FA-15916 / Floating-point arithmetic / Open access

ULP lookup reports NaN as infinity · case 01

ULP lookup reports NaN as infinity.

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

ROOT CAUSE

ULP lookup reports NaN as infinity. The faulty expression is if math.isnan(x): return 'infinity'.

THE FAILURE

ULP lookup reports NaN as infinity. The faulty expression is if math.isnan(x): return 'infinity'.

Unsuccessful approach: The attempted local correction if math.isnan(x): return '0x0.0p+0' still violates the explicit regression fixtures.

Case contract

Return a finite binary64 ulp as a hex string; NaN maps to nan and either infinity maps to infinity. For subnormals and zero the ulp is the minimum positive subnormal.

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(bits):
    x=struct.unpack('>d',bits.to_bytes(8,'big'))[0]
    if math.isnan(x): return 'infinity'
    if math.isinf(x): return 'infinity'
    x=abs(x)
    if x == 0: return float.fromhex('0x0.0000000000001p-1022').hex()
    m,e=math.frexp(x)
    e=max(e-53,-1074)
    return math.ldexp(1.0,e).hex()
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('zero', solve(0), '0x0.0000000000001p-1022')
check('negative zero', solve(1<<63), '0x0.0000000000001p-1022')
check('subnormal', solve(N), '0x0.0000000000001p-1022')
check('power boundary', solve((1023+N)<<52), math.ldexp(1.0,N-52).hex())
check('negative power', solve((1<<63)|((1023+N)<<52)), math.ldexp(1.0,N-52).hex())
check('below power', solve(((1023+N)<<52)-1), math.ldexp(1.0,N-53).hex())
check('infinity', solve(0x7ff0000000000000), 'infinity')
check('nan', solve(0x7ff8000000000000|N), 'nan')
check('maximum', solve(0x7fefffffffffffff), '0x1.0000000000000p+971')
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	`0x0.0000000000001p-1022`	`0x0.0000000000001p-1022`	Passed
negative zero	`0x0.0000000000001p-1022`	`0x0.0000000000001p-1022`	Passed
subnormal	`0x0.0000000000001p-1022`	`0x0.0000000000001p-1022`	Passed
power boundary	`0x1.0000000000000p-51`	`0x1.0000000000000p-51`	Passed
negative power	`0x1.0000000000000p-51`	`0x1.0000000000000p-51`	Passed
below power	`0x1.0000000000000p-52`	`0x1.0000000000000p-52`	Passed
infinity	`infinity`	`infinity`	Passed
nan	`infinity`	`nan`	Failed
maximum	`0x1.0000000000000p+971`	`0x1.0000000000000p+971`	Passed

SHA-256 / ff59651799f00f817688e577534546d60ef5993ee5f9ab48b6944c844a4e8fe0

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(bits):
    x=struct.unpack('>d',bits.to_bytes(8,'big'))[0]
    if math.isnan(x): return '0x0.0p+0'
    if math.isinf(x): return 'infinity'
    x=abs(x)
    if x == 0: return float.fromhex('0x0.0000000000001p-1022').hex()
    m,e=math.frexp(x)
    e=max(e-53,-1074)
    return math.ldexp(1.0,e).hex()
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('zero', solve(0), '0x0.0000000000001p-1022')
check('negative zero', solve(1<<63), '0x0.0000000000001p-1022')
check('subnormal', solve(N), '0x0.0000000000001p-1022')
check('power boundary', solve((1023+N)<<52), math.ldexp(1.0,N-52).hex())
check('negative power', solve((1<<63)|((1023+N)<<52)), math.ldexp(1.0,N-52).hex())
check('below power', solve(((1023+N)<<52)-1), math.ldexp(1.0,N-53).hex())
check('infinity', solve(0x7ff0000000000000), 'infinity')
check('nan', solve(0x7ff8000000000000|N), 'nan')
check('maximum', solve(0x7fefffffffffffff), '0x1.0000000000000p+971')
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	`0x0.0000000000001p-1022`	`0x0.0000000000001p-1022`	Passed
negative zero	`0x0.0000000000001p-1022`	`0x0.0000000000001p-1022`	Passed
subnormal	`0x0.0000000000001p-1022`	`0x0.0000000000001p-1022`	Passed
power boundary	`0x1.0000000000000p-51`	`0x1.0000000000000p-51`	Passed
negative power	`0x1.0000000000000p-51`	`0x1.0000000000000p-51`	Passed
below power	`0x1.0000000000000p-52`	`0x1.0000000000000p-52`	Passed
infinity	`infinity`	`infinity`	Passed
nan	`0x0.0p+0`	`nan`	Failed
maximum	`0x1.0000000000000p+971`	`0x1.0000000000000p+971`	Passed

SHA-256 / 912332f7933980399a231db82652c6bfa40c922b3d6ea118aabaccfbf1b39b4c

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 9 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:39:31.496730+00:00.

Case digest / b01169dbdd77aadf0c905e5a2bf707d01ebf6430149614c9631dc6a86095bd8a