qtty_core/units/angular/

mod.rs

// SPDX-License-Identifier: BSD-3-Clause
// Copyright (C) 2026 Vallés Puig, Ramon

//! Angular quantities and utilities.
//!
//! This module defines the **`Angular` dimension**, a blanket [`AngularUnit`] trait that extends
//! [`Unit`] for all angular units, common angular units (degrees, radians, arcseconds, etc.), and a set of
//! convenience methods on [`Quantity<U>`] where `U: AngularUnit`.
//!
//! # Design overview
//!
//! * **Canonical unit:** Degrees are taken as the canonical *scaling* unit for this dimension. That is,
//!   `Degree::RATIO == 1.0`, and all other angular units express how many *degrees* correspond to one of that unit.
//!   For example, `Radian::RATIO == 180.0 / PI` because 1 radian = 180/π degrees.
//! * **Associated constants:** The `AngularUnit` trait exposes precomputed constants (`FULL_TURN`, `HALF_TURN`,
//!   `QUARTER_TURN`) expressed *in the receiving unit* for ergonomic range‑wrapping. These are derived from `τ`
//!   radians and then converted to the target unit to avoid cumulative error from chained conversions.
//! * **Trigonometry:** `sin`, `cos`, `tan`, and `sin_cos` methods are provided on angular quantities; they convert to
//!   radians internally and then call the corresponding `f64` intrinsic.
//! * **Wrapping helpers:** Utility methods to wrap any angle into common ranges — `[0, 360)` (or unit equivalent),
//!   `(-180, 180]`, and the latitude‑style quarter fold `[-90, 90]`.
//!
//! ## Edge cases
//!
//! Wrapping and trig operations follow IEEE‑754 semantics from `f64`: if the underlying numeric is `NaN` or
//! `±∞`, results will generally be `NaN`.
//!
//! ## Unit symbols
//!
//! Unit `SYMBOL`s are used for display (e.g., `format!("{}", angle)`) and follow conventional unit symbols.
//! Unicode symbols are used where standard notation requires them (e.g., `°`, `′`, `″`, `μas`).
//!
//! ## Examples
//!
//! Convert between degrees and radians and evaluate a trig function:
//!
//! ```rust
//! use qtty_core::angular::{Degrees, Radians};
//!
//! let angle: Degrees = Degrees::new(90.0);
//! let r: Radians = angle.to();
//! assert!((r.value() - core::f64::consts::FRAC_PI_2).abs() < 1e-12);
//! assert!((angle.sin() - 1.0).abs() < 1e-12);
//! ```
//!
//! Wrap into the conventional signed range:
//!
//! ```rust
//! use qtty_core::angular::Degrees;
//! let a = Degrees::new(370.0).wrap_signed();
//! assert_eq!(a.value(), 10.0);
//! ```

use crate::scalar::Transcendental;
use crate::{Quantity, Unit};
use core::f64::consts::TAU;
use qtty_derive::Unit;

#[inline]
fn rem_euclid(x: f64, modulus: f64) -> f64 {
    #[cfg(feature = "std")]
    {
        x.rem_euclid(modulus)
    }
    #[cfg(not(feature = "std"))]
    {
        let r = crate::libm::fmod(x, modulus);
        if r < 0.0 {
            r + modulus
        } else {
            r
        }
    }
}

/// Re-export from the dimension module.
pub use crate::dimension::Angular;

/// Blanket extension trait for any [`Unit`] whose dimension is [`Angular`].
///
/// These associated constants provide the size of key turn fractions *expressed in the implementing unit*.
/// They are computed via a compile-time conversion from `TAU` radians (i.e., a full revolution) and then scaled.
/// This keeps all fractions derived from the same base value.
///
pub trait AngularUnit: Unit<Dim = Angular> {
    /// One full revolution (τ radians / 360°) expressed in this unit.
    const FULL_TURN: f64;
    /// Half a revolution (π radians / 180°) expressed in this unit.
    const HALF_TURN: f64;
    /// A quarter revolution (π/2 radians / 90°) expressed in this unit.
    const QUARTER_TURN: f64;
}
impl<T: Unit<Dim = Angular>> AngularUnit for T {
    /// One full revolution (360°) expressed in T unit.
    const FULL_TURN: f64 = Radians::new(TAU).to_const::<T>().value();
    /// Half a revolution (180°) expressed in T unit.
    const HALF_TURN: f64 = Radians::new(TAU).to_const::<T>().value() * 0.5;
    /// Quarter revolution (90°) expressed in T unit.
    const QUARTER_TURN: f64 = Radians::new(TAU).to_const::<T>().value() * 0.25;
}

#[cfg(feature = "astro")]
mod astro;
#[cfg(feature = "astro")]
pub use astro::*;
#[cfg(feature = "navigation")]
mod navigation;
#[cfg(feature = "navigation")]
pub use navigation::*;

impl<U: AngularUnit + Copy> Quantity<U> {
    /// Constant representing τ radians (2π rad == 360°).
    ///
    /// For angular quantities, `TAU` and [`Self::FULL_TURN`] are identical by construction.
    pub const TAU: Quantity<U> = Quantity::<U>::new(U::FULL_TURN);
    /// One full revolution (360°) expressed as `Quantity<U>`.
    pub const FULL_TURN: Quantity<U> = Quantity::<U>::new(U::FULL_TURN);
    /// Half a revolution (180°) expressed as `Quantity<U>`.
    pub const HALF_TURN: Quantity<U> = Quantity::<U>::new(U::HALF_TURN);
    /// Quarter revolution (90°) expressed as `Quantity<U>`.
    pub const QUARTER_TURN: Quantity<U> = Quantity::<U>::new(U::QUARTER_TURN);

    /// Sign of the *raw numeric* in this unit (same semantics as `f64::signum()`).
    #[inline]
    pub const fn signum_const(self) -> f64 {
        self.value().signum()
    }

    /// Normalize into the canonical positive range `[0, FULL_TURN)`.
    ///
    /// Shorthand for [`Self::wrap_pos`].
    #[inline]
    pub fn normalize(self) -> Self {
        self.wrap_pos()
    }

    /// Wrap into the positive range `[0, FULL_TURN)` using Euclidean remainder.
    ///
    /// IEEE‑754 note: `NaN`/`±∞` inputs generally produce `NaN`.
    #[inline]
    pub fn wrap_pos(self) -> Self {
        Self::new(rem_euclid(self.value(), U::FULL_TURN))
    }

    /// Wrap into the signed range `(-HALF_TURN, HALF_TURN]`.
    ///
    /// *Upper bound is inclusive*; lower bound is exclusive. Useful for computing minimal signed angular differences.
    ///
    /// IEEE‑754 note: `NaN`/`±∞` inputs generally produce `NaN`.
    #[inline]
    pub fn wrap_signed(self) -> Self {
        let full = U::FULL_TURN;
        let half = 0.5 * full;
        let x = self.value();
        let y = rem_euclid(x + half, full) - half;
        let norm = if y <= -half { y + full } else { y };
        Self::new(norm)
    }

    /// Wrap into the alternate signed range `[-HALF_TURN, HALF_TURN)`.
    ///
    /// Lower bound inclusive; upper bound exclusive. Equivalent to `self.wrap_signed()` with the boundary flipped.
    ///
    /// IEEE‑754 note: `NaN`/`±∞` inputs generally produce `NaN`.
    #[inline]
    pub fn wrap_signed_lo(self) -> Self {
        let mut y = self.wrap_signed().value(); // now in (-half, half]
        let half = 0.5 * U::FULL_TURN;
        if y >= half {
            // move +half to -half
            y -= U::FULL_TURN;
        }
        Self::new(y)
    }

    /// "Latitude fold": map into `[-QUARTER_TURN, +QUARTER_TURN]`.
    ///
    /// Useful for folding polar coordinates (e.g., converting declination‑like angles to a limited range).
    ///
    /// IEEE‑754 note: `NaN`/`±∞` inputs generally produce `NaN`.
    #[inline]
    pub fn wrap_quarter_fold(self) -> Self {
        let full = U::FULL_TURN;
        let half = 0.5 * full;
        let quarter = 0.25 * full;
        let y = rem_euclid(self.value() + quarter, full);
        // quarter - |y - half| yields [-quarter, quarter]
        Self::new(quarter - (y - half).abs())
    }

    /// Signed smallest angular separation in `(-HALF_TURN, HALF_TURN]`.
    #[inline]
    pub fn signed_separation(self, other: Self) -> Self {
        (self - other).wrap_signed()
    }

    /// Absolute smallest angular separation (magnitude only).
    #[inline]
    pub fn abs_separation(self, other: Self) -> Self {
        let sep = self.signed_separation(other);
        Self::new(sep.value().abs())
    }

    /// Normalize into the signed half-open interval `(-HALF_TURN, +HALF_TURN]`.
    ///
    /// For radians this is `(-π, π]`; for degrees this is `(-180°, 180°]`. This is the conventional
    /// "shortest signed difference" range. It is an alias for [`Self::wrap_signed`] provided to
    /// match the naming used by downstream callers (e.g. NSB).
    ///
    /// IEEE‑754 note: `NaN`/`±∞` inputs generally produce `NaN`.
    ///
    /// # Examples
    ///
    /// In‑range value:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::FRAC_PI_2;
    /// assert!((Radians::new(FRAC_PI_2).wrap_to_signed_pi().value() - FRAC_PI_2).abs() < 1e-12);
    /// ```
    ///
    /// Slightly out of range (just past π):
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// let v = Radians::new(PI + 0.1).wrap_to_signed_pi().value();
    /// assert!((v - (-PI + 0.1)).abs() < 1e-12);
    /// ```
    ///
    /// Far out of range (7π wraps to π):
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// let v = Radians::new(7.0 * PI).wrap_to_signed_pi().value();
    /// assert!((v - PI).abs() < 1e-12);
    /// ```
    ///
    /// Boundary at +π is inclusive:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// assert!((Radians::new(PI).wrap_to_signed_pi().value() - PI).abs() < 1e-12);
    /// ```
    ///
    /// Negative values:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// let v = Radians::new(-3.0 * PI / 2.0).wrap_to_signed_pi().value();
    /// assert!((v - PI / 2.0).abs() < 1e-12);
    /// ```
    ///
    /// `NaN` propagates:
    /// ```
    /// use qtty_core::angular::Radians;
    /// assert!(Radians::new(f64::NAN).wrap_to_signed_pi().value().is_nan());
    /// ```
    #[inline]
    pub fn wrap_to_signed_pi(self) -> Self {
        self.wrap_signed()
    }

    /// Normalize into the unsigned range `[0, FULL_TURN)`.
    ///
    /// For radians this is `[0, 2π)`; for degrees this is `[0°, 360°)`. Alias for
    /// [`Self::wrap_pos`] provided to match the naming used by downstream callers (e.g. NSB).
    ///
    /// IEEE‑754 note: `NaN`/`±∞` inputs generally produce `NaN`.
    ///
    /// # Examples
    ///
    /// In‑range value passes through:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::FRAC_PI_2;
    /// assert!((Radians::new(FRAC_PI_2).wrap_to_unsigned_pi().value() - FRAC_PI_2).abs() < 1e-12);
    /// ```
    ///
    /// Slightly out of range:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::TAU;
    /// let v = Radians::new(TAU + 0.5).wrap_to_unsigned_pi().value();
    /// assert!((v - 0.5).abs() < 1e-12);
    /// ```
    ///
    /// Far out of range (7π → π):
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// let v = Radians::new(7.0 * PI).wrap_to_unsigned_pi().value();
    /// assert!((v - PI).abs() < 1e-12);
    /// ```
    ///
    /// Boundary 2π folds back to 0:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::TAU;
    /// assert!(Radians::new(TAU).wrap_to_unsigned_pi().value().abs() < 1e-12);
    /// ```
    ///
    /// Negative values are folded into the positive range:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::{PI, TAU};
    /// let v = Radians::new(-PI / 2.0).wrap_to_unsigned_pi().value();
    /// assert!((v - (TAU - PI / 2.0)).abs() < 1e-12);
    /// ```
    ///
    /// `NaN` propagates:
    /// ```
    /// use qtty_core::angular::Radians;
    /// assert!(Radians::new(f64::NAN).wrap_to_unsigned_pi().value().is_nan());
    /// ```
    #[inline]
    pub fn wrap_to_unsigned_pi(self) -> Self {
        self.wrap_pos()
    }

    /// Fold into the closed interval `[0, HALF_TURN]`.
    ///
    /// For radians this is `[0, π]`; for degrees this is `[0°, 180°]`. This is the magnitude of
    /// the shortest signed angular distance from the origin and matches the semantics used by
    /// callers such as NSB when reducing ecliptic longitude separations.
    ///
    /// Implementation: takes the absolute value of [`Self::wrap_signed`], so the result is in
    /// `[0, HALF_TURN]` (the upper bound is reachable when the input maps to exactly `+HALF_TURN`).
    ///
    /// IEEE‑754 note: `NaN`/`±∞` inputs generally produce `NaN`.
    ///
    /// # Examples
    ///
    /// In‑range value:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::FRAC_PI_3;
    /// assert!((Radians::new(FRAC_PI_3).fold_to_pi().value() - FRAC_PI_3).abs() < 1e-12);
    /// ```
    ///
    /// Slightly out of range (just past π folds back symmetrically):
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// let v = Radians::new(PI + 0.1).fold_to_pi().value();
    /// assert!((v - (PI - 0.1)).abs() < 1e-12);
    /// ```
    ///
    /// Far out of range (7π folds to π):
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// let v = Radians::new(7.0 * PI).fold_to_pi().value();
    /// assert!((v - PI).abs() < 1e-12);
    /// ```
    ///
    /// Boundary at π is reachable:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// assert!((Radians::new(PI).fold_to_pi().value() - PI).abs() < 1e-12);
    /// ```
    ///
    /// Negative values are folded:
    /// ```
    /// use qtty_core::angular::Radians;
    /// use core::f64::consts::PI;
    /// let v = Radians::new(-PI / 4.0).fold_to_pi().value();
    /// assert!((v - PI / 4.0).abs() < 1e-12);
    /// ```
    ///
    /// `NaN` propagates:
    /// ```
    /// use qtty_core::angular::Radians;
    /// assert!(Radians::new(f64::NAN).fold_to_pi().value().is_nan());
    /// ```
    #[inline]
    pub fn fold_to_pi(self) -> Self {
        Self::new(self.wrap_signed().value().abs())
    }
}

// ─────────────────────────────────────────────────────────────────────────────
// Generic trigonometric implementations for any Transcendental scalar type
// ─────────────────────────────────────────────────────────────────────────────

impl<U: AngularUnit + Copy, S: Transcendental> Quantity<U, S> {
    /// Sine of the angle.
    ///
    /// Converts the angle to radians and computes the sine.
    /// Works with any scalar type that implements [`Transcendental`] (e.g., `f32`, `f64`).
    #[inline]
    pub fn sin(self) -> S {
        let x_rad = self.to::<Radian>().value();
        x_rad.sin()
    }

    /// Cosine of the angle.
    ///
    /// Converts the angle to radians and computes the cosine.
    /// Works with any scalar type that implements [`Transcendental`] (e.g., `f32`, `f64`).
    #[inline]
    pub fn cos(self) -> S {
        let x_rad = self.to::<Radian>().value();
        x_rad.cos()
    }

    /// Tangent of the angle.
    ///
    /// Converts the angle to radians and computes the tangent.
    /// Works with any scalar type that implements [`Transcendental`] (e.g., `f32`, `f64`).
    #[inline]
    pub fn tan(self) -> S {
        let x_rad = self.to::<Radian>().value();
        x_rad.tan()
    }

    /// Simultaneously compute sine and cosine.
    ///
    /// Converts the angle to radians and computes both sine and cosine.
    /// Works with any scalar type that implements [`Transcendental`] (e.g., `f32`, `f64`).
    #[inline]
    pub fn sin_cos(self) -> (S, S) {
        let x_rad = self.to::<Radian>().value();
        x_rad.sin_cos()
    }
}

/// Degree.
#[derive(Clone, Copy, Debug, PartialEq, PartialOrd, Unit)]
#[unit(symbol = "°", dimension = Angular, ratio = 1.0)]
pub struct Degree;
/// Type alias shorthand for [`Degree`].
pub type Deg = Degree;
/// Convenience alias for a degree quantity.
pub type Degrees = Quantity<Deg>;
/// One degree.
pub const DEG: Degrees = Degrees::new(1.0);

/// Radian.
#[derive(Clone, Copy, Debug, PartialEq, PartialOrd, Unit)]
#[unit(symbol = "rad", dimension = Angular, ratio = 180.0 / core::f64::consts::PI)]
pub struct Radian;
/// Type alias shorthand for [`Radian`].
pub type Rad = Radian;
/// Convenience alias for a radian quantity.
pub type Radians = Quantity<Rad>;
/// One radian.
pub const RAD: Radians = Radians::new(1.0);

/// Milliradian (`1/1000` radian).
#[derive(Clone, Copy, Debug, PartialEq, PartialOrd, Unit)]
#[unit(symbol = "mrad", dimension = Angular, ratio = (180.0 / core::f64::consts::PI) / 1_000.0)]
pub struct Milliradian;
/// Type alias shorthand for [`Milliradian`].
pub type Mrad = Milliradian;
/// Convenience alias for a milliradian quantity.
pub type Milliradians = Quantity<Mrad>;
/// One milliradian.
pub const MRAD: Milliradians = Milliradians::new(1.0);

/// Turn (full revolution; `360` degrees).
#[derive(Clone, Copy, Debug, PartialEq, PartialOrd, Unit)]
#[unit(symbol = "tr", dimension = Angular, ratio = 360.0)]
pub struct Turn;
/// Convenience alias for a turn quantity.
pub type Turns = Quantity<Turn>;
/// One turn.
pub const TURN: Turns = Turns::new(1.0);

impl Degrees {
    /// Construct from **DMS** components (`deg`, `min`, `sec`).
    ///
    /// Sign is taken from `deg`; the magnitude of `min` and `sec` is always added.
    /// No range checking is performed. Use one of the wrapping helpers if you need a canonical range.
    ///
    /// ```rust
    /// use qtty_core::angular::Degrees;
    /// let lat = Degrees::from_dms(-33, 52, 0.0); // −33°52′00″
    /// assert!(lat.value() < 0.0);
    /// ```
    pub const fn from_dms(deg: i32, min: u32, sec: f64) -> Self {
        let sign = if deg < 0 { -1.0 } else { 1.0 };
        let d_abs = if deg < 0 { -(deg as f64) } else { deg as f64 };
        let m = min as f64 / 60.0;
        let s = sec / 3600.0;
        let total = sign * (d_abs + m + s);
        Self::new(total)
    }

    /// Construct from explicit sign and magnitude components.
    ///
    /// `sign < 0` produces a negative result; any other value (including `0`)
    /// produces a positive result.
    pub const fn from_dms_sign(sign: i8, deg: u32, min: u32, sec: f64) -> Self {
        let s = if sign < 0 { -1.0 } else { 1.0 };
        let total = (deg as f64) + (min as f64) / 60.0 + (sec / 3600.0);
        Self::new(s * total)
    }
}

/// Canonical list of always-available (base) angular units.
///
/// Exported (`#[doc(hidden)]`) for use in `qtty`'s scalar alias generation and
/// compile-time consistency checks.  Feature-gated units (astro, navigation)
/// are in their sub-modules and registered via `register_builtin_units_extend!`.
#[macro_export]
#[doc(hidden)]
macro_rules! angular_units {
    ($cb:path) => {
        $cb!(Degree, Radian, Milliradian, Turn);
    };
}

// Generate bidirectional From impls between base angular units.
angular_units!(crate::impl_unit_from_conversions);

// ─────────────────────────────────────────────────────────────────────────────
// Cross-unit ops: default units
// ─────────────────────────────────────────────────────────────────────────────
#[cfg(feature = "cross-unit-ops")]
angular_units!(crate::impl_unit_cross_unit_ops);

// ── Cross-feature: astro × navigation ────────────────────────────────────────
#[cfg(all(feature = "astro", feature = "navigation"))]
crate::__impl_from_each_extra_to_bases!(
    {Arcminute, Arcsecond, MilliArcsecond, MicroArcsecond, HourAngle}
    Gradian
);
#[cfg(all(feature = "astro", feature = "navigation", feature = "cross-unit-ops"))]
crate::__impl_cross_ops_each_extra_to_bases!(
    {Arcminute, Arcsecond, MilliArcsecond, MicroArcsecond, HourAngle}
    Gradian
);

// Compile-time check: every base angular unit is registered as BuiltinUnit.
#[cfg(test)]
angular_units!(crate::assert_units_are_builtin);

#[cfg(all(test, feature = "std"))]
mod tests {
    use super::*;
    use approx::{assert_abs_diff_eq, assert_relative_eq};
    use core::f64::consts::{PI, TAU};
    use proptest::prelude::*;

    // ─────────────────────────────────────────────────────────────────────────────
    // Angular unit constants
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn test_full_turn() {
        assert_abs_diff_eq!(Radian::FULL_TURN, TAU, epsilon = 1e-12);
        assert_eq!(Degree::FULL_TURN, 360.0);
        #[cfg(feature = "astro")]
        assert_eq!(Arcsecond::FULL_TURN, 1_296_000.0);
    }

    #[test]
    fn test_half_turn() {
        assert_abs_diff_eq!(Radian::HALF_TURN, PI, epsilon = 1e-12);
        assert_eq!(Degree::HALF_TURN, 180.0);
        #[cfg(feature = "astro")]
        assert_eq!(Arcsecond::HALF_TURN, 648_000.0);
    }

    #[test]
    fn test_quarter_turn() {
        assert_abs_diff_eq!(Radian::QUARTER_TURN, PI / 2.0, epsilon = 1e-12);
        assert_eq!(Degree::QUARTER_TURN, 90.0);
        #[cfg(feature = "astro")]
        assert_eq!(Arcsecond::QUARTER_TURN, 324_000.0);
    }

    #[test]
    fn test_quantity_constants() {
        assert_eq!(Degrees::FULL_TURN.value(), 360.0);
        assert_eq!(Degrees::HALF_TURN.value(), 180.0);
        assert_eq!(Degrees::QUARTER_TURN.value(), 90.0);
        assert_eq!(Degrees::TAU.value(), 360.0);
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // Conversions
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn conversion_degrees_to_radians() {
        let deg = Degrees::new(180.0);
        let rad = deg.to::<Radian>();
        assert_abs_diff_eq!(rad.value(), PI, epsilon = 1e-12);
    }

    #[test]
    fn conversion_radians_to_degrees() {
        let rad = Radians::new(PI);
        let deg = rad.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 180.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_degrees_to_arcseconds() {
        let deg = Degrees::new(1.0);
        let arcs = deg.to::<Arcsecond>();
        assert_abs_diff_eq!(arcs.value(), 3600.0, epsilon = 1e-9);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_arcseconds_to_degrees() {
        let arcs = Arcseconds::new(3600.0);
        let deg = arcs.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 1.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_degrees_to_milliarcseconds() {
        let deg = Degrees::new(1.0);
        let mas = deg.to::<MilliArcsecond>();
        assert_abs_diff_eq!(mas.value(), 3_600_000.0, epsilon = 1e-6);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_hour_angles_to_degrees() {
        let ha = HourAngles::new(1.0);
        let deg = ha.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 15.0, epsilon = 1e-12);
    }

    #[test]
    fn conversion_roundtrip() {
        let original = Degrees::new(123.456);
        let rad = original.to::<Radian>();
        let back = rad.to::<Degree>();
        assert_abs_diff_eq!(back.value(), original.value(), epsilon = 1e-12);
    }

    #[test]
    fn from_impl_degrees_radians() {
        let deg = Degrees::new(90.0);
        let rad: Radians = deg.into();
        assert_abs_diff_eq!(rad.value(), PI / 2.0, epsilon = 1e-12);

        let rad2 = Radians::new(PI);
        let deg2: Degrees = rad2.into();
        assert_abs_diff_eq!(deg2.value(), 180.0, epsilon = 1e-12);
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // Trig functions
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn test_trig() {
        let a = Degrees::new(90.0);
        assert!((a.sin() - 1.0).abs() < 1e-12);
        assert!(a.cos().abs() < 1e-12);
    }

    #[test]
    fn trig_sin_known_values() {
        assert_abs_diff_eq!(Degrees::new(0.0).sin(), 0.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(30.0).sin(), 0.5, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(90.0).sin(), 1.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(180.0).sin(), 0.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(270.0).sin(), -1.0, epsilon = 1e-12);
    }

    #[test]
    fn trig_cos_known_values() {
        assert_abs_diff_eq!(Degrees::new(0.0).cos(), 1.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(60.0).cos(), 0.5, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(90.0).cos(), 0.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(180.0).cos(), -1.0, epsilon = 1e-12);
    }

    #[test]
    fn trig_tan_known_values() {
        assert_abs_diff_eq!(Degrees::new(0.0).tan(), 0.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(45.0).tan(), 1.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(180.0).tan(), 0.0, epsilon = 1e-12);
    }

    #[test]
    fn trig_sin_cos_consistency() {
        let angle = Degrees::new(37.5);
        let (sin, cos) = angle.sin_cos();
        assert_abs_diff_eq!(sin, angle.sin(), epsilon = 1e-15);
        assert_abs_diff_eq!(cos, angle.cos(), epsilon = 1e-15);
    }

    #[test]
    fn trig_pythagorean_identity() {
        let angle = Degrees::new(123.456);
        let sin = angle.sin();
        let cos = angle.cos();
        assert_abs_diff_eq!(sin * sin + cos * cos, 1.0, epsilon = 1e-12);
    }

    #[test]
    fn trig_radians() {
        assert_abs_diff_eq!(Radians::new(0.0).sin(), 0.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Radians::new(PI / 2.0).sin(), 1.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Radians::new(PI).cos(), -1.0, epsilon = 1e-12);
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // signum
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn signum_positive() {
        assert_eq!(Degrees::new(45.0).signum(), 1.0);
    }

    #[test]
    fn signum_negative() {
        assert_eq!(Degrees::new(-45.0).signum(), -1.0);
    }

    #[test]
    fn signum_zero() {
        assert_eq!(Degrees::new(0.0).signum(), 1.0);
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // wrap_pos (normalize)
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn wrap_pos_basic() {
        assert_abs_diff_eq!(
            Degrees::new(370.0).wrap_pos().value(),
            10.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(Degrees::new(720.0).wrap_pos().value(), 0.0, epsilon = 1e-12);
        assert_abs_diff_eq!(Degrees::new(0.0).wrap_pos().value(), 0.0, epsilon = 1e-12);
    }

    #[test]
    fn wrap_pos_negative() {
        assert_abs_diff_eq!(
            Degrees::new(-10.0).wrap_pos().value(),
            350.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-370.0).wrap_pos().value(),
            350.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-720.0).wrap_pos().value(),
            0.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn wrap_pos_boundary() {
        assert_abs_diff_eq!(Degrees::new(360.0).wrap_pos().value(), 0.0, epsilon = 1e-12);
        assert_abs_diff_eq!(
            Degrees::new(-360.0).wrap_pos().value(),
            0.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn normalize_is_wrap_pos() {
        let angle = Degrees::new(450.0);
        assert_eq!(angle.normalize().value(), angle.wrap_pos().value());
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // wrap_signed: (-180, 180]
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn test_wrap_signed() {
        let a = Degrees::new(370.0).wrap_signed();
        assert_eq!(a.value(), 10.0);
        let b = Degrees::new(-190.0).wrap_signed();
        assert_eq!(b.value(), 170.0);
    }

    #[test]
    fn wrap_signed_basic() {
        assert_abs_diff_eq!(
            Degrees::new(10.0).wrap_signed().value(),
            10.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-10.0).wrap_signed().value(),
            -10.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn wrap_signed_over_180() {
        assert_abs_diff_eq!(
            Degrees::new(190.0).wrap_signed().value(),
            -170.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(270.0).wrap_signed().value(),
            -90.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn wrap_signed_boundary_180() {
        assert_abs_diff_eq!(
            Degrees::new(180.0).wrap_signed().value(),
            180.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-180.0).wrap_signed().value(),
            180.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn wrap_signed_large_values() {
        assert_abs_diff_eq!(
            Degrees::new(540.0).wrap_signed().value(),
            180.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-540.0).wrap_signed().value(),
            180.0,
            epsilon = 1e-12
        );
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // wrap_quarter_fold: [-90, 90]
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn wrap_quarter_fold_basic() {
        assert_abs_diff_eq!(
            Degrees::new(0.0).wrap_quarter_fold().value(),
            0.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(45.0).wrap_quarter_fold().value(),
            45.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-45.0).wrap_quarter_fold().value(),
            -45.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn wrap_quarter_fold_boundary() {
        assert_abs_diff_eq!(
            Degrees::new(90.0).wrap_quarter_fold().value(),
            90.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-90.0).wrap_quarter_fold().value(),
            -90.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn wrap_quarter_fold_over_90() {
        assert_abs_diff_eq!(
            Degrees::new(100.0).wrap_quarter_fold().value(),
            80.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(135.0).wrap_quarter_fold().value(),
            45.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(180.0).wrap_quarter_fold().value(),
            0.0,
            epsilon = 1e-12
        );
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // Separation helpers
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn signed_separation_basic() {
        let a = Degrees::new(30.0);
        let b = Degrees::new(50.0);
        assert_abs_diff_eq!(a.signed_separation(b).value(), -20.0, epsilon = 1e-12);
        assert_abs_diff_eq!(b.signed_separation(a).value(), 20.0, epsilon = 1e-12);
    }

    #[test]
    fn signed_separation_wrap() {
        let a = Degrees::new(10.0);
        let b = Degrees::new(350.0);
        assert_abs_diff_eq!(a.signed_separation(b).value(), 20.0, epsilon = 1e-12);
        assert_abs_diff_eq!(b.signed_separation(a).value(), -20.0, epsilon = 1e-12);
    }

    #[test]
    fn abs_separation() {
        let a = Degrees::new(30.0);
        let b = Degrees::new(50.0);
        assert_abs_diff_eq!(a.abs_separation(b).value(), 20.0, epsilon = 1e-12);
        assert_abs_diff_eq!(b.abs_separation(a).value(), 20.0, epsilon = 1e-12);
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // wrap_to_signed_pi / wrap_to_unsigned_pi / fold_to_pi
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn wrap_to_signed_pi_matches_wrap_signed_radians() {
        for &x in &[
            -7.0 * PI,
            -PI - 0.1,
            -PI,
            -1.0,
            0.0,
            1.0,
            PI,
            PI + 0.1,
            7.0 * PI,
        ] {
            let a = Radians::new(x);
            assert_abs_diff_eq!(
                a.wrap_to_signed_pi().value(),
                a.wrap_signed().value(),
                epsilon = 1e-12
            );
        }
    }

    #[test]
    fn wrap_to_signed_pi_degree_analog() {
        // The same generic helper provides the (-180°, 180°] semantics for Degrees.
        assert_abs_diff_eq!(
            Degrees::new(190.0).wrap_to_signed_pi().value(),
            -170.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(180.0).wrap_to_signed_pi().value(),
            180.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-180.0).wrap_to_signed_pi().value(),
            180.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(7.0 * 180.0).wrap_to_signed_pi().value(),
            180.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn wrap_to_unsigned_pi_matches_wrap_pos_radians() {
        for &x in &[-7.0 * PI, -PI, -1.0, 0.0, 1.0, PI, TAU, 7.0 * PI] {
            let a = Radians::new(x);
            assert_abs_diff_eq!(
                a.wrap_to_unsigned_pi().value(),
                a.wrap_pos().value(),
                epsilon = 1e-12
            );
        }
    }

    #[test]
    fn wrap_to_unsigned_pi_degree_analog() {
        assert_abs_diff_eq!(
            Degrees::new(370.0).wrap_to_unsigned_pi().value(),
            10.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-10.0).wrap_to_unsigned_pi().value(),
            350.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(360.0).wrap_to_unsigned_pi().value(),
            0.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn fold_to_pi_radians() {
        assert_abs_diff_eq!(Radians::new(0.5).fold_to_pi().value(), 0.5, epsilon = 1e-12);
        assert_abs_diff_eq!(
            Radians::new(-0.5).fold_to_pi().value(),
            0.5,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Radians::new(PI + 0.1).fold_to_pi().value(),
            PI - 0.1,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Radians::new(7.0 * PI).fold_to_pi().value(),
            PI,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(Radians::new(PI).fold_to_pi().value(), PI, epsilon = 1e-12);
        assert_abs_diff_eq!(Radians::new(0.0).fold_to_pi().value(), 0.0, epsilon = 1e-12);
    }

    #[test]
    fn fold_to_pi_degree_analog() {
        assert_abs_diff_eq!(
            Degrees::new(190.0).fold_to_pi().value(),
            170.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-30.0).fold_to_pi().value(),
            30.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(360.0 * 7.0 + 50.0).fold_to_pi().value(),
            50.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn fold_to_pi_nan_propagates() {
        assert!(Radians::new(f64::NAN).fold_to_pi().value().is_nan());
        assert!(Degrees::new(f64::NAN).fold_to_pi().value().is_nan());
    }

    /// Parity with NSB's existing fold semantics: `delta_lambda.to_degrees().abs().min(180.0)`
    /// applied to the signed difference of two ecliptic longitudes must equal
    /// `(a - b).fold_to_pi()` (in degrees).
    #[test]
    fn fold_to_pi_matches_nsb_legacy_loop() {
        // Reference implementation mirroring the historic NSB normalization
        // (`while delta > π { delta -= 2π } / while delta < -π { delta += 2π }` then `.abs()`).
        fn nsb_legacy_fold(mut delta: f64) -> f64 {
            while delta > PI {
                delta -= TAU;
            }
            while delta < -PI {
                delta += TAU;
            }
            delta.abs()
        }

        let samples = [
            -7.5 * PI,
            -PI - 1e-9,
            -PI,
            -PI / 2.0,
            -1e-12,
            0.0,
            1e-12,
            PI / 4.0,
            PI - 1e-9,
            PI,
            PI + 1e-9,
            3.0 * PI / 2.0,
            7.5 * PI,
        ];
        for &x in &samples {
            let helper = Radians::new(x).fold_to_pi().value();
            let legacy = nsb_legacy_fold(x);
            assert_abs_diff_eq!(helper, legacy, epsilon = 1e-9);
        }
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // DMS / HMS construction
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn degrees_from_dms_positive() {
        let d = Degrees::from_dms(12, 30, 0.0);
        assert_abs_diff_eq!(d.value(), 12.5, epsilon = 1e-12);
    }

    #[test]
    fn degrees_from_dms_negative() {
        let d = Degrees::from_dms(-33, 52, 0.0);
        assert!(d.value() < 0.0);
        assert_abs_diff_eq!(d.value(), -(33.0 + 52.0 / 60.0), epsilon = 1e-12);
    }

    #[test]
    fn degrees_from_dms_with_seconds() {
        let d = Degrees::from_dms(10, 20, 30.0);
        assert_abs_diff_eq!(
            d.value(),
            10.0 + 20.0 / 60.0 + 30.0 / 3600.0,
            epsilon = 1e-12
        );
    }

    #[test]
    fn degrees_from_dms_sign() {
        let pos = Degrees::from_dms_sign(1, 45, 30, 0.0);
        let neg = Degrees::from_dms_sign(-1, 45, 30, 0.0);
        assert_abs_diff_eq!(pos.value(), 45.5, epsilon = 1e-12);
        assert_abs_diff_eq!(neg.value(), -45.5, epsilon = 1e-12);
    }

    #[test]
    fn degrees_from_dms_sign_zero_is_positive() {
        let zero_sign = Degrees::from_dms_sign(0, 45, 30, 0.0);
        assert_abs_diff_eq!(zero_sign.value(), 45.5, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn hour_angles_from_hms() {
        let ha = HourAngles::from_hms(5, 30, 0.0);
        assert_abs_diff_eq!(ha.value(), 5.5, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn hour_angles_from_hms_negative() {
        let ha = HourAngles::from_hms(-3, 15, 0.0);
        assert_abs_diff_eq!(ha.value(), -3.25, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn hour_angles_to_degrees() {
        let ha = HourAngles::new(6.0);
        let deg = ha.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 90.0, epsilon = 1e-12);
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // Display formatting
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn display_degrees() {
        let d = Degrees::new(45.5);
        assert_eq!(format!("{}", d), "45.5 °");
    }

    #[test]
    fn display_radians() {
        let r = Radians::new(1.0);
        assert_eq!(format!("{}", r), "1 rad");
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // Unit constants
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn unit_constants() {
        assert_eq!(DEG.value(), 1.0);
        assert_eq!(RAD.value(), 1.0);
        assert_eq!(MRAD.value(), 1.0);
        #[cfg(feature = "astro")]
        {
            assert_eq!(ARCM.value(), 1.0);
            assert_eq!(ARCS.value(), 1.0);
            assert_eq!(MAS.value(), 1.0);
            assert_eq!(UAS.value(), 1.0);
            assert_eq!(HOUR_ANGLE.value(), 1.0);
        }
        #[cfg(feature = "navigation")]
        assert_eq!(GON.value(), 1.0);
        assert_eq!(TURN.value(), 1.0);
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // wrap_signed_lo: [-180, 180)
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    fn wrap_signed_lo_boundary_half_turn() {
        // +half turn should map to -half turn to make the upper bound exclusive.
        assert_abs_diff_eq!(
            Degrees::new(180.0).wrap_signed_lo().value(),
            -180.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Degrees::new(-180.0).wrap_signed_lo().value(),
            -180.0,
            epsilon = 1e-12
        );
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // New unit conversions and tests
    // ─────────────────────────────────────────────────────────────────────────────

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_degrees_to_arcminutes() {
        let deg = Degrees::new(1.0);
        let arcm = deg.to::<Arcminute>();
        assert_abs_diff_eq!(arcm.value(), 60.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_arcminutes_to_degrees() {
        let arcm = Arcminutes::new(60.0);
        let deg = arcm.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 1.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_arcminutes_to_arcseconds() {
        let arcm = Arcminutes::new(1.0);
        let arcs = arcm.to::<Arcsecond>();
        assert_abs_diff_eq!(arcs.value(), 60.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_arcseconds_to_microarcseconds() {
        let arcs = Arcseconds::new(1.0);
        let uas = arcs.to::<MicroArcsecond>();
        assert_abs_diff_eq!(uas.value(), 1_000_000.0, epsilon = 1e-6);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn conversion_microarcseconds_to_degrees() {
        let uas = MicroArcseconds::new(3_600_000_000.0);
        let deg = uas.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 1.0, epsilon = 1e-9);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn conversion_degrees_to_gradians() {
        let deg = Degrees::new(90.0);
        let gon = deg.to::<Gradian>();
        assert_abs_diff_eq!(gon.value(), 100.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn conversion_gradians_to_degrees() {
        let gon = Gradians::new(400.0);
        let deg = gon.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 360.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn conversion_gradians_to_radians() {
        let gon = Gradians::new(200.0);
        let rad = gon.to::<Radian>();
        assert_abs_diff_eq!(rad.value(), PI, epsilon = 1e-12);
    }

    #[test]
    fn conversion_degrees_to_turns() {
        let deg = Degrees::new(360.0);
        let turn = deg.to::<Turn>();
        assert_abs_diff_eq!(turn.value(), 1.0, epsilon = 1e-12);
    }

    #[test]
    fn conversion_milliradians_to_radians() {
        let mrad = Milliradians::new(1_000.0);
        let rad = mrad.to::<Radian>();
        assert_abs_diff_eq!(rad.value(), 1.0, epsilon = 1e-12);
    }

    #[test]
    fn conversion_turns_to_degrees() {
        let turn = Turns::new(2.5);
        let deg = turn.to::<Degree>();
        assert_abs_diff_eq!(deg.value(), 900.0, epsilon = 1e-12);
    }

    #[test]
    fn conversion_turns_to_radians() {
        let turn = Turns::new(1.0);
        let rad = turn.to::<Radian>();
        assert_abs_diff_eq!(rad.value(), TAU, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn from_impl_new_units() {
        // Test From trait implementations for new units
        let deg = Degrees::new(1.0);
        let arcm: Arcminutes = deg.into();
        assert_abs_diff_eq!(arcm.value(), 60.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn from_impl_gradian_to_deg() {
        let gon = Gradians::new(100.0);
        let deg: Degrees = gon.into();
        assert_abs_diff_eq!(deg.value(), 90.0, epsilon = 1e-12);
    }

    #[test]
    fn from_impl_turn_to_deg() {
        let turn = Turns::new(0.25);
        let deg: Degrees = turn.into();
        assert_abs_diff_eq!(deg.value(), 90.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn roundtrip_arcminute_arcsecond() {
        let original = Arcminutes::new(5.0);
        let arcs = original.to::<Arcsecond>();
        let back = arcs.to::<Arcminute>();
        assert_abs_diff_eq!(back.value(), original.value(), epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn roundtrip_gradian_degree() {
        let original = Gradians::new(123.456);
        let deg = original.to::<Degree>();
        let back = deg.to::<Gradian>();
        assert_abs_diff_eq!(back.value(), original.value(), epsilon = 1e-12);
    }

    #[test]
    fn roundtrip_turn_radian() {
        let original = Turns::new(2.717);
        let rad = original.to::<Radian>();
        let back = rad.to::<Turn>();
        assert_abs_diff_eq!(back.value(), original.value(), epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn gradian_full_turn() {
        assert_abs_diff_eq!(Gradian::FULL_TURN, 400.0, epsilon = 1e-12);
    }

    #[test]
    fn turn_full_turn() {
        assert_abs_diff_eq!(Turn::FULL_TURN, 1.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn arcminute_full_turn() {
        assert_abs_diff_eq!(Arcminute::FULL_TURN, 21_600.0, epsilon = 1e-9);
    }

    #[test]
    #[cfg(feature = "astro")]
    fn microarcsecond_conversion_chain() {
        // Test a long conversion chain
        let uas = MicroArcseconds::new(1e9);
        let mas = uas.to::<MilliArcsecond>();
        let arcs = mas.to::<Arcsecond>();
        let arcm = arcs.to::<Arcminute>();
        let deg = arcm.to::<Degree>();

        assert_abs_diff_eq!(mas.value(), 1_000_000.0, epsilon = 1e-6);
        assert_abs_diff_eq!(arcs.value(), 1_000.0, epsilon = 1e-9);
        assert_abs_diff_eq!(arcm.value(), 1_000.0 / 60.0, epsilon = 1e-9);
        assert_relative_eq!(deg.value(), 1_000.0 / 3600.0, max_relative = 1e-9);
    }

    #[test]
    fn wrap_pos_with_turns() {
        let turn = Turns::new(2.7);
        let wrapped = turn.wrap_pos();
        assert_abs_diff_eq!(wrapped.value(), 0.7, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn wrap_signed_with_gradians() {
        let gon = Gradians::new(350.0);
        let wrapped = gon.wrap_signed();
        assert_abs_diff_eq!(wrapped.value(), -50.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(feature = "navigation")]
    fn trig_with_gradians() {
        let gon = Gradians::new(100.0); // 90 degrees
        assert_abs_diff_eq!(gon.sin(), 1.0, epsilon = 1e-12);
        assert_abs_diff_eq!(gon.cos(), 0.0, epsilon = 1e-12);
    }

    #[test]
    fn trig_with_turns() {
        let turn = Turns::new(0.25); // 90 degrees
        assert_abs_diff_eq!(turn.sin(), 1.0, epsilon = 1e-12);
        assert_abs_diff_eq!(turn.cos(), 0.0, epsilon = 1e-12);
    }

    #[test]
    #[cfg(all(feature = "astro", feature = "navigation"))]
    fn all_units_to_degrees() {
        // Verify all units convert correctly to degrees
        assert_abs_diff_eq!(
            Radians::new(PI).to::<Degree>().value(),
            180.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Arcminutes::new(60.0).to::<Degree>().value(),
            1.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Arcseconds::new(3600.0).to::<Degree>().value(),
            1.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            MilliArcseconds::new(3_600_000.0).to::<Degree>().value(),
            1.0,
            epsilon = 1e-9
        );
        assert_abs_diff_eq!(
            MicroArcseconds::new(3_600_000_000.0).to::<Degree>().value(),
            1.0,
            epsilon = 1e-6
        );
        assert_abs_diff_eq!(
            Gradians::new(100.0).to::<Degree>().value(),
            90.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            Turns::new(1.0).to::<Degree>().value(),
            360.0,
            epsilon = 1e-12
        );
        assert_abs_diff_eq!(
            HourAngles::new(1.0).to::<Degree>().value(),
            15.0,
            epsilon = 1e-12
        );
    }

    // ─────────────────────────────────────────────────────────────────────────────
    // Property-based tests
    // ─────────────────────────────────────────────────────────────────────────────

    proptest! {
        #[test]
        fn prop_wrap_pos_range(angle in -1e6..1e6f64) {
            let wrapped = Degrees::new(angle).wrap_pos();
            prop_assert!(wrapped.value() >= 0.0);
            prop_assert!(wrapped.value() < 360.0);
        }

        #[test]
        fn prop_wrap_signed_range(angle in -1e6..1e6f64) {
            let wrapped = Degrees::new(angle).wrap_signed();
            prop_assert!(wrapped.value() > -180.0);
            prop_assert!(wrapped.value() <= 180.0);
        }

        #[test]
        fn prop_wrap_quarter_fold_range(angle in -1e6..1e6f64) {
            let wrapped = Degrees::new(angle).wrap_quarter_fold();
            prop_assert!(wrapped.value() >= -90.0);
            prop_assert!(wrapped.value() <= 90.0);
        }

        #[test]
        fn prop_pythagorean_identity(angle in -360.0..360.0f64) {
            let a = Degrees::new(angle);
            let sin = a.sin();
            let cos = a.cos();
            assert_abs_diff_eq!(sin * sin + cos * cos, 1.0, epsilon = 1e-12);
        }

        #[test]
        fn prop_conversion_roundtrip(angle in -1e6..1e6f64) {
            let deg = Degrees::new(angle);
            let rad = deg.to::<Radian>();
            let back = rad.to::<Degree>();
            assert_relative_eq!(back.value(), deg.value(), max_relative = 1e-12);
        }

        #[test]
        fn prop_abs_separation_symmetric(a in -360.0..360.0f64, b in -360.0..360.0f64) {
            let da = Degrees::new(a);
            let db = Degrees::new(b);
            assert_abs_diff_eq!(
                da.abs_separation(db).value(),
                db.abs_separation(da).value(),
                epsilon = 1e-12
            );
        }
    }

    /// Invoke derive-generated PartialEq/Clone/Debug on each unit struct to
    /// cover the #[derive] attribute lines tracked by llvm-cov.
    #[test]
    fn derive_coverage_unit_structs() {
        // Direct struct value comparisons invoke <T as PartialEq>::eq() which
        // is the derive-generated implementation, covering the #[derive] line.
        assert!(Degree == Degree);
        assert!(Radian == Radian);
        assert!(Milliradian == Milliradian);
        #[cfg(feature = "astro")]
        {
            assert!(Arcminute == Arcminute);
            assert!(Arcsecond == Arcsecond);
            assert!(MilliArcsecond == MilliArcsecond);
            assert!(MicroArcsecond == MicroArcsecond);
            assert!(HourAngle == HourAngle);
        }
        #[cfg(feature = "navigation")]
        assert!(Gradian == Gradian);
        assert!(Turn == Turn);
        // signum_const: cover both positive and negative branches
        let pos = Degrees::new(90.0);
        let neg = Degrees::new(-45.0);
        assert_eq!(pos.signum_const(), 1.0);
        assert_eq!(neg.signum_const(), -1.0);
    }
}