{"abstract":"Negative coefficients in truncate mode quantize one LSB too high.","category":"Digital signal filters","checks":7,"contract":"Input [coeffs, f, B, mode]: quantize each decimal coefficient to a B-bit two's-complement code with f fractional bits; \"nearest\" rounds half away from zero, \"truncate\" floors. Codes saturate to [-2^(B-1), 2^(B-1)-1]. Return {\"codes\", \"saturated\": count of clipped codes, \"max_error\": max |code/2^f - c| after saturation as a fraction string}.","evaluation_group":"w2-digital_signal_filters-coefficient-quantization","failed_approach":"The attempted repair uses ceil(v) - 1, which is wrong for values already on the grid.","family":"w2-digital_signal_filters-coefficient-quantization-truncation-direction","id":"FA-91601","implementations":{"attempt":{"sha256":"b2e3e7986de598a0734f5a3dbc431c41efc72479a8a3d2c2cdc074987069ac59","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    coeffs, f, B, mode = x\n    scale = 2 ** f\n    hi, lo = 2 ** (B - 1) - 1, -2 ** (B - 1)\n    codes = []\n    sat = 0\n    err = Fraction(0)\n    for s in coeffs:\n        c = Fraction(s)\n        v = c * scale\n        if mode == 'nearest':\n            q = math.floor(abs(v) + Fraction(1, 2)) * (1 if v >= 0 else -1)\n        else:\n            q = math.ceil(v) - 1\n        if q > hi or q < lo:\n            sat += 1\n            q = max(lo, min(hi, q))\n        codes.append(q)\n        err = max(err, abs(Fraction(q, scale) - c))\n    return {'codes': codes, 'saturated': sat, 'max_error': str(err)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['regression: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['control: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['control: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}]], [['regression: random quantize 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}], ['regression: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['control: random quantize 4', [['-1.49', '-1.91'], 2, 3, 'nearest'], {'codes': [-4, -4], 'saturated': 2, 'max_error': '91/100'}]], [['regression: random quantize 11', [['-0.158', '1.311', '1.13', '-0.89'], 6, 8, 'truncate'], {'codes': [-11, 83, 72, -57], 'saturated': 0, 'max_error': '113/8000'}], ['regression: random quantize 14', [['-1.84', '1.735', '0.56', '1.37'], 3, 6, 'truncate'], {'codes': [-15, 13, 4, 10], 'saturated': 0, 'max_error': '3/25'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 5', [['1.92'], 4, 6, 'truncate'], {'codes': [30], 'saturated': 0, 'max_error': '9/200'}], ['control: random quantize 6', [['2.04', '0.49'], 3, 6, 'nearest'], {'codes': [16, 4], 'saturated': 0, 'max_error': '1/25'}], ['control: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}]], [['regression: random quantize 17', [['-0.86'], 2, 5, 'truncate'], {'codes': [-4], 'saturated': 0, 'max_error': '7/50'}], ['regression: random quantize 18', [['0.742', '0.423', '0.231', '-0.3'], 4, 6, 'truncate'], {'codes': [11, 6, 3, -5], 'saturated': 0, 'max_error': '109/2000'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 13', [['0.615'], 3, 4, 'nearest'], {'codes': [5], 'saturated': 0, 'max_error': '1/100'}], ['control: random quantize 16', [['0.334'], 6, 7, 'truncate'], {'codes': [21], 'saturated': 0, 'max_error': '47/8000'}], ['control: random quantize 20', [['-1.201', '-0.66', '-1.739', '-0.86'], 2, 5, 'nearest'], {'codes': [-5, -3, -7, -3], 'saturated': 0, 'max_error': '11/100'}], ['control: random quantize 21', [['1.81'], 6, 7, 'truncate'], {'codes': [63], 'saturated': 1, 'max_error': '1321/1600'}]], [['regression: random quantize 24', [['-1.135', '-1.03'], 4, 7, 'truncate'], {'codes': [-19, -17], 'saturated': 0, 'max_error': '21/400'}], ['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 22', [['-1.31', '1.54', '-0.187'], 5, 7, 'nearest'], {'codes': [-42, 49, -6], 'saturated': 0, 'max_error': '7/800'}], ['control: random quantize 23', [['-0.61', '1.01'], 6, 8, 'nearest'], {'codes': [-39, 65], 'saturated': 0, 'max_error': '9/1600'}], ['control: random quantize 25', [['0.186', '0.87', '-2.12', '1.06'], 6, 9, 'nearest'], {'codes': [12, 56, -136, 68], 'saturated': 0, 'max_error': '1/200'}], ['control: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}]]]\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":"fa7a26492ef8ae2cf398e8d6bc5bfb67dd403e0b43d3b8d3330a26acbdf8db18","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    coeffs, f, B, mode = x\n    scale = 2 ** f\n    hi, lo = 2 ** (B - 1) - 1, -2 ** (B - 1)\n    codes = []\n    sat = 0\n    err = Fraction(0)\n    for s in coeffs:\n        c = Fraction(s)\n        v = c * scale\n        if mode == 'nearest':\n            q = math.floor(abs(v) + Fraction(1, 2)) * (1 if v >= 0 else -1)\n        else:\n            q = int(v)\n        if q > hi or q < lo:\n            sat += 1\n            q = max(lo, min(hi, q))\n        codes.append(q)\n        err = max(err, abs(Fraction(q, scale) - c))\n    return {'codes': codes, 'saturated': sat, 'max_error': str(err)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['regression: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['control: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['control: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}]], [['regression: random quantize 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}], ['regression: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['control: random quantize 4', [['-1.49', '-1.91'], 2, 3, 'nearest'], {'codes': [-4, -4], 'saturated': 2, 'max_error': '91/100'}]], [['regression: random quantize 11', [['-0.158', '1.311', '1.13', '-0.89'], 6, 8, 'truncate'], {'codes': [-11, 83, 72, -57], 'saturated': 0, 'max_error': '113/8000'}], ['regression: random quantize 14', [['-1.84', '1.735', '0.56', '1.37'], 3, 6, 'truncate'], {'codes': [-15, 13, 4, 10], 'saturated': 0, 'max_error': '3/25'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 5', [['1.92'], 4, 6, 'truncate'], {'codes': [30], 'saturated': 0, 'max_error': '9/200'}], ['control: random quantize 6', [['2.04', '0.49'], 3, 6, 'nearest'], {'codes': [16, 4], 'saturated': 0, 'max_error': '1/25'}], ['control: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}]], [['regression: random quantize 17', [['-0.86'], 2, 5, 'truncate'], {'codes': [-4], 'saturated': 0, 'max_error': '7/50'}], ['regression: random quantize 18', [['0.742', '0.423', '0.231', '-0.3'], 4, 6, 'truncate'], {'codes': [11, 6, 3, -5], 'saturated': 0, 'max_error': '109/2000'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 13', [['0.615'], 3, 4, 'nearest'], {'codes': [5], 'saturated': 0, 'max_error': '1/100'}], ['control: random quantize 16', [['0.334'], 6, 7, 'truncate'], {'codes': [21], 'saturated': 0, 'max_error': '47/8000'}], ['control: random quantize 20', [['-1.201', '-0.66', '-1.739', '-0.86'], 2, 5, 'nearest'], {'codes': [-5, -3, -7, -3], 'saturated': 0, 'max_error': '11/100'}], ['control: random quantize 21', [['1.81'], 6, 7, 'truncate'], {'codes': [63], 'saturated': 1, 'max_error': '1321/1600'}]], [['regression: random quantize 24', [['-1.135', '-1.03'], 4, 7, 'truncate'], {'codes': [-19, -17], 'saturated': 0, 'max_error': '21/400'}], ['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 22', [['-1.31', '1.54', '-0.187'], 5, 7, 'nearest'], {'codes': [-42, 49, -6], 'saturated': 0, 'max_error': '7/800'}], ['control: random quantize 23', [['-0.61', '1.01'], 6, 8, 'nearest'], {'codes': [-39, 65], 'saturated': 0, 'max_error': '9/1600'}], ['control: random quantize 25', [['0.186', '0.87', '-2.12', '1.06'], 6, 9, 'nearest'], {'codes': [12, 56, -136, 68], 'saturated': 0, 'max_error': '1/200'}], ['control: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}]]]\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"},"fixed":{"sha256":"a028efcdbfb3bf6463238a15f35d33f8803401137b4b97a2e0591f8fd87d9502","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    coeffs, f, B, mode = x\n    scale = 2 ** f\n    hi, lo = 2 ** (B - 1) - 1, -2 ** (B - 1)\n    codes = []\n    sat = 0\n    err = Fraction(0)\n    for s in coeffs:\n        c = Fraction(s)\n        v = c * scale\n        if mode == 'nearest':\n            q = math.floor(abs(v) + Fraction(1, 2)) * (1 if v >= 0 else -1)\n        else:\n            q = math.floor(v)\n        if q > hi or q < lo:\n            sat += 1\n            q = max(lo, min(hi, q))\n        codes.append(q)\n        err = max(err, abs(Fraction(q, scale) - c))\n    return {'codes': codes, 'saturated': sat, 'max_error': str(err)}\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['regression: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['regression: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['control: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['control: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}]], [['regression: random quantize 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}], ['regression: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['control: random quantize 4', [['-1.49', '-1.91'], 2, 3, 'nearest'], {'codes': [-4, -4], 'saturated': 2, 'max_error': '91/100'}]], [['regression: random quantize 11', [['-0.158', '1.311', '1.13', '-0.89'], 6, 8, 'truncate'], {'codes': [-11, 83, 72, -57], 'saturated': 0, 'max_error': '113/8000'}], ['regression: random quantize 14', [['-1.84', '1.735', '0.56', '1.37'], 3, 6, 'truncate'], {'codes': [-15, 13, 4, 10], 'saturated': 0, 'max_error': '3/25'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 5', [['1.92'], 4, 6, 'truncate'], {'codes': [30], 'saturated': 0, 'max_error': '9/200'}], ['control: random quantize 6', [['2.04', '0.49'], 3, 6, 'nearest'], {'codes': [16, 4], 'saturated': 0, 'max_error': '1/25'}], ['control: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}]], [['regression: random quantize 17', [['-0.86'], 2, 5, 'truncate'], {'codes': [-4], 'saturated': 0, 'max_error': '7/50'}], ['regression: random quantize 18', [['0.742', '0.423', '0.231', '-0.3'], 4, 6, 'truncate'], {'codes': [11, 6, 3, -5], 'saturated': 0, 'max_error': '109/2000'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 13', [['0.615'], 3, 4, 'nearest'], {'codes': [5], 'saturated': 0, 'max_error': '1/100'}], ['control: random quantize 16', [['0.334'], 6, 7, 'truncate'], {'codes': [21], 'saturated': 0, 'max_error': '47/8000'}], ['control: random quantize 20', [['-1.201', '-0.66', '-1.739', '-0.86'], 2, 5, 'nearest'], {'codes': [-5, -3, -7, -3], 'saturated': 0, 'max_error': '11/100'}], ['control: random quantize 21', [['1.81'], 6, 7, 'truncate'], {'codes': [63], 'saturated': 1, 'max_error': '1321/1600'}]], [['regression: random quantize 24', [['-1.135', '-1.03'], 4, 7, 'truncate'], {'codes': [-19, -17], 'saturated': 0, 'max_error': '21/400'}], ['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['repair check: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 22', [['-1.31', '1.54', '-0.187'], 5, 7, 'nearest'], {'codes': [-42, 49, -6], 'saturated': 0, 'max_error': '7/800'}], ['control: random quantize 23', [['-0.61', '1.01'], 6, 8, 'nearest'], {'codes': [-39, 65], 'saturated': 0, 'max_error': '9/1600'}], ['control: random quantize 25', [['0.186', '0.87', '-2.12', '1.06'], 6, 9, 'nearest'], {'codes': [12, 56, -136, 68], 'saturated': 0, 'max_error': '1/200'}], ['control: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}]]]\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 with a stipulated toy contract; exact rational arithmetic or fixed-decimal rounding keeps outputs strict JSON. It is not a production DSP library and claims no standards conformance. 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-digital_signal_filters-coefficient-quantization-truncation-direction","generated_at":"2026-09-29T14:51:37.551260+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Coefficient quantization decides whether a fixed-point filter still meets spec; rounding and saturation slips shift poles.","repair":"Use floor for two's-complement truncation.","root_cause":"Truncation uses int(), which rounds toward zero, instead of floor.","sha256":"b74af35eaaac3e9c16541faee36cf4910b18f859d30d0712a57da1c29f26ac49","title":"Coefficient quantizer truncates toward zero · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.878,"exit_code":1,"observations":[{"actual":{"codes":[-3,2],"max_error":"3/40","saturated":0},"check":"regression: negative truncate","expected":{"codes":[-3,2],"max_error":"3/40","saturated":0},"passed":true},{"actual":{"codes":[-15,12],"max_error":"9/100","saturated":0},"check":"regression: random quantize 0","expected":{"codes":[-15,12],"max_error":"9/100","saturated":0},"passed":true},{"actual":{"codes":[1,-2,2],"max_error":"1/4","saturated":0},"check":"repair check: exact grid truncate","expected":{"codes":[2,-1,3],"max_error":"0","saturated":0},"passed":false},{"actual":{"codes":[1,2,-1],"max_error":"1/8","saturated":0},"check":"control: tie cases nearest","expected":{"codes":[1,2,-1],"max_error":"1/8","saturated":0},"passed":true},{"actual":{"codes":[127,127],"max_error":"1/128","saturated":1},"check":"control: positive 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