Garbage test in formulas.

1 files changed, 72 insertions, 6 deletions

diff --git a/analysis/scalarmults/formulas.ipynb b/analysis/scalarmults/formulas.ipynb
index 9b16ee5..576da1e 100644
--- a/analysis/scalarmults/formulas.ipynb
+++ b/analysis/scalarmults/formulas.ipynb
@@ -12,13 +12,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 21,
    "id": "09d92ba3-ede4-40c3-a061-a9c328e26fb5",
    "metadata": {},
    "outputs": [],
    "source": [
     "import io\n",
     "import json\n",
+    "import random\n",
     "\n",
     "from pprint import pprint\n",
     "import tabulate\n",
@@ -102,7 +103,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 26,
    "id": "e045a4cf-97db-4a2f-a191-582987f6473d",
    "metadata": {},
    "outputs": [
@@ -145,6 +146,8 @@
     "        r1r2_aff = params.curve.affine_add(r1_aff, r2_aff)\n",
     "        r1r2 = r1r2_aff.to_model(coords, params.curve)\n",
     "        zeros = Point(coords, **{var: mod(0, p) for var in coords.variables})\n",
+    "        random.seed(hash(r1_aff) + hash(r2_aff))\n",
+    "        garbage = Point(coords, **{var: mod(random.randint(0, p), p) for var in coords.variables})\n",
     "\n",
     "        adds = set(formula for formula in coords.formulas.values() if formula.shortname == \"add\")\n",
     "        dbls = set(formula for formula in coords.formulas.values() if formula.shortname == \"dbl\")\n",
@@ -166,6 +169,9 @@
     "            ZerospP = add(p, zeros, orderbig, **params.curve.parameters)[0]\n",
     "            # P1 + P2 = ? such that P1 - P2 = ord2\n",
     "            PpQord2 = add(p, r1, r2, **params.curve.parameters)[0]\n",
+    "            # P + garbage = ?\n",
+    "            PpGarbage = add(p, orderbig, garbage, **params.curve.parameters)[0]\n",
+    "            GarbagepP = add(p, garbage, orderbig, **params.curve.parameters)[0]\n",
     "            res[\"PpP\"] = eval_test(orderbig2, PpP, params.curve)\n",
     "            res[\"PpInfty\"] = eval_test(orderbig, PpInfty, params.curve)\n",
     "            res[\"InftypP\"] = eval_test(orderbig, InftypP, params.curve)\n",
@@ -175,15 +181,19 @@
     "            res[\"PpZeros\"] = eval_test(None, PpZeros, params.curve)\n",
     "            res[\"ZerospP\"] = eval_test(None, ZerospP, params.curve)\n",
     "            res[\"PpQDifford2\"] = eval_test(r1r2, PpQord2, params.curve)\n",
+    "            res[\"PpGarbage\"] = eval_test(None, PpGarbage, params.curve)\n",
+    "            res[\"GarbagepP\"] = eval_test(None, GarbagepP, params.curve)\n",
     "        for dbl in dbls:\n",
     "            res = {}\n",
     "            results_dbl[coords_name][dbl.name] = res\n",
     "            O2twice = dbl(p, order2, **params.curve.parameters)[0]\n",
     "            Inftytwice = dbl(p, infty, **params.curve.parameters)[0]\n",
     "            Zerostwice = dbl(p, zeros, **params.curve.parameters)[0]\n",
+    "            Garbagetwice = dbl(p, garbage, **params.curve.parameters)[0]\n",
     "            res[\"O2twice\"] = eval_test(infty, O2twice, params.curve)\n",
     "            res[\"Inftytwice\"] = eval_test(infty, Inftytwice, params.curve)\n",
-    "            res[\"Zerostwice\"] = eval_test(None, Zerostwice, params.curve)"
+    "            res[\"Zerostwice\"] = eval_test(None, Zerostwice, params.curve)\n",
+    "            res[\"Garbagetwice\"] = eval_test(None, Garbagetwice, params.curve)"
    ]
   },
   {
@@ -216,12 +226,13 @@
     "   `add-2002-bj, add-2007-bl, add-2015-rcb, madd-2015-rcb`\n",
     " - `P + -P = infty` and `-P + P = infty`: All correct, no zeros, no affine, on curve.\n",
     " - `zeros + P = ?` and `P + zeros = ?`: Three behavior classes, in one, the zeros propagate, in another the formula makes up an affine point that is not zeros but is not on the curve. In the final class, the formula makes up some point that is neither zeros, nor affine nor on the curve. These cases happen for the `madd`/`zadd` variants.\n",
-    " - `P + Q = ?, where P - Q = Ord2`: The exceptional case for (otherwise complete) RCB formulas."
+    " - `P + Q = ?, where P - Q = Ord2`: The exceptional case for (otherwise complete) RCB formulas.\n",
+    " - `P + garbage = ?` and `garbage + P = ?`:"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 28,
    "id": "d0928c16-9688-4d65-a559-5895d1b7c85b",
    "metadata": {
     "editable": true,
@@ -263,6 +274,8 @@
        "<tr><td>jacobian  </td><td>add-1998-cmo-2</td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-cmo-2</td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-cmo-2</td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1998-cmo-2</td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1998-cmo-2</td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -272,6 +285,8 @@
        "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd-2008-g   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -281,6 +296,8 @@
        "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1998-cmo  </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2001-b    </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2001-b    </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2001-b    </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -290,6 +307,8 @@
        "<tr><td>jacobian  </td><td>add-2001-b    </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2001-b    </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2001-b    </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-2001-b    </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-2001-b    </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd          </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd          </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd          </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -299,6 +318,8 @@
        "<tr><td>jacobian  </td><td>madd          </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd          </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd          </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd          </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd          </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>InftypP    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
@@ -308,6 +329,8 @@
        "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>ZerospP    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>mmadd-2007-bl </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -317,6 +340,8 @@
        "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1986-cc   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>InftypP    </td><td>False     </td><td>False   </td><td>False    </td><td>False      </td></tr>\n",
@@ -326,6 +351,8 @@
        "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>ZerospP    </td><td>Undefined </td><td>False   </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>zadd-2007-m   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -335,6 +362,8 @@
        "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd-2007-bl  </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -344,6 +373,8 @@
        "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-2007-bl   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -353,6 +384,8 @@
        "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>add-1998-hnm  </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -362,6 +395,8 @@
        "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>jacobian  </td><td>madd-2004-hmv </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>InftypP    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
@@ -371,6 +406,8 @@
        "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>ZerospP    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>mmadd-1998-cmo</td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2015-rcb  </td><td>PpP        </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
        "<tr><td>projective</td><td>add-2015-rcb  </td><td>PpInfty    </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
        "<tr><td>projective</td><td>add-2015-rcb  </td><td>InftypP    </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
@@ -380,6 +417,8 @@
        "<tr><td>projective</td><td>add-2015-rcb  </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2015-rcb  </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2015-rcb  </td><td>PpQDifford2</td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>add-2015-rcb  </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>add-2015-rcb  </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo-2</td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo-2</td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo-2</td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -389,6 +428,8 @@
        "<tr><td>projective</td><td>add-1998-cmo-2</td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo-2</td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo-2</td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>projective</td><td>add-1998-cmo-2</td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>add-1998-cmo-2</td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-1998-cmo </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-1998-cmo </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-1998-cmo </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -398,6 +439,8 @@
        "<tr><td>projective</td><td>madd-1998-cmo </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-1998-cmo </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-1998-cmo </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>projective</td><td>madd-1998-cmo </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>madd-1998-cmo </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2002-bj   </td><td>PpP        </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
        "<tr><td>projective</td><td>add-2002-bj   </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2002-bj   </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -407,6 +450,8 @@
        "<tr><td>projective</td><td>add-2002-bj   </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2002-bj   </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2002-bj   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>projective</td><td>add-2002-bj   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>add-2002-bj   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo  </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo  </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo  </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -416,6 +461,8 @@
        "<tr><td>projective</td><td>add-1998-cmo  </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo  </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-1998-cmo  </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>projective</td><td>add-1998-cmo  </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>add-1998-cmo  </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-2015-rcb </td><td>PpP        </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
        "<tr><td>projective</td><td>madd-2015-rcb </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-2015-rcb </td><td>InftypP    </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
@@ -425,6 +472,8 @@
        "<tr><td>projective</td><td>madd-2015-rcb </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-2015-rcb </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>madd-2015-rcb </td><td>PpQDifford2</td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>madd-2015-rcb </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>madd-2015-rcb </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2007-bl   </td><td>PpP        </td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
        "<tr><td>projective</td><td>add-2007-bl   </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2007-bl   </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -434,6 +483,8 @@
        "<tr><td>projective</td><td>add-2007-bl   </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2007-bl   </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>projective</td><td>add-2007-bl   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>projective</td><td>add-2007-bl   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>projective</td><td>add-2007-bl   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>add-2008-s    </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>add-2008-s    </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>add-2008-s    </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -443,6 +494,8 @@
        "<tr><td>xyzz      </td><td>add-2008-s    </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>add-2008-s    </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>add-2008-s    </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>xyzz      </td><td>add-2008-s    </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>xyzz      </td><td>add-2008-s    </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>InftypP    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
@@ -452,6 +505,8 @@
        "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>ZerospP    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>xyzz      </td><td>mmadd-2008-s  </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -461,6 +516,8 @@
        "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>xyzz      </td><td>madd-2008-s   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>madd-2009-bl  </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>madd-2009-bl  </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>madd-2009-bl  </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -470,6 +527,8 @@
        "<tr><td>modified  </td><td>madd-2009-bl  </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>madd-2009-bl  </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>madd-2009-bl  </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>modified  </td><td>madd-2009-bl  </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>modified  </td><td>madd-2009-bl  </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-2009-bl   </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-2009-bl   </td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-2009-bl   </td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -479,6 +538,8 @@
        "<tr><td>modified  </td><td>add-2009-bl   </td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-2009-bl   </td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-2009-bl   </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>modified  </td><td>add-2009-bl   </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>modified  </td><td>add-2009-bl   </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>PpInfty    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>InftypP    </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
@@ -488,6 +549,8 @@
        "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>PpZeros    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>ZerospP    </td><td>Undefined </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>modified  </td><td>add-1998-cmo-2</td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>PpP        </td><td>False     </td><td>True    </td><td>False    </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>PpInfty    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>InftypP    </td><td>False     </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
@@ -497,6 +560,8 @@
        "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>PpZeros    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>ZerospP    </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>PpQDifford2</td><td>True      </td><td>False   </td><td>True     </td><td>True       </td></tr>\n",
+       "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>PpGarbage  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
+       "<tr><td>modified  </td><td>mmadd-2009-bl </td><td>GarbagepP  </td><td>Undefined </td><td>False   </td><td>True     </td><td>False      </td></tr>\n",
        "</tbody>\n",
        "</table>"
       ],
@@ -513,11 +578,12 @@
     "test_filter = None\n",
     "groups = {}\n",
     "clusters = {}\n",
+    "clustering_tests = (\"PpP\", \"PpInfty\", \"InftypP\",\"PpQDifford2\")\n",
     "for coords_name, vals in results_add.items():\n",
     "    for name, formula in vals.items():\n",
     "        ident = set()\n",
     "        for k, v in formula.items():\n",
-    "            if k in (\"PpP\", \"PpInfty\", \"InftypP\",\"PpQDifford2\"):\n",
+    "            if k in clustering_tests:\n",
     "                ident.add((k, v[0])) #, v[1], v[2], v[3]\n",
     "            if test_filter is None or k in test_filter:\n",
     "                item = (v[0], v[1], v[2], v[3])\n",