TMS320C55x DSP Function Floating Point Issue

No experience with the C55xx or it's DSPLIB. Looking at the User Guide, the sqrt_16() function takes it's arguments are in Q.15 fixed point fractional format. This means 1 is really 1 x 2^-15. See guide

http://www.ti.com/litv/pdf/spru422j

However there is a bug with sqrt_16().

http://e2e.ti.com/support/dsp/tms320c5000_power-efficient_dsps/f/109/t/96590.aspx
http://processors.wiki.ti.com/index.php/DSPLIB#sqrt_16_has_off-by-one_error_and_is_coded_inefficiently

The bug effectively adds 0.5 x 2^-15 before doing the sqrt, ie

x = 1
a = (x+0.5) * 2^-15 = 4.577e-5
b = sqrt(a) = 6.765e-3 = 221.7 x 2^-15 = r x 2^-15
r = 222

Thanks for the clear explanation. All the results make sense now, except sqrt(0).

When I calculate the sqrt(0), the result it gives is 1.

However, following the your steps, the result should be 128, instead of 1:

x = 0

a = (x+0.5)*2^-15 = 1.5259e-5

b = sqrt(a) = 3.906e-3 = 128 * 2^-15 = r * 2^-15

r=128

Could you please explain this?

Thanks,

Qingkun

Brian Willoughby's post suggests that the rounding, or adding 0.5, occurs within the algorithm on each succesive approximation. You would have to look at the source code and trace each iteration for successive errors.

The steps that I detailed is just a guess at the what the real algorithm is doing. Sorry, I should have said that. I don't have the source code. It would be a lot of work for me to detail each step of the iteration. I don't know the C55xx processor well enough. If you need an answer, unverify my post and hopefully a more knowledgable person can answer you.

I see. Still thank you a lot. Your answer almost make everything make sense.