decimal-scaled 0.1.0

//! `num-traits` 0.2 trait implementations for [`I128`].
//!
//! Allows generic numeric code (nalgebra, ndarray, statrs, and other
//! crates that accept "any number type") to use `I128<SCALE>` as a
//! scalar. Crates that provide generic numeric algorithms almost
//! universally bound on [`num_traits`] traits rather than defining
//! their own numeric interfaces.
//!
//! # Trait coverage
//!
//! - [`num_traits::Zero`] / [`num_traits::One`] — additive and
//!   multiplicative identities.
//! - [`num_traits::Num`] — umbrella numeric trait combining
//!   `Zero + One + PartialEq + Add + Sub + Mul + Div + Rem` with a
//!   `from_str_radix` constructor.
//! - [`num_traits::Bounded`] — `min_value()` / `max_value()` for
//!   generic clamping code.
//! - [`num_traits::Signed`] — `abs`, `signum`, `is_positive`,
//!   `is_negative`, `abs_sub`.
//! - [`num_traits::FromPrimitive`] / [`num_traits::ToPrimitive`] —
//!   fallible conversions to and from the primitive numeric types.
//! - [`num_traits::CheckedAdd`] / [`num_traits::CheckedSub`] /
//!   [`num_traits::CheckedMul`] / [`num_traits::CheckedDiv`] /
//!   [`num_traits::CheckedRem`] / [`num_traits::CheckedNeg`] —
//!   overflow-safe variants returning `Option<Self>`.
//!
//! # `from_str_radix`
//!
//! [`num_traits::Num::from_str_radix`] delegates to
//! [`core::str::FromStr`] for `radix == 10` and rejects every other
//! radix. The compile-time signature is stable regardless of whether
//! the underlying `FromStr` implementation is complete.
//!
//! # `CheckedMul` / `CheckedDiv`
//!
//! Both traits delegate to the inherent [`I128::checked_mul`] and
//! [`I128::checked_div`] methods. The trait and inherent paths are
//! bit-identical. `CheckedAdd`, `CheckedSub`, `CheckedRem`, and
//! `CheckedNeg` operate directly on the raw `i128` storage and
//! delegate to `i128`'s own checked intrinsics; no rescaling is
//! needed for those operations.

use num_traits::{
    Bounded, CheckedAdd, CheckedDiv, CheckedMul, CheckedNeg, CheckedRem, CheckedSub,
    FromPrimitive, Num, NumCast, One, Signed, ToPrimitive, Zero,
};

use crate::core_type::{I128, ParseDecimalError};

// ---------------------------------------------------------------------------
// Zero / One
// ---------------------------------------------------------------------------

impl<const SCALE: u32> Zero for I128<SCALE> {
    /// Returns the additive identity for `I128<SCALE>`.
    ///
    /// Equivalent to [`I128::ZERO`].
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Zero;
    ///
    /// assert_eq!(I128s12::zero(), I128s12::ZERO);
    /// ```
    #[inline]
    fn zero() -> Self {
        Self::ZERO
    }

    /// Returns `true` if `self` equals the additive identity.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Zero;
    ///
    /// assert!(I128s12::ZERO.is_zero());
    /// assert!(!I128s12::ONE.is_zero());
    /// ```
    #[inline]
    fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<const SCALE: u32> One for I128<SCALE> {
    /// Returns the multiplicative identity for `I128<SCALE>`.
    ///
    /// Equivalent to [`I128::ONE`].
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::One;
    ///
    /// assert_eq!(I128s12::one(), I128s12::ONE);
    /// ```
    #[inline]
    fn one() -> Self {
        Self::ONE
    }

    /// Returns `true` if `self` equals the multiplicative identity.
    ///
    /// Provided explicitly rather than relying on the default so that
    /// the check is a single integer comparison instead of going through
    /// the multiplication chain.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::One;
    ///
    /// assert!(I128s12::ONE.is_one());
    /// assert!(!I128s12::ZERO.is_one());
    /// ```
    #[inline]
    fn is_one(&self) -> bool {
        self.0 == Self::multiplier()
    }
}

// ---------------------------------------------------------------------------
// Num
// ---------------------------------------------------------------------------

impl<const SCALE: u32> Num for I128<SCALE> {
    type FromStrRadixErr = ParseDecimalError;

    /// Parses a decimal string in the given radix.
    ///
    /// Only `radix == 10` is supported; `I128<SCALE>` is a base-10 type
    /// by construction. Any other radix returns `ParseDecimalError::InvalidChar`
    /// without attempting to parse the string.
    ///
    /// For `radix == 10` the call delegates to the [`core::str::FromStr`]
    /// implementation on `I128<SCALE>`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Num;
    ///
    /// let v = I128s12::from_str_radix("1", 10).expect("parse 1");
    /// assert_eq!(v, I128s12::ONE);
    ///
    /// assert!(I128s12::from_str_radix("1", 16).is_err());
    /// ```
    fn from_str_radix(s: &str, radix: u32) -> Result<Self, Self::FromStrRadixErr> {
        if radix != 10 {
            return Err(ParseDecimalError::InvalidChar);
        }
        s.parse::<Self>()
    }
}

// ---------------------------------------------------------------------------
// Bounded
// ---------------------------------------------------------------------------

impl<const SCALE: u32> Bounded for I128<SCALE> {
    /// Returns the smallest representable value, equal to [`I128::MIN`].
    ///
    /// The raw storage is `i128::MIN`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Bounded;
    ///
    /// assert_eq!(I128s12::min_value(), I128s12::MIN);
    /// ```
    #[inline]
    fn min_value() -> Self {
        Self::MIN
    }

    /// Returns the largest representable value, equal to [`I128::MAX`].
    ///
    /// The raw storage is `i128::MAX`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Bounded;
    ///
    /// assert_eq!(I128s12::max_value(), I128s12::MAX);
    /// ```
    #[inline]
    fn max_value() -> Self {
        Self::MAX
    }
}

// ---------------------------------------------------------------------------
// Signed
// ---------------------------------------------------------------------------

impl<const SCALE: u32> Signed for I128<SCALE> {
    /// Returns the absolute value of `self`.
    ///
    /// Delegates to the inherent [`I128::abs`] method.
    ///
    /// # Panics
    ///
    /// Panics in debug mode when called on `I128::MIN` because the
    /// positive counterpart of `i128::MIN` is not representable. In
    /// release mode the result wraps.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Signed;
    ///
    /// let pos = I128s12::from_bits(1_500_000_000_000);
    /// let neg = I128s12::from_bits(-1_500_000_000_000);
    /// assert_eq!(neg.abs(), pos);
    /// ```
    #[inline]
    fn abs(&self) -> Self {
        I128::abs(*self)
    }

    /// Returns the sign of `self` as a scaled `I128`: `-ONE`, `ZERO`, or `+ONE`.
    ///
    /// Delegates to the inherent [`I128::signum`] method.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Signed;
    ///
    /// assert_eq!(I128s12::from_bits(5).signum(), I128s12::ONE);
    /// assert_eq!(I128s12::from_bits(-5).signum(), -I128s12::ONE);
    /// assert_eq!(I128s12::ZERO.signum(), I128s12::ZERO);
    /// ```
    #[inline]
    fn signum(&self) -> Self {
        I128::signum(*self)
    }

    /// Returns `true` if `self` is strictly greater than zero.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Signed;
    ///
    /// assert!(I128s12::ONE.is_positive());
    /// assert!(!I128s12::ZERO.is_positive());
    /// assert!(!(-I128s12::ONE).is_positive());
    /// ```
    #[inline]
    fn is_positive(&self) -> bool {
        self.0 > 0
    }

    /// Returns `true` if `self` is strictly less than zero.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Signed;
    ///
    /// assert!((-I128s12::ONE).is_negative());
    /// assert!(!I128s12::ZERO.is_negative());
    /// assert!(!I128s12::ONE.is_negative());
    /// ```
    #[inline]
    fn is_negative(&self) -> bool {
        self.0 < 0
    }

    /// Returns `self - other` when `self > other`, otherwise `ZERO`.
    ///
    /// Matches the `num_traits::Signed::abs_sub` contract: the result is
    /// never negative. This is not the same as `(self - other).abs()`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::Signed;
    ///
    /// let two = I128s12::from_bits(2_000_000_000_000);
    /// let five = I128s12::from_bits(5_000_000_000_000);
    /// let three = I128s12::from_bits(3_000_000_000_000);
    ///
    /// assert_eq!(five.abs_sub(&two), three);
    /// assert_eq!(two.abs_sub(&five), I128s12::ZERO);
    /// assert_eq!(five.abs_sub(&five), I128s12::ZERO);
    /// ```
    #[inline]
    fn abs_sub(&self, other: &Self) -> Self {
        if *self <= *other {
            Self::ZERO
        } else {
            *self - *other
        }
    }
}

// ---------------------------------------------------------------------------
// FromPrimitive / ToPrimitive
// ---------------------------------------------------------------------------

impl<const SCALE: u32> FromPrimitive for I128<SCALE> {
    /// Constructs a `I128<SCALE>` from an `i64` integer value.
    ///
    /// Scales `n` by `10^SCALE`. Returns `None` when the multiplication
    /// overflows `i128`, which can occur at pathologically large scale
    /// values. At `SCALE <= 18` the call always succeeds for any `i64`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::FromPrimitive;
    ///
    /// assert_eq!(I128s12::from_i64(0), Some(I128s12::ZERO));
    /// assert_eq!(I128s12::from_i64(1), Some(I128s12::ONE));
    /// assert_eq!(I128s12::from_i64(-42), Some(I128s12::from_bits(-42_000_000_000_000)));
    /// ```
    #[inline]
    fn from_i64(n: i64) -> Option<Self> {
        (n as i128)
            .checked_mul(Self::multiplier())
            .map(Self)
    }

    /// Constructs a `I128<SCALE>` from a `u64` integer value.
    ///
    /// Scales `n` by `10^SCALE`. Returns `None` on overflow. At
    /// `SCALE <= 18` the call always succeeds for any `u64`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::FromPrimitive;
    ///
    /// assert_eq!(I128s12::from_u64(0), Some(I128s12::ZERO));
    /// assert_eq!(I128s12::from_u64(42), Some(I128s12::from_bits(42_000_000_000_000)));
    /// ```
    #[inline]
    fn from_u64(n: u64) -> Option<Self> {
        (n as i128)
            .checked_mul(Self::multiplier())
            .map(Self)
    }

    /// Constructs a `I128<SCALE>` from an `i128` integer value.
    ///
    /// Returns `None` when scaling overflows. Delegates to the existing
    /// [`TryFrom<i128>`] implementation.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::FromPrimitive;
    ///
    /// assert_eq!(I128s12::from_i128(7), Some(I128s12::from_bits(7_000_000_000_000)));
    /// assert_eq!(I128s12::from_i128(i128::MAX), None);
    /// ```
    #[inline]
    fn from_i128(n: i128) -> Option<Self> {
        Self::try_from(n).ok()
    }

    /// Constructs a `I128<SCALE>` from a `u128` integer value.
    ///
    /// Returns `None` when `n > i128::MAX` or when scaling overflows.
    /// Delegates to the existing [`TryFrom<u128>`] implementation.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::FromPrimitive;
    ///
    /// assert_eq!(I128s12::from_u128(99), Some(I128s12::from_bits(99_000_000_000_000)));
    /// assert_eq!(I128s12::from_u128(u128::MAX), None);
    /// ```
    #[inline]
    fn from_u128(n: u128) -> Option<Self> {
        Self::try_from(n).ok()
    }

    /// Constructs a `I128<SCALE>` from an `f32` value.
    ///
    /// Returns `None` for `NaN`, infinities, or finite values whose
    /// scaled representation overflows `i128`. Delegates to the existing
    /// [`TryFrom<f32>`] implementation.
    ///
    /// # Precision
    ///
    /// Lossy: involves f32 or f64 at some point; result may lose precision.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::FromPrimitive;
    ///
    /// assert_eq!(I128s12::from_f32(0.0), Some(I128s12::ZERO));
    /// assert_eq!(I128s12::from_f32(1.0), Some(I128s12::ONE));
    /// assert_eq!(I128s12::from_f32(f32::NAN), None);
    /// assert_eq!(I128s12::from_f32(f32::INFINITY), None);
    /// ```
    #[inline]
    fn from_f32(n: f32) -> Option<Self> {
        Self::try_from(n).ok()
    }

    /// Constructs a `I128<SCALE>` from an `f64` value.
    ///
    /// Returns `None` for `NaN`, infinities, or finite values whose
    /// scaled representation overflows `i128`. Delegates to the existing
    /// [`TryFrom<f64>`] implementation.
    ///
    /// # Precision
    ///
    /// Lossy: involves f32 or f64 at some point; result may lose precision.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::FromPrimitive;
    ///
    /// assert_eq!(I128s12::from_f64(0.0), Some(I128s12::ZERO));
    /// assert_eq!(I128s12::from_f64(1.0), Some(I128s12::ONE));
    /// assert_eq!(I128s12::from_f64(f64::NAN), None);
    /// assert_eq!(I128s12::from_f64(1e30), None);
    /// ```
    #[inline]
    fn from_f64(n: f64) -> Option<Self> {
        Self::try_from(n).ok()
    }
}

impl<const SCALE: u32> ToPrimitive for I128<SCALE> {
    /// Converts `self` to `i64` by truncating the fractional part toward zero.
    ///
    /// Returns `None` when the integer part of `self` falls outside
    /// `i64`'s range. Unlike `to_int_lossy`, which saturates, this method
    /// is contractually fallible.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::ToPrimitive;
    ///
    /// let v = I128s12::from_bits(2_500_000_000_000); // 2.5
    /// assert_eq!(v.to_i64(), Some(2));
    /// assert_eq!(I128s12::MAX.to_i64(), None);
    /// ```
    #[inline]
    fn to_i64(&self) -> Option<i64> {
        let raw = self.0 / Self::multiplier();
        i64::try_from(raw).ok()
    }

    /// Converts `self` to `u64` by truncating the fractional part toward zero.
    ///
    /// Returns `None` for negative values and for values whose integer part
    /// exceeds `u64::MAX`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::ToPrimitive;
    ///
    /// let v = I128s12::from_bits(42_000_000_000_000);
    /// assert_eq!(v.to_u64(), Some(42));
    /// assert_eq!((-I128s12::ONE).to_u64(), None);
    /// ```
    #[inline]
    fn to_u64(&self) -> Option<u64> {
        if self.0 < 0 {
            return None;
        }
        let raw = self.0 / Self::multiplier();
        u64::try_from(raw).ok()
    }

    /// Converts `self` to `i128` by truncating the fractional part toward zero.
    ///
    /// Always returns `Some` because `self.0 / 10^SCALE` fits in `i128`
    /// by construction.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::ToPrimitive;
    ///
    /// let v = I128s12::from_bits(42_000_000_000_000);
    /// assert_eq!(v.to_i128(), Some(42));
    /// assert!(I128s12::MAX.to_i128().is_some());
    /// ```
    #[inline]
    fn to_i128(&self) -> Option<i128> {
        Some(self.0 / Self::multiplier())
    }

    /// Converts `self` to `u128` by truncating the fractional part toward zero.
    ///
    /// Returns `None` for negative values.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::ToPrimitive;
    ///
    /// assert_eq!(I128s12::ZERO.to_u128(), Some(0));
    /// assert_eq!(I128s12::from_bits(-1).to_u128(), None);
    /// ```
    #[inline]
    fn to_u128(&self) -> Option<u128> {
        if self.0 < 0 {
            return None;
        }
        u128::try_from(self.0 / Self::multiplier()).ok()
    }

    /// Converts `self` to `f32`.
    ///
    /// Uses the [`I128::to_f32_lossy`] helper. Always returns `Some`; the
    /// result may be `+/-inf` for very large magnitudes.
    ///
    /// # Precision
    ///
    /// Lossy: involves f32 or f64 at some point; result may lose precision.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::ToPrimitive;
    ///
    /// let v = I128s12::from_bits(1_500_000_000_000); // 1.5
    /// assert_eq!(v.to_f32(), Some(1.5_f32));
    /// ```
    #[inline]
    fn to_f32(&self) -> Option<f32> {
        Some((*self).to_f32_lossy())
    }

    /// Converts `self` to `f64`.
    ///
    /// Uses the [`I128::to_f64_lossy`] helper. Always returns `Some`; the
    /// result may be `+/-inf` for very large magnitudes.
    ///
    /// # Precision
    ///
    /// Lossy: involves f32 or f64 at some point; result may lose precision.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::ToPrimitive;
    ///
    /// let v = I128s12::from_bits(1_500_000_000_000); // 1.5
    /// assert_eq!(v.to_f64(), Some(1.5_f64));
    /// ```
    #[inline]
    fn to_f64(&self) -> Option<f64> {
        Some((*self).to_f64_lossy())
    }
}

// ---------------------------------------------------------------------------
// NumCast
// ---------------------------------------------------------------------------
//
// `NumCast` is the generic-cast bridge in the `num-traits` ecosystem:
// any `T: ToPrimitive` can be cast to a `NumCast` type, with the
// implementation choosing which `to_X` / `from_X` pair to dispatch
// through.
//
// Dispatch strategy: prefer the `f64` path for inputs that carry
// fractional information (e.g. `1.5_f64`), and fall back to the
// lossless `i128` path for integer inputs. The decision uses a
// round-trip equality check: if `(int as f64) == n.to_f64()` the
// input is integer-shaped and the integer path is taken, preserving
// precision even for `i64`/`u64` values above f64's 53-bit mantissa.

impl<const SCALE: u32> NumCast for I128<SCALE> {
    /// Casts any `T: ToPrimitive` value to `I128<SCALE>`.
    ///
    /// Uses the `f64` conversion path for inputs that carry fractional
    /// information, and the `i128` path for integer-shaped inputs. The
    /// integer path is taken when `(to_i128() as f64) == to_f64()`, which
    /// holds for true integer types even when their magnitude exceeds f64's
    /// exact-integer range of 2^53. Returns `None` when neither path
    /// produces a representable value.
    ///
    /// # Precision
    ///
    /// Lossy: involves f32 or f64 at some point; result may lose precision.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::NumCast;
    ///
    /// let from_int: I128s12 = NumCast::from(42_i32).unwrap();
    /// assert_eq!(from_int, I128s12::from_bits(42_000_000_000_000));
    ///
    /// let from_float: I128s12 = NumCast::from(1.5_f64).unwrap();
    /// assert_eq!(from_float, I128s12::from_f64_lossy(1.5));
    ///
    /// let nan: Option<I128s12> = NumCast::from(f64::NAN);
    /// assert!(nan.is_none());
    /// ```
    #[inline]
    fn from<T: ToPrimitive>(n: T) -> Option<Self> {
        // Read f64 early so we can distinguish integer vs. fractional inputs.
        let f = n.to_f64();
        // Integer fast path: if `n` round-trips through i128 and the f64
        // value matches, take the integer path. This preserves precision for
        // i64/u64 values above f64's 2^53 exact-integer boundary.
        if let Some(int) = n.to_i128() {
            let take_int_path = match f {
                None => true,
                Some(fv) => fv.is_finite() && ((int as f64) == fv),
            };
            if take_int_path {
                return <Self as FromPrimitive>::from_i128(int);
            }
        }
        // Float path — preserves fractional information for f32/f64 inputs.
        // Returns None for NaN, infinity, or out-of-range values.
        if let Some(fv) = f {
            return <Self as FromPrimitive>::from_f64(fv);
        }
        None
    }
}

// ---------------------------------------------------------------------------
// Checked* family
// ---------------------------------------------------------------------------
//
// CheckedAdd, CheckedSub, CheckedRem, and CheckedNeg delegate directly to
// i128's checked intrinsics; no rescaling is required for those operations.
//
// CheckedMul and CheckedDiv delegate to the inherent I128::checked_mul and
// I128::checked_div methods. The trait and inherent paths are bit-identical.

impl<const SCALE: u32> CheckedAdd for I128<SCALE> {
    /// Adds `rhs` to `self`, returning `None` on overflow.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::CheckedAdd;
    ///
    /// let two = I128s12::from_bits(2_000_000_000_000);
    /// assert_eq!(I128s12::ONE.checked_add(I128s12::ONE), Some(two));
    /// assert_eq!(I128s12::MAX.checked_add(I128s12::ONE), None);
    /// ```
    #[inline]
    fn checked_add(&self, rhs: &Self) -> Option<Self> {
        self.0.checked_add(rhs.0).map(Self)
    }
}

impl<const SCALE: u32> CheckedSub for I128<SCALE> {
    /// Subtracts `rhs` from `self`, returning `None` on underflow.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::CheckedSub;
    ///
    /// let three = I128s12::from_bits(3_000_000_000_000);
    /// let two = I128s12::from_bits(2_000_000_000_000);
    /// assert_eq!(three.checked_sub(two), Some(I128s12::ONE));
    /// assert_eq!(I128s12::MIN.checked_sub(I128s12::ONE), None);
    /// ```
    #[inline]
    fn checked_sub(&self, rhs: &Self) -> Option<Self> {
        self.0.checked_sub(rhs.0).map(Self)
    }
}

impl<const SCALE: u32> CheckedMul for I128<SCALE> {
    /// Multiplies `self` by `v`, returning `None` when the result overflows `i128`.
    ///
    /// Delegates to the inherent [`I128::checked_mul`] method, which uses a
    /// 256-bit intermediate product so that only the final result needs to
    /// fit in `i128`. Returns `None` only when the quotient after rescaling
    /// overflows. The trait and inherent paths are bit-identical.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::CheckedMul;
    ///
    /// let half = I128s12::from_bits(500_000_000_000);
    /// let quarter = I128s12::from_bits(250_000_000_000);
    /// assert_eq!(half.checked_mul(half), Some(quarter));
    ///
    /// let two = I128s12::from_bits(2_000_000_000_000);
    /// assert_eq!(I128s12::MAX.checked_mul(two), None);
    /// ```
    #[inline]
    fn checked_mul(&self, v: &Self) -> Option<Self> {
        (*self).checked_mul(*v)
    }
}

impl<const SCALE: u32> CheckedDiv for I128<SCALE> {
    /// Divides `self` by `v`, returning `None` on division by zero or overflow.
    ///
    /// Delegates to the inherent [`I128::checked_div`] method, which uses a
    /// 256-bit widening divide. Returns `None` on division by zero or when the
    /// result overflows `i128` (the only case is `I128::MIN / -ONE`). The
    /// trait and inherent paths are bit-identical.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::CheckedDiv;
    ///
    /// let half = I128s12::from_bits(500_000_000_000);
    /// let two = I128s12::from_bits(2_000_000_000_000);
    /// let quarter = I128s12::from_bits(250_000_000_000);
    /// assert_eq!(half.checked_div(two), Some(quarter));
    /// assert_eq!(I128s12::ONE.checked_div(I128s12::ZERO), None);
    /// ```
    #[inline]
    fn checked_div(&self, v: &Self) -> Option<Self> {
        (*self).checked_div(*v)
    }
}

impl<const SCALE: u32> CheckedRem for I128<SCALE> {
    /// Computes `self % rhs`, returning `None` when `rhs` is zero.
    ///
    /// Because both operands share the same `SCALE`, no rescaling is needed.
    /// Delegates directly to `i128::checked_rem`.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::CheckedRem;
    ///
    /// let a = I128s12::from_bits(5_500_000_000_000); // 5.5
    /// let b = I128s12::from_bits(2_000_000_000_000); // 2.0
    /// let expected = I128s12::from_bits(1_500_000_000_000); // 1.5
    /// assert_eq!(a.checked_rem(b), Some(expected));
    /// assert_eq!(a.checked_rem(I128s12::ZERO), None);
    /// ```
    #[inline]
    fn checked_rem(&self, rhs: &Self) -> Option<Self> {
        self.0.checked_rem(rhs.0).map(Self)
    }
}

impl<const SCALE: u32> CheckedNeg for I128<SCALE> {
    /// Negates `self`, returning `None` for `I128::MIN`.
    ///
    /// `i128::MIN` has no positive counterpart in two's-complement, so
    /// negating it overflows. All other values succeed.
    ///
    /// # Precision
    ///
    /// Strict: all arithmetic is integer-only; result is bit-exact.
    ///
    /// # Examples
    ///
    /// ```
    /// use decimal_scaled::I128s12;
    /// use num_traits::CheckedNeg;
    ///
    /// assert_eq!(I128s12::ONE.checked_neg(), Some(-I128s12::ONE));
    /// assert_eq!(I128s12::ZERO.checked_neg(), Some(I128s12::ZERO));
    /// assert_eq!(I128s12::MIN.checked_neg(), None);
    /// ```
    #[inline]
    fn checked_neg(&self) -> Option<Self> {
        self.0.checked_neg().map(Self)
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::core_type::{I128, I128s12};

    // ---------------------------------------------------------------------------
    // Zero / One
    // ---------------------------------------------------------------------------

    #[test]
    fn zero_is_zero_const() {
        assert_eq!(<I128s12 as Zero>::zero(), I128s12::ZERO);
    }

    #[test]
    fn zero_is_zero_predicate() {
        assert!(<I128s12 as Zero>::is_zero(&I128s12::ZERO));
        assert!(!<I128s12 as Zero>::is_zero(&I128s12::ONE));
        assert!(!<I128s12 as Zero>::is_zero(&I128s12::from_bits(1)));
    }

    #[test]
    fn one_is_one_const() {
        assert_eq!(<I128s12 as One>::one(), I128s12::ONE);
    }

    #[test]
    fn one_is_one_predicate() {
        assert!(<I128s12 as One>::is_one(&I128s12::ONE));
        assert!(!<I128s12 as One>::is_one(&I128s12::ZERO));
        // A non-canonical raw value (1 LSB) is not "one".
        assert!(!<I128s12 as One>::is_one(&I128s12::from_bits(1)));
    }

    // ---------------------------------------------------------------------------
    // Bounded
    // ---------------------------------------------------------------------------

    #[test]
    fn bounded_min_max() {
        assert_eq!(<I128s12 as Bounded>::min_value(), I128s12::MIN);
        assert_eq!(<I128s12 as Bounded>::max_value(), I128s12::MAX);
    }

    // ---------------------------------------------------------------------------
    // Signed
    // ---------------------------------------------------------------------------

    #[test]
    fn signed_abs_basic() {
        let pos = I128s12::from_bits(1_500_000_000_000);
        let neg = I128s12::from_bits(-1_500_000_000_000);
        assert_eq!(<I128s12 as Signed>::abs(&pos), pos);
        assert_eq!(<I128s12 as Signed>::abs(&neg), pos);
        assert_eq!(<I128s12 as Signed>::abs(&I128s12::ZERO), I128s12::ZERO);
    }

    #[test]
    fn signed_signum_basic() {
        let pos = I128s12::from_bits(1_500_000_000_000);
        let neg = I128s12::from_bits(-1_500_000_000_000);
        assert_eq!(<I128s12 as Signed>::signum(&pos), I128s12::ONE);
        assert_eq!(<I128s12 as Signed>::signum(&neg), -I128s12::ONE);
        assert_eq!(<I128s12 as Signed>::signum(&I128s12::ZERO), I128s12::ZERO);
    }

    #[test]
    fn signed_is_positive_negative() {
        let pos = I128s12::from_bits(1_500_000_000_000);
        let neg = I128s12::from_bits(-1_500_000_000_000);
        assert!(<I128s12 as Signed>::is_positive(&pos));
        assert!(!<I128s12 as Signed>::is_positive(&neg));
        assert!(!<I128s12 as Signed>::is_positive(&I128s12::ZERO));

        assert!(!<I128s12 as Signed>::is_negative(&pos));
        assert!(<I128s12 as Signed>::is_negative(&neg));
        assert!(!<I128s12 as Signed>::is_negative(&I128s12::ZERO));
    }

    /// `abs_sub(a, b)` clamps to zero when `a <= b`.
    #[test]
    fn signed_abs_sub_clamps_to_zero() {
        let two = I128s12::from_bits(2_000_000_000_000);
        let five = I128s12::from_bits(5_000_000_000_000);

        // 5 - 2 = 3 (positive case)
        let three = I128s12::from_bits(3_000_000_000_000);
        assert_eq!(<I128s12 as Signed>::abs_sub(&five, &two), three);

        // 2 - 5 clamps to ZERO (a <= b)
        assert_eq!(<I128s12 as Signed>::abs_sub(&two, &five), I128s12::ZERO);

        // 5 - 5 = ZERO (equal inputs)
        assert_eq!(<I128s12 as Signed>::abs_sub(&five, &five), I128s12::ZERO);
    }

    // ---------------------------------------------------------------------------
    // FromPrimitive
    // ---------------------------------------------------------------------------

    #[test]
    fn from_primitive_i64_in_range() {
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i64(0),
            Some(I128s12::ZERO)
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i64(1),
            Some(I128s12::ONE)
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i64(42),
            Some(I128s12::from_bits(42_000_000_000_000))
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i64(-42),
            Some(I128s12::from_bits(-42_000_000_000_000))
        );
    }

    #[test]
    fn from_primitive_u64_in_range() {
        assert_eq!(
            <I128s12 as FromPrimitive>::from_u64(0),
            Some(I128s12::ZERO)
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_u64(42),
            Some(I128s12::from_bits(42_000_000_000_000))
        );
        // u64::MAX * 10^12 fits in i128, so this succeeds.
        let large = <I128s12 as FromPrimitive>::from_u64(u64::MAX);
        assert!(large.is_some());
    }

    #[test]
    fn from_primitive_i128_overflow_returns_none() {
        // i128::MAX cannot be scaled by 10^12 — TryFrom returns Err,
        // FromPrimitive surfaces that as None.
        assert_eq!(<I128s12 as FromPrimitive>::from_i128(i128::MAX), None);
        assert_eq!(<I128s12 as FromPrimitive>::from_i128(i128::MIN), None);

        // Small values succeed.
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i128(7),
            Some(I128s12::from_bits(7_000_000_000_000))
        );
    }

    #[test]
    fn from_primitive_u128_overflow_returns_none() {
        // u128::MAX > i128::MAX — the first try_from step fails.
        assert_eq!(<I128s12 as FromPrimitive>::from_u128(u128::MAX), None);

        // Small values succeed.
        assert_eq!(
            <I128s12 as FromPrimitive>::from_u128(99),
            Some(I128s12::from_bits(99_000_000_000_000))
        );
    }

    #[test]
    fn from_primitive_f32_basic() {
        assert_eq!(
            <I128s12 as FromPrimitive>::from_f32(0.0),
            Some(I128s12::ZERO)
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_f32(1.0),
            Some(I128s12::ONE)
        );
        // Non-finite inputs return None.
        assert_eq!(<I128s12 as FromPrimitive>::from_f32(f32::NAN), None);
        assert_eq!(<I128s12 as FromPrimitive>::from_f32(f32::INFINITY), None);
        assert_eq!(<I128s12 as FromPrimitive>::from_f32(f32::NEG_INFINITY), None);
    }

    #[test]
    fn from_primitive_f64_basic() {
        assert_eq!(
            <I128s12 as FromPrimitive>::from_f64(0.0),
            Some(I128s12::ZERO)
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_f64(1.0),
            Some(I128s12::ONE)
        );
        // Use a value that is not close to any well-known math constant
        // so the approx_constant lint stays quiet.
        let v = <I128s12 as FromPrimitive>::from_f64(1.234567890123_f64);
        assert!(v.is_some());

        // Non-finite inputs return None.
        assert_eq!(<I128s12 as FromPrimitive>::from_f64(f64::NAN), None);
        assert_eq!(<I128s12 as FromPrimitive>::from_f64(f64::INFINITY), None);

        // Finite but out-of-range: 1e30 * 10^12 = 1e42 > i128::MAX.
        assert_eq!(<I128s12 as FromPrimitive>::from_f64(1e30), None);
    }

    /// `FromPrimitive` provides default impls for `from_i32`, `from_u32`, etc.
    /// via `from_i64` / `from_u64`. Verify the delegation chain works.
    #[test]
    fn from_primitive_smaller_int_types_via_default_impl() {
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i32(7),
            Some(I128s12::from_bits(7_000_000_000_000))
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i16(-3),
            Some(I128s12::from_bits(-3_000_000_000_000))
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_i8(0),
            Some(I128s12::ZERO)
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_u32(7),
            Some(I128s12::from_bits(7_000_000_000_000))
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_u16(3),
            Some(I128s12::from_bits(3_000_000_000_000))
        );
        assert_eq!(
            <I128s12 as FromPrimitive>::from_u8(255),
            Some(I128s12::from_bits(255_000_000_000_000))
        );
    }

    // ---------------------------------------------------------------------------
    // ToPrimitive
    // ---------------------------------------------------------------------------

    #[test]
    fn to_primitive_i64_in_range() {
        let v = I128s12::from_bits(42_000_000_000_000);
        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&v), Some(42_i64));

        let neg = I128s12::from_bits(-42_000_000_000_000);
        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&neg), Some(-42_i64));

        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&I128s12::ZERO), Some(0_i64));
    }

    #[test]
    fn to_primitive_i64_truncates_toward_zero() {
        // 2.5 truncates to 2
        let v = I128s12::from_bits(2_500_000_000_000);
        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&v), Some(2_i64));

        // -2.5 truncates to -2 (toward zero, not toward -inf)
        let neg = I128s12::from_bits(-2_500_000_000_000);
        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&neg), Some(-2_i64));
    }

    #[test]
    fn to_primitive_i64_out_of_range_returns_none() {
        // I128::MAX integer part ~= 1.7e26, which exceeds i64::MAX.
        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&I128s12::MAX), None);
        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&I128s12::MIN), None);
    }

    #[test]
    fn to_primitive_u64_negative_returns_none() {
        let neg = I128s12::from_bits(-1_000_000_000_000);
        assert_eq!(<I128s12 as ToPrimitive>::to_u64(&neg), None);
    }

    #[test]
    fn to_primitive_u64_in_range() {
        let v = I128s12::from_bits(42_000_000_000_000);
        assert_eq!(<I128s12 as ToPrimitive>::to_u64(&v), Some(42_u64));

        assert_eq!(<I128s12 as ToPrimitive>::to_u64(&I128s12::ZERO), Some(0_u64));
    }

    #[test]
    fn to_primitive_i128_always_succeeds() {
        // Even MAX and MIN succeed because the integer part is bounded
        // by i128::MAX / 10^12, which is well within i128.
        assert!(<I128s12 as ToPrimitive>::to_i128(&I128s12::MAX).is_some());
        assert!(<I128s12 as ToPrimitive>::to_i128(&I128s12::MIN).is_some());
        assert_eq!(
            <I128s12 as ToPrimitive>::to_i128(&I128s12::ZERO),
            Some(0_i128)
        );
        assert_eq!(
            <I128s12 as ToPrimitive>::to_i128(&I128s12::from_bits(42_000_000_000_000)),
            Some(42_i128)
        );
    }

    #[test]
    fn to_primitive_u128_negative_returns_none() {
        assert_eq!(
            <I128s12 as ToPrimitive>::to_u128(&I128s12::from_bits(-1)),
            None
        );
    }

    #[test]
    fn to_primitive_u128_in_range() {
        assert_eq!(
            <I128s12 as ToPrimitive>::to_u128(&I128s12::ZERO),
            Some(0_u128)
        );
        assert_eq!(
            <I128s12 as ToPrimitive>::to_u128(&I128s12::from_bits(99_000_000_000_000)),
            Some(99_u128)
        );
    }

    #[test]
    fn to_primitive_f64_round_trip_within_lsb() {
        let lsb = 1.0 / (I128s12::multiplier() as f64);
        // Use a value not close to any well-known math constant.
        let v = I128s12::from_f64_lossy(1.234567890123_f64);
        let back = <I128s12 as ToPrimitive>::to_f64(&v).expect("to_f64 always returns Some");
        assert!(
            (back - 1.234567890123_f64).abs() <= lsb * 2.0,
            "round-trip exceeded 2 LSB: back = {back}, lsb = {lsb}"
        );
    }

    #[test]
    fn to_primitive_f32_matches_to_f32_lossy() {
        let v = I128s12::from_bits(1_500_000_000_000);
        assert_eq!(
            <I128s12 as ToPrimitive>::to_f32(&v),
            Some(v.to_f32_lossy())
        );
    }

    /// `ToPrimitive` provides default impls for `to_i32`, `to_u32`, etc.
    /// via `to_i64` / `to_u64`. Verify the delegation chain works.
    #[test]
    fn to_primitive_smaller_int_types_via_default_impl() {
        let v = I128s12::from_bits(42_000_000_000_000);
        assert_eq!(<I128s12 as ToPrimitive>::to_i32(&v), Some(42_i32));
        assert_eq!(<I128s12 as ToPrimitive>::to_u32(&v), Some(42_u32));
        assert_eq!(<I128s12 as ToPrimitive>::to_i16(&v), Some(42_i16));
        assert_eq!(<I128s12 as ToPrimitive>::to_u16(&v), Some(42_u16));
        assert_eq!(<I128s12 as ToPrimitive>::to_i8(&v), Some(42_i8));
        assert_eq!(<I128s12 as ToPrimitive>::to_u8(&v), Some(42_u8));

        // Out-of-range narrowing returns None.
        let big = I128s12::from_bits(40_000_000_000_000_000); // 40_000
        assert_eq!(<I128s12 as ToPrimitive>::to_i8(&big), None);
        assert_eq!(<I128s12 as ToPrimitive>::to_u8(&big), None);
    }

    // ---------------------------------------------------------------------------
    // CheckedAdd / CheckedSub
    // ---------------------------------------------------------------------------

    #[test]
    fn checked_add_basic() {
        let one = I128s12::ONE;
        let two = I128s12::from_bits(2_000_000_000_000);
        assert_eq!(
            <I128s12 as CheckedAdd>::checked_add(&one, &one),
            Some(two)
        );
    }

    #[test]
    fn checked_add_overflow_returns_none() {
        // MAX + ONE overflows.
        assert_eq!(
            <I128s12 as CheckedAdd>::checked_add(&I128s12::MAX, &I128s12::ONE),
            None
        );
        // MAX + ZERO is fine.
        assert_eq!(
            <I128s12 as CheckedAdd>::checked_add(&I128s12::MAX, &I128s12::ZERO),
            Some(I128s12::MAX)
        );
    }

    #[test]
    fn checked_sub_basic() {
        let three = I128s12::from_bits(3_000_000_000_000);
        let two = I128s12::from_bits(2_000_000_000_000);
        assert_eq!(
            <I128s12 as CheckedSub>::checked_sub(&three, &two),
            Some(I128s12::ONE)
        );
    }

    #[test]
    fn checked_sub_underflow_returns_none() {
        // MIN - ONE underflows.
        assert_eq!(
            <I128s12 as CheckedSub>::checked_sub(&I128s12::MIN, &I128s12::ONE),
            None
        );
    }

    // ---------------------------------------------------------------------------
    // CheckedMul / CheckedDiv / CheckedRem
    // ---------------------------------------------------------------------------

    #[test]
    fn checked_mul_basic() {
        let half = I128s12::from_bits(500_000_000_000); // 0.5
        let quarter = I128s12::from_bits(250_000_000_000); // 0.25
        assert_eq!(
            <I128s12 as CheckedMul>::checked_mul(&half, &half),
            Some(quarter)
        );
    }

    #[test]
    fn checked_mul_overflow_returns_none() {
        // MAX * 2 overflows.
        let two = I128s12::from_bits(2_000_000_000_000);
        assert_eq!(
            <I128s12 as CheckedMul>::checked_mul(&I128s12::MAX, &two),
            None
        );
    }

    #[test]
    fn checked_div_basic() {
        let half = I128s12::from_bits(500_000_000_000); // 0.5
        let quarter = I128s12::from_bits(250_000_000_000); // 0.25
        let two = I128s12::from_bits(2_000_000_000_000); // 2.0
        // 0.5 / 2.0 == 0.25
        assert_eq!(
            <I128s12 as CheckedDiv>::checked_div(&half, &two),
            Some(quarter)
        );
    }

    #[test]
    fn checked_div_by_zero_returns_none() {
        assert_eq!(
            <I128s12 as CheckedDiv>::checked_div(&I128s12::ONE, &I128s12::ZERO),
            None
        );
    }

    #[test]
    fn checked_div_overflow_returns_none() {
        // The only true checked_div overflow is MIN / -ONE (negating i128::MIN
        // overflows in two's-complement).
        let neg_one = -I128s12::ONE;
        assert_eq!(
            <I128s12 as CheckedDiv>::checked_div(&I128s12::MIN, &neg_one),
            None
        );
        // MAX / ONE returns Some(MAX) via the widening path.
        assert_eq!(
            <I128s12 as CheckedDiv>::checked_div(&I128s12::MAX, &I128s12::ONE),
            Some(I128s12::MAX)
        );
    }

    #[test]
    fn checked_rem_basic() {
        let a = I128s12::from_bits(5_500_000_000_000); // 5.5
        let b = I128s12::from_bits(2_000_000_000_000); // 2.0
        let expected = I128s12::from_bits(1_500_000_000_000); // 1.5
        assert_eq!(
            <I128s12 as CheckedRem>::checked_rem(&a, &b),
            Some(expected)
        );
    }

    #[test]
    fn checked_rem_by_zero_returns_none() {
        assert_eq!(
            <I128s12 as CheckedRem>::checked_rem(&I128s12::ONE, &I128s12::ZERO),
            None
        );
    }

    // ---------------------------------------------------------------------------
    // CheckedNeg
    // ---------------------------------------------------------------------------

    #[test]
    fn checked_neg_basic() {
        let one = I128s12::ONE;
        let neg_one = -I128s12::ONE;
        assert_eq!(
            <I128s12 as CheckedNeg>::checked_neg(&one),
            Some(neg_one)
        );
        assert_eq!(
            <I128s12 as CheckedNeg>::checked_neg(&I128s12::ZERO),
            Some(I128s12::ZERO)
        );
    }

    #[test]
    fn checked_neg_min_returns_none() {
        // i128::MIN has no positive counterpart, so checked_neg returns None.
        assert_eq!(
            <I128s12 as CheckedNeg>::checked_neg(&I128s12::MIN),
            None
        );
    }

    // ---------------------------------------------------------------------------
    // CheckedMul / CheckedDiv trait-vs-inherent alignment
    // ---------------------------------------------------------------------------
    //
    // Assert that the num-traits trait impls and the inherent methods
    // produce bit-identical results for 256 deterministic pairs plus
    // boundary cases. A failure here means the two paths diverged.

    /// Generates a deterministic sequence of `i128` values using a
    /// linear congruential generator seeded from `seed`.
    fn lcg_i128_seq(seed: i128, n: usize) -> Vec<i128> {
        // LCG constants from Knuth TAOCP Vol 2 (applied in i128 with wrapping).
        let mut state: i128 = seed;
        let mut out = Vec::with_capacity(n);
        for _ in 0..n {
            state = state
                .wrapping_mul(6_364_136_223_846_793_005_i128)
                .wrapping_add(1_442_695_040_888_963_407_i128);
            out.push(state);
        }
        out
    }

    /// For 256 deterministic pairs, `<I128 as CheckedMul>::checked_mul`
    /// must equal `I128::checked_mul` (the inherent method).
    #[test]
    fn checked_mul_trait_matches_inherent_256_pairs() {
        let seeds = lcg_i128_seq(0x1234_5678_9ABC_DEF0, 512);
        for pair in seeds.chunks_exact(2) {
            let a = I128s12::from_bits(pair[0]);
            let b = I128s12::from_bits(pair[1]);
            let trait_result = <I128s12 as CheckedMul>::checked_mul(&a, &b);
            let inherent_result = a.checked_mul(b);
            assert_eq!(
                trait_result, inherent_result,
                "CheckedMul trait != inherent for a={a:?} b={b:?}"
            );
        }
    }

    /// For 256 deterministic pairs, `<I128 as CheckedDiv>::checked_div`
    /// must equal `I128::checked_div` (the inherent method).
    #[test]
    fn checked_div_trait_matches_inherent_256_pairs() {
        let seeds = lcg_i128_seq(0xDEAD_BEEF_CAFE_0001, 512);
        for pair in seeds.chunks_exact(2) {
            let a = I128s12::from_bits(pair[0]);
            // Avoid divide-by-zero: if the LCG lands on zero, substitute ONE.
            // The by-zero case is covered by a dedicated test.
            let b_bits = if pair[1] == 0 { I128s12::multiplier() } else { pair[1] };
            let b = I128s12::from_bits(b_bits);
            let trait_result = <I128s12 as CheckedDiv>::checked_div(&a, &b);
            let inherent_result = a.checked_div(b);
            assert_eq!(
                trait_result, inherent_result,
                "CheckedDiv trait != inherent for a={a:?} b={b:?}"
            );
        }
    }

    /// Boundary cases for CheckedMul trait-vs-inherent alignment.
    #[test]
    fn checked_mul_trait_matches_inherent_boundary() {
        let cases: &[(I128s12, I128s12)] = &[
            (I128s12::MAX, I128s12::ZERO),
            (I128s12::MIN, I128s12::ZERO),
            (I128s12::MAX, I128s12::ONE),
            (I128s12::MIN, I128s12::ONE),
            (I128s12::MAX, I128s12::MAX),
            (I128s12::MIN, I128s12::MIN),
            (I128s12::from_bits(0), I128s12::from_bits(0)),
            (I128s12::from_bits(1), I128s12::from_bits(1)),
            (I128s12::from_bits(-1), I128s12::from_bits(1)),
            (I128s12::from_bits(1), I128s12::from_bits(-1)),
            (I128s12::from_bits(-1), I128s12::from_bits(-1)),
        ];
        for &(a, b) in cases {
            let trait_result = <I128s12 as CheckedMul>::checked_mul(&a, &b);
            let inherent_result = a.checked_mul(b);
            assert_eq!(
                trait_result, inherent_result,
                "CheckedMul trait != inherent at boundary a={a:?} b={b:?}"
            );
        }
    }

    /// Boundary cases for CheckedDiv trait-vs-inherent alignment.
    #[test]
    fn checked_div_trait_matches_inherent_boundary() {
        let neg_one = -I128s12::ONE;
        let cases: &[(I128s12, I128s12)] = &[
            (I128s12::MAX, I128s12::ONE),
            (I128s12::MIN, I128s12::ONE),
            (I128s12::MAX, I128s12::MAX),
            (I128s12::MIN, I128s12::MIN),
            (I128s12::ZERO, I128s12::ONE),
            (I128s12::ONE, I128s12::MAX),
            // divide by zero — both must return None
            (I128s12::ONE, I128s12::ZERO),
            (I128s12::MAX, I128s12::ZERO),
            // true overflow case: MIN / -ONE
            (I128s12::MIN, neg_one),
            (I128s12::from_bits(1), I128s12::from_bits(1)),
            (I128s12::from_bits(-1), I128s12::from_bits(1)),
            (I128s12::from_bits(1), I128s12::from_bits(-1)),
            (I128s12::from_bits(-1), I128s12::from_bits(-1)),
        ];
        for &(a, b) in cases {
            let trait_result = <I128s12 as CheckedDiv>::checked_div(&a, &b);
            let inherent_result = a.checked_div(b);
            assert_eq!(
                trait_result, inherent_result,
                "CheckedDiv trait != inherent at boundary a={a:?} b={b:?}"
            );
        }
    }

    // ---------------------------------------------------------------------------
    // Num::from_str_radix
    // ---------------------------------------------------------------------------

    /// Non-base-10 radix is rejected without delegating to FromStr.
    #[test]
    fn from_str_radix_non_ten_returns_invalid() {
        let result = <I128s12 as Num>::from_str_radix("1", 16);
        assert!(result.is_err());

        let result_2 = <I128s12 as Num>::from_str_radix("1", 2);
        assert!(result_2.is_err());
    }

    /// Base-10 delegates to the FromStr implementation.
    #[test]
    fn from_str_radix_base_ten_delegates_to_from_str() {
        let parsed = <I128s12 as Num>::from_str_radix("1", 10).expect("parse 1");
        assert_eq!(parsed, I128s12::ONE);
    }

    // ---------------------------------------------------------------------------
    // Cross-scale exercise — non-default SCALE
    // ---------------------------------------------------------------------------

    /// At SCALE = 6 the trait surface works correctly.
    #[test]
    fn traits_compile_at_scale_6() {
        type D6 = I128<6>;
        assert_eq!(<D6 as Zero>::zero(), D6::ZERO);
        assert_eq!(<D6 as One>::one(), D6::ONE);
        assert_eq!(<D6 as Bounded>::min_value(), D6::MIN);
        assert_eq!(<D6 as Bounded>::max_value(), D6::MAX);

        let v: D6 = <D6 as FromPrimitive>::from_i64(42).unwrap();
        assert_eq!(<D6 as ToPrimitive>::to_i64(&v), Some(42_i64));
    }

    // ---------------------------------------------------------------------------
    // NumCast
    // ---------------------------------------------------------------------------

    /// `NumCast::from` round-trips an in-range `i32` exactly.
    #[test]
    fn numcast_from_i32() {
        let v: I128s12 = <I128s12 as NumCast>::from(42_i32).expect("in-range");
        assert_eq!(v, <I128s12 as From<i32>>::from(42_i32));
    }

    /// `NumCast::from` preserves the fractional part of an `f64` input
    /// because the float path runs before the integer truncation path.
    #[test]
    fn numcast_from_f64_preserves_fractional() {
        let v: I128s12 = <I128s12 as NumCast>::from(1.5_f64).expect("in-range");
        assert_eq!(v, I128s12::from_f64_lossy(1.5_f64));
    }

    /// `NumCast::from` returns `None` for `f64::NAN`.
    #[test]
    fn numcast_from_f64_nan_returns_none() {
        assert!(<I128s12 as NumCast>::from(f64::NAN).is_none());
    }

    /// `NumCast::from` returns `None` for finite out-of-range `f64`.
    #[test]
    fn numcast_from_f64_out_of_range_returns_none() {
        assert!(<I128s12 as NumCast>::from(1e30_f64).is_none());
    }

    /// `NumCast::from` keeps integer inputs exact for `i64` values above
    /// f64's 53-bit mantissa range, validating the integer fast path.
    #[test]
    fn numcast_from_i64_above_f64_mantissa_is_exact() {
        // 2^54 = 18_014_398_509_481_984 — above f64's exact-integer range.
        let v: i64 = 1_i64 << 54;
        let d: I128s12 = <I128s12 as NumCast>::from(v).expect("in-range");
        assert_eq!(<I128s12 as ToPrimitive>::to_i64(&d), Some(v));
    }
}