$acosh
Definition
Computes inverse hyperbolic cosine.
Expression operator · Arithmetic · Studio Visual: available. Studio validates the complete expression separately.
Syntax
{ "$acosh": <expression> }
Replace angle-bracket placeholders with expressions or values.
Expression supplying the value to process. A field reference such as "$price" reads from the current document.
The value goes directly after the operator name; do not add an input wrapper.
Behavior
The following observations use the example expression below. Each row substitutes one argument while retaining the other example arguments. A missing field differs from an explicit null; the result shown is what Core actually returned.
For the input argument:
| Input case | Supplied value | Result |
|---|---|---|
| null | null | Error — $acosh expects a numeric argument |
| missing | Field absent | Error — $acosh expects a numeric argument |
| decimal | 2.5 | 1.566799236972411 (double) |
| numeric string | "12" | Error — $acosh expects a numeric argument |
| text | "hello" | Error — $acosh expects a numeric argument |
| boolean | true | Error — $acosh expects a numeric argument |
| typed date | {"$date":"2026-01-15T15:00:00Z"} | Error — $acosh expects a numeric argument |
| empty array | [] | Error — $acosh expects a numeric argument |
| numeric array | [1,2,3] | Error — $acosh expects a numeric argument |
| object | {"x":1} | Error — $acosh expects a numeric argument |
Argument handling
| Invocation | Result |
|---|---|
| {"$acosh":[]} | Error — $acosh expects a numeric argument |
| {"$acosh":{"unexpected":1}} | Error — $acosh expects a numeric argument |
Examples
Expression:
{
"$acosh": 1
}
Input document:
{}
Observed SrotaX result: 0.0 (double).
Detailed input cases
Expand the complete argument-by-argument test matrix
Each table changes only the indicated argument from the example above. Other arguments retain their baseline values. Values normally come from the input field probe; literal configuration arguments are replaced directly. “Missing” means the field is absent, not explicitly null. Numeric strings are strings, not numbers.
Argument: input
| Input case | Supplied value | SrotaX result |
|---|---|---|
| null | null | Error — $acosh expects a numeric argument |
| missing | Field absent | Error — $acosh expects a numeric argument |
| zero | 0 | Error — $acosh is undefined for values less than 1 |
| negative | -2 | Error — $acosh is undefined for values less than 1 |
| decimal | 2.5 | 1.566799236972411 (double) |
| numeric string | "12" | Error — $acosh expects a numeric argument |
| text | "hello" | Error — $acosh expects a numeric argument |
| empty string | "" | Error — $acosh expects a numeric argument |
| boolean | true | Error — $acosh expects a numeric argument |
| false | false | Error — $acosh expects a numeric argument |
| typed date | {"$date":"2026-01-15T15:00:00Z"} | Error — $acosh expects a numeric argument |
| decimal128 | {"$numberDecimal":"1.25"} | 0.6931471805599453 (double) |
| empty array | [] | Error — $acosh expects a numeric argument |
| numeric array | [1,2,3] | Error — $acosh expects a numeric argument |
| mixed array | [1,null,"x",3] | Error — $acosh expects a numeric argument |
| nested array | [[1,2],[3]] | Error — $acosh expects a numeric argument |
| empty object | {} | Error — $acosh expects a numeric argument |
| object | {"x":1} | Error — $acosh expects a numeric argument |
| ISO date string | "2026-01-15T15:00:00Z" | Error — $acosh expects a numeric argument |
Verification
This page records 22 executed cases. It covers individual argument substitutions, not every cross-product of arguments, locale, daylight-saving transitions, numeric overflow, collation or resource limits. No untested behavior is guaranteed.
Download exact expressions, inputs and SrotaX results. Errors are observed messages, not stable public error codes. The reference generator reads the checked-in execution report; do not edit generated observations by hand.
MongoDB differences
Compared with MongoDB 9.0.4: 2 exact BSON matches, 17 both rejected, 3 value/type/acceptance differences, 0 object-field-order differences.
“Exact” includes numeric BSON types and object key order. A value of 3 as int32 differs from 3.0 as double. Object-field-order differences are reported separately; object key ordering is not enforced by the engine regression baseline. Both rejected does not mean the error codes or messages match. This is finite-case evidence, not full compatibility certification.
Show observed differences
| Tested case | SrotaX | MongoDB |
|---|---|---|
| input / null | Error — $acosh expects a numeric argument | null |
| input / missing | Error — $acosh expects a numeric argument | null |
| input / decimal128 | 0.6931471805599453 (double) | 0.6931471805599453094172321214581766 (decimal128) |