[llvm] [LoopIdiomRecognize] Enable clmul optimization for CRC loops (PR #203405)

[Ramkumar Ramachandra via llvm-commits]

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@@ -376,6 +376,54 @@ CRCTable HashRecognize::genSarwateTable(const APInt &GenPoly,
   return Table;
 }
 
+// Divide one GF(2) polynomial by another.
+static APInt calculateGF2Quotient(APInt Dividend, const APInt &Divisor) {
+  unsigned DivisorDeg = Divisor.getActiveBits() - 1;
+  APInt Quotient = APInt::getZero(Dividend.getBitWidth());
+  unsigned DividendDeg;
+  while (!Dividend.isZero() &&
+         (DividendDeg = Dividend.getActiveBits() - 1) >= DivisorDeg) {
+    unsigned Shift = DividendDeg - DivisorDeg;
+    Quotient.setBit(Shift);
+    Dividend ^= Divisor.shl(Shift);
+  }
+  return Quotient;
+}
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artagnon wrote:

This looks like the translation of the floor division algorithm for polynomial rings:

```
def floor_division(S, P):
    Q = 0
    while S != 0 and deg(S) >= deg(P):
        T = S[deg(S)] / P[deg(P)]
        Q = Q + T
        S = S - T * P
    return Q
```

Could rename the function floorDivideGF2, and add this as a comment? Could also clarify the function, and write a quick degree helper lambda?

https://github.com/llvm/llvm-project/pull/203405