In MongoDB, the $atanh aggregation pipeline operator returns the hyperbolic arctangent (inverse hyperbolic tangent) of a value.

The return value is in radians.

$atanh accepts any valid expression that resolves to a number between -1 and 1.

The $atanh operator was introduced in MongoDB 4.2.

Example

Suppose we have a collection called test with the following document:

{ "_id" : 1, "data" : 0.5 }

We can use the $atanh operator to return the hyperbolic arctangent of the data field:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        _id: 0,
        hyperbolicArctangent: { $atanh: "$data" }
      }
    }
  ]
)

Result:

{ "hyperbolicArctangent" : 0.5493061443340549 }

Convert to Degrees

As mentioned, $atanh returns its result in radians. You can use the $radiansToDegrees operator if you want the result in degrees.

Example:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        _id: 0,
        radians: { $atanh: "$data" },
        degrees: { $radiansToDegrees: { $atanh: "$data" } }
      }
    }
  ]
)

Result:

{ "radians" : 0.5493061443340549, "degrees" : 31.472923730945382 }

In this example, the first field presents the result in radians, and the second field presents it in degrees.

128-Bit Decimal Values

By default, the $atanh operator returns values as a double, but it can also return values as a 128-bit decimal as long as the expression resolves to a 128-bit decimal value.

Suppose we add the following document to our collection:

{ "_id" : 2, "data" : NumberDecimal("0.1301023541559787031443874490659") }

Let’s run the the $atanh operator against that document:

db.test.aggregate(
  [
    { $match: { _id: 2 } },
    { $project: { 
        _id: 0,
        result: { $atanh: "$data" }
      }
    }
  ]
)

Result:

{ "result" : NumberDecimal("0.1308439651155512740523796431117568") }

The output is 128-bit decimal.

Out of Range Values

The $atanh operator accepts any valid expression that resolves to a number between -1 and 1. Values outside of that range will cause an error.

Suppose we add the following document to our collection:

{ "_id" : 3, "data" : 2 }

Let’s run the the $atanh operator against that document:

db.test.aggregate(
  [
    { $match: { _id: 3 } },
    { $project: { 
        _id: 0,
        result: { $atanh: "$data" }
      }
    }
  ]
)

Result:

uncaught exception: Error: command failed: {
	"ok" : 0,
	"errmsg" : "cannot apply $atanh to 2, value must in [-1,1]",
	"code" : 50989,
	"codeName" : "Location50989"
} : aggregate failed :
_getErrorWithCode@src/mongo/shell/utils.js:25:13
doassert@src/mongo/shell/assert.js:18:14
_assertCommandWorked@src/mongo/shell/assert.js:618:17
assert.commandWorked@src/mongo/shell/assert.js:708:16
DB.prototype._runAggregate@src/mongo/shell/db.js:266:5
DBCollection.prototype.aggregate@src/mongo/shell/collection.js:1046:12
@(shell):1:1

Null Values

Null values return null when using the $atanh operator.

Suppose we add the following document to our collection:

{ "_id" : 4, "data" : null }

Let’s run the the $atanh operator against that document:

db.test.aggregate(
  [
    { $match: { _id: 4 } },
    { $project: { 
        _id: 0,
        result: { $atanh: "$data" }
      }
    }
  ]
)

Result:

{ "result" : null }

We can see that the result is null.

NaN Values

If the argument resolves to NaN, $atanh returns NaN.

Example:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        _id: 0,
        result: { $atanh: 1 * "$data" }
      }
    }
  ]
)

Result:

{ "result" : NaN }

Non-Existent Fields

If the $atanh operator is applied against a field that doesn’t exist, null is returned.

Example:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        _id: 0,
        result: { $atanh: "$name" }
      }
    }
  ]
)

Result:

{ "result" : null }

Infinity

Providing Infinity or -Infinity will return an out of range error (like we saw earlier).

Suppose we add the following document to the collection:

{ "_id" : 5, "data" : Infinity }

Let’s run $atanh again:

db.test.aggregate(
  [
    { $match: { _id: 5 } },
    { $project: { 
        _id: 0,
        result: { $atanh: "$data" }
      }
    }
  ]
)

Result:

uncaught exception: Error: command failed: {
	"ok" : 0,
	"errmsg" : "cannot apply $atanh to inf, value must in [-1,1]",
	"code" : 50989,
	"codeName" : "Location50989"
} : aggregate failed :
_getErrorWithCode@src/mongo/shell/utils.js:25:13
doassert@src/mongo/shell/assert.js:18:14
_assertCommandWorked@src/mongo/shell/assert.js:618:17
assert.commandWorked@src/mongo/shell/assert.js:708:16
DB.prototype._runAggregate@src/mongo/shell/db.js:266:5
DBCollection.prototype.aggregate@src/mongo/shell/collection.js:1046:12
@(shell):1:1