Further improve serialization of "homogenous" lists

[fingolfin]

Recently @antonydellavecchia implemented optimizations that dramatically reduced the overhead for serializing e.g. Vector{Int}.

We should push this further to extend to other types of homogeneous vectors. For example, here I am serializing a vector of finite field elements (FFEs), all over the same finite field.

julia> F = GF(911)
Galois field with characteristic 911

julia> save("ffe.json", F.([0,1,2,3]))

julia> save("intvec.json", [0,1,2,3]) # for comparison

This is the resulting ffe.json (after pretty printing and with the _ns entry removed):

{
   "data" : {
      "vector" : [
         {
            "data" : {
               "data" : 0,
               "parent" : {
                  "data" : {
                     "characteristic" : 911
                  },
                  "id" : "92c02e5f-dfa2-4318-9031-4b78a9f33b02",
                  "type" : "Nemo.fpField"
               }
            },
            "id" : "e070f5f4-8261-4378-adc3-a8c918509843",
            "type" : "Nemo.fpFieldElem"
         },
         {
            "data" : {
               "data" : 1,
               "parent" : {
                  "id" : "92c02e5f-dfa2-4318-9031-4b78a9f33b02",
                  "type" : "#backref",
                  "version" : 1
               }
            },
            "id" : "d57f0213-951a-41e0-9c6b-b89549711dca",
            "type" : "Nemo.fpFieldElem"
         },
         {
            "data" : {
               "data" : 2,
               "parent" : {
                  "id" : "92c02e5f-dfa2-4318-9031-4b78a9f33b02",
                  "type" : "#backref",
                  "version" : 1
               }
            },
            "id" : "26713fb3-5e71-4ef5-8f5d-d650a04d0cca",
            "type" : "Nemo.fpFieldElem"
         },
         {
            "data" : {
               "data" : 3,
               "parent" : {
                  "id" : "92c02e5f-dfa2-4318-9031-4b78a9f33b02",
                  "type" : "#backref",
                  "version" : 1
               }
            },
            "id" : "ba90ef62-50b4-4da8-9975-2e2e8df7a6ea",
            "type" : "Nemo.fpFieldElem"
         }
      ]
   },
   "id" : "e6416bbb-8976-47ba-a433-377a8b1eec2f",
   "type" : "Vector"
}

For references, this is intvec.json (I am leaving out the namespace bit)

{
   "data" : {
      "entry_type" : "Base.Int",
      "vector" : [
         "0",
         "1",
         "2",
         "3"
      ]
   },
   "id" : "160c2eb6-4740-4cd5-b50e-b850ad3ba984",
   "type" : "Vector"
}

Some observations:

• for FFEs (finite field elements) of a prime field, I don't think we should assign an id for them / should not consider them for backrefs
• storing the parent repeatedly in there should be redundant

Here is how it could look like (I did not check whether:

{
   "data" : {
      "entry_parent" : {
         "data" : {
            "characteristic" : 911
         },
         "id" : "92c02e5f-dfa2-4318-9031-4b78a9f33b02",
         "type" : "Nemo.fpField"
      }
      "entry_type" : "Nemo.fpFieldElem"
      "vector" : [
         {
            "data" : 0
         },
         {
            "data" : 1
         },
         {
            "data" : 2
         },
         {
            "data" : 3
         }
      ]
   },
   "id" : "e6416bbb-8976-47ba-a433-377a8b1eec2f",
   "type" : "Vector"
}

And why stop there, we can special case and say "FFEs essentially just store an integer", and compact it further:

{
   "data" : {
      "entry_parent" : {
         "data" : {
            "characteristic" : 911
         },
         "id" : "92c02e5f-dfa2-4318-9031-4b78a9f33b02",
         "type" : "Nemo.fpField"
      }
      "entry_type" : "Nemo.fpFieldElem"
      "vector" : [
         0,
         1,
         2,
         3
      ]
   },
   "id" : "e6416bbb-8976-47ba-a433-377a8b1eec2f",
   "type" : "Vector"
}

So really, what we are storing here is a Vector{Int16} plus the parent plus the information that this parent should be used to re-create the elements of the vector.

[lgoettgens]

Resolved by #2102.