Database Manual / Reference / Query Language / Expressions

$atanh (expression operator)

$atanh

Returns the inverse hyperbolic tangent (hyperbolic arc tangent) of a value.

$atanh has the following syntax:

{ $atanh: <expression> }

$atanh takes any valid expression that resolves to a number between -1 and 1, e.g. -1 <= value <= 1.

$atanh returns values in radians. Use $radiansToDegrees operator to convert the output value from radians to degrees.

By default $atanh returns values as a double. $atanh can also return values as a 128-bit decimal as long as the <expression> resolves to a 128-bit decimal value.

For more information on expressions, see Expressions.

Behavior

null, NaN, and +/- Infinity

If the argument resolves to a value of null or refers to a field that is missing, $atanh returns null. If the argument resolves to NaN, $atanh returns NaN. If the argument resolves to negative or positive infinity, $atanh throws an error. If the argument resolves to +1 or -1, $atanh returns Infinity and -Infinity respectively.

ExampleResults

{ $atanh: NaN }

NaN

{ $atanh: null }

null

{ $atanh: 1 }

Infinity

{ $atanh: -1}

-Infinity

{ $atanh : Infinity}

or

{ $atanh : -Infinity }

Throws an error message resembling the following formatted output:

"errmsg" :
  "Failed to optimize pipeline :: caused by :: cannot
  apply $atanh to -inf, value must in (-inf,inf)"

Example

The trigonometry collection contains a document that stores a value along the x axis of a 2-D graph:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("0.5")
}

The following aggregation operation uses the $atanh expression to calculate inverse hyperbolic tangent of x-coordinate and add it to the input document using the $addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "y-coordinate" : {
        $radiansToDegrees : { $atanh : "$x-coordinate" }
      }
    }
  }
])

The $radiansToDegrees expression converts the radian value returned by $atanh to the equivalent value in degrees.

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("0.5"),
  "y-coordinate" : Decimal128("31.47292373094538001977241539068589")
}

Since x-coordinate is stored as a 128-bit decimal, the output of $atanh is a 128-bit decimal.

The trigonometry collection contains a document that stores a value along the x axis of a 2-D graph:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("0.5")
}

The following aggregation operation uses the $atanh expression to calculate inverse hyperbolic tangent of x-coordinate and add it to the input document using the $addFields pipeline stage.

db.trigonometry.aggregate([
  {
    $addFields : {
      "y-coordinate" : {
        $atanh : "$x-coordinate"
      }
    }
  }
])

The command returns the following output:

{
  "_id" : ObjectId("5c50782193f833234ba90d85"),
  "x-coordinate" : Decimal128("0.5"),
  "y-coordinate" : Decimal128("0.5493061443340548456976226184612628")
}

Since x-coordinate is stored as a 128-bit decimal, the output of $asin is a 128-bit decimal.