precision errors. microblaze vs matlab single precision... huh?

Hi all embedded gurus out there,
I am working on an embedded platform using microblaze. I am trying
to implement an algo, which does a inverse matrix function on the
microblaze (via C) and then port the results back to matlab.
so this is the scenario.

1) matlab generates some numbers, passes them to microblaze via the
UART (ie. PC to UART)
2) microblaze will then generate the matrix, and then calculate its
inverse and do other stuff (dot product of matrices etc etc).
3) microblaze will then send the result back to PC via UART.

Ok..so here's the problem.
the result obtained differs from matlab's result (I coded the same
implementation also in matlab). the result obtained varies up to an
error of 1 decimal place!!!

How I tried to debug
1) step through the C code using the debugger for microblaze. (this is
very cool tool).
2) at each step of the way, look at how the variables change for each
operation in the C code running on microblaze...and also observe how
the variables change in matlab


this is what I noticed
thinking it was due to matlab processing it in double precision, i
type cast the whole matlab routine in single precision. then I tried
to verify it again in the same way. And I get the same problem

can anyone help? As a result of this precision errors, the whole algo
fails to work. I am really not sure which one to trust now.

Would appreciate if anyone can help me on the same. The current
microblaze platform is using hardware FPU.

Chris

 

Hi,

What rounding mode are you using for Matlab?
MicroBlaze only uses round-to-nearest rounding mode.

In order to get exactly the same every result operation in Matlab has to be
done in single-precision.

Göran

 

Hi Goran,
I am using type cast to single in matlab. Once you round the first
variable to single in matlab, it should round everything after that to
single already. Cos all resulting variables after that are already in
single precision. right?

by the way, you say " In order to get exactly the same every result
operation in Matlab has to be
done in single-precision."

but my question is, the difference in values of the result amount to
orders of >0.5 occasionally! Isnt that a bit too much difference in
results?

Is the FPU inaccurate or am i seeing things...


Chris

 

Hi,

May 2 cents : It seems to me that Desktop PC FPU use larger mantissa
internally than what is strictly required by the IEEE SP standard,
especially for some operations (such as /,sqrt). That *might* explain
your results.

Also, did you check that the matrix inversion algorithm you used is
robust enough in terms of numerical stability ?

Hope it can help.

Steven

chriskoh a écrit :

 

Hi Steven,
so matlab results are more accurate?
the matrix inversion algorithm method is rather robust actually in
terms of numerical stability. What I noticed however is that the
matrix formed already by my C code running on microblaze before the
inversion has already some numerical differences with matlab's
version. simple C code vs matlab single precision code.
but different results obtained. All discovered by stepping through the
C code running on microblaze.
the matrix was formed simply by a dot product.

Chris

 

That expectation might be realistic for expression containing only
multiplications and divisions. However, as soon as the expression
contains additions of a large and a small value or a subtraction
between two more or less equal values, the result depends heavily on
the floating point representation.

What exactly is "single precision floating point" ?

I can think about at least a dozen representations that are using that
name, in which each representations might return a different result
with problematic parameters.

Paul

 

A couple a questions
- Are your matrices anywhere near being singular?
- Are the algorithms the same and implemented identically on the
two systems? That will be most critical near singularity but even away
from it there can be traps.
- Is the data used the same? What do you lose transferring the
data back and forth?
- Finally, what happens when yo perform the obvious sanity check
abd multiply the original matrix by its inverse?

Robert

 

Good day Paul,
so which one is the correct one? PC's matlab of xilinx FPU? What
do I make out of the results?

Chris

 

Which one works? IE what hapens when you multiply the original matrix
by its calculated inverse?

Robert