FA-16706 / Floating-point arithmetic / Open access
Interpolation clamps a decreasing interval as though increasing · case 01
Interpolation clamps a decreasing interval as though increasing.
ROOT CAUSE
Interpolation clamps a decreasing interval as though increasing. The faulty expression is result=min(b,max(a,result)).
VERIFIED REPAIR
Apply the contract at this fault site using result=min(max(a,b),max(min(a,b),result)).
Unsuccessful approach: The attempted local correction result=max(a,min(b,result)) still violates the explicit regression fixtures.
Case contract
Interpolate finite a and b at t in [0,1], preserving endpoints and avoiding overflow in a difference or an endpoint sum. Return domain marker outside the interval. Finite results are rendered to eleven significant decimal digits; modeled domain violations and arithmetic errors are explicit strings.
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
def render(x):
if math.isnan(x): return 'nan'
if math.isinf(x): return '-infinity' if x<0 else '+infinity'
return format(x,'.11g')
N = 1
observations = []
def solve(a,b,t):
try:
if not 0<=t<=1: return 'domain'
if t==0: return render(a)
if t==1: return render(b)
if (a<=0<=b) or (b<=0<=a):
result=(1-t)*a+t*b
else:
result=a+t*(b-a)
result=min(b,max(a,result))
return render(result)
except (ValueError, OverflowError, ZeroDivisionError, TypeError):
return "arithmetic-error"
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('opposite asymmetric', solve(-float(N),float(N),0.25), render(-N/2))
check('opposite extremes', solve(-1e308,1e308,0.5), "0")
check('same extremes', solve(1e308,1.5e308,0.5), render(1.25e308))
check('first endpoint', solve(-0.0,float(N),0.0), "-0")
check('last endpoint', solve(float(N),-0.0,1.0), "-0")
check('increasing', solve(float(N),float(N+8),0.25), render(N+2))
check('decreasing', solve(float(N+8),float(N),0.25), render(N+6))
check('negative same sign', solve(-float(N+8),-float(N),0.25), render(-N-6))
check('outside', solve(float(N),float(N+8),1.5), "domain")
check('tiny blend', solve(N*1e-300,3*N*1e-300,0.5), render(2*N*1e-300))
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 |
|---|---|---|---|
| opposite asymmetric | -0.5 | -0.5 | Passed |
| opposite extremes | 0 | 0 | Passed |
| same extremes | 1.25e+308 | 1.25e+308 | Passed |
| first endpoint | -0 | -0 | Passed |
| last endpoint | -0 | -0 | Passed |
| increasing | 3 | 3 | Passed |
| decreasing | 1 | 7 | Failed |
| negative same sign | -7 | -7 | Passed |
| outside | domain | domain | Passed |
| tiny blend | 2e-300 | 2e-300 | Passed |
SHA-256 / e00f7f7ec6bc5e8c6fd94a64c39212d73e4717cb4566b435d667215a5a71ba9f
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
def render(x):
if math.isnan(x): return 'nan'
if math.isinf(x): return '-infinity' if x<0 else '+infinity'
return format(x,'.11g')
N = 1
observations = []
def solve(a,b,t):
try:
if not 0<=t<=1: return 'domain'
if t==0: return render(a)
if t==1: return render(b)
if (a<=0<=b) or (b<=0<=a):
result=(1-t)*a+t*b
else:
result=a+t*(b-a)
result=max(a,min(b,result))
return render(result)
except (ValueError, OverflowError, ZeroDivisionError, TypeError):
return "arithmetic-error"
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('opposite asymmetric', solve(-float(N),float(N),0.25), render(-N/2))
check('opposite extremes', solve(-1e308,1e308,0.5), "0")
check('same extremes', solve(1e308,1.5e308,0.5), render(1.25e308))
check('first endpoint', solve(-0.0,float(N),0.0), "-0")
check('last endpoint', solve(float(N),-0.0,1.0), "-0")
check('increasing', solve(float(N),float(N+8),0.25), render(N+2))
check('decreasing', solve(float(N+8),float(N),0.25), render(N+6))
check('negative same sign', solve(-float(N+8),-float(N),0.25), render(-N-6))
check('outside', solve(float(N),float(N+8),1.5), "domain")
check('tiny blend', solve(N*1e-300,3*N*1e-300,0.5), render(2*N*1e-300))
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 |
|---|---|---|---|
| opposite asymmetric | -0.5 | -0.5 | Passed |
| opposite extremes | 0 | 0 | Passed |
| same extremes | 1.25e+308 | 1.25e+308 | Passed |
| first endpoint | -0 | -0 | Passed |
| last endpoint | -0 | -0 | Passed |
| increasing | 3 | 3 | Passed |
| decreasing | 9 | 7 | Failed |
| negative same sign | -7 | -7 | Passed |
| outside | domain | domain | Passed |
| tiny blend | 2e-300 | 2e-300 | Passed |
SHA-256 / 850ece1676355fde272f1e4141666effd94108503c88ccacb8ec7971aeedc888
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
def render(x):
if math.isnan(x): return 'nan'
if math.isinf(x): return '-infinity' if x<0 else '+infinity'
return format(x,'.11g')
N = 1
observations = []
def solve(a,b,t):
try:
if not 0<=t<=1: return 'domain'
if t==0: return render(a)
if t==1: return render(b)
if (a<=0<=b) or (b<=0<=a):
result=(1-t)*a+t*b
else:
result=a+t*(b-a)
result=min(max(a,b),max(min(a,b),result))
return render(result)
except (ValueError, OverflowError, ZeroDivisionError, TypeError):
return "arithmetic-error"
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('opposite asymmetric', solve(-float(N),float(N),0.25), render(-N/2))
check('opposite extremes', solve(-1e308,1e308,0.5), "0")
check('same extremes', solve(1e308,1.5e308,0.5), render(1.25e308))
check('first endpoint', solve(-0.0,float(N),0.0), "-0")
check('last endpoint', solve(float(N),-0.0,1.0), "-0")
check('increasing', solve(float(N),float(N+8),0.25), render(N+2))
check('decreasing', solve(float(N+8),float(N),0.25), render(N+6))
check('negative same sign', solve(-float(N+8),-float(N),0.25), render(-N-6))
check('outside', solve(float(N),float(N+8),1.5), "domain")
check('tiny blend', solve(N*1e-300,3*N*1e-300,0.5), render(2*N*1e-300))
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 |
|---|---|---|---|
| opposite asymmetric | -0.5 | -0.5 | Passed |
| opposite extremes | 0 | 0 | Passed |
| same extremes | 1.25e+308 | 1.25e+308 | Passed |
| first endpoint | -0 | -0 | Passed |
| last endpoint | -0 | -0 | Passed |
| increasing | 3 | 3 | Passed |
| decreasing | 7 | 7 | Passed |
| negative same sign | -7 | -7 | Passed |
| outside | domain | domain | Passed |
| tiny blend | 2e-300 | 2e-300 | Passed |
SHA-256 / 7bba9214b3973ac4980ab464b751f476a070ab000f3d7b17449065c0764f5c1b
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 2026-09-29T14:39:38.746657+00:00.
Case digest / fda58352a16b0e7331a28cedfbe96a359cdf3e79c168ce4a74c2990a5a995804