FA-16701 / Floating-point arithmetic / Open access

Interpolation attaches t to the wrong endpoint · case 01

Interpolation attaches t to the wrong endpoint.

Verified by executionVariant 1 · 10 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Interpolation attaches t to the wrong endpoint. The faulty expression is result=ta+(1-t)b.

VERIFIED REPAIR

Apply the contract at this fault site using result=(1-t)*a+t*b.

Unsuccessful approach: The attempted local correction result=t*(a+b) 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=t*a+(1-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`	Failed
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 / 9900db796a2208431bb25add9eef2de64a493a3026ccde4caa77736874d5bece

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=t*(a+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`	`-0.5`	Failed
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 / 01df62ad03180d126596a1928d218bb4728e063a166e675be2302891cc40d317

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 2026-09-29T14:39:38.748147+00:00.

Case digest / 17f314100a8ab9f0d4582dd97d96701e0474d3f117beda4eb5e13e965de3ceef