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FA-16251 / Floating-point arithmetic / Open access

Inverse sine loses the sign in the magnitude branch · case 01

Inverse sine loses the sign in the magnitude branch.

Verified by executionVariant 1 · 7 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Inverse sine loses the sign in the magnitude branch. The faulty expression is return render(result).

VERIFIED REPAIR

Apply the contract at this fault site using return render(math.copysign(result,x)).

Unsuccessful approach: The attempted local correction return render(-result) still violates the explicit regression fixtures.

Case contract

Evaluate inverse hyperbolic sine for finite binary64 values with tiny-value preservation and a large-value logarithmic branch. 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:
        a=abs(x)
        if a<1e-8: return render(x)
        if a>1e150:
            result=math.log(a)+math.log(2)
        else:
            result=math.log1p(a+a*a/(1+math.sqrt(1+a*a)))
        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('tiny', solve(N*2.0**-60), render(N*2.0**-60))
check('negative tiny', solve(-N*2.0**-60), render(-N*2.0**-60))
check('large', solve(N*1e300), render(math.asinh(N*1e300)))
check('negative large', solve(-N*1e300), render(math.asinh(-N*1e300)))
check('normal', solve(float(N)), render(math.asinh(N)))
check('negative normal', solve(-float(N)), render(math.asinh(-N)))
check('negative zero', solve(-0.0), "-0")
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
tiny8.6736173799e-198.6736173799e-19Passed
negative tiny-8.6736173799e-19-8.6736173799e-19Passed
large691.46867508691.46867508Passed
negative large691.46867508-691.46867508Failed
normal0.881373587020.88137358702Passed
negative normal0.88137358702-0.88137358702Failed
negative zero-0-0Passed

SHA-256 / 72ff425477f434772d1059b3ead6055c93b3bf8eed6f150e927af0b79a2b1637

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:
        a=abs(x)
        if a<1e-8: return render(x)
        if a>1e150:
            result=math.log(a)+math.log(2)
        else:
            result=math.log1p(a+a*a/(1+math.sqrt(1+a*a)))
        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('tiny', solve(N*2.0**-60), render(N*2.0**-60))
check('negative tiny', solve(-N*2.0**-60), render(-N*2.0**-60))
check('large', solve(N*1e300), render(math.asinh(N*1e300)))
check('negative large', solve(-N*1e300), render(math.asinh(-N*1e300)))
check('normal', solve(float(N)), render(math.asinh(N)))
check('negative normal', solve(-float(N)), render(math.asinh(-N)))
check('negative zero', solve(-0.0), "-0")
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
tiny8.6736173799e-198.6736173799e-19Passed
negative tiny-8.6736173799e-19-8.6736173799e-19Passed
large-691.46867508691.46867508Failed
negative large-691.46867508-691.46867508Passed
normal-0.881373587020.88137358702Failed
negative normal-0.88137358702-0.88137358702Passed
negative zero-0-0Passed

SHA-256 / e02300a660326a89a7cb18b4a2dde31ee3f600a60b9e9dd5970eae320e260326

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:
        a=abs(x)
        if a<1e-8: return render(x)
        if a>1e150:
            result=math.log(a)+math.log(2)
        else:
            result=math.log1p(a+a*a/(1+math.sqrt(1+a*a)))
        return render(math.copysign(result,x))
    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('tiny', solve(N*2.0**-60), render(N*2.0**-60))
check('negative tiny', solve(-N*2.0**-60), render(-N*2.0**-60))
check('large', solve(N*1e300), render(math.asinh(N*1e300)))
check('negative large', solve(-N*1e300), render(math.asinh(-N*1e300)))
check('normal', solve(float(N)), render(math.asinh(N)))
check('negative normal', solve(-float(N)), render(math.asinh(-N)))
check('negative zero', solve(-0.0), "-0")
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
tiny8.6736173799e-198.6736173799e-19Passed
negative tiny-8.6736173799e-19-8.6736173799e-19Passed
large691.46867508691.46867508Passed
negative large-691.46867508-691.46867508Passed
normal0.881373587020.88137358702Passed
negative normal-0.88137358702-0.88137358702Passed
negative zero-0-0Passed

SHA-256 / 63b2caefba5e573952c603b31c9fbd968c653bd31fa97b5a6acc0ceaedc2a138

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 2026-09-29T14:39:34.705045+00:00.

Case digest / 023972ca084627de360874c23daea38142b387e6d7f11f951ed7be1356f7009b