lidavidm commented on code in PR #12590:
URL: https://github.com/apache/arrow/pull/12590#discussion_r860144865


##########
python/pyarrow/tests/test_udf.py:
##########
@@ -0,0 +1,501 @@
+# 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.
+
+
+import pytest
+
+import pyarrow as pa
+from pyarrow import compute as pc
+
+# UDFs are all tested with a dataset scan
+pytestmark = pytest.mark.dataset
+
+
+try:
+    import pyarrow.dataset as ds
+except ImportError:
+    ds = None
+
+global_batch_length = 10
+
+
+def mock_udf_context(batch_length=global_batch_length):
+    from pyarrow._compute import _get_scalar_udf_context
+    return _get_scalar_udf_context(pa.default_memory_pool(), batch_length)
+
+
+@pytest.fixture(scope="session")
+def unary_func_fixture():
+    def unary_function(ctx, scalar1):
+        return pc.call_function("add", [scalar1, 1])
+    func_name = "y=x+k"
+    unary_doc = {"summary": "add function",
+                 "description": "test add function"}
+    pc.register_scalar_function(unary_function,
+                                func_name,
+                                unary_doc,
+                                {"array": pa.int64()},
+                                pa.int64())
+    return unary_function, func_name
+
+
+@pytest.fixture(scope="session")
+def binary_func_fixture():
+    def binary_function(ctx, m, x):
+        return pc.call_function("multiply", [m, x])
+    func_name = "y=mx"
+    binary_doc = {"summary": "y=mx",
+                  "description": "find y from y = mx"}
+    pc.register_scalar_function(binary_function,
+                                func_name,
+                                binary_doc,
+                                {"m": pa.int64(),
+                                 "x": pa.int64(),
+                                 },
+                                pa.int64())
+    return binary_function, func_name
+
+
+@pytest.fixture(scope="session")
+def ternary_func_fixture():
+    def ternary_function(ctx, m, x, c):
+        mx = pc.call_function("multiply", [m, x])
+        return pc.call_function("add", [mx, c])
+    ternary_doc = {"summary": "y=mx+c",
+                   "description": "find y from y = mx + c"}
+    func_name = "y=mx+c"
+    pc.register_scalar_function(ternary_function,
+                                func_name,
+                                ternary_doc,
+                                {
+                                    "array1": pa.int64(),
+                                    "array2": pa.int64(),
+                                    "array3": pa.int64(),
+                                },
+                                pa.int64())
+    return ternary_function, func_name
+
+
+@pytest.fixture(scope="session")
+def varargs_func_fixture():
+    def varargs_function(ctx, *values):
+        base_val = values[:2]
+        res = pc.call_function("add", base_val)
+        for other_val in values[2:]:
+            res = pc.call_function("add", [res, other_val])
+        return res
+    func_name = "z=ax+by+c"
+    varargs_doc = {"summary": "z=ax+by+c",
+                   "description": "find z from z = ax + by + c"
+                   }
+    pc.register_scalar_function(varargs_function,
+                                func_name,
+                                varargs_doc,
+                                {
+                                    "array1": pa.int64(),
+                                    "array2": pa.int64(),
+                                    "array3": pa.int64(),
+                                    "array4": pa.int64(),
+                                    "array5": pa.int64(),
+                                },
+                                pa.int64())
+    return varargs_function, func_name
+
+
+@pytest.fixture(scope="session")
+def random_with_udf_ctx_func_fixture():
+    def random_with_udf_ctx(context, one, two):
+        proxy_pool = pa.proxy_memory_pool(context.memory_pool)
+        ans = pc.add(one, two, memory_pool=proxy_pool)
+        res = pa.array([ans.as_py()], memory_pool=proxy_pool)
+        return res
+    in_types = {"one": pa.int64(),
+                "two": pa.int64(),
+                }
+    func_doc = {
+        "summary": "test udf context",
+        "description": "udf context test"
+    }
+    func_name = "test_udf_context"
+    pc.register_scalar_function(random_with_udf_ctx,
+                                func_name, func_doc,
+                                in_types,
+                                pa.int64())
+    return random_with_udf_ctx, func_name
+
+
+@pytest.fixture(scope="session")
+def output_check_func_fixture():
+    # The objective of this fixture is to evaluate,
+    # how the UDF interface respond to unexpected
+    # output types. The types chosen at the test
+    # end are either of different Arrow data type
+    # or non-Arrow type.
+    def output_check(ctx, array):
+        ar = pc.call_function("add", [array, 1])
+        ar = ar.cast(pa.int32())
+        return ar
+    func_name = "test_output_value"
+    in_types = {"array": pa.int64()}
+    out_type = pa.int64()
+    doc = {
+        "summary": "add function scalar",
+        "description": "add function"
+    }
+    pc.register_scalar_function(output_check, func_name, doc,
+                                in_types, out_type)
+    return output_check, func_name
+
+
+@pytest.fixture(scope="session")
+def nullary_check_func_fixture():
+    # this needs to return array values
+    def nullary_check(context):
+        return pa.array([42] * context.batch_length, type=pa.int64(),
+                        memory_pool=context.memory_pool)
+
+    func_doc = {
+        "summary": "random function",
+        "description": "generates a random value"
+    }
+    func_name = "test_random_func"
+    pc.register_scalar_function(nullary_check,
+                                func_name,
+                                func_doc,
+                                {},
+                                pa.int64())
+
+    return nullary_check, func_name
+
+
+@pytest.fixture(scope="session")
+def output_python_type_func_fixture():
+    # This fixture helps to check the response
+    # when the function return value is not an Arrow
+    # defined data type. Instead here the returned value
+    # is of type int in Python.
+    def const_return(ctx, scalar):
+        return 42
+
+    func_name = "test_output_type"
+    in_types = {"array": pa.int64()}
+    out_type = pa.int64()
+    doc = {
+        "summary": "add function scalar",
+        "description": "add function"
+    }
+    pc.register_scalar_function(const_return, func_name, doc,
+                                in_types, out_type)
+    return const_return, func_name
+
+
+@pytest.fixture(scope="session")
+def varargs_check_func_fixture():
+    def varargs_check(ctx, *values):
+        base_val = values[:2]
+        res = pc.call_function("add", base_val)
+        for other_val in values[2:]:
+            res = pc.call_function("add", [res, other_val])
+        return res
+    func_name = "test_varargs_function"
+    in_types = {"array1": pa.int64(),
+                "array2": pa.int64(),
+                }
+    doc = {"summary": "n add function",
+           "description": "add N number of arrays"
+           }
+    pc.register_scalar_function(varargs_check, func_name, doc,
+                                in_types, pa.int64())
+
+    return varargs_check, func_name
+
+
+@pytest.fixture(scope="session")
+def raise_func_fixture():
+    def raise_func(ctx):
+        raise ValueError("Test function with raise")
+    func_name = "test_raise"
+    doc = {
+        "summary": "test function with raise",
+        "description": "function with a raise"
+    }
+    pc.register_scalar_function(raise_func, func_name, doc,
+                                {}, pa.int64())
+    return raise_func, func_name
+
+
+def check_scalar_function(func_fixture,
+                          input,
+                          run_in_dataset=True,
+                          batch_length=global_batch_length):
+    function, name = func_fixture
+    expected_output = function(mock_udf_context(batch_length), *input)
+    func = pc.get_function(name)
+    assert func.name == name
+
+    result = pc.call_function(name, input)
+
+    assert result == expected_output
+    if run_in_dataset:
+        field_names = [f'field{index}' for index, in_arr in input]
+        table = pa.Table.from_arrays(input, field_names)
+        dataset = ds.dataset(table)
+        func_args = [ds.field(field_name) for field_name in field_names]
+        result_table = dataset.to_table(
+            columns={'result': ds.field('')._call(name, func_args)})
+        assert result_table.column(0).chunks[0] == expected_output
+
+
+def test_scalar_udf_array_unary(unary_func_fixture):
+    check_scalar_function(unary_func_fixture,
+                          [
+                              pa.array([10, 20], pa.int64())
+                          ],
+                          mock_udf_context()

Review Comment:
   Hmm, wait. Why is this being passed as the third argument to 
`check_scalar_function`? The types don't match.



##########
python/pyarrow/_compute.pyx:
##########
@@ -2251,3 +2338,219 @@ cdef CExpression _bind(Expression filter, Schema 
schema) except *:
 
     return GetResultValue(filter.unwrap().Bind(
         deref(pyarrow_unwrap_schema(schema).get())))
+
+
+cdef class ScalarUdfContext:
+    """A container to hold user-defined-function related
+    entities. `batch_length` and `MemoryPool` are important
+    entities in defining functions which require these details. 
+
+    Example
+    -------
+
+    ScalarUdfContext is used with the scalar user-defined-functions. 
+    When defining such a function, the first parameter must be a
+    ScalarUdfContext object. This object can be used to hold important
+    information. This can be further enhanced depending on the use 
+    cases of user-defined-functions. 
+
+    >>> def random(context, one, two):
+            return pc.add(one, two, memory_pool=context.memory_pool)
+    """
+
+    def __init__(self):
+        raise TypeError("Do not call {}'s constructor directly"
+                        .format(self.__class__.__name__))
+
+    cdef void init(self, const CScalarUdfContext &c_context):
+        self.c_context = c_context
+
+    @property
+    def batch_length(self):
+        """
+        Returns the length of the batch associated with the
+        user-defined-function. Useful when the batch_length
+        is required to do computations specially when scalars
+        are parameters of the user-defined-function.
+
+        Returns
+        -------
+        batch_length : int
+            The number of batches used when calling 
+            user-defined-function. 
+        """
+        return self.c_context.batch_length
+
+    @property
+    def memory_pool(self):
+        """
+        Returns the MemoryPool associated with the 
+        user-defined-function. An already initialized
+        MemoryPool can be used within the
+        user-defined-function. 
+
+        Returns
+        -------
+        memory_pool : MemoryPool
+            MemoryPool is obtained from the KernelContext
+            and passed to the ScalarUdfContext.
+        """
+        return box_memory_pool(self.c_context.pool)
+
+
+cdef inline CFunctionDoc _make_function_doc(dict func_doc) except *:
+    """
+    Helper function to generate the FunctionDoc
+    This function accepts a dictionary and expect the 
+    summary(str), description(str) and arg_names(List[str]) keys. 
+    """
+    cdef:
+        CFunctionDoc f_doc
+        vector[c_string] c_arg_names
+
+    f_doc.summary = tobytes(func_doc["summary"])
+    f_doc.description = tobytes(func_doc["description"])
+    for arg_name in func_doc["arg_names"]:
+        c_arg_names.push_back(tobytes(arg_name))
+    f_doc.arg_names = c_arg_names
+    # UDFOptions integration:
+    # TODO: https://issues.apache.org/jira/browse/ARROW-16041
+    f_doc.options_class = tobytes("")
+    f_doc.options_required = False
+    return f_doc
+
+cdef _scalar_udf_callback(user_function, const CScalarUdfContext& c_context, 
inputs):
+    """
+    Helper callback function used to wrap the ScalarUdfContext from Python to 
C++
+    execution.
+    """
+    cdef ScalarUdfContext context = ScalarUdfContext.__new__(ScalarUdfContext)
+    context.init(c_context)
+    return user_function(context, *inputs)
+
+
+def register_scalar_function(func, func_name, function_doc, in_types,
+                             out_type):
+    """
+    Register a user-defined scalar function. 
+
+    A scalar function is a function that executes elementwise
+    operations on arrays or scalars, and therefore whose results
+    generally do not depend on the order of the values in the

Review Comment:
   CC @vibhatha 



##########
python/pyarrow/_compute.pyx:
##########
@@ -2251,3 +2338,219 @@ cdef CExpression _bind(Expression filter, Schema 
schema) except *:
 
     return GetResultValue(filter.unwrap().Bind(
         deref(pyarrow_unwrap_schema(schema).get())))
+
+
+cdef class ScalarUdfContext:
+    """A container to hold user-defined-function related
+    entities. `batch_length` and `MemoryPool` are important
+    entities in defining functions which require these details. 
+
+    Example
+    -------
+
+    ScalarUdfContext is used with the scalar user-defined-functions. 
+    When defining such a function, the first parameter must be a
+    ScalarUdfContext object. This object can be used to hold important
+    information. This can be further enhanced depending on the use 
+    cases of user-defined-functions. 
+
+    >>> def random(context, one, two):
+            return pc.add(one, two, memory_pool=context.memory_pool)
+    """
+
+    def __init__(self):
+        raise TypeError("Do not call {}'s constructor directly"
+                        .format(self.__class__.__name__))
+
+    cdef void init(self, const CScalarUdfContext &c_context):
+        self.c_context = c_context
+
+    @property
+    def batch_length(self):
+        """
+        Returns the length of the batch associated with the
+        user-defined-function. Useful when the batch_length
+        is required to do computations specially when scalars
+        are parameters of the user-defined-function.
+
+        Returns
+        -------
+        batch_length : int
+            The number of batches used when calling 
+            user-defined-function. 
+        """
+        return self.c_context.batch_length
+
+    @property
+    def memory_pool(self):
+        """
+        Returns the MemoryPool associated with the 
+        user-defined-function. An already initialized
+        MemoryPool can be used within the
+        user-defined-function. 
+
+        Returns
+        -------
+        memory_pool : MemoryPool
+            MemoryPool is obtained from the KernelContext
+            and passed to the ScalarUdfContext.
+        """
+        return box_memory_pool(self.c_context.pool)
+
+
+cdef inline CFunctionDoc _make_function_doc(dict func_doc) except *:
+    """
+    Helper function to generate the FunctionDoc
+    This function accepts a dictionary and expect the 
+    summary(str), description(str) and arg_names(List[str]) keys. 
+    """
+    cdef:
+        CFunctionDoc f_doc
+        vector[c_string] c_arg_names
+
+    f_doc.summary = tobytes(func_doc["summary"])
+    f_doc.description = tobytes(func_doc["description"])
+    for arg_name in func_doc["arg_names"]:
+        c_arg_names.push_back(tobytes(arg_name))
+    f_doc.arg_names = c_arg_names
+    # UDFOptions integration:
+    # TODO: https://issues.apache.org/jira/browse/ARROW-16041
+    f_doc.options_class = tobytes("")
+    f_doc.options_required = False
+    return f_doc
+
+cdef _scalar_udf_callback(user_function, const CScalarUdfContext& c_context, 
inputs):
+    """
+    Helper callback function used to wrap the ScalarUdfContext from Python to 
C++
+    execution.
+    """
+    cdef ScalarUdfContext context = ScalarUdfContext.__new__(ScalarUdfContext)
+    context.init(c_context)
+    return user_function(context, *inputs)
+
+
+def register_scalar_function(func, func_name, function_doc, in_types,
+                             out_type):
+    """
+    Register a user-defined scalar function. 
+
+    A scalar function is a function that executes elementwise
+    operations on arrays or scalars, and therefore whose results
+    generally do not depend on the order of the values in the
+    arguments. Accepts and returns arrays that are all of the
+    same size. These functions roughly correspond to the functions
+    used in SQL expressions.

Review Comment:
   CC @vibhatha 



##########
python/pyarrow/tests/test_udf.py:
##########
@@ -0,0 +1,501 @@
+# 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.
+
+
+import pytest
+
+import pyarrow as pa
+from pyarrow import compute as pc
+
+# UDFs are all tested with a dataset scan
+pytestmark = pytest.mark.dataset
+
+
+try:
+    import pyarrow.dataset as ds
+except ImportError:
+    ds = None
+
+global_batch_length = 10
+
+
+def mock_udf_context(batch_length=global_batch_length):
+    from pyarrow._compute import _get_scalar_udf_context
+    return _get_scalar_udf_context(pa.default_memory_pool(), batch_length)
+
+
+@pytest.fixture(scope="session")
+def unary_func_fixture():
+    def unary_function(ctx, scalar1):
+        return pc.call_function("add", [scalar1, 1])
+    func_name = "y=x+k"
+    unary_doc = {"summary": "add function",
+                 "description": "test add function"}
+    pc.register_scalar_function(unary_function,
+                                func_name,
+                                unary_doc,
+                                {"array": pa.int64()},
+                                pa.int64())
+    return unary_function, func_name
+
+
+@pytest.fixture(scope="session")
+def binary_func_fixture():
+    def binary_function(ctx, m, x):
+        return pc.call_function("multiply", [m, x])
+    func_name = "y=mx"
+    binary_doc = {"summary": "y=mx",
+                  "description": "find y from y = mx"}
+    pc.register_scalar_function(binary_function,
+                                func_name,
+                                binary_doc,
+                                {"m": pa.int64(),
+                                 "x": pa.int64(),
+                                 },
+                                pa.int64())
+    return binary_function, func_name
+
+
+@pytest.fixture(scope="session")
+def ternary_func_fixture():
+    def ternary_function(ctx, m, x, c):
+        mx = pc.call_function("multiply", [m, x])
+        return pc.call_function("add", [mx, c])
+    ternary_doc = {"summary": "y=mx+c",
+                   "description": "find y from y = mx + c"}
+    func_name = "y=mx+c"
+    pc.register_scalar_function(ternary_function,
+                                func_name,
+                                ternary_doc,
+                                {
+                                    "array1": pa.int64(),
+                                    "array2": pa.int64(),
+                                    "array3": pa.int64(),
+                                },
+                                pa.int64())
+    return ternary_function, func_name
+
+
+@pytest.fixture(scope="session")
+def varargs_func_fixture():
+    def varargs_function(ctx, *values):
+        base_val = values[:2]
+        res = pc.call_function("add", base_val)
+        for other_val in values[2:]:
+            res = pc.call_function("add", [res, other_val])
+        return res
+    func_name = "z=ax+by+c"
+    varargs_doc = {"summary": "z=ax+by+c",
+                   "description": "find z from z = ax + by + c"
+                   }
+    pc.register_scalar_function(varargs_function,
+                                func_name,
+                                varargs_doc,
+                                {
+                                    "array1": pa.int64(),
+                                    "array2": pa.int64(),
+                                    "array3": pa.int64(),
+                                    "array4": pa.int64(),
+                                    "array5": pa.int64(),
+                                },
+                                pa.int64())
+    return varargs_function, func_name
+
+
+@pytest.fixture(scope="session")
+def random_with_udf_ctx_func_fixture():
+    def random_with_udf_ctx(context, one, two):
+        proxy_pool = pa.proxy_memory_pool(context.memory_pool)
+        ans = pc.add(one, two, memory_pool=proxy_pool)
+        res = pa.array([ans.as_py()], memory_pool=proxy_pool)
+        return res
+    in_types = {"one": pa.int64(),
+                "two": pa.int64(),
+                }
+    func_doc = {
+        "summary": "test udf context",
+        "description": "udf context test"
+    }
+    func_name = "test_udf_context"
+    pc.register_scalar_function(random_with_udf_ctx,
+                                func_name, func_doc,
+                                in_types,
+                                pa.int64())
+    return random_with_udf_ctx, func_name
+
+
+@pytest.fixture(scope="session")
+def output_check_func_fixture():
+    # The objective of this fixture is to evaluate,
+    # how the UDF interface respond to unexpected
+    # output types. The types chosen at the test
+    # end are either of different Arrow data type
+    # or non-Arrow type.
+    def output_check(ctx, array):
+        ar = pc.call_function("add", [array, 1])
+        ar = ar.cast(pa.int32())
+        return ar
+    func_name = "test_output_value"
+    in_types = {"array": pa.int64()}
+    out_type = pa.int64()
+    doc = {
+        "summary": "add function scalar",
+        "description": "add function"
+    }
+    pc.register_scalar_function(output_check, func_name, doc,
+                                in_types, out_type)
+    return output_check, func_name
+
+
+@pytest.fixture(scope="session")
+def nullary_check_func_fixture():
+    # this needs to return array values
+    def nullary_check(context):
+        return pa.array([42] * context.batch_length, type=pa.int64(),
+                        memory_pool=context.memory_pool)
+
+    func_doc = {
+        "summary": "random function",
+        "description": "generates a random value"
+    }
+    func_name = "test_random_func"
+    pc.register_scalar_function(nullary_check,
+                                func_name,
+                                func_doc,
+                                {},
+                                pa.int64())
+
+    return nullary_check, func_name
+
+
+@pytest.fixture(scope="session")
+def output_python_type_func_fixture():
+    # This fixture helps to check the response
+    # when the function return value is not an Arrow
+    # defined data type. Instead here the returned value
+    # is of type int in Python.
+    def const_return(ctx, scalar):
+        return 42
+
+    func_name = "test_output_type"
+    in_types = {"array": pa.int64()}
+    out_type = pa.int64()
+    doc = {
+        "summary": "add function scalar",
+        "description": "add function"
+    }
+    pc.register_scalar_function(const_return, func_name, doc,
+                                in_types, out_type)
+    return const_return, func_name
+
+
+@pytest.fixture(scope="session")
+def varargs_check_func_fixture():
+    def varargs_check(ctx, *values):
+        base_val = values[:2]
+        res = pc.call_function("add", base_val)
+        for other_val in values[2:]:
+            res = pc.call_function("add", [res, other_val])
+        return res
+    func_name = "test_varargs_function"
+    in_types = {"array1": pa.int64(),
+                "array2": pa.int64(),
+                }
+    doc = {"summary": "n add function",
+           "description": "add N number of arrays"
+           }
+    pc.register_scalar_function(varargs_check, func_name, doc,
+                                in_types, pa.int64())
+
+    return varargs_check, func_name
+
+
+@pytest.fixture(scope="session")
+def raise_func_fixture():
+    def raise_func(ctx):
+        raise ValueError("Test function with raise")
+    func_name = "test_raise"
+    doc = {
+        "summary": "test function with raise",
+        "description": "function with a raise"
+    }
+    pc.register_scalar_function(raise_func, func_name, doc,
+                                {}, pa.int64())
+    return raise_func, func_name
+
+
+def check_scalar_function(func_fixture,
+                          input,
+                          run_in_dataset=True,
+                          batch_length=global_batch_length):
+    function, name = func_fixture
+    expected_output = function(mock_udf_context(batch_length), *input)
+    func = pc.get_function(name)
+    assert func.name == name
+
+    result = pc.call_function(name, input)
+
+    assert result == expected_output
+    if run_in_dataset:
+        field_names = [f'field{index}' for index, in_arr in input]
+        table = pa.Table.from_arrays(input, field_names)
+        dataset = ds.dataset(table)
+        func_args = [ds.field(field_name) for field_name in field_names]
+        result_table = dataset.to_table(
+            columns={'result': ds.field('')._call(name, func_args)})
+        assert result_table.column(0).chunks[0] == expected_output
+
+
+def test_scalar_udf_array_unary(unary_func_fixture):
+    check_scalar_function(unary_func_fixture,
+                          [
+                              pa.array([10, 20], pa.int64())
+                          ],
+                          mock_udf_context()
+                          )
+
+
+def test_scalar_udf_array_binary(binary_func_fixture):
+    check_scalar_function(binary_func_fixture,
+                          [
+                              pa.array([10, 20], pa.int64()),
+                              pa.array([2, 4], pa.int64())
+                          ],
+                          mock_udf_context()
+                          )
+
+
+def test_scalar_udf_array_ternary(ternary_func_fixture):
+    check_scalar_function(ternary_func_fixture,
+                          [
+                              pa.array([10, 20], pa.int64()),
+                              pa.array([2, 4], pa.int64()),
+                              pa.array([5, 10], pa.int64())
+                          ],
+                          mock_udf_context()
+                          )
+
+
+def test_scalar_udf_array_varargs(varargs_func_fixture):
+    check_scalar_function(varargs_func_fixture,
+                          [
+                              pa.array([2, 3], pa.int64()),
+                              pa.array([10, 20], pa.int64()),
+                              pa.array([3, 7], pa.int64()),
+                              pa.array([20, 30], pa.int64()),
+                              pa.array([5, 10], pa.int64())
+                          ],
+                          mock_udf_context
+                          )
+
+
+def test_registration_errors():
+    # validate function name
+    doc = {
+        "summary": "test udf input",
+        "description": "parameters are validated"
+    }
+    in_types = {"scalar": pa.int64()}
+    out_type = pa.int64()
+
+    def test_reg_function(context):
+        return pa.array([10])
+
+    with pytest.raises(TypeError):
+        pc.register_scalar_function(test_reg_function,
+                                    None, doc, in_types,
+                                    out_type)
+
+    # validate function
+    with pytest.raises(TypeError, match="func must be a callable"):
+        pc.register_scalar_function(None, "test_none_function", doc, in_types,
+                                    out_type)
+
+    # validate output type
+    expected_expr = "DataType expected, got <class 'NoneType'>"
+    with pytest.raises(TypeError, match=expected_expr):
+        pc.register_scalar_function(test_reg_function,
+                                    "test_output_function", doc, in_types,
+                                    None)
+
+    # validate input type
+    expected_expr = r'in_types must be a dictionary of DataType'
+    with pytest.raises(TypeError, match=expected_expr):
+        pc.register_scalar_function(test_reg_function,
+                                    "test_input_function", doc, None,
+                                    out_type)
+
+    # register an already registered function
+    # first registration
+    pc.register_scalar_function(test_reg_function,
+                                "test_reg_function", doc, {},
+                                out_type)
+    # second registration
+    expected_expr = "Already have a function registered with name:" \
+        + " test_reg_function"
+    with pytest.raises(pa.lib.ArrowKeyError, match=expected_expr):
+        pc.register_scalar_function(test_reg_function,
+                                    "test_reg_function", doc, {},
+                                    out_type)
+
+
+def test_varargs_function_validation(varargs_check_func_fixture):
+    _function, func_name = varargs_check_func_fixture

Review Comment:
   ```suggestion
       _, func_name = varargs_check_func_fixture
   ```
   is what's usually done to ignore things in unpacking



##########
python/pyarrow/tests/test_udf.py:
##########
@@ -0,0 +1,545 @@
+# 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.
+
+
+import pytest
+
+import pyarrow as pa
+from pyarrow import compute as pc
+
+
+# Marks all of the tests in this module
+# Ignore these with pytest ... -m 'not udf'
+# pytestmark = pytest.mark.udf
+
+unary_doc = {"summary": "add function",
+             "description": "test add function"}
+
+
+@pytest.fixture(scope="session")
+def udf_context():
+    return pc._get_scalar_udf_context(pa.default_memory_pool(), 0)
+
+
+@pytest.fixture(scope="session")
+def unary_func_fixture():
+    def unary_function(udf_context, scalar1):
+        return pc.call_function("add", [scalar1, 1])
+    return unary_function
+
+
+binary_doc = {"summary": "y=mx",
+              "description": "find y from y = mx"}
+
+
+@pytest.fixture(scope="session")
+def binary_func_fixture():
+    def binary_function(ctx, m, x):
+        return pc.call_function("multiply", [m, x])
+    return binary_function
+
+
+ternary_doc = {"summary": "y=mx+c",
+               "description": "find y from y = mx + c"}
+
+
+@pytest.fixture(scope="session")
+def ternary_func_fixture():
+    def ternary_function(ctx, m, x, c):
+        mx = pc.call_function("multiply", [m, x])
+        return pc.call_function("add", [mx, c])
+    return ternary_function
+
+
+varargs_doc = {"summary": "z=ax+by+c",
+               "description": "find z from z = ax + by + c"
+               }
+
+
+@pytest.fixture(scope="session")
+def varargs_func_fixture():
+    def varargs_function(ctx, *values):
+        base_val = values[:2]
+        res = pc.call_function("add", base_val)
+        for other_val in values[2:]:
+            res = pc.call_function("add", [res, other_val])
+        return res
+    return varargs_function
+
+
+@pytest.fixture(scope="session")
+def random_with_udf_ctx_func_fixture():
+    def random_with_udf_ctx(context, one, two):
+        old_pool = pa.default_memory_pool()
+        proxy_pool = pa.proxy_memory_pool(context.memory_pool)
+        pa.set_memory_pool(proxy_pool)
+        try:
+            ans = pc.add(one, two, memory_pool=proxy_pool)
+            allocated_before = proxy_pool.bytes_allocated()
+            # allocating 64 bytes
+            res = pa.array([ans.as_py()], memory_pool=proxy_pool)
+            allocated_after = proxy_pool.bytes_allocated()
+        finally:
+            pa.set_memory_pool(old_pool)
+        assert allocated_before == 0
+        assert allocated_after == 64
+        assert context.batch_length == 2
+        return res

Review Comment:
   CC @vibhatha 



##########
python/pyarrow/_compute.pyx:
##########
@@ -2275,3 +2279,205 @@ cdef CExpression _bind(Expression filter, Schema 
schema) except *:
 
     return GetResultValue(filter.unwrap().Bind(
         deref(pyarrow_unwrap_schema(schema).get())))
+
+
+cdef class ScalarUdfContext:
+    """
+    Per-invocation function context/state.
+
+    This object will always be the first argument to a user-defined
+    function. It should not be used outside of a call to the function.
+    """
+
+    def __init__(self):
+        raise TypeError("Do not call {}'s constructor directly"
+                        .format(self.__class__.__name__))
+
+    cdef void init(self, const CScalarUdfContext &c_context):
+        self.c_context = c_context
+
+    @property
+    def batch_length(self):
+        """
+        The common length of all input arguments (int).
+
+        In the case that all arguments are scalars, this value
+        is used to pass the "actual length" of the arguments,
+        e.g. because the scalar values are encoding a column
+        with a constant value.
+        """
+        return self.c_context.batch_length
+
+    @property
+    def memory_pool(self):
+        """
+        A memory pool for allocations (:class:`MemoryPool`).
+        """
+        return box_memory_pool(self.c_context.pool)
+
+
+cdef inline CFunctionDoc _make_function_doc(dict func_doc) except *:
+    """
+    Helper function to generate the FunctionDoc
+    This function accepts a dictionary and expect the 
+    summary(str), description(str) and arg_names(List[str]) keys. 
+    """
+    cdef:
+        CFunctionDoc f_doc
+        vector[c_string] c_arg_names
+
+    f_doc.summary = tobytes(func_doc["summary"])
+    f_doc.description = tobytes(func_doc["description"])
+    for arg_name in func_doc["arg_names"]:
+        c_arg_names.push_back(tobytes(arg_name))
+    f_doc.arg_names = c_arg_names
+    # UDFOptions integration:
+    # TODO: https://issues.apache.org/jira/browse/ARROW-16041
+    f_doc.options_class = b""
+    f_doc.options_required = False
+    return f_doc
+
+
+cdef object box_scalar_udf_context(const CScalarUdfContext& c_context):
+    cdef ScalarUdfContext context = ScalarUdfContext.__new__(ScalarUdfContext)
+    context.init(c_context)
+    return context
+
+
+cdef _scalar_udf_callback(user_function, const CScalarUdfContext& c_context, 
inputs):
+    """
+    Helper callback function used to wrap the ScalarUdfContext from Python to 
C++
+    execution.
+    """
+    context = box_scalar_udf_context(c_context)
+    return user_function(context, *inputs)
+
+
+def _get_scalar_udf_context(memory_pool, batch_length):
+    cdef CScalarUdfContext c_context
+    c_context.pool = maybe_unbox_memory_pool(memory_pool)
+    c_context.batch_length = batch_length
+    context = box_scalar_udf_context(c_context)
+    return context
+
+
+def register_scalar_function(func, func_name, function_doc, in_types,
+                             out_type):
+    """
+    Register a user-defined scalar function. 
+
+    A scalar function is a function that executes elementwise
+    operations on arrays or scalars, and therefore whose results
+    generally do not depend on the order of the values in the
+    arguments. Accepts and returns arrays that are all of the
+    same size. These functions roughly correspond to the functions
+    used in SQL expressions.
+
+    Parameters
+    ----------
+    func : callable
+        A callable implementing the user-defined function.
+        It must take arguments equal to the number of
+        in_types defined. It must return an Array or Scalar
+        matching the out_type. It must return a Scalar if
+        all arguments are scalar, else it must return an Array.
+
+        To define a varargs function, pass a callable that takes
+        varargs. The last in_type will be the type of the all
+        varargs arguments.
+    func_name : str
+        Name of the function. This name must be globally unique. 
+    function_doc : dict
+        A dictionary object with keys "summary" (str),
+        and "description" (str).
+    in_types : Dict[str, DataType]
+        A dictionarym mapping function argument names to
+        their respective DataType.
+        The argument names will be used to generate
+        documentation for the function. The number of
+        arguments specified here determines the function
+        arity.
+    out_type : DataType
+        Output type of the function.
+
+    Examples
+    --------
+
+    >>> import pyarrow.compute as pc
+    >>> 
+    >>> func_doc = {}
+    >>> func_doc["summary"] = "simple udf"
+    >>> func_doc["description"] = "add a constant to a scalar"
+    >>> 
+    >>> def add_constant(ctx, array):
+    ...     return pc.add(array, 1)
+    >>> 
+    >>> func_name = "py_add_func"
+    >>> in_types = {"array": pa.int64()}
+    >>> out_type = pa.int64()
+    >>> pc.register_scalar_function(add_constant, func_name, func_doc,
+    ...                   in_types, out_type)
+    >>> 
+    >>> func = pc.get_function(func_name)
+    >>> func.name
+    'py_add_func'
+    >>> answer = pc.call_function(func_name, [pa.array([20])])
+    >>> answer
+    <pyarrow.lib.Int64Array object at 0x10c22e700>
+    [
+    21
+    ]
+    """
+    cdef:
+        c_string c_func_name
+        CArity c_arity
+        CFunctionDoc c_func_doc
+        vector[shared_ptr[CDataType]] c_in_types
+        PyObject* c_function
+        shared_ptr[CDataType] c_out_type
+        CScalarUdfOptions c_options
+
+    c_func_name = tobytes(func_name)
+
+    if callable(func):
+        c_function = <PyObject*>func
+    else:
+        raise TypeError("func must be a callable")
+
+    func_spec = inspect.getfullargspec(func)
+    num_args = -1
+    if isinstance(in_types, dict):
+        for in_type in in_types.values():
+            if isinstance(in_type, DataType):

Review Comment:
   CC @vibhatha 



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