FA-16581 / Floating-point arithmetic / Open access

Infinity addition treats equal signs as invalid · case 01

Infinity addition treats equal signs as invalid.

Verified by executionVariant 1 · 14 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Infinity addition treats equal signs as invalid. The faulty expression is if math.isinf(a) and math.isinf(b):.

VERIFIED REPAIR

Apply the contract at this fault site using if math.isinf(a) and math.isinf(b) and a!=b:.

Unsuccessful approach: The attempted local correction if math.isinf(a) or math.isinf(b): still violates the explicit regression fixtures.

Case contract

Stipulated binary64 addition policy: propagate first signaling NaN, otherwise largest quiet-NaN diagnostic payload (left wins ties); quiet propagated NaNs preserving sign. Opposite infinities produce canonical quiet NaN. Finite values use Python binary64 addition. Return bits and invalid flag.

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(ab,bb):
    mask=(1<<52)-1
    an=(ab>>52)&2047==2047 and bool(ab&mask)
    bn=(bb>>52)&2047==2047 and bool(bb&mask)
    asig=an and not bool(ab&(1<<51))
    bsig=bn and not bool(bb&(1<<51))
    if asig or bsig:
        chosen=ab if asig else bb
        return [chosen|(1<<51),True]
    if an or bn:
        if an and bn:
            chosen=ab if (ab&((1<<51)-1)) >= (bb&((1<<51)-1)) else bb
        else:
            chosen=ab if an else bb
        return [chosen,False]
    a=struct.unpack('>d',ab.to_bytes(8,'big'))[0]
    b=struct.unpack('>d',bb.to_bytes(8,'big'))[0]
    if math.isinf(a) and math.isinf(b):
        return [0x7ff8000000000000,True]
    result=a+b
    return [int.from_bytes(struct.pack('>d',result),'big'),False]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('left signaling', solve(0x7ff0000000000000|N,0x3ff0000000000000), [0x7ff8000000000000|N,True])
check('right signaling', solve(0x3ff0000000000000,0xfff0000000000000|N), [0xfff8000000000000|N,True])
check('signaling precedence', solve(0x7ff8000000000064,0x7ff0000000000000|N), [0x7ff8000000000000|N,True])
check('two signaling', solve(0xfff0000000000000|N,0x7ff0000000000010), [0xfff8000000000000|N,True])
check('larger right payload', solve(0x7ff8000000000000|N,0xfff8000000000064), [0xfff8000000000064,False])
check('larger left payload', solve(0xfff8000000000064,0x7ff8000000000000|N), [0xfff8000000000064,False])
check('equal left wins', solve(0xfff8000000000000|N,0x7ff8000000000000|N), [0xfff8000000000000|N,False])
check('positive quiet', solve(0x7ff8000000000000|N,0x3ff0000000000000), [0x7ff8000000000000|N,False])
check('quiet left only', solve(0xfff8000000000000|N,0x3ff0000000000000), [0xfff8000000000000|N,False])
check('quiet right only', solve(0x3ff0000000000000,0xfff8000000000000|N), [0xfff8000000000000|N,False])
check('opposite infinities', solve(0x7ff0000000000000,0xfff0000000000000), [0x7ff8000000000000,True])
check('same infinity', solve(0xfff0000000000000,0xfff0000000000000), [0xfff0000000000000,False])
check('finite addition', solve(0x3ff0000000000000,0x3ff0000000000000), [0x4000000000000000,False])
check('negative zeros', solve(1<<63,1<<63), [1<<63,False])
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
left signaling	`[9221120237041090561, True]`	`[9221120237041090561, True]`	Passed
right signaling	`[18444492273895866369, True]`	`[18444492273895866369, True]`	Passed
signaling precedence	`[9221120237041090561, True]`	`[9221120237041090561, True]`	Passed
two signaling	`[18444492273895866369, True]`	`[18444492273895866369, True]`	Passed
larger right payload	`[18444492273895866468, False]`	`[18444492273895866468, False]`	Passed
larger left payload	`[18444492273895866468, False]`	`[18444492273895866468, False]`	Passed
equal left wins	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
positive quiet	`[9221120237041090561, False]`	`[9221120237041090561, False]`	Passed
quiet left only	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
quiet right only	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
opposite infinities	`[9221120237041090560, True]`	`[9221120237041090560, True]`	Passed
same infinity	`[9221120237041090560, True]`	`[18442240474082181120, False]`	Failed
finite addition	`[4611686018427387904, False]`	`[4611686018427387904, False]`	Passed
negative zeros	`[9223372036854775808, False]`	`[9223372036854775808, False]`	Passed

SHA-256 / f712c22002e0de60e46a4e4a7086785fcdf8849d36b3c604cfcfde4b29c3da6e

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(ab,bb):
    mask=(1<<52)-1
    an=(ab>>52)&2047==2047 and bool(ab&mask)
    bn=(bb>>52)&2047==2047 and bool(bb&mask)
    asig=an and not bool(ab&(1<<51))
    bsig=bn and not bool(bb&(1<<51))
    if asig or bsig:
        chosen=ab if asig else bb
        return [chosen|(1<<51),True]
    if an or bn:
        if an and bn:
            chosen=ab if (ab&((1<<51)-1)) >= (bb&((1<<51)-1)) else bb
        else:
            chosen=ab if an else bb
        return [chosen,False]
    a=struct.unpack('>d',ab.to_bytes(8,'big'))[0]
    b=struct.unpack('>d',bb.to_bytes(8,'big'))[0]
    if math.isinf(a) or math.isinf(b):
        return [0x7ff8000000000000,True]
    result=a+b
    return [int.from_bytes(struct.pack('>d',result),'big'),False]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('left signaling', solve(0x7ff0000000000000|N,0x3ff0000000000000), [0x7ff8000000000000|N,True])
check('right signaling', solve(0x3ff0000000000000,0xfff0000000000000|N), [0xfff8000000000000|N,True])
check('signaling precedence', solve(0x7ff8000000000064,0x7ff0000000000000|N), [0x7ff8000000000000|N,True])
check('two signaling', solve(0xfff0000000000000|N,0x7ff0000000000010), [0xfff8000000000000|N,True])
check('larger right payload', solve(0x7ff8000000000000|N,0xfff8000000000064), [0xfff8000000000064,False])
check('larger left payload', solve(0xfff8000000000064,0x7ff8000000000000|N), [0xfff8000000000064,False])
check('equal left wins', solve(0xfff8000000000000|N,0x7ff8000000000000|N), [0xfff8000000000000|N,False])
check('positive quiet', solve(0x7ff8000000000000|N,0x3ff0000000000000), [0x7ff8000000000000|N,False])
check('quiet left only', solve(0xfff8000000000000|N,0x3ff0000000000000), [0xfff8000000000000|N,False])
check('quiet right only', solve(0x3ff0000000000000,0xfff8000000000000|N), [0xfff8000000000000|N,False])
check('opposite infinities', solve(0x7ff0000000000000,0xfff0000000000000), [0x7ff8000000000000,True])
check('same infinity', solve(0xfff0000000000000,0xfff0000000000000), [0xfff0000000000000,False])
check('finite addition', solve(0x3ff0000000000000,0x3ff0000000000000), [0x4000000000000000,False])
check('negative zeros', solve(1<<63,1<<63), [1<<63,False])
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
left signaling	`[9221120237041090561, True]`	`[9221120237041090561, True]`	Passed
right signaling	`[18444492273895866369, True]`	`[18444492273895866369, True]`	Passed
signaling precedence	`[9221120237041090561, True]`	`[9221120237041090561, True]`	Passed
two signaling	`[18444492273895866369, True]`	`[18444492273895866369, True]`	Passed
larger right payload	`[18444492273895866468, False]`	`[18444492273895866468, False]`	Passed
larger left payload	`[18444492273895866468, False]`	`[18444492273895866468, False]`	Passed
equal left wins	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
positive quiet	`[9221120237041090561, False]`	`[9221120237041090561, False]`	Passed
quiet left only	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
quiet right only	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
opposite infinities	`[9221120237041090560, True]`	`[9221120237041090560, True]`	Passed
same infinity	`[9221120237041090560, True]`	`[18442240474082181120, False]`	Failed
finite addition	`[4611686018427387904, False]`	`[4611686018427387904, False]`	Passed
negative zeros	`[9223372036854775808, False]`	`[9223372036854775808, False]`	Passed

SHA-256 / 31a1740958087f3d27c5a5825fa317c0e4be3a90df3b5f933325140813d377bc

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(ab,bb):
    mask=(1<<52)-1
    an=(ab>>52)&2047==2047 and bool(ab&mask)
    bn=(bb>>52)&2047==2047 and bool(bb&mask)
    asig=an and not bool(ab&(1<<51))
    bsig=bn and not bool(bb&(1<<51))
    if asig or bsig:
        chosen=ab if asig else bb
        return [chosen|(1<<51),True]
    if an or bn:
        if an and bn:
            chosen=ab if (ab&((1<<51)-1)) >= (bb&((1<<51)-1)) else bb
        else:
            chosen=ab if an else bb
        return [chosen,False]
    a=struct.unpack('>d',ab.to_bytes(8,'big'))[0]
    b=struct.unpack('>d',bb.to_bytes(8,'big'))[0]
    if math.isinf(a) and math.isinf(b) and a!=b:
        return [0x7ff8000000000000,True]
    result=a+b
    return [int.from_bytes(struct.pack('>d',result),'big'),False]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('left signaling', solve(0x7ff0000000000000|N,0x3ff0000000000000), [0x7ff8000000000000|N,True])
check('right signaling', solve(0x3ff0000000000000,0xfff0000000000000|N), [0xfff8000000000000|N,True])
check('signaling precedence', solve(0x7ff8000000000064,0x7ff0000000000000|N), [0x7ff8000000000000|N,True])
check('two signaling', solve(0xfff0000000000000|N,0x7ff0000000000010), [0xfff8000000000000|N,True])
check('larger right payload', solve(0x7ff8000000000000|N,0xfff8000000000064), [0xfff8000000000064,False])
check('larger left payload', solve(0xfff8000000000064,0x7ff8000000000000|N), [0xfff8000000000064,False])
check('equal left wins', solve(0xfff8000000000000|N,0x7ff8000000000000|N), [0xfff8000000000000|N,False])
check('positive quiet', solve(0x7ff8000000000000|N,0x3ff0000000000000), [0x7ff8000000000000|N,False])
check('quiet left only', solve(0xfff8000000000000|N,0x3ff0000000000000), [0xfff8000000000000|N,False])
check('quiet right only', solve(0x3ff0000000000000,0xfff8000000000000|N), [0xfff8000000000000|N,False])
check('opposite infinities', solve(0x7ff0000000000000,0xfff0000000000000), [0x7ff8000000000000,True])
check('same infinity', solve(0xfff0000000000000,0xfff0000000000000), [0xfff0000000000000,False])
check('finite addition', solve(0x3ff0000000000000,0x3ff0000000000000), [0x4000000000000000,False])
check('negative zeros', solve(1<<63,1<<63), [1<<63,False])
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
left signaling	`[9221120237041090561, True]`	`[9221120237041090561, True]`	Passed
right signaling	`[18444492273895866369, True]`	`[18444492273895866369, True]`	Passed
signaling precedence	`[9221120237041090561, True]`	`[9221120237041090561, True]`	Passed
two signaling	`[18444492273895866369, True]`	`[18444492273895866369, True]`	Passed
larger right payload	`[18444492273895866468, False]`	`[18444492273895866468, False]`	Passed
larger left payload	`[18444492273895866468, False]`	`[18444492273895866468, False]`	Passed
equal left wins	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
positive quiet	`[9221120237041090561, False]`	`[9221120237041090561, False]`	Passed
quiet left only	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
quiet right only	`[18444492273895866369, False]`	`[18444492273895866369, False]`	Passed
opposite infinities	`[9221120237041090560, True]`	`[9221120237041090560, True]`	Passed
same infinity	`[18442240474082181120, False]`	`[18442240474082181120, False]`	Passed
finite addition	`[4611686018427387904, False]`	`[4611686018427387904, False]`	Passed
negative zeros	`[9223372036854775808, False]`	`[9223372036854775808, False]`	Passed

SHA-256 / a22a003c8dfdecc224fbfc96d6bd9268c4c9fc9fb4044fdbdad84b62a3040788

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 2026-09-29T14:39:37.678459+00:00.

Case digest / dc8a01c1b652cab9fed6acde3d1f28050771e4c62eb4079c4f3f87bcdec7cf97