[Feature](func) Support function QUANTILE_STATE_TO/FROM_BASE64 (apache#59664)

### What problem does this PR solve?

Issue Number: close #xxx

Related PR: apache#59607 

Problem Summary:

### Release note

None

### Check List (For Author)

- Test <!-- At least one of them must be included. -->
    - [x] Regression test
    - [ ] Unit Test
    - [ ] Manual test (add detailed scripts or steps below)
    - [ ] No need to test or manual test. Explain why:
- [ ] This is a refactor/code format and no logic has been changed.
        - [ ] Previous test can cover this change.
        - [ ] No code files have been changed.
        - [ ] Other reason <!-- Add your reason?  -->

- Behavior changed:
    - [ ] No.
    - [ ] Yes. <!-- Explain the behavior change -->

- Does this need documentation?
    - [ ] No.
- [ ] Yes. <!-- Add document PR link here. eg:
apache/doris-website#1214 -->

### Check List (For Reviewer who merge this PR)

- [ ] Confirm the release note
- [ ] Confirm test cases
- [ ] Confirm document
- [ ] Add branch pick label <!-- Add branch pick label that this PR
should merge into -->

Author: linrrzqqq

be/src/vec/functions/function_quantile_state.cpp

@@ -29,6 +29,7 @@
 #include "common/compiler_util.h" // IWYU pragma: keep
 #include "common/status.h"
 #include "util/quantile_state.h"
+#include "util/url_coding.h"
 #include "vec/aggregate_functions/aggregate_function.h"
 #include "vec/columns/column.h"
 #include "vec/columns/column_complex.h"
@@ -45,9 +46,11 @@
 #include "vec/data_types/data_type_nullable.h"
 #include "vec/data_types/data_type_number.h"
 #include "vec/data_types/data_type_quantilestate.h" // IWYU pragma: keep
+#include "vec/data_types/data_type_string.h"
 #include "vec/functions/function.h"
 #include "vec/functions/function_const.h"
 #include "vec/functions/function_helpers.h"
+#include "vec/functions/function_totype.h"
 #include "vec/functions/simple_function_factory.h"
 #include "vec/utils/util.hpp"
 
@@ -210,10 +213,134 @@ class FunctionQuantileStatePercent : public IFunction {
     }
 };
 
+class FunctionQuantileStateFromBase64 : public IFunction {
+public:
+    static constexpr auto name = "quantile_state_from_base64";
+    String get_name() const override { return name; }
+
+    static FunctionPtr create() { return std::make_shared<FunctionQuantileStateFromBase64>(); }
+
+    DataTypePtr get_return_type_impl(const DataTypes& arguments) const override {
+        return std::make_shared<DataTypeNullable>(std::make_shared<DataTypeQuantileState>());
+    }
+
+    size_t get_number_of_arguments() const override { return 1; }
+
+    bool use_default_implementation_for_nulls() const override { return true; }
+
+    Status execute_impl(FunctionContext* context, Block& block, const ColumnNumbers& arguments,
+                        uint32_t result, size_t input_rows_count) const override {
+        auto res_null_map = ColumnUInt8::create(input_rows_count, 0);
+        auto res_data_column = ColumnQuantileState::create();
+        auto& null_map = res_null_map->get_data();
+        auto& res = res_data_column->get_data();
+
+        auto& argument_column = block.get_by_position(arguments[0]).column;
+        const auto& str_column = static_cast<const ColumnString&>(*argument_column);
+        const ColumnString::Chars& data = str_column.get_chars();
+        const ColumnString::Offsets& offsets = str_column.get_offsets();
+
+        res.reserve(input_rows_count);
+
+        std::string decode_buff;
+        int64_t last_decode_buff_len = 0;
+        int64_t curr_decode_buff_len = 0;
+        for (size_t i = 0; i < input_rows_count; ++i) {
+            const char* src_str = reinterpret_cast<const char*>(&data[offsets[i - 1]]);
+            int64_t src_size = offsets[i] - offsets[i - 1];
+
+            if (src_size == 0 || 0 != src_size % 4) {
+                res.emplace_back();
+                null_map[i] = 1;
+                continue;
+            }
+
+            curr_decode_buff_len = src_size + 3;
+            if (curr_decode_buff_len > last_decode_buff_len) {
+                decode_buff.resize(curr_decode_buff_len);
+                last_decode_buff_len = curr_decode_buff_len;
+            }
+            auto outlen = base64_decode(src_str, src_size, decode_buff.data());
+            if (outlen < 0) {
+                res.emplace_back();
+                null_map[i] = 1;
+            } else {
+                doris::Slice decoded_slice(decode_buff.data(), outlen);
+                doris::QuantileState quantile_state;
+                if (!quantile_state.deserialize(decoded_slice)) {
+                    return Status::RuntimeError(fmt::format(
+                            "quantile_state_from_base64 decode failed: base64: {}", src_str));
+                } else {
+                    res.emplace_back(std::move(quantile_state));
+                }
+            }
+        }
+
+        block.get_by_position(result).column =
+                ColumnNullable::create(std::move(res_data_column), std::move(res_null_map));
+        return Status::OK();
+    }
+};
+
+struct NameQuantileStateToBase64 {
+    static constexpr auto name = "quantile_state_to_base64";
+};
+
+struct QuantileStateToBase64 {
+    using ReturnType = DataTypeString;
+    static constexpr auto PrimitiveTypeImpl = PrimitiveType::TYPE_QUANTILE_STATE;
+    using Type = DataTypeQuantileState::FieldType;
+    using ReturnColumnType = ColumnString;
+    using Chars = ColumnString::Chars;
+    using Offsets = ColumnString::Offsets;
+
+    static Status vector(const std::vector<QuantileState>& data, Chars& chars, Offsets& offsets) {
+        size_t size = data.size();
+        offsets.resize(size);
+        size_t output_char_size = 0;
+        for (size_t i = 0; i < size; ++i) {
+            auto& quantile_state_val = const_cast<QuantileState&>(data[i]);
+            auto ser_size = quantile_state_val.get_serialized_size();
+            output_char_size += (int)(4.0 * ceil((double)ser_size / 3.0));
+        }
+        ColumnString::check_chars_length(output_char_size, size);
+        chars.resize(output_char_size);
+        auto* chars_data = chars.data();
+
+        size_t cur_ser_size = 0;
+        size_t last_ser_size = 0;
+        std::string ser_buff;
+        size_t encoded_offset = 0;
+        for (size_t i = 0; i < size; ++i) {
+            auto& quantile_state_val = const_cast<QuantileState&>(data[i]);
+
+            cur_ser_size = quantile_state_val.get_serialized_size();
+            if (cur_ser_size > last_ser_size) {
+                last_ser_size = cur_ser_size;
+                ser_buff.resize(cur_ser_size);
+            }
+            size_t real_size =
+                    quantile_state_val.serialize(reinterpret_cast<uint8_t*>(ser_buff.data()));
+            auto outlen = base64_encode((const unsigned char*)ser_buff.data(), real_size,
+                                        chars_data + encoded_offset);
+            DCHECK(outlen > 0);
+
+            encoded_offset += outlen;
+            offsets[i] = cast_set<uint32_t>(encoded_offset);
+        }
+        return Status::OK();
+    }
+};
+
+using FunctionQuantileStateToBase64 =
+        FunctionUnaryToType<QuantileStateToBase64, NameQuantileStateToBase64>;
+
 void register_function_quantile_state(SimpleFunctionFactory& factory) {
     factory.register_function<FunctionConst<QuantileStateEmpty, false>>();
     factory.register_function<FunctionQuantileStatePercent>();
     factory.register_function<FunctionToQuantileState>();
+    factory.register_function<FunctionQuantileStateFromBase64>();
+    factory.register_function<FunctionQuantileStateToBase64>();
 }
 
 } // namespace doris::vectorized

be/test/vec/function/function_quantile_state_test.cpp

@@ -0,0 +1,216 @@
+// 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 <gtest/gtest.h>
+
+#include <string>
+
+#include "function_test_util.h"
+#include "runtime/define_primitive_type.h"
+#include "util/quantile_state.h"
+#include "util/url_coding.h"
+#include "vec/core/types.h"
+#include "vec/data_types/data_type_quantilestate.h"
+#include "vec/data_types/data_type_string.h"
+
+namespace doris::vectorized {
+
+TEST(function_quantile_state_test, function_quantile_state_to_base64) {
+    std::string func_name = "quantile_state_to_base64";
+    InputTypeSet input_types = {PrimitiveType::TYPE_QUANTILE_STATE};
+
+    QuantileState empty_quantile_state;
+
+    QuantileState single_quantile_state;
+    single_quantile_state.add_value(1.0);
+
+    QuantileState multi_quantile_state;
+    multi_quantile_state.add_value(1.0);
+    multi_quantile_state.add_value(2.0);
+    multi_quantile_state.add_value(3.0);
+    multi_quantile_state.add_value(4.0);
+    multi_quantile_state.add_value(5.0);
+
+    QuantileState explicit_quantile_state;
+    for (int i = 0; i < 100; i++) {
+        explicit_quantile_state.add_value(static_cast<double>(i));
+    }
+
+    QuantileState tdigest_quantile_state;
+    for (int i = 0; i < 3000; i++) {
+        tdigest_quantile_state.add_value(static_cast<double>(i));
+    }
+
+    uint8_t buf[65536];
+    unsigned char encoded_buf[131072];
+
+    std::string empty_base64;
+    {
+        size_t len = empty_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        empty_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    std::string single_base64;
+    {
+        size_t len = single_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        single_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    std::string multi_base64;
+    {
+        size_t len = multi_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        multi_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    std::string explicit_base64;
+    {
+        size_t len = explicit_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        explicit_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    std::string tdigest_base64;
+    {
+        size_t len = tdigest_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        tdigest_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    {
+        DataSet data_set = {{{&empty_quantile_state}, empty_base64},
+                            {{&single_quantile_state}, single_base64},
+                            {{&multi_quantile_state}, multi_base64},
+                            {{&explicit_quantile_state}, explicit_base64},
+                            {{&tdigest_quantile_state}, tdigest_base64}};
+
+        static_cast<void>(check_function<DataTypeString, true>(func_name, input_types, data_set));
+    }
+}
+
+TEST(function_quantile_state_test, function_quantile_state_from_base64) {
+    std::string func_name = "quantile_state_from_base64";
+    InputTypeSet input_types = {PrimitiveType::TYPE_STRING};
+
+    // Create quantile states for comparison
+    QuantileState empty_quantile_state;
+
+    QuantileState single_quantile_state;
+    single_quantile_state.add_value(1.0);
+
+    QuantileState multi_quantile_state;
+    multi_quantile_state.add_value(1.0);
+    multi_quantile_state.add_value(2.0);
+    multi_quantile_state.add_value(3.0);
+    multi_quantile_state.add_value(4.0);
+    multi_quantile_state.add_value(5.0);
+
+    uint8_t buf[65536];
+    unsigned char encoded_buf[131072];
+    std::string empty_base64;
+    std::string single_base64;
+    std::string multi_base64;
+
+    {
+        size_t len = empty_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        empty_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    {
+        size_t len = single_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        single_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    {
+        size_t len = multi_quantile_state.serialize(buf);
+        size_t encoded_len = base64_encode(buf, len, encoded_buf);
+        multi_base64 = std::string(reinterpret_cast<char*>(encoded_buf), encoded_len);
+    }
+
+    {
+        char decoded_buf[65536];
+        int decoded_len = base64_decode(empty_base64.c_str(), empty_base64.length(), decoded_buf);
+        EXPECT_GT(decoded_len, 0);
+
+        QuantileState decoded_empty;
+        doris::Slice slice(decoded_buf, decoded_len);
+        EXPECT_TRUE(decoded_empty.deserialize(slice));
+
+        EXPECT_TRUE(std::isnan(empty_quantile_state.get_value_by_percentile(0.5)));
+        EXPECT_TRUE(std::isnan(decoded_empty.get_value_by_percentile(0.5)));
+    }
+
+    {
+        char decoded_buf[65536];
+        int decoded_len = base64_decode(single_base64.c_str(), single_base64.length(), decoded_buf);
+        EXPECT_GT(decoded_len, 0);
+
+        QuantileState decoded_single;
+        doris::Slice slice(decoded_buf, decoded_len);
+        EXPECT_TRUE(decoded_single.deserialize(slice));
+
+        EXPECT_NEAR(single_quantile_state.get_value_by_percentile(0.5),
+                    decoded_single.get_value_by_percentile(0.5), 0.01);
+    }
+
+    {
+        char decoded_buf[65536];
+        int decoded_len = base64_decode(multi_base64.c_str(), multi_base64.length(), decoded_buf);
+        EXPECT_GT(decoded_len, 0);
+
+        QuantileState decoded_multi;
+        doris::Slice slice(decoded_buf, decoded_len);
+        EXPECT_TRUE(decoded_multi.deserialize(slice));
+
+        EXPECT_NEAR(multi_quantile_state.get_value_by_percentile(0.5),
+                    decoded_multi.get_value_by_percentile(0.5), 0.01);
+        EXPECT_NEAR(multi_quantile_state.get_value_by_percentile(0.9),
+                    decoded_multi.get_value_by_percentile(0.9), 0.01);
+    }
+}
+
+TEST(function_quantile_state_test, function_quantile_state_roundtrip) {
+    QuantileState original;
+    for (int i = 0; i < 50; i++) {
+        original.add_value(static_cast<double>(i * 2));
+    }
+
+    uint8_t ser_buf[65536];
+    size_t ser_len = original.serialize(ser_buf);
+
+    unsigned char encoded_buf[131072];
+    size_t encoded_len = base64_encode(ser_buf, ser_len, encoded_buf);
+    std::string base64_str(reinterpret_cast<char*>(encoded_buf), encoded_len);
+
+    char decoded_buf[65536];
+    int decoded_len = base64_decode(base64_str.c_str(), base64_str.length(), decoded_buf);
+    EXPECT_GT(decoded_len, 0);
+
+    QuantileState recovered;
+    doris::Slice slice(decoded_buf, decoded_len);
+    EXPECT_TRUE(recovered.deserialize(slice));
+
+    EXPECT_NEAR(original.get_value_by_percentile(0.5), recovered.get_value_by_percentile(0.5),
+                0.01);
+    EXPECT_NEAR(original.get_value_by_percentile(0.9), recovered.get_value_by_percentile(0.9),
+                0.01);
+}
+
+} // namespace doris::vectorized