TimeScales.hpp

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#pragma once
 
#include <cmath>
#include <janus/janus.hpp>
#include <vulcan/time/JulianDate.hpp>
#include <vulcan/time/LeapSeconds.hpp>
#include <vulcan/time/TimeConstants.hpp>
 
namespace vulcan::time {
 
// =============================================================================
// Enumeration of Time Scales
// =============================================================================
 
enum class TimeScale {
    UTC, 
    TAI, 
    TT,  
    TDB, 
    GPS, 
    UT1  
};
 
// =============================================================================
// TAI ↔ TT Conversions (Templated - Fixed Offset)
// =============================================================================

template <typename Scalar>
[[nodiscard]] constexpr Scalar tai_to_tt(const Scalar &tai_jd) {
    return tai_jd +
           constants::time::TT_TAI_OFFSET / constants::time::SECONDS_PER_DAY;
}

template <typename Scalar>
[[nodiscard]] constexpr Scalar tt_to_tai(const Scalar &tt_jd) {
    return tt_jd -
           constants::time::TT_TAI_OFFSET / constants::time::SECONDS_PER_DAY;
}
 
// =============================================================================
// TAI ↔ GPS Conversions (Templated - Fixed Offset)
// =============================================================================

template <typename Scalar>
[[nodiscard]] constexpr Scalar tai_to_gps(const Scalar &tai_jd) {
    return tai_jd +
           constants::time::GPS_TAI_OFFSET / constants::time::SECONDS_PER_DAY;
}

template <typename Scalar>
[[nodiscard]] constexpr Scalar gps_to_tai(const Scalar &gps_jd) {
    return gps_jd +
           constants::time::TAI_GPS_OFFSET / constants::time::SECONDS_PER_DAY;
}
 
// =============================================================================
// TAI ↔ UTC Conversions (Templated with Leap Second Parameter)
// =============================================================================

template <typename Scalar>
[[nodiscard]] constexpr Scalar utc_to_tai(const Scalar &utc_jd, int delta_at) {
    return utc_jd +
           static_cast<double>(delta_at) / constants::time::SECONDS_PER_DAY;
}

template <typename Scalar>
[[nodiscard]] constexpr Scalar tai_to_utc(const Scalar &tai_jd, int delta_at) {
    return tai_jd -
           static_cast<double>(delta_at) / constants::time::SECONDS_PER_DAY;
}
 
// =============================================================================
// TAI ↔ UTC Conversions (Numeric with Automatic Lookup)
// =============================================================================

[[nodiscard]] inline double utc_to_tai(double utc_jd) {
    int delta_at = leap_seconds_at_utc(utc_jd);
    return utc_to_tai(utc_jd, delta_at);
}

[[nodiscard]] inline double tai_to_utc(double tai_jd) {
    int delta_at = leap_seconds_at_tai(tai_jd);
    return tai_to_utc(tai_jd, delta_at);
}
 
// =============================================================================
// UTC ↔ GPS Conversions (Convenience)
// =============================================================================

template <typename Scalar>
[[nodiscard]] constexpr Scalar utc_to_gps(const Scalar &utc_jd, int delta_at) {
    Scalar tai_jd = utc_to_tai(utc_jd, delta_at);
    return tai_to_gps(tai_jd);
}

template <typename Scalar>
[[nodiscard]] constexpr Scalar gps_to_utc(const Scalar &gps_jd, int delta_at) {
    Scalar tai_jd = gps_to_tai(gps_jd);
    return tai_to_utc(tai_jd, delta_at);
}

[[nodiscard]] inline double utc_to_gps(double utc_jd) {
    int delta_at = leap_seconds_at_utc(utc_jd);
    return utc_to_gps(utc_jd, delta_at);
}

[[nodiscard]] inline double gps_to_utc(double gps_jd) {
    // GPS JD to TAI JD, then lookup
    double tai_jd = gps_to_tai(gps_jd);
    int delta_at = leap_seconds_at_tai(tai_jd);
    return gps_to_utc(gps_jd, delta_at);
}
 
// =============================================================================
// TT ↔ TDB Conversions (Templated - Periodic Approximation)
// =============================================================================

template <typename Scalar> [[nodiscard]] Scalar tt_to_tdb(const Scalar &tt_jd) {
    // Julian centuries since J2000.0 TT
    Scalar T = jd_to_j2000_centuries(tt_jd);
 
    // Mean anomaly of Earth around Sun (radians)
    // g = 357.5277233° + 35999.05034° * T
    Scalar g = (357.5277233 + 35999.05034 * T) * M_PI / 180.0;
 
    // TDB - TT in seconds (simplified Fairhead & Bretagnon)
    Scalar dt = 0.001657 * janus::sin(g);
 
    return tt_jd + dt / constants::time::SECONDS_PER_DAY;
}

template <typename Scalar>
[[nodiscard]] Scalar tdb_to_tt(const Scalar &tdb_jd) {
    // First approximation: TT ≈ TDB
    Scalar T = jd_to_j2000_centuries(tdb_jd);
 
    // Mean anomaly
    Scalar g = (357.5277233 + 35999.05034 * T) * M_PI / 180.0;
 
    // Correction
    Scalar dt = 0.001657 * janus::sin(g);
 
    return tdb_jd - dt / constants::time::SECONDS_PER_DAY;
}
 
// =============================================================================
// Symbolic UTC ↔ TAI with Interpolated Leap Seconds
// =============================================================================

template <typename Scalar>
[[nodiscard]] Scalar utc_to_tai_symbolic(const Scalar &utc_jd) {
    Scalar delta_at = leap_seconds_symbolic(utc_jd);
    return utc_jd + delta_at / constants::time::SECONDS_PER_DAY;
}

template <typename Scalar>
[[nodiscard]] Scalar tai_to_utc_symbolic(const Scalar &tai_jd) {
    // Approximate: use TAI JD in interpolator (error < 37 seconds offset)
    // This is acceptable for smooth optimization purposes
    Scalar delta_at = leap_seconds_symbolic(tai_jd);
    return tai_jd - delta_at / constants::time::SECONDS_PER_DAY;
}
 
} // namespace vulcan::time