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[SPARK-55557][SQL][4.0] Hyperbolic functions should not overflow with large inputs #54804

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[SPARK-55557][SQL][4.0] Hyperbolic functions should not overflow with large inputs #54804

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40 changes: 33 additions & 7 deletions sql/catalyst/src/main/scala/org/apache/spark/sql/catalyst/expressions/mathExpressions.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -412,10 +412,28 @@ case class Cosh(child: Expression) extends UnaryMathExpression(math.cosh, "COSH"
since = "3.0.0",
group = "math_funcs")
case class Acosh(child: Expression)
extends UnaryMathExpression((x: Double) => StrictMath.log(x + math.sqrt(x * x - 1.0)), "ACOSH") {
extends UnaryMathExpression((x: Double) => x match {
// in case of large values, the square would lead to Infinity; also, - 1 would be ignored due
// to numeric precision. So log(x + sqrt(x * x - 1)) becomes log(2x) = log(2) + log(x) for
// positive values.
case x if x >= Math.sqrt(Double.MaxValue) =>
StrictMath.log(2) + StrictMath.log(x)
case x if x < 1 =>
Double.NaN
case _ => StrictMath.log(x + math.sqrt(x * x - 1.0)) }, "ACOSH") {
override def doGenCode(ctx: CodegenContext, ev: ExprCode): ExprCode = {
defineCodeGen(ctx, ev,
c => s"java.lang.StrictMath.log($c + java.lang.Math.sqrt($c * $c - 1.0))")
nullSafeCodeGen(ctx, ev, c => {
val sm = "java.lang.StrictMath"
s"""
|if ($c >= ${Math.sqrt(Double.MaxValue)}) {
| ${ev.value} = $sm.log($c) + $sm.log(2);
|} else if ($c < 1) {
| ${ev.value} = java.lang.Double.NaN;
|} else {
| ${ev.value} = $sm.log($c + java.lang.Math.sqrt($c * $c - 1.0));
|}
|""".stripMargin
})
}
override protected def withNewChildInternal(newChild: Expression): Acosh = copy(child = newChild)
}
Expand Down Expand Up @@ -842,12 +860,20 @@ case class Sinh(child: Expression) extends UnaryMathExpression(math.sinh, "SINH"
group = "math_funcs")
case class Asinh(child: Expression)
extends UnaryMathExpression((x: Double) => x match {
case Double.NegativeInfinity => Double.NegativeInfinity
// in case of large values, the square would lead to Infinity; also, + 1 would be ignored due
// to numeric precision. So log(x + sqrt(x * x + 1)) becomes log(2x) = log(2) + log(x) for
// positive values. Since the function is symmetric, for large values we can use
// signum(x) + log(2|x|)
case x if Math.abs(x) >= Math.sqrt(Double.MaxValue) - 1 =>
Math.signum(x) * (StrictMath.log(2) + StrictMath.log(Math.abs(x)))
case _ => StrictMath.log(x + math.sqrt(x * x + 1.0)) }, "ASINH") {
override def doGenCode(ctx: CodegenContext, ev: ExprCode): ExprCode = {
defineCodeGen(ctx, ev, c =>
s"$c == Double.NEGATIVE_INFINITY ? Double.NEGATIVE_INFINITY : " +
s"java.lang.StrictMath.log($c + java.lang.Math.sqrt($c * $c + 1.0))")
defineCodeGen(ctx, ev, c => {
val sm = "java.lang.StrictMath"
s"$sm.abs($c) >= ${Math.sqrt(Double.MaxValue) - 1} ? " +
s"$sm.signum($c) * ($sm.log($sm.abs($c)) + $sm.log(2)) :" +
s"$sm.log($c + java.lang.Math.sqrt($c * $c + 1.0))"
})
}
override protected def withNewChildInternal(newChild: Expression): Asinh = copy(child = newChild)
}
Expand Down
16 changes: 15 additions & 1 deletion ...alyst/src/test/scala/org/apache/spark/sql/catalyst/expressions/MathExpressionsSuite.scala
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Original file line number Diff line number Diff line change
Expand Up @@ -280,7 +280,9 @@ class MathExpressionsSuite extends SparkFunSuite with ExpressionEvalHelper {
}

test("acosh") {
testUnary(Acosh, (x: Double) => StrictMath.log(x + math.sqrt(x * x - 1.0)))
def f: (Double) => Double = (x: Double) => StrictMath.log(x + math.sqrt(x * x - 1.0))
testUnary(Acosh, f, (10 to 20).map(_ * 0.1))
testUnary(Acosh, f, (-20 to 9).map(_ * 0.1), expectNaN = true)
checkConsistencyBetweenInterpretedAndCodegen(Cosh, DoubleType)

val nullLit = Literal.create(null, NullType)
Expand Down Expand Up @@ -963,4 +965,16 @@ class MathExpressionsSuite extends SparkFunSuite with ExpressionEvalHelper {
checkEvaluation(WidthBucket(5.35, 0.024, Double.NegativeInfinity, 5L), null)
checkEvaluation(WidthBucket(5.35, 0.024, Double.PositiveInfinity, 5L), null)
}

test("SPARK-55557: hyperbolic functions should not overflow with large inputs") {
checkEvaluation(Asinh(Double.MaxValue), 710.4758600739439)
checkEvaluation(Asinh(Math.sqrt(Double.MaxValue)), 355.58450362725193)
checkEvaluation(Acosh(Double.MaxValue), 710.4758600739439)
checkEvaluation(Acosh(Math.sqrt(Double.MaxValue)), 355.58450362725193)
checkEvaluation(Asinh(Double.MinValue), -710.4758600739439)
checkEvaluation(Asinh(-Math.sqrt(Double.MaxValue)), -355.58450362725193)
checkNaN(Acosh(Double.MinValue))
checkNaN(Acosh(-Math.sqrt(Double.MaxValue) + 1))
checkNaN(Acosh(-Math.sqrt(Double.MaxValue) + 2))
}
}