FA-49866 / PCM sample encoding / Open access

Pcm alaw code selection: negative magnitude rule · case 01

A-law negative input omits its complement offset at quantization boundaries.

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

ROOT CAUSE

A-law negative input omits its complement offset at quantization boundaries.

VERIFIED REPAIR

Use the stated conversion contract at negative magnitude rule.

Unsuccessful approach: Applying the offset to positive samples breaks positive low bins.

Case contract

Stipulated bounded A-law-style PCM encoder with negative complement offset, thirteen-bit working magnitude, segment-specific shifts and alternating wire mask.

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
        magnitude=(-sample if negative else sample)>>3
        magnitude=min(magnitude,4095)
        segment=0
        while segment<7 and magnitude>=(32<<segment):
            segment+=1
        shift=1 if segment<2 else segment
        mantissa=(magnitude>>shift)&15
        code=(0 if negative else 128)|(segment<<4)|mantissa
        out.append(code^85)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 8, -8, 16, -16],)), [213, 213, 85, 212, 85])
check('oracle 2', solve(*([256, -256, 264, -264],)), [197, 90, 197, 69])
check('oracle 3', solve(*([32767, -32768, 40000, -40000],)), [170, 42, 170, 42])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([1024, 2048, 8192],)), [229, 149, 181])
check('oracle 6', solve(*([1, -1, 127, -128],)), [213, 85, 210, 82])
check('oracle 7', solve(*([512, -513, 4096, -4097],)), [245, 117, 133, 5])
if N == 1: check('variant packet 1', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 2: check('variant packet 2', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 3: check('variant packet 3', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 4: check('variant packet 4', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 5: check('variant packet 5', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
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	`[213, 213, 85, 212, 84]`	`[213, 213, 85, 212, 85]`	Failed
oracle 2	`[197, 69, 197, 69]`	`[197, 90, 197, 69]`	Failed
oracle 3	`[170, 42, 170, 42]`	`[170, 42, 170, 42]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[229, 149, 181]`	`[229, 149, 181]`	Passed
oracle 6	`[213, 85, 210, 93]`	`[213, 85, 210, 82]`	Failed
oracle 7	`[245, 117, 133, 5]`	`[245, 117, 133, 5]`	Passed
variant packet 1	`[213, 213, 85, 212, 84, 213, 213, 85, 212, 84]`	`[213, 213, 85, 212, 85, 213, 213, 85, 212, 85]`	Failed

SHA-256 / 595b66b88707c2a78b05b691f686c5b12128a60a51452e38dd2c97dca96cc736

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
        magnitude=(abs(sample)-1)>>3
        magnitude=min(magnitude,4095)
        segment=0
        while segment<7 and magnitude>=(32<<segment):
            segment+=1
        shift=1 if segment<2 else segment
        mantissa=(magnitude>>shift)&15
        code=(0 if negative else 128)|(segment<<4)|mantissa
        out.append(code^85)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 8, -8, 16, -16],)), [213, 213, 85, 212, 85])
check('oracle 2', solve(*([256, -256, 264, -264],)), [197, 90, 197, 69])
check('oracle 3', solve(*([32767, -32768, 40000, -40000],)), [170, 42, 170, 42])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([1024, 2048, 8192],)), [229, 149, 181])
check('oracle 6', solve(*([1, -1, 127, -128],)), [213, 85, 210, 82])
check('oracle 7', solve(*([512, -513, 4096, -4097],)), [245, 117, 133, 5])
if N == 1: check('variant packet 1', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 2: check('variant packet 2', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 3: check('variant packet 3', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 4: check('variant packet 4', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 5: check('variant packet 5', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
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	`[218, 213, 85, 213, 85]`	`[213, 213, 85, 212, 85]`	Failed
oracle 2	`[218, 90, 197, 69]`	`[197, 90, 197, 69]`	Failed
oracle 3	`[170, 42, 170, 42]`	`[170, 42, 170, 42]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[250, 234, 138]`	`[229, 149, 181]`	Failed
oracle 6	`[213, 85, 210, 82]`	`[213, 85, 210, 82]`	Passed
oracle 7	`[202, 117, 154, 5]`	`[245, 117, 133, 5]`	Failed
variant packet 1	`[218, 213, 85, 213, 85, 218, 213, 85, 213, 85]`	`[213, 213, 85, 212, 85, 213, 213, 85, 212, 85]`	Failed

SHA-256 / 9e13219722da37ecbfaa5ec83c0a1c5ba6e0f0d5236b95cc8f7f3a76cdcf6401

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
        magnitude=(-sample-1 if negative else sample)>>3
        magnitude=min(magnitude,4095)
        segment=0
        while segment<7 and magnitude>=(32<<segment):
            segment+=1
        shift=1 if segment<2 else segment
        mantissa=(magnitude>>shift)&15
        code=(0 if negative else 128)|(segment<<4)|mantissa
        out.append(code^85)
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('oracle 1', solve(*([0, 8, -8, 16, -16],)), [213, 213, 85, 212, 85])
check('oracle 2', solve(*([256, -256, 264, -264],)), [197, 90, 197, 69])
check('oracle 3', solve(*([32767, -32768, 40000, -40000],)), [170, 42, 170, 42])
check('oracle 4', solve(*([],)), [])
check('oracle 5', solve(*([1024, 2048, 8192],)), [229, 149, 181])
check('oracle 6', solve(*([1, -1, 127, -128],)), [213, 85, 210, 82])
check('oracle 7', solve(*([512, -513, 4096, -4097],)), [245, 117, 133, 5])
if N == 1: check('variant packet 1', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 2: check('variant packet 2', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 3: check('variant packet 3', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 4: check('variant packet 4', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
if N == 5: check('variant packet 5', solve(*[[0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16, 0, 8, -8, 16, -16]]), [213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85, 213, 213, 85, 212, 85])
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	`[213, 213, 85, 212, 85]`	`[213, 213, 85, 212, 85]`	Passed
oracle 2	`[197, 90, 197, 69]`	`[197, 90, 197, 69]`	Passed
oracle 3	`[170, 42, 170, 42]`	`[170, 42, 170, 42]`	Passed
oracle 4	`[]`	`[]`	Passed
oracle 5	`[229, 149, 181]`	`[229, 149, 181]`	Passed
oracle 6	`[213, 85, 210, 82]`	`[213, 85, 210, 82]`	Passed
oracle 7	`[245, 117, 133, 5]`	`[245, 117, 133, 5]`	Passed
variant packet 1	`[213, 213, 85, 212, 85, 213, 213, 85, 212, 85]`	`[213, 213, 85, 212, 85, 213, 213, 85, 212, 85]`	Passed

SHA-256 / df99ba847feb88c82ec2203b6e947d4ae1167b17d32ccde326bc8d136c175a7b

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 2026-09-29T14:45:03.879506+00:00.

Case digest / c46a1788e822427e26fa5a645533b78f1bff68d9421a3b58105e3de25bf429b6