[doc](agg) add doc for aggregate function entropy

docs/sql-manual/sql-functions/aggregate-functions/entropy.md

@@ -0,0 +1,101 @@
+---
+{
+    "title": "ENTROPY",
+    "language": "en",
+    "description": "Calculate the Shannon entropy of all non-null values in the specified column or expression."
+}
+---
+
+## Description
+
+Computes the Shannon entropy of all non-null values in the specified column or expression.
+
+Entropy measures the uncertainty or randomness of a distribution. This function builds an empirical frequency map of the input values and computes entropy in bits using the base‑2 logarithm.
+
+The Shannon entropy is defined as:
+
+$
+Entropy(X) = -\sum_{i=1}^{k} p_i \log_2(p_i)
+$
+
+Where:
+
+- $k$ is the number of distinct non-null values  
+- $p_i = \frac{\text{count}(x_i)}{\text{total non-null count}}$
+
+## Syntax
+
+```sql
+ENTROPY(<expr1> [, <expr2>, ... , <exprN>])
+```
+
+## Parameters
+
+| Parameter | Description |
+|----------|-------------|
+| `<expr1> [, <expr2>, ...]` | One or more expressions or columns. Supported types: TinyInt, SmallInt, Integer, BigInt, LargeInt, Float, Double, Decimal, String, IPv4/IPv6, Array, Map,Struct. When multiple expressions are provided, their values are serialized together to form a single composite key, and entropy is computed over the frequency distribution of these composite keys. |
+
+## Return Value
+
+Returns a DOUBLE representing the Shannon entropy in bits.
+
+- Returns NULL if all values are NULL or the input is empty.
+- Ignores NULL values during computation.
+
+## Examples
+
+```sql
+CREATE TABLE t1 (
+    id INT,
+    v  INT
+) DISTRIBUTED BY HASH(id) BUCKETS 1
+PROPERTIES ("replication_num"="1");
+
+INSERT INTO t1 VALUES
+    (1, 1),
+    (2, 2),
+    (3, 2),
+    (4, NULL);
+```
+
+```sql
+SELECT entropy(v) FROM t1;
+```
+
+Distribution: `{1:1, 2:2}`      $H = -\left(\frac{1}{3}\log_2\frac{1}{3} + \frac{2}{3}\log_2\frac{2}{3}\right)=0.9183$
+
+```text
++--------------------+
+| entropy(x)         |
++--------------------+
+| 0.9182958340544896 |
++--------------------+
+```
+
+```sql
+SELECT entropy(1);
+```
+
+Only one distinct value → entropy = 0
+
+```text
++------------+
+| entropy(1) |
++------------+
+|          0 |
++------------+
+```
+
+```sql
+SELECT entropy(NULL) FROM t1;
+```
+
+Returns NULL if all values are NULL or the input is empty.
+
+```sql
++---------------+
+| entropy(NULL) |
++---------------+
+|          NULL |
++---------------+
+```

i18n/zh-CN/docusaurus-plugin-content-docs/current/sql-manual/sql-functions/aggregate-functions/entropy.md

@@ -0,0 +1,103 @@
+---
+{
+    "title": "ENTROPY",
+    "language": "zh-CN",
+    "description": "计算指定列或表达式中所有非 NULL 值的香农熵（Shannon Entropy）。"
+}
+---
+
+## 描述
+
+计算指定列或表达式中所有非 NULL 值的香农熵（Shannon Entropy）。
+
+熵用于衡量分布的不确定性或随机性。该函数会基于输入值构建经验频率分布，并使用以 2 为底的对数计算熵，单位为 比特（bits）。
+
+香农熵的定义如下：
+
+$
+Entropy(X) = -\sum_{i=1}^{k} p_i \log_2(p_i)
+$
+
+其中：
+
+- $k$ 为非 NULL 的不同值的数量  
+- $p_i = \frac{x_i的数量}{\text{所有非null值数量}}$
+
+## 语法
+
+```sql
+ENTROPY(<expr1> [, <expr2>, ... , <exprN>])
+```
+
+## 参数
+
+| 参数 | 说明 |
+|------|------|
+| `<expr1> [, <expr2>, ...]` | 一个或多个表达式或列。支持的类型包括：TinyInt、SmallInt、Integer、BigInt、LargeInt、Float、Double、Decimal、String、IPv4/IPv6、Array、Map、Struct 等。当提供多列时，每行的多个值会被序列化为一个复合键，并基于复合键的频率分布计算熵。 |
+
+## 返回值
+
+返回一个 DOUBLE，表示以比特为单位的香农熵。
+
+- 如果所有值均为 NULL 或输入为空，则返回 NULL。
+- 计算过程中会忽略 NULL 值。
+
+## 举例
+
+```sql
+CREATE TABLE t1 (
+    id INT,
+    v  INT
+) DISTRIBUTED BY HASH(id) BUCKETS 1
+PROPERTIES ("replication_num"="1");
+
+INSERT INTO t1 VALUES
+    (1, 1),
+    (2, 2),
+    (3, 2),
+    (4, NULL);
+```
+
+```sql
+SELECT entropy(v) FROM t1;
+```
+
+频率分布：`{1:1, 2:2}`  
+
+熵的计算：  $H = -\left(\frac{1}{3}\log_2\frac{1}{3} + \frac{2}{3}\log_2\frac{2}{3}\right)=0.9183$
+
+```text
++--------------------+
+| entropy(x)         |
++--------------------+
+| 0.9182958340544896 |
++--------------------+
+```
+
+```sql
+SELECT entropy(1);
+```
+
+只有一个唯一值 → 熵 = 0
+
+```text
++------------+
+| entropy(1) |
++------------+
+|          0 |
++------------+
+```
+
+```sql
+SELECT entropy(NULL) FROM t1;
+```
+
+当所有值均为 NULL 或输入为空时返回 NULL。
+
+```text
++---------------+
+| entropy(NULL) |
++---------------+
+|          NULL |
++---------------+
+```

sidebars.ts

@@ -1895,6 +1895,7 @@ const sidebars: SidebarsConfig = {
                                 'sql-manual/sql-functions/aggregate-functions/count-by-enum',
                                 'sql-manual/sql-functions/aggregate-functions/covar',
                                 'sql-manual/sql-functions/aggregate-functions/covar-samp',
+                                'sql-manual/sql-functions/aggregate-functions/entropy',
                                 'sql-manual/sql-functions/aggregate-functions/group-array-intersect',
                                 'sql-manual/sql-functions/aggregate-functions/group-array-union',
                                 'sql-manual/sql-functions/aggregate-functions/group-bit-and',