Classes
struct	RootGenerator
	Eager-by-one Moon-phase roots in JDE(TT); next refines the following root before returning. More...

Enumerations
enum class	NumericPolicy : uint8_t { CONJUNCTION , PHASE }
	The existing conjunction and principal-phase numerical conventions. More...

Functions
template<NumericPolicy POLICY>
auto	objective_at (const double diff, const double target_deg) -> double
	Map elongation to the Newton objective; conjunction uses its local near-360° unwrap.
template<NumericPolicy POLICY>
auto	miss_at (const double diff, const double target_deg) -> double
	Signed mean-rate miss; conjunction keeps +180°, principal phases fold it to -180°.
template<NumericPolicy POLICY>
auto	bracket_rejected (const double left_diff, const double right_diff, const double target_deg) -> bool
	Reject endpoints outside the policy's local branch.
template<NumericPolicy POLICY>
auto	reject_bracket (const double left_jde, const double left_diff, const double right_jde, const double right_diff, const double target_deg) -> void
	Report rejected endpoints using the policy's raw or folded elongations.
template<NumericPolicy POLICY>
auto	reject_estimate (const double jde, const double est_jde, const double miss_deg, const double elongation_deg, const double target_deg) -> void
	Report an estimate outside the refinement allowance without reevaluating positions.
template<NumericPolicy POLICY>
auto	reject_seed (const double jde, const double target_deg) -> void
	Report a candidate root time whose elongation misses the target by more than one degree.
template<NumericPolicy POLICY>
auto	newton_method (const double left_jde, const double right_jde, const double target_deg, const std::size_t iterations=toolbox::NEWTON_MAX_ITERATIONS) -> double
	Refine a root in [left_jde, right_jde), on the TT scale.
template<NumericPolicy POLICY>
auto	first_root_range_after (const double jde, const double target_deg) -> std::pair< double, double >
	Approximate the range of the first root after the given JDE for a target elongation.
template<NumericPolicy POLICY>
auto	next_root (const double jde, const double target_deg) -> double
	Find the next root after a known root for the same target elongation.
template<NumericPolicy POLICY>
auto	first_root_after (const double jde, const double target_deg) -> double
	Estimate, bracket and refine the first root after a JDE(TT).
template<NumericPolicy POLICY>
auto	roots_before (RootGenerator< POLICY > gen, const double end_jde) -> std::vector< double >
	Collect roots strictly before end_jde, testing each root only after next() advances.

Variables
constexpr double	BRACKET_TOLERANCE_DEG
	How near the target elongation a bracket endpoint must sit before Newton's method accepts it, in degrees.
constexpr double	ESTIMATE_TOLERANCE_DEG
	How far the mean-rate extrapolation may miss the root and still be worth refining, in degrees.
constexpr double	BRACKET_HALF_WIDTH_DAYS
	Half the width of the bracket handed to Newton's method, in days.

Enumeration Type Documentation

◆ NumericPolicy

enum class astro::moon_phase::detail::NumericPolicy : uint8_t

strong

The existing conjunction and principal-phase numerical conventions.

Enumerator
CONJUNCTION
PHASE

Function Documentation

◆ bracket_rejected()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::bracket_rejected	(	const double	left_diff,
		const double	right_diff,
		const double	target_deg )->bool

inlinenodiscard

Reject endpoints outside the policy's local branch.

Note: Only conjunction accepts a right endpoint whose elongation is exactly +0.0°.

◆ first_root_after()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::first_root_after	(	const double	jde,
		const double	target_deg )->double

inlinenodiscard

Estimate, bracket and refine the first root after a JDE(TT).

◆ first_root_range_after()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::first_root_range_after	(	const double	jde,
		const double	target_deg )->std::pair< double, double >

inlinenodiscard

Approximate the range of the first root after the given JDE for a target elongation.

Parameters

jde	The JDE on the TT scale.
target_deg	Zero for conjunction, a principal elongation otherwise.

Returns: The bracket [left, right) containing the first root after jde.

Exceptions

std::invalid_argument If the mean-rate estimate lands too far from the target.

◆ miss_at()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::miss_at	(	const double	diff,
		const double	target_deg )->double

inlinenodiscard

Signed mean-rate miss; conjunction keeps +180°, principal phases fold it to -180°.

◆ newton_method()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::newton_method	(	const double	left_jde,
		const double	right_jde,
		const double	target_deg,
		const std::size_t	iterations = toolbox::NEWTON_MAX_ITERATIONS )->double

inlinenodiscard

Refine a root in [left_jde, right_jde), on the TT scale.

Precondition: The endpoints bracket a root on the policy's continuous branch; conjunction has target 0°.

Parameters

iterations The Newton iteration cap; zero retains the bracket midpoint.

Exceptions

std::invalid_argument If the endpoints fail the policy's bracket check.

◆ next_root()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::next_root	(	const double	jde,
		const double	target_deg )->double

inlinenodiscard

Find the next root after a known root for the same target elongation.

Parameters

jde	The known root JDE.
target_deg	The target elongation, in degrees.

Returns: The next root JDE.

Exceptions

std::invalid_argument If jde is not a root for the target.

◆ objective_at()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::objective_at	(	const double	diff,
		const double	target_deg )->double

inlinenodiscard

Map elongation to the Newton objective; conjunction uses its local near-360° unwrap.

Note: Subtracting 360° only above 345° keeps the conjunction branch continuous near the root. It is not the principal phase's global [-180°, 180°) fold.

Precondition: diff is in [0°, 360°); target_deg is 0° for conjunction, a principal elongation otherwise.

◆ reject_bracket()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::reject_bracket	(	const double	left_jde,
		const double	left_diff,
		const double	right_jde,
		const double	right_diff,
		const double	target_deg )->void

inline

Report rejected endpoints using the policy's raw or folded elongations.

◆ reject_estimate()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::reject_estimate	(	const double	jde,
		const double	est_jde,
		const double	miss_deg,
		const double	elongation_deg,
		const double	target_deg )->void

inline

Report an estimate outside the refinement allowance without reevaluating positions.

◆ reject_seed()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::reject_seed	(	const double	jde,
		const double	target_deg )->void

inline

Report a candidate root time whose elongation misses the target by more than one degree.

◆ roots_before()

template<NumericPolicy POLICY>

auto astro::moon_phase::detail::roots_before	(	RootGenerator< POLICY >	gen,
		const double	end_jde )->std::vector< double >

inlinenodiscard

Collect roots strictly before end_jde, testing each root only after next() advances.

Variable Documentation

◆ BRACKET_HALF_WIDTH_DAYS

double astro::moon_phase::detail::BRACKET_HALF_WIDTH_DAYS

inlineconstexpr

Half the width of the bracket handed to Newton's method, in days.

Note: A 14.5°/day rate is about 19% above the 12.19°/day mean: correcting a 30° miss can leave about 30 / 12.19 * 0.19 = 0.47 day of timing error, below this half-width. Including that error, endpoints lie within about 0.47 + 0.5 = 0.97 day of the root: 0.97 * 14.5 ≈ 14.1°, still below the 15° endpoint tolerance.

◆ BRACKET_TOLERANCE_DEG

double astro::moon_phase::detail::BRACKET_TOLERANCE_DEG

inlineconstexpr

How near the target elongation a bracket endpoint must sit before Newton's method accepts it, in degrees.

◆ ESTIMATE_TOLERANCE_DEG

double astro::moon_phase::detail::ESTIMATE_TOLERANCE_DEG

inlineconstexpr

How far the mean-rate extrapolation may miss the root and still be worth refining, in degrees.

Classes

Enumerations

Functions

Variables

Enumeration Type Documentation

◆ NumericPolicy

Function Documentation

◆ bracket_rejected()

◆ first_root_after()

◆ first_root_range_after()

◆ miss_at()

◆ newton_method()

◆ next_root()

◆ objective_at()

◆ reject_bracket()

◆ reject_estimate()

◆ reject_seed()

◆ roots_before()

Variable Documentation

◆ BRACKET_HALF_WIDTH_DAYS

◆ BRACKET_TOLERANCE_DEG

◆ ESTIMATE_TOLERANCE_DEG