mapper_parsing_exception is thrown for "NaN" values for fields with ignore_malformed=true

Elasticsearch version:
5.4.1

Description of the problem including expected versus actual behavior:
mapper_parsing_exception is thrown for numeric field with ignore_malformed=true when inserting a "NaN" value.
I would expect that no exception is returned for a field with ignore_malformed=true

Steps to reproduce:
First create an index with a mapping with a numeric field with ignore_malformed = true:

PUT nan_test
{
  "mappings": {
    "test_type": {
      "properties": {
        "number_one": {
          "type": "scaled_float",
          "scaling_factor": 1,
          "ignore_malformed": true
        }
      }
    }
  }
}

{"acknowledged":true,"shards_acknowledged":true}

Then insert a malformed number, works as expected:

PUT nan_test/test_type/1?pretty
{
  "number_one": "not a number"
}

{
  "_index" : "nan_test",
  "_type" : "test_type",
  "_id" : "1",
  "_version" : 1,
  "result" : "created",
  "_shards" : {
    "total" : 2,
    "successful" : 2,
    "failed" : 0
  },
  "created" : true
}

Now, let's insert a number with the "NaN" string value:

PUT nan_test/test_type/2?pretty
{
  "number_one": "NaN"
}

{
  "error" : {
    "root_cause" : [
      {
        "type" : "mapper_parsing_exception",
        "reason" : "failed to parse [number_one]"
      }
    ],
    "type" : "mapper_parsing_exception",
    "reason" : "failed to parse [number_one]",
    "caused_by" : {
      "type" : "illegal_argument_exception",
      "reason" : "[scaled_float] only supports finite values, but got [NaN]"
    }
  },
  "status" : 400
}

Shouldn't ignore_malformed = true ignore all mapper_parsing_exception?
If not, how can I ignore the exception raised by "NaN" values?
Note that NaN has no special meaning in json, so it seems strange that it is considered a special input value.

[clintongormley]

Related to #12366

Same problem with the "Infinity" and "-Infinity" values.

"reason" : "[scaled_float] only supports finite values, but got [-Infinity]"

[colings86]

This is a bug, ignore_malformed should mean the error is suppressed here.