2 files changed, 78 insertions, 6 deletions

diff --git a/src/third_party/s2/util/math/mathutil.cc b/src/third_party/s2/util/math/mathutil.cc
index 35ab462027c..7ca3b890f8a 100755
--- a/src/third_party/s2/util/math/mathutil.cc
+++ b/src/third_party/s2/util/math/mathutil.cc
@@ -16,6 +16,19 @@ using std::vector;
 #include "base/integral_types.h"
 #include "base/logging.h"
 
+  template <class IntOut, class FloatIn>
+  IntOut MathUtil::Round(FloatIn x) {
+    COMPILE_ASSERT(!MathLimits<FloatIn>::kIsInteger, FloatIn_is_integer);
+    COMPILE_ASSERT(MathLimits<IntOut>::kIsInteger, IntOut_is_not_integer);
+
+    // We don't use sgn(x) below because there is no need to distinguish the
+    // (x == 0) case.  Also note that there are specialized faster versions
+    // of this function for Intel processors at the bottom of this file.
+    return static_cast<IntOut>(x < 0 ? (x - 0.5) : (x + 0.5));
+  }
+
+template int MathUtil::Round<int,double>(double x);
+
 MathUtil::QuadraticRootType MathUtil::RealRootsForQuadratic(long double a,
                                                         long double b,
                                                         long double c,
diff --git a/src/third_party/s2/util/math/mathutil.h b/src/third_party/s2/util/math/mathutil.h
index 74ac26c5838..bf607475b64 100755
--- a/src/third_party/s2/util/math/mathutil.h
+++ b/src/third_party/s2/util/math/mathutil.h
@@ -317,6 +317,33 @@ class MathUtil {
                            vector<bool>* shards_to_read);
 
   // --------------------------------------------------------------------
+  // Round, IntRound
+  //   These functions round a floating-point number to an integer.  They
+  //   work for positive or negative numbers.
+  //
+  //   Values that are halfway between two integers may be rounded up or
+  //   down, for example IntRound(0.5) == 0 and IntRound(1.5) == 2.  This
+  //   allows these functions to be implemented efficiently on Intel
+  //   processors (see the template specializations at the bottom of this
+  //   file).  You should not use these functions if you care about which
+  //   way such half-integers are rounded.
+  //
+  //   Example usage:
+  //     double y, z;
+  //     int x = IntRound(y + 3.7);
+  //     int64 b = Round<int64>(0.3 * z);
+  //
+  //   Note that the floating-point template parameter is typically inferred
+  //   from the argument type, i.e. there is no need to specify it explicitly.
+  // --------------------------------------------------------------------
+  template <class IntOut, class FloatIn>
+  static IntOut Round(FloatIn x);
+
+  // Example usage: IntRound(3.6) (no need for IntRound<double>(3.6)).
+  template <class FloatIn>
+  static int IntRound(FloatIn x) { return Round<int>(x); }
+
+  // --------------------------------------------------------------------
   // FastIntRound, FastInt64Round
   //   Fast routines for converting floating-point numbers to integers.
   //
@@ -329,10 +356,11 @@ class MathUtil {
   //   floating-point pipeline (unless programs are compiled specifically
   //   for the Pentium 4, which has a new instruction to avoid this).
   //
-  //   Numbers that are halfway between two integers follow the deafult
+  //   Numbers that are halfway between two integers may be rounded up or
+  //   down.  This is because the conversion is done using the default
   //   rounding mode, which rounds towards the closest even number in case
   //   of ties.  So for example, FastIntRound(0.5) == 0, but
-  //   FastIntRound(1.5) == 2. These functions should only be used with
+  //   FastIntRound(1.5) == 2.  These functions should only be used with
   //   applications that don't care about which way such half-integers are
   //   rounded.
   //
@@ -340,8 +368,10 @@ class MathUtil {
   //   functions (for "int" and "int64" only), but it's safer to call them
   //   directly.
   //
-  //   This functions are equivalent to rint() and llrint().
-  // --------------------------------------------------------------------
+  //   This functions are equivalent to lrint() and llrint() as defined in
+  //   the ISO C99 standard.  Unfortunately this standard does not seem to
+  //   widely adopted yet and these functions are not available by default.
+  //   --------------------------------------------------------------------
 
   static int32 FastIntRound(double x) {
     // This function is not templatized because gcc doesn't seem to be able
@@ -369,7 +399,7 @@ class MathUtil {
     return result;
 #endif  // if defined __x86_64__ || ...
 #else
-    return static_cast<int32>(rint(x));
+    return Round<int32, double>(x);
 #endif  // if defined __GNUC__ && ...
   }
 
@@ -395,7 +425,7 @@ class MathUtil {
     return result;
 #endif  // if defined __i386__
 #else
-    return static_cast<int64>(llrint(x));
+    return Round<int64, double>(x);
 #endif  // if defined __GNUC__ && ...
   }
 
@@ -656,6 +686,35 @@ class MathUtil {
   }
 };
 
+// ========================================================================= //
+
+#if (defined __i386__ || defined __x86_64__) && defined __GNUC__
+
+// We define template specializations of Round() to get the more efficient
+// Intel versions when possible.  Note that gcc does not currently support
+// partial specialization of templatized functions.
+template<>
+inline int32 MathUtil::Round<int32, double>(double x) {
+  return FastIntRound(x);
+}
+
+template<>
+inline int32 MathUtil::Round<int32, float>(float x) {
+  return FastIntRound(x);
+}
+
+template<>
+inline int64 MathUtil::Round<int64, double>(double x) {
+  return FastInt64Round(x);
+}
+
+template<>
+inline int64 MathUtil::Round<int64, float>(float x) {
+  return FastInt64Round(x);
+}
+
+#endif
+
 template<typename T>
 bool MathUtil::WithinFraction(const T x, const T y, const T fraction) {
   // not just "0 <= fraction" to fool the compiler for unsigned types