FA-49796 / PCM sample encoding / Open access

Pcm two tap predictor: prediction division · case 01

Dividing predictor terms separately changes integer rounding.

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

ROOT CAUSE

Dividing predictor terms separately changes integer rounding.

THE FAILURE

Dividing predictor terms separately changes integer rounding.

Unsuccessful approach: Truncation does not match the declared floor predictor on negative sums.

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]//divisor+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	`[[5, 3, -15, -11], -11, -15]`	`[[6, 5, -12, -7], -7, -12]`	Failed
oracle 2	`[[0, 2, 3], 3, 2]`	`[[0, 2, 3], 3, 2]`	Passed
oracle 3	`[[-1, -3], -3, -1]`	`[[0, -2], -2, 0]`	Failed
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	`[[-2, -3, -6], -6, -3]`	`[[-1, -2, -4], -4, -2]`	Failed
variant packet 1	`[[5, 3, -15, -11, -8, -9, -26, -21], -21, -26]`	`[[6, 5, -12, -7, -3, -3, -19, -13], -13, -19]`	Failed

SHA-256 / ce25bd065f058a7c4c4f4d40500300263b4c80d758145b4909534123ffcd5d7e

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=int((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, -6], -6, -12]`	`[[6, 5, -12, -7], -7, -12]`	Failed
oracle 2	`[[1, 3, 4], 4, 3]`	`[[0, 2, 3], 3, 2]`	Failed
oracle 3	`[[0, -1], -1, 0]`	`[[0, -2], -2, 0]`	Failed
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	`[[0, 0, -2], -2, 0]`	`[[-1, -2, -4], -4, -2]`	Failed
variant packet 1	`[[6, 5, -12, -6, -1, -1, -17, -11], -11, -17]`	`[[6, 5, -12, -7, -3, -3, -19, -13], -13, -19]`	Failed

SHA-256 / e12b181742a0889fbf45c93f0c7c9e1dfcd42266ef1a19e135190b9fd60502f1

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 / 23a278f92d053167175bc152dd4d80d4fbb7eaffb3f3a204ed65005abe4b9f45