FA-15981 / Floating-point arithmetic / Open access

Truncation applies the nearest rounding increment · case 01

Truncation applies the nearest rounding increment.

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

ROOT CAUSE

Truncation applies the nearest rounding increment. The faulty expression is else: increment=bool(g).

THE FAILURE

Truncation applies the nearest rounding increment. The faulty expression is else: increment=bool(g).

Unsuccessful approach: The attempted local correction else: increment=inexact 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 (r or 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=bool(g)
    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	`[3, True, True]`	`[3, True, True]`	Passed
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	`[-2, True, True]`	`[-1, True, False]`	Failed
exact	`[1, False, False]`	`[1, False, False]`	Passed

SHA-256 / 8f51572393f6806b5ff5c998ed7b6ae9a5471c91043b2c741ea8cfc32b541b0d

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 (r or 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=inexact
    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	`[3, True, True]`	`[3, True, True]`	Passed
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	`[-2, True, True]`	`[-1, True, False]`	Failed
exact	`[1, False, False]`	`[1, False, False]`	Passed

SHA-256 / c0f7dbb507d62cf756a6f3fd6083f402f946e0cb539d395a4ebeb7bdac30ea88

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 / 3ef74efd0041497b037d85e9013701aa3e440eba22b9c53150d4bbac69b3d601