TMS320F28069: adding floating point number error

Howard Zou

Genius 12365 points

Part Number: TMS320F28069

Hi, the customer is testing 28069 by doing multiple times adding in both CPU and CLA.

In CLA, ClaTask4 is to add the number 11.7 for 20001 times.

ClaTask8 is to initiate the variables and will execute once.

Below is the code in main.c, to add 11.7 for 20001 times in CPU and then force ClaTask4.

They've got the result below:

ClaTmpData1 is the result of adding 11.7 for 20001 times in CLA.

ClaTmpData2 is the result of adding 11.7 for 20001 times in CPU.

But 11.7*20001=234011.7 which is different from the result of CPU or CLA.

And I've tested it on 28379d launchpad and got exactly the same result. and I've noticed that even by adding 11.7 once, I got the result below

Can you tell me why or what I can do to debug? Thanks.

over 8 years ago

0 Howard Zou over 8 years ago

TI__Genius 12365 points

ClaTask4 code is here.

0 Richard Poley over 8 years ago in reply to Howard Zou

TI__Mastermind 27200 points

Howard,

When you repeatedly increment a floating-point number with a fixed floating-point number you will eventually reach the point where the accumulated value cannot be represented with the same exponent as the increment. When this happens, precision will be lost. It's a consequence of using floating-point, and it will happen with any CPU. The attached slide may make it clearer.

If you compute the actual value of 11.7 * 20001 you will find the answer is 2340117. Therefore both answers are wrong, as I have explained. You cannot reach the right answer in single precision floating point.

The fact that they are different is likely due to a slightly different floating-point conversion, however before looking into this further I'd like to ask; what are you doing with the result?

Regards,

Richard

FP precision.pdf

0 Richard Poley over 8 years ago in reply to Richard Poley

TI__Mastermind 27200 points

Correction: the result is 234011.7 (missed the decimal point) but both results are still wrong.

Regards,

Richard

0 Howard Zou over 8 years ago in reply to Richard Poley

TI__Genius 12365 points

Thanks. The customer is just doing test to measure the calculating ability of the device. So you mean that because the fixed floating-point number has fixed 8 bits to represent the exponent, 23 bits for fraction, so there are cases that the precision will be lost, right?

0 Richard Poley over 8 years ago in reply to Howard Zou

TI__Mastermind 27200 points

That is correct.

0 Richard Poley over 8 years ago in reply to Richard Poley

TI__Mastermind 27200 points

Howard,

Just to add: one other thing which might be contributing or causing this error is the rounding modes used in the float conversion. This could also explain why you see a difference between CPU and CLA results. Please take a look at this post:

https://e2e.ti.com/support/microcontrollers/c2000/f/171/p/500481/1815777

Regards,

Richard

0 Howard Zou over 8 years ago in reply to Richard Poley

TI__Genius 12365 points

Thank you, it helps a lot. Do you have any idea how I can get the right answer with adding 11.7 for 20001 times? Now I can get the same results with CLA and CPU, but the result is still wrong. Any modification in the code can do that?

0 Richard Poley over 8 years ago in reply to Howard Zou

TI__Mastermind 27200 points

Howard,

You cannot do this with single precision float. It's a limitation of the numeric type.

You could use IQ math to get a more precise answer in this case. You would need Q13 or lower to get enough range, but there will still be a small error.

Another option is to use a 64-bit "long double" data type. That would give the answer 234011.70000007941.

The errors are:
float: +41.909
_IQ13: -0.9766
long double: +0.00000007941

Regards,

Richard

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TMS320F28069: adding floating point number error