#13676: improve i0_bw pcc

[KalaivaniMCW]

Ticket

Link to Github Issue #13676

Problem description

Current implementation of i0_bw uses reciprocal op which has an ongoing issue #14672

What's changed

• Reimplemented i0_bw using i1 approach
• implemented ttnn::i1 using ttnn::i0
• Note: yet to add GS and BH implementation - once kernel is finalized
• Updated input range in doc and sweeps

• Profiling : On main vs On branch

op,count,python min dispatch time (ms),python mean dispatch time(ms),python mean dispatch + sync time (ms),C++ mean dispatch time (ms) ttnn.i0_bw,800,0.97,0.997,3.717,0.364 (main ) ttnn.i0_bw,800,0.241,0.244,0.884,0.086 (branch)

Checklist

• [x] Post commit CI passes https://github.com/tenstorrent/tt-metal/actions/runs/11960875200
• [ ] Blackhole Post commit (if applicable)
• [ ] Model regression CI testing passes (if applicable)
• [ ] Device performance regression CI testing passes (if applicable)
• [x] New/Existing tests provide coverage for changes

[KalaivaniMCW]

Hi @rdjogoTT , I would like your thoughts on this kernel implementation of i1 (corresponding torch op torch.special.i1 ) and another approach in here. In both cases k = 0 to 10, same as in the i0 kernel.

In the former approach (in this PR), i1 is computed based on the current i0 kernel and gives a pcc upto 0.996 in the latter approach it sticks to the general formula, although it is not successful in giving a good pcc

Would like to know if there is any other approach we can try ?

We need this op to implement backward op for i0 efficiently.

[rdjogoTT]

@KalaivaniMCW I think the approach of implementing i1 as a polynomial is correct. I took a quick look at https://github.com/tenstorrent/tt-metal/pull/15325 and found that if I change line 17 in tt_metal/hw/ckernels/wormhole_b0/metal/llk_api/llk_sfpu/ckernel_sfpu_i1.h to be:

    ((coef0 + (coef1 + (coef2 + (coef3 + (coef4 + (coef5 + (coef6 + (coef7 + (coef8 + (coef9 + coef10 * t2) * t2) * t2) * t2) * t2) * t2) * t2) * t2 ) * t2) * t2) * t2)

then the i1 test gets PCC ~= 0.999998 and the i0_bw test gets PCC ~= 0.9998. The change is that you might be missing a * t2 term in your POLYVAL10_I1. Can you double check that this is it? I haven't taken too close of a look so I might be wrong, but I compared the polynomial you have in i1 to the one you have in i0 and the i0 one has this extra term present.

Similarly, I see that in this PR, the POLYVAL10_DERIVATIVE you defined does not make use of the coef0 term. Not sure if this was intentional or not, so please check.

[KalaivaniMCW]

@rdjogoTT In POLYVAL10_DERIVATIVE I pass the coef0 term just to compare with current implementation, what happens is the coef0 is with 0 (i.e. k coef) and so it gets ignored. Let me test POLYVAL10_I1 once again. Thank you for the feedback!