[SPARK-17506][SQL] Improve the check double values equality rule.

## What changes were proposed in this pull request?

In `ExpressionEvalHelper`, we check the equality between two double values by comparing whether the expected value is within the range [target - tolerance, target + tolerance], but this can cause a negative false when the compared numerics are very large.
Before：
```
val1 = 1.6358558070241E306
val2 = 1.6358558070240974E306
ExpressionEvalHelper.compareResults(val1, val2)
false
```
In fact, `val1` and `val2` are but with different precisions, we should tolerant this case by comparing with percentage range, eg.,expected is within range [target - target * tolerance_percentage, target + target * tolerance_percentage].
After:
```
val1 = 1.6358558070241E306
val2 = 1.6358558070240974E306
ExpressionEvalHelper.compareResults(val1, val2)
true
```

## How was this patch tested?

Exsiting testcases.

Author: jiangxingbo <jiangxb1987@gmail.com>

Closes #15059 from jiangxb1987/deq.

2 files changed, 30 insertions, 7 deletions

diff --git a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ArithmeticExpressionSuite.scala b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ArithmeticExpressionSuite.scala
index 687387507e..5c9824289b 100644
--- a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ArithmeticExpressionSuite.scala
+++ b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ArithmeticExpressionSuite.scala
@@ -170,11 +170,9 @@ class ArithmeticExpressionSuite extends SparkFunSuite with ExpressionEvalHelper
     checkEvaluation(Remainder(positiveLongLit, positiveLongLit), 0L)
     checkEvaluation(Remainder(negativeLongLit, negativeLongLit), 0L)
 
-    // TODO: the following lines would fail the test due to inconsistency result of interpret
-    // and codegen for remainder between giant values, seems like a numeric stability issue
-    // DataTypeTestUtils.numericTypeWithoutDecimal.foreach { tpe =>
-    //  checkConsistencyBetweenInterpretedAndCodegen(Remainder, tpe, tpe)
-    // }
+    DataTypeTestUtils.numericTypeWithoutDecimal.foreach { tpe =>
+      checkConsistencyBetweenInterpretedAndCodegen(Remainder, tpe, tpe)
+    }
   }
 
   test("Abs") {
diff --git a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ExpressionEvalHelper.scala b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ExpressionEvalHelper.scala
index 668543a28b..f0c149c02b 100644
--- a/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ExpressionEvalHelper.scala
+++ b/sql/catalyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/ExpressionEvalHelper.scala
@@ -19,6 +19,7 @@ package org.apache.spark.sql.catalyst.expressions
 
 import org.scalacheck.Gen
 import org.scalactic.TripleEqualsSupport.Spread
+import org.scalatest.exceptions.TestFailedException
 import org.scalatest.prop.GeneratorDrivenPropertyChecks
 
 import org.apache.spark.SparkFunSuite
@@ -289,13 +290,37 @@ trait ExpressionEvalHelper extends GeneratorDrivenPropertyChecks {
     (result, expected) match {
       case (result: Array[Byte], expected: Array[Byte]) =>
         java.util.Arrays.equals(result, expected)
-      case (result: Double, expected: Spread[Double @unchecked]) =>
-        expected.asInstanceOf[Spread[Double]].isWithin(result)
       case (result: Double, expected: Double) if result.isNaN && expected.isNaN =>
         true
+      case (result: Double, expected: Double) =>
+        relativeErrorComparison(result, expected)
       case (result: Float, expected: Float) if result.isNaN && expected.isNaN =>
         true
       case _ => result == expected
     }
   }
+
+  /**
+   * Private helper function for comparing two values using relative tolerance.
+   * Note that if x or y is extremely close to zero, i.e., smaller than Double.MinPositiveValue,
+   * the relative tolerance is meaningless, so the exception will be raised to warn users.
+   *
+   * TODO: this duplicates functions in spark.ml.util.TestingUtils.relTol and
+   * spark.mllib.util.TestingUtils.relTol, they could be moved to common utils sub module for the
+   * whole spark project which does not depend on other modules. See more detail in discussion:
+   * https://github.com/apache/spark/pull/15059#issuecomment-246940444
+   */
+  private def relativeErrorComparison(x: Double, y: Double, eps: Double = 1E-8): Boolean = {
+    val absX = math.abs(x)
+    val absY = math.abs(y)
+    val diff = math.abs(x - y)
+    if (x == y) {
+      true
+    } else if (absX < Double.MinPositiveValue || absY < Double.MinPositiveValue) {
+      throw new TestFailedException(
+        s"$x or $y is extremely close to zero, so the relative tolerance is meaningless.", 0)
+    } else {
+      diff < eps * math.min(absX, absY)
+    }
+  }
 }