From 77c5dbabc6c4b65580629cd7064a13d74ddf5a63 Mon Sep 17 00:00:00 2001
From: Jakob Botsch Nielsen <Jakob.botsch.nielsen@gmail.com>
Date: Mon, 4 Mar 2024 10:15:29 +0100
Subject: [PATCH] JIT: Support subtraction in scalar evolution (#99154)
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Represent `x - y` as `x + y * -1` (this works even for MinValue).

For example:
```csharp
public static int Foo(int[] arr, int k)
{
    int sum = 0;
    for (int i = arr.Length - 1; i >= 0; i -= k)
    {
        sum += arr[i];
    }

    return sum;
}
```
analyzes to
```
STMT00007 ( ??? ... ??? )
N004 (  0,  0) [000044] DA---------                         ▌  STORE_LCL_VAR int    V03 loc1         d:3 $VN.Void
N003 (  0,  0) [000043] -----------                         └──▌  PHI       int    $241
N001 (  0,  0) [000053] ----------- pred BB03                  ├──▌  PHI_ARG   int    V03 loc1         u:4
N002 (  0,  0) [000051] ----------- pred BB02                  └──▌  PHI_ARG   int    V03 loc1         u:2 $201
  => <L00, V03.2, (V01.1 * -1)>
```

```csharp
public static int Bar(int n)
{
    int sum = n * n;
    for (int i = 0; i < n; i++)
    {
        sum -= i;
    }

    return sum;
}
```

analyzes to
```
N004 (  0,  0) [000029] DA---------                         ▌  STORE_LCL_VAR int    V01 loc0         d:3 $VN.Void
N003 (  0,  0) [000028] -----------                         └──▌  PHI       int    $140
N001 (  0,  0) [000033] ----------- pred BB03                  ├──▌  PHI_ARG   int    V01 loc0         u:4
N002 (  0,  0) [000031] ----------- pred BB02                  └──▌  PHI_ARG   int    V01 loc0         u:2 $100
  => <L00, V01.2, <L00, (V02.2 (0) * -1), -1>>

```
for `sum`. It would be `<L00, V01.2, <L00, 0, -1>>` if we resolved SSA
defs during simplification -- I'll make that change in a future PR.

Also add some more documentation around the symbolic way we resolve
addrecs.
---
 src/coreclr/jit/scev.cpp | 49 +++++++++++++++++++++++++++++++++++++++-
 1 file changed, 48 insertions(+), 1 deletion(-)

diff --git a/src/coreclr/jit/scev.cpp b/src/coreclr/jit/scev.cpp
index 911cb1ff05026..5819b56bdfd3a 100644
--- a/src/coreclr/jit/scev.cpp
+++ b/src/coreclr/jit/scev.cpp
@@ -469,12 +469,53 @@ Scev* ScalarEvolutionContext::AnalyzeNew(BasicBlock* block, GenTree* tree, int d
 
             assert(ssaDsc->GetBlock() != nullptr);
 
+            // Try simple but most common case first, where we have a direct
+            // add recurrence like i = i + 1.
             Scev* simpleAddRec = CreateSimpleAddRec(store, enterScev, ssaDsc->GetBlock(), ssaDsc->GetDefNode()->Data());
             if (simpleAddRec != nullptr)
             {
                 return simpleAddRec;
             }
 
+            // Otherwise try a more powerful approach; we create a symbolic
+            // node representing the recurrence and then invoke the analysis
+            // recursively. This handles for example cases like
+            //
+            //   int i = start;
+            //   while (i < n)
+            //   {
+            //     int j = i + 1;
+            //     ...
+            //     i = j;
+            //   }
+            // => <L, start, 1>
+            //
+            // where we need to follow SSA defs. In this case the analysis will result in
+            // <symbolic node> + 1. The symbolic node represents a recurrence,
+            // so this corresponds to the infinite sequence [start, start + 1,
+            // start + 1 + 1, ...] which can be represented by <L, start, 1>.
+            //
+            // This approach also generalizes to handle chains of recurrences.
+            // For example:
+            //
+            //   int i = 0;
+            //   int j = 0;
+            //   while (i < n)
+            //   {
+            //     j++;
+            //     i += j;
+            //   }
+            // => <L, 0, <L, 1, 1>>
+            //
+            // Here `i` will analyze to <symbolic node> + <L, [initial value of j], 1>.
+            // Like before this corresponds to an infinite sequence
+            // [start, start + <L, [initial value of j], 1>, start + 2 * <L, [initial value of j], 1>, ...]
+            // which again can be represented as <L, start, <L, [initial value of j], 1>>.
+            //
+            // More generally, as long as we have only additions and only a
+            // single operand is the recurrence, we can represent it as an add
+            // recurrence. See MakeAddRecFromRecursiveScev for the details.
+            //
             ScevConstant* symbolicAddRec = NewConstant(data->TypeGet(), 0xdeadbeef);
             m_ephemeralCache.Emplace(store, symbolicAddRec);
 
@@ -515,6 +556,7 @@ Scev* ScalarEvolutionContext::AnalyzeNew(BasicBlock* block, GenTree* tree, int d
             return NewExtension(cast->IsUnsigned() ? ScevOper::ZeroExtend : ScevOper::SignExtend, TYP_LONG, op);
         }
         case GT_ADD:
+        case GT_SUB:
         case GT_MUL:
         case GT_LSH:
         {
@@ -532,6 +574,10 @@ Scev* ScalarEvolutionContext::AnalyzeNew(BasicBlock* block, GenTree* tree, int d
                 case GT_ADD:
                     oper = ScevOper::Add;
                     break;
+                case GT_SUB:
+                    oper = ScevOper::Add;
+                    op2  = NewBinop(ScevOper::Mul, op2, NewConstant(op2->Type, -1));
+                    break;
                 case GT_MUL:
                     oper = ScevOper::Mul;
                     break;
@@ -651,7 +697,8 @@ void ScalarEvolutionContext::ExtractAddOperands(ScevBinop* binop, ArrayStack<Sce
 //   recursiveScev - A symbolic node whose appearance represents the value of "scev"
 //
 // Returns:
-//   A non-recursive addrec
+//   A non-recursive addrec, or nullptr if the recursive SCEV is not
+//   representable as an add recurrence.
 //
 Scev* ScalarEvolutionContext::MakeAddRecFromRecursiveScev(Scev* startScev, Scev* scev, Scev* recursiveScev)
 {