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use crate::{ClockDrift, Dt, LocalSpacetime, Real, TSpan};
impl Dt {
/// Computes the accumulated **proper time** (Δτ) experienced by a clock moving along a
/// coordinate-time path from `self` to `end`.
///
/// Proper time is the actual time measured by a real physical clock (onboard spacecraft
/// clock, probe, etc.). This function evaluates the exact relativistic rate
/// dτ/dt = √K_eff from the library’s unified master Lagrangian at each sample point
/// and integrates using composite Simpson’s rule.
///
/// Use this whenever velocity, gravitational potential, or spacetime curvature changes
/// along the trajectory (e.g. planetary flybys, cislunar transfers, deep-space maneuvers,
/// or strong-field regions). It automatically includes special-relativistic velocity
/// effects, general-relativistic gravitational time dilation, and the built-in
/// Planck-scale saturation term.
///
/// # Parameters
/// - `end` — the ending coordinate time of the interval.
/// - `samples` — slice of `LocalSpacetime` snapshots evaluated at **uniformly spaced**
/// points along the path (must contain at least two entries). These samples can be
/// freely reused elsewhere (e.g. for light-time calculations in `ObserverState`).
///
/// # Returns
/// The accumulated proper-time interval Δτ (exact 36-digit precision).
///
/// # Example
/// ```rust
/// use deep_time::{Scale, TSpan, LocalSpacetime, Dt};
///
/// let start = Dt::from_sec(0, Scale::TAI);
/// let end = Dt::from_sec(1000, Scale::TAI);
///
/// // Constant metric example (α = 0.9 → dτ/dt = 0.9)
/// let slow = LocalSpacetime::new(0.9, 0.0, 0.0);
/// let samples = [slow; 2];
///
/// let delta_tau = start.proper_time_interval_samples(end, &samples);
/// assert_eq!(delta_tau, TSpan::from_sec(900));
///
/// // Update onboard proper time clock
/// let onboard_tau = start.to(Scale::Custom).add(delta_tau);
/// ```
pub const fn proper_time_interval_samples(self, end: Dt, samples: &[LocalSpacetime]) -> TSpan {
if samples.len() < 2 || self.eq(&end) {
return TSpan::ZERO;
}
let mut dt = end.to_tai_since(self);
let sign = if dt.sec < 0 { f!(-1.0) } else { f!(1.0) };
if sign < f!(0.0) {
dt = dt.neg();
}
let dt_sec = dt.to_sec_f();
let num_intervals = samples.len() - 1;
if num_intervals <= 1 {
// Fast trapezoidal rule for constant-rate cases
let rate0 = Self::rate_from_local(&samples[0]);
let rate1 = Self::rate_from_local(&samples[samples.len() - 1]);
let integral = f!(0.5) * (rate0 + rate1 - f!(2.0)) * dt_sec;
return TSpan::from_sec_f(sign * (dt_sec + integral));
}
// Simpson’s rule quadrature (high-order accuracy)
let n = f!(num_intervals);
let h = dt_sec / n;
let mut s = f!(0.0);
let mut i = 0;
while i <= num_intervals {
let local = &samples[i];
let rate = Self::rate_from_local(local);
let coeff = if i == 0 || i == num_intervals {
f!(1.0)
} else if i % 2 == 0 {
f!(2.0)
} else {
f!(4.0)
};
s += coeff * (rate - f!(1.0));
i += 1;
}
let integral = (h / f!(3.0)) * s;
TSpan::from_sec_f(sign * (dt_sec + integral))
}
/// Computes the relativistic correction (Δτ − Δt) using pre-computed samples.
///
/// Returns how much the onboard clock has gained or lost relative to coordinate time.
/// Positive values mean the clock ran fast; negative values mean it ran slow.
///
/// # Parameters
/// - `end` — ending coordinate time.
/// - `samples` — uniformly spaced `LocalSpacetime` snapshots (see
/// [`proper_time_interval_samples`] for details and example).
///
/// # Returns
/// The relativistic correction as a `TSpan`.
pub const fn relativistic_correction_with_samples(
self,
end: Dt,
samples: &[LocalSpacetime],
) -> TSpan {
let dtau = self.proper_time_interval_samples(end, samples);
let dt = end.to_tai_since(self);
dtau.sub(dt)
}
/// Private helper: instantaneous proper-time rate dτ/dt from a `LocalSpacetime` snapshot.
#[inline]
const fn rate_from_local(spacetime: &LocalSpacetime) -> Real {
let drift = ClockDrift::from_local_spacetime(spacetime);
f!(1.0) + drift.rate().to_sec_f()
}
}