{"abstract":"Multiplying two negative numbers saturates to -32768 instead of 32767.","category":"PLC ladder logic scan cycles","checks":8,"contract":"16-bit INT math rung followed by a later fault-clearing rung, one op per scan; ops is a list of [a, b, ADD|SUB|MUL, clear]. A result outside -32768..32767 sets the overflow bit V for that instruction and the overflow trap; the stored result is saturated to 32767/-32768 when clamp is set or wrapped as 16-bit two's complement otherwise. V is recomputed per instruction. The later rung clears the trap when clear is true; a trap still set at end of scan halts the processor. Return [result, V, trap] per scan, then \"halted\" and stop if faulted.","contract_signature":"clamp, ops","evaluation_group":"w2-plc-ladder-logic-scan-cycles-int-math-overflow-trap","failed_approach":"Using the result sign but clamping negatives to -32767 misses the true minimum.","family":"w2-plc-ladder-logic-scan-cycles-int-math-overflow-trap-clamp-sign","id":"FA-92326","implementations":{"attempt":{"sha256":"56f69cdf10e2f042b83a4c51615eb708614a8284c518811c4916980074aa01fa","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(clamp, ops):\n    trap = False\n    out = []\n    for a, b, op, clear in ops:\n        if op == 'ADD':\n            r = a + b\n        elif op == 'SUB':\n            r = a - b\n        else:\n            r = a * b\n        v = not (-32768 <= r <= 32767)\n        if v:\n            trap = True\n            if clamp:\n                r = 32767 if r > 0 else -32767\n            else:\n                r = (r + 32768) % 65536 - 32768\n        if clear:\n            trap = False\n        out.append([r, v, trap])\n        if trap:\n            out.append('halted')\n            break\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['regression: scenario 8',\n   [True,\n    [[-30000, -256, 'MUL', True],\n     [-1, 17551, 'ADD', True],\n     [-200, 22315, 'MUL', False],\n     [-30000, 30000, 'ADD', True]]],\n   [[32767, True, False], [17550, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[-32768, -20192, 'SUB', True],\n     [12968, -30310, 'ADD', False],\n     [-31305, 2, 'SUB', False],\n     [11091, 200, 'MUL', True],\n     [10310, 200, 'SUB', False]]],\n   [[-12576, False, False],\n    [-17342, False, False],\n    [-31307, False, False],\n    [-10024, True, False],\n    [10110, False, False]]],\n  ['control: scenario 2',\n   [True,\n    [[27834, -6307, 'SUB', False],\n     [30000, -15473, 'SUB', False],\n     [-1, 1, 'MUL', False],\n     [-30000, -4507, 'SUB', True],\n     [-21177, 21481, 'MUL', False],\n     [31159, 1, 'SUB', False]]],\n   [[32767, True, True], 'halted']],\n  ['control: scenario 3',\n   [False,\n    [[18788, 200, 'SUB', True],\n     [20369, -23104, 'MUL', False],\n     [-32768, 10449, 'ADD', False],\n     [-17550, 18799, 'ADD', False],\n     [1, 32767, 'MUL', False]]],\n   [[18588, False, False], [8640, True, True], 'halted']]],\n [['regression: scenario 2',\n   [True,\n    [[-1048, 30000, 'ADD', False],\n     [2, -13120, 'SUB', False],\n     [29306, -32768, 'SUB', True],\n     [-9919, -24931, 'MUL', True]]],\n   [[28952, False, False], [13122, False, False], [32767, True, False], [32767, True, False]]],\n  ['regression: scenario 5',\n   [True,\n    [[32767, -13835, 'MUL', True],\n     [2, -30000, 'SUB', False],\n     [9813, -200, 'SUB', False],\n     [-9454, -19431, 'ADD', True],\n     [26200, 2, 'MUL', False],\n     [2, -30000, 'SUB', True],\n     [-13629, -30000, 'MUL', True]]],\n   [[-32768, True, False],\n    [30002, False, False],\n    [10013, False, False],\n    [-28885, False, False],\n    [32767, True, True],\n    'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[-15041, -14459, 'SUB', False],\n     [13071, -30000, 'ADD', True],\n     [-17526, -1, 'MUL', True],\n     [-30000, 200, 'MUL', False]]],\n   [[-582, False, False], [-16929, False, False], [17526, False, False], [29312, True, True], 'halted']],\n  ['control: scenario 3',\n   [False,\n    [[-10436, -32034, 'MUL', True],\n     [2, 22108, 'SUB', False],\n     [7659, 2, 'MUL', False],\n     [5339, 1, 'MUL', False]]],\n   [[7688, True, False], [-22106, False, False], [15318, False, False], [5339, False, False]]]],\n [['regression: scenario 9',\n   [True,\n    [[-10100, 19610, 'ADD', True],\n     [-32768, -106, 'MUL', False],\n     [-15096, 200, 'SUB', False],\n     [3930, 7872, 'ADD', False],\n     [1, -15393, 'MUL', True],\n     [-27515, -200, 'MUL', True],\n     [32767, 9291, 'SUB', True]]],\n   [[9510, False, False], [32767, True, True], 'halted']],\n  ['regression: scenario 13',\n   [True,\n    [[200, -10922, 'SUB', True],\n     [-1, -20952, 'SUB', True],\n     [-200, -3607, 'ADD', True],\n     [-32768, -19464, 'ADD', False],\n     [1, -200, 'ADD', False],\n     [30000, 1, 'SUB', True],\n     [32767, 32767, 'MUL', True],\n     [19302, 22544, 'SUB', True]]],\n   [[11122, False, False], [20951, False, False], [-3807, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[15094, -24454, 'MUL', False],\n     [-30000, 24363, 'MUL', True],\n     [2, -14871, 'MUL', False],\n     [1, -26550, 'MUL', True],\n     [-1, -7090, 'SUB', False],\n     [32767, 1, 'MUL', True],\n     [-32768, 15967, 'ADD', False],\n     [21457, -28729, 'SUB', True]]],\n   [[-9924, True, True], 'halted']],\n  ['control: scenario 2',\n   [False,\n    [[-200, -200, 'ADD', True],\n     [32767, 200, 'MUL', False],\n     [-9390, 1, 'MUL', False],\n     [-11169, -28064, 'ADD', True],\n     [22720, -1, 'ADD', False],\n     [-200, -1, 'ADD', False],\n     [-12859, 1, 'ADD', True]]],\n   [[-400, False, False], [-200, True, True], 'halted']]],\n [['regression: scenario 31',\n   [True,\n    [[-2900, -200, 'MUL', True],\n     [23750, 200, 'SUB', False],\n     [200, -31152, 'MUL', True],\n     [30000, -32768, 'SUB', True]]],\n   [[32767, True, False], [23550, False, False], [-32768, True, False], [32767, True, False]]],\n  ['regression: scenario 9',\n   [True,\n    [[10861, -200, 'SUB', False],\n     [2, 6241, 'ADD', True],\n     [30000, 1, 'ADD', True],\n     [-20637, -27040, 'ADD', False],\n     [14992, -200, 'ADD', True],\n     [30305, -32768, 'MUL', False]]],\n   [[11061, False, False], [6243, False, False], [30001, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[-26759, 2, 'SUB', True],\n     [-30000, -32768, 'SUB', False],\n     [-3730, -31438, 'ADD', False],\n     [200, 200, 'SUB', True],\n     [-24761, 200, 'SUB', True],\n     [-20747, 200, 'SUB', False],\n     [200, 19789, 'SUB', True]]],\n   [[-26761, False, False], [2768, False, False], [30368, True, True], 'halted']],\n  ['control: scenario 2',\n   [False,\n    [[30000, -32768, 'ADD', True],\n     [4451, 31437, 'SUB', False],\n     [-1, 22093, 'MUL', False],\n     [-30000, -18488, 'SUB', False],\n     [30000, -28921, 'MUL', True],\n     [-200, 23349, 'ADD', True],\n     [-32768, 200, 'SUB', False]]],\n   [[-2768, False, False],\n    [-26986, False, False],\n    [-22093, False, False],\n    [-11512, False, False],\n    [1104, True, False],\n    [23149, False, False],\n    [32568, True, True],\n    'halted']]],\n [['regression: scenario 14',\n   [True,\n    [[200, 2, 'SUB', True],\n     [30382, 5446, 'ADD', True],\n     [-200, 30000, 'SUB', False],\n     [-19301, -200, 'MUL', True],\n     [1112, 32767, 'ADD', True],\n     [1, 21509, 'SUB', False],\n     [-32768, 28969, 'ADD', True]]],\n   [[198, False, False],\n    [32767, True, False],\n    [-30200, False, False],\n    [32767, True, False],\n    [32767, True, False],\n    [-21508, False, False],\n    [-3799, False, False]]],\n  ['regression: scenario 15',\n   [True,\n    [[30398, 26515, 'SUB', True],\n     [-32768, -3816, 'ADD', False],\n     [23577, -13673, 'SUB', False],\n     [-22301, -32768, 'SUB', True],\n     [30000, -200, 'MUL', True],\n     [-28303, 30000, 'SUB', True],\n     [-29315, -30000, 'SUB', True]]],\n   [[3883, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [True,\n    [[160, 2, 'SUB', True], [200, 200, 'SUB', True], [222, 200, 'SUB', False], [200, -32768, 'ADD', True]]],\n   [[158, False, False], [0, False, False], [22, False, False], [-32568, False, False]]],\n  ['regression: scenario 2',\n   [True,\n    [[30000, 1574, 'SUB', True],\n     [-783, -29319, 'SUB', True],\n     [2, 1803, 'SUB', False],\n     [200, 2, 'ADD', True],\n     [9942, 32767, 'MUL', True],\n     [-30000, -19084, 'MUL', True],\n     [-10106, -30460, 'ADD', False],\n     [2, 32767, 'ADD', True]]],\n   [[28426, False, False],\n    [28536, False, False],\n    [-1801, False, False],\n    [202, False, False],\n    [32767, True, False],\n    [32767, True, False],\n    [-32768, True, True],\n    'halted']]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"a0933727706f134031fbcb26db34495b491dc350b5d1c74798d26e7d4c583e83","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(clamp, ops):\n    trap = False\n    out = []\n    for a, b, op, clear in ops:\n        if op == 'ADD':\n            r = a + b\n        elif op == 'SUB':\n            r = a - b\n        else:\n            r = a * b\n        v = not (-32768 <= r <= 32767)\n        if v:\n            trap = True\n            if clamp:\n                r = 32767 if a > 0 else -32768\n            else:\n                r = (r + 32768) % 65536 - 32768\n        if clear:\n            trap = False\n        out.append([r, v, trap])\n        if trap:\n            out.append('halted')\n            break\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['regression: scenario 8',\n   [True,\n    [[-30000, -256, 'MUL', True],\n     [-1, 17551, 'ADD', True],\n     [-200, 22315, 'MUL', False],\n     [-30000, 30000, 'ADD', True]]],\n   [[32767, True, False], [17550, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[-32768, -20192, 'SUB', True],\n     [12968, -30310, 'ADD', False],\n     [-31305, 2, 'SUB', False],\n     [11091, 200, 'MUL', True],\n     [10310, 200, 'SUB', False]]],\n   [[-12576, False, False],\n    [-17342, False, False],\n    [-31307, False, False],\n    [-10024, True, False],\n    [10110, False, False]]],\n  ['control: scenario 2',\n   [True,\n    [[27834, -6307, 'SUB', False],\n     [30000, -15473, 'SUB', False],\n     [-1, 1, 'MUL', False],\n     [-30000, -4507, 'SUB', True],\n     [-21177, 21481, 'MUL', False],\n     [31159, 1, 'SUB', False]]],\n   [[32767, True, True], 'halted']],\n  ['control: scenario 3',\n   [False,\n    [[18788, 200, 'SUB', True],\n     [20369, -23104, 'MUL', False],\n     [-32768, 10449, 'ADD', False],\n     [-17550, 18799, 'ADD', False],\n     [1, 32767, 'MUL', False]]],\n   [[18588, False, False], [8640, True, True], 'halted']]],\n [['regression: scenario 2',\n   [True,\n    [[-1048, 30000, 'ADD', False],\n     [2, -13120, 'SUB', False],\n     [29306, -32768, 'SUB', True],\n     [-9919, -24931, 'MUL', True]]],\n   [[28952, False, False], [13122, False, False], [32767, True, False], [32767, True, False]]],\n  ['regression: scenario 5',\n   [True,\n    [[32767, -13835, 'MUL', True],\n     [2, -30000, 'SUB', False],\n     [9813, -200, 'SUB', False],\n     [-9454, -19431, 'ADD', True],\n     [26200, 2, 'MUL', False],\n     [2, -30000, 'SUB', True],\n     [-13629, -30000, 'MUL', True]]],\n   [[-32768, True, False],\n    [30002, False, False],\n    [10013, False, False],\n    [-28885, False, False],\n    [32767, True, True],\n    'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[-15041, -14459, 'SUB', False],\n     [13071, -30000, 'ADD', True],\n     [-17526, -1, 'MUL', True],\n     [-30000, 200, 'MUL', False]]],\n   [[-582, False, False], [-16929, False, False], [17526, False, False], [29312, True, True], 'halted']],\n  ['control: scenario 3',\n   [False,\n    [[-10436, -32034, 'MUL', True],\n     [2, 22108, 'SUB', False],\n     [7659, 2, 'MUL', False],\n     [5339, 1, 'MUL', False]]],\n   [[7688, True, False], [-22106, False, False], [15318, False, False], [5339, False, False]]]],\n [['regression: scenario 9',\n   [True,\n    [[-10100, 19610, 'ADD', True],\n     [-32768, -106, 'MUL', False],\n     [-15096, 200, 'SUB', False],\n     [3930, 7872, 'ADD', False],\n     [1, -15393, 'MUL', True],\n     [-27515, -200, 'MUL', True],\n     [32767, 9291, 'SUB', True]]],\n   [[9510, False, False], [32767, True, True], 'halted']],\n  ['regression: scenario 13',\n   [True,\n    [[200, -10922, 'SUB', True],\n     [-1, -20952, 'SUB', True],\n     [-200, -3607, 'ADD', True],\n     [-32768, -19464, 'ADD', False],\n     [1, -200, 'ADD', False],\n     [30000, 1, 'SUB', True],\n     [32767, 32767, 'MUL', True],\n     [19302, 22544, 'SUB', True]]],\n   [[11122, False, False], [20951, False, False], [-3807, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[15094, -24454, 'MUL', False],\n     [-30000, 24363, 'MUL', True],\n     [2, -14871, 'MUL', False],\n     [1, -26550, 'MUL', True],\n     [-1, -7090, 'SUB', False],\n     [32767, 1, 'MUL', True],\n     [-32768, 15967, 'ADD', False],\n     [21457, -28729, 'SUB', True]]],\n   [[-9924, True, True], 'halted']],\n  ['control: scenario 2',\n   [False,\n    [[-200, -200, 'ADD', True],\n     [32767, 200, 'MUL', False],\n     [-9390, 1, 'MUL', False],\n     [-11169, -28064, 'ADD', True],\n     [22720, -1, 'ADD', False],\n     [-200, -1, 'ADD', False],\n     [-12859, 1, 'ADD', True]]],\n   [[-400, False, False], [-200, True, True], 'halted']]],\n [['regression: scenario 31',\n   [True,\n    [[-2900, -200, 'MUL', True],\n     [23750, 200, 'SUB', False],\n     [200, -31152, 'MUL', True],\n     [30000, -32768, 'SUB', True]]],\n   [[32767, True, False], [23550, False, False], [-32768, True, False], [32767, True, False]]],\n  ['regression: scenario 9',\n   [True,\n    [[10861, -200, 'SUB', False],\n     [2, 6241, 'ADD', True],\n     [30000, 1, 'ADD', True],\n     [-20637, -27040, 'ADD', False],\n     [14992, -200, 'ADD', True],\n     [30305, -32768, 'MUL', False]]],\n   [[11061, False, False], [6243, False, False], [30001, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [False,\n    [[-26759, 2, 'SUB', True],\n     [-30000, -32768, 'SUB', False],\n     [-3730, -31438, 'ADD', False],\n     [200, 200, 'SUB', True],\n     [-24761, 200, 'SUB', True],\n     [-20747, 200, 'SUB', False],\n     [200, 19789, 'SUB', True]]],\n   [[-26761, False, False], [2768, False, False], [30368, True, True], 'halted']],\n  ['control: scenario 2',\n   [False,\n    [[30000, -32768, 'ADD', True],\n     [4451, 31437, 'SUB', False],\n     [-1, 22093, 'MUL', False],\n     [-30000, -18488, 'SUB', False],\n     [30000, -28921, 'MUL', True],\n     [-200, 23349, 'ADD', True],\n     [-32768, 200, 'SUB', False]]],\n   [[-2768, False, False],\n    [-26986, False, False],\n    [-22093, False, False],\n    [-11512, False, False],\n    [1104, True, False],\n    [23149, False, False],\n    [32568, True, True],\n    'halted']]],\n [['regression: scenario 14',\n   [True,\n    [[200, 2, 'SUB', True],\n     [30382, 5446, 'ADD', True],\n     [-200, 30000, 'SUB', False],\n     [-19301, -200, 'MUL', True],\n     [1112, 32767, 'ADD', True],\n     [1, 21509, 'SUB', False],\n     [-32768, 28969, 'ADD', True]]],\n   [[198, False, False],\n    [32767, True, False],\n    [-30200, False, False],\n    [32767, True, False],\n    [32767, True, False],\n    [-21508, False, False],\n    [-3799, False, False]]],\n  ['regression: scenario 15',\n   [True,\n    [[30398, 26515, 'SUB', True],\n     [-32768, -3816, 'ADD', False],\n     [23577, -13673, 'SUB', False],\n     [-22301, -32768, 'SUB', True],\n     [30000, -200, 'MUL', True],\n     [-28303, 30000, 'SUB', True],\n     [-29315, -30000, 'SUB', True]]],\n   [[3883, False, False], [-32768, True, True], 'halted']],\n  ['control: wrap with cleared traps',\n   [False,\n    [[30000, 5000, 'ADD', True],\n     [-30000, 5000, 'SUB', True],\n     [200, 200, 'MUL', False],\n     [1, 1, 'ADD', False]]],\n   [[-30536, True, False], [30536, True, False], [-25536, True, True], 'halted']],\n  ['regression: saturation both signs',\n   [True,\n    [[-2, -20000, 'MUL', True],\n     [-20000, 20000, 'SUB', True],\n     [32767, 0, 'ADD', False],\n     [1, 1, 'ADD', False]]],\n   [[32767, True, False], [-32768, True, False], [32767, False, False], [2, False, False]]],\n  ['control: exact limits',\n   [False, [[-32767, 1, 'SUB', False], [32766, 1, 'ADD', False], [3, 4, 'MUL', False]]],\n   [[-32768, False, False], [32767, False, False], [12, False, False]]],\n  ['control: overflow then clean ops',\n   [True, [[32767, 1, 'ADD', True], [5, 5, 'ADD', False], [7, 7, 'SUB', False]]],\n   [[32767, True, False], [10, False, False], [0, False, False]]],\n  ['control: scenario 1',\n   [True,\n    [[160, 2, 'SUB', True], [200, 200, 'SUB', True], [222, 200, 'SUB', False], [200, -32768, 'ADD', True]]],\n   [[158, False, False], [0, False, False], [22, False, False], [-32568, False, False]]],\n  ['regression: scenario 2',\n   [True,\n    [[30000, 1574, 'SUB', True],\n     [-783, -29319, 'SUB', True],\n     [2, 1803, 'SUB', False],\n     [200, 2, 'ADD', True],\n     [9942, 32767, 'MUL', True],\n     [-30000, -19084, 'MUL', True],\n     [-10106, -30460, 'ADD', False],\n     [2, 32767, 'ADD', True]]],\n   [[28426, False, False],\n    [28536, False, False],\n    [-1801, False, False],\n    [202, False, False],\n    [32767, True, False],\n    [32767, True, False],\n    [-32768, True, True],\n    'halted']]]]\nfor label, args, expected in fixtures[N-1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"A deterministic bounded teaching model of one PLC instruction or rung pattern evaluated scan by scan. The stated contract is a stipulated toy convention, not a claim of conformance to any vendor controller or IEC 61131-3 runtime. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-plc-ladder-logic-scan-cycles-int-math-overflow-trap-clamp-sign","generated_at":"2026-09-29T14:51:44.560399+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Ladder programs are executed as repeated scans; each defect here changes what a rung, timer, counter or data-table instruction reports on a particular scan, which is how commissioning and field faults are actually observed.","root_cause":"The clamp chooses the limit from the sign of operand a rather than the true result.","sha256":"43b1c693eb24d8b248225bbf8c8ba28a017bb5d4b06900500ca1c81db69977d1","title":"INT saturation direction follows the first operand · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":40.612,"exit_code":1,"observations":[{"actual":[[32767,true,false],[-32767,true,false],[32767,false,false],[2,false,false]],"check":"regression: saturation both signs","expected":[[32767,true,false],[-32768,true,false],[32767,false,false],[2,false,false]],"passed":false},{"actual":[[32767,true,false],[17550,false,false],[-32767,true,true],"halted"],"check":"regression: scenario 8","expected":[[32767,true,false],[17550,false,false],[-32768,true,true],"halted"],"passed":false},{"actual":[[-30536,true,false],[30536,true,false],[-25536,true,true],"halted"],"check":"control: wrap with cleared traps","expected":[[-30536,true,false],[30536,true,false],[-25536,true,true],"halted"],"passed":true},{"actual":[[-32768,false,false],[32767,false,false],[12,false,false]],"check":"control: exact limits","expected":[[-32768,false,false],[32767,false,false],[12,false,false]],"passed":true},{"actual":[[32767,true,false],[10,false,false],[0,false,false]],"check":"control: overflow then clean ops","expected":[[32767,true,false],[10,false,false],[0,false,false]],"passed":true},{"actual":[[-12576,false,false],[-17342,false,false],[-31307,false,false],[-10024,true,false],[10110,false,false]],"check":"control: scenario 1","expected":[[-12576,false,false],[-17342,false,false],[-31307,false,false],[-10024,true,false],[10110,false,false]],"passed":true},{"actual":[[32767,true,true],"halted"],"check":"control: scenario 2","expected":[[32767,true,true],"halted"],"passed":true},{"actual":[[18588,false,false],[8640,true,true],"halted"],"check":"control: scenario 3","expected":[[18588,false,false],[8640,true,true],"halted"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: saturation both signs\", \"actual\": [[32767, true, false], [-32767, true, false], [32767, false, false], [2, false, false]], \"expected\": [[32767, true, false], [-32768, true, false], [32767, false, false], [2, false, false]], \"passed\": false}, {\"check\": \"regression: scenario 8\", \"actual\": [[32767, true, false], [17550, false, false], [-32767, true, true], \"halted\"], \"expected\": [[32767, true, false], [17550, false, false], [-32768, true, true], \"halted\"], \"passed\": false}, {\"check\": \"control: wrap with cleared traps\", \"actual\": [[-30536, true, false], [30536, true, false], [-25536, true, true], \"halted\"], \"expected\": [[-30536, true, false], [30536, true, false], [-25536, true, true], \"halted\"], \"passed\": true}, {\"check\": \"control: exact limits\", \"actual\": [[-32768, false, false], [32767, false, false], [12, false, false]], \"expected\": [[-32768, false, false], [32767, false, false], [12, false, false]], \"passed\": true}, {\"check\": \"control: overflow then clean ops\", \"actual\": [[32767, true, false], [10, false, false], [0, false, false]], \"expected\": [[32767, true, false], [10, false, false], [0, false, false]], \"passed\": true}, {\"check\": \"control: scenario 1\", \"actual\": [[-12576, false, false], [-17342, false, false], [-31307, false, false], [-10024, true, false], [10110, false, false]], \"expected\": [[-12576, false, false], [-17342, false, false], [-31307, false, false], [-10024, true, false], [10110, false, false]], \"passed\": true}, {\"check\": \"control: scenario 2\", \"actual\": [[32767, true, true], \"halted\"], \"expected\": [[32767, true, true], \"halted\"], \"passed\": true}, {\"check\": \"control: scenario 3\", \"actual\": [[18588, false, false], [8640, true, true], \"halted\"], \"expected\": [[18588, false, false], [8640, true, true], \"halted\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.102,"exit_code":1,"observations":[{"actual":[[-32768,true,false],[-32768,true,false],[32767,false,false],[2,false,false]],"check":"regression: saturation both signs","expected":[[32767,true,false],[-32768,true,false],[32767,false,false],[2,false,false]],"passed":false},{"actual":[[-32768,true,false],[17550,false,false],[-32768,true,true],"halted"],"check":"regression: scenario 8","expected":[[32767,true,false],[17550,false,false],[-32768,true,true],"halted"],"passed":false},{"actual":[[-30536,true,false],[30536,true,false],[-25536,true,true],"halted"],"check":"control: wrap with cleared traps","expected":[[-30536,true,false],[30536,true,false],[-25536,true,true],"halted"],"passed":true},{"actual":[[-32768,false,false],[32767,false,false],[12,false,false]],"check":"control: exact limits","expected":[[-32768,false,false],[32767,false,false],[12,false,false]],"passed":true},{"actual":[[32767,true,false],[10,false,false],[0,false,false]],"check":"control: overflow then clean ops","expected":[[32767,true,false],[10,false,false],[0,false,false]],"passed":true},{"actual":[[-12576,false,false],[-17342,false,false],[-31307,false,false],[-10024,true,false],[10110,false,false]],"check":"control: scenario 1","expected":[[-12576,false,false],[-17342,false,false],[-31307,false,false],[-10024,true,false],[10110,false,false]],"passed":true},{"actual":[[32767,true,true],"halted"],"check":"control: scenario 2","expected":[[32767,true,true],"halted"],"passed":true},{"actual":[[18588,false,false],[8640,true,true],"halted"],"check":"control: scenario 3","expected":[[18588,false,false],[8640,true,true],"halted"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression: saturation both signs\", \"actual\": [[-32768, true, false], [-32768, true, false], [32767, false, false], [2, false, false]], \"expected\": [[32767, true, false], [-32768, true, false], [32767, false, false], [2, false, false]], \"passed\": false}, {\"check\": \"regression: scenario 8\", \"actual\": [[-32768, true, false], [17550, false, false], [-32768, true, true], \"halted\"], \"expected\": [[32767, true, false], [17550, false, false], [-32768, true, true], \"halted\"], \"passed\": false}, {\"check\": \"control: wrap with cleared traps\", \"actual\": [[-30536, true, false], [30536, true, false], [-25536, true, true], \"halted\"], \"expected\": [[-30536, true, false], [30536, true, false], [-25536, true, true], \"halted\"], \"passed\": true}, {\"check\": \"control: exact limits\", \"actual\": [[-32768, false, false], [32767, false, false], [12, false, false]], \"expected\": [[-32768, false, false], [32767, false, false], [12, false, false]], \"passed\": true}, {\"check\": \"control: overflow then clean ops\", \"actual\": [[32767, true, false], [10, false, false], [0, false, false]], \"expected\": [[32767, true, false], [10, false, false], [0, false, false]], \"passed\": true}, {\"check\": \"control: scenario 1\", \"actual\": [[-12576, false, false], [-17342, false, false], [-31307, false, false], [-10024, true, false], [10110, false, false]], \"expected\": [[-12576, false, false], [-17342, false, false], [-31307, false, false], [-10024, true, false], [10110, false, false]], \"passed\": true}, {\"check\": \"control: scenario 2\", \"actual\": [[32767, true, true], \"halted\"], \"expected\": [[32767, true, true], \"halted\"], \"passed\": true}, {\"check\": \"control: scenario 3\", \"actual\": [[18588, false, false], [8640, true, true], \"halted\"], \"expected\": [[18588, false, false], [8640, true, true], \"halted\"], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}