/***************************************************************************************************

Insert to an empty leaf
=======================

  STATE                 OLD STATE                                       NEW STATE
  =====                 =========                                       =========

                         oldRoot                                          newRoot
                            ▲                                               ▲
                            │                                               │
          ┌───────┐     ┏━━━┻━━━┓                         ┌───────┐     ┏━━━┻━━━┓
   top    │Sibling├────▶┃ Hash  ┃◀─┐                      │Sibling├────▶┃ Hash  ┃◀─┐
          └───────┘     ┗━━━━━━━┛  │                      └───────┘     ┗━━━━━━━┛  │
                                   │                                               │
                                   │                                               │
                               ┏━━━┻━━━┓   ┌───────┐                           ┏━━━┻━━━┓   ┌───────┐
   top                  ┌─────▶┃ Hash  ┃◀──┤Sibling│                    ┌─────▶┃ Hash  ┃◀──┤Sibling│
                        │      ┗━━━━━━━┛   └───────┘                    │      ┗━━━━━━━┛   └───────┘
                        │                                               │
                        │                                               │
        ┌───────┐   ┏━━━┻━━━┓                           ┌───────┐   ┏━━━┻━━━┓
   top  │Sibling├──▶┃ Hash  ┃◀─────┐                    │Sibling├──▶┃ Hash  ┃◀─────┐
        └───────┘   ┗━━━━━━━┛      │                    └───────┘   ┗━━━━━━━┛      │
                                   │                                               │
                                   │                                               │
                              ┌────┴────┐                                     ┌────┴────┐
  old0                        │    0    │                                     │New1Leaf │
                              └─────────┘                                     └─────────┘


                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
   na                ┃ Hash  ┃                                      ┃ Hash  ┃
                     ┗━━━━━━━┛                                      ┗━━━━━━━┛


                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
   na                ┃ Hash  ┃                                      ┃ Hash  ┃
                     ┗━━━━━━━┛                                      ┗━━━━━━━┛



Insert to a used leaf.
=====================

  STATE                 OLD STATE                                       NEW STATE
  =====                 =========                                       =========


                         oldRoot                                          newRoot
                            ▲                                               ▲
                            │                                               │
          ┌───────┐     ┏━━━┻━━━┓                         ┌───────┐     ┏━━━┻━━━┓
   top    │Sibling├────▶┃ Hash  ┃◀─┐                      │Sibling├────▶┃ Hash  ┃◀─┐
          └───────┘     ┗━━━━━━━┛  │                      └───────┘     ┗━━━━━━━┛  │
                                   │                                               │
                                   │                                               │
                               ┏━━━┻━━━┓   ┌───────┐                           ┏━━━┻━━━┓   ┌───────┐
   top                  ┌─────▶┃ Hash  ┃◀──┤Sibling│                    ┌─────▶┃ Hash  ┃◀──┤Sibling│
                        │      ┗━━━━━━━┛   └───────┘                    │      ┗━━━━━━━┛   └───────┘
                        │                                               │
                        │                                               │
        ┌───────┐   ┏━━━┻━━━┓                           ┌───────┐   ┏━━━┻━━━┓
   top  │Sibling├──▶┃ Hash  ┃◀─────┐                    │Sibling├──▶┃ Hash  ┃◀─────┐
        └───────┘   ┗━━━━━━━┛      │                    └───────┘   ┗━━━━━━━┛      │
                                   │                                               │
                                   │                                               │
                              ┌────┴────┐                                      ┏━━━┻━━━┓   ┌───────┐
  old1                        │Old1Leaf │                               ┌─────▶┃ Hash  ┃◀──┼─  0   │
                              └─────────┘                               │      ┗━━━━━━━┛   └───────┘
                                                                        │
                                                                        │
                     ┏━━━━━━━┓                          ┌───────┐   ┏━━━┻━━━┓
   bot               ┃ Hash  ┃                          │   0  ─┼──▶┃ Hash  ┃◀─────┐
                     ┗━━━━━━━┛                          └───────┘   ┗━━━━━━━┛      │
                                                                                   │
                                                                                   │
                     ┏━━━━━━━┓                                                 ┏━━━┻━━━┓   ┌───────┐
   bot               ┃ Hash  ┃                                          ┌─────▶┃ Hash  ┃◀──│   0   │
                     ┗━━━━━━━┛                                          │      ┗━━━━━━━┛   └───────┘
                                                                        │
                                                                        │
                     ┏━━━━━━━┓                        ┌─────────┐   ┏━━━┻━━━┓   ┌─────────┐
  new1               ┃ Hash  ┃                        │Old1Leaf ├──▶┃ Hash  ┃◀──│New1Leaf │
                     ┗━━━━━━━┛                        └─────────┘   ┗━━━━━━━┛   └─────────┘


                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
   na                ┃ Hash  ┃                                      ┃ Hash  ┃
                     ┗━━━━━━━┛                                      ┗━━━━━━━┛


                     ┏━━━━━━━┓                                      ┏━━━━━━━┓
   na                ┃ Hash  ┃                                      ┃ Hash  ┃
                     ┗━━━━━━━┛                                      ┗━━━━━━━┛

***************************************************************************************************/

include "../node_modules/circom/circuits/gates.circom";
include "../node_modules/circom/circuits/bitify.circom";

template SMTInsert(nLevels) {
    signal input oldRoot;
    signal input newRoot;
    signal input siblings[nLevels];
    signal input oldHKey;
    signal input oldHValue;
    signal input newHKey;
    signal input newHValue;

    component hash1Old = SMTHash1();
    hash1Old.l <== oldHKey;
    hash1Old.r <== oldHValue;

    component hash1New = SMTHash1();
    hash1New.l <== newHKey;
    hash1New.r <== newHValue;

    component n2bOld = Num2BinStrinct();
    component n2bNew = Num2BinStrinct();

    component dmtLevIns = SMTLevIns(nLevels);
    for (var i=0; i<nLevels; i++) dmtLevIns.siblings[i] <== siblings[i];

    component xors[nLevels];
    for (var i=0; i<nLevels; i++) {
        xors[i] = XOR();
        xors[i].a <== n2bOld.out[i];
        xors[i].a <== n2bNew.out[i];
    }

    component isOld0 = IsZero();
    isOld0.in <== oldHValue;

    component sm[nLevels];
    for (var i=0; i<sm; i++) {
        sm[i] = SMTInsertSM();
        if (i==0) {
            sm[i].prevst_top <== 1;
            sm[i].prevst_old1 <== 0;
            sm[i].prevst_old0 <== 0;
            sm[i].prevst_bot <== 0;
            sm[i].prevst_new1 <== 0;
            sm[i].prevst_na <== 0;
        } else {
            sm[i].prevst_top <== sm[i-1].st_top;
            sm[i].prevst_old1 <== sm[i-1].st_old1;
            sm[i].prevst_old0 <== sm[i-1].st_old0;
            sm[i].prevst_bot <== sm[i-1].st_bot;
            sm[i].prevst_new1 <== sm[i-1].st_new1;
            sm[i].prevst_na <== sm[i-1].st_na;
        }
        sm[i].is0 <== isOld0.out;
        sm[i].xor <== xors[i].out;
        sm[i].levIns <== dmtLevIns.out[i];
    }
    sm[nLevels-1].prevst_na === 1;

    component levels[nLevels];
    for (var i=nLevels-1; i != -1; i--) {
        levels[i] = SMTInsertLevel();

        levels[i].st_top <== sm[i].st_top;
        levels[i].st_old1 <== sm[i].st_old1;
        levels[i].st_old0 <== sm[i].st_old0;
        levels[i].st_bot <== sm[i].st_bot;
        levels[i].st_new1 <== sm[i].st_new1;
        levels[i].st_na <==sm[i].st_na;

        levels[i].sibling <== siblings[i];
        levels[i].old1leaf <== hash1Old.out;
        levels[i].new1leaf <== hash1New.out;

        levels[i].new1lrbit <== n2bNew.out[i];
        if (i==nLevels-1) {
            levels[i].oldChild <== 0;
            levels[i].newChild <== 0;
        } else {
            levels[i].oldChild <== levels[i+1].oldRoot;
            levels[i].newChild <== levels[i+1].newRoot;
        }
    }

    levels[0].oldRoot === oldRoot;
    levels[0].newRoot === newRoot;
}