FA-49811 / PCM sample encoding / Open access

Pcm two tap predictor: history shift · case 01

Both predictor taps retain the newest decoded sample.

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

ROOT CAUSE

Both predictor taps retain the newest decoded sample.

VERIFIED REPAIR

Use the stated conversion contract at history shift.

Unsuccessful approach: Never shifting the older tap freezes obsolete history.

Case contract

Stipulated two-history adaptive PCM decoder with explicit integer predictor coefficients, floor divisor, signed residual nibble and fixed residual amplitude scale.

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(codes, last, older, coefficients, divisor, delta):
    out=[]
    for code in codes:
        predicted=(last*coefficients[0]+older*coefficients[1])//divisor
        signed=code-16 if code&8 else code
        sample=predicted+signed*delta
        older,last=sample,sample
        out.append(sample)
    return [out,last,older]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 15, 8, 7], 3, 1, [3, -1], 2, 2)), [[6, 5, -12, -7], -7, -12])
check('oracle 2', solve(*([1, 2, 3], 2, -3, [1, 1], 3, 1)), [[0, 2, 3], 3, 2])
check('oracle 3', solve(*([0, 0], -2, 1, [1, 2], 3, 4)), [[0, -2], -2, 0])
check('oracle 4', solve(*([], 5, 2, [2, -1], 1, 1)), [[], 5, 2])
check('oracle 5', solve(*([8, 0, 7], 0, 0, [1, 0], 1, 3)), [[-24, -24, -3], -3, -24])
check('oracle 6', solve(*([15, 15, 1], 4, 3, [2, -1], 2, 2)), [[0, -4, -2], -2, -4])
check('oracle 7', solve(*([2, 0, 14], -3, -1, [3, 1], 4, 1)), [[-1, -2, -4], -4, -2])
if N == 1: check('variant packet 1', solve(*[[1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13], -13, -19])
if N == 2: check('variant packet 2', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18], -18, -24])
if N == 3: check('variant packet 3', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23], -23, -29])
if N == 4: check('variant packet 4', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23, -18, -18, -34, -28], -28, -34])
if N == 5: check('variant packet 5', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23, -18, -18, -34, -28, -23, -23, -39, -33], -33, -39])
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	`[[6, 4, -12, 2], 2, 2]`	`[[6, 5, -12, -7], -7, -12]`	Failed
oracle 2	`[[0, 2, 4], 4, 4]`	`[[0, 2, 3], 3, 2]`	Failed
oracle 3	`[[0, 0], 0, 0]`	`[[0, -2], -2, 0]`	Failed
oracle 4	`[[], 5, 2]`	`[[], 5, 2]`	Passed
oracle 5	`[[-24, -24, -3], -3, -3]`	`[[-24, -24, -3], -3, -24]`	Failed
oracle 6	`[[0, -2, 1], 1, 1]`	`[[0, -4, -2], -2, -4]`	Failed
oracle 7	`[[-1, -1, -3], -3, -3]`	`[[-1, -2, -4], -4, -2]`	Failed
variant packet 1	`[[6, 4, -12, 2, 4, 2, -14, 0], 0, 0]`	`[[6, 5, -12, -7, -3, -3, -19, -13], -13, -19]`	Failed

SHA-256 / 2e974dd8dfa406cda5447ab692baf0f608f7a942883ec09a5c192f02be6d71cd

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(codes, last, older, coefficients, divisor, delta):
    out=[]
    for code in codes:
        predicted=(last*coefficients[0]+older*coefficients[1])//divisor
        signed=code-16 if code&8 else code
        sample=predicted+signed*delta
        older,last=older,sample
        out.append(sample)
    return [out,last,older]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 15, 8, 7], 3, 1, [3, -1], 2, 2)), [[6, 5, -12, -7], -7, -12])
check('oracle 2', solve(*([1, 2, 3], 2, -3, [1, 1], 3, 1)), [[0, 2, 3], 3, 2])
check('oracle 3', solve(*([0, 0], -2, 1, [1, 2], 3, 4)), [[0, -2], -2, 0])
check('oracle 4', solve(*([], 5, 2, [2, -1], 1, 1)), [[], 5, 2])
check('oracle 5', solve(*([8, 0, 7], 0, 0, [1, 0], 1, 3)), [[-24, -24, -3], -3, -24])
check('oracle 6', solve(*([15, 15, 1], 4, 3, [2, -1], 2, 2)), [[0, -4, -2], -2, -4])
check('oracle 7', solve(*([2, 0, 14], -3, -1, [3, 1], 4, 1)), [[-1, -2, -4], -4, -2])
if N == 1: check('variant packet 1', solve(*[[1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13], -13, -19])
if N == 2: check('variant packet 2', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18], -18, -24])
if N == 3: check('variant packet 3', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23], -23, -29])
if N == 4: check('variant packet 4', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23, -18, -18, -34, -28], -28, -34])
if N == 5: check('variant packet 5', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23, -18, -18, -34, -28, -23, -23, -39, -33], -33, -39])
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	`[[6, 6, -8, 1], 1, 1]`	`[[6, 5, -12, -7], -7, -12]`	Failed
oracle 2	`[[0, 1, 2], 2, -3]`	`[[0, 2, 3], 3, 2]`	Failed
oracle 3	`[[0, 0], 0, 1]`	`[[0, -2], -2, 0]`	Failed
oracle 4	`[[], 5, 2]`	`[[], 5, 2]`	Passed
oracle 5	`[[-24, -24, -3], -3, 0]`	`[[-24, -24, -3], -3, -24]`	Failed
oracle 6	`[[0, -4, -4], -4, 3]`	`[[0, -4, -2], -2, -4]`	Failed
oracle 7	`[[-1, -1, -3], -3, -1]`	`[[-1, -2, -4], -4, -2]`	Failed
variant packet 1	`[[6, 6, -8, 1, 3, 2, -14, -8], -8, 1]`	`[[6, 5, -12, -7, -3, -3, -19, -13], -13, -19]`	Failed

SHA-256 / 3f35b187441d645e515398150d9998e2e5ad6cf7a9430b034fd82bebbb90abb4

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(codes, last, older, coefficients, divisor, delta):
    out=[]
    for code in codes:
        predicted=(last*coefficients[0]+older*coefficients[1])//divisor
        signed=code-16 if code&8 else code
        sample=predicted+signed*delta
        older,last=last,sample
        out.append(sample)
    return [out,last,older]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([1, 15, 8, 7], 3, 1, [3, -1], 2, 2)), [[6, 5, -12, -7], -7, -12])
check('oracle 2', solve(*([1, 2, 3], 2, -3, [1, 1], 3, 1)), [[0, 2, 3], 3, 2])
check('oracle 3', solve(*([0, 0], -2, 1, [1, 2], 3, 4)), [[0, -2], -2, 0])
check('oracle 4', solve(*([], 5, 2, [2, -1], 1, 1)), [[], 5, 2])
check('oracle 5', solve(*([8, 0, 7], 0, 0, [1, 0], 1, 3)), [[-24, -24, -3], -3, -24])
check('oracle 6', solve(*([15, 15, 1], 4, 3, [2, -1], 2, 2)), [[0, -4, -2], -2, -4])
check('oracle 7', solve(*([2, 0, 14], -3, -1, [3, 1], 4, 1)), [[-1, -2, -4], -4, -2])
if N == 1: check('variant packet 1', solve(*[[1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13], -13, -19])
if N == 2: check('variant packet 2', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18], -18, -24])
if N == 3: check('variant packet 3', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23], -23, -29])
if N == 4: check('variant packet 4', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23, -18, -18, -34, -28], -28, -34])
if N == 5: check('variant packet 5', solve(*[[1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7, 1, 15, 8, 7], 3, 1, [3, -1], 2, 2]), [[6, 5, -12, -7, -3, -3, -19, -13, -8, -8, -24, -18, -13, -13, -29, -23, -18, -18, -34, -28, -23, -23, -39, -33], -33, -39])
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	`[[6, 5, -12, -7], -7, -12]`	`[[6, 5, -12, -7], -7, -12]`	Passed
oracle 2	`[[0, 2, 3], 3, 2]`	`[[0, 2, 3], 3, 2]`	Passed
oracle 3	`[[0, -2], -2, 0]`	`[[0, -2], -2, 0]`	Passed
oracle 4	`[[], 5, 2]`	`[[], 5, 2]`	Passed
oracle 5	`[[-24, -24, -3], -3, -24]`	`[[-24, -24, -3], -3, -24]`	Passed
oracle 6	`[[0, -4, -2], -2, -4]`	`[[0, -4, -2], -2, -4]`	Passed
oracle 7	`[[-1, -2, -4], -4, -2]`	`[[-1, -2, -4], -4, -2]`	Passed
variant packet 1	`[[6, 5, -12, -7, -3, -3, -19, -13], -13, -19]`	`[[6, 5, -12, -7, -3, -3, -19, -13], -13, -19]`	Passed

SHA-256 / ba7d0315b3a843c45e96018a179224e53d7c27b1fe15d824d8ba802823a86617

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 2026-09-29T14:45:03.457660+00:00.

Case digest / d8284a65fa766101cd774763621400da874bca1edfbf7218c6bea820f6c00328