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FA-17221 / Floating-point arithmetic / Open access

Scaled square root clamps a negative operand to zero · case 01

Scaled square root clamps a negative operand to zero.

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

ROOT CAUSE

Scaled square root clamps a negative operand to zero. The faulty expression is if x<0: return '0'.

VERIFIED REPAIR

Apply the contract at this fault site using if x<0: return 'domain'.

Unsuccessful approach: The attempted local correction if x<0: x=abs(x) still violates the explicit regression fixtures.

Case contract

Nonnegative square root of finite binary64 x via exponent normalization. Negative input returns domain; negative zero is preserved. 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(x):
    try:
        if x<0: return '0'
        if x==0: return render(x)
        m,e=math.frexp(x)
        q,r=divmod(e,2)
        root=math.sqrt(math.ldexp(m,r))
        return render(math.ldexp(root,q))
    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('square', solve(float(N*N)), render(float(N)))
check('normal', solve(float(N)), render(math.sqrt(N)))
check('huge', solve(1e300), "1e+150")
check('tiny', solve(1e-300), "1e-150")
check('odd exponent', solve(2.0), render(math.sqrt(2)))
check('positive root zero', solve(0.0), "0")
check('negative domain', solve(-float(N)), "domain")
check('negative zero', solve(-0.0), "-0")
check('subnormal', solve(math.ldexp(1.0,-1074)), render(math.ldexp(1.0,-537)))
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 fixtureActualExpectedOutcome
square11Passed
normal11Passed
huge1e+1501e+150Passed
tiny1e-1501e-150Passed
odd exponent1.41421356241.4142135624Passed
positive root zero00Passed
negative domain0domainFailed
negative zero-0-0Passed
subnormal2.2227587495e-1622.2227587495e-162Passed

SHA-256 / 88e32b29505ac97e30114d6352852739f4a66e526b02dc5570de4d38809582bd

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(x):
    try:
        if x<0: x=abs(x)
        if x==0: return render(x)
        m,e=math.frexp(x)
        q,r=divmod(e,2)
        root=math.sqrt(math.ldexp(m,r))
        return render(math.ldexp(root,q))
    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('square', solve(float(N*N)), render(float(N)))
check('normal', solve(float(N)), render(math.sqrt(N)))
check('huge', solve(1e300), "1e+150")
check('tiny', solve(1e-300), "1e-150")
check('odd exponent', solve(2.0), render(math.sqrt(2)))
check('positive root zero', solve(0.0), "0")
check('negative domain', solve(-float(N)), "domain")
check('negative zero', solve(-0.0), "-0")
check('subnormal', solve(math.ldexp(1.0,-1074)), render(math.ldexp(1.0,-537)))
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 fixtureActualExpectedOutcome
square11Passed
normal11Passed
huge1e+1501e+150Passed
tiny1e-1501e-150Passed
odd exponent1.41421356241.4142135624Passed
positive root zero00Passed
negative domain1domainFailed
negative zero-0-0Passed
subnormal2.2227587495e-1622.2227587495e-162Passed

SHA-256 / 33755f8b821ca7be3c330defa157dd8f06c240335425aaa4443f80fc59c00adf

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(x):
    try:
        if x<0: return 'domain'
        if x==0: return render(x)
        m,e=math.frexp(x)
        q,r=divmod(e,2)
        root=math.sqrt(math.ldexp(m,r))
        return render(math.ldexp(root,q))
    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('square', solve(float(N*N)), render(float(N)))
check('normal', solve(float(N)), render(math.sqrt(N)))
check('huge', solve(1e300), "1e+150")
check('tiny', solve(1e-300), "1e-150")
check('odd exponent', solve(2.0), render(math.sqrt(2)))
check('positive root zero', solve(0.0), "0")
check('negative domain', solve(-float(N)), "domain")
check('negative zero', solve(-0.0), "-0")
check('subnormal', solve(math.ldexp(1.0,-1074)), render(math.ldexp(1.0,-537)))
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 fixtureActualExpectedOutcome
square11Passed
normal11Passed
huge1e+1501e+150Passed
tiny1e-1501e-150Passed
odd exponent1.41421356241.4142135624Passed
positive root zero00Passed
negative domaindomaindomainPassed
negative zero-0-0Passed
subnormal2.2227587495e-1622.2227587495e-162Passed

SHA-256 / a2be440e40877a8ca6d5cbe5e4d7abbf5c9581a86035cddc86c6c1bf1b225c3e

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 2026-09-29T14:39:44.233745+00:00.

Case digest / 68288e084bc9bbf481d7fa441d08ad368340bd1477eac03030d0d0511fc4e2c1