FA-16931 / Floating-point arithmetic / Open access

Decimal fused multiply-add rounds inputs to working precision · case 01

Decimal fused multiply-add rounds inputs to working precision.

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

ROOT CAUSE

Decimal fused multiply-add rounds inputs to working precision. The faulty expression is av=ctx.create_decimal(a); bv=ctx.create_decimal(b); cv=ctx.create_decimal(c).

THE FAILURE

Decimal fused multiply-add rounds inputs to working precision. The faulty expression is av=ctx.create_decimal(a); bv=ctx.create_decimal(b); cv=ctx.create_decimal(c).

Unsuccessful approach: The attempted local correction av=Decimal(a); bv=Decimal(b); cv=ctx.create_decimal(c) still violates the explicit regression fixtures.

Case contract

Decimal fused multiply-add rounds a*b+c once in a fresh precision-limited half-even context. Inputs are decimal strings; return final decimal string and Inexact flag.

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 decimal
from decimal import Decimal, Context, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_DOWN

N = 1
observations = []
def solve(a,b,c,precision):
    ctx=Context(prec=precision,rounding=ROUND_HALF_EVEN)
    for signal in ctx.traps: ctx.traps[signal]=False
    av=ctx.create_decimal(a); bv=ctx.create_decimal(b); cv=ctx.create_decimal(c)
    result=ctx.fma(av,bv,cv)
    return [str(result),ctx.flags[decimal.Inexact]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('cancellation', solve("1.23","4.56","-5.61",3), ["-0.0012",False])
check('opposite cancellation', solve("-1.23","4.56","5.61",3), ["0.0012",False])
check('tiny addend', solve("1","1","0.005",3), ["1.00",True])
check('odd tie', solve("1","1","0.015",3), ["1.02",True])
check('variable exact', solve(str(N),"2","3",3), [str(2*N+3),False])
check('addend precision', solve("1.23456","1","-1.23455",3), ["0.00001",False])
check('operand precision', solve("1.23456","1","0",3), ["1.23",True])
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
cancellation	`['-0.0012', False]`	`['-0.0012', False]`	Passed
opposite cancellation	`['0.0012', False]`	`['0.0012', False]`	Passed
tiny addend	`['1.00', True]`	`['1.00', True]`	Passed
odd tie	`['1.02', True]`	`['1.02', True]`	Passed
variable exact	`['5', False]`	`['5', False]`	Passed
addend precision	`['0.00', True]`	`['0.00001', False]`	Failed
operand precision	`['1.23', True]`	`['1.23', True]`	Passed

SHA-256 / a54a4ec73c9535e8fc708a0594e910966b66e738219c35c790f2cb1e1fa2b220

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
import decimal
from decimal import Decimal, Context, ROUND_HALF_EVEN, ROUND_HALF_UP, ROUND_DOWN

N = 1
observations = []
def solve(a,b,c,precision):
    ctx=Context(prec=precision,rounding=ROUND_HALF_EVEN)
    for signal in ctx.traps: ctx.traps[signal]=False
    av=Decimal(a); bv=Decimal(b); cv=ctx.create_decimal(c)
    result=ctx.fma(av,bv,cv)
    return [str(result),ctx.flags[decimal.Inexact]]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
check('cancellation', solve("1.23","4.56","-5.61",3), ["-0.0012",False])
check('opposite cancellation', solve("-1.23","4.56","5.61",3), ["0.0012",False])
check('tiny addend', solve("1","1","0.005",3), ["1.00",True])
check('odd tie', solve("1","1","0.015",3), ["1.02",True])
check('variable exact', solve(str(N),"2","3",3), [str(2*N+3),False])
check('addend precision', solve("1.23456","1","-1.23455",3), ["0.00001",False])
check('operand precision', solve("1.23456","1","0",3), ["1.23",True])
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
cancellation	`['-0.0012', False]`	`['-0.0012', False]`	Passed
opposite cancellation	`['0.0012', False]`	`['0.0012', False]`	Passed
tiny addend	`['1.00', True]`	`['1.00', True]`	Passed
odd tie	`['1.02', True]`	`['1.02', True]`	Passed
variable exact	`['5', False]`	`['5', False]`	Passed
addend precision	`['0.00456', True]`	`['0.00001', False]`	Failed
operand precision	`['1.23', True]`	`['1.23', True]`	Passed

SHA-256 / b9e70590f9481e2a03b8751880e896101fccd0d46a63776f2036bf106e77135c

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 7 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 2026-09-29T14:39:41.621633+00:00.

Case digest / ae7c09f0c7a589033d6af55712fd047edcf2aad1f2e4388eaf3cad7d3d297dab