Added support for fast integer divisions by a constant

Sped up tensor slicing by a factor of 3 by using these fast integer divisions.

unsupported/Eigen/CXX11/src/Tensor/TensorIntDiv.h

@@ -0,0 +1,82 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2014 Benoit Steiner <benoit.steiner.goog@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#ifndef EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
+#define EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H
+
+
+namespace Eigen {
+
+/** \internal
+  *
+  * \class TensorIntDiv
+  * \ingroup CXX11_Tensor_Module
+  *
+  * \brief Fast integer division by a constant.
+  *
+  * See the paper from Granlund and Montgomery for explanation.
+  *   (at http://dx.doi.org/10.1145/773473.178249)
+  *
+  * \sa Tensor
+  */
+
+namespace internal {
+
+template <typename T>
+struct TensorIntDivisor {
+ public:
+  TensorIntDivisor() {
+    multiplier = 0;
+    shift1 = 0;
+    shift2 = 0;
+  }
+
+  // Must have 1 <= divider <= 2^31-1
+  TensorIntDivisor(const T divider) {
+    static const int N = 32;
+    eigen_assert(divider > 0);
+    eigen_assert(divider <= (1<<(N-1)) - 1);
+
+    // fast ln2
+    const int leading_zeros = __builtin_clz(divider);
+    const int l = N - (leading_zeros+1);
+
+    multiplier = (static_cast<uint64_t>(1) << (N+l)) / divider - (static_cast<uint64_t>(1) << N) + 1;
+    shift1 = (std::min)(1, l);
+    shift2 = (std::max)(0, l-1);
+  }
+
+  // Must have 0 <= numerator <= 2^32-1
+  T divide(const T numerator) const {
+    static const int N = 32;
+    eigen_assert(numerator >= 0);
+    eigen_assert(numerator <= (1ull<<N) - 1);
+
+    uint32_t t1 = (multiplier * numerator) >> 32;
+    uint32_t t = (static_cast<uint32_t>(numerator) - t1) >> shift1;
+    return (t1 + t) >> shift2;
+  }
+
+ private:
+  uint64_t multiplier;
+  int32_t shift1;
+  int32_t shift2;
+};
+
+
+template <typename T>
+static T operator / (const T& numerator, const TensorIntDivisor<T>& divisor) {
+  return divisor.divide(numerator);
+}
+
+
+} // end namespace internal
+} // end namespace Eigen
+
+#endif // EIGEN_CXX11_TENSOR_TENSOR_INTDIV_H