Added polynomial induction variables analysis. With tests.

Rationale:
Information on polynomial sequences is nice to further enhance
BCE and last-value assignment. In this case, this CL enables more
loop optimizations for benchpress' Sum (80 x speedup). Also
changed rem-based geometric induction to wrap-around induction.

Test: test-art-host

Change-Id: Ie4d2659edefb814edda2c971c1f70ba400c31111
diff --git a/test/618-checker-induction/src/Main.java b/test/618-checker-induction/src/Main.java
index f85479a..87a69b2 100644
--- a/test/618-checker-induction/src/Main.java
+++ b/test/618-checker-induction/src/Main.java
@@ -25,7 +25,7 @@
   /// CHECK-DAG: Phi loop:{{B\d+}} outer_loop:none
   //
   /// CHECK-START: void Main.deadSingleLoop() loop_optimization (after)
-  /// CHECK-NOT: Phi loop:{{B\d+}} outer_loop:none
+  /// CHECK-NOT: Phi
   static void deadSingleLoop() {
     for (int i = 0; i < 4; i++) {
     }
@@ -35,7 +35,7 @@
   /// CHECK-DAG: Phi loop:{{B\d+}} outer_loop:none
   //
   /// CHECK-START: void Main.deadSingleLoop() loop_optimization (after)
-  /// CHECK-NOT: Phi loop:{{B\d+}} outer_loop:none
+  /// CHECK-NOT: Phi
   static void deadSingleLoopN(int n) {
     for (int i = 0; i < n; i++) {
     }
@@ -56,7 +56,7 @@
   /// CHECK-DAG: Phi loop:{{B\d+}}      outer_loop:<<Loop>>
   //
   /// CHECK-START: void Main.deadNestedLoops() loop_optimization (after)
-  /// CHECK-NOT: Phi loop:{{B\d+}}
+  /// CHECK-NOT: Phi
   static void deadNestedLoops() {
     for (int i = 0; i < 4; i++) {
       for (int j = 0; j < 4; j++) {
@@ -74,7 +74,7 @@
   /// CHECK-DAG: Phi loop:{{B\d+}}       outer_loop:none
   //
   /// CHECK-START: void Main.deadNestedAndFollowingLoops() loop_optimization (after)
-  /// CHECK-NOT: Phi loop:{{B\d+}}
+  /// CHECK-NOT: Phi
   static void deadNestedAndFollowingLoops() {
     for (int i = 0; i < 4; i++) {
       for (int j = 0; j < 4; j++) {
@@ -96,7 +96,7 @@
   /// CHECK-DAG: Phi loop:{{B\d+}} outer_loop:none
   //
   /// CHECK-START: void Main.deadConditional(int) loop_optimization (after)
-  /// CHECK-NOT: Phi loop:{{B\d+}}
+  /// CHECK-NOT: Phi
   public static void deadConditional(int n) {
     int k = 0;
     int m = 0;
@@ -116,7 +116,7 @@
   /// CHECK-DAG: Phi loop:<<Loop>>      outer_loop:none
   //
   /// CHECK-START: void Main.deadConditionalCycle(int) loop_optimization (after)
-  /// CHECK-NOT: Phi loop:{{B\d+}}
+  /// CHECK-NOT: Phi
   public static void deadConditionalCycle(int n) {
     int k = 0;
     int m = 0;
@@ -215,12 +215,11 @@
   /// CHECK-DAG:               Return [<<Phi1>>] loop:none
   //
   /// CHECK-START: int Main.closedFormInductionUp() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.closedFormInductionUp() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 12395
-  /// CHECK-DAG:               Return [<<Int>>] loop:none
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 12395 loop:none
+  /// CHECK-DAG:               Return [<<Int>>]  loop:none
   static int closedFormInductionUp() {
     int closed = 12345;
     for (int i = 0; i < 10; i++) {
@@ -235,8 +234,13 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: int Main.closedFormInductionInAndDown(int) loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
+  //
+  /// CHECK-START: int Main.closedFormInductionInAndDown(int) instruction_simplifier$after_bce (after)
+  /// CHECK-DAG: <<Par:i\d+>>  ParameterValue        loop:none
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant -50       loop:none
+  /// CHECK-DAG: <<Add:i\d+>>  Add [<<Int>>,<<Par>>] loop:none
+  /// CHECK-DAG:               Return [<<Add>>]      loop:none
   static int closedFormInductionInAndDown(int closed) {
     for (int i = 0; i < 10; i++) {
       closed -= 5;
@@ -252,12 +256,10 @@
   /// CHECK-DAG:               Return [<<Phi1>>] loop:none
   //
   /// CHECK-START: int Main.closedFormNested() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:loop{{B\d+}}
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.closedFormNested() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 100
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 100  loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   static int closedFormNested() {
     int closed = 0;
@@ -277,13 +279,11 @@
   /// CHECK-DAG:               Return [<<Phi1>>] loop:none
   //
   /// CHECK-START: int Main.closedFormNestedAlt() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:loop{{B\d+}}
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.closedFormNestedAlt() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 15082
-  /// CHECK-DAG:               Return [<<Int>>] loop:none
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 15082 loop:none
+  /// CHECK-DAG:               Return [<<Int>>]  loop:none
   static int closedFormNestedAlt() {
     int closed = 12345;
     for (int i = 0; i < 17; i++) {
@@ -360,11 +360,10 @@
   /// CHECK-DAG:              Return [<<Phi>>] loop:none
   //
   /// CHECK-START: int Main.mainIndexReturned() loop_optimization (after)
-  /// CHECK-NOT:              Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:              Return loop:none
+  /// CHECK-NOT:              Phi
   //
   /// CHECK-START: int Main.mainIndexReturned() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 10
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 10   loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   static int mainIndexReturned() {
     int i;
@@ -378,11 +377,10 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: int Main.periodicReturned9() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.periodicReturned9() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 1
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 1    loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   static int periodicReturned9() {
     int k = 0;
@@ -398,11 +396,10 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: int Main.periodicReturned10() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.periodicReturned10() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0    loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   static int periodicReturned10() {
     int k = 0;
@@ -412,7 +409,18 @@
     return k;
   }
 
-  // If ever replaced by closed form, last value should be correct!
+  /// CHECK-START: int Main.getSum21() loop_optimization (before)
+  /// CHECK-DAG: <<Phi1:i\d+>> Phi               loop:<<Loop:B\d+>> outer_loop:none
+  /// CHECK-DAG: <<Phi2:i\d+>> Phi               loop:<<Loop>>      outer_loop:none
+  /// CHECK-DAG: <<Phi3:i\d+>> Phi               loop:<<Loop>>      outer_loop:none
+  /// CHECK-DAG:               Return [<<Phi3>>] loop:none
+  //
+  /// CHECK-START: int Main.getSum21() loop_optimization (after)
+  /// CHECK-NOT:               Phi
+  //
+  /// CHECK-START: int Main.getSum21() instruction_simplifier$after_bce (after)
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 21   loop:none
+  /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static int getSum21() {
     int k = 0;
     int sum = 0;
@@ -436,8 +444,7 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: int Main.periodicReturnedN(int) loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   static int periodicReturnedN(int n) {
     int k = 0;
     for (int i = 0; i < n; i++) {
@@ -480,11 +487,10 @@
   /// CHECK-EVAL: "<<Loop1>>" != "<<Loop2>>"
   //
   /// CHECK-START: int Main.closedFeed() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.closedFeed() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 20
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 20   loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static int closedFeed() {
     int closed = 0;
@@ -505,11 +511,10 @@
   /// CHECK-DAG:               Return [<<Phi1>>] loop:none
   //
   /// CHECK-START: int Main.closedLargeUp() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:B\d+ outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.closedLargeUp() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant -10
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant -10  loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static int closedLargeUp() {
     int closed = 0;
@@ -525,11 +530,10 @@
   /// CHECK-DAG:               Return [<<Phi1>>] loop:none
   //
   /// CHECK-START: int Main.closedLargeDown() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:B\d+ outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.closedLargeDown() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 10
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 10   loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static int closedLargeDown() {
     int closed = 0;
@@ -548,11 +552,10 @@
   /// CHECK-DAG:               Return [<<Phi5>>] loop:none
   //
   /// CHECK-START: int Main.waterFall() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:B\d+ outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: int Main.waterFall() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 50
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 50   loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static int waterFall() {
     int i = 0;
@@ -570,11 +573,10 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom1() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom1() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0    loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static boolean periodicBoolIdiom1() {
     boolean x = true;
@@ -590,11 +592,10 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom2() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom2() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0    loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static boolean periodicBoolIdiom2() {
     boolean x = true;
@@ -610,11 +611,10 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom3() loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom3() instruction_simplifier$after_bce (after)
-  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0
+  /// CHECK-DAG: <<Int:i\d+>>  IntConstant 0    loop:none
   /// CHECK-DAG:               Return [<<Int>>] loop:none
   private static boolean periodicBoolIdiom3() {
     boolean x = true;
@@ -630,8 +630,7 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom1N(boolean, int) loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   private static boolean periodicBoolIdiom1N(boolean x, int n) {
     for (int i = 0; i < n; i++) {
       x = !x;
@@ -645,8 +644,7 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom2N(boolean, int) loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   private static boolean periodicBoolIdiom2N(boolean x, int n) {
     for (int i = 0; i < n; i++) {
       x = (x != true);
@@ -660,8 +658,7 @@
   /// CHECK-DAG:               Return [<<Phi2>>] loop:none
   //
   /// CHECK-START: boolean Main.periodicBoolIdiom3N(boolean, int) loop_optimization (after)
-  /// CHECK-NOT:               Phi    loop:{{B\d+}} outer_loop:none
-  /// CHECK-DAG:               Return loop:none
+  /// CHECK-NOT:               Phi
   private static boolean periodicBoolIdiom3N(boolean x, int n) {
     for (int i = 0; i < n; i++) {
       x = (x == false);