[llvm] [AggressiveInstCombine] Match long high-half multiply (PR #168396)

[David Green via llvm-commits]

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@@ -1466,6 +1466,307 @@ static bool foldLibCalls(Instruction &I, TargetTransformInfo &TTI,
   return false;
 }
 
+/// Match high part of long multiplication.
+///
+/// Considering a multiply made up of high and low parts, we can split the
+/// multiply into:
+///  x * y == (xh*T + xl) * (yh*T + yl)
+/// where xh == x>>32 and xl == x & 0xffffffff. T = 2^32.
+/// This expands to
+///  xh*yh*T*T + xh*yl*T + xl*yh*T + xl*yl
+/// which can be drawn as
+/// [  xh*yh  ]
+///      [  xh*yl  ]
+///      [  xl*yh  ]
+///           [  xl*yl  ]
+/// We are looking for the "high" half, which is xh*yh + xh*yl>>32 + xl*yh>>32 +
+/// some carrys. The carry makes this difficult and there are multiple ways of
+/// representing it. The ones we attempt to support here are:
+///  Carry:  xh*yh + carry + lowsum
+///          carry = lowsum < xh*yl ? 0x1000000 : 0
+///          lowsum = xh*yl + xl*yh + (xl*yl>>32)
+///  Ladder: xh*yh + c2>>32 + c3>>32
+///          c2 = xh*yl + (xl*yl>>32); c3 = c2&0xffffffff + xl*yh
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davemgreen wrote:

That's an interesting one - the graph looks like a simpler version of what I have called ladder. It has less cross-edges, but I've incorporated it into the logic of FoldMulHighLadder. It would be nice if some of these canonicalized together but they are different enough that it seems difficult without matching the whole tree again.

https://github.com/llvm/llvm-project/pull/168396