[SPARK-20211][SQL][BACKPORT-2.2] Fix the Precision and Scale of Decimal Values when the Input is BigDecimal between -1.0 and 1.0

### What changes were proposed in this pull request?

This PR is to backport #18244 to 2.2

---

The precision and scale of decimal values are wrong when the input is BigDecimal between -1.0 and 1.0.

The BigDecimal's precision is the digit count starts from the leftmost nonzero digit based on the [JAVA's BigDecimal definition](https://docs.oracle.com/javase/7/docs/api/java/math/BigDecimal.html). However, our Decimal decision follows the database decimal standard, which is the total number of digits, including both to the left and the right of the decimal point. Thus, this PR is to fix the issue by doing the conversion.

Before this PR, the following queries failed:
```SQL
select 1 > 0.0001
select floor(0.0001)
select ceil(0.0001)
```

### How was this patch tested?
Added test cases.

Author: gatorsmile <[email protected]>

Closes #18297 from gatorsmile/backport18244.

(cherry picked from commit 6265119)
Signed-off-by: Wenchen Fan <[email protected]>

Author: gatorsmile

sql/catalyst/src/main/scala/org/apache/spark/sql/types/Decimal.scala

@@ -124,7 +124,15 @@ final class Decimal extends Ordered[Decimal] with Serializable {
   def set(decimal: BigDecimal): Decimal = {
     this.decimalVal = decimal
     this.longVal = 0L
-    this._precision = decimal.precision
+    if (decimal.precision <= decimal.scale) {
+      // For Decimal, we expect the precision is equal to or large than the scale, however,
+      // in BigDecimal, the digit count starts from the leftmost nonzero digit of the exact
+      // result. For example, the precision of 0.01 equals to 1 based on the definition, but
+      // the scale is 2. The expected precision should be 3.
+      this._precision = decimal.scale + 1
+    } else {
+      this._precision = decimal.precision
+    }
     this._scale = decimal.scale
     this
   }

sql/catalyst/src/test/scala/org/apache/spark/sql/types/DecimalSuite.scala

@@ -34,6 +34,16 @@ class DecimalSuite extends SparkFunSuite with PrivateMethodTester {
 
   test("creating decimals") {
     checkDecimal(new Decimal(), "0", 1, 0)
+    checkDecimal(Decimal(BigDecimal("0.09")), "0.09", 3, 2)
+    checkDecimal(Decimal(BigDecimal("0.9")), "0.9", 2, 1)
+    checkDecimal(Decimal(BigDecimal("0.90")), "0.90", 3, 2)
+    checkDecimal(Decimal(BigDecimal("0.0")), "0.0", 2, 1)
+    checkDecimal(Decimal(BigDecimal("0")), "0", 1, 0)
+    checkDecimal(Decimal(BigDecimal("1.0")), "1.0", 2, 1)
+    checkDecimal(Decimal(BigDecimal("-0.09")), "-0.09", 3, 2)
+    checkDecimal(Decimal(BigDecimal("-0.9")), "-0.9", 2, 1)
+    checkDecimal(Decimal(BigDecimal("-0.90")), "-0.90", 3, 2)
+    checkDecimal(Decimal(BigDecimal("-1.0")), "-1.0", 2, 1)
     checkDecimal(Decimal(BigDecimal("10.030")), "10.030", 5, 3)
     checkDecimal(Decimal(BigDecimal("10.030"), 4, 1), "10.0", 4, 1)
     checkDecimal(Decimal(BigDecimal("-9.95"), 4, 1), "-10.0", 4, 1)

sql/core/src/test/resources/sql-tests/inputs/arithmetic.sql

@@ -32,3 +32,27 @@ select 1 - 2;
 select 2 * 5;
 select 5 % 3;
 select pmod(-7, 3);
+
+-- math functions
+select cot(1);
+select cot(null);
+select cot(0);
+select cot(-1);
+
+-- ceil and ceiling
+select ceiling(0);
+select ceiling(1);
+select ceil(1234567890123456);
+select ceiling(1234567890123456);
+select ceil(0.01);
+select ceiling(-0.10);
+
+-- floor
+select floor(0);
+select floor(1);
+select floor(1234567890123456);
+select floor(0.01);
+select floor(-0.10);
+
+-- comparison operator
+select 1 > 0.00001

sql/core/src/test/resources/sql-tests/results/arithmetic.sql.out

@@ -1,5 +1,5 @@
 -- Automatically generated by SQLQueryTestSuite
--- Number of queries: 28
+-- Number of queries: 44
 
 
 -- !query 0
@@ -224,3 +224,135 @@ select pmod(-7, 3)
 struct<pmod(-7, 3):int>
 -- !query 27 output
 2
+
+
+-- !query 28
+select cot(1)
+-- !query 28 schema
+struct<>
+-- !query 28 output
+org.apache.spark.sql.AnalysisException
+Undefined function: 'cot'. This function is neither a registered temporary function nor a permanent function registered in the database 'default'.; line 1 pos 7
+
+
+-- !query 29
+select cot(null)
+-- !query 29 schema
+struct<>
+-- !query 29 output
+org.apache.spark.sql.AnalysisException
+Undefined function: 'cot'. This function is neither a registered temporary function nor a permanent function registered in the database 'default'.; line 1 pos 7
+
+
+-- !query 30
+select cot(0)
+-- !query 30 schema
+struct<>
+-- !query 30 output
+org.apache.spark.sql.AnalysisException
+Undefined function: 'cot'. This function is neither a registered temporary function nor a permanent function registered in the database 'default'.; line 1 pos 7
+
+
+-- !query 31
+select cot(-1)
+-- !query 31 schema
+struct<>
+-- !query 31 output
+org.apache.spark.sql.AnalysisException
+Undefined function: 'cot'. This function is neither a registered temporary function nor a permanent function registered in the database 'default'.; line 1 pos 7
+
+
+-- !query 32
+select ceiling(0)
+-- !query 32 schema
+struct<CEIL(CAST(0 AS DOUBLE)):bigint>
+-- !query 32 output
+0
+
+
+-- !query 33
+select ceiling(1)
+-- !query 33 schema
+struct<CEIL(CAST(1 AS DOUBLE)):bigint>
+-- !query 33 output
+1
+
+
+-- !query 34
+select ceil(1234567890123456)
+-- !query 34 schema
+struct<CEIL(1234567890123456):bigint>
+-- !query 34 output
+1234567890123456
+
+
+-- !query 35
+select ceiling(1234567890123456)
+-- !query 35 schema
+struct<CEIL(1234567890123456):bigint>
+-- !query 35 output
+1234567890123456
+
+
+-- !query 36
+select ceil(0.01)
+-- !query 36 schema
+struct<CEIL(0.01):decimal(1,0)>
+-- !query 36 output
+1
+
+
+-- !query 37
+select ceiling(-0.10)
+-- !query 37 schema
+struct<CEIL(-0.10):decimal(1,0)>
+-- !query 37 output
+0
+
+
+-- !query 38
+select floor(0)
+-- !query 38 schema
+struct<FLOOR(CAST(0 AS DOUBLE)):bigint>
+-- !query 38 output
+0
+
+
+-- !query 39
+select floor(1)
+-- !query 39 schema
+struct<FLOOR(CAST(1 AS DOUBLE)):bigint>
+-- !query 39 output
+1
+
+
+-- !query 40
+select floor(1234567890123456)
+-- !query 40 schema
+struct<FLOOR(1234567890123456):bigint>
+-- !query 40 output
+1234567890123456
+
+
+-- !query 41
+select floor(0.01)
+-- !query 41 schema
+struct<FLOOR(0.01):decimal(1,0)>
+-- !query 41 output
+0
+
+
+-- !query 42
+select floor(-0.10)
+-- !query 42 schema
+struct<FLOOR(-0.10):decimal(1,0)>
+-- !query 42 output
+-1
+
+
+-- !query 43
+select 1 > 0.00001
+-- !query 43 schema
+struct<(CAST(1 AS BIGINT) > 0):boolean>
+-- !query 43 output
+true