benibus commented on code in PR #8510:
URL: https://github.com/apache/arrow/pull/8510#discussion_r1126907080


##########
cpp/src/arrow/extension/fixed_shape_tensor.cc:
##########
@@ -0,0 +1,299 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you 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.
+
+#include "arrow/extension/fixed_shape_tensor.h"
+
+#include "arrow/array/array_nested.h"
+#include "arrow/array/array_primitive.h"
+#include "arrow/json/rapidjson_defs.h"  // IWYU pragma: keep
+#include "arrow/tensor.h"
+#include "arrow/util/logging.h"
+#include "arrow/util/sort.h"
+
+#include <rapidjson/document.h>
+#include <rapidjson/writer.h>
+
+namespace rj = arrow::rapidjson;
+
+namespace arrow {
+namespace extension {
+
+bool FixedShapeTensorType::ExtensionEquals(const ExtensionType& other) const {
+  if (extension_name() != other.extension_name()) {
+    return false;
+  }
+  const auto& other_ext = static_cast<const FixedShapeTensorType&>(other);
+
+  auto is_permutation_trivial = [](const std::vector<int64_t>& permutation) {
+    for (size_t i = 1; i < permutation.size(); ++i) {
+      if (permutation[i - 1] + 1 != permutation[i]) {
+        return false;
+      }
+    }
+    return true;
+  };
+  const bool permutation_equivalent =
+      (permutation_ == other_ext.permutation()) ||
+      ((permutation_.empty() && 
is_permutation_trivial(other_ext.permutation())) &&
+       (is_permutation_trivial(permutation_) || 
other_ext.permutation().empty()));
+
+  return storage_type()->Equals(other_ext.storage_type()) &&
+         shape_ == other_ext.shape() && dim_names_ == other_ext.dim_names() &&
+         permutation_equivalent;
+}
+
+std::string FixedShapeTensorType::Serialize() const {
+  rj::Document document;
+  document.SetObject();
+  rj::Document::AllocatorType& allocator = document.GetAllocator();
+
+  rj::Value shape(rj::kArrayType);
+  for (auto v : shape_) {
+    shape.PushBack(v, allocator);
+  }
+  document.AddMember(rj::Value("shape", allocator), shape, allocator);
+
+  if (!permutation_.empty()) {
+    rj::Value permutation(rj::kArrayType);
+    for (auto v : permutation_) {
+      permutation.PushBack(v, allocator);
+    }
+    document.AddMember(rj::Value("permutation", allocator), permutation, 
allocator);
+  }
+
+  if (!dim_names_.empty()) {
+    rj::Value dim_names(rj::kArrayType);
+    for (std::string v : dim_names_) {
+      dim_names.PushBack(rj::Value{}.SetString(v.c_str(), allocator), 
allocator);
+    }
+    document.AddMember(rj::Value("dim_names", allocator), dim_names, 
allocator);
+  }
+
+  rj::StringBuffer buffer;
+  rj::Writer<rj::StringBuffer> writer(buffer);
+  document.Accept(writer);
+  return buffer.GetString();
+}
+
+Result<std::shared_ptr<DataType>> FixedShapeTensorType::Deserialize(
+    std::shared_ptr<DataType> storage_type, const std::string& 
serialized_data) const {
+  if (storage_type->id() != Type::FIXED_SIZE_LIST) {
+    return Status::Invalid("Expected FixedSizeList storage type, got ",
+                           storage_type->ToString());
+  }
+  auto value_type =
+      
internal::checked_pointer_cast<FixedSizeListType>(storage_type)->value_type();
+  rj::Document document;
+  if (document.Parse(serialized_data.data(), 
serialized_data.length()).HasParseError() ||
+      !document.HasMember("shape") || !document["shape"].IsArray()) {
+    return Status::Invalid("Invalid serialized JSON data: ", serialized_data);
+  }
+
+  std::vector<int64_t> shape;
+  for (auto& x : document["shape"].GetArray()) {
+    shape.emplace_back(x.GetInt64());
+  }
+  std::vector<int64_t> permutation;
+  if (document.HasMember("permutation")) {
+    for (auto& x : document["permutation"].GetArray()) {
+      permutation.emplace_back(x.GetInt64());
+    }
+    if (shape.size() != permutation.size()) {
+      return Status::Invalid("Invalid permutation");
+    }
+  }
+  std::vector<std::string> dim_names;
+  if (document.HasMember("dim_names")) {
+    for (auto& x : document["dim_names"].GetArray()) {
+      dim_names.emplace_back(x.GetString());
+    }
+    if (shape.size() != dim_names.size()) {
+      return Status::Invalid("Invalid dim_names");
+    }
+  }
+
+  return fixed_shape_tensor(value_type, shape, permutation, dim_names);
+}
+
+std::shared_ptr<Array> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<ArrayData> data) const {
+  return std::make_shared<ExtensionArray>(data);
+}
+
+Result<std::shared_ptr<Array>> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<Tensor> tensor) const {
+  auto permutation = internal::ArgSort(tensor->strides());
+  std::reverse(permutation.begin(), permutation.end());
+  if (permutation[0] != 0) {
+    return Status::Invalid(
+        "Only first-major tensors can be zero-copy converted to arrays");
+  }
+
+  auto cell_shape = tensor->shape();
+  cell_shape.erase(cell_shape.begin());
+  if (cell_shape != shape_) {
+    return Status::Invalid("Expected cell shape does not match input tensor 
shape");
+  }
+
+  permutation.erase(permutation.begin());
+  for (auto& x : permutation) {
+    x--;
+  }
+
+  auto ext_type = internal::checked_pointer_cast<ExtensionType>(
+      fixed_shape_tensor(tensor->type(), cell_shape, permutation, 
tensor->dim_names()));
+
+  std::shared_ptr<FixedSizeListArray> arr;
+  std::shared_ptr<Array> value_array;
+  switch (tensor->type_id()) {
+    case Type::UINT8: {
+      value_array = std::make_shared<UInt8Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT8: {
+      value_array = std::make_shared<Int8Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT16: {
+      value_array = std::make_shared<UInt16Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT16: {
+      value_array = std::make_shared<Int16Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT32: {
+      value_array = std::make_shared<UInt32Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT32: {
+      value_array = std::make_shared<Int32Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT64: {
+      value_array = std::make_shared<Int64Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT64: {
+      value_array = std::make_shared<Int64Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::HALF_FLOAT: {
+      value_array = std::make_shared<HalfFloatArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::FLOAT: {
+      value_array = std::make_shared<FloatArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::DOUBLE: {
+      value_array = std::make_shared<DoubleArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    default: {
+      return Status::NotImplemented("Unsupported tensor type: ",
+                                    tensor->type()->ToString());
+    }
+  }
+  arr = std::make_shared<FixedSizeListArray>(ext_type->storage_type(), 
tensor->shape()[0],
+                                             value_array);
+  auto ext_data = arr->data();
+  ext_data->type = ext_type;
+  return MakeArray(ext_data);
+}
+
+Result<std::shared_ptr<Tensor>> FixedShapeTensorType::ToTensor(
+    std::shared_ptr<Array> arr) {
+  // To convert an array of n dimensional tensors to a n+1 dimensional tensor 
we
+  // interpret the array's length as the first dimension the new tensor. 
Further, we
+  // define n+1 dimensional tensor's strides by front appending a new stride 
to the n
+  // dimensional tensor's strides.
+
+  ARROW_CHECK(is_tensor_supported(this->value_type_->id()));
+
+  ARROW_DCHECK_EQ(arr->null_count(), 0) << "Null values not supported in 
tensors.";
+  auto ext_arr = internal::checked_pointer_cast<FixedSizeListArray>(
+      internal::checked_pointer_cast<ExtensionArray>(arr)->storage());
+
+  std::vector<int64_t> shape = this->shape();
+  shape.insert(shape.begin(), 1, arr->length());
+
+  std::vector<int64_t> tensor_strides = this->strides();
+  tensor_strides.insert(tensor_strides.begin(), 1, arr->length() * 
tensor_strides[0]);
+
+  std::shared_ptr<Buffer> buffer = ext_arr->values()->data()->buffers[1];
+  return *Tensor::Make(ext_arr->value_type(), buffer, shape, tensor_strides, 
dim_names());

Review Comment:
   It might be best to let `Tensor::Make` recompute the strides here (based on 
the `shape`). We would get a multiplication overflow check baked in. You'd just 
have to pass an empty vector.
   
   Also, would `permutation` play a role in this conversion? i.e. would `shape` 
potentially need to permuted before passing it to the `Tensor` to reflect a 
row-major layout in the buffer`? (actually not sure)



##########
cpp/src/arrow/extension/fixed_shape_tensor.cc:
##########
@@ -0,0 +1,299 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you 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.
+
+#include "arrow/extension/fixed_shape_tensor.h"
+
+#include "arrow/array/array_nested.h"
+#include "arrow/array/array_primitive.h"
+#include "arrow/json/rapidjson_defs.h"  // IWYU pragma: keep
+#include "arrow/tensor.h"
+#include "arrow/util/logging.h"
+#include "arrow/util/sort.h"
+
+#include <rapidjson/document.h>
+#include <rapidjson/writer.h>
+
+namespace rj = arrow::rapidjson;
+
+namespace arrow {
+namespace extension {
+
+bool FixedShapeTensorType::ExtensionEquals(const ExtensionType& other) const {
+  if (extension_name() != other.extension_name()) {
+    return false;
+  }
+  const auto& other_ext = static_cast<const FixedShapeTensorType&>(other);
+
+  auto is_permutation_trivial = [](const std::vector<int64_t>& permutation) {
+    for (size_t i = 1; i < permutation.size(); ++i) {
+      if (permutation[i - 1] + 1 != permutation[i]) {
+        return false;
+      }
+    }
+    return true;
+  };
+  const bool permutation_equivalent =
+      (permutation_ == other_ext.permutation()) ||
+      ((permutation_.empty() && 
is_permutation_trivial(other_ext.permutation())) &&
+       (is_permutation_trivial(permutation_) || 
other_ext.permutation().empty()));
+
+  return storage_type()->Equals(other_ext.storage_type()) &&
+         shape_ == other_ext.shape() && dim_names_ == other_ext.dim_names() &&
+         permutation_equivalent;
+}
+
+std::string FixedShapeTensorType::Serialize() const {
+  rj::Document document;
+  document.SetObject();
+  rj::Document::AllocatorType& allocator = document.GetAllocator();
+
+  rj::Value shape(rj::kArrayType);
+  for (auto v : shape_) {
+    shape.PushBack(v, allocator);
+  }
+  document.AddMember(rj::Value("shape", allocator), shape, allocator);
+
+  if (!permutation_.empty()) {
+    rj::Value permutation(rj::kArrayType);
+    for (auto v : permutation_) {
+      permutation.PushBack(v, allocator);
+    }
+    document.AddMember(rj::Value("permutation", allocator), permutation, 
allocator);
+  }
+
+  if (!dim_names_.empty()) {
+    rj::Value dim_names(rj::kArrayType);
+    for (std::string v : dim_names_) {
+      dim_names.PushBack(rj::Value{}.SetString(v.c_str(), allocator), 
allocator);
+    }
+    document.AddMember(rj::Value("dim_names", allocator), dim_names, 
allocator);
+  }
+
+  rj::StringBuffer buffer;
+  rj::Writer<rj::StringBuffer> writer(buffer);
+  document.Accept(writer);
+  return buffer.GetString();
+}
+
+Result<std::shared_ptr<DataType>> FixedShapeTensorType::Deserialize(
+    std::shared_ptr<DataType> storage_type, const std::string& 
serialized_data) const {
+  if (storage_type->id() != Type::FIXED_SIZE_LIST) {
+    return Status::Invalid("Expected FixedSizeList storage type, got ",
+                           storage_type->ToString());
+  }
+  auto value_type =
+      
internal::checked_pointer_cast<FixedSizeListType>(storage_type)->value_type();
+  rj::Document document;
+  if (document.Parse(serialized_data.data(), 
serialized_data.length()).HasParseError() ||
+      !document.HasMember("shape") || !document["shape"].IsArray()) {
+    return Status::Invalid("Invalid serialized JSON data: ", serialized_data);
+  }
+
+  std::vector<int64_t> shape;
+  for (auto& x : document["shape"].GetArray()) {
+    shape.emplace_back(x.GetInt64());
+  }
+  std::vector<int64_t> permutation;
+  if (document.HasMember("permutation")) {
+    for (auto& x : document["permutation"].GetArray()) {
+      permutation.emplace_back(x.GetInt64());
+    }
+    if (shape.size() != permutation.size()) {
+      return Status::Invalid("Invalid permutation");
+    }
+  }
+  std::vector<std::string> dim_names;
+  if (document.HasMember("dim_names")) {
+    for (auto& x : document["dim_names"].GetArray()) {
+      dim_names.emplace_back(x.GetString());
+    }
+    if (shape.size() != dim_names.size()) {
+      return Status::Invalid("Invalid dim_names");
+    }
+  }
+
+  return fixed_shape_tensor(value_type, shape, permutation, dim_names);
+}
+
+std::shared_ptr<Array> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<ArrayData> data) const {
+  return std::make_shared<ExtensionArray>(data);
+}
+
+Result<std::shared_ptr<Array>> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<Tensor> tensor) const {
+  auto permutation = internal::ArgSort(tensor->strides());
+  std::reverse(permutation.begin(), permutation.end());
+  if (permutation[0] != 0) {
+    return Status::Invalid(
+        "Only first-major tensors can be zero-copy converted to arrays");
+  }
+
+  auto cell_shape = tensor->shape();
+  cell_shape.erase(cell_shape.begin());
+  if (cell_shape != shape_) {
+    return Status::Invalid("Expected cell shape does not match input tensor 
shape");
+  }
+
+  permutation.erase(permutation.begin());
+  for (auto& x : permutation) {
+    x--;
+  }
+
+  auto ext_type = internal::checked_pointer_cast<ExtensionType>(
+      fixed_shape_tensor(tensor->type(), cell_shape, permutation, 
tensor->dim_names()));

Review Comment:
   Wouldn't we override the new extension type with `this->dim_names()` rather 
than the tensor's? Keep in mind that a 3D input tensor would (potentially) have 
3 `dim_names`, but the `shape` we'd be passing to the new type would only have 
2 dimensions - so there would be a mismatch (which would be detected in `Make`).



##########
cpp/src/arrow/extension/fixed_shape_tensor.cc:
##########
@@ -0,0 +1,299 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you 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.
+
+#include "arrow/extension/fixed_shape_tensor.h"
+
+#include "arrow/array/array_nested.h"
+#include "arrow/array/array_primitive.h"
+#include "arrow/json/rapidjson_defs.h"  // IWYU pragma: keep
+#include "arrow/tensor.h"
+#include "arrow/util/logging.h"
+#include "arrow/util/sort.h"
+
+#include <rapidjson/document.h>
+#include <rapidjson/writer.h>
+
+namespace rj = arrow::rapidjson;
+
+namespace arrow {
+namespace extension {
+
+bool FixedShapeTensorType::ExtensionEquals(const ExtensionType& other) const {
+  if (extension_name() != other.extension_name()) {
+    return false;
+  }
+  const auto& other_ext = static_cast<const FixedShapeTensorType&>(other);
+
+  auto is_permutation_trivial = [](const std::vector<int64_t>& permutation) {
+    for (size_t i = 1; i < permutation.size(); ++i) {
+      if (permutation[i - 1] + 1 != permutation[i]) {
+        return false;
+      }
+    }
+    return true;
+  };
+  const bool permutation_equivalent =
+      (permutation_ == other_ext.permutation()) ||
+      ((permutation_.empty() && 
is_permutation_trivial(other_ext.permutation())) &&
+       (is_permutation_trivial(permutation_) || 
other_ext.permutation().empty()));
+
+  return storage_type()->Equals(other_ext.storage_type()) &&
+         shape_ == other_ext.shape() && dim_names_ == other_ext.dim_names() &&
+         permutation_equivalent;
+}
+
+std::string FixedShapeTensorType::Serialize() const {
+  rj::Document document;
+  document.SetObject();
+  rj::Document::AllocatorType& allocator = document.GetAllocator();
+
+  rj::Value shape(rj::kArrayType);
+  for (auto v : shape_) {
+    shape.PushBack(v, allocator);
+  }
+  document.AddMember(rj::Value("shape", allocator), shape, allocator);
+
+  if (!permutation_.empty()) {
+    rj::Value permutation(rj::kArrayType);
+    for (auto v : permutation_) {
+      permutation.PushBack(v, allocator);
+    }
+    document.AddMember(rj::Value("permutation", allocator), permutation, 
allocator);
+  }
+
+  if (!dim_names_.empty()) {
+    rj::Value dim_names(rj::kArrayType);
+    for (std::string v : dim_names_) {
+      dim_names.PushBack(rj::Value{}.SetString(v.c_str(), allocator), 
allocator);
+    }
+    document.AddMember(rj::Value("dim_names", allocator), dim_names, 
allocator);
+  }
+
+  rj::StringBuffer buffer;
+  rj::Writer<rj::StringBuffer> writer(buffer);
+  document.Accept(writer);
+  return buffer.GetString();
+}
+
+Result<std::shared_ptr<DataType>> FixedShapeTensorType::Deserialize(
+    std::shared_ptr<DataType> storage_type, const std::string& 
serialized_data) const {
+  if (storage_type->id() != Type::FIXED_SIZE_LIST) {
+    return Status::Invalid("Expected FixedSizeList storage type, got ",
+                           storage_type->ToString());
+  }
+  auto value_type =
+      
internal::checked_pointer_cast<FixedSizeListType>(storage_type)->value_type();
+  rj::Document document;
+  if (document.Parse(serialized_data.data(), 
serialized_data.length()).HasParseError() ||
+      !document.HasMember("shape") || !document["shape"].IsArray()) {
+    return Status::Invalid("Invalid serialized JSON data: ", serialized_data);
+  }
+
+  std::vector<int64_t> shape;
+  for (auto& x : document["shape"].GetArray()) {
+    shape.emplace_back(x.GetInt64());
+  }
+  std::vector<int64_t> permutation;
+  if (document.HasMember("permutation")) {
+    for (auto& x : document["permutation"].GetArray()) {
+      permutation.emplace_back(x.GetInt64());
+    }
+    if (shape.size() != permutation.size()) {
+      return Status::Invalid("Invalid permutation");
+    }
+  }
+  std::vector<std::string> dim_names;
+  if (document.HasMember("dim_names")) {
+    for (auto& x : document["dim_names"].GetArray()) {
+      dim_names.emplace_back(x.GetString());
+    }
+    if (shape.size() != dim_names.size()) {
+      return Status::Invalid("Invalid dim_names");
+    }
+  }
+
+  return fixed_shape_tensor(value_type, shape, permutation, dim_names);
+}
+
+std::shared_ptr<Array> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<ArrayData> data) const {
+  return std::make_shared<ExtensionArray>(data);
+}
+
+Result<std::shared_ptr<Array>> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<Tensor> tensor) const {
+  auto permutation = internal::ArgSort(tensor->strides());
+  std::reverse(permutation.begin(), permutation.end());
+  if (permutation[0] != 0) {
+    return Status::Invalid(
+        "Only first-major tensors can be zero-copy converted to arrays");
+  }
+
+  auto cell_shape = tensor->shape();
+  cell_shape.erase(cell_shape.begin());
+  if (cell_shape != shape_) {
+    return Status::Invalid("Expected cell shape does not match input tensor 
shape");
+  }
+
+  permutation.erase(permutation.begin());
+  for (auto& x : permutation) {
+    x--;
+  }
+
+  auto ext_type = internal::checked_pointer_cast<ExtensionType>(
+      fixed_shape_tensor(tensor->type(), cell_shape, permutation, 
tensor->dim_names()));
+
+  std::shared_ptr<FixedSizeListArray> arr;
+  std::shared_ptr<Array> value_array;
+  switch (tensor->type_id()) {
+    case Type::UINT8: {
+      value_array = std::make_shared<UInt8Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT8: {
+      value_array = std::make_shared<Int8Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT16: {
+      value_array = std::make_shared<UInt16Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT16: {
+      value_array = std::make_shared<Int16Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT32: {
+      value_array = std::make_shared<UInt32Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT32: {
+      value_array = std::make_shared<Int32Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT64: {
+      value_array = std::make_shared<Int64Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT64: {
+      value_array = std::make_shared<Int64Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::HALF_FLOAT: {
+      value_array = std::make_shared<HalfFloatArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::FLOAT: {
+      value_array = std::make_shared<FloatArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::DOUBLE: {
+      value_array = std::make_shared<DoubleArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    default: {
+      return Status::NotImplemented("Unsupported tensor type: ",
+                                    tensor->type()->ToString());
+    }
+  }
+  arr = std::make_shared<FixedSizeListArray>(ext_type->storage_type(), 
tensor->shape()[0],
+                                             value_array);
+  auto ext_data = arr->data();
+  ext_data->type = ext_type;
+  return MakeArray(ext_data);
+}
+
+Result<std::shared_ptr<Tensor>> FixedShapeTensorType::ToTensor(
+    std::shared_ptr<Array> arr) {
+  // To convert an array of n dimensional tensors to a n+1 dimensional tensor 
we
+  // interpret the array's length as the first dimension the new tensor. 
Further, we
+  // define n+1 dimensional tensor's strides by front appending a new stride 
to the n
+  // dimensional tensor's strides.
+
+  ARROW_CHECK(is_tensor_supported(this->value_type_->id()));
+
+  ARROW_DCHECK_EQ(arr->null_count(), 0) << "Null values not supported in 
tensors.";
+  auto ext_arr = internal::checked_pointer_cast<FixedSizeListArray>(
+      internal::checked_pointer_cast<ExtensionArray>(arr)->storage());
+
+  std::vector<int64_t> shape = this->shape();
+  shape.insert(shape.begin(), 1, arr->length());
+
+  std::vector<int64_t> tensor_strides = this->strides();
+  tensor_strides.insert(tensor_strides.begin(), 1, arr->length() * 
tensor_strides[0]);
+
+  std::shared_ptr<Buffer> buffer = ext_arr->values()->data()->buffers[1];
+  return *Tensor::Make(ext_arr->value_type(), buffer, shape, tensor_strides, 
dim_names());
+}
+
+Result<std::shared_ptr<DataType>> FixedShapeTensorType::Make(

Review Comment:
   We could probably refactor `internal::ValidateTensorParams` into multiple 
functions so we can re-use some of `Tensor`'s validation logic for type, shape, 
strides - which is currently more extensive.
   
   If it's ok with you, I can try contributing to this more directly. I'm 
pretty sure I have push access to your fork...



##########
cpp/src/arrow/extension/fixed_shape_tensor.cc:
##########
@@ -0,0 +1,299 @@
+// Licensed to the Apache Software Foundation (ASF) under one
+// or more contributor license agreements.  See the NOTICE file
+// distributed with this work for additional information
+// regarding copyright ownership.  The ASF licenses this file
+// to you 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.
+
+#include "arrow/extension/fixed_shape_tensor.h"
+
+#include "arrow/array/array_nested.h"
+#include "arrow/array/array_primitive.h"
+#include "arrow/json/rapidjson_defs.h"  // IWYU pragma: keep
+#include "arrow/tensor.h"
+#include "arrow/util/logging.h"
+#include "arrow/util/sort.h"
+
+#include <rapidjson/document.h>
+#include <rapidjson/writer.h>
+
+namespace rj = arrow::rapidjson;
+
+namespace arrow {
+namespace extension {
+
+bool FixedShapeTensorType::ExtensionEquals(const ExtensionType& other) const {
+  if (extension_name() != other.extension_name()) {
+    return false;
+  }
+  const auto& other_ext = static_cast<const FixedShapeTensorType&>(other);
+
+  auto is_permutation_trivial = [](const std::vector<int64_t>& permutation) {
+    for (size_t i = 1; i < permutation.size(); ++i) {
+      if (permutation[i - 1] + 1 != permutation[i]) {
+        return false;
+      }
+    }
+    return true;
+  };
+  const bool permutation_equivalent =
+      (permutation_ == other_ext.permutation()) ||
+      ((permutation_.empty() && 
is_permutation_trivial(other_ext.permutation())) &&
+       (is_permutation_trivial(permutation_) || 
other_ext.permutation().empty()));
+
+  return storage_type()->Equals(other_ext.storage_type()) &&
+         shape_ == other_ext.shape() && dim_names_ == other_ext.dim_names() &&
+         permutation_equivalent;
+}
+
+std::string FixedShapeTensorType::Serialize() const {
+  rj::Document document;
+  document.SetObject();
+  rj::Document::AllocatorType& allocator = document.GetAllocator();
+
+  rj::Value shape(rj::kArrayType);
+  for (auto v : shape_) {
+    shape.PushBack(v, allocator);
+  }
+  document.AddMember(rj::Value("shape", allocator), shape, allocator);
+
+  if (!permutation_.empty()) {
+    rj::Value permutation(rj::kArrayType);
+    for (auto v : permutation_) {
+      permutation.PushBack(v, allocator);
+    }
+    document.AddMember(rj::Value("permutation", allocator), permutation, 
allocator);
+  }
+
+  if (!dim_names_.empty()) {
+    rj::Value dim_names(rj::kArrayType);
+    for (std::string v : dim_names_) {
+      dim_names.PushBack(rj::Value{}.SetString(v.c_str(), allocator), 
allocator);
+    }
+    document.AddMember(rj::Value("dim_names", allocator), dim_names, 
allocator);
+  }
+
+  rj::StringBuffer buffer;
+  rj::Writer<rj::StringBuffer> writer(buffer);
+  document.Accept(writer);
+  return buffer.GetString();
+}
+
+Result<std::shared_ptr<DataType>> FixedShapeTensorType::Deserialize(
+    std::shared_ptr<DataType> storage_type, const std::string& 
serialized_data) const {
+  if (storage_type->id() != Type::FIXED_SIZE_LIST) {
+    return Status::Invalid("Expected FixedSizeList storage type, got ",
+                           storage_type->ToString());
+  }
+  auto value_type =
+      
internal::checked_pointer_cast<FixedSizeListType>(storage_type)->value_type();
+  rj::Document document;
+  if (document.Parse(serialized_data.data(), 
serialized_data.length()).HasParseError() ||
+      !document.HasMember("shape") || !document["shape"].IsArray()) {
+    return Status::Invalid("Invalid serialized JSON data: ", serialized_data);
+  }
+
+  std::vector<int64_t> shape;
+  for (auto& x : document["shape"].GetArray()) {
+    shape.emplace_back(x.GetInt64());
+  }
+  std::vector<int64_t> permutation;
+  if (document.HasMember("permutation")) {
+    for (auto& x : document["permutation"].GetArray()) {
+      permutation.emplace_back(x.GetInt64());
+    }
+    if (shape.size() != permutation.size()) {
+      return Status::Invalid("Invalid permutation");
+    }
+  }
+  std::vector<std::string> dim_names;
+  if (document.HasMember("dim_names")) {
+    for (auto& x : document["dim_names"].GetArray()) {
+      dim_names.emplace_back(x.GetString());
+    }
+    if (shape.size() != dim_names.size()) {
+      return Status::Invalid("Invalid dim_names");
+    }
+  }
+
+  return fixed_shape_tensor(value_type, shape, permutation, dim_names);
+}
+
+std::shared_ptr<Array> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<ArrayData> data) const {
+  return std::make_shared<ExtensionArray>(data);
+}
+
+Result<std::shared_ptr<Array>> FixedShapeTensorType::MakeArray(
+    std::shared_ptr<Tensor> tensor) const {
+  auto permutation = internal::ArgSort(tensor->strides());
+  std::reverse(permutation.begin(), permutation.end());
+  if (permutation[0] != 0) {
+    return Status::Invalid(
+        "Only first-major tensors can be zero-copy converted to arrays");
+  }
+
+  auto cell_shape = tensor->shape();
+  cell_shape.erase(cell_shape.begin());
+  if (cell_shape != shape_) {
+    return Status::Invalid("Expected cell shape does not match input tensor 
shape");
+  }
+
+  permutation.erase(permutation.begin());
+  for (auto& x : permutation) {
+    x--;
+  }
+
+  auto ext_type = internal::checked_pointer_cast<ExtensionType>(
+      fixed_shape_tensor(tensor->type(), cell_shape, permutation, 
tensor->dim_names()));
+
+  std::shared_ptr<FixedSizeListArray> arr;
+  std::shared_ptr<Array> value_array;
+  switch (tensor->type_id()) {
+    case Type::UINT8: {
+      value_array = std::make_shared<UInt8Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT8: {
+      value_array = std::make_shared<Int8Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT16: {
+      value_array = std::make_shared<UInt16Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT16: {
+      value_array = std::make_shared<Int16Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT32: {
+      value_array = std::make_shared<UInt32Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT32: {
+      value_array = std::make_shared<Int32Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::UINT64: {
+      value_array = std::make_shared<Int64Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::INT64: {
+      value_array = std::make_shared<Int64Array>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::HALF_FLOAT: {
+      value_array = std::make_shared<HalfFloatArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::FLOAT: {
+      value_array = std::make_shared<FloatArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    case Type::DOUBLE: {
+      value_array = std::make_shared<DoubleArray>(tensor->size(), 
tensor->data());
+      break;
+    }
+    default: {
+      return Status::NotImplemented("Unsupported tensor type: ",
+                                    tensor->type()->ToString());
+    }
+  }
+  arr = std::make_shared<FixedSizeListArray>(ext_type->storage_type(), 
tensor->shape()[0],
+                                             value_array);
+  auto ext_data = arr->data();
+  ext_data->type = ext_type;
+  return MakeArray(ext_data);
+}
+
+Result<std::shared_ptr<Tensor>> FixedShapeTensorType::ToTensor(

Review Comment:
   This function returns a `Result` but none of the potential errors are 
propagated (my guess is the signature changed at some point)



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