FA-16686 / Floating-point arithmetic / Open access
Same-sign interpolation adds endpoints before weighting · case 01
Same-sign interpolation adds endpoints before weighting.
ROOT CAUSE
Same-sign interpolation adds endpoints before weighting. The faulty expression is result=((1-t)*(a+b)+t*(a+b))/2.
VERIFIED REPAIR
Apply the contract at this fault site using result=a+t*(b-a).
Unsuccessful approach: The attempted local correction result=(a+b)/2 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=((1-t)*(a+b)+t*(a+b))/2
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 | 1.5e+308 | 1.25e+308 | Failed |
| first endpoint | -0 | -0 | Passed |
| last endpoint | -0 | -0 | Passed |
| increasing | 5 | 3 | Failed |
| decreasing | 5 | 7 | Failed |
| negative same sign | -5 | -7 | Failed |
| outside | domain | domain | Passed |
| tiny blend | 2e-300 | 2e-300 | Passed |
SHA-256 / 43ba177ba0be34b6688d498fe46dc97d2f3ee59ad7069b25bf57e8a0f8c896e3
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+b)/2
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 | 1.5e+308 | 1.25e+308 | Failed |
| first endpoint | -0 | -0 | Passed |
| last endpoint | -0 | -0 | Passed |
| increasing | 5 | 3 | Failed |
| decreasing | 5 | 7 | Failed |
| negative same sign | -5 | -7 | Failed |
| outside | domain | domain | Passed |
| tiny blend | 2e-300 | 2e-300 | Passed |
SHA-256 / 203587bfda8095e867e958126de1cef4d3ac732260416dd589d21f1b9c5bcc94
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 2026-09-29T14:39:38.704989+00:00.
Case digest / c56fa48a70725b586a5cd1daf200ab6ff5e50654b2faed483c14580a4fa977d1