FA-16086 / Floating-point arithmetic / Open access
ULP distance validates only its left operand · case 01
ULP distance validates only its left operand.
ROOT CAUSE
ULP distance validates only its left operand. The faulty expression is if not math.isfinite(a): return None.
THE FAILURE
ULP distance validates only its left operand. The faulty expression is if not math.isfinite(a): return None.
Unsuccessful approach: The attempted local correction if not math.isfinite(a) or math.isinf(b): return None still violates the explicit regression fixtures.
Case contract
Distance between finite binary64 values in representable steps, treating the two zeros as a single position; NaN or infinity yields null. Negative and positive subnormals are adjacent through zero.
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(a,b):
if not math.isfinite(a): return None
ab=int.from_bytes(struct.pack('>d',a),'big')
bb=int.from_bytes(struct.pack('>d',b),'big')
a_index=-(ab&((1<<63)-1)) if ab>>63 else ab
b_index=-(bb&((1<<63)-1)) if bb>>63 else bb
return abs(a_index-b_index)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('same', solve(float(N),float(N)), 0)
check('zero signs', solve(-0.0,0.0), 0)
check('negative adjacent', solve(-float(N),math.nextafter(-float(N),-math.inf)), 1)
check('positive adjacent', solve(float(N),math.nextafter(float(N),math.inf)), 1)
check('cross zero', solve(-math.ldexp(float(N),-1074),math.ldexp(float(N),-1074)), 2*N)
check('reverse cross', solve(math.ldexp(float(N),-1074),-math.ldexp(float(N),-1074)), 2*N)
check('nan left', solve(float("nan"),1.0), None)
check('nan right', solve(1.0,float("nan")), None)
check('infinity', solve(math.inf,math.inf), None)
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 |
|---|---|---|---|
| same | 0 | 0 | Passed |
| zero signs | 0 | 0 | Passed |
| negative adjacent | 1 | 1 | Passed |
| positive adjacent | 1 | 1 | Passed |
| cross zero | 2 | 2 | Passed |
| reverse cross | 2 | 2 | Passed |
| nan left | None | None | Passed |
| nan right | 4613937818241073152 | None | Failed |
| infinity | None | None | Passed |
SHA-256 / 75cc95054f78389fc2b56cd56037cb8858a086498fd53b1e33603dbabaa21fed
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(a,b):
if not math.isfinite(a) or math.isinf(b): return None
ab=int.from_bytes(struct.pack('>d',a),'big')
bb=int.from_bytes(struct.pack('>d',b),'big')
a_index=-(ab&((1<<63)-1)) if ab>>63 else ab
b_index=-(bb&((1<<63)-1)) if bb>>63 else bb
return abs(a_index-b_index)
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('same', solve(float(N),float(N)), 0)
check('zero signs', solve(-0.0,0.0), 0)
check('negative adjacent', solve(-float(N),math.nextafter(-float(N),-math.inf)), 1)
check('positive adjacent', solve(float(N),math.nextafter(float(N),math.inf)), 1)
check('cross zero', solve(-math.ldexp(float(N),-1074),math.ldexp(float(N),-1074)), 2*N)
check('reverse cross', solve(math.ldexp(float(N),-1074),-math.ldexp(float(N),-1074)), 2*N)
check('nan left', solve(float("nan"),1.0), None)
check('nan right', solve(1.0,float("nan")), None)
check('infinity', solve(math.inf,math.inf), None)
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 |
|---|---|---|---|
| same | 0 | 0 | Passed |
| zero signs | 0 | 0 | Passed |
| negative adjacent | 1 | 1 | Passed |
| positive adjacent | 1 | 1 | Passed |
| cross zero | 2 | 2 | Passed |
| reverse cross | 2 | 2 | Passed |
| nan left | None | None | Passed |
| nan right | 4613937818241073152 | None | Failed |
| infinity | None | None | Passed |
SHA-256 / c1f004bcf525bff7e7b008d20dd61b4b269de8caa8fa513661b86ceb112f762d
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.
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Sign in to the archive ↗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 2026-09-29T14:39:33.258410+00:00.
Case digest / 4eaaa1d9386b7fa8a95cb9049e9d57d719a0d3cb4db619e18ecd495b3bcbb3a6