feat: 完善日月食与月掩几何链路并扩展历法接口

- 新增日月食中心带、偏食带、阴影足迹、等时线、食分线及升落边界计算，支持极区与混合食拓扑
- 新增日食单时刻阴影求解器、站心状态查询、批量采样和 ΔT 覆盖接口
- 重构恒星与行星月掩路径，补充有限盘面接触、站心修正、掩带宽度、极区投影及升落边界
- 扩展 SVG 与 GeoJSON 输出，支持详细面板、全球/极区/地球投影、边界闭合、时间标记和拓扑签名
- 扩展日月食候选搜索、局地搜索、沙罗序列预计算与范围外推，补充系列锚点和成员一致性校验
- 补齐古历纪年、儒略历独有闰日、多公历候选、历法改革跨日及精确日期运算接口
- 优化 ΔT、章动、恒星时、月球地平线、事件根搜索和本地星历缓存，降低重复计算开销并提升边界稳定

basic/nutation_memo.go

@@ -0,0 +1,75 @@
+package basic
+
+import (
+	"math"
+	"sync"
+	"sync/atomic"
+)
+
+// Nutation2000B 是 jd 的纯函数，但升落、星历与掩星路径会对同一批瞬时反复求值：一条计算链里
+// 地球自转、状态上下文与几何装配各自求一次同一个瞬时。这里用有界直接映射表记住结果：
+// 槽位固定、无分配、RWMutex 保证 c-shared 宿主多线程安全。章动只依赖传入的 jd，与 ΔT 世代无关。
+// Nutation2000B is a pure function of jd, yet the rise/set, ephemeris and occultation chains evaluate
+// it repeatedly for the same instants from independent code paths. This bounded direct-mapped memo
+// removes that redundancy with fixed slots, no allocation and an RWMutex for the c-shared host.
+// Nutation depends only on its argument, so no ΔT generation stamp is needed.
+const nutationMemoBits = 13
+
+const nutationMemoSize = 1 << nutationMemoBits
+
+type nutationMemoEntry struct {
+	// key 是 math.Float64bits(jd)+1，0 表示空槽（避免 jd=0 与空槽同码）。
+	key        uint64
+	dpsi, deps float64
+}
+
+var (
+	nutationMemoMu    sync.RWMutex
+	nutationMemoTable [nutationMemoSize]nutationMemoEntry
+	nutationMemoHits  uint64
+	nutationMemoMiss  uint64
+)
+
+func nutationMemoIndex(jd float64) uint64 {
+	bits := math.Float64bits(jd)
+	return (bits ^ (bits >> 31)) & (nutationMemoSize - 1)
+}
+
+func nutationMemoLoad(jd float64) (float64, float64, bool) {
+	key := math.Float64bits(jd) + 1
+	entry := &nutationMemoTable[nutationMemoIndex(jd)]
+	nutationMemoMu.RLock()
+	entryKey, dpsi, deps := entry.key, entry.dpsi, entry.deps
+	nutationMemoMu.RUnlock()
+	if key != 0 && entryKey == key {
+		atomic.AddUint64(&nutationMemoHits, 1)
+		return dpsi, deps, true
+	}
+	atomic.AddUint64(&nutationMemoMiss, 1)
+	return 0, 0, false
+}
+
+func nutationMemoStore(jd, dpsi, deps float64) {
+	key := math.Float64bits(jd) + 1
+	if key == 0 {
+		return
+	}
+	nutationMemoMu.Lock()
+	nutationMemoTable[nutationMemoIndex(jd)] = nutationMemoEntry{key: key, dpsi: dpsi, deps: deps}
+	nutationMemoMu.Unlock()
+}
+
+// nutationMemoStats 返回命中/未命中计数，供测试守护命中率。
+func nutationMemoStats() (uint64, uint64) {
+	return atomic.LoadUint64(&nutationMemoHits), atomic.LoadUint64(&nutationMemoMiss)
+}
+
+func resetNutationMemo() {
+	nutationMemoMu.Lock()
+	for i := range nutationMemoTable {
+		nutationMemoTable[i] = nutationMemoEntry{}
+	}
+	nutationMemoMu.Unlock()
+	atomic.StoreUint64(&nutationMemoHits, 0)
+	atomic.StoreUint64(&nutationMemoMiss, 0)
+}