FA-89786 / Instruction set emulation / Open access

Rotate left is circular instead of through carry · case 01

rol feeds bit 7 back into bit 0 instead of the carry flag.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The rotate uses the outgoing bit as the incoming bit.

VERIFIED REPAIR

Shift the old carry into bit 0 and move bit 7 into carry.

Unsuccessful approach: Dropping the 8-bit mask leaves a 9-bit accumulator.

Case contract

Input [a, c, ops] with ops asl, lsr, rol, ror, asr on an 8-bit value and a carry bit. asl: C = bit 7, shift left. lsr: C = bit 0, shift right with 0. rol: shift left, bit 0 = old C, new C = old bit 7. ror: shift right, bit 7 = old C, new C = old bit 0. asr: C = bit 0, shift right keeping bit 7. Report [A, C, Z, N] after each op.

Why this case matters

Rotate-through-carry instructions implement multi-byte shifts in 8-bit code; emulating them with circular rotates or sequenced updates breaks arithmetic libraries.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    a, c, ops = args
    out = []
    for op in ops:
        if op == 'asl':
            c = a >> 7
            a = (a << 1) & 0xFF
        elif op == 'lsr':
            c = a & 1
            a = a >> 1
        elif op == 'rol':
            a, c = ((a << 1) | (a >> 7)) & 0xFF, a >> 7
        elif op == 'ror':
            a, c = (a >> 1) | (c << 7), a & 1
        elif op == 'asr':
            c = a & 1
            a = (a >> 1) | (a & 0x80)
        out.append([a, c, int(a == 0), a >> 7])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0]]), ('rotate left with carry in', [65, 1, ['rol', 'rol']], [[131, 0, 0, 1], [6, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [4, 1, ['ror', 'ror']], [[130, 0, 0, 1], [65, 0, 0, 0]]), ('arithmetic right shift keeps sign', [197, 0, ['asr', 'asr', 'asr']], [[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [5, 0, ['lsr', 'lsr']], [[2, 1, 0, 0], [1, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [86, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0]]), ('rotate left with carry in', [66, 1, ['rol', 'rol']], [[133, 0, 0, 1], [10, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [6, 1, ['ror', 'ror']], [[131, 0, 0, 1], [65, 1, 0, 0]]), ('arithmetic right shift keeps sign', [198, 0, ['asr', 'asr', 'asr']], [[227, 0, 0, 1], [241, 1, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [9, 0, ['lsr', 'lsr']], [[4, 1, 0, 0], [2, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [87, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[175, 0, 0, 1], [87, 1, 0, 0], [171, 1, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0]]), ('rotate left with carry in', [67, 1, ['rol', 'rol']], [[135, 0, 0, 1], [14, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [8, 1, ['ror', 'ror']], [[132, 0, 0, 1], [66, 0, 0, 0]]), ('arithmetic right shift keeps sign', [199, 0, ['asr', 'asr', 'asr']], [[227, 1, 0, 1], [241, 1, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [13, 0, ['lsr', 'lsr']], [[6, 1, 0, 0], [3, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [88, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[177, 0, 0, 1], [88, 1, 0, 0], [172, 0, 0, 1], [214, 0, 0, 1], [172, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0], [160, 0, 0, 1]]), ('rotate left with carry in', [68, 1, ['rol', 'rol']], [[137, 0, 0, 1], [18, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [10, 1, ['ror', 'ror']], [[133, 0, 0, 1], [66, 1, 0, 0]]), ('arithmetic right shift keeps sign', [200, 0, ['asr', 'asr', 'asr']], [[228, 0, 0, 1], [242, 0, 0, 1], [249, 0, 0, 1]]), ('logical right shift carry', [17, 0, ['lsr', 'lsr']], [[8, 1, 0, 0], [4, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [89, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[179, 0, 0, 1], [89, 1, 0, 0], [172, 1, 0, 1], [214, 0, 0, 1], [172, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0], [160, 0, 0, 1], [64, 1, 0, 0]]), ('rotate left with carry in', [69, 1, ['rol', 'rol']], [[139, 0, 0, 1], [22, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [12, 1, ['ror', 'ror']], [[134, 0, 0, 1], [67, 0, 0, 0]]), ('arithmetic right shift keeps sign', [201, 0, ['asr', 'asr', 'asr']], [[228, 1, 0, 1], [242, 0, 0, 1], [249, 0, 0, 1]]), ('logical right shift carry', [21, 0, ['lsr', 'lsr']], [[10, 1, 0, 0], [5, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [90, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[181, 0, 0, 1], [90, 1, 0, 0], [173, 0, 0, 1], [214, 1, 0, 1], [172, 1, 0, 1]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
rotate left through carry	`[[3, 1, 0, 0], [6, 0, 0, 0], [12, 0, 0, 0], [24, 0, 0, 0]]`	`[[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0]]`	Failed
rotate left with carry in	`[[130, 0, 0, 1], [5, 1, 0, 0]]`	`[[131, 0, 0, 1], [6, 1, 0, 0]]`	Failed
rotate right through carry	`[[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]`	`[[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]`	Passed
rotate right carry into bit seven	`[[130, 0, 0, 1], [65, 0, 0, 0]]`	`[[130, 0, 0, 1], [65, 0, 0, 0]]`	Passed
arithmetic right shift keeps sign	`[[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]`	`[[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]`	Passed
logical right shift carry	`[[2, 1, 0, 0], [1, 0, 0, 0]]`	`[[2, 1, 0, 0], [1, 0, 0, 0]]`	Passed
shift left carry out	`[[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]`	`[[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]`	Passed
mixed sequence	`[[172, 0, 0, 1], [86, 0, 0, 0], [43, 0, 0, 0], [21, 1, 0, 0], [42, 0, 0, 0]]`	`[[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]]`	Failed

SHA-256 / 8872f8843ec0cfbf79ce6ae5e24f90c51722b44751d802e4ab65d39a623fb870

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    a, c, ops = args
    out = []
    for op in ops:
        if op == 'asl':
            c = a >> 7
            a = (a << 1) & 0xFF
        elif op == 'lsr':
            c = a & 1
            a = a >> 1
        elif op == 'rol':
            a, c = ((a << 1) | c), a >> 7
        elif op == 'ror':
            a, c = (a >> 1) | (c << 7), a & 1
        elif op == 'asr':
            c = a & 1
            a = (a >> 1) | (a & 0x80)
        out.append([a, c, int(a == 0), a >> 7])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0]]), ('rotate left with carry in', [65, 1, ['rol', 'rol']], [[131, 0, 0, 1], [6, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [4, 1, ['ror', 'ror']], [[130, 0, 0, 1], [65, 0, 0, 0]]), ('arithmetic right shift keeps sign', [197, 0, ['asr', 'asr', 'asr']], [[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [5, 0, ['lsr', 'lsr']], [[2, 1, 0, 0], [1, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [86, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0]]), ('rotate left with carry in', [66, 1, ['rol', 'rol']], [[133, 0, 0, 1], [10, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [6, 1, ['ror', 'ror']], [[131, 0, 0, 1], [65, 1, 0, 0]]), ('arithmetic right shift keeps sign', [198, 0, ['asr', 'asr', 'asr']], [[227, 0, 0, 1], [241, 1, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [9, 0, ['lsr', 'lsr']], [[4, 1, 0, 0], [2, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [87, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[175, 0, 0, 1], [87, 1, 0, 0], [171, 1, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0]]), ('rotate left with carry in', [67, 1, ['rol', 'rol']], [[135, 0, 0, 1], [14, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [8, 1, ['ror', 'ror']], [[132, 0, 0, 1], [66, 0, 0, 0]]), ('arithmetic right shift keeps sign', [199, 0, ['asr', 'asr', 'asr']], [[227, 1, 0, 1], [241, 1, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [13, 0, ['lsr', 'lsr']], [[6, 1, 0, 0], [3, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [88, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[177, 0, 0, 1], [88, 1, 0, 0], [172, 0, 0, 1], [214, 0, 0, 1], [172, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0], [160, 0, 0, 1]]), ('rotate left with carry in', [68, 1, ['rol', 'rol']], [[137, 0, 0, 1], [18, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [10, 1, ['ror', 'ror']], [[133, 0, 0, 1], [66, 1, 0, 0]]), ('arithmetic right shift keeps sign', [200, 0, ['asr', 'asr', 'asr']], [[228, 0, 0, 1], [242, 0, 0, 1], [249, 0, 0, 1]]), ('logical right shift carry', [17, 0, ['lsr', 'lsr']], [[8, 1, 0, 0], [4, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [89, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[179, 0, 0, 1], [89, 1, 0, 0], [172, 1, 0, 1], [214, 0, 0, 1], [172, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0], [160, 0, 0, 1], [64, 1, 0, 0]]), ('rotate left with carry in', [69, 1, ['rol', 'rol']], [[139, 0, 0, 1], [22, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [12, 1, ['ror', 'ror']], [[134, 0, 0, 1], [67, 0, 0, 0]]), ('arithmetic right shift keeps sign', [201, 0, ['asr', 'asr', 'asr']], [[228, 1, 0, 1], [242, 0, 0, 1], [249, 0, 0, 1]]), ('logical right shift carry', [21, 0, ['lsr', 'lsr']], [[10, 1, 0, 0], [5, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [90, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[181, 0, 0, 1], [90, 1, 0, 0], [173, 0, 0, 1], [214, 1, 0, 1], [172, 1, 0, 1]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
rotate left through carry	`[[258, 1, 0, 2], [517, 2, 0, 4], [1034, 4, 0, 8], [2068, 8, 0, 16]]`	`[[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0]]`	Failed
rotate left with carry in	`[[131, 0, 0, 1], [262, 1, 0, 2]]`	`[[131, 0, 0, 1], [6, 1, 0, 0]]`	Failed
rotate right through carry	`[[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]`	`[[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]`	Passed
rotate right carry into bit seven	`[[130, 0, 0, 1], [65, 0, 0, 0]]`	`[[130, 0, 0, 1], [65, 0, 0, 0]]`	Passed
arithmetic right shift keeps sign	`[[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]`	`[[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]`	Passed
logical right shift carry	`[[2, 1, 0, 0], [1, 0, 0, 0]]`	`[[2, 1, 0, 0], [1, 0, 0, 0]]`	Passed
shift left carry out	`[[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]`	`[[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]`	Passed
mixed sequence	`[[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]]`	`[[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]]`	Passed

SHA-256 / 775c8e1566dfa6c780a71da943508a64b5a76864411f8f3ef3ed736c09dfe41f

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(*args):
    a, c, ops = args
    out = []
    for op in ops:
        if op == 'asl':
            c = a >> 7
            a = (a << 1) & 0xFF
        elif op == 'lsr':
            c = a & 1
            a = a >> 1
        elif op == 'rol':
            a, c = ((a << 1) | c) & 0xFF, a >> 7
        elif op == 'ror':
            a, c = (a >> 1) | (c << 7), a & 1
        elif op == 'asr':
            c = a & 1
            a = (a >> 1) | (a & 0x80)
        out.append([a, c, int(a == 0), a >> 7])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0]]), ('rotate left with carry in', [65, 1, ['rol', 'rol']], [[131, 0, 0, 1], [6, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [4, 1, ['ror', 'ror']], [[130, 0, 0, 1], [65, 0, 0, 0]]), ('arithmetic right shift keeps sign', [197, 0, ['asr', 'asr', 'asr']], [[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [5, 0, ['lsr', 'lsr']], [[2, 1, 0, 0], [1, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [86, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0]]), ('rotate left with carry in', [66, 1, ['rol', 'rol']], [[133, 0, 0, 1], [10, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [6, 1, ['ror', 'ror']], [[131, 0, 0, 1], [65, 1, 0, 0]]), ('arithmetic right shift keeps sign', [198, 0, ['asr', 'asr', 'asr']], [[227, 0, 0, 1], [241, 1, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [9, 0, ['lsr', 'lsr']], [[4, 1, 0, 0], [2, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [87, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[175, 0, 0, 1], [87, 1, 0, 0], [171, 1, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0]]), ('rotate left with carry in', [67, 1, ['rol', 'rol']], [[135, 0, 0, 1], [14, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [8, 1, ['ror', 'ror']], [[132, 0, 0, 1], [66, 0, 0, 0]]), ('arithmetic right shift keeps sign', [199, 0, ['asr', 'asr', 'asr']], [[227, 1, 0, 1], [241, 1, 0, 1], [248, 1, 0, 1]]), ('logical right shift carry', [13, 0, ['lsr', 'lsr']], [[6, 1, 0, 0], [3, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [88, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[177, 0, 0, 1], [88, 1, 0, 0], [172, 0, 0, 1], [214, 0, 0, 1], [172, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0], [160, 0, 0, 1]]), ('rotate left with carry in', [68, 1, ['rol', 'rol']], [[137, 0, 0, 1], [18, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [10, 1, ['ror', 'ror']], [[133, 0, 0, 1], [66, 1, 0, 0]]), ('arithmetic right shift keeps sign', [200, 0, ['asr', 'asr', 'asr']], [[228, 0, 0, 1], [242, 0, 0, 1], [249, 0, 0, 1]]), ('logical right shift carry', [17, 0, ['lsr', 'lsr']], [[8, 1, 0, 0], [4, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [89, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[179, 0, 0, 1], [89, 1, 0, 0], [172, 1, 0, 1], [214, 0, 0, 1], [172, 1, 0, 1]])], [('rotate left through carry', [129, 0, ['rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol', 'rol']], [[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0], [40, 0, 0, 0], [80, 0, 0, 0], [160, 0, 0, 1], [64, 1, 0, 0]]), ('rotate left with carry in', [69, 1, ['rol', 'rol']], [[139, 0, 0, 1], [22, 1, 0, 0]]), ('rotate right through carry', [1, 1, ['ror', 'ror', 'ror']], [[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]), ('rotate right carry into bit seven', [12, 1, ['ror', 'ror']], [[134, 0, 0, 1], [67, 0, 0, 0]]), ('arithmetic right shift keeps sign', [201, 0, ['asr', 'asr', 'asr']], [[228, 1, 0, 1], [242, 0, 0, 1], [249, 0, 0, 1]]), ('logical right shift carry', [21, 0, ['lsr', 'lsr']], [[10, 1, 0, 0], [5, 0, 0, 0]]), ('shift left carry out', [192, 0, ['asl', 'asl', 'asl']], [[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]), ('mixed sequence', [90, 1, ['rol', 'lsr', 'ror', 'asr', 'asl']], [[181, 0, 0, 1], [90, 1, 0, 0], [173, 0, 0, 1], [214, 1, 0, 1], [172, 1, 0, 1]])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
rotate left through carry	`[[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0]]`	`[[2, 1, 0, 0], [5, 0, 0, 0], [10, 0, 0, 0], [20, 0, 0, 0]]`	Passed
rotate left with carry in	`[[131, 0, 0, 1], [6, 1, 0, 0]]`	`[[131, 0, 0, 1], [6, 1, 0, 0]]`	Passed
rotate right through carry	`[[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]`	`[[128, 1, 0, 1], [192, 0, 0, 1], [96, 0, 0, 0]]`	Passed
rotate right carry into bit seven	`[[130, 0, 0, 1], [65, 0, 0, 0]]`	`[[130, 0, 0, 1], [65, 0, 0, 0]]`	Passed
arithmetic right shift keeps sign	`[[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]`	`[[226, 1, 0, 1], [241, 0, 0, 1], [248, 1, 0, 1]]`	Passed
logical right shift carry	`[[2, 1, 0, 0], [1, 0, 0, 0]]`	`[[2, 1, 0, 0], [1, 0, 0, 0]]`	Passed
shift left carry out	`[[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]`	`[[128, 1, 0, 1], [0, 1, 1, 0], [0, 0, 1, 0]]`	Passed
mixed sequence	`[[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]]`	`[[173, 0, 0, 1], [86, 1, 0, 0], [171, 0, 0, 1], [213, 1, 0, 1], [170, 1, 0, 1]]`	Passed

SHA-256 / de8760719a9feb4472a520069eb43b45e11f0d828e5e7b90f90a7deae26e520b

Verification & scope

A deterministic bounded teaching model of one emulator rule; the instruction semantics are a stipulated contract inspired by common ISAs and are not a claim of cycle-exact or architectural 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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:51:20.622185+00:00.

Case digest / 33d94fb42cfe9dbe987ef354376b1bee18c4dfa7a50ded7e97c3dfd7759ffee0