decimal_scaled/

rounding.rs

//! Rounding-mode selector for scale-narrowing operations.
//!
//! Passed to every `*_with(mode)` sibling on every decimal width —
//! [`crate::D38::rescale_with`], `mul_with`, `div_with`, `to_int_with`,
//! `from_f64_with`, every `*_strict_with` on the wide tier, etc. — to
//! control how fractional digits are discarded when the result has
//! lower precision than the working intermediate. The six modes cover
//! IEEE-754's five rounding rules (`HalfToEven`, `HalfTowardZero`,
//! `Trunc`, `Floor`, `Ceiling`) plus the commercial `HalfAwayFromZero`
//! rule expected by users coming from `bigdecimal` / `rust_decimal`.
//!
//! The default mode is `HalfToEven` (IEEE-754 default; no systematic
//! bias). The `rounding-*` Cargo features let a downstream crate flip
//! the crate-wide default at compile time.

/// Selector for the rounding rule applied when a scale-narrowing
/// operation discards fractional digits.
///
/// See the module-level documentation for when each rule applies.
///
/// # Precision
///
/// N/A: this is a tag; no arithmetic is performed by constructing
/// or comparing variants.
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub enum RoundingMode {
    /// Round to nearest; on ties, round to the even neighbour.
    /// IEEE-754 `roundTiesToEven`; also called banker's rounding.
    /// Unbiased — repeated rounding does not drift sums. Crate default.
    ///
    /// Examples (truncate to integer): `0.5 -> 0`, `1.5 -> 2`,
    /// `2.5 -> 2`, `-0.5 -> 0`, `-1.5 -> -2`.
    HalfToEven,
    /// Round to nearest; on ties, round away from zero. Commercial
    /// rounding. Mildly biased in magnitude.
    ///
    /// Examples: `0.5 -> 1`, `1.5 -> 2`, `-0.5 -> -1`, `-1.5 -> -2`.
    HalfAwayFromZero,
    /// Round to nearest; on ties, round toward zero. Mildly biased
    /// toward zero. Rare in practice; included for completeness.
    ///
    /// Examples: `0.5 -> 0`, `1.5 -> 1`, `-0.5 -> 0`, `-1.5 -> -1`.
    HalfTowardZero,
    /// Truncate toward zero. Discards the fractional part. Cheapest
    /// in integer arithmetic; matches Rust's `as` cast for integer
    /// narrowing.
    ///
    /// Examples: `0.7 -> 0`, `-0.7 -> 0`, `1.9 -> 1`, `-1.9 -> -1`.
    Trunc,
    /// Round toward negative infinity (floor).
    ///
    /// Examples: `0.7 -> 0`, `-0.7 -> -1`, `1.9 -> 1`, `-1.9 -> -2`.
    Floor,
    /// Round toward positive infinity (ceiling).
    ///
    /// Examples: `0.7 -> 1`, `-0.7 -> 0`, `1.9 -> 2`, `-1.9 -> -1`.
    Ceiling,
}

/// Compile-time default `RoundingMode` for the no-arg `rescale` and
/// future default-rounding methods.
///
/// Selected by Cargo feature flags (priority order: first match wins):
/// 1. `rounding-half-away-from-zero` → `HalfAwayFromZero`
/// 2. `rounding-half-toward-zero` → `HalfTowardZero`
/// 3. `rounding-trunc` → `Trunc`
/// 4. `rounding-floor` → `Floor`
/// 5. `rounding-ceiling` → `Ceiling`
/// 6. (none) → `HalfToEven` (IEEE-754 default; banker's rounding)
#[cfg(feature = "rounding-half-away-from-zero")]
pub const DEFAULT_ROUNDING_MODE: RoundingMode = RoundingMode::HalfAwayFromZero;

#[cfg(all(
    not(feature = "rounding-half-away-from-zero"),
    feature = "rounding-half-toward-zero"
))]
pub const DEFAULT_ROUNDING_MODE: RoundingMode = RoundingMode::HalfTowardZero;

#[cfg(all(
    not(feature = "rounding-half-away-from-zero"),
    not(feature = "rounding-half-toward-zero"),
    feature = "rounding-trunc"
))]
pub const DEFAULT_ROUNDING_MODE: RoundingMode = RoundingMode::Trunc;

#[cfg(all(
    not(feature = "rounding-half-away-from-zero"),
    not(feature = "rounding-half-toward-zero"),
    not(feature = "rounding-trunc"),
    feature = "rounding-floor"
))]
pub const DEFAULT_ROUNDING_MODE: RoundingMode = RoundingMode::Floor;

#[cfg(all(
    not(feature = "rounding-half-away-from-zero"),
    not(feature = "rounding-half-toward-zero"),
    not(feature = "rounding-trunc"),
    not(feature = "rounding-floor"),
    feature = "rounding-ceiling"
))]
pub const DEFAULT_ROUNDING_MODE: RoundingMode = RoundingMode::Ceiling;

#[cfg(not(any(
    feature = "rounding-half-away-from-zero",
    feature = "rounding-half-toward-zero",
    feature = "rounding-trunc",
    feature = "rounding-floor",
    feature = "rounding-ceiling",
)))]
pub const DEFAULT_ROUNDING_MODE: RoundingMode = RoundingMode::HalfToEven;

/// Strategy hook for the rounding-mode family.
///
/// Given a *truncated-toward-zero* quotient and the per-operation
/// numerator / divisor context, returns `true` if the quotient should
/// be bumped one step "away from zero" in the result's direction to
/// satisfy this mode. Caller is responsible for the actual bump (it
/// is `q + 1` when the result is positive, `q − 1` when negative).
///
/// The three inputs collapse the per-step numerics that every mode
/// cares about into mode-independent booleans / orderings:
///
/// - `cmp_r` — three-way comparison of `|r|` against `|m| − |r|`. This
///   is exactly the round-up condition (`|r| > |m| − |r|` ⇔ `2·|r| > |m|`)
///   without the doubling-overflow risk. `Equal` flags the half-way tie,
///   which only occurs when the divisor is even.
/// - `q_is_odd` — parity of the truncated quotient. Drives the
///   half-to-even tie break.
/// - `result_positive` — sign of the true result (`sign(n) == sign(m)`).
///   Drives `Floor` / `Ceiling`.
///
/// Caller pre-handles the `r == 0` case (no rounding needed).
///
/// `#[inline(always)]` because the entire body is one match on a
/// 6-variant enum. The hot operator path instantiates this with a
/// const `mode` (`DEFAULT_ROUNDING_MODE`), so const-propagation can
/// collapse the match away once inlined.
#[inline(always)]
pub(crate) fn should_bump(
    mode: RoundingMode,
    cmp_r: ::core::cmp::Ordering,
    q_is_odd: bool,
    result_positive: bool,
) -> bool {
    use ::core::cmp::Ordering;
    match mode {
        RoundingMode::HalfToEven => match cmp_r {
            Ordering::Less => false,
            Ordering::Greater => true,
            Ordering::Equal => q_is_odd,
        },
        RoundingMode::HalfAwayFromZero => !matches!(cmp_r, Ordering::Less),
        RoundingMode::HalfTowardZero => matches!(cmp_r, Ordering::Greater),
        RoundingMode::Trunc => false,
        RoundingMode::Floor => !result_positive,
        RoundingMode::Ceiling => result_positive,
    }
}

/// Applies `mode` to integer division `raw / divisor`, returning the
/// rounded quotient.
///
/// Used by `D38::rescale_with` and by the multiplier-and-divide
/// fast paths in `mg_divide`. The whole mode-specific logic is
/// delegated to [`should_bump`]; this function is just the i128
/// arithmetic wrapper that builds its inputs and applies the bump.
#[inline(always)]
pub(crate) fn apply_rounding(raw: i128, divisor: i128, mode: RoundingMode) -> i128 {
    let quotient = raw / divisor;
    let remainder = raw % divisor;

    if remainder == 0 {
        return quotient;
    }

    let abs_rem = remainder.unsigned_abs();
    let abs_div = divisor.unsigned_abs();
    let comp = abs_div - abs_rem;
    let cmp_r = abs_rem.cmp(&comp);
    let q_is_odd = (quotient & 1) != 0;
    let result_positive = (raw < 0) == (divisor < 0);

    if should_bump(mode, cmp_r, q_is_odd, result_positive) {
        if result_positive { quotient + 1 } else { quotient - 1 }
    } else {
        quotient
    }
}

/// `true` when the crate is built with [`DEFAULT_ROUNDING_MODE`] set to
/// [`RoundingMode::HalfToEven`] — i.e. none of the `rounding-*` feature
/// flags is selected. Used by tests whose expected values assume the
/// default IEEE-754 rounding to short-circuit themselves under a
/// non-default rounding feature build.
#[cfg(test)]
pub(crate) const DEFAULT_IS_HALF_TO_EVEN: bool = matches!(
    DEFAULT_ROUNDING_MODE,
    RoundingMode::HalfToEven
);

#[cfg(test)]
mod tests {
    use super::*;

    fn modes() -> [RoundingMode; 6] {
        [
            RoundingMode::HalfToEven,
            RoundingMode::HalfAwayFromZero,
            RoundingMode::HalfTowardZero,
            RoundingMode::Trunc,
            RoundingMode::Floor,
            RoundingMode::Ceiling,
        ]
    }

    /// Zero remainder is exact for every mode.
    #[test]
    fn zero_remainder_is_quotient_for_all_modes() {
        for m in modes() {
            assert_eq!(apply_rounding(20, 10, m), 2, "{m:?}");
            assert_eq!(apply_rounding(-20, 10, m), -2, "{m:?}");
            assert_eq!(apply_rounding(0, 10, m), 0, "{m:?}");
        }
    }

    /// Half-to-even: ties go to even neighbour.
    #[test]
    fn half_to_even_ties() {
        let m = RoundingMode::HalfToEven;
        assert_eq!(apply_rounding(5, 10, m), 0);     // 0.5 -> 0 (even)
        assert_eq!(apply_rounding(15, 10, m), 2);    // 1.5 -> 2
        assert_eq!(apply_rounding(25, 10, m), 2);    // 2.5 -> 2 (even)
        assert_eq!(apply_rounding(35, 10, m), 4);    // 3.5 -> 4
        assert_eq!(apply_rounding(-5, 10, m), 0);    // -0.5 -> 0
        assert_eq!(apply_rounding(-15, 10, m), -2);  // -1.5 -> -2
        assert_eq!(apply_rounding(-25, 10, m), -2);  // -2.5 -> -2
        assert_eq!(apply_rounding(-35, 10, m), -4);  // -3.5 -> -4
    }

    /// Half-away-from-zero: ties go away from zero.
    #[test]
    fn half_away_from_zero_ties() {
        let m = RoundingMode::HalfAwayFromZero;
        assert_eq!(apply_rounding(5, 10, m), 1);
        assert_eq!(apply_rounding(15, 10, m), 2);
        assert_eq!(apply_rounding(25, 10, m), 3);
        assert_eq!(apply_rounding(-5, 10, m), -1);
        assert_eq!(apply_rounding(-15, 10, m), -2);
        assert_eq!(apply_rounding(-25, 10, m), -3);
    }

    /// Half-toward-zero: ties go toward zero.
    #[test]
    fn half_toward_zero_ties() {
        let m = RoundingMode::HalfTowardZero;
        assert_eq!(apply_rounding(5, 10, m), 0);
        assert_eq!(apply_rounding(15, 10, m), 1);
        assert_eq!(apply_rounding(25, 10, m), 2);
        assert_eq!(apply_rounding(-5, 10, m), 0);
        assert_eq!(apply_rounding(-15, 10, m), -1);
        assert_eq!(apply_rounding(-25, 10, m), -2);
    }

    /// Trunc: always toward zero, regardless of magnitude.
    #[test]
    fn trunc_always_toward_zero() {
        let m = RoundingMode::Trunc;
        assert_eq!(apply_rounding(7, 10, m), 0);
        assert_eq!(apply_rounding(9, 10, m), 0);
        assert_eq!(apply_rounding(19, 10, m), 1);
        assert_eq!(apply_rounding(-7, 10, m), 0);
        assert_eq!(apply_rounding(-19, 10, m), -1);
    }

    /// Floor: always toward negative infinity.
    #[test]
    fn floor_toward_negative_infinity() {
        let m = RoundingMode::Floor;
        assert_eq!(apply_rounding(1, 10, m), 0);
        assert_eq!(apply_rounding(7, 10, m), 0);
        assert_eq!(apply_rounding(9, 10, m), 0);
        assert_eq!(apply_rounding(-1, 10, m), -1);
        assert_eq!(apply_rounding(-7, 10, m), -1);
        assert_eq!(apply_rounding(-19, 10, m), -2);
    }

    /// Ceiling: always toward positive infinity.
    #[test]
    fn ceiling_toward_positive_infinity() {
        let m = RoundingMode::Ceiling;
        assert_eq!(apply_rounding(1, 10, m), 1);
        assert_eq!(apply_rounding(7, 10, m), 1);
        assert_eq!(apply_rounding(19, 10, m), 2);
        assert_eq!(apply_rounding(-1, 10, m), 0);
        assert_eq!(apply_rounding(-7, 10, m), 0);
        assert_eq!(apply_rounding(-19, 10, m), -1);
    }

    /// Non-half values go to the nearest neighbour for every "half"
    /// mode and ignore the half-tie rule.
    #[test]
    fn non_half_goes_to_nearest() {
        for m in [
            RoundingMode::HalfToEven,
            RoundingMode::HalfAwayFromZero,
            RoundingMode::HalfTowardZero,
        ] {
            assert_eq!(apply_rounding(4, 10, m), 0, "{m:?} 0.4");
            assert_eq!(apply_rounding(6, 10, m), 1, "{m:?} 0.6");
            assert_eq!(apply_rounding(-4, 10, m), 0, "{m:?} -0.4");
            assert_eq!(apply_rounding(-6, 10, m), -1, "{m:?} -0.6");
        }
    }
}