Computing the norm of Falcon signature polynomial $s_2$
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描述
When computing the square norm of the signature polynomial $s_2$ we are doing some `u32` comparisons in order to compute the square of the centered values using `norm_sq`.
On the other hand, during the probabilistic product check, we are also range checking the coefficients of $s_2$ to be less than Falcon prime.
It seems like there is some redundant checks on these coefficients and it would be nice to find a way to optimize them.
I have now added bound checks on the coefficients of `s2` similar to those on `h`.
This has unfortunately led to an increase in the number of cycles, the current cycle count is just shy of 60000 cycles. We can comeback to this to see if we can optimize these checks.
_Originally posted by @Al-Kindi-0 in https://github.com/0xPolygonMiden/miden-vm/pull/1661#discussion_r1967664373_
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