
division without loss of precision.  I also have a 64 bit squareroot
function lurking somewhere in the depths of my harddrive.  I'm not sure how
all of this would work if the type was say complex, but I'm sure it could be
worked on.

I'll look for the pdf I mentioned above and if I find it I'll post a url.  I
think this is a great place to start as I believe there is a reasonable
demand for fixed point arithemetic in embedded computers.

Stephen

----- Original Message -----
From: "Kevin Atkinson" <kevin_at_[hidden]>
To: "Boost mailing list" <boost_at_[hidden]>
Sent: Wednesday, February 26, 2003 9:28 PM
Subject: [boost] Is there any Interest in a Fixed Point Library?

>
> Is there any interest in a fixed point math library.  Using templates the
> compiler can keep track of the radix point for you making using fixed
> point math a lot less tedious and error prone.
>
> Attached is a rudimentary implementation which would work acceptably when
> the exponent is not too large or too small.  If the exponent is smaller or
> larger than the size of the underlying integer in bits this code will
> likely behave badly.
>
> I plan to use the attached code to avoid having to deal with serializing
> floating point numbers.  A exponent of -30 (-31 if using an unsigned 32
> bit integer) is especially useful for representing numbers between 0 and
> 1.  The precision will actually be a bit better than a 32 bit float since
> the exponent does not have to be stored.
>
> Comments on the code welcome.  I am not a numerical analysis specialist so
> don't expect me to write a fixed point library for anything beyond simple
> arithmetic.
>
> --
> http://kevin.atkinson.dhs.org
>

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