{"abstract":"A coefficient that quantizes exactly to the most negative code is reported as saturated.","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 counts only positive overflow.","family":"w2-digital_signal_filters-coefficient-quantization-saturation-counting","id":"FA-91611","implementations":{"attempt":{"sha256":"b1e7acceb64c27cf2603badea0bb1b99ba179e6aca3197051a34224b9e0c93fe","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:\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: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['regression: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['repair check: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}], ['control: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}]], [['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['regression: random quantize 44', [['0.844', '-1.78', '0.304', '0.84'], 2, 3, 'nearest'], {'codes': [3, -4, 1, 3], 'saturated': 1, 'max_error': '39/50'}], ['repair check: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: integer multiple truncate', [['-0.5', '1.25'], 3, 6, 'truncate'], {'codes': [-4, 10], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['control: random quantize 1', [['-1.919', '-2.19', '0.764', '-2.046'], 4, 7, 'truncate'], {'codes': [-31, -36, 12, -33], 'saturated': 0, 'max_error': '3/50'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}]], [['regression: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['regression: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}], ['repair check: random quantize 15', [['-1.005', '-0.11', '-0.221', '-0.679'], 6, 7, 'truncate'], {'codes': [-64, -8, -15, -44], 'saturated': 1, 'max_error': '3/200'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['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 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}]], [['regression: random quantize 44', [['0.844', '-1.78', '0.304', '0.84'], 2, 3, 'nearest'], {'codes': [3, -4, 1, 3], 'saturated': 1, 'max_error': '39/50'}], ['regression: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['repair check: random quantize 32', [['-1.79', '-1.633', '-0.38'], 3, 4, 'nearest'], {'codes': [-8, -8, -3], 'saturated': 2, 'max_error': '79/100'}], ['control: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['control: 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'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}], ['control: random quantize 13', [['0.615'], 3, 4, 'nearest'], {'codes': [5], 'saturated': 0, 'max_error': '1/100'}]], [['regression: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}], ['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['repair check: random quantize 37', [['-1.95', '-1.54', '0.854'], 6, 7, 'truncate'], {'codes': [-64, -64, 54], 'saturated': 2, 'max_error': '19/20'}], ['control: 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'}], ['control: random quantize 16', [['0.334'], 6, 7, 'truncate'], {'codes': [21], 'saturated': 0, 'max_error': '47/8000'}], ['control: random quantize 17', [['-0.86'], 2, 5, 'truncate'], {'codes': [-4], 'saturated': 0, 'max_error': '7/50'}], ['control: 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'}]]]\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":"1409e72da9473390945cc8c510ef5d7245b7d5e8a5f7c7c632cb9b4cf0588501","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: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['regression: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['repair check: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}], ['control: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}]], [['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['regression: random quantize 44', [['0.844', '-1.78', '0.304', '0.84'], 2, 3, 'nearest'], {'codes': [3, -4, 1, 3], 'saturated': 1, 'max_error': '39/50'}], ['repair check: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: integer multiple truncate', [['-0.5', '1.25'], 3, 6, 'truncate'], {'codes': [-4, 10], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['control: random quantize 1', [['-1.919', '-2.19', '0.764', '-2.046'], 4, 7, 'truncate'], {'codes': [-31, -36, 12, -33], 'saturated': 0, 'max_error': '3/50'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}]], [['regression: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['regression: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}], ['repair check: random quantize 15', [['-1.005', '-0.11', '-0.221', '-0.679'], 6, 7, 'truncate'], {'codes': [-64, -8, -15, -44], 'saturated': 1, 'max_error': '3/200'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['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 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}]], [['regression: random quantize 44', [['0.844', '-1.78', '0.304', '0.84'], 2, 3, 'nearest'], {'codes': [3, -4, 1, 3], 'saturated': 1, 'max_error': '39/50'}], ['regression: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['repair check: random quantize 32', [['-1.79', '-1.633', '-0.38'], 3, 4, 'nearest'], {'codes': [-8, -8, -3], 'saturated': 2, 'max_error': '79/100'}], ['control: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['control: 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'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}], ['control: random quantize 13', [['0.615'], 3, 4, 'nearest'], {'codes': [5], 'saturated': 0, 'max_error': '1/100'}]], [['regression: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}], ['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['repair check: random quantize 37', [['-1.95', '-1.54', '0.854'], 6, 7, 'truncate'], {'codes': [-64, -64, 54], 'saturated': 2, 'max_error': '19/20'}], ['control: 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'}], ['control: random quantize 16', [['0.334'], 6, 7, 'truncate'], {'codes': [21], 'saturated': 0, 'max_error': '47/8000'}], ['control: random quantize 17', [['-0.86'], 2, 5, 'truncate'], {'codes': [-4], 'saturated': 0, 'max_error': '7/50'}], ['control: 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'}]]]\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":"656354c50b345fe0b7bb651098fa1891e5ded255763947761cc0cd3888b1f2bc","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: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['regression: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['repair check: negative overflow', [['-1.5'], 7, 8, 'truncate'], {'codes': [-128], 'saturated': 1, 'max_error': '1/2'}], ['control: tie cases nearest', [['0.125', '0.375', '-0.125'], 2, 8, 'nearest'], {'codes': [1, 2, -1], 'saturated': 0, 'max_error': '1/8'}], ['control: negative truncate', [['-0.3', '0.3'], 3, 8, 'truncate'], {'codes': [-3, 2], 'saturated': 0, 'max_error': '3/40'}], ['control: exact grid', [['0.5', '-0.25'], 2, 4, 'nearest'], {'codes': [2, -1], 'saturated': 0, 'max_error': '0'}], ['control: exact grid truncate', [['0.5', '-0.25', '0.75'], 2, 4, 'truncate'], {'codes': [2, -1, 3], 'saturated': 0, 'max_error': '0'}]], [['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['regression: random quantize 44', [['0.844', '-1.78', '0.304', '0.84'], 2, 3, 'nearest'], {'codes': [3, -4, 1, 3], 'saturated': 1, 'max_error': '39/50'}], ['repair check: random quantize 8', [['0.08', '-2.194', '-0.29'], 4, 6, 'nearest'], {'codes': [1, -32, -5], 'saturated': 1, 'max_error': '97/500'}], ['control: integer multiple truncate', [['-0.5', '1.25'], 3, 6, 'truncate'], {'codes': [-4, 10], 'saturated': 0, 'max_error': '0'}], ['control: random quantize 0', [['-1.79', '1.59'], 3, 5, 'truncate'], {'codes': [-15, 12], 'saturated': 0, 'max_error': '9/100'}], ['control: random quantize 1', [['-1.919', '-2.19', '0.764', '-2.046'], 4, 7, 'truncate'], {'codes': [-31, -36, 12, -33], 'saturated': 0, 'max_error': '3/50'}], ['control: random quantize 2', [['-0.09', '-0.09', '0.397'], 4, 7, 'nearest'], {'codes': [-1, -1, 6], 'saturated': 0, 'max_error': '11/400'}]], [['regression: negative full scale', [['-1'], 7, 8, 'nearest'], {'codes': [-128], 'saturated': 0, 'max_error': '0'}], ['regression: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}], ['repair check: random quantize 15', [['-1.005', '-0.11', '-0.221', '-0.679'], 6, 7, 'truncate'], {'codes': [-64, -8, -15, -44], 'saturated': 1, 'max_error': '3/200'}], ['control: random quantize 3', [['-1.8'], 3, 5, 'nearest'], {'codes': [-14], 'saturated': 0, 'max_error': '1/20'}], ['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 7', [['-2.111', '2.022', '-1.492'], 3, 6, 'truncate'], {'codes': [-17, 16, -12], 'saturated': 0, 'max_error': '11/500'}]], [['regression: random quantize 44', [['0.844', '-1.78', '0.304', '0.84'], 2, 3, 'nearest'], {'codes': [3, -4, 1, 3], 'saturated': 1, 'max_error': '39/50'}], ['regression: positive overflow', [['1', '0.99'], 7, 8, 'nearest'], {'codes': [127, 127], 'saturated': 1, 'max_error': '1/128'}], ['repair check: random quantize 32', [['-1.79', '-1.633', '-0.38'], 3, 4, 'nearest'], {'codes': [-8, -8, -3], 'saturated': 2, 'max_error': '79/100'}], ['control: random quantize 9', [['-0.92', '1.79'], 4, 5, 'truncate'], {'codes': [-15, 15], 'saturated': 1, 'max_error': '341/400'}], ['control: 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'}], ['control: random quantize 12', [['-0.52', '-2.037', '1.37'], 3, 6, 'nearest'], {'codes': [-4, -16, 11], 'saturated': 0, 'max_error': '37/1000'}], ['control: random quantize 13', [['0.615'], 3, 4, 'nearest'], {'codes': [5], 'saturated': 0, 'max_error': '1/100'}]], [['regression: random quantize 26', [['-1.848', '0.82', '-1.59'], 2, 3, 'truncate'], {'codes': [-4, 3, -4], 'saturated': 2, 'max_error': '106/125'}], ['regression: random quantize 28', [['1.91', '-1.259'], 2, 4, 'truncate'], {'codes': [7, -6], 'saturated': 0, 'max_error': '241/1000'}], ['repair check: random quantize 37', [['-1.95', '-1.54', '0.854'], 6, 7, 'truncate'], {'codes': [-64, -64, 54], 'saturated': 2, 'max_error': '19/20'}], ['control: 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'}], ['control: random quantize 16', [['0.334'], 6, 7, 'truncate'], {'codes': [21], 'saturated': 0, 'max_error': '47/8000'}], ['control: random quantize 17', [['-0.86'], 2, 5, 'truncate'], {'codes': [-4], 'saturated': 0, 'max_error': '7/50'}], ['control: 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'}]]]\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-saturation-counting","generated_at":"2026-09-29T14:51:37.556809+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":"Count only codes strictly outside the representable range.","root_cause":"The clipping test uses >= hi and <= lo.","sha256":"e9ef750258d2a0b16849aa4db55a2ed7ef59fdfbb238f99276354e96e824730c","title":"Coefficient quantizer counts codes that land exactly on a rail · case 01","variant":1,"variant_policy":"Five numbered records share a model and 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