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diff --git a/kaldi_io/src/tools/openfst/include/fst/sparse-power-weight.h b/kaldi_io/src/tools/openfst/include/fst/sparse-power-weight.h
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+// sparse-power-weight.h
+
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+//
+// Copyright 2005-2010 Google, Inc.
+// Author: krr@google.com (Kasturi Rangan Raghavan)
+// Inspiration: allauzen@google.com (Cyril Allauzen)
+//
+// \file
+// Cartesian power weight semiring operation definitions.
+// Uses SparseTupleWeight as underlying representation.
+
+#ifndef FST_LIB_SPARSE_POWER_WEIGHT_H__
+#define FST_LIB_SPARSE_POWER_WEIGHT_H__
+
+#include<string>
+
+#include <fst/sparse-tuple-weight.h>
+#include <fst/weight.h>
+
+
+namespace fst {
+
+// Below SparseTupleWeight*Mapper are used in conjunction with
+// SparseTupleWeightMap to compute the respective semiring operations
+template<class W, class K>
+struct SparseTupleWeightPlusMapper {
+  W Map(const K& k, const W& v1, const W& v2) const {
+    return Plus(v1, v2);
+  }
+};
+
+template<class W, class K>
+struct SparseTupleWeightTimesMapper {
+  W Map(const K& k, const W& v1, const W& v2) const {
+    return Times(v1, v2);
+  }
+};
+
+template<class W, class K>
+struct SparseTupleWeightDivideMapper {
+  SparseTupleWeightDivideMapper(DivideType divide_type) {
+    divide_type_ = divide_type;
+  }
+  W Map(const K& k, const W& v1, const W& v2) const {
+    return Divide(v1, v2, divide_type_);
+  }
+  DivideType divide_type_;
+};
+
+template<class W, class K>
+struct SparseTupleWeightApproxMapper {
+  SparseTupleWeightApproxMapper(float delta) { delta_ = delta; }
+  W Map(const K& k, const W& v1, const W& v2) const {
+    return ApproxEqual(v1, v2, delta_) ? W::One() : W::Zero();
+  }
+  float delta_;
+};
+
+// Sparse cartesian power semiring: W ^ n
+// Forms:
+//  - a left semimodule when W is a left semiring,
+//  - a right semimodule when W is a right semiring,
+//  - a bisemimodule when W is a semiring,
+//    the free semimodule of rank n over W
+// The Times operation is overloaded to provide the
+// left and right scalar products.
+// K is the key value type. kNoKey(-1) is reserved for internal use
+template <class W, class K = int>
+class SparsePowerWeight : public SparseTupleWeight<W, K> {
+ public:
+  using SparseTupleWeight<W, K>::Zero;
+  using SparseTupleWeight<W, K>::One;
+  using SparseTupleWeight<W, K>::NoWeight;
+  using SparseTupleWeight<W, K>::Quantize;
+  using SparseTupleWeight<W, K>::Reverse;
+
+  typedef SparsePowerWeight<typename W::ReverseWeight, K> ReverseWeight;
+
+  SparsePowerWeight() {}
+
+  SparsePowerWeight(const SparseTupleWeight<W, K> &w) :
+    SparseTupleWeight<W, K>(w) { }
+
+  template <class Iterator>
+  SparsePowerWeight(Iterator begin, Iterator end) :
+    SparseTupleWeight<W, K>(begin, end) { }
+
+  SparsePowerWeight(const K &key, const W &w) :
+    SparseTupleWeight<W, K>(key, w) { }
+
+  static const SparsePowerWeight<W, K> &Zero() {
+    static const SparsePowerWeight<W, K> zero(SparseTupleWeight<W, K>::Zero());
+    return zero;
+  }
+
+  static const SparsePowerWeight<W, K> &One() {
+    static const SparsePowerWeight<W, K> one(SparseTupleWeight<W, K>::One());
+    return one;
+  }
+
+  static const SparsePowerWeight<W, K> &NoWeight() {
+    static const SparsePowerWeight<W, K> no_weight(
+        SparseTupleWeight<W, K>::NoWeight());
+    return no_weight;
+  }
+
+  // Overide this: Overwrite the Type method to reflect the key type
+  // if using non-default key type.
+  static const string &Type() {
+    static string type;
+    if(type.empty()) {
+      type = W::Type() + "_^n";
+      if(sizeof(K) != sizeof(uint32)) {
+        string size;
+        Int64ToStr(8 * sizeof(K), &size);
+        type += "_" + size;
+      }
+    }
+    return type;
+  }
+
+  static uint64 Properties() {
+    uint64 props = W::Properties();
+    return props & (kLeftSemiring | kRightSemiring |
+                    kCommutative | kIdempotent);
+  }
+
+  SparsePowerWeight<W, K> Quantize(float delta = kDelta) const {
+    return SparseTupleWeight<W, K>::Quantize(delta);
+  }
+
+  ReverseWeight Reverse() const {
+    return SparseTupleWeight<W, K>::Reverse();
+  }
+};
+
+// Semimodule plus operation
+template <class W, class K>
+inline SparsePowerWeight<W, K> Plus(const SparsePowerWeight<W, K> &w1,
+                                    const SparsePowerWeight<W, K> &w2) {
+  SparsePowerWeight<W, K> ret;
+  SparseTupleWeightPlusMapper<W, K> operator_mapper;
+  SparseTupleWeightMap(&ret, w1, w2, operator_mapper);
+  return ret;
+}
+
+// Semimodule times operation
+template <class W, class K>
+inline SparsePowerWeight<W, K> Times(const SparsePowerWeight<W, K> &w1,
+                                     const SparsePowerWeight<W, K> &w2) {
+  SparsePowerWeight<W, K> ret;
+  SparseTupleWeightTimesMapper<W, K> operator_mapper;
+  SparseTupleWeightMap(&ret, w1, w2, operator_mapper);
+  return ret;
+}
+
+// Semimodule divide operation
+template <class W, class K>
+inline SparsePowerWeight<W, K> Divide(const SparsePowerWeight<W, K> &w1,
+                                      const SparsePowerWeight<W, K> &w2,
+                                      DivideType type = DIVIDE_ANY) {
+  SparsePowerWeight<W, K> ret;
+  SparseTupleWeightDivideMapper<W, K> operator_mapper(type);
+  SparseTupleWeightMap(&ret, w1, w2, operator_mapper);
+  return ret;
+}
+
+// Semimodule dot product
+template <class W, class K>
+inline const W& DotProduct(const SparsePowerWeight<W, K> &w1,
+                    const SparsePowerWeight<W, K> &w2) {
+  const SparsePowerWeight<W, K>& product = Times(w1, w2);
+  W ret(W::Zero());
+  for (SparseTupleWeightIterator<W, K> it(product); !it.Done(); it.Next()) {
+    ret = Plus(ret, it.Value().second);
+  }
+  return ret;
+}
+
+template <class W, class K>
+inline bool ApproxEqual(const SparsePowerWeight<W, K> &w1,
+                        const SparsePowerWeight<W, K> &w2,
+                        float delta = kDelta) {
+  SparseTupleWeight<W, K> ret;
+  SparseTupleWeightApproxMapper<W, K> operator_mapper(kDelta);
+  SparseTupleWeightMap(&ret, w1, w2, operator_mapper);
+  return ret == SparsePowerWeight<W, K>::One();
+}
+
+template <class W, class K>
+inline SparsePowerWeight<W, K> Times(const W &k,
+                                     const SparsePowerWeight<W, K> &w2) {
+  SparsePowerWeight<W, K> w1(k);
+  return Times(w1, w2);
+}
+
+template <class W, class K>
+inline SparsePowerWeight<W, K> Times(const SparsePowerWeight<W, K> &w1,
+                                     const W &k) {
+  SparsePowerWeight<W, K> w2(k);
+  return Times(w1, w2);
+}
+
+template <class W, class K>
+inline SparsePowerWeight<W, K> Divide(const SparsePowerWeight<W, K> &w1,
+                                      const W &k,
+                                      DivideType divide_type = DIVIDE_ANY) {
+  SparsePowerWeight<W, K> w2(k);
+  return Divide(w1, w2, divide_type);
+}
+
+}  // namespace fst
+
+#endif  // FST_LIB_SPARSE_POWER_WEIGHT_H__