FAILURE MAP
← Case archive

FA-15891 / Floating-point arithmetic / Open access

Stepping checks only source NaNs · case 01

Stepping checks only source NaNs.

Verified by executionVariant 1 · 12 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Stepping checks only source NaNs. The faulty expression is math.isnan(x).

VERIFIED REPAIR

Apply the contract at this fault site using math.isnan(x) or math.isnan(y).

Unsuccessful approach: The attempted local correction math.isnan(x) and math.isnan(y) still violates the explicit regression fixtures.

Case contract

Return the binary64 bit pattern one representable step from x toward y, or canonical quiet NaN for NaN operands. Equal operands return the exact bits of y, including zero sign.

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
N = 1
observations = []
def solve(xb, yb):
    x=struct.unpack('>d', xb.to_bytes(8,'big'))[0]
    y=struct.unpack('>d', yb.to_bytes(8,'big'))[0]
    if math.isnan(x):
        return 0x7ff8000000000000
    if x == y:
        return yb
    if x == 0:
        return (yb & (1<<63)) | 1
    if x > 0:
        return xb+1 if y>x else xb-1
    return xb-1 if y>x else xb+1
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('positive step', solve(0x3ff0000000000000, 0x4000000000000000), 0x3ff0000000000001)
check('positive reverse', solve(0x3ff0000000000000, 0), 0x3fefffffffffffff)
check('negative forward', solve(0xbff0000000000000, 0), 0xbfefffffffffffff)
check('negative away', solve(0xbff0000000000000, 0xc000000000000000), 0xbff0000000000001)
check('negative zero equality', solve(0, 1<<63), 1<<63)
check('positive zero equality', solve(1<<63, 0), 0)
check('zero negative', solve(0, 0xbff0000000000000), (1<<63)|1)
check('zero positive', solve(1<<63, 0x3ff0000000000000), 1)
check('nan target', solve(0x3ff0000000000000, (0x7ff<<52)|N), 0x7ff8000000000000)
check('nan source', solve((0x7ff<<52)|N, 0), 0x7ff8000000000000)
check('finite step varies', solve((1023+N)<<52, 0), ((1023+N)<<52)-1)
check('infinity inward', solve(0x7ff0000000000000, 0), 0x7fefffffffffffff)
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
positive step46071824188000174094607182418800017409Passed
positive reverse46071824188000174074607182418800017407Passed
negative forward1383055445565479321513830554455654793215Passed
negative away1383055445565479321713830554455654793217Passed
negative zero equality92233720368547758089223372036854775808Passed
positive zero equality00Passed
zero negative92233720368547758099223372036854775809Passed
zero positive11Passed
nan target46071824188000174079221120237041090560Failed
nan source92211202370410905609221120237041090560Passed
finite step varies46116860184273879034611686018427387903Passed
infinity inward92188684372274053119218868437227405311Passed

SHA-256 / 81ec973ff4e1c58ef4410f5bb75ff930f82b88e96c432ad951e017dbb059302c

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
N = 1
observations = []
def solve(xb, yb):
    x=struct.unpack('>d', xb.to_bytes(8,'big'))[0]
    y=struct.unpack('>d', yb.to_bytes(8,'big'))[0]
    if math.isnan(x) and math.isnan(y):
        return 0x7ff8000000000000
    if x == y:
        return yb
    if x == 0:
        return (yb & (1<<63)) | 1
    if x > 0:
        return xb+1 if y>x else xb-1
    return xb-1 if y>x else xb+1
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('positive step', solve(0x3ff0000000000000, 0x4000000000000000), 0x3ff0000000000001)
check('positive reverse', solve(0x3ff0000000000000, 0), 0x3fefffffffffffff)
check('negative forward', solve(0xbff0000000000000, 0), 0xbfefffffffffffff)
check('negative away', solve(0xbff0000000000000, 0xc000000000000000), 0xbff0000000000001)
check('negative zero equality', solve(0, 1<<63), 1<<63)
check('positive zero equality', solve(1<<63, 0), 0)
check('zero negative', solve(0, 0xbff0000000000000), (1<<63)|1)
check('zero positive', solve(1<<63, 0x3ff0000000000000), 1)
check('nan target', solve(0x3ff0000000000000, (0x7ff<<52)|N), 0x7ff8000000000000)
check('nan source', solve((0x7ff<<52)|N, 0), 0x7ff8000000000000)
check('finite step varies', solve((1023+N)<<52, 0), ((1023+N)<<52)-1)
check('infinity inward', solve(0x7ff0000000000000, 0), 0x7fefffffffffffff)
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
positive step46071824188000174094607182418800017409Passed
positive reverse46071824188000174074607182418800017407Passed
negative forward1383055445565479321513830554455654793215Passed
negative away1383055445565479321713830554455654793217Passed
negative zero equality92233720368547758089223372036854775808Passed
positive zero equality00Passed
zero negative92233720368547758099223372036854775809Passed
zero positive11Passed
nan target46071824188000174079221120237041090560Failed
nan source92188684372274053149221120237041090560Failed
finite step varies46116860184273879034611686018427387903Passed
infinity inward92188684372274053119218868437227405311Passed

SHA-256 / 393e158e194c11a3c5c44688b23407fd0a7ddfef56c4f6f80ea32e991f58699c

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
import math
import struct
N = 1
observations = []
def solve(xb, yb):
    x=struct.unpack('>d', xb.to_bytes(8,'big'))[0]
    y=struct.unpack('>d', yb.to_bytes(8,'big'))[0]
    if math.isnan(x) or math.isnan(y):
        return 0x7ff8000000000000
    if x == y:
        return yb
    if x == 0:
        return (yb & (1<<63)) | 1
    if x > 0:
        return xb+1 if y>x else xb-1
    return xb-1 if y>x else xb+1
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('positive step', solve(0x3ff0000000000000, 0x4000000000000000), 0x3ff0000000000001)
check('positive reverse', solve(0x3ff0000000000000, 0), 0x3fefffffffffffff)
check('negative forward', solve(0xbff0000000000000, 0), 0xbfefffffffffffff)
check('negative away', solve(0xbff0000000000000, 0xc000000000000000), 0xbff0000000000001)
check('negative zero equality', solve(0, 1<<63), 1<<63)
check('positive zero equality', solve(1<<63, 0), 0)
check('zero negative', solve(0, 0xbff0000000000000), (1<<63)|1)
check('zero positive', solve(1<<63, 0x3ff0000000000000), 1)
check('nan target', solve(0x3ff0000000000000, (0x7ff<<52)|N), 0x7ff8000000000000)
check('nan source', solve((0x7ff<<52)|N, 0), 0x7ff8000000000000)
check('finite step varies', solve((1023+N)<<52, 0), ((1023+N)<<52)-1)
check('infinity inward', solve(0x7ff0000000000000, 0), 0x7fefffffffffffff)
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
positive step46071824188000174094607182418800017409Passed
positive reverse46071824188000174074607182418800017407Passed
negative forward1383055445565479321513830554455654793215Passed
negative away1383055445565479321713830554455654793217Passed
negative zero equality92233720368547758089223372036854775808Passed
positive zero equality00Passed
zero negative92233720368547758099223372036854775809Passed
zero positive11Passed
nan target92211202370410905609221120237041090560Passed
nan source92211202370410905609221120237041090560Passed
finite step varies46116860184273879034611686018427387903Passed
infinity inward92188684372274053119218868437227405311Passed

SHA-256 / c9950755b0dc041dffe873301bca78d9e7b725e9a4889164fce6ad10d526d497

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 2026-09-29T14:39:31.329181+00:00.

Case digest / a78198a4b3310fd87aacdedc5392fff142a3c74f0693c4d713c371f5e9e12f07