$atanh (aggregation)

• $atanh

New in version 4.2.

Returns the inverse hyperbolic tangent (hyperbolic arc tangent) ofa value.

$atanh has the following syntax:

{ $atanh: <expression> }

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

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

By default $atanh returns values as a double.$atanh can also return values as a128-bit decimalas long as the <expression> resolves to a 128-bit decimal value.

For more information on expressions, seeExpressions.

Behavior

null, NaN, and +/- Infinity

If the argument resolves to a value of null or refers to a fieldthat is missing, $atanh returns null. If theargument 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.

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

Example

• Inverse Hyperbolic Tangent of Value in Degrees
• Inverse Hyperbolic Tangent of Value in Radians

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

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

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

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

The $radiansToDegrees expression converts theradian value returned by $atanh to the equivalentvalue in degrees.

The command returns the following output:

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

Since x-coordinate is stored as a128-bit decimal, the output of$atanh is a 128-bit decimal.

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

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

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

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

The command returns the following output:

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

Since x-coordinate is stored as a128-bit decimal, the output of$asin is a 128-bit decimal.