[Feature](func) Support function QUANTILE_STATE_TO/FROM_BASE64

docs/sql-manual/sql-functions/scalar-functions/quantile-functions/quantile-state-from-base64.md

@@ -0,0 +1,68 @@
+---
+{
+    "title": "QUANTILE_STATE_FROM_BASE64",
+    "language": "en"
+}
+---
+
+## Description
+
+Converts a base64 encoded string (usually generated by `QUANTILE_STATE_TO_BASE64`) to a QUANTILE_STATE type. Returns NULL if the input string is invalid or NULL.
+
+## Syntax
+
+```sql
+QUANTILE_STATE_FROM_BASE64(<input>)
+```
+
+## Parameters
+
+| Parameter | Description |
+| --------- | ----------- |
+| `<input>` | A base64 encoded string, usually generated by `QUANTILE_STATE_TO_BASE64`. Returns NULL if the string is invalid. |
+
+## Return Value
+
+Returns the quantile_state parsed from the base64 encoding. Returns NULL if the string is invalid.
+
+## Examples
+
+```sql
+select
+  quantile_state_to_base64(
+    quantile_state_from_base64(
+      quantile_state_to_base64(to_quantile_state(1.0, 2048))
+    )
+  ) = quantile_state_to_base64(to_quantile_state(1.0, 2048)) AS equal_test;
+```
+```text
++------------+
+| equal_test |
++------------+
+|          1 |
++------------+
+```
+
+```sql
+select quantile_state_from_base64('not_base64!');
+```
+
+```text
++-------------------------------------------+
+| quantile_state_from_base64('not_base64!') |
++-------------------------------------------+
+| NULL                                      |
++-------------------------------------------+
+```
+
+```sql
+select quantile_state_from_base64(NULL);
+```
+
+```text
++----------------------------------+
+| quantile_state_from_base64(NULL) |
++----------------------------------+
+| NULL                             |
++----------------------------------+
+```

docs/sql-manual/sql-functions/scalar-functions/quantile-functions/quantile-state-to-base64.md

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+---
+{
+    "title": "QUANTILE_STATE_TO_BASE64",
+    "language": "en"
+}
+---
+
+## Description
+
+Converts a QUANTILE_STATE type to a base64 encoded string.
+
+## Syntax
+
+```sql
+QUANTILE_STATE_TO_BASE64(<quantile_state_input>)
+```
+
+## Parameters
+
+| Parameter | Description |
+| --------- | ----------- |
+| `<quantile_state_input>` | Data of QUANTILE_STATE type. |
+
+## Return Value
+
+The Base64 encoded string of the QUANTILE_STATE.
+Returns `NULL` if the QUANTILE_STATE is `NULL`.
+
+::: note
+
+Since the order of elements in QUANTILE_STATE cannot be guaranteed, the base64 result generated from the same QUANTILE_STATE content is not guaranteed to be always the same, but the QUANTILE_STATE decoded by quantile_state_from_base64 is guaranteed to be the same.
+
+:::
+
+## Examples
+
+```sql
+select quantile_state_to_base64(quantile_state_empty());
+```
+
+```text
++--------------------------------------------------+
+| quantile_state_to_base64(quantile_state_empty()) |
++--------------------------------------------------+
+| AAAARQA=                                         |
++--------------------------------------------------+
+```
+
+```sql
+select quantile_state_to_base64(to_quantile_state(1, 2048));
+```
+
+```text
++------------------------------------------------------+
+| quantile_state_to_base64(to_quantile_state(1, 2048)) |
++------------------------------------------------------+
+| AAAARQEAAAAAAADwPw==                                 |
++------------------------------------------------------+
+```
+
+```sql
+select
+  quantile_percent(
+    quantile_union(
+      quantile_state_from_base64(
+        quantile_state_to_base64(to_quantile_state(1, 2048))
+      )
+    ),
+    0.5
+  ) as nested_test;
+```
+
+```text
++-------------+
+| nested_test |
++-------------+
+|           1 |
++-------------+
+```
+
+```sql
+select quantile_state_to_base64(NULL);
+```
+
+```text
++--------------------------------+
+| quantile_state_to_base64(NULL) |
++--------------------------------+
+| NULL                           |
++--------------------------------+
+```

i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/quantile-functions/quantile-state-from-base64.md

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+---
+{
+    "title": "QUANTILE_STATE_FROM_BASE64",
+    "language": "zh-CN",
+    "description": "将一个 base64 编码的字符串（通常由 QUANTILE_STATE_TO_BASE64 函数生成）转换为 QUANTILE_STATE 类型。如果输入字符串不合法或为 NULL，则返回 NULL。"
+}
+---
+
+## 描述
+
+将一个 base64 编码的字符串（通常由 `QUANTILE_STATE_TO_BASE64` 函数生成）转换为 QUANTILE_STATE 类型。如果输入字符串不合法或为 NULL，则返回 NULL。
+
+## 语法
+
+```sql
+QUANTILE_STATE_FROM_BASE64(<input>)
+```
+
+## 参数
+
+| 参数     | 说明                                                                     |
+| -------- | ------------------------------------------------------------------------ |
+| `<input>` | base64 编码的字符串，通常由 `QUANTILE_STATE_TO_BASE64` 函数生成。如果字符串不合法，则返回 NULL。 |
+
+## 返回值
+返回由 base64 编码解析后得到的 quantile_state参数，若字符串不合法，则返回 NULL。
+
+## 示例
+
+```sql
+select
+  quantile_state_to_base64(
+    quantile_state_from_base64(
+      quantile_state_to_base64(to_quantile_state(1.0, 2048))
+    )
+  ) = quantile_state_to_base64(to_quantile_state(1.0, 2048)) AS equal_test;
+```
+```text
++------------+
+| equal_test |
++------------+
+|          1 |
++------------+
+```
+
+```sql
+select quantile_state_from_base64('not_base64!');
+```
+
+```text
++-------------------------------------------+
+| quantile_state_from_base64('not_base64!') |
++-------------------------------------------+
+| NULL                                      |
++-------------------------------------------+
+```
+
+```sql
+select quantile_state_from_base64(NULL);
+```
+```text
++----------------------------------+
+| quantile_state_from_base64(NULL) |
++----------------------------------+
+| NULL                             |
++----------------------------------+
+```

i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/scalar-functions/quantile-functions/quantile-state-to-base64.md

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+---
+{
+    "title": "QUANTILE_STATE_TO_BASE64",
+    "language": "zh-CN",
+    "description": "将一个 QUANTILE_STATE 类型转换为一个 base64 编码的字符串。"
+}
+---
+
+## 描述
+
+将一个 QUANTILE_STATE 类型转换为一个 base64 编码的字符串。
+
+## 语法
+
+```sql
+QUANTILE_STATE_TO_BASE64(<quantile_state_input>)
+```
+
+## 参数
+
+| 参数            | 说明        |
+|---------------|-----------|
+| `<quantile_state_input>` | QUANTILE_STATE 类型数据。 |
+
+## 返回值
+
+QUANTILE_STATE 基于 Base64 编码后的字符串。  
+若 QUANTILE_STATE 为 `NULL` 时，返回值为 `NULL`。
+
+::: note
+
+由于不能保证 QUANTILE_STATE 中元素的顺序，因此不能保证相同内容的 QUANTILE_STATE 生成的 base64 结果始终相同，但可以保证 quantile_state_from_base64 解码后的 QUANTILE_STATE 相同。
+
+:::
+
+## 示例
+
+```sql
+select quantile_state_to_base64(quantile_state_empty());
+```
+
+```text
++--------------------------------------------------+
+| quantile_state_to_base64(quantile_state_empty()) |
++--------------------------------------------------+
+| AAAARQA=                                         |
++--------------------------------------------------+
+```
+
+```sql
+select quantile_state_to_base64(to_quantile_state(1, 2048));
+```
+
+```text
++------------------------------------------------------+
+| quantile_state_to_base64(to_quantile_state(1, 2048)) |
++------------------------------------------------------+
+| AAAARQEAAAAAAADwPw==                                 |
++------------------------------------------------------+
+```
+
+```sql
+select
+  quantile_percent(
+    quantile_union(
+      quantile_state_from_base64(
+        quantile_state_to_base64(to_quantile_state(1, 2048))
+      )
+    ),
+    0.5
+  ) as nested_test;
+```
+
+```text
++-------------+
+| nested_test |
++-------------+
+|           1 |
++-------------+
+```
+
+```sql
+select quantile_state_to_base64(NULL);
+```
+
+```text
++--------------------------------+
+| quantile_state_to_base64(NULL) |
++--------------------------------+
+| NULL                           |
++--------------------------------+
+```