feat: 引入可切换星历模型并扩展天象观测链路
- 新增半解析、旧模型、自定义与多源堆叠星历实例，提供 Context、Instance、SPK 读取及状态与视位置计算 - 统一太阳、月球和行星实例接口，扩展黄经穿越、留、相位、最近角距、偕日可见、任意高度升落、轨道节点及凌日等天象查询 - 完善日月食、月掩与凌日的月缘剖面、有限盘面接触、站心修正、局地可见性、全球路径和地图输出 - 新增 SVG、GeoJSON、KML 天象输出及凌日、月掩和月缘地形相关缓存与几何求解 - 新增恒星星表导入与查询，支持 CSV、Hipparcos、BSC5、Stellarium 等格式及名称、交叉标识、锥面检索和星等过滤 - 补充 IAU 2006、地球定向、折射消光、大气观测、轨道传播及半解析行星/月球数据支持 - 将默认未来民用时标切换为 TimeScaleLeapHour，更新 2027–2400 农历速查表、中文日期解析和时区边界处理 - 增加事件基线、跨模型回归、几何边界、月缘地形和输出契约测试，完善中英文手册、示例资源、NOTICE 与忽略规则
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package planets
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import (
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_ "embed"
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"sync"
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)
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// 现代段为 J2000 ± 1000 儒略年。
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const (
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ModernStart = 2086295.0
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ModernEnd = 2816795.0
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)
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var (
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//go:embed long.bin
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longTable []byte
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//go:embed modern.bin
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modernTable []byte
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)
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var (
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defaultOnce sync.Once
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defaultModel *Model
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)
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// Default 内置长时段表叠加现代段，首次调用时解析 / built-in long-range plus modern tables, parsed on first use.
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func Default() *Model {
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defaultOnce.Do(func() {
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m, err := Parse(longTable)
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if err == nil {
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err = m.WithModernSegment(modernTable, ModernStart, ModernEnd)
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}
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if err != nil {
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panic(err)
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}
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defaultModel = m
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})
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return defaultModel
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}
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// GM 天体号 1..8 的 GM 与太阳 GM，au³/日²；EMB 为地月合计，越界返回 0 / GM of body id and of the Sun, au³/day².
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func GM(id int) (body, sun float64) {
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if id < 1 || id > 8 {
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return 0, gmSol
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}
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return gmp[id-1], gmSol
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}
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//go:embed fast.bin
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var fastTable []byte
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var (
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fastOnce sync.Once
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fastModel *Model
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)
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// Fast 快速档表（n ≥ 0 用），首次调用时解析 / the fast-tier table used for n ≥ 0, parsed on first use.
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func Fast() *Model {
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fastOnce.Do(func() {
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m, err := Parse(fastTable)
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if err != nil {
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panic(err)
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}
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fastModel = m
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})
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return fastModel
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}
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// Package planets 行星半解析级数运行时（PLN1/PLN2/PLN3 表，日心，J2000 平黄道）。
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package planets
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import (
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"encoding/binary"
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"errors"
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"math"
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"sync"
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)
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const (
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j2000 = 2451545.0
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millennium = 365250.0
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blendDays = 36525.0
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auKM = 149597870.691
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tMid = -2.0
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tHalf = 10.0
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emrat = 81.3005682214972
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gmSol = 2.9591220836841438269e-04
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maxDeg = 24
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)
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// Body 编号 / body id；3 为地月质心。
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const (
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Mercury = 1
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Venus = 2
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EMB = 3
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Mars = 4
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Jupiter = 5
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Saturn = 6
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Uranus = 7
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Neptune = 8
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)
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var ci0 = [17]float64{4.402608631669, 3.176134461576, 1.753470369433, 6.203500014141, 4.091360003050,
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1.713740719173, 5.598641292287, 2.805136360408, 2.326989734620, 0.5995461070350,
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0.8740185101070, 5.481225395663, 5.311897933164, 0.0, 5.19846640063,
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1.62790513602, 2.35555563875}
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var ci1 = [17]float64{26087.90314068555, 10213.28554743445, 6283.075850353215, 3340.612434145457,
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1731.170452721855, 1704.450855027201, 1428.948917844273, 1364.756513629990,
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1361.923207632842, 529.6909615623250, 213.2990861084880, 74.78165903077800,
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38.13297222612500, 0.3595362285049309, 77713.7714481804, 84334.6615717837,
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83286.9142477147}
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var gmp = [8]float64{4.9125474514508118699e-11, 7.2434524861627027000e-10, 8.9970116036316091182e-10,
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9.5495351057792580598e-11, 2.8253458420837780000e-07, 8.4597151856806587398e-08,
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1.2920249167819693900e-08, 1.5243589007842762800e-08}
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// topDMu 必须逐步按 float64 舍入（与 Python 参考求值一致），不能写成常量表达式。
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var topDMu = func() float64 {
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f0, f1, d := 529.6909622785881, 213.2990811942489, 880.0
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return (f0 - f1) / d
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}()
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// skyToVSOP skyfield ecliptic_J2000 → VSOP2013 动力学黄道；求值时用其转置。
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var skyToVSOP = func() [3][3]float64 {
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as := 180 / math.Pi * 3600
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return mul(transpose(mul(rz(-0.05188/as), rx(84381.41136/as))), rx(84381.448/as))
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}()
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// element 的项按包络阶降序排列，第 d 阶只覆盖前 cnt[d] 项。
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type element struct {
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secular []float64
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arg []int32
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cnt []int
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c, s [][]float64
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}
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const (
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maxKeys = 8192
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maxTab = 512
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topBits = 6
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// 超出此值的幅角乘数必然撑破幂表，先在 int64 下拒绝，保证转 int 不溢出。
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maxKeyAbs = maxTab << (2 * topBits)
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)
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var errBadKey = errors.New("planets: argument multiplier out of range")
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// factor 幂表槽位；neg 表示取共轭。
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type factor struct {
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slot int32
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neg bool
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}
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type body struct {
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top bool
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f, l0 float64
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rgm float64
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// 幂表：VSOP 每个基本幅角一段，TOP 每个 6 位数字层一段
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tabMax [17]int
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tabOff [17]int
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keyOff []int32
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factors []factor
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keyNeg []bool
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el [6]element
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// legDeg 长期项与包络用到的最高 Legendre 阶。
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legDeg int
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}
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// Model 已解析的 PLN1 表，只读、可并发求值 / parsed PLN1 table, safe for concurrent use.
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type Model struct {
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bodies [9]*body
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modernBodies [9]*body
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modernStart float64
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modernEnd float64
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}
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type reader struct {
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b []byte
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p int
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err error
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}
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func (r *reader) take(n int) []byte {
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if r.err != nil || r.p+n > len(r.b) {
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r.err = errors.New("planets: truncated table")
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return make([]byte, n)
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}
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s := r.b[r.p : r.p+n]
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r.p += n
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return s
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}
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func (r *reader) u8() uint8 { return r.take(1)[0] }
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func (r *reader) f64() float64 { return math.Float64frombits(binary.LittleEndian.Uint64(r.take(8))) }
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func (r *reader) f32() float32 { return math.Float32frombits(binary.LittleEndian.Uint32(r.take(4))) }
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func (r *reader) uvar() uint64 {
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n, shift := uint64(0), uint(0)
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for {
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c := r.u8()
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n |= uint64(c&0x7F) << shift
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shift += 7
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if c < 0x80 || r.err != nil || shift > 56 {
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return n
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}
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}
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}
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func (r *reader) zvar() int64 {
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z := r.uvar()
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if z%2 == 0 {
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return int64(z >> 1)
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}
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return -int64(z>>1) - 1
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}
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// Parse 解析 PLN1 表 / parse a PLN1 table.
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func Parse(b []byte) (*Model, error) {
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bodies, err := parseBodies(b)
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if err != nil {
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return nil, err
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}
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return &Model{bodies: bodies}, nil
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}
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// WithModernSegment 为长时段表叠加现代段表，[jdStart, jdEnd] 内优先使用 / add a modern-era segment used inside [jdStart, jdEnd].
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func (m *Model) WithModernSegment(b []byte, jdStart, jdEnd float64) error {
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bodies, err := parseBodies(b)
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if err != nil {
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return err
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}
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m.modernBodies, m.modernStart, m.modernEnd = bodies, jdStart, jdEnd
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return nil
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}
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func parseBodies(b []byte) (bodies [9]*body, err error) {
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r := &reader{b: b}
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magic := string(r.take(4))
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if magic != "PLN1" && magic != "PLN2" && magic != "PLN3" {
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return bodies, errors.New("planets: bad magic")
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}
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quant, packed := magic == "PLN2", magic == "PLN3"
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for n := int(r.u8()); n > 0 && r.err == nil; n-- {
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id := int(r.u8())
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if id < 1 || id > 8 {
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return bodies, errors.New("planets: bad body id")
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}
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bd := &body{top: r.u8() != 0}
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secDeg := int(r.u8())
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bd.f, bd.l0 = r.f64(), r.f64()
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bd.rgm = math.Sqrt(gmp[id-1] + gmSol)
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nk := r.uvar()
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if nk > maxKeys {
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return bodies, errors.New("planets: too many arguments")
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}
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if err := readKeys(r, bd, int(nk)); err != nil {
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return bodies, err
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}
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bd.legDeg = secDeg
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sortedArgs := packed && r.u8() != 0
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for v := range bd.el {
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var err error
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if packed {
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err = readElement3(r, &bd.el[v], secDeg, int(nk), sortedArgs)
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} else {
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err = readElement(r, &bd.el[v], secDeg, int(nk), quant)
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}
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if err != nil {
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return bodies, err
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}
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if d := len(bd.el[v].cnt) - 1; d > bd.legDeg {
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bd.legDeg = d
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}
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}
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bodies[id] = bd
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}
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if r.err != nil {
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return bodies, r.err
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}
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if r.p != len(b) {
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return bodies, errors.New("planets: trailing bytes")
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}
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return bodies, nil
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}
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// readKeys 把整数幅角拆成幂表槽位：VSOP 按基本幅角升序，TOP 按 6 位数字层由低到高。
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func readKeys(r *reader, bd *body, nk int) error {
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type raw struct{ fund, k int }
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keys := make([][]raw, nk)
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bd.keyNeg = make([]bool, nk)
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for j := 0; j < nk && r.err == nil; j++ {
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if bd.top {
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k := r.zvar()
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if k > maxKeyAbs || k < -maxKeyAbs {
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return errBadKey
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}
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a := int(k)
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if a < 0 {
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a, bd.keyNeg[j] = -a, true
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}
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for lvl := 0; lvl < 3; lvl++ {
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d := a >> uint(topBits*lvl)
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if lvl < 2 {
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d &= 1<<topBits - 1
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}
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keys[j] = append(keys[j], raw{lvl, d})
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}
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continue
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}
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mb := r.take(3)
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mask := int(mb[0]) | int(mb[1])<<8 | int(mb[2])<<16
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for i := 0; i < 17; i++ {
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if mask>>uint(i)&1 != 0 {
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k := r.zvar()
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if k > maxKeyAbs || k < -maxKeyAbs {
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return errBadKey
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}
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keys[j] = append(keys[j], raw{i, int(k)})
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}
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}
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}
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if r.err != nil {
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return r.err
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}
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for _, ks := range keys {
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for _, f := range ks {
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a := f.k
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if a < 0 {
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a = -a
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}
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if a > bd.tabMax[f.fund] {
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bd.tabMax[f.fund] = a
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}
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}
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}
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n := 0
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for i := range bd.tabMax {
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bd.tabOff[i] = n
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if bd.tabMax[i] > 0 || (bd.top && i < 3) {
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n += bd.tabMax[i] + 1
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}
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}
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if n > maxTab {
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return errors.New("planets: power table too large")
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}
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bd.keyOff = make([]int32, nk+1)
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for j, ks := range keys {
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for _, f := range ks {
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a, neg := f.k, false
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if a < 0 {
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a, neg = -a, true
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}
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if !bd.top && a == 0 {
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continue
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}
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bd.factors = append(bd.factors, factor{int32(bd.tabOff[f.fund] + a), neg})
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}
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bd.keyOff[j+1] = int32(len(bd.factors))
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}
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return nil
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}
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|
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// readElement 把文件里按包络阶分块的列序重排为逐项连续；quant 为 PLN2 整数量化系数。
|
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func readElement(r *reader, e *element, secDeg, nk int, quant bool) error {
|
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if secDeg > maxDeg {
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return errors.New("planets: secular degree too high")
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}
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n64 := r.uvar()
|
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if n64 > uint64(nk) {
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return errors.New("planets: too many terms")
|
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}
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nint := int(n64)
|
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e.secular = make([]float64, secDeg+1)
|
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for i := range e.secular {
|
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e.secular[i] = r.f64()
|
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}
|
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args, env := make([]int32, nint), make([]int, nint)
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top := 0
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for j := 0; j < nint; j++ {
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a := r.uvar()
|
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if a >= uint64(nk) {
|
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return errors.New("planets: argument index out of range")
|
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}
|
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args[j], env[j] = int32(a), int(r.u8())
|
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if env[j] > maxDeg {
|
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return errors.New("planets: envelope degree too high")
|
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}
|
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if env[j] > top {
|
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top = env[j]
|
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}
|
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}
|
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// 按包络阶降序的稳定排序：pos[j] 为文件第 j 项的新位置
|
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pos := make([]int, nint)
|
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e.arg = make([]int32, nint)
|
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k := 0
|
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for d := top; d >= 0; d-- {
|
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for j := 0; j < nint; j++ {
|
||||
if env[j] == d {
|
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pos[j], e.arg[k] = k, args[j]
|
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k++
|
||||
}
|
||||
}
|
||||
}
|
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coef := func() float64 { return float64(r.f32()) }
|
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if quant {
|
||||
step := r.f64()
|
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coef = func() float64 { return float64(r.zvar()) * step }
|
||||
}
|
||||
if nint == 0 {
|
||||
return r.err
|
||||
}
|
||||
e.cnt = make([]int, top+1)
|
||||
e.c, e.s = make([][]float64, top+1), make([][]float64, top+1)
|
||||
for d := 0; d <= top; d++ {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] >= d {
|
||||
e.cnt[d]++
|
||||
}
|
||||
}
|
||||
e.c[d], e.s[d] = make([]float64, e.cnt[d]), make([]float64, e.cnt[d])
|
||||
for _, dst := range [][]float64{e.c[d], e.s[d]} {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] >= d {
|
||||
dst[pos[j]] = coef()
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return r.err
|
||||
}
|
||||
|
||||
// Heliocentric 日心位置，km，J2000 平黄道 / heliocentric position, km, mean ecliptic J2000.
|
||||
func (m *Model) Heliocentric(id int, jdTDB float64) ([3]float64, error) {
|
||||
pos, _, err := m.state(id, jdTDB, false)
|
||||
return pos, err
|
||||
}
|
||||
|
||||
// HeliocentricState 日心位置（km）与密切速度（km/日），J2000 平黄道 / heliocentric position and osculating velocity.
|
||||
func (m *Model) HeliocentricState(id int, jdTDB float64) (pos, vel [3]float64, err error) {
|
||||
return m.state(id, jdTDB, true)
|
||||
}
|
||||
|
||||
// state wantVel 为 false 时 vel 不计算、恒为零。
|
||||
func (m *Model) state(id int, jdTDB float64, wantVel bool) (pos, vel [3]float64, err error) {
|
||||
if id < 1 || id > 8 {
|
||||
return pos, vel, errors.New("planets: body not in table")
|
||||
}
|
||||
bd := m.bodies[id]
|
||||
if bd == nil {
|
||||
return pos, vel, errors.New("planets: body not in table")
|
||||
}
|
||||
t := (jdTDB - j2000) / millennium
|
||||
md := m.modernBodies[id]
|
||||
sky := func(p, v [3]float64) ([3]float64, [3]float64, error) {
|
||||
if !wantVel {
|
||||
return toSky(p), v, nil
|
||||
}
|
||||
return toSky(p), toSky(v), nil
|
||||
}
|
||||
if md == nil || jdTDB <= m.modernStart || jdTDB >= m.modernEnd {
|
||||
p, v := bd.ellxyz(bd.elements(t), wantVel)
|
||||
return sky(p, v)
|
||||
}
|
||||
w, dw := m.modernWeight(jdTDB)
|
||||
pm, vm := md.ellxyz(md.elements(t), wantVel)
|
||||
if w == 1 {
|
||||
return sky(pm, vm)
|
||||
}
|
||||
pl, vl := bd.ellxyz(bd.elements(t), wantVel)
|
||||
for i := range pos {
|
||||
pos[i] = pl[i] + w*(pm[i]-pl[i])
|
||||
if wantVel {
|
||||
vel[i] = vl[i] + w*(vm[i]-vl[i]) + dw*(pm[i]-pl[i])
|
||||
}
|
||||
}
|
||||
return sky(pos, vel)
|
||||
}
|
||||
|
||||
// modernWeight 现代段权重及其对 JD 的导数；两端各 blendDays 内用 smoothstep 过渡，位置与速度均连续。
|
||||
func (m *Model) modernWeight(jd float64) (w, dw float64) {
|
||||
u, sign := (jd-m.modernStart)/blendDays, 1.0
|
||||
if e := (m.modernEnd - jd) / blendDays; e < u {
|
||||
u, sign = e, -1
|
||||
}
|
||||
if u >= 1 {
|
||||
return 1, 0
|
||||
}
|
||||
return u * u * (3 - 2*u), sign * 6 * u * (1 - u) / blendDays
|
||||
}
|
||||
|
||||
// toSky 动力学黄道 au → skyfield ecliptic_J2000 km。
|
||||
func toSky(p [3]float64) (out [3]float64) {
|
||||
for i := range out {
|
||||
out[i] = (skyToVSOP[0][i]*p[0] + skyToVSOP[1][i]*p[1] + skyToVSOP[2][i]*p[2]) * auKM
|
||||
}
|
||||
return out
|
||||
}
|
||||
|
||||
// cmul 显式转换阻止编译器融合乘加，保证与 Python 参考求值逐位一致。
|
||||
func cmul(ar, ai, br, bi float64) (float64, float64) {
|
||||
return float64(ar*br) - float64(ai*bi), float64(ar*bi) + float64(ai*br)
|
||||
}
|
||||
|
||||
// phasors 填充每个幅角的 (cos, sin)。
|
||||
// tc、ts 为倍角表工作区，只读取本次写入的槽位，复用时不必清零。
|
||||
func (bd *body) phasors(t float64, pc, ps, tc, ts []float64) {
|
||||
for i := range bd.tabMax {
|
||||
if bd.tabMax[i] == 0 && !(bd.top && i < 3) {
|
||||
continue
|
||||
}
|
||||
var s, c float64
|
||||
if bd.top {
|
||||
s, c = math.Sincos(topDMu * t * float64(int(1)<<uint(topBits*i)))
|
||||
} else {
|
||||
s, c = math.Sincos(ci0[i] + ci1[i]*t)
|
||||
}
|
||||
o := bd.tabOff[i]
|
||||
tc[o], ts[o] = 1, 0
|
||||
for j := 1; j <= bd.tabMax[i]; j++ {
|
||||
tc[o+j], ts[o+j] = cmul(tc[o+j-1], ts[o+j-1], c, s)
|
||||
}
|
||||
if bd.top && i == 2 {
|
||||
break
|
||||
}
|
||||
}
|
||||
for j := 0; j+1 < len(bd.keyOff); j++ {
|
||||
fs := bd.factors[bd.keyOff[j]:bd.keyOff[j+1]]
|
||||
r, im := 1.0, 0.0
|
||||
if len(fs) > 0 {
|
||||
r, im = tc[fs[0].slot], ts[fs[0].slot]
|
||||
if fs[0].neg {
|
||||
im = -im
|
||||
}
|
||||
fs = fs[1:]
|
||||
}
|
||||
for _, f := range fs {
|
||||
br, bi := tc[f.slot], ts[f.slot]
|
||||
if f.neg {
|
||||
bi = -bi
|
||||
}
|
||||
r, im = cmul(r, im, br, bi)
|
||||
}
|
||||
if bd.keyNeg[j] {
|
||||
im = -im
|
||||
}
|
||||
pc[j], ps[j] = r, im
|
||||
}
|
||||
}
|
||||
|
||||
type scratch struct{ buf []float64 }
|
||||
|
||||
var scratchPool = sync.Pool{New: func() interface{} { return new(scratch) }}
|
||||
|
||||
// elements t 为 TDB 千年（J2000 起算）。
|
||||
func (bd *body) elements(t float64) [6]float64 {
|
||||
x := (t - tMid) / tHalf
|
||||
var leg [maxDeg + 1]float64
|
||||
leg[0], leg[1] = 1, x
|
||||
for k := 2; k <= bd.legDeg; k++ {
|
||||
leg[k] = (leg[k-1]*x*float64(2*k-1) - leg[k-2]*float64(k-1)) / float64(k)
|
||||
}
|
||||
nk := len(bd.keyNeg)
|
||||
sc := scratchPool.Get().(*scratch)
|
||||
defer scratchPool.Put(sc)
|
||||
if cap(sc.buf) < 2*nk+2*maxTab {
|
||||
sc.buf = make([]float64, 2*nk+2*maxTab)
|
||||
}
|
||||
// 各段在读取前都会被完整写入，复用时不必清零。
|
||||
buf := sc.buf[:2*nk+2*maxTab]
|
||||
pc, ps := buf[:nk], buf[nk:2*nk]
|
||||
bd.phasors(t, pc, ps, buf[2*nk:2*nk+maxTab], buf[2*nk+maxTab:])
|
||||
var el [6]float64
|
||||
for v := range bd.el {
|
||||
e := &bd.el[v]
|
||||
sum := 0.0
|
||||
for i, c := range e.secular {
|
||||
sum += c * leg[i]
|
||||
}
|
||||
// 逐阶做点积再乘 Legendre 值，避免逐项累加包络系数的读改写。
|
||||
for d := range e.cnt {
|
||||
cd, sd := e.c[d], e.s[d]
|
||||
arg := e.arg[:len(cd)]
|
||||
s0, s1 := 0.0, 0.0
|
||||
for i, a := range arg {
|
||||
s0 += cd[i] * pc[a]
|
||||
s1 += sd[i] * ps[a]
|
||||
}
|
||||
sum += leg[d] * (s0 + s1)
|
||||
}
|
||||
el[v] = sum
|
||||
}
|
||||
// 先归约平经度再加周期和，与 Python 参考求值一致。
|
||||
lm := math.Mod(bd.l0+bd.f*t, 2*math.Pi)
|
||||
if lm < 0 {
|
||||
lm += 2 * math.Pi
|
||||
}
|
||||
el[1] += lm
|
||||
return el
|
||||
}
|
||||
|
||||
// EarthFromEMB 由地月质心与地心月球合成物理地心 / Earth centre from EMB and geocentric Moon.
|
||||
func EarthFromEMB(emb, moon [3]float64) [3]float64 {
|
||||
k := 1 / (1 + emrat)
|
||||
return [3]float64{emb[0] - moon[0]*k, emb[1] - moon[1]*k, emb[2] - moon[2]*k}
|
||||
}
|
||||
|
||||
// ellxyz VSOP2013 椭圆元件 (a,l,k,h,q,p) → 动力学黄道位置（au）与速度（au/日）。
|
||||
func (bd *body) ellxyz(el [6]float64, wantVel bool) (pos, vel [3]float64) {
|
||||
a, l, k, h, q, p := el[0], el[1], el[2], el[3], el[4], el[5]
|
||||
fi := math.Sqrt(1 - k*k - h*h)
|
||||
ki := math.Sqrt(1 - q*q - p*p)
|
||||
u := 1 / (1 + fi)
|
||||
ex := math.Hypot(k, h)
|
||||
gl := math.Mod(l, 2*math.Pi)
|
||||
if gl < 0 {
|
||||
gl += 2 * math.Pi
|
||||
}
|
||||
gm := gl - math.Atan2(h, k)
|
||||
e := gl + (ex-0.125*ex*ex*ex)*math.Sin(gm) + 0.5*ex*ex*math.Sin(2*gm) + 0.375*ex*ex*ex*math.Sin(3*gm)
|
||||
var zs, zc float64
|
||||
for it := 0; it < 20; it++ {
|
||||
zs, zc = math.Sincos(e)
|
||||
z3r, z3i := k*zc+h*zs, k*zs-h*zc
|
||||
dl := gl - e + z3i
|
||||
e += dl / (1 - z3r)
|
||||
if math.Abs(dl) < 1e-15 {
|
||||
break
|
||||
}
|
||||
}
|
||||
zs, zc = math.Sincos(e)
|
||||
z3r, z3i := k*zc+h*zs, k*zs-h*zc
|
||||
rsa := 1 - z3r
|
||||
z1r, z1i := u*k*z3i, u*h*z3i
|
||||
z2r, z2i := z1i, -z1r
|
||||
xcw := (-k + zc + z2r) / rsa
|
||||
xsw := (-h + zs + z2i) / rsa
|
||||
xm := p*xcw - q*xsw
|
||||
xr := a * rsa
|
||||
pos = [3]float64{xr * (xcw - 2*p*xm), xr * (xsw + 2*q*xm), -2 * xr * ki * xm}
|
||||
if !wantVel {
|
||||
return pos, vel
|
||||
}
|
||||
xms := a * (h + xsw) / fi
|
||||
xmc := a * (k + xcw) / fi
|
||||
xn := bd.rgm / math.Pow(a, 1.5)
|
||||
vel = [3]float64{xn * ((2*p*p-1)*xms + 2*p*q*xmc), xn * ((1-2*q*q)*xmc - 2*p*q*xms), 2 * xn * ki * (p*xms + q*xmc)}
|
||||
return pos, vel
|
||||
}
|
||||
|
||||
func rx(a float64) [3][3]float64 {
|
||||
s, c := math.Sincos(a)
|
||||
return [3][3]float64{{1, 0, 0}, {0, c, -s}, {0, s, c}}
|
||||
}
|
||||
|
||||
func rz(a float64) [3][3]float64 {
|
||||
s, c := math.Sincos(a)
|
||||
return [3][3]float64{{c, -s, 0}, {s, c, 0}, {0, 0, 1}}
|
||||
}
|
||||
|
||||
func mul(a, b [3][3]float64) (out [3][3]float64) {
|
||||
for i := 0; i < 3; i++ {
|
||||
for j := 0; j < 3; j++ {
|
||||
for k := 0; k < 3; k++ {
|
||||
out[i][j] += a[i][k] * b[k][j]
|
||||
}
|
||||
}
|
||||
}
|
||||
return out
|
||||
}
|
||||
|
||||
func transpose(a [3][3]float64) (out [3][3]float64) {
|
||||
for i := 0; i < 3; i++ {
|
||||
for j := 0; j < 3; j++ {
|
||||
out[i][j] = a[j][i]
|
||||
}
|
||||
}
|
||||
return out
|
||||
}
|
||||
@@ -0,0 +1,166 @@
|
||||
// 被测契约：内置表与参考向量一致（< 10 cm），现代段区间外回落长时段表，接缝连续，可并发求值。
|
||||
package planets
|
||||
|
||||
import (
|
||||
"bufio"
|
||||
"math"
|
||||
"os"
|
||||
"strconv"
|
||||
"strings"
|
||||
"sync"
|
||||
"testing"
|
||||
)
|
||||
|
||||
func sq(x float64) float64 { return x * x }
|
||||
|
||||
func longOnly(t *testing.T) *Model {
|
||||
m, err := Parse(longTable)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
return m
|
||||
}
|
||||
|
||||
func checkVectors(t *testing.T, m *Model, path string) {
|
||||
f, err := os.Open(path)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
defer f.Close()
|
||||
n := 0
|
||||
sc := bufio.NewScanner(f)
|
||||
for sc.Scan() {
|
||||
parts := strings.Split(sc.Text(), ",")
|
||||
var v [8]float64
|
||||
for i := range v {
|
||||
if v[i], err = strconv.ParseFloat(parts[i], 64); err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
}
|
||||
id := int(v[0])
|
||||
p, vel, err := m.HeliocentricState(id, v[1])
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
d := math.Sqrt(sq(p[0]-v[2]) + sq(p[1]-v[3]) + sq(p[2]-v[4]))
|
||||
dv := math.Sqrt(sq(vel[0]-v[5]) + sq(vel[1]-v[6]) + sq(vel[2]-v[7]))
|
||||
if !(d <= 1e-4 && dv <= 1e-6) {
|
||||
t.Errorf("body %d jd %.1f: %.3e km, %.3e km/day", id, v[1], d, dv)
|
||||
}
|
||||
n++
|
||||
}
|
||||
if n < 100 {
|
||||
t.Fatalf("only %d vectors", n)
|
||||
}
|
||||
}
|
||||
|
||||
func TestLongTableMatchesReference(t *testing.T) {
|
||||
checkVectors(t, longOnly(t), "testdata/long.csv")
|
||||
}
|
||||
|
||||
func TestModernSegmentMatchesReference(t *testing.T) {
|
||||
checkVectors(t, Default(), "testdata/modern.csv")
|
||||
}
|
||||
|
||||
func TestFastTableMatchesReference(t *testing.T) {
|
||||
checkVectors(t, Fast(), "testdata/fast.csv")
|
||||
}
|
||||
|
||||
func TestFallsBackOutsideModern(t *testing.T) {
|
||||
long, dual := longOnly(t), Default()
|
||||
for _, jd := range []float64{ModernStart, ModernEnd, ModernStart - 1, ModernEnd + 1, 625000.5, 5000000.5} {
|
||||
for id := 1; id <= 8; id++ {
|
||||
a, _ := long.Heliocentric(id, jd)
|
||||
b, _ := dual.Heliocentric(id, jd)
|
||||
if a != b {
|
||||
t.Errorf("body %d jd %.1f: did not fall back to long table", id, jd)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestSeamContinuous(t *testing.T) {
|
||||
m := Default()
|
||||
const h = 0.5
|
||||
for _, jd := range []float64{ModernStart, ModernEnd, ModernStart + blendDays/2, ModernEnd - blendDays/2} {
|
||||
for id := 1; id <= 8; id++ {
|
||||
a, _ := m.Heliocentric(id, jd-h)
|
||||
b, _ := m.Heliocentric(id, jd+h)
|
||||
_, v, _ := m.HeliocentricState(id, jd)
|
||||
var d, vn float64
|
||||
for i := range v {
|
||||
d += sq((b[i]-a[i])/(2*h) - v[i])
|
||||
vn += sq(v[i])
|
||||
}
|
||||
if d, vn = math.Sqrt(d), math.Sqrt(vn); d > 1e-3*vn {
|
||||
t.Errorf("body %d jd %.1f: velocity differs from finite difference by %.3f of %.0f km/day", id, jd, d, vn)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestParseRejectsTruncated(t *testing.T) {
|
||||
for _, b := range [][]byte{longTable, modernTable} {
|
||||
for _, n := range []int{0, 3, 5, 40, len(b) / 2, len(b) - 1} {
|
||||
if _, err := Parse(b[:n]); err == nil {
|
||||
t.Errorf("len %d: expected error", n)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestConcurrentMatchesSerial(t *testing.T) {
|
||||
m := Default()
|
||||
const n = 64
|
||||
var want [n][3]float64
|
||||
for i := range want {
|
||||
want[i], _ = m.Heliocentric(1+i%8, 2451545.0+float64(i)*977.3)
|
||||
}
|
||||
var wg sync.WaitGroup
|
||||
var bad [8]bool
|
||||
for g := 0; g < 8; g++ {
|
||||
wg.Add(1)
|
||||
go func(g int) {
|
||||
defer wg.Done()
|
||||
for i := 0; i < n; i++ {
|
||||
if got, _ := m.Heliocentric(1+i%8, 2451545.0+float64(i)*977.3); got != want[i] {
|
||||
bad[g] = true
|
||||
}
|
||||
}
|
||||
}(g)
|
||||
}
|
||||
wg.Wait()
|
||||
for g, b := range bad {
|
||||
if b {
|
||||
t.Fatalf("goroutine %d saw a mismatch", g)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkHeliocentricState(b *testing.B) {
|
||||
m := Default()
|
||||
for id := 1; id <= 8; id++ {
|
||||
id := id
|
||||
b.Run(strconv.Itoa(id), func(b *testing.B) {
|
||||
for i := 0; i < b.N; i++ {
|
||||
m.HeliocentricState(id, 2378496.0+float64(i%14610)*10)
|
||||
}
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
func TestZigzagDecodeBeyond32Bits(t *testing.T) {
|
||||
for _, want := range []int64{0, -1, 1, 1<<31 - 1, -1 << 31, 1 << 40, -(1 << 40) - 7, 1<<55 + 3} {
|
||||
z := uint64(want<<1) ^ uint64(want>>63)
|
||||
var b []byte
|
||||
for z >= 0x80 {
|
||||
b = append(b, byte(z)|0x80)
|
||||
z >>= 7
|
||||
}
|
||||
b = append(b, byte(z))
|
||||
r := &reader{b: b}
|
||||
if got := r.zvar(); got != want || r.err != nil || r.p != len(b) {
|
||||
t.Errorf("zvar(%d) = %d, err %v, read %d/%d", want, got, r.err, r.p, len(b))
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,193 @@
|
||||
package planets
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"errors"
|
||||
"math/bits"
|
||||
)
|
||||
|
||||
// bitReader 按位读取，字节内高位在前。
|
||||
type bitReader struct {
|
||||
b []byte
|
||||
p int // 位位置
|
||||
err error
|
||||
}
|
||||
|
||||
// window 返回从当前位开始的 64 位窗口（高位对齐，越界补零），有效位至少 57 位。
|
||||
func (br *bitReader) window() uint64 {
|
||||
i := br.p >> 3
|
||||
var w uint64
|
||||
if i+8 <= len(br.b) {
|
||||
w = binary.BigEndian.Uint64(br.b[i:])
|
||||
} else {
|
||||
for k := 0; k < 8; k++ {
|
||||
w <<= 8
|
||||
if i+k < len(br.b) {
|
||||
w |= uint64(br.b[i+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
return w << uint(br.p&7)
|
||||
}
|
||||
|
||||
func (br *bitReader) skip(n int) {
|
||||
br.p += n
|
||||
if br.p > 8*len(br.b) {
|
||||
br.err = errors.New("planets: truncated bit stream")
|
||||
}
|
||||
}
|
||||
|
||||
func (br *bitReader) get(n int) uint64 {
|
||||
if n == 0 || br.err != nil {
|
||||
return 0
|
||||
}
|
||||
if n > 56 {
|
||||
hi := br.get(n - 32)
|
||||
return hi<<32 | br.get(32)
|
||||
}
|
||||
v := br.window() >> uint(64-n)
|
||||
br.skip(n)
|
||||
return v
|
||||
}
|
||||
|
||||
// gamma Elias-gamma，编码值为 n+1。
|
||||
func (br *bitReader) gamma() int {
|
||||
if br.err != nil {
|
||||
return 0
|
||||
}
|
||||
z := bits.LeadingZeros64(br.window())
|
||||
if z > 28 {
|
||||
br.err = errors.New("planets: bad gamma code")
|
||||
return 0
|
||||
}
|
||||
v := br.get(2*z + 1)
|
||||
return int(v) - 1
|
||||
}
|
||||
|
||||
func unzigzag(z int) int {
|
||||
if z&1 == 0 {
|
||||
return z >> 1
|
||||
}
|
||||
return -(z >> 1) - 1
|
||||
}
|
||||
|
||||
// readElement3 读取 PLN3 元件位流：包络游程、幅角号（定长或同阶升序间隔）、成对共享位宽的量化系数。
|
||||
func readElement3(r *reader, e *element, secDeg, nk int, sortedArgs bool) error {
|
||||
if secDeg > maxDeg {
|
||||
return errors.New("planets: secular degree too high")
|
||||
}
|
||||
n64 := r.uvar()
|
||||
if n64 > uint64(nk) {
|
||||
return errors.New("planets: too many terms")
|
||||
}
|
||||
nint := int(n64)
|
||||
e.secular = make([]float64, secDeg+1)
|
||||
for i := range e.secular {
|
||||
e.secular[i] = r.f64()
|
||||
}
|
||||
step := r.f64()
|
||||
size := r.uvar()
|
||||
if r.err != nil {
|
||||
return r.err
|
||||
}
|
||||
if size > uint64(len(r.b)-r.p) {
|
||||
return errors.New("planets: truncated table")
|
||||
}
|
||||
br := &bitReader{b: r.take(int(size))}
|
||||
if r.err != nil {
|
||||
return r.err
|
||||
}
|
||||
env := make([]int, 0, nint)
|
||||
for runs := br.gamma(); runs > 0 && br.err == nil; runs-- {
|
||||
d := int(br.get(4))
|
||||
cnt := br.gamma() + 1
|
||||
if d > maxDeg || len(env)+cnt > nint {
|
||||
return errors.New("planets: bad envelope runs")
|
||||
}
|
||||
for ; cnt > 0; cnt-- {
|
||||
env = append(env, d)
|
||||
}
|
||||
}
|
||||
if br.err != nil {
|
||||
return br.err
|
||||
}
|
||||
if len(env) != nint {
|
||||
return errors.New("planets: envelope count mismatch")
|
||||
}
|
||||
args := make([]int32, nint)
|
||||
nbits := bits.Len(uint(nk - 1))
|
||||
if nbits == 0 {
|
||||
nbits = 1
|
||||
}
|
||||
prev, cur := -1, -1
|
||||
for j := 0; j < nint; j++ {
|
||||
a := 0
|
||||
if sortedArgs {
|
||||
if env[j] != cur {
|
||||
prev, cur = -1, env[j]
|
||||
}
|
||||
a = prev + 1 + br.gamma()
|
||||
prev = a
|
||||
} else {
|
||||
a = int(br.get(nbits))
|
||||
}
|
||||
if a >= nk {
|
||||
return errors.New("planets: argument index out of range")
|
||||
}
|
||||
args[j] = int32(a)
|
||||
}
|
||||
top := 0
|
||||
for _, d := range env {
|
||||
if d > top {
|
||||
top = d
|
||||
}
|
||||
}
|
||||
// 按包络阶降序的稳定排序：pos[j] 为位流第 j 项的新位置
|
||||
pos := make([]int, nint)
|
||||
e.arg = make([]int32, nint)
|
||||
k := 0
|
||||
for d := top; d >= 0; d-- {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] == d {
|
||||
pos[j], e.arg[k] = k, args[j]
|
||||
k++
|
||||
}
|
||||
}
|
||||
}
|
||||
if nint == 0 {
|
||||
return br.err
|
||||
}
|
||||
e.cnt = make([]int, top+1)
|
||||
e.c, e.s = make([][]float64, top+1), make([][]float64, top+1)
|
||||
for d := 0; d <= top; d++ {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] >= d {
|
||||
e.cnt[d]++
|
||||
}
|
||||
}
|
||||
e.c[d], e.s[d] = make([]float64, e.cnt[d]), make([]float64, e.cnt[d])
|
||||
}
|
||||
width := 0
|
||||
coef := func() float64 {
|
||||
neg := br.get(1) != 0
|
||||
v := float64(br.get(width))
|
||||
if neg {
|
||||
v = -v
|
||||
}
|
||||
return v * step
|
||||
}
|
||||
for d := 0; d <= top; d++ {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] < d {
|
||||
continue
|
||||
}
|
||||
width += unzigzag(br.gamma())
|
||||
if width < 0 || width > 63 {
|
||||
return errors.New("planets: bad coefficient width")
|
||||
}
|
||||
e.c[d][pos[j]] = coef()
|
||||
e.s[d][pos[j]] = coef()
|
||||
}
|
||||
}
|
||||
return br.err
|
||||
}
|
||||
@@ -0,0 +1,108 @@
|
||||
1,-1931455,-62833473.893474385,-11738779.389872823,6761826.5210533086,14582.743821870408,-3696554.6520415167,-230752.33664395515
|
||||
1,-982346.61040627258,-54594365.924901746,-40249361.98021353,3524624.2650957904,1711348.2495792741,-2996593.1799513367,-395982.00376442779
|
||||
1,-664723.78605570132,19568697.79645298,41744274.883307591,670482.25088474201,-4562923.694390011,2147128.8468987569,659053.82913683238
|
||||
1,421526.7353404928,-8560427.7447433379,46317092.227732658,4314797.4566545757,-4930648.2616276676,-487278.75317214674,484118.99164901557
|
||||
1,613717.16879534395,50633858.869895719,-23956414.024757061,-7062273.6544543374,1013728.6378109402,4113246.5162761854,200754.98254079727
|
||||
1,1204502.931725678,12176372.939927423,-66239425.365220524,-6319067.7063551536,3316934.4824261386,1057323.5527012271,-251499.67586286186
|
||||
1,2332037.5255191391,21884339.865066517,40755036.895314112,1284676.9193076652,-4545596.9765684316,2165482.7567381081,597004.52219926508
|
||||
1,2469806.8315679757,-23900066.995238971,41442929.584906727,5578718.794936697,-4493684.7198801376,-1942325.6042346412,253081.92401840785
|
||||
1,3655932.6525249016,-15625619.077793298,-67848691.682821631,-4521720.6778781908,3243436.5201193294,-809742.86308659229,-339015.81050683191
|
||||
1,3836523.2060893951,-44660371.648988307,-49451083.941693358,-618447.01226177043,2254980.1946469825,-2714128.8424649457,-418801.59788438171
|
||||
1,4285288.7909884127,52518688.948609084,-29805567.862637836,-6735289.4021467147,1232776.764282319,3732096.7001830083,230849.22404800789
|
||||
1,4496271.6919694338,-40970592.544536121,28277840.586867347,5648729.3139325604,-3280728.4638769156,-3416752.9628165388,-49932.553514436906
|
||||
1,4837980.1486025397,1645090.9344821104,-69537420.91412662,-6340653.6856198637,3343740.3474207832,158105.36204072251,-234192.53407119896
|
||||
1,5331864.0411642483,56436986.11134512,-10013566.797446055,-4887819.6523256069,-109367.85533025698,4144364.1988601065,384240.87884015433
|
||||
2,-1598084.2773930961,43003955.157424711,98305699.451780051,-3674993.2754645608,-2802072.3434968451,1196582.1047978092,127925.75419764339
|
||||
2,-1225915.9647452403,-105799331.6546907,17266220.875921905,5448318.3185304673,-515830.63036713895,-3005601.8309584637,65563.844435925843
|
||||
2,-692096.24148116377,57989042.114105493,90667249.141690865,-4073847.1424257746,-2573020.4274585145,1613889.7017710209,127850.96939677013
|
||||
2,187593.29539150605,88716670.998645633,61780084.21283368,-5352144.289310039,-1748825.6132587346,2466373.3962477297,92879.321422775989
|
||||
2,1095203.2899014666,-28055976.399595186,103606769.6181515,1995508.7866806835,-2935392.8241721937,-809364.24893465871,170514.82278035372
|
||||
2,1701846.1254665717,97535014.661751598,47044008.494557619,-5367299.3750670673,-1327226.8208148675,2710755.9973209505,99606.614997275887
|
||||
2,2308050.3265216323,88645800.762682974,-63055996.742153667,-5936287.7132207472,1734508.3510735633,2453166.5504519013,-69784.367334436451
|
||||
2,2618496.2093246514,-107562369.13024026,-341415.88202046097,6161142.2754273145,-7777.3418237289252,-3038598.744264584,-44914.178817536522
|
||||
2,2879637.9671252463,-48468367.056526691,-97016501.64084211,1106714.6549768529,2687368.2707796628,-1364202.5907063801,-175128.24677738719
|
||||
2,3346858.0548557155,106831470.41331172,-18993290.60020487,-6260502.5255921204,518381.71200490242,2967330.6535282987,31607.927781469803
|
||||
2,3973215.4673080323,-107553033.53270063,5512389.6949170651,5754080.8874512324,-170022.93112917306,-3030413.6719801705,-65506.191032127062
|
||||
2,4148003.3935663197,-68635460.407738149,82792845.939131647,5650823.9669022858,-2337871.1223638346,-1942368.6204800094,70190.903086091581
|
||||
2,5025748.652984336,-65871835.11454805,-86028739.428212389,391478.07920932205,2388128.1732157101,-1843921.3359892734,-167133.09745928633
|
||||
3,-1931455,-150473987.96749708,5883801.5462573338,1923538.0693601375,-147750.77739770696,-2551129.8230871521,-64692.224256650203
|
||||
3,-918186.82549542841,-110863312.67125413,-104059875.81935193,-1447641.1284470859,1713423.8837573638,-1862737.5626304727,-50191.130090461993
|
||||
3,-525169.90033902903,-108728624.19648589,-106174934.76442857,-1447046.7364528317,1749962.9826123023,-1830523.1413526826,-42808.60152032529
|
||||
3,-50015.837424891302,-149982079.27249333,-3735673.6772040366,427139.6470313305,15740.218431437454,-2565618.2023071856,-40691.97342836282
|
||||
3,214407.52228800766,-139371492.31200913,52274662.357543275,1085025.4423712757,-952112.96382766985,-2404320.8379542879,-31843.061662426342
|
||||
3,1092521.8990238593,-143790137.01210663,-43703238.619850412,-293384.56270973664,701894.38456182287,-2463479.4317906653,-21730.323819369802
|
||||
3,1416030.9360990282,4715646.8583583701,146871512.13379583,964593.70751670678,-2618153.9695822895,79500.610125824591,1050.1823758632122
|
||||
3,2378056.2365927286,132175681.75762367,68573450.673263684,36102.118903539522,-1227453.9501712061,2275388.4270697795,992.35470886810526
|
||||
3,2770178.8802035637,-96073210.551071092,-116446639.19599527,251893.53166848375,1944783.6443092676,-1649407.9808276175,2750.6892199300423
|
||||
3,3490087.2680593487,-116931603.97130293,-94309444.772382304,737564.25139874162,1579032.93677497,-2018306.6882843499,10434.31654207087
|
||||
3,3769866.3212560304,-127516758.11987072,-78677929.492055118,852483.08219713217,1316292.4725816047,-2206426.8100802186,14611.194917333378
|
||||
3,4284440.5978102293,-112416610.03425916,95623333.507418022,-638513.85279376747,-1699509.7377296686,-1978353.8742986633,26186.310126968638
|
||||
3,4957447.7597313328,142255916.9256832,-51303194.995899975,-64333.678592950368,845279.42989303696,2400859.4156803214,-37339.426391242741
|
||||
3,5263563.8233592883,147955932.18912891,27452790.244904704,-1372245.362749584,-495436.32893261855,2509475.863939683,-34341.816687568724
|
||||
4,-1664596.7865721234,-119841287.66127659,214629928.90642872,7344645.1552384049,-1655802.7048651963,-982284.96186421195,60183.350695118723
|
||||
4,-599478.89874812448,19090267.437296763,-208769610.16352469,-3666610.8099194989,2240788.5261324784,274377.16941586416,-84098.028036331903
|
||||
4,-248716.27738850471,-154449764.37564087,193160125.03983238,8769981.5271898061,-1480039.323526321,-1211794.2744412571,37903.534240361609
|
||||
4,-112103.65643933322,17691024.283197854,242177683.63147894,3086072.6061628261,-1934726.3720257443,252551.67760584434,76282.778405779973
|
||||
4,378411.62997224135,-8672878.7757398747,242792687.49380925,4407000.5889353165,-1949667.1450878531,43212.109817951103,69667.886183071954
|
||||
4,1255789.973287046,-192079105.05521163,157457863.51673391,8991618.7145916373,-1208438.3833928432,-1471532.5260416819,9657.0171547220471
|
||||
4,2044206.5422547688,194353817.05443475,90208178.629202545,-3389383.5649577067,-786794.70067758078,2068074.8551034597,63532.552021373755
|
||||
4,2441004.9649596373,-174313155.28191385,-157340974.30781519,1001405.9012954868,1481922.0390659207,-1375297.4273268564,-65315.162482488347
|
||||
4,2610794.6258488195,31989205.642540239,-213194100.97962344,-5250336.265857337,2143934.4120386043,493820.56649056997,-40245.452173118872
|
||||
4,2952388.8482214063,197069112.07688695,73317863.285269588,-2687997.6104657804,-668614.76648096298,2150676.6897385409,60120.667137577468
|
||||
4,3868758.0927022072,192914598.65039673,-73336897.859198287,-4566452.8727918556,769453.22488924093,2158351.9605830782,32987.56225437281
|
||||
4,4106866.1883822149,-241022196.44414705,-61422556.733652458,2154472.241932245,531691.21472895541,-1826155.8443803398,-45117.620717894984
|
||||
4,4746544.2486086572,-117391484.90056048,-207574278.58181453,-2820662.3897265969,1811419.4700026382,-824291.99336024781,-33996.751894926485
|
||||
5,-1931455,-772690726.7694149,199332711.69978821,23295938.166143727,-289038.54449519527,-1061347.3055243213,12007.908902628149
|
||||
5,-1325996.6449592349,180480396.53800517,747681529.3589071,-7061549.837683348,-1101428.977350777,300005.9999717772,32090.033005237256
|
||||
5,-664681.44631013274,377609983.18746608,-667612150.77084684,-9468349.3027604315,978337.75683869782,594515.05479369068,-28858.505204890796
|
||||
5,-96501.675953416852,745409433.90775657,-90178932.856628656,-20083056.667049114,133001.91904592334,1161264.6514902934,-5676.8781348387647
|
||||
5,485342.37627524836,-188169392.61670572,758382147.73369586,3425868.8939713552,-1100205.1825472682,-229560.89454249665,28938.263893912637
|
||||
5,1173238.7993086451,706406117.20131779,240698978.76893193,-17876182.623419557,-370304.80656013114,1115951.9215193791,6376.9069425374564
|
||||
5,1615370.7769106091,587916367.11441386,461603151.21851331,-15229806.500849891,-705175.11843080819,938661.97823352518,13959.615618576123
|
||||
5,1826785.1037350758,561244956.97043788,-507505051.95698571,-11470186.947058314,746881.90311591025,887888.26927937986,-20231.729480225269
|
||||
5,2451545,598557823.64564335,439626178.58140647,-15226066.168285085,-683430.92717100971,963863.88426159602,11307.635576089893
|
||||
5,2753599.0637343237,226296031.21838596,-742092562.48249567,-1522612.6982041863,1065195.404953395,383426.92661061988,-25255.290575995921
|
||||
5,3114874.3738181461,182074976.44964525,732676104.37929857,-7896536.1257198798,-1115983.1714703941,327024.97186968755,22427.346278442008
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||||
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8,2551052.7434542929,-4526193433.9997454,-51573718.972142957,105436927.26526648,2150.5357920604706,-465599.16471895081,9559.6966650015784
|
||||
8,2558314.4581084568,-3295761155.2466497,-3118266248.2066631,140204014.56534061,320764.81585671741,-338087.78936397546,-431.91082854534318
|
||||
8,2561890.4046752327,-1958100725.8851564,-4090751860.6025405,129409771.15190539,420877.40047634736,-200987.72102560525,-5578.9986223014475
|
||||
8,2564589.685945244,-760914840.92699397,-4465291790.1114178,109531758.72521909,459080.90627958684,-75863.104390858934,-9021.4875984333194
|
||||
8,2565365.3985973313,-402705260.04360342,-4510173189.0474281,102190270.21002667,464204.289063123,-39701.366105638313,-9901.9634829219503
|
||||
8,2577128.7351568425,4063158326.450985,-1899046528.6230195,-54582189.461109929,195324.14397010318,429416.14201630664,-13338.337280032993
|
||||
8,2577639.2677030656,4156848887.0918455,-1677337974.2934921,-61306355.070811465,171705.71896734723,438844.23145891394,-12998.860875238814
|
||||
8,2590334.2671391643,2551568660.1077352,3655932137.800746,-134153558.93984658,-388890.16345552931,272864.08933394216,3360.640120554986
|
||||
8,2595997.4277934292,37773325.03103219,4469555495.9632492,-92935556.987670049,-472655.42525418487,6209.7956580738428,10754.201784382836
|
||||
8,2596685.4703123774,-286895917.49701768,4462098033.6312971,-85307382.119633496,-470697.19817468972,-27739.298698894698,11409.702362744896
|
||||
8,2596902.4767300789,-388928940.05981785,4454940494.0463638,-82810114.572604403,-469648.39004792296,-38233.341019808875,11605.007660958332
|
||||
8,2599958.6811479013,-1782169056.1175373,4115713526.8735213,-43680559.438126236,-434429.57460043562,-183751.83576328747,13792.792755929899
|
||||
8,2607461.5385275586,-4193230528.7213321,1674681138.3096232,62225813.142429605,-177260.09163831593,-432059.0036235493,13001.539905357038
|
||||
8,2618665.2202832801,-3250023335.285738,-3168971013.4188023,140236923.48816052,325919.40749394702,-333797.546804482,-652.59817942365294
|
||||
8,2622969.6595060355,-1582570981.3352432,-4249876080.7904916,124034955.79179592,437769.22545015934,-161344.2189749362,-6780.1116099869841
|
||||
8,2636101.3604303026,3786803574.9413924,-2411196370.8757682,-37687369.190034173,249711.19062637916,398625.37203822302,-13974.815244520825
|
||||
8,2641305.6078180475,4468798320.0026255,-85895304.933750868,-101328004.63431399,6596.7738907046041,473413.23014396202,-9893.9751535678788
|
||||
8,2646186.7395561016,3915312960.5546041,2132161751.9031265,-134240821.67659056,-228126.16996093906,416630.56287164864,-3298.3681064604652
|
||||
8,2652672.8788275202,1663881276.0043931,4136756606.8938818,-123611043.02195102,-438270.92664133152,177630.39391310574,6431.2100302141353
|
||||
8,2655817.3911270499,219785749.22791481,4463263509.9894085,-97010220.425259113,-473179.29779453663,26586.317384063539,10369.654307483805
|
||||
8,2657675.7904352564,-656630609.61434937,4425518715.3262663,-76029772.428152174,-466737.09407372319,-66085.82882942626,12124.966785228149
|
||||
8,2660712.9689958571,-2019547932.2566075,4006991703.4158711,-35945852.310723387,-422853.19846211537,-208898.02393021624,14043.04767638558
|
||||
8,2673114.1483041537,-4457711275.731514,-821251442.49612474,119776838.96361506,81388.889813181144,-458516.1448204632,7564.4191923903936
|
||||
8,2690567.3579719397,1779461093.5289602,-4147398168.7292647,44401164.328235,427115.64410711214,187754.00468843628,-13722.99411462197
|
||||
8,2697604.4441013052,4074198250.6007028,-1875430067.8756185,-55383222.92921342,193806.32315346526,430636.83853234345,-13329.570761693534
|
||||
8,2699249.9134048764,4328807272.1854143,-1142596776.8940125,-76333170.184159264,115350.11566701748,456995.56269231607,-12077.248946626141
|
||||
8,2706019.8488313816,3997227680.8626189,1971891678.0083015,-132867371.08309914,-209945.04280054438,424710.63738171145,-3898.8831999334243
|
||||
8,2718979.4228122425,-1163171001.215251,4322869903.8510981,-62226712.085603632,-455440.08743300638,-118027.05269884451,12948.617456017653
|
||||
8,2720458.1684011132,-1821486575.6392598,4097686632.4290538,-42372266.789472751,-433225.53999166028,-186749.60482359972,13855.405861248497
|
||||
8,2722283.5085893935,-2573535703.2165141,3681941417.3559513,-16463193.678856162,-387642.15866765898,-266591.13521970907,14427.076269908897
|
||||
8,2725810.706325612,-3738582649.8687687,2519171796.5516214,34388362.155940868,-265802.23094043205,-387093.55974022025,14090.722544401899
|
||||
8,2728509.8327481919,-4297490641.7929354,1391891783.1064818,70496563.126268998,-147584.15665937983,-442149.17962123925,12530.842011877694
|
||||
8,2730729.1316622673,-4510474257.14645,380024121.28463286,96252962.544459686,-42231.984556383264,-465397.67224199011,10549.981431427683
|
||||
8,2731022.0789917279,-4520726329.4518166,243551733.70164382,99297856.406226501,-27766.870181607937,-466239.64912174264,10236.822079610331
|
||||
8,2742359.3750335346,-2020929810.8783176,-4062298751.94416,130333809.57045616,415873.15691872191,-205802.18714607431,-5353.064139407973
|
||||
8,2745002.8418905083,-857629252.40640724,-4452227774.6234665,111505708.18844627,458683.30284085334,-85617.601805857557,-8812.9795582470269
|
||||
8,2747657.219437053,373558148.4211542,-4510901256.8479471,84307866.610288709,464538.66325567727,40683.65653023425,-11578.860241889808
|
||||
8,2749649.840763649,1286739996.4421947,-4333380391.6026087,59558083.143449381,447752.89189448353,137546.06094952556,-13155.309086603038
|
||||
8,2752433.6495864699,2459078917.6055379,-3778101942.0373502,21065693.248819966,390401.14398965676,258384.44563385475,-14345.105804929401
|
||||
8,2761257.4085423201,4459503277.0635357,-308325355.11825836,-96585992.921304777,29516.137033078154,470814.36001048546,-10395.582251357788
|
||||
|
Reference in New Issue
Block a user