FA-49851 / PCM sample encoding / Open access

Pcm mulaw code selection: mantissa shift · case 01

Mu-law mantissa extraction leaves three discarded precision bits.

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

ROOT CAUSE

Mu-law mantissa extraction leaves three discarded precision bits.

VERIFIED REPAIR

Use the stated conversion contract at mantissa shift.

Unsuccessful approach: Discarding four bits halves mantissa resolution.

Case contract

Bounded mu-law-style selection model: clamp magnitude32635, add bias132, select segment and mantissa then complement the full eight-bit code.

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):
    out=[]
    for sample in samples:
        negative=sample<0
        amplitude=min(32635,abs(sample))+132
        exponent=0
        while exponent<7 and amplitude>=(256<<exponent):
            exponent+=1
        mantissa=(amplitude>>exponent)&15
        code=(128 if negative else 0)|(exponent<<4)|mantissa
        out.append((~code)&255)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, -1, 100, -100],)), [255, 255, 127, 242, 114])
check('oracle 2', solve(*([124, 125, -124],)), [239, 239, 111])
check('oracle 3', solve(*([32635, 40000, -40000],)), [128, 128, 0])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([1000, 4000, 16000],)), [206, 175, 144])
check('oracle 6', solve(*([380, 892, 1916],)), [223, 207, 191])
check('oracle 7', solve(*([-1000, -4000, -16000],)), [78, 47, 16])
if N == 1: check('variant packet 1', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 2: check('variant packet 2', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 3: check('variant packet 3', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 4: check('variant packet 4', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 5: check('variant packet 5', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
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	`[251, 250, 122, 247, 119]`	`[255, 255, 127, 242, 114]`	Failed
oracle 2	`[239, 239, 111]`	`[239, 239, 111]`	Passed
oracle 3	`[128, 128, 0]`	`[128, 128, 0]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[194, 174, 147]`	`[206, 175, 144]`	Failed
oracle 6	`[223, 207, 191]`	`[223, 207, 191]`	Passed
oracle 7	`[66, 46, 19]`	`[78, 47, 16]`	Failed
variant packet 1	`[251, 250, 122, 247, 119, 251, 250, 122, 247, 119]`	`[255, 255, 127, 242, 114, 255, 255, 127, 242, 114]`	Failed

SHA-256 / 44b5e6f0e0f73ee2a23ff408479297bcc07da1c4d7a01c3515fe54194dd6ee30

2 / The unsuccessful fix

Exit 1

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

N = 1
observations = []
def solve(samples):
    out=[]
    for sample in samples:
        negative=sample<0
        amplitude=min(32635,abs(sample))+132
        exponent=0
        while exponent<7 and amplitude>=(256<<exponent):
            exponent+=1
        mantissa=(amplitude>>(exponent+4))&15
        code=(128 if negative else 0)|(exponent<<4)|mantissa
        out.append((~code)&255)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, -1, 100, -100],)), [255, 255, 127, 242, 114])
check('oracle 2', solve(*([124, 125, -124],)), [239, 239, 111])
check('oracle 3', solve(*([32635, 40000, -40000],)), [128, 128, 0])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([1000, 4000, 16000],)), [206, 175, 144])
check('oracle 6', solve(*([380, 892, 1916],)), [223, 207, 191])
check('oracle 7', solve(*([-1000, -4000, -16000],)), [78, 47, 16])
if N == 1: check('variant packet 1', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 2: check('variant packet 2', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 3: check('variant packet 3', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 4: check('variant packet 4', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 5: check('variant packet 5', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
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	`[247, 247, 119, 241, 113]`	`[255, 255, 127, 242, 114]`	Failed
oracle 2	`[231, 231, 103]`	`[239, 239, 111]`	Failed
oracle 3	`[128, 128, 0]`	`[128, 128, 0]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[199, 167, 144]`	`[206, 175, 144]`	Failed
oracle 6	`[215, 199, 183]`	`[223, 207, 191]`	Failed
oracle 7	`[71, 39, 16]`	`[78, 47, 16]`	Failed
variant packet 1	`[247, 247, 119, 241, 113, 247, 247, 119, 241, 113]`	`[255, 255, 127, 242, 114, 255, 255, 127, 242, 114]`	Failed

SHA-256 / 6e62ec0cc6a6f51323dc6446a3cf184cbfdc00683e0e02bd9d2d634e3d9f1606

3 / The verified repair

Exit 0

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

N = 1
observations = []
def solve(samples):
    out=[]
    for sample in samples:
        negative=sample<0
        amplitude=min(32635,abs(sample))+132
        exponent=0
        while exponent<7 and amplitude>=(256<<exponent):
            exponent+=1
        mantissa=(amplitude>>(exponent+3))&15
        code=(128 if negative else 0)|(exponent<<4)|mantissa
        out.append((~code)&255)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 1, -1, 100, -100],)), [255, 255, 127, 242, 114])
check('oracle 2', solve(*([124, 125, -124],)), [239, 239, 111])
check('oracle 3', solve(*([32635, 40000, -40000],)), [128, 128, 0])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([1000, 4000, 16000],)), [206, 175, 144])
check('oracle 6', solve(*([380, 892, 1916],)), [223, 207, 191])
check('oracle 7', solve(*([-1000, -4000, -16000],)), [78, 47, 16])
if N == 1: check('variant packet 1', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 2: check('variant packet 2', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 3: check('variant packet 3', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 4: check('variant packet 4', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
if N == 5: check('variant packet 5', solve(*[[0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100, 0, 1, -1, 100, -100]]), [255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114, 255, 255, 127, 242, 114])
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	`[255, 255, 127, 242, 114]`	`[255, 255, 127, 242, 114]`	Passed
oracle 2	`[239, 239, 111]`	`[239, 239, 111]`	Passed
oracle 3	`[128, 128, 0]`	`[128, 128, 0]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[206, 175, 144]`	`[206, 175, 144]`	Passed
oracle 6	`[223, 207, 191]`	`[223, 207, 191]`	Passed
oracle 7	`[78, 47, 16]`	`[78, 47, 16]`	Passed
variant packet 1	`[255, 255, 127, 242, 114, 255, 255, 127, 242, 114]`	`[255, 255, 127, 242, 114, 255, 255, 127, 242, 114]`	Passed

SHA-256 / 9a61544a71b8062ad93686f3ed544e53c854273e6558ea0c346d7822c4809892

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 2026-09-29T14:45:03.755586+00:00.

Case digest / 01df75109baeb8d81d8949b71bb4d501b1266e5d3897e65625b55e0e7486c177