FA-49941 / PCM sample encoding / Open access

Pcm companding segment code: segment comparison · case 01

Exact segment boundaries remain in their lower region.

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

ROOT CAUSE

Exact segment boundaries remain in their lower region.

VERIFIED REPAIR

Use the stated conversion contract at segment comparison.

Unsuccessful approach: Comparing the current lower bound advances one segment too far.

Case contract

Encode bounded PCM magnitude into an explicitly stipulated piecewise companding table: sign sideband, selected lower-bound segment and shifted residual mantissa.

Why this case matters

Offline PCM interchange uses these exact bounded packet and sample representation decisions.

1 / The failure

Exit 1

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

N = 1
observations = []
def solve(samples, edges, shifts):
    out=[]
    for sample in samples:
        negative=sample<0
        magnitude=abs(sample)
        segment=0
        while segment+1<len(edges) and magnitude>edges[segment+1]:
            segment+=1
        residual=max(0,magnitude-edges[segment])
        mantissa=residual>>shifts[segment]
        out.append([negative,segment,mantissa])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])
check('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])
check('oracle 4', solve(*([], [0, 8], [1, 3])), [])
check('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])
check('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])
if N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
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
oracle 1	`[[True, 2, 0], [True, 0, 4], [False, 0, 0], [False, 0, 4], [False, 2, 0]]`	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Failed
oracle 2	`[[False, 0, 0], [False, 0, 2], [False, 0, 3], [False, 1, 1]]`	`[[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]]`	Failed
oracle 3	`[[False, 0, 0], [False, 0, 1], [False, 0, 1]]`	`[[False, 0, 0], [False, 0, 1], [False, 0, 1]]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[True, 0, 8], [False, 0, 8], [False, 1, 0]]`	`[[True, 1, 0], [False, 1, 0], [False, 1, 0]]`	Failed
oracle 6	`[[False, 0, 0], [False, 0, 1], [False, 1, 15]]`	`[[False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Failed
oracle 7	`[[False, 1, 3], [True, 1, 3]]`	`[[False, 1, 3], [True, 1, 3]]`	Passed
variant packet 1	`[[True, 2, 0], [True, 0, 4], [False, 0, 0], [False, 0, 4], [False, 2, 0], [True, 2, 0], [True, 0, 4], [False, 0, 0], [False, 0, 4], [False, 2, 0]]`	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Failed

SHA-256 / cdef62dcc44e05a288b96902a3b80febb8c663b8d0889f1024a3a27cdabd0df0

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(samples, edges, shifts):
    out=[]
    for sample in samples:
        negative=sample<0
        magnitude=abs(sample)
        segment=0
        while segment+1<len(edges) and magnitude>=edges[segment]:
            segment+=1
        residual=max(0,magnitude-edges[segment])
        mantissa=residual>>shifts[segment]
        out.append([negative,segment,mantissa])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])
check('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])
check('oracle 4', solve(*([], [0, 8], [1, 3])), [])
check('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])
check('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])
if N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
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
oracle 1	`[[True, 2, 0], [True, 2, 0], [False, 1, 0], [False, 2, 0], [False, 2, 0]]`	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Failed
oracle 2	`[[False, 1, 0], [False, 1, 0], [False, 2, 0], [False, 2, 0]]`	`[[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]]`	Failed
oracle 3	`[[False, 0, 0], [False, 0, 1], [False, 0, 1]]`	`[[False, 0, 0], [False, 0, 1], [False, 0, 1]]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[True, 1, 0], [False, 1, 0], [False, 1, 0]]`	`[[True, 1, 0], [False, 1, 0], [False, 1, 0]]`	Passed
oracle 6	`[[False, 1, 0], [False, 2, 0], [False, 2, 0]]`	`[[False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Failed
oracle 7	`[[False, 1, 3], [True, 1, 3]]`	`[[False, 1, 3], [True, 1, 3]]`	Passed
variant packet 1	`[[True, 2, 0], [True, 2, 0], [False, 1, 0], [False, 2, 0], [False, 2, 0], [True, 2, 0], [True, 2, 0], [False, 1, 0], [False, 2, 0], [False, 2, 0]]`	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Failed

SHA-256 / c7b4bc35f6559ea3591f2f6c341df4fc87ea23b64bd488e9a419372618fa1686

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(samples, edges, shifts):
    out=[]
    for sample in samples:
        negative=sample<0
        magnitude=abs(sample)
        segment=0
        while segment+1<len(edges) and magnitude>=edges[segment+1]:
            segment+=1
        residual=max(0,magnitude-edges[segment])
        mantissa=residual>>shifts[segment]
        out.append([negative,segment,mantissa])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([-15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3])), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 2', solve(*([0, 2, 3, 8], [0, 3, 8], [0, 2, 2])), [[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]])
check('oracle 3', solve(*([1, 2, 3], [0], [1])), [[False, 0, 0], [False, 0, 1], [False, 0, 1]])
check('oracle 4', solve(*([], [0, 8], [1, 3])), [])
check('oracle 5', solve(*([-8, 8, 9], [0, 8], [0, 3])), [[True, 1, 0], [False, 1, 0], [False, 1, 0]])
check('oracle 6', solve(*([0, 1, 16], [0, 1, 16], [0, 0, 2])), [[False, 0, 0], [False, 1, 0], [False, 2, 0]])
check('oracle 7', solve(*([7, -7], [0, 4], [1, 0])), [[False, 1, 3], [True, 1, 3]])
if N == 1: check('variant packet 1', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 2: check('variant packet 2', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 3: check('variant packet 3', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 4: check('variant packet 4', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
if N == 5: check('variant packet 5', solve(*[[-15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15, -15, -4, 0, 4, 15], [0, 4, 12], [0, 1, 3]]), [[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]])
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
oracle 1	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Passed
oracle 2	`[[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]]`	`[[False, 0, 0], [False, 0, 2], [False, 1, 0], [False, 2, 0]]`	Passed
oracle 3	`[[False, 0, 0], [False, 0, 1], [False, 0, 1]]`	`[[False, 0, 0], [False, 0, 1], [False, 0, 1]]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[[True, 1, 0], [False, 1, 0], [False, 1, 0]]`	`[[True, 1, 0], [False, 1, 0], [False, 1, 0]]`	Passed
oracle 6	`[[False, 0, 0], [False, 1, 0], [False, 2, 0]]`	`[[False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Passed
oracle 7	`[[False, 1, 3], [True, 1, 3]]`	`[[False, 1, 3], [True, 1, 3]]`	Passed
variant packet 1	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	`[[True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0], [True, 2, 0], [True, 1, 0], [False, 0, 0], [False, 1, 0], [False, 2, 0]]`	Passed

SHA-256 / b936e90cfccecaa5f1228a45a07d89abce9fee9d748bd2a380bf8851476f5bbf

Verification & scope

Stipulated finite model; no claim of hardware timing or full file-format 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 2026-09-29T14:45:04.626047+00:00.

Case digest / b41fdb07e426c39fcbe16b456b0d5857f163b08f12084f7adb0c14e003bbe1ca