Database Manual / Reference / Query Language / Expressions

$atanh (expression operator)（表达式运算符）

$atanh

Returns the inverse hyperbolic tangent (hyperbolic arc tangent) of a value.返回值的反双曲正切（双曲反正切）。

$atanh has the following syntax:具有以下语法：

{ $atanh: <expression> }

$atanh takes any valid expression that resolves to a number between -1 and 1, e.g. -1 <= value <= 1.$atanh接受任何解析为-1到1之间的数字的有效表达式，例如-1<=value<=1。

$atanh returns values in radians. Use $radiansToDegrees operator to convert the output value from radians to degrees.$atanh返回以弧度为单位的值。使用$radiasToDegrees运算符将输出值从弧度转换为度数。

By default $atanh returns values as a double. $atanh can also return values as a 128-bit decimal as long as the <expression> resolves to a 128-bit decimal value.默认情况下，$atanh以double形式返回值。只要<expression>解析为128位十进制值，$atanh也可以返回128位十进制的值。

For more information on expressions, see Expressions.有关表达式的详细信息，请参阅表达式。

Behavior行为

null, NaN, and +/- Infinity

If the argument resolves to a value of null or refers to a field that is missing, $atanh returns null. 如果参数解析为null值或引用缺少的字段，$atanh将返回null。If the argument resolves to NaN, $atanh returns NaN. 如果参数解析为NaN，$atanh将返回NaN。If the argument resolves to negative or positive infinity, $atanh throws an error. 如果参数解析为负无穷大或正无穷大，$atanh将抛出错误。If the argument resolves to +1 or -1, $atanh returns Infinity and -Infinity respectively.如果参数解析为+1或-1，$atanh将分别返回Infinity和-Infinity。

Example示例Results结果
{ $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:抛出类似以下格式化输出的错误消息：

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

Example示例

Inverse Hyperbolic Tangent in Degrees以度为单位的反双曲正切

The trigonometry collection contains a document that stores a value along the x axis of a 2-D graph:trigonometry集合包含一个文档，该文档存储了沿二维图x轴的值：

{
  "_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 $addFields pipeline stage.以下聚合操作使用$atanh表达式计算x-coordinate的反双曲正切，并使用$addFields管道阶段将其添加到输入文档中。

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

The $radiansToDegrees expression converts the radian value returned by $atanh to the equivalent value in degrees.$radiansToDegrees表达式将$atanh返回的弧度值转换为以度为单位的等效值。

The command returns the following output:该命令返回以下输出：

{
  "_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 $atanh is a 128-bit decimal.由于x-coordinate存储为128位十进制，因此$atanh的输出为128位十进制。

Inverse Hyperbolic Tangent in Radians以弧度为单位的反双曲正切

The trigonometry collection contains a document that stores a value along the x axis of a 2-D graph:trigonometry集合包含一个文档，该文档存储了沿二维图x轴的值：

{
  "_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 $addFields pipeline stage.以下聚合操作使用$atanh表达式计算x-coordinate的反双曲正切，并使用$addFields管道阶段将其添加到输入文档中。

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

The command returns the following output:该命令返回以下输出：

{
  "_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 $asin is a 128-bit decimal.由于x-coordinate存储为128位十进制，因此$asin的输出是128位十进制。