[llvm] [VPlan] Introduce explicit ExtractFromEnd recipes for live-outs. (PR #100658)

[via llvm-commits]

================
@@ -8614,20 +8637,108 @@ static void addLiveOutsForFirstOrderRecurrences(VPlan &Plan) {
   }
   VPValue *OneVPV = Plan.getOrAddLiveIn(
       ConstantInt::get(Plan.getCanonicalIV()->getScalarType(), 1));
+  VPValue *TwoVPV = Plan.getOrAddLiveIn(
+      ConstantInt::get(Plan.getCanonicalIV()->getScalarType(), 2));
 
   for (auto &HeaderPhi : VectorRegion->getEntryBasicBlock()->phis()) {
     auto *FOR = dyn_cast<VPFirstOrderRecurrencePHIRecipe>(&HeaderPhi);
     if (!FOR)
       continue;
 
+    // This is the second phase of vectorizing first-order recurrences, creating
+    // extract for users outside the loop. An overview of the transformation is
+    // described below. Suppose we have the following loop with some use after
+    // the loop of the last a[i-1],
+    //
+    //   for (int i = 0; i < n; ++i) {
+    //     t = a[i - 1];
+    //     b[i] = a[i] - t;
+    //   }
+    //   use t;
+    //
+    // There is a first-order recurrence on "a". For this loop, the shorthand
+    // scalar IR looks like:
+    //
+    //   scalar.ph:
+    //     s.init = a[-1]
+    //     br scalar.body
+    //
+    //   scalar.body:
+    //     i = phi [0, scalar.ph], [i+1, scalar.body]
+    //     s1 = phi [s.init, scalar.ph], [s2, scalar.body]
+    //     s2 = a[i]
+    //     b[i] = s2 - s1
+    //     br cond, scalar.body, exit.block
+    //
+    //   exit.block:
+    //     use = lcssa.phi [s1, scalar.body]
+    //
+    // In this example, s1 is a recurrence because it's value depends on the
+    // previous iteration. In the first phase of vectorization, we created a
+    // VPFirstOrderRecurrencePHIRecipe v1 for s1. Now we create the extracts
+    // for users in the scalar preheader and exit block.
+    //
+    //   vector.ph:
+    //     v_init = vector(..., ..., ..., a[-1])
+    //     br vector.body
+    //
+    //   vector.body
+    //     i = phi [0, vector.ph], [i+4, vector.body]
+    //     v1 = phi [v_init, vector.ph], [v2, vector.body]
+    //     v2 = a[i]
+    //     b[i] = v2 - v1
+    //     b[i, i+1, i+2, i+3] = v2 - v3
+    //     br cond, vector.body, middle.block
+    //
+    //   middle.block:
+    //     s.penultimate = v2(2)
----------------
ayalz wrote:

```suggestion
    //     vector.recur.extract.for.phi = v2(2)
```
? Admittedly worth renaming.

https://github.com/llvm/llvm-project/pull/100658