FA-15956 / Floating-point arithmetic / Open access

Nearest rounding loses the round bit after a guard · case 01

Nearest rounding loses the round bit after a guard.

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

ROOT CAUSE

Nearest rounding loses the round bit after a guard. The faulty expression is bool(g and (s or q%2)).

THE FAILURE

Nearest rounding loses the round bit after a guard. The faulty expression is bool(g and (s or q%2)).

Unsuccessful approach: The attempted local correction bool(g and q%2) still violates the explicit regression fixtures.

Case contract

Round a nonnegative integer significand q with guard, round and sticky bits. Modes are nearest-even, nearest-away, zero, up, down; sign is +1 or -1. Return rounded signed integer, inexact flag, and whether rounding incremented the magnitude.

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(q,g,r,s,sign,mode):
    inexact=bool(g or r or s)
    if mode == 'nearest-even': increment=bool(g and (s or q%2))
    elif mode == 'nearest-away': increment=bool(g)
    elif mode == 'up': increment=sign>0 and inexact
    elif mode == 'down': increment=sign<0 and inexact
    else: increment=False
    value=sign*(q+int(increment))
    return [value,inexact,bool(increment)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('tie even', solve(2*N,1,0,0,1,"nearest-even"), [2*N,True,False])
check('tie odd', solve(2*N+1,1,0,0,1,"nearest-even"), [2*N+2,True,True])
check('above tie sticky', solve(2*N,1,0,1,1,"nearest-even"), [2*N+1,True,True])
check('above tie round', solve(2*N,1,1,0,1,"nearest-even"), [2*N+1,True,True])
check('below half', solve(2*N,0,1,1,1,"nearest-even"), [2*N,True,False])
check('nearest away', solve(2*N,1,0,0,-1,"nearest-away"), [-2*N-1,True,True])
check('up positive', solve(N,0,0,1,1,"up"), [N+1,True,True])
check('up negative', solve(N,1,1,1,-1,"up"), [-N,True,False])
check('down negative', solve(N,0,1,0,-1,"down"), [-N-1,True,True])
check('down positive', solve(N,1,1,1,1,"down"), [N,True,False])
check('truncate', solve(N,1,1,1,-1,"zero"), [-N,True,False])
check('exact', solve(N,0,0,0,1,"up"), [N,False,False])
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
tie even	`[2, True, False]`	`[2, True, False]`	Passed
tie odd	`[4, True, True]`	`[4, True, True]`	Passed
above tie sticky	`[3, True, True]`	`[3, True, True]`	Passed
above tie round	`[2, True, False]`	`[3, True, True]`	Failed
below half	`[2, True, False]`	`[2, True, False]`	Passed
nearest away	`[-3, True, True]`	`[-3, True, True]`	Passed
up positive	`[2, True, True]`	`[2, True, True]`	Passed
up negative	`[-1, True, False]`	`[-1, True, False]`	Passed
down negative	`[-2, True, True]`	`[-2, True, True]`	Passed
down positive	`[1, True, False]`	`[1, True, False]`	Passed
truncate	`[-1, True, False]`	`[-1, True, False]`	Passed
exact	`[1, False, False]`	`[1, False, False]`	Passed

SHA-256 / 5b794035c71c932b2a149b92280c1f39d6db43c27467d5e4645a8e682045acf2

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(q,g,r,s,sign,mode):
    inexact=bool(g or r or s)
    if mode == 'nearest-even': increment=bool(g and q%2)
    elif mode == 'nearest-away': increment=bool(g)
    elif mode == 'up': increment=sign>0 and inexact
    elif mode == 'down': increment=sign<0 and inexact
    else: increment=False
    value=sign*(q+int(increment))
    return [value,inexact,bool(increment)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('tie even', solve(2*N,1,0,0,1,"nearest-even"), [2*N,True,False])
check('tie odd', solve(2*N+1,1,0,0,1,"nearest-even"), [2*N+2,True,True])
check('above tie sticky', solve(2*N,1,0,1,1,"nearest-even"), [2*N+1,True,True])
check('above tie round', solve(2*N,1,1,0,1,"nearest-even"), [2*N+1,True,True])
check('below half', solve(2*N,0,1,1,1,"nearest-even"), [2*N,True,False])
check('nearest away', solve(2*N,1,0,0,-1,"nearest-away"), [-2*N-1,True,True])
check('up positive', solve(N,0,0,1,1,"up"), [N+1,True,True])
check('up negative', solve(N,1,1,1,-1,"up"), [-N,True,False])
check('down negative', solve(N,0,1,0,-1,"down"), [-N-1,True,True])
check('down positive', solve(N,1,1,1,1,"down"), [N,True,False])
check('truncate', solve(N,1,1,1,-1,"zero"), [-N,True,False])
check('exact', solve(N,0,0,0,1,"up"), [N,False,False])
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
tie even	`[2, True, False]`	`[2, True, False]`	Passed
tie odd	`[4, True, True]`	`[4, True, True]`	Passed
above tie sticky	`[2, True, False]`	`[3, True, True]`	Failed
above tie round	`[2, True, False]`	`[3, True, True]`	Failed
below half	`[2, True, False]`	`[2, True, False]`	Passed
nearest away	`[-3, True, True]`	`[-3, True, True]`	Passed
up positive	`[2, True, True]`	`[2, True, True]`	Passed
up negative	`[-1, True, False]`	`[-1, True, False]`	Passed
down negative	`[-2, True, True]`	`[-2, True, True]`	Passed
down positive	`[1, True, False]`	`[1, True, False]`	Passed
truncate	`[-1, True, False]`	`[-1, True, False]`	Passed
exact	`[1, False, False]`	`[1, False, False]`	Passed

SHA-256 / 4852e2ecc96128fe716cea7446ae021a8b4ad7c7ba40f34db4706de06230ab63

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 12 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:39:32.099669+00:00.

Case digest / b9a9a6bce63bb6bf0f016cded5e0f8549e86aa9ec5de05200626940924dec225