/** Exact amounts in currency units; decimal formatting is presentation, never a tax rule. */
export type FiscalFraction = { numerator: string; denominator: string };
function parts(value: FiscalFraction): [bigint, bigint] {
    if (
        !/^-?\d{1,80}$/.test(value.numerator) ||
        !/^\d{1,80}$/.test(value.denominator) ||
        BigInt(value.denominator) === 0n
    )
        throw new Error(
            'Representação racional inválida; sem substituição por zero.',
        );
    return [BigInt(value.numerator), BigInt(value.denominator)];
}
export function fraction(n: bigint, d = 1n): FiscalFraction {
    if (d === 0n) throw new Error('Denominador nulo.');
    if (d < 0n) {
        n = -n;
        d = -d;
    }
    let a = n < 0n ? -n : n,
        b = d;
    while (b) {
        const r = a % b;
        a = b;
        b = r;
    }
    return {
        numerator: String(n / (a || 1n)),
        denominator: String(d / (a || 1n)),
    };
}
export function decimalFraction(raw: string): FiscalFraction {
    if (!/^\d{1,18}(\.\d{1,6})?$/.test(raw))
        throw new Error('Montante decimal inválido.');
    const [a, b = ''] = raw.split('.');
    return fraction(BigInt(a + b), 10n ** BigInt(b.length));
}
export function addFractions(values: FiscalFraction[]): FiscalFraction {
    return values.reduce((a, b) => {
        const [an, ad] = parts(a),
            [bn, bd] = parts(b);
        return fraction(an * bd + bn * ad, ad * bd);
    }, fraction(0n));
}
export function subtractFractions(
    a: FiscalFraction,
    b: FiscalFraction,
): FiscalFraction {
    const [an, ad] = parts(a),
        [bn, bd] = parts(b);
    return fraction(an * bd - bn * ad, ad * bd);
}
export function positiveFraction(value: FiscalFraction): FiscalFraction {
    return parts(value)[0] > 0n ? value : fraction(0n);
}
export function fractionPresentation(value: FiscalFraction): {
    decimal: string;
    approximate: boolean;
} {
    const [raw, d] = parts(value),
        n = raw < 0n ? -raw : raw,
        scaled = n * 1000000n;
    const q = (scaled + d / 2n) / d,
        dec = (q % 1000000n)
            .toString()
            .padStart(6, '0')
            .replace(/0+$/, '')
            .padEnd(2, '0');
    return {
        decimal: `${raw < 0n ? '-' : ''}${q / 1000000n}.${dec}`,
        approximate: scaled % d !== 0n,
    };
}
export function fractionLabel(value: FiscalFraction): string {
    parts(value);
    return `${value.numerator}/${value.denominator}`;
}