feat(hugr-llvm): Emit divmod and mod operations

[croyzor]

Relates to #1702 .

[codecov]

Codecov Report

Attention: Patch coverage is 94.40559% with 16 lines in your changes missing coverage. Please review.

Project coverage is 83.40%. Comparing base (41905f9) to head (57823a8).
Report is 3 commits behind head on main.

Files with missing lines	Patch %	Lines
hugr-llvm/src/extension/int.rs	94.40%	2 Missing and 14 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2025      +/-   ##
==========================================
- Coverage   83.79%   83.40%   -0.39%     
==========================================
  Files         211      213       +2     
  Lines       39757    40482     +725     
  Branches    36435    36696     +261     
==========================================
+ Hits        33314    33764     +450     
- Misses       4567     4829     +262     
- Partials     1876     1889      +13     

Flag	Coverage Δ
python	85.84% <ø> (-6.40%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[aborgna-q]

This is used in various other places (conversions.rs:156 and int.rs:359,377,396,549 on main). Should we rename this to get_int_width and call it on those places to?

Also, no need to clone the array,

let [TypeArg::BoundedNat { n }] = args.node.args() else { bail!(...) }
*n

should do the trick.

[aborgna-q]

This caught me by surprise. Why are we doing "signed dividend, unsigned divisor" in div/mod ???

The docs say that the operand may be any non-zero unsigned value,

hugr/hugr-core/src/std_extensions/arithmetic/int_ops.rs

Lines 194 to 195 in 41905f9

	idivmod_s => "given signed integer -2^{N-1} <= n < 2^{N-1} and unsigned 0 <= m < 2^N, generates \
	signed q and unsigned r where q*m+r=n, 0<=r<m (m=0 will call panic)",

so to be correct in the lowering we need to allow any non-zero value here and return.

Even more, LLVM's signed remainder is not modulo; its result has the same sign as the dividend.
To lower things correctly here we need to do a lot of extra logic

$$ \texttt{hugr-divmod-s}(n: signed, m: unsigned) = $$ $$ \begin{cases} (0, n) \qquad\qquad\qquad\qquad\qquad\qquad & \text{if } m \geq 2^{N-1} \text{ and } n>0\\ (-1, r-n) & \text{if } m \geq 2^{N-1} \text{ and } n<0\\ (\texttt{llvm-signed-div}(n,m), &\\ \quad \texttt{llvm-signed-rem}(n,m)) & \text{if } m < 2^{N-1} \text{ and } n>0\\ (\texttt{llvm-signed-div}(n,m), 0) & \text{if } m < 2^{N-1} \text{ and } n<0 \text{ and } \texttt{llvm-signed-rem}(n,m)= 0 \\ (\texttt{llvm-signed-div}(n,m)-1, & \\ \quad n-\texttt{llvm-signed-rem}(n,m)) & \text{if } m < 2^{N-1} \text{ and } n<0 \text{ and } \texttt{llvm-signed-rem}(n,m) \neq 0 \end{cases} $$

💀

[croyzor]

I think we can write the second case ($m \geq 2^{N -1} \text{ and } n &lt; 0$) as (-1, n + m).
qm + r = qm + n + m where q = -1 gets us back n more simply

[croyzor]

Plus the last case should be (llvm-signed-div(n, m) - 1, m - llvm-signed-rem(n,m)) (m instead of n in the snd element)

[croyzor]

Actually the last case should be llvm-signed-div(n, m) - 1, m + llvm-signed-rem(n, m)) because the result of llvm-signed-rem will be negative to match the dividend