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FA-90146 / Bytecode virtual machines / Open access

Branch relaxation: displacement -128 considered out of range · case 01

Backward branches of exactly -128 bytes are widened, growing code for no reason.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The fit test uses abs(off) > 127, which rejects the valid minimum -128.

VERIFIED REPAIR

Short displacements are valid from -128 to 127 inclusive.

Unsuccessful approach: Accepting +128 lets a forward branch overflow its 8-bit field.

Case contract

Assemble ["label", name], ["data", nbytes], ["jmp", label], ["jz", label]. Branches start in the short form (2 bytes, signed 8-bit displacement from the end of the instruction, valid -128..127). A short branch whose displacement does not fit is widened (jmp.w 3 bytes, jz.w 4 bytes) and addresses are recomputed until no branch changes (branches never shrink). Report duplicate or undefined labels; otherwise return each branch as [address, mnemonic, displacement from its own end] and the total size.

Why this case matters

Variable-length branch encodings need fixpoint relaxation to produce correct displacements.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(prog):
    labels_seen = set()
    for ins in prog:
        if ins[0] == 'label':
            if ins[1] in labels_seen:
                return ['duplicate-label', ins[1]]
            labels_seen.add(ins[1])
    for ins in prog:
        if ins[0] in ('jmp', 'jz') and ins[1] not in labels_seen:
            return ['undefined-label', ins[1]]
    long_form = set()
    def size(i, ins):
        if i in long_form:
            return 4 if ins[0] == 'jz' else 3
        return 2
    rounds = 0
    while True:
        rounds += 1
        addr = 0
        addrs = []
        where = {}
        for i, ins in enumerate(prog):
            addrs.append(addr)
            if ins[0] == 'label':
                where[ins[1]] = addr
            elif ins[0] == 'data':
                addr += ins[1]
            else:
                addr += size(i, ins)
        changed = False
        for i, ins in enumerate(prog):
            if ins[0] in ('jmp', 'jz') and i not in long_form:
                off = where[ins[1]] - (addrs[i] + 2)
                if abs(off) > 127:
                    long_form.add(i)
                    changed = True
        if not changed or rounds > len(prog):
            break
    out = []
    for i, ins in enumerate(prog):
        if ins[0] in ('jmp', 'jz'):
            suffix = '.w' if i in long_form else ''
            out.append([addrs[i], ins[0] + suffix, where[ins[1]] - (addrs[i] + size(i, ins))])
    return {'branches': out, 'size': addr}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: three-step widening cascade',
   ([['data', 1],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 1], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}),
  ('forward branch just around the short limit',
   ([['data', 1], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 201], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 1], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}),
  ('duplicate label', ([['label', 'a'], ['data', 1], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 1]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 2],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[2, 'jmp.w', 129], [15, 'jz.w', 128], [134, 'jmp.w', 128]], 'size': 266}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 2], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [130, 'jmp.w', -133]], 'size': 133}),
  ('forward branch just around the short limit',
   ([['data', 2], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[2, 'jmp', 127], [131, 'jz.w', 128]], 'size': 263}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 202], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 202], [206, 'jmp', -2]], 'size': 208}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 2], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [4, 'jmp', -4]], 'size': 6}),
  ('duplicate label', ([['label', 'a'], ['data', 2], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 2]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 3],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[3, 'jmp.w', 129], [16, 'jz.w', 128], [135, 'jmp.w', 128]], 'size': 267}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 3], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [131, 'jmp.w', -134]], 'size': 134}),
  ('forward branch just around the short limit',
   ([['data', 3], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[3, 'jmp', 127], [132, 'jz.w', 128]], 'size': 264}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 203], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 203], [207, 'jmp', -2]], 'size': 209}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 3], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [5, 'jmp', -5]], 'size': 7}),
  ('duplicate label', ([['label', 'a'], ['data', 3], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 3]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 4],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[4, 'jmp.w', 129], [17, 'jz.w', 128], [136, 'jmp.w', 128]], 'size': 268}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 4], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [132, 'jmp.w', -135]], 'size': 135}),
  ('forward branch just around the short limit',
   ([['data', 4], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[4, 'jmp', 127], [133, 'jz.w', 128]], 'size': 265}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 204], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 204], [208, 'jmp', -2]], 'size': 210}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 4], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [6, 'jmp', -6]], 'size': 8}),
  ('duplicate label', ([['label', 'a'], ['data', 4], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 4]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 5],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[5, 'jmp.w', 129], [18, 'jz.w', 128], [137, 'jmp.w', 128]], 'size': 269}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 5], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [133, 'jmp.w', -136]], 'size': 136}),
  ('forward branch just around the short limit',
   ([['data', 5], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[5, 'jmp', 127], [134, 'jz.w', 128]], 'size': 266}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 205], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 205], [209, 'jmp', -2]], 'size': 211}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 5], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [7, 'jmp', -7]], 'size': 9}),
  ('duplicate label', ([['label', 'a'], ['data', 5], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 5]],), ['undefined-label', 'nowhere'])]]
for label, args, expected in cases[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 fixtureActualExpectedOutcome
regression: three-step widening cascade{'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}{'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}Passed
backward branch exactly -128 stays short{'branches': [[126, 'jz.w', -130], [131, 'jmp.w', -134]], 'size': 134}{'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}Failed
forward branch just around the short limit{'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}{'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}Passed
wide conditional branch is four bytes{'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}{'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}Passed
short branches to adjacent labels{'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}{'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}Passed
duplicate label['duplicate-label', 'a']['duplicate-label', 'a']Passed
undefined label['undefined-label', 'nowhere']['undefined-label', 'nowhere']Passed

SHA-256 / 0d0050b095048f4429dfc66544f91c5f5b0e87213f611410e72539b9b75521cb

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(prog):
    labels_seen = set()
    for ins in prog:
        if ins[0] == 'label':
            if ins[1] in labels_seen:
                return ['duplicate-label', ins[1]]
            labels_seen.add(ins[1])
    for ins in prog:
        if ins[0] in ('jmp', 'jz') and ins[1] not in labels_seen:
            return ['undefined-label', ins[1]]
    long_form = set()
    def size(i, ins):
        if i in long_form:
            return 4 if ins[0] == 'jz' else 3
        return 2
    rounds = 0
    while True:
        rounds += 1
        addr = 0
        addrs = []
        where = {}
        for i, ins in enumerate(prog):
            addrs.append(addr)
            if ins[0] == 'label':
                where[ins[1]] = addr
            elif ins[0] == 'data':
                addr += ins[1]
            else:
                addr += size(i, ins)
        changed = False
        for i, ins in enumerate(prog):
            if ins[0] in ('jmp', 'jz') and i not in long_form:
                off = where[ins[1]] - (addrs[i] + 2)
                if off < -128 or off > 128:
                    long_form.add(i)
                    changed = True
        if not changed or rounds > len(prog):
            break
    out = []
    for i, ins in enumerate(prog):
        if ins[0] in ('jmp', 'jz'):
            suffix = '.w' if i in long_form else ''
            out.append([addrs[i], ins[0] + suffix, where[ins[1]] - (addrs[i] + size(i, ins))])
    return {'branches': out, 'size': addr}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: three-step widening cascade',
   ([['data', 1],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 1], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}),
  ('forward branch just around the short limit',
   ([['data', 1], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 201], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 1], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}),
  ('duplicate label', ([['label', 'a'], ['data', 1], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 1]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 2],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[2, 'jmp.w', 129], [15, 'jz.w', 128], [134, 'jmp.w', 128]], 'size': 266}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 2], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [130, 'jmp.w', -133]], 'size': 133}),
  ('forward branch just around the short limit',
   ([['data', 2], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[2, 'jmp', 127], [131, 'jz.w', 128]], 'size': 263}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 202], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 202], [206, 'jmp', -2]], 'size': 208}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 2], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [4, 'jmp', -4]], 'size': 6}),
  ('duplicate label', ([['label', 'a'], ['data', 2], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 2]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 3],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[3, 'jmp.w', 129], [16, 'jz.w', 128], [135, 'jmp.w', 128]], 'size': 267}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 3], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [131, 'jmp.w', -134]], 'size': 134}),
  ('forward branch just around the short limit',
   ([['data', 3], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[3, 'jmp', 127], [132, 'jz.w', 128]], 'size': 264}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 203], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 203], [207, 'jmp', -2]], 'size': 209}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 3], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [5, 'jmp', -5]], 'size': 7}),
  ('duplicate label', ([['label', 'a'], ['data', 3], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 3]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 4],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[4, 'jmp.w', 129], [17, 'jz.w', 128], [136, 'jmp.w', 128]], 'size': 268}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 4], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [132, 'jmp.w', -135]], 'size': 135}),
  ('forward branch just around the short limit',
   ([['data', 4], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[4, 'jmp', 127], [133, 'jz.w', 128]], 'size': 265}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 204], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 204], [208, 'jmp', -2]], 'size': 210}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 4], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [6, 'jmp', -6]], 'size': 8}),
  ('duplicate label', ([['label', 'a'], ['data', 4], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 4]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 5],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[5, 'jmp.w', 129], [18, 'jz.w', 128], [137, 'jmp.w', 128]], 'size': 269}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 5], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [133, 'jmp.w', -136]], 'size': 136}),
  ('forward branch just around the short limit',
   ([['data', 5], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[5, 'jmp', 127], [134, 'jz.w', 128]], 'size': 266}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 205], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 205], [209, 'jmp', -2]], 'size': 211}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 5], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [7, 'jmp', -7]], 'size': 9}),
  ('duplicate label', ([['label', 'a'], ['data', 5], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 5]],), ['undefined-label', 'nowhere'])]]
for label, args, expected in cases[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 fixtureActualExpectedOutcome
regression: three-step widening cascade{'branches': [[1, 'jmp', 127], [13, 'jz', 127], [130, 'jmp', 128]], 'size': 261}{'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}Failed
backward branch exactly -128 stays short{'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}{'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}Passed
forward branch just around the short limit{'branches': [[1, 'jmp', 127], [130, 'jz', 128]], 'size': 260}{'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}Failed
wide conditional branch is four bytes{'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}{'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}Passed
short branches to adjacent labels{'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}{'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}Passed
duplicate label['duplicate-label', 'a']['duplicate-label', 'a']Passed
undefined label['undefined-label', 'nowhere']['undefined-label', 'nowhere']Passed

SHA-256 / e1b1a93e55f528ed9e5ea0380f9a559923f6dfbadba41faf43f11feca379758f

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(prog):
    labels_seen = set()
    for ins in prog:
        if ins[0] == 'label':
            if ins[1] in labels_seen:
                return ['duplicate-label', ins[1]]
            labels_seen.add(ins[1])
    for ins in prog:
        if ins[0] in ('jmp', 'jz') and ins[1] not in labels_seen:
            return ['undefined-label', ins[1]]
    long_form = set()
    def size(i, ins):
        if i in long_form:
            return 4 if ins[0] == 'jz' else 3
        return 2
    rounds = 0
    while True:
        rounds += 1
        addr = 0
        addrs = []
        where = {}
        for i, ins in enumerate(prog):
            addrs.append(addr)
            if ins[0] == 'label':
                where[ins[1]] = addr
            elif ins[0] == 'data':
                addr += ins[1]
            else:
                addr += size(i, ins)
        changed = False
        for i, ins in enumerate(prog):
            if ins[0] in ('jmp', 'jz') and i not in long_form:
                off = where[ins[1]] - (addrs[i] + 2)
                if off < -128 or off > 127:
                    long_form.add(i)
                    changed = True
        if not changed or rounds > len(prog):
            break
    out = []
    for i, ins in enumerate(prog):
        if ins[0] in ('jmp', 'jz'):
            suffix = '.w' if i in long_form else ''
            out.append([addrs[i], ins[0] + suffix, where[ins[1]] - (addrs[i] + size(i, ins))])
    return {'branches': out, 'size': addr}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[('regression: three-step widening cascade',
   ([['data', 1],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 1], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}),
  ('forward branch just around the short limit',
   ([['data', 1], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 201], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 1], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}),
  ('duplicate label', ([['label', 'a'], ['data', 1], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 1]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 2],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[2, 'jmp.w', 129], [15, 'jz.w', 128], [134, 'jmp.w', 128]], 'size': 266}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 2], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [130, 'jmp.w', -133]], 'size': 133}),
  ('forward branch just around the short limit',
   ([['data', 2], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[2, 'jmp', 127], [131, 'jz.w', 128]], 'size': 263}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 202], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 202], [206, 'jmp', -2]], 'size': 208}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 2], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [4, 'jmp', -4]], 'size': 6}),
  ('duplicate label', ([['label', 'a'], ['data', 2], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 2]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 3],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[3, 'jmp.w', 129], [16, 'jz.w', 128], [135, 'jmp.w', 128]], 'size': 267}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 3], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [131, 'jmp.w', -134]], 'size': 134}),
  ('forward branch just around the short limit',
   ([['data', 3], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[3, 'jmp', 127], [132, 'jz.w', 128]], 'size': 264}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 203], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 203], [207, 'jmp', -2]], 'size': 209}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 3], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [5, 'jmp', -5]], 'size': 7}),
  ('duplicate label', ([['label', 'a'], ['data', 3], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 3]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 4],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[4, 'jmp.w', 129], [17, 'jz.w', 128], [136, 'jmp.w', 128]], 'size': 268}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 4], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [132, 'jmp.w', -135]], 'size': 135}),
  ('forward branch just around the short limit',
   ([['data', 4], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[4, 'jmp', 127], [133, 'jz.w', 128]], 'size': 265}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 204], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 204], [208, 'jmp', -2]], 'size': 210}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 4], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [6, 'jmp', -6]], 'size': 8}),
  ('duplicate label', ([['label', 'a'], ['data', 4], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 4]],), ['undefined-label', 'nowhere'])],
 [('regression: three-step widening cascade',
   ([['data', 5],
     ['jmp', 'A'],
     ['data', 10],
     ['jz', 'B'],
     ['data', 115],
     ['label', 'A'],
     ['jmp', 'C'],
     ['data', 10],
     ['label', 'B'],
     ['data', 118],
     ['label', 'C'],
     ['data', 1]],),
   {'branches': [[5, 'jmp.w', 129], [18, 'jz.w', 128], [137, 'jmp.w', 128]], 'size': 269}),
  ('backward branch exactly -128 stays short',
   ([['label', 'top'], ['data', 126], ['jz', 'top'], ['data', 5], ['jmp', 'top']],),
   {'branches': [[126, 'jz', -128], [133, 'jmp.w', -136]], 'size': 136}),
  ('forward branch just around the short limit',
   ([['data', 5], ['jmp', 'e'], ['data', 127], ['label', 'e'], ['jz', 'f'], ['data', 128], ['label', 'f']],),
   {'branches': [[5, 'jmp', 127], [134, 'jz.w', 128]], 'size': 266}),
  ('wide conditional branch is four bytes',
   ([['jz', 'x'], ['data', 205], ['label', 'x'], ['jmp', 'x']],),
   {'branches': [[0, 'jz.w', 205], [209, 'jmp', -2]], 'size': 211}),
  ('short branches to adjacent labels',
   ([['jz', 'a'], ['label', 'a'], ['data', 5], ['jmp', 'a']],),
   {'branches': [[0, 'jz', 0], [7, 'jmp', -7]], 'size': 9}),
  ('duplicate label', ([['label', 'a'], ['data', 5], ['label', 'a']],), ['duplicate-label', 'a']),
  ('undefined label', ([['jmp', 'nowhere'], ['data', 5]],), ['undefined-label', 'nowhere'])]]
for label, args, expected in cases[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 fixtureActualExpectedOutcome
regression: three-step widening cascade{'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}{'branches': [[1, 'jmp.w', 129], [14, 'jz.w', 128], [133, 'jmp.w', 128]], 'size': 265}Passed
backward branch exactly -128 stays short{'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}{'branches': [[126, 'jz', -128], [129, 'jmp.w', -132]], 'size': 132}Passed
forward branch just around the short limit{'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}{'branches': [[1, 'jmp', 127], [130, 'jz.w', 128]], 'size': 262}Passed
wide conditional branch is four bytes{'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}{'branches': [[0, 'jz.w', 201], [205, 'jmp', -2]], 'size': 207}Passed
short branches to adjacent labels{'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}{'branches': [[0, 'jz', 0], [3, 'jmp', -3]], 'size': 5}Passed
duplicate label['duplicate-label', 'a']['duplicate-label', 'a']Passed
undefined label['undefined-label', 'nowhere']['undefined-label', 'nowhere']Passed

SHA-256 / 5a4b39057fb8f9e7546d6e8ccf83030c6152d4ff3e885d18e02aaf74ad35f1c5

Verification & scope

A deterministic, bounded teaching model of one bytecode virtual machine mechanism with a stipulated instruction encoding; it is not a production VM and claims no conformance to any real specification. 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 2026-09-29T14:51:23.954014+00:00.

Case digest / b68c762e88916d9704d58036bf88068935254ed8346760a980536ae3f7006984