diff --git a/mlir/lib/IR/AsmPrinter.cpp b/mlir/lib/IR/AsmPrinter.cpp
--- a/mlir/lib/IR/AsmPrinter.cpp
+++ b/mlir/lib/IR/AsmPrinter.cpp
@@ -555,18 +555,40 @@
   llvm::ScopedHashTable<StringRef, char> usedNames;
   llvm::BumpPtrAllocator usedNameAllocator;
 
+  // If testing that SSA IDs are being used in tests directly.
+#ifdef MLIR_TEST_SSA_ID_SEQUENCE_ASSUMED
+  static constexpr unsigned initID() {
+    // This could be more random seed, but given the intention is just to
+    // ensure 0 is not assumged, should suffice.
+    return __LINE__ + 42;
+  }
+
+  static unsigned incrementID(unsigned &id) {
+    unsigned int ij = id;
+    // Use MINSTD to increment (period 2^31-1).
+    id = (16807l * ij) % 2147483647;
+    return ij;
+  };
+#else
+  static constexpr unsigned initID() { return 0; }
+
+  static unsigned incrementID(unsigned &id) { return id++; }
+#endif
+
   /// This is the next value ID to assign in numbering.
-  unsigned nextValueID = 0;
+  unsigned nextValueID;
   /// This is the next ID to assign to a region entry block argument.
-  unsigned nextArgumentID = 0;
+  unsigned nextArgumentID;
   /// This is the next ID to assign when a name conflict is detected.
-  unsigned nextConflictID = 0;
+  unsigned nextConflictID;
 };
 } // end anonymous namespace
 
 SSANameState::SSANameState(
     Operation *op,
-    DialectInterfaceCollection<OpAsmDialectInterface> &interfaces) {
+    DialectInterfaceCollection<OpAsmDialectInterface> &interfaces)
+    : nextValueID(initID()), nextArgumentID(initID()),
+      nextConflictID(initID()) {
   llvm::ScopedHashTable<StringRef, char>::ScopeTy usedNamesScope(usedNames);
   numberValuesInOp(*op, interfaces);
 
@@ -704,7 +726,7 @@
       continue;
     if (isEntryBlock) {
       specialNameBuffer.resize(strlen("arg"));
-      specialName << nextArgumentID++;
+      specialName << incrementID(nextArgumentID);
     }
     setValueName(arg, specialName.str());
   }
@@ -740,7 +762,7 @@
 
   // If the first result wasn't numbered, give it a default number.
   if (valueIDs.try_emplace(resultBegin, nextValueID).second)
-    ++nextValueID;
+    incrementID(nextValueID);
 
   // If this operation has multiple result groups, mark it.
   if (resultGroups.size() != 1) {
@@ -790,7 +812,7 @@
 void SSANameState::setValueName(Value value, StringRef name) {
   // If the name is empty, the value uses the default numbering.
   if (name.empty()) {
-    valueIDs[value] = nextValueID++;
+    valueIDs[value] = incrementID(nextValueID);
     return;
   }
 
@@ -846,7 +868,7 @@
     probeName.push_back('_');
     while (true) {
       probeName.resize(name.size() + 1);
-      probeName += llvm::utostr(nextConflictID++);
+      probeName += llvm::utostr(incrementID(nextConflictID));
       if (!usedNames.count(probeName)) {
         name = StringRef(probeName).copy(usedNameAllocator);
         break;