FA-81651 / MIDI event timing / Open access

14-bit pitch bend to cents: cents truncated · case 01

A bend worth 12.5 cents reports 12 and fractional values always shrink toward zero.

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

ROOT CAUSE

The scaled magnitude is truncated instead of rounded half away from zero.

VERIFIED REPAIR

Restore the cent rounding step so that it reads `int(c + Fraction(1, 2))`.

Unsuccessful approach: Python round rounds exact halves to even, so 12.5 still becomes 12.

Case contract

Input [lsb, msb, range_semitones] with 7-bit data bytes. value = msb*128 + lsb, offset = value - 8192. Positive offsets scale to +range by dividing by 8191, negative ones by 8192. cents = offset * range * 100 / divisor, rounded half away from zero. Invalid bytes or negative range return None.

Why this case matters

MIDI sequencers, file readers and synth drivers depend on exact event ordering and tick/time arithmetic.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    lsb, msb, rng = x
    if not all(isinstance(v, int) and 0 <= v <= 127 for v in (lsb, msb)) or rng < 0:
        return None
    value = (msb << 7) | lsb
    offset = value - 8192
    den = 8191 if offset > 0 else 8192
    c = Fraction(abs(offset) * rng * 100, den)
    cents = int(c)
    return cents if offset >= 0 else -cents
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([0, 64, 2], 0), ([127, 127, 2], 200), ([0, 0, 2], -200), ([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38)], [([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([1, 64, 2], 0), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 56, 3], -38)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 128, 2], None), ([128, 64, 2], None), ([0, 88, 1], 38)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 56, 3], -38), ([128, 64, 2], None), ([0, 64, -1], None), ([127, 127, 12], 1200), ([0, 0, 12], -1200), ([64, 100, 2], 114)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 0, 12], -1200), ([64, 100, 2], 114), ([0, 88, 1], 38), ([127, 127, 48], 4800), ([0, 0, 48], -4800), ([100, 127, 48], 4784)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
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 0	`0`	`0`	Passed
oracle 1	`200`	`200`	Passed
oracle 2	`-200`	`-200`	Passed
oracle 3	`100`	`100`	Passed
oracle 4	`-100`	`-100`	Passed
oracle 5	`-12`	`-13`	Failed
oracle 6	`-62`	`-63`	Failed
oracle 7	`-37`	`-38`	Failed

SHA-256 / 546e8c4efb19cf092da35eacf84137da782134d12412489f9a78a9016a899668

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    lsb, msb, rng = x
    if not all(isinstance(v, int) and 0 <= v <= 127 for v in (lsb, msb)) or rng < 0:
        return None
    value = (msb << 7) | lsb
    offset = value - 8192
    den = 8191 if offset > 0 else 8192
    c = Fraction(abs(offset) * rng * 100, den)
    cents = round(c)
    return cents if offset >= 0 else -cents
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([0, 64, 2], 0), ([127, 127, 2], 200), ([0, 0, 2], -200), ([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38)], [([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([1, 64, 2], 0), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 56, 3], -38)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 128, 2], None), ([128, 64, 2], None), ([0, 88, 1], 38)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 56, 3], -38), ([128, 64, 2], None), ([0, 64, -1], None), ([127, 127, 12], 1200), ([0, 0, 12], -1200), ([64, 100, 2], 114)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 0, 12], -1200), ([64, 100, 2], 114), ([0, 88, 1], 38), ([127, 127, 48], 4800), ([0, 0, 48], -4800), ([100, 127, 48], 4784)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
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 0	`0`	`0`	Passed
oracle 1	`200`	`200`	Passed
oracle 2	`-200`	`-200`	Passed
oracle 3	`100`	`100`	Passed
oracle 4	`-100`	`-100`	Passed
oracle 5	`-12`	`-13`	Failed
oracle 6	`-62`	`-63`	Failed
oracle 7	`-38`	`-38`	Passed

SHA-256 / a6a287db0de85c093b807e7f6be2265b4997726189d15cac667d5750c5f10e29

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    lsb, msb, rng = x
    if not all(isinstance(v, int) and 0 <= v <= 127 for v in (lsb, msb)) or rng < 0:
        return None
    value = (msb << 7) | lsb
    offset = value - 8192
    den = 8191 if offset > 0 else 8192
    c = Fraction(abs(offset) * rng * 100, den)
    cents = int(c + Fraction(1, 2))
    return cents if offset >= 0 else -cents
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([0, 64, 2], 0), ([127, 127, 2], 200), ([0, 0, 2], -200), ([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38)], [([0, 96, 2], 100), ([0, 32, 2], -100), ([0, 56, 1], -13), ([0, 24, 1], -63), ([1, 64, 2], 0), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 56, 3], -38)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 40, 1], -38), ([127, 63, 2], 0), ([0, 72, 12], 150), ([0, 128, 2], None), ([128, 64, 2], None), ([0, 88, 1], 38)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 56, 3], -38), ([128, 64, 2], None), ([0, 64, -1], None), ([127, 127, 12], 1200), ([0, 0, 12], -1200), ([64, 100, 2], 114)], [([0, 56, 1], -13), ([0, 24, 1], -63), ([0, 0, 12], -1200), ([64, 100, 2], 114), ([0, 88, 1], 38), ([127, 127, 48], 4800), ([0, 0, 48], -4800), ([100, 127, 48], 4784)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
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 0	`0`	`0`	Passed
oracle 1	`200`	`200`	Passed
oracle 2	`-200`	`-200`	Passed
oracle 3	`100`	`100`	Passed
oracle 4	`-100`	`-100`	Passed
oracle 5	`-13`	`-13`	Passed
oracle 6	`-63`	`-63`	Passed
oracle 7	`-38`	`-38`	Passed

SHA-256 / fb8896cfa96ca11ba0e5b9547ef6dff1e0b8f65cb4393fb166d7f710c504af8d

Verification & scope

A deterministic bounded teaching model with a stipulated toy contract; it is not a complete Standard MIDI File or MIDI 1.0/2.0 implementation. 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 2026-09-29T14:50:05.037643+00:00.

Case digest / c4bd0678d41d632f5f79c87fe89ae8f13557e31607fa52f9b70f691618fb388e