toolbox.hpp File Reference

#include <cmath>
#include <format>
#include <limits>
#include <cstddef>
#include <numbers>
#include <numeric>
#include <cstdint>
#include <concepts>
#include <algorithm>
#include <stdexcept>
#include <type_traits>

Classes
struct	astro::toolbox::Angle< Unit >
	Represents an angle. More...
struct	astro::toolbox::Distance< Unit >
	Represents a distance. More...
struct	astro::toolbox::SphericalCoordinate
	Represents a position in a spherical coordinate system. More...
struct	astro::toolbox::GoldenSectionRules< LowerProbe, MoveLower, Finished >
	Arithmetic, comparison and stopping rules supplied by an extremum-search caller. More...
struct	astro::toolbox::GoldenSectionBracket
	The final bracket; converged is false when the update budget runs out. More...

Namespaces
namespace	astro
namespace	astro::toolbox
namespace	astro::toolbox::literals

Typedefs
using	astro::toolbox::AngleDeg
	An angle measured in degrees.
using	astro::toolbox::AngleRad
using	astro::toolbox::DistanceAu
	A distance measured in astronomical units; see AngleDeg for the alias convention.
using	astro::toolbox::DistanceKm

Enumerations
enum class	astro::toolbox::AngleUnit : uint8_t { astro::toolbox::RAD , astro::toolbox::DEG }
enum class	astro::toolbox::DistanceUnit : uint8_t { astro::toolbox::AU , astro::toolbox::KM }
	The unit of distance, either AU or KM. More...

Functions
constexpr auto	astro::toolbox::normalize_deg (const double deg) -> double
	Normalize degree to [0, 360).
constexpr auto	astro::toolbox::normalize_rad (const double rad) -> double
	Normalize radian to [0, 2π).
constexpr auto	astro::toolbox::normalize_pm180 (const double deg) -> double
	Normalize degree to [-180, 180). Useful for hour angles, where sign carries meaning.
auto	astro::toolbox::remainder_deg (const double difference_deg) -> double
	Return the IEEE remainder in [-180°, 180°], retaining signed zero and either sign at 180°.
auto	astro::toolbox::unwrap_near (const double wrapped_deg, const double reference_deg) -> double
	Shift an angle by whole turns toward a reference, without normalizing either input.
constexpr auto	astro::toolbox::deg_to_rad (const double deg) -> double
	Convert degree to radian.
constexpr auto	astro::toolbox::rad_to_deg (const double rad) -> double
	Convert radian to degree.
constexpr auto	astro::toolbox::arcmin_to_deg (const double arcmin) -> double
	Convert minutes to degrees.
constexpr auto	astro::toolbox::arcsec_to_deg (const double arcsec) -> double
	Convert seconds to degrees.
auto	astro::toolbox::canonical_longitude_difference (const AngleDeg difference) -> AngleDeg
	Canonicalize a finite directed longitude difference to (-180, 180] degrees.
constexpr auto	astro::toolbox::literals::operator""_deg (const long double value) -> AngleDeg
constexpr auto	astro::toolbox::literals::operator""_arcmin (const long double value) -> AngleDeg
constexpr auto	astro::toolbox::literals::operator""_arcsec (const long double value) -> AngleDeg
constexpr auto	astro::toolbox::literals::operator""_rad (const long double value) -> AngleRad
constexpr auto	astro::toolbox::au_to_km (const double au) -> double
	Convert from AU to KM.
constexpr auto	astro::toolbox::km_to_au (const double km) -> double
	Convert from KM to AU.
auto	astro::toolbox::ulp (const double x) -> double
	The gap between x and the next representable double — one unit in the last place.
template<typename Func> requires std::invocable<const Func&, double> and std::convertible_to<std::invoke_result_t<const Func&, double>, double>
auto	astro::toolbox::newton_method (const Func &f, const double start_jde, const double end_jde, const double mean_rate_deg_per_day, const std::size_t max_iterations=NEWTON_MAX_ITERATIONS) -> double
	Apply Newton's method to find the JDE at which f crosses zero.
template<typename Func, typename Rules> requires std::invocable<const Func&, double> and std::convertible_to<std::invoke_result_t<const Func&, double>, double>
auto	astro::toolbox::golden_section_bracket (const Func &f, const double lower, const double upper, const double tolerance, const std::size_t maximum_updates, const Rules &rules) -> GoldenSectionBracket
	Contract a unimodal bracket using the caller's numerical rules.

Variables
constexpr double	astro::toolbox::DEG_PER_RAD
	The number of degrees in a radian.
constexpr double	astro::toolbox::LONGITUDE_PERIOD_DEG
	The angular period of an ecliptic longitude, in degrees.
constexpr double	astro::toolbox::SIDEREAL_RATE_DEG_PER_DAY
	The mean angular rate of Earth's rotation relative to the stars, in degrees per day. Used to convert between time offsets and hour angle offsets.
constexpr double	astro::toolbox::SOLAR_MEAN_MOTION_DEG_PER_DAY
	The Sun's mean apparent motion along the ecliptic, in degrees per day. A tropical year of 365.2422 days carries it through a full 360°.
constexpr double	astro::toolbox::MOON_ELONGATION_RATE_DEG_PER_DAY
	The mean rate at which the Moon's apparent longitude pulls away from the Sun's, in degrees per day. A synodic month of 29.530588853 days closes a full 360°.
constexpr uint32_t	astro::toolbox::MIN_PER_DEG
	The number of minutes in a degree.
constexpr uint32_t	astro::toolbox::SEC_PER_MIN
	The number of seconds in a minute.
constexpr uint32_t	astro::toolbox::SEC_PER_DEG
	The number of seconds in a degree.
constexpr double	astro::toolbox::AU_KM_SCALE
	The scaling factor from AU to KM.
constexpr double	astro::toolbox::NEWTON_INITIAL_STEP_DAYS
	The initial half-width of the central difference approximating f', in days.
constexpr double	astro::toolbox::NEWTON_MIN_STEP_ULP
	The floor on that half-width, as a multiple of ulp(jde).
constexpr double	astro::toolbox::NEWTON_RESIDUAL_TOL_ULP
	The residual tolerance, as a multiple of the angle swept during one ulp(jde).
constexpr std::size_t	astro::toolbox::NEWTON_MAX_ITERATIONS
	The Newton iteration budget.
constexpr double	astro::toolbox::INV_PHI
	(√5 − 1)/2, rounded directly to binary64.
constexpr double	astro::toolbox::INV_PHI_SQ
	(3 − √5)/2, rounded independently of INV_PHI.