[Bug Report] HiFi4 gives more inaccurate result than HiFi2 in bfloat16 multiplication on FPU

[jeongu-moreh]

Describe the bug
It is expected that HiFi4 gives more accurate result compared to HiFi2 for bfloat16 multiplication but in some cases it does not.

To Reproduce
For bfloat16 multiplication (mul_tiles) on Wormhole B0:

• 1.3125 × 7.96875
  • HiFi2: 10.4375
  • HiFi4: 10.5

In this case the mantissa of 7.96875 is 0b1.1111111 (least significant bit is 1) so HiFi2 and HiFi4 give different results according to this comment: #12453 (comment). If I understood correctly, HiFi2 caculates 1.3125 × 7.9375 (mantissa 0b1.1111110) = 10.41796875 and then it is rounded to 10.4375 so the result is as expected. However, HiFi4 must calculate with the full precision so its result must be 10.458984375 and 10.4375 when rounded, which is different from the actual result. I wonder if this is intended behavior of the hardware or a bug in LLK.

Expected behavior
HiFi4 gives the same result with HiFi2.