FA-89341 / Instruction set emulation / Open access

SBC treats the carry flag as a borrow flag · case 01

Subtraction with carry set comes out one too small and with carry clear one too large.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The carry input of SBC is inverted, as if carry set meant borrow.

VERIFIED REPAIR

Add the ones complement of the operand plus the carry unchanged.

Unsuccessful approach: Two's complement negation of the operand ignores the carry and is off by one when a borrow is pending.

Case contract

Input [a, c, ops] for an 8-bit accumulator with carry c; V starts 0. adc m: s = a+m+c, A = s & 0xFF, C = s > 0xFF, V = signed overflow of the 8-bit add. sbc m is adc of (m xor 0xFF) with the same carry (carry set means no borrow). cmp m: C = a >= m (unsigned), N/Z from (a-m) & 0xFF, A and V unchanged. After each op report [A, N, V, Z, C] where N is bit 7 and Z is result == 0.

Why this case matters

CPU emulators live or die on flag semantics; carry-as-inverted-borrow and overflow are the classic 8-bit emulation bugs.

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
    v = 0
    out = []
    for op, m in ops:
        if op == 'cmp':
            r = (a - m) & 0xFF
            c = int(a >= m)
            out.append([a, r >> 7, v, int(r == 0), c])
            continue
        if op == 'sbc':
            m = m ^ 0xFF
            c = 1 - c
        s = a + m + c
        r = s & 0xFF
        v = int(((a ^ r) & (m ^ r) & 0x80) != 0)
        c = int(s > 0xFF)
        a = r
        out.append([a, r >> 7, v, int(r == 0), c])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('adc without carry', [17, 0, [['adc', 32], ['adc', 5]]], [[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 145]]], [[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 254]]], [[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 126]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [241, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [127, 0, [['adc', 128], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [56, 1, [['adc', 255]]], [[56, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [81, 0, [['sbc', 16], ['sbc', 63]]], [[64, 0, 0, 0, 1], [1, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 62], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 193]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [18, 0, [['adc', 32], ['adc', 5]]], [[50, 0, 0, 0, 0], [55, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 146]]], [[160, 1, 1, 0, 0], [50, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 253]]], [[0, 0, 0, 1, 1], [254, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 125]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [242, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [126, 0, [['adc', 129], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [57, 1, [['adc', 255]]], [[57, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [82, 0, [['sbc', 16], ['sbc', 63]]], [[65, 0, 0, 0, 1], [2, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 61], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 194]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [19, 0, [['adc', 32], ['adc', 5]]], [[51, 0, 0, 0, 0], [56, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 147]]], [[160, 1, 1, 0, 0], [51, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 252]]], [[0, 0, 0, 1, 1], [253, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 124]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [243, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [125, 0, [['adc', 130], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [58, 1, [['adc', 255]]], [[58, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [83, 0, [['sbc', 16], ['sbc', 63]]], [[66, 0, 0, 0, 1], [3, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 60], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 195]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [20, 0, [['adc', 32], ['adc', 5]]], [[52, 0, 0, 0, 0], [57, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 148]]], [[160, 1, 1, 0, 0], [52, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 251]]], [[0, 0, 0, 1, 1], [252, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 123]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [244, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [124, 0, [['adc', 131], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [59, 1, [['adc', 255]]], [[59, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [84, 0, [['sbc', 16], ['sbc', 63]]], [[67, 0, 0, 0, 1], [4, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 59], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 196]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [21, 0, [['adc', 32], ['adc', 5]]], [[53, 0, 0, 0, 0], [58, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 149]]], [[160, 1, 1, 0, 0], [53, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 250]]], [[0, 0, 0, 1, 1], [251, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 122]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [245, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [123, 0, [['adc', 132], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [60, 1, [['adc', 255]]], [[60, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [85, 0, [['sbc', 16], ['sbc', 63]]], [[68, 0, 0, 0, 1], [5, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 58], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 197]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])]]
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
adc without carry	`[[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]`	`[[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]`	Passed
adc signed overflow both ways	`[[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]`	`[[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]`	Passed
adc carry out to zero	`[[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]`	`[[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]`	Passed
sbc with carry set (no borrow)	`[[31, 0, 0, 0, 1], [110, 0, 0, 0, 0], [240, 1, 0, 0, 0]]`	`[[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [241, 1, 0, 0, 0]]`	Failed
sum of exactly 0xFF	`[[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]`	`[[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]`	Passed
carry in wraps operand	`[[56, 0, 0, 0, 1]]`	`[[56, 0, 0, 0, 1]]`	Passed
sbc with carry clear (borrow)	`[[65, 0, 0, 0, 1], [1, 0, 0, 0, 1]]`	`[[64, 0, 0, 0, 1], [1, 0, 0, 0, 1]]`	Failed
cmp orders and keeps accumulator	`[[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]`	`[[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]`	Passed
sbc to exactly zero	`[[255, 1, 0, 0, 0], [255, 0, 0, 0, 1]]`	`[[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]]`	Failed

SHA-256 / 8e5d1c4fdf7c8b9d063b2880b45a33cf5bae029561fb159510b8d27aa5017816

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
    v = 0
    out = []
    for op, m in ops:
        if op == 'cmp':
            r = (a - m) & 0xFF
            c = int(a >= m)
            out.append([a, r >> 7, v, int(r == 0), c])
            continue
        if op == 'sbc':
            m = (-m) & 0xFF
        s = a + m + c
        r = s & 0xFF
        v = int(((a ^ r) & (m ^ r) & 0x80) != 0)
        c = int(s > 0xFF)
        a = r
        out.append([a, r >> 7, v, int(r == 0), c])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('adc without carry', [17, 0, [['adc', 32], ['adc', 5]]], [[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 145]]], [[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 254]]], [[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 126]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [241, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [127, 0, [['adc', 128], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [56, 1, [['adc', 255]]], [[56, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [81, 0, [['sbc', 16], ['sbc', 63]]], [[64, 0, 0, 0, 1], [1, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 62], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 193]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [18, 0, [['adc', 32], ['adc', 5]]], [[50, 0, 0, 0, 0], [55, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 146]]], [[160, 1, 1, 0, 0], [50, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 253]]], [[0, 0, 0, 1, 1], [254, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 125]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [242, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [126, 0, [['adc', 129], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [57, 1, [['adc', 255]]], [[57, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [82, 0, [['sbc', 16], ['sbc', 63]]], [[65, 0, 0, 0, 1], [2, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 61], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 194]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [19, 0, [['adc', 32], ['adc', 5]]], [[51, 0, 0, 0, 0], [56, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 147]]], [[160, 1, 1, 0, 0], [51, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 252]]], [[0, 0, 0, 1, 1], [253, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 124]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [243, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [125, 0, [['adc', 130], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [58, 1, [['adc', 255]]], [[58, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [83, 0, [['sbc', 16], ['sbc', 63]]], [[66, 0, 0, 0, 1], [3, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 60], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 195]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [20, 0, [['adc', 32], ['adc', 5]]], [[52, 0, 0, 0, 0], [57, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 148]]], [[160, 1, 1, 0, 0], [52, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 251]]], [[0, 0, 0, 1, 1], [252, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 123]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [244, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [124, 0, [['adc', 131], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [59, 1, [['adc', 255]]], [[59, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [84, 0, [['sbc', 16], ['sbc', 63]]], [[67, 0, 0, 0, 1], [4, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 59], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 196]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [21, 0, [['adc', 32], ['adc', 5]]], [[53, 0, 0, 0, 0], [58, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 149]]], [[160, 1, 1, 0, 0], [53, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 250]]], [[0, 0, 0, 1, 1], [251, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 122]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [245, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [123, 0, [['adc', 132], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [60, 1, [['adc', 255]]], [[60, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [85, 0, [['sbc', 16], ['sbc', 63]]], [[68, 0, 0, 0, 1], [5, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 58], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 197]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])]]
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
adc without carry	`[[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]`	`[[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]`	Passed
adc signed overflow both ways	`[[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]`	`[[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]`	Passed
adc carry out to zero	`[[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]`	`[[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]`	Passed
sbc with carry set (no borrow)	`[[33, 0, 0, 0, 1], [114, 0, 0, 0, 0], [244, 1, 0, 0, 0]]`	`[[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [241, 1, 0, 0, 0]]`	Failed
sum of exactly 0xFF	`[[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]`	`[[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]`	Passed
carry in wraps operand	`[[56, 0, 0, 0, 1]]`	`[[56, 0, 0, 0, 1]]`	Passed
sbc with carry clear (borrow)	`[[65, 0, 0, 0, 1], [3, 0, 0, 0, 1]]`	`[[64, 0, 0, 0, 1], [1, 0, 0, 0, 1]]`	Failed
cmp orders and keeps accumulator	`[[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]`	`[[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]`	Passed
sbc to exactly zero	`[[1, 0, 0, 0, 1], [1, 0, 0, 0, 0]]`	`[[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]]`	Failed

SHA-256 / 346c259c9d415f385e4db2b2bb118e633515160c2b34d88a9816f85d4c007275

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
    v = 0
    out = []
    for op, m in ops:
        if op == 'cmp':
            r = (a - m) & 0xFF
            c = int(a >= m)
            out.append([a, r >> 7, v, int(r == 0), c])
            continue
        if op == 'sbc':
            m = m ^ 0xFF
        s = a + m + c
        r = s & 0xFF
        v = int(((a ^ r) & (m ^ r) & 0x80) != 0)
        c = int(s > 0xFF)
        a = r
        out.append([a, r >> 7, v, int(r == 0), c])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('adc without carry', [17, 0, [['adc', 32], ['adc', 5]]], [[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 145]]], [[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 254]]], [[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 126]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [241, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [127, 0, [['adc', 128], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [56, 1, [['adc', 255]]], [[56, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [81, 0, [['sbc', 16], ['sbc', 63]]], [[64, 0, 0, 0, 1], [1, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 62], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 193]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [18, 0, [['adc', 32], ['adc', 5]]], [[50, 0, 0, 0, 0], [55, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 146]]], [[160, 1, 1, 0, 0], [50, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 253]]], [[0, 0, 0, 1, 1], [254, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 125]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [242, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [126, 0, [['adc', 129], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [57, 1, [['adc', 255]]], [[57, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [82, 0, [['sbc', 16], ['sbc', 63]]], [[65, 0, 0, 0, 1], [2, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 61], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 194]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [19, 0, [['adc', 32], ['adc', 5]]], [[51, 0, 0, 0, 0], [56, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 147]]], [[160, 1, 1, 0, 0], [51, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 252]]], [[0, 0, 0, 1, 1], [253, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 124]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [243, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [125, 0, [['adc', 130], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [58, 1, [['adc', 255]]], [[58, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [83, 0, [['sbc', 16], ['sbc', 63]]], [[66, 0, 0, 0, 1], [3, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 60], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 195]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [20, 0, [['adc', 32], ['adc', 5]]], [[52, 0, 0, 0, 0], [57, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 148]]], [[160, 1, 1, 0, 0], [52, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 251]]], [[0, 0, 0, 1, 1], [252, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 123]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [244, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [124, 0, [['adc', 131], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [59, 1, [['adc', 255]]], [[59, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [84, 0, [['sbc', 16], ['sbc', 63]]], [[67, 0, 0, 0, 1], [4, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 59], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 196]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])], [('adc without carry', [21, 0, [['adc', 32], ['adc', 5]]], [[53, 0, 0, 0, 0], [58, 0, 0, 0, 0]]), ('adc signed overflow both ways', [80, 0, [['adc', 80], ['adc', 149]]], [[160, 1, 1, 0, 0], [53, 0, 1, 0, 1]]), ('adc carry out to zero', [255, 1, [['adc', 0], ['adc', 250]]], [[0, 0, 0, 1, 1], [251, 1, 0, 0, 0]]), ('sbc with carry set (no borrow)', [80, 1, [['sbc', 48], ['sbc', 176], ['sbc', 122]]], [[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [245, 1, 0, 0, 0]]), ('sum of exactly 0xFF', [123, 0, [['adc', 132], ['adc', 0]]], [[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]), ('carry in wraps operand', [60, 1, [['adc', 255]]], [[60, 0, 0, 0, 1]]), ('sbc with carry clear (borrow)', [85, 0, [['sbc', 16], ['sbc', 63]]], [[68, 0, 0, 0, 1], [5, 0, 0, 0, 1]]), ('cmp orders and keeps accumulator', [64, 0, [['cmp', 64], ['cmp', 65], ['cmp', 58], ['adc', 1]]], [[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]), ('sbc to exactly zero', [33, 1, [['sbc', 33], ['cmp', 197]]], [[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]])]]
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
adc without carry	`[[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]`	`[[49, 0, 0, 0, 0], [54, 0, 0, 0, 0]]`	Passed
adc signed overflow both ways	`[[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]`	`[[160, 1, 1, 0, 0], [49, 0, 1, 0, 1]]`	Passed
adc carry out to zero	`[[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]`	`[[0, 0, 0, 1, 1], [255, 1, 0, 0, 0]]`	Passed
sbc with carry set (no borrow)	`[[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [241, 1, 0, 0, 0]]`	`[[32, 0, 0, 0, 1], [112, 0, 0, 0, 0], [241, 1, 0, 0, 0]]`	Passed
sum of exactly 0xFF	`[[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]`	`[[255, 1, 0, 0, 0], [255, 1, 0, 0, 0]]`	Passed
carry in wraps operand	`[[56, 0, 0, 0, 1]]`	`[[56, 0, 0, 0, 1]]`	Passed
sbc with carry clear (borrow)	`[[64, 0, 0, 0, 1], [1, 0, 0, 0, 1]]`	`[[64, 0, 0, 0, 1], [1, 0, 0, 0, 1]]`	Passed
cmp orders and keeps accumulator	`[[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]`	`[[64, 0, 0, 1, 1], [64, 1, 0, 0, 0], [64, 0, 0, 0, 1], [66, 0, 0, 0, 0]]`	Passed
sbc to exactly zero	`[[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]]`	`[[0, 0, 0, 1, 1], [0, 0, 0, 0, 0]]`	Passed

SHA-256 / 58a4c81da0eb7d88650983228bfe73501050a0d7ba3958d61a2761d574d0f53f

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 2026-09-29T14:51:16.608739+00:00.

Case digest / b699530f20ce9e5d7bfaf7be21a5d1f36968dc5393d8b7b9d3368d94b5fc5c69