Fix for issue 10534. Implement int.pow correctly using exponentiation by squaring.

Note that int.pow is now considerably slower than double.pow.

R=floitsch@google.com

Review URL: https://codereview.chromium.org//14619027

git-svn-id: https://dart.googlecode.com/svn/branches/bleeding_edge/dart@22635 260f80e4-7a28-3924-810f-c04153c831b5

runtime/lib/integers.dart

@@ -164,12 +164,17 @@ class _IntegerImplementation {
   double toDouble() { return new _Double.fromInteger(this); }
 
   int pow(int exponent) {
-    double res = this.toDouble().pow(exponent);
-    if (res.isInfinite) {
-      // Use Bigint instead.
-      throw "_IntegerImplementation.pow not implemented for large integers.";
+    // Exponentiation by squaring.
+    int base = this;
+    int result = 1;
+    while (exponent != 0) {
+      if ((exponent & 1) == 1) {
+        result *= base;
+      }
+      exponent >>= 1;
+      base *= base;
     }
-    return res.toInt();
+    return result;
   }
 
   String toStringAsFixed(int fractionDigits) {

runtime/lib/math_patch.dart

@@ -5,8 +5,11 @@
 import "dart:typed_data";
 
 // A VM patch of the dart:math library.
+
+// If [x] is an [int] and [exponent] is a non-negative [int], the result is
+// an [int], otherwise the result is a [double].
 patch num pow(num x, num exponent) {
-  if (exponent is int) {
+  if ((x is int) && (exponent is int) && (exponent >= 0)) {
     return x.pow(exponent);
   }
   // Double.pow will call exponent.toDouble().

tests/standalone/pow_test.dart

@@ -85,14 +85,23 @@ var expectedResults =
 void main() {
   int exp = 0;
   for (int val in expectedResults) {
-    Expect.equals(val, pow(2, exp++));
+    Expect.equals(val, pow(2, exp));
+    Expect.equals(val.toDouble(), pow(2, exp.toDouble()));
+    exp++;
   }
+
   // Optimize it.
   for (int i = 0; i < 8888; i++) {
     pow(2, 3);
+    pow(2.0, 3.0);
   }
   exp = 0;
   for (int val in expectedResults) {
-    Expect.equals(val, pow(2, exp++));
+    Expect.equals(val, pow(2, exp));
+    Expect.equals(val.toDouble(), pow(2, exp.toDouble()));
+    exp++;
   }
+  // Test Bigints.
+  Expect.equals(5559917313492231481, pow(11, 18));
+  Expect.equals(672749994932560009201, pow(11, 20));
 }

tests/standalone/standalone.status

@@ -102,6 +102,7 @@ io/process_exit_negative_test: Fail, OK # relies on a static error that is a war
 package/package_isolate_test: Skip # spawnUri does not work in dart2js. See issue 3051
 debugger/*: Skip # Do not run standalone vm debugger tests with dart2js.
 left_shift_bit_and_op_test: Skip # Integers exceed dart2js precision.
+pow_test: Skip # Precision > 53 bits.
 
 [ $compiler == dart2js && $jscl ]
 assert_test: Fail, OK # Assumes unspecified fields on the AssertionError.