[feature](Nereids): Convert log(x) to ln(x) (#52862)

### What problem does this PR solve?
Problem Summary:

* In MySQL, LOG(col, e) is equivalent to LN(col), where e is Euler’s
number (~2.71828).
* Currently, MySQL also supports LOG(col) as a shorthand for LOG(col, e)
(i.e., natural logarithm).
* This conversion replaces LOG(col) with LN(col) when only a single
argument is provided.
 
 doc: apache/doris-website#2605

Author: zhangstar333

fe/fe-core/src/main/java/org/apache/doris/nereids/rules/expression/ExpressionOptimization.java

@@ -25,6 +25,7 @@
 import org.apache.doris.nereids.rules.expression.rules.DistinctPredicatesRule;
 import org.apache.doris.nereids.rules.expression.rules.ExtractCommonFactorRule;
 import org.apache.doris.nereids.rules.expression.rules.LikeToEqualRewrite;
+import org.apache.doris.nereids.rules.expression.rules.LogToLn;
 import org.apache.doris.nereids.rules.expression.rules.NullSafeEqualToEqual;
 import org.apache.doris.nereids.rules.expression.rules.SimplifyComparisonPredicate;
 import org.apache.doris.nereids.rules.expression.rules.SimplifyConflictCompound;
@@ -61,7 +62,8 @@ public class ExpressionOptimization extends ExpressionRewrite {
                     TopnToMax.INSTANCE,
                     NullSafeEqualToEqual.INSTANCE,
                     LikeToEqualRewrite.INSTANCE,
-                    BetweenToEqual.INSTANCE
+                    BetweenToEqual.INSTANCE,
+                    LogToLn.INSTANCE
             )
     );
 

fe/fe-core/src/main/java/org/apache/doris/nereids/rules/expression/ExpressionRuleType.java

@@ -34,6 +34,7 @@ public enum ExpressionRuleType {
     EXTRACT_COMMON_FACTOR,
     FOLD_CONSTANT_ON_BE,
     FOLD_CONSTANT_ON_FE,
+    LOG_TO_LN,
     IN_PREDICATE_DEDUP,
     IN_PREDICATE_EXTRACT_NON_CONSTANT,
     IN_PREDICATE_TO_EQUAL_TO,

fe/fe-core/src/main/java/org/apache/doris/nereids/rules/expression/rules/LogToLn.java

@@ -0,0 +1,56 @@
+// 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.
+
+package org.apache.doris.nereids.rules.expression.rules;
+
+import org.apache.doris.nereids.rules.expression.ExpressionPatternMatcher;
+import org.apache.doris.nereids.rules.expression.ExpressionPatternRuleFactory;
+import org.apache.doris.nereids.rules.expression.ExpressionRuleType;
+import org.apache.doris.nereids.trees.expressions.Expression;
+import org.apache.doris.nereids.trees.expressions.functions.scalar.Ln;
+import org.apache.doris.nereids.trees.expressions.functions.scalar.Log;
+
+import com.google.common.collect.ImmutableList;
+
+import java.util.List;
+
+/**
+ * In MySQL, LOG(col, e) is equivalent to LN(col), where e is Euler’s number (~2.71828).
+ * Currently, MySQL also supports LOG(col) as a shorthand for LOG(col, e) (i.e., natural logarithm).
+ * This conversion replaces LOG(col) with LN(col) when only a single argument is provided.
+ */
+public class LogToLn implements ExpressionPatternRuleFactory {
+
+    public static final LogToLn INSTANCE = new LogToLn();
+
+    @Override
+    public List<ExpressionPatternMatcher<? extends Expression>> buildRules() {
+        return ImmutableList.of(
+                matchesType(Log.class).then(LogToLn::rewrite)
+                        .toRule(ExpressionRuleType.LOG_TO_LN)
+        );
+    }
+
+    /** rewrite */
+    public static Expression rewrite(Log log) {
+        if (log.arity() == 1) {
+            return new Ln(log.child(0));
+        } else {
+            return log;
+        }
+    }
+}

fe/fe-core/src/main/java/org/apache/doris/nereids/trees/expressions/functions/scalar/Log.java

@@ -37,9 +37,17 @@ public class Log extends ScalarFunction
         implements BinaryExpression, ExplicitlyCastableSignature, AlwaysNullable {
 
     public static final List<FunctionSignature> SIGNATURES = ImmutableList.of(
+            FunctionSignature.ret(DoubleType.INSTANCE).args(DoubleType.INSTANCE),
             FunctionSignature.ret(DoubleType.INSTANCE).args(DoubleType.INSTANCE, DoubleType.INSTANCE)
     );
 
+    /**
+     * constructor with 1 arguments.
+     */
+    public Log(Expression arg0) {
+        super("log", arg0);
+    }
+
     /**
      * constructor with 2 arguments.
      */
@@ -52,8 +60,13 @@ public Log(Expression arg0, Expression arg1) {
      */
     @Override
     public Log withChildren(List<Expression> children) {
-        Preconditions.checkArgument(children.size() == 2);
-        return new Log(children.get(0), children.get(1));
+        Preconditions.checkArgument(children.size() == 1 || children.size() == 2,
+                "Log function should have 1 or 2 children, but got: %s", children.size());
+        if (children.size() == 1) {
+            return new Log(children.get(0));
+        } else {
+            return new Log(children.get(0), children.get(1));
+        }
     }
 
     @Override

regression-test/data/query_p0/sql_functions/math_functions/test_math_unary_always_nullable.out

@@ -149,3 +149,17 @@
 7	\N	true
 8	\N	true
 
+-- !dlog_tbl_1 --
+1	0.09531017980432493	0.09531017980432493	1.0986122886681098	1.0986122886681098
+2	\N	\N	1.0986122886681098	1.0986122886681098
+3	\N	\N	1.0986122886681098	1.0986122886681098
+4	\N	\N	1.0986122886681098	1.0986122886681098
+5	\N	\N	1.0986122886681098	1.0986122886681098
+6	\N	\N	1.0986122886681098	1.0986122886681098
+7	\N	\N	1.0986122886681098	1.0986122886681098
+8	\N	\N	1.0986122886681098	1.0986122886681098
+9	0.1823215567939546	0.1823215567939546	1.0986122886681098	1.0986122886681098
+10	0.7884573603642703	0.7884573603642703	1.0986122886681098	1.0986122886681098
+11	1.2237754316221157	1.2237754316221157	1.0986122886681098	1.0986122886681098
+12	1.7227665977411035	1.7227665977411035	1.0986122886681098	1.0986122886681098
+

regression-test/suites/query_p0/sql_functions/math_functions/test_math_unary_always_nullable.groovy

@@ -110,4 +110,13 @@ suite("test_math_unary_alway_nullable") {
         select rowid, dsqrt(val), dsqrt(val) is null from test_math_unary_alway_nullable order by rowid;
     """
 
+    sql """
+        insert into test_math_unary_alway_nullable values
+        (9, 1.2), (10, 2.2), (11, 3.4), (12, 5.6)
+    """
+
+    qt_dlog_tbl_1 """
+        select rowid, log(val), ln(val), log(3), ln(3) from test_math_unary_alway_nullable order by rowid;
+    """
+
 }