FA-16591 / Floating-point arithmetic / Open access

Floating total order only flips the negative sign bit · case 01

Floating total order only flips the negative sign bit.

Verified by executionVariant 1 · 9 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Floating total order only flips the negative sign bit. The faulty expression is return bits^(1<<63).

VERIFIED REPAIR

Apply the contract at this fault site using return ((~bits)&((1<<64)-1)) if bits>>63 else (bits|(1<<63)).

Unsuccessful approach: The attempted local correction return -(bits&((1<<63)-1)) if bits>>63 else bits still violates the explicit regression fixtures.

Case contract

Sort unsigned binary64 encodings by the stipulated IEEE-style total encoding order: negative NaNs, negative infinity, negative finite, negative zero, positive zero, positive finite, positive infinity, positive NaNs. Within signed NaNs, reversing bits on negatives reverses quietness and payload ordering. Preserve all encodings.

Why this case matters

An offline floating representation model isolates a reproducible arithmetic fault.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
N = 1
observations = []
def solve(values):
    def order(bits):
        return bits^(1<<63)
    return sorted(values,key=order)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('zero order', solve([0,1<<63]), [1<<63,0])
check('negative magnitudes', solve([0xbff0000000000000,0xc000000000000000]), [0xc000000000000000,0xbff0000000000000])
check('positive magnitudes', solve([0x4000000000000000,0x3ff0000000000000]), [0x3ff0000000000000,0x4000000000000000])
check('infinity and nan', solve([0x7ff8000000000000|N,0x7ff0000000000000]), [0x7ff0000000000000,0x7ff8000000000000|N])
check('negative nan order', solve([0xfff0000000000000|N,0xfff8000000000000|N]), [0xfff8000000000000|N,0xfff0000000000000|N])
check('positive payloads', solve([0x7ff8000000000064,0x7ff8000000000000|N]), [0x7ff8000000000000|N,0x7ff8000000000064])
check('negative payloads', solve([0xfff8000000000000|N,0xfff8000000000064]), [0xfff8000000000064,0xfff8000000000000|N])
check('mixed signs', solve([N,(1<<63)|N]), [(1<<63)|N,N])
check('duplicates', solve([N,N]), [N,N])
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
zero order	`[9223372036854775808, 0]`	`[9223372036854775808, 0]`	Passed
negative magnitudes	`[13830554455654793216, 13835058055282163712]`	`[13835058055282163712, 13830554455654793216]`	Failed
positive magnitudes	`[4607182418800017408, 4611686018427387904]`	`[4607182418800017408, 4611686018427387904]`	Passed
infinity and nan	`[9218868437227405312, 9221120237041090561]`	`[9218868437227405312, 9221120237041090561]`	Passed
negative nan order	`[18442240474082181121, 18444492273895866369]`	`[18444492273895866369, 18442240474082181121]`	Failed
positive payloads	`[9221120237041090561, 9221120237041090660]`	`[9221120237041090561, 9221120237041090660]`	Passed
negative payloads	`[18444492273895866369, 18444492273895866468]`	`[18444492273895866468, 18444492273895866369]`	Failed
mixed signs	`[9223372036854775809, 1]`	`[9223372036854775809, 1]`	Passed
duplicates	`[1, 1]`	`[1, 1]`	Passed

SHA-256 / b681932b5d0195f07c56a15de28ae7014e83d58201b0e2f02bcd622a607ac396

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
N = 1
observations = []
def solve(values):
    def order(bits):
        return -(bits&((1<<63)-1)) if bits>>63 else bits
    return sorted(values,key=order)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('zero order', solve([0,1<<63]), [1<<63,0])
check('negative magnitudes', solve([0xbff0000000000000,0xc000000000000000]), [0xc000000000000000,0xbff0000000000000])
check('positive magnitudes', solve([0x4000000000000000,0x3ff0000000000000]), [0x3ff0000000000000,0x4000000000000000])
check('infinity and nan', solve([0x7ff8000000000000|N,0x7ff0000000000000]), [0x7ff0000000000000,0x7ff8000000000000|N])
check('negative nan order', solve([0xfff0000000000000|N,0xfff8000000000000|N]), [0xfff8000000000000|N,0xfff0000000000000|N])
check('positive payloads', solve([0x7ff8000000000064,0x7ff8000000000000|N]), [0x7ff8000000000000|N,0x7ff8000000000064])
check('negative payloads', solve([0xfff8000000000000|N,0xfff8000000000064]), [0xfff8000000000064,0xfff8000000000000|N])
check('mixed signs', solve([N,(1<<63)|N]), [(1<<63)|N,N])
check('duplicates', solve([N,N]), [N,N])
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
zero order	`[0, 9223372036854775808]`	`[9223372036854775808, 0]`	Failed
negative magnitudes	`[13835058055282163712, 13830554455654793216]`	`[13835058055282163712, 13830554455654793216]`	Passed
positive magnitudes	`[4607182418800017408, 4611686018427387904]`	`[4607182418800017408, 4611686018427387904]`	Passed
infinity and nan	`[9218868437227405312, 9221120237041090561]`	`[9218868437227405312, 9221120237041090561]`	Passed
negative nan order	`[18444492273895866369, 18442240474082181121]`	`[18444492273895866369, 18442240474082181121]`	Passed
positive payloads	`[9221120237041090561, 9221120237041090660]`	`[9221120237041090561, 9221120237041090660]`	Passed
negative payloads	`[18444492273895866468, 18444492273895866369]`	`[18444492273895866468, 18444492273895866369]`	Passed
mixed signs	`[9223372036854775809, 1]`	`[9223372036854775809, 1]`	Passed
duplicates	`[1, 1]`	`[1, 1]`	Passed

SHA-256 / 5c4515172805da372c387f57fbd58a25509533e7ae254ab5aaeee953158b2b71

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
N = 1
observations = []
def solve(values):
    def order(bits):
        return ((~bits)&((1<<64)-1)) if bits>>63 else (bits|(1<<63))
    return sorted(values,key=order)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('zero order', solve([0,1<<63]), [1<<63,0])
check('negative magnitudes', solve([0xbff0000000000000,0xc000000000000000]), [0xc000000000000000,0xbff0000000000000])
check('positive magnitudes', solve([0x4000000000000000,0x3ff0000000000000]), [0x3ff0000000000000,0x4000000000000000])
check('infinity and nan', solve([0x7ff8000000000000|N,0x7ff0000000000000]), [0x7ff0000000000000,0x7ff8000000000000|N])
check('negative nan order', solve([0xfff0000000000000|N,0xfff8000000000000|N]), [0xfff8000000000000|N,0xfff0000000000000|N])
check('positive payloads', solve([0x7ff8000000000064,0x7ff8000000000000|N]), [0x7ff8000000000000|N,0x7ff8000000000064])
check('negative payloads', solve([0xfff8000000000000|N,0xfff8000000000064]), [0xfff8000000000064,0xfff8000000000000|N])
check('mixed signs', solve([N,(1<<63)|N]), [(1<<63)|N,N])
check('duplicates', solve([N,N]), [N,N])
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
zero order	`[9223372036854775808, 0]`	`[9223372036854775808, 0]`	Passed
negative magnitudes	`[13835058055282163712, 13830554455654793216]`	`[13835058055282163712, 13830554455654793216]`	Passed
positive magnitudes	`[4607182418800017408, 4611686018427387904]`	`[4607182418800017408, 4611686018427387904]`	Passed
infinity and nan	`[9218868437227405312, 9221120237041090561]`	`[9218868437227405312, 9221120237041090561]`	Passed
negative nan order	`[18444492273895866369, 18442240474082181121]`	`[18444492273895866369, 18442240474082181121]`	Passed
positive payloads	`[9221120237041090561, 9221120237041090660]`	`[9221120237041090561, 9221120237041090660]`	Passed
negative payloads	`[18444492273895866468, 18444492273895866369]`	`[18444492273895866468, 18444492273895866369]`	Passed
mixed signs	`[9223372036854775809, 1]`	`[9223372036854775809, 1]`	Passed
duplicates	`[1, 1]`	`[1, 1]`	Passed

SHA-256 / 63936deb9efcf833d064d15cba3f033e86676025c33703575b243fb2a1586d24

Verification & scope

Controlled binary64 or explicitly stipulated miniature format; no hardware exception flags or platform floating environment are modeled. 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 2026-09-29T14:39:37.899530+00:00.

Case digest / 713810e5a0548bed57ce131f55c713bfb83dc19ec3a26898312f1c6d044f9af3