"""PyTorch 批量运动学 + 可微胶囊间隙（与 webapp/js/ik-solver.js 同口径）。

数据来自 ml/assets/kin.json（node ml/prep/export_kin.cjs 生成）：
  - cum_xf / fk / orient：与 JS cumXf / fk(q,0) / orient(q) 一致（角度制输入）
  - gaps(q, cap)：所有 |Δg|≥2 胶囊对的 间隙 = 线段距离 − (r_i + r_j + margin)。
    宽相位复刻 JS 的簇球筛选（被筛掉的对间隙必 > cap），故 min(gap, cap) 与 JS gapMatrix 逐位同口径；
    筛选在 no_grad 下做，幸存对的精确距离保留梯度（APG / FK 损失用）。
"""
import json, math, os
import torch

HERE = os.path.dirname(os.path.abspath(__file__))
DEFAULT_KIN = os.path.join(HERE, '..', 'assets', 'kin.json')
D2R = math.pi / 180.0


def rot_axis(d, a):
    """d: [3] 单位轴；a: [...] 弧度 → [..., 3, 3]（Rodrigues，右手）"""
    c, s = torch.cos(a), torch.sin(a)
    x, y, z = float(d[0]), float(d[1]), float(d[2])
    C = 1 - c
    row0 = torch.stack([c + x * x * C, x * y * C - z * s, x * z * C + y * s], -1)
    row1 = torch.stack([y * x * C + z * s, c + y * y * C, y * z * C - x * s], -1)
    row2 = torch.stack([z * x * C - y * s, z * y * C + x * s, c + z * z * C], -1)
    return torch.stack([row0, row1, row2], -2)


def seg_seg_dist(p1, q1, p2, q2, eps=1e-12):
    """两线段最近距离（Ericson, Real-Time Collision Detection §5.1.9），[..., 3] → [...]"""
    d1, d2, r = q1 - p1, q2 - p2, p1 - p2
    a = (d1 * d1).sum(-1); e = (d2 * d2).sum(-1); f = (d2 * r).sum(-1)
    c = (d1 * r).sum(-1); b = (d1 * d2).sum(-1)
    denom = a * e - b * b
    s = torch.where(denom > eps, ((b * f - c * e) / denom.clamp_min(eps)).clamp(0, 1), torch.zeros_like(a))
    t = (b * s + f) / e.clamp_min(eps)
    # t 越界：夹回 [0,1] 并重算 s
    t_lo, t_hi = t < 0, t > 1
    s = torch.where(t_lo, (-c / a.clamp_min(eps)).clamp(0, 1), s)
    s = torch.where(t_hi, ((b - c) / a.clamp_min(eps)).clamp(0, 1), s)
    t = t.clamp(0, 1)
    # 第二条退化成点时，仍须在第一条上投影，而不是固定取其起点。
    s = torch.where(e <= eps, (-c / a.clamp_min(eps)).clamp(0, 1), s)
    s = torch.where(a <= eps, torch.zeros_like(s), s)
    t = torch.where(e <= eps, torch.zeros_like(t), t)
    c1 = p1 + d1 * s.unsqueeze(-1)
    c2 = p2 + d2 * t.unsqueeze(-1)
    return ((c1 - c2).pow(2).sum(-1) + 1e-18).sqrt()


class Kin:
    def __init__(self, path=DEFAULT_KIN, device='cpu', dtype=torch.float32):
        with open(path, 'r', encoding='utf-8') as f:
            K = json.load(f)
        self.fp = K['fp']
        self.device, self.dtype = device, dtype
        T = lambda x, dt=dtype: torch.tensor(x, dtype=dt, device=device)
        self.P = T(K['P']); self.D = [list(map(float, d)) for d in K['D']]
        lim = K['lim']
        self.lo = T([l[0] for l in lim]); self.hi = T([l[1] for l in lim]); self.cont = T([l[2] for l in lim]).bool()
        self.tcp0 = T(K['tcp0']); self.capm = float(K['capm'])
        caps = K['caps']
        self.cap_g = torch.tensor([c['g'] for c in caps], device=device)
        self.cap_a = T([c['a'] for c in caps]); self.cap_b = T([c['b'] for c in caps]); self.cap_r = T([c['r'] for c in caps])
        cl = K['clusters']
        self.cl_g = torch.tensor([c['g'] for c in cl], device=device)
        self.cl_c = T([c['c'] for c in cl])
        cp = K['cpairs']
        self.cp_a = torch.tensor([p[0] for p in cp], device=device)
        self.cp_b = torch.tensor([p[1] for p in cp], device=device)
        self.cp_lim = T([p[2] + p[3] + self.capm for p in cp])
        # 每个簇对展开成胶囊对（全组合），按簇对连续存放
        ci, cj, start, cnt = [], [], [], []
        for p in cp:
            A, B = cl[p[0]]['caps'], cl[p[1]]['caps']
            start.append(len(ci)); cnt.append(len(A) * len(B))
            for i in A:
                for j in B:
                    ci.append(i); cj.append(j)
        self.pi = torch.tensor(ci, device=device, dtype=torch.long)
        self.pj = torch.tensor(cj, device=device, dtype=torch.long)
        self.cp_start = torch.tensor(start, device=device, dtype=torch.long)
        self.cp_cnt = torch.tensor(cnt, device=device, dtype=torch.long)
        hl = 0.5 * (self.cap_b - self.cap_a).norm(dim=-1)
        self.pair_need = self.cap_r[self.pi] + self.cap_r[self.pj] + self.capm
        self.pair_bl = hl[self.pi] + hl[self.pj] + self.cap_r[self.pi] + self.cap_r[self.pj] + self.capm
        gi, gj = self.cap_g[self.pi], self.cap_g[self.pj]
        self.pair_gp = torch.minimum(gi, gj) * 7 + torch.maximum(gi, gj)
        self.lever = T(K['lever'])
        table = [[0.0] * 7 for _ in range(6)]
        for group in range(1, 7):
            endpoints = [c[key] for c in caps if c['g'] == group for key in ('a', 'b')]
            if not endpoints:
                continue
            pivot, axis = K['P'][group - 1], K['D'][group - 1]
            unit = [v / math.hypot(*axis) for v in axis]
            relative = [[e[j] - pivot[j] for j in range(3)] for e in endpoints]
            radius = max(math.hypot(*v) for v in relative)
            radial = max(math.hypot(v[1] * unit[2] - v[2] * unit[1],
                                    v[2] * unit[0] - v[0] * unit[2],
                                    v[0] * unit[1] - v[1] * unit[0]) for v in relative)
            for joint in range(group):
                chain = sum(math.dist(K['P'][j], K['P'][j + 1]) for j in range(joint, group - 1))
                table[joint][group] = (chain + (radial if joint == group - 1 else radius)) * D2R
        self.cert_groups = torch.tensor([a * 7 + b for a in range(7) for b in range(a + 2, 7)], device=device)
        # 三角不等式给出全姿态界，不用随机姿态最大值冒充上界。
        self.cert_lever = T([[table[k][b] if a <= k < b else 0.0 for k in range(6)]
                             for a in range(7) for b in range(a + 2, 7)])

    # ---------------- 运动学 ----------------
    def _checked_xf(self, q, xf):
        """xf 是按行对应 q 的位姿数组，行数不匹配会静默广播出错（宽相位筛到别的行 ⇒ device assert 或错间隙）。"""
        if xf is None:
            return self.cum_xf(q)
        Rs, Ts = xf
        if Rs.shape[0] != q.shape[0] or Ts.shape[0] != q.shape[0]:
            raise ValueError('xf 的行数 %d 与 q 的行数 %d 不符' % (Rs.shape[0], q.shape[0]))
        return xf

    def cum_xf(self, q):
        """q: [B,6] 度 → Rs [B,7,3,3], Ts [B,7,3]"""
        B = q.shape[0]
        R = torch.eye(3, dtype=q.dtype, device=q.device).expand(B, 3, 3)
        Tt = torch.zeros(B, 3, dtype=q.dtype, device=q.device)
        Rs, Ts = [R], [Tt]
        for k in range(6):
            Rk = rot_axis(self.D[k], q[:, k] * D2R)
            Pk = self.P[k].to(q.dtype)
            tk = Pk - torch.einsum('bij,j->bi', Rk, Pk)
            Tt = torch.einsum('bij,bj->bi', R, tk) + Tt
            R = R @ Rk
            Rs.append(R); Ts.append(Tt)
        return torch.stack(Rs, 1), torch.stack(Ts, 1)

    def fk(self, q, xf=None):
        Rs, Ts = xf if xf is not None else self.cum_xf(q)
        return torch.einsum('bij,j->bi', Rs[:, 6], self.tcp0.to(q.dtype)) + Ts[:, 6]

    def orient(self, q, xf=None):
        Rs, _ = xf if xf is not None else self.cum_xf(q)
        return Rs[:, 6]

    def jac(self, q, xf=None):
        """几何雅可比（对度）：返回 (Jv [B,3,6] mm/deg, Jw [B,3,6] 单位轴/deg)"""
        Rs, Ts = xf if xf is not None else self.cum_xf(q)
        p = self.fk(q, (Rs, Ts))
        Jv, Jw = [], []
        for k in range(6):
            d = torch.tensor(self.D[k], dtype=q.dtype, device=q.device)
            a = Rs[:, k] @ d
            o = torch.einsum('bij,j->bi', Rs[:, k], self.P[k].to(q.dtype)) + Ts[:, k]
            Jv.append(torch.linalg.cross(a, p - o, dim=-1) * D2R)
            Jw.append(a * D2R)
        return torch.stack(Jv, -1), torch.stack(Jw, -1)

    def caps_world(self, q, xf=None):
        Rs, Ts = xf if xf is not None else self.cum_xf(q)
        Rg, Tg = Rs[:, self.cap_g], Ts[:, self.cap_g]               # [B,C,3,3], [B,C,3]
        a = torch.einsum('bcij,cj->bci', Rg, self.cap_a.to(q.dtype)) + Tg
        b = torch.einsum('bcij,cj->bci', Rg, self.cap_b.to(q.dtype)) + Tg
        return a, b

    # ---------------- 间隙 ----------------
    # 2026-10-19（用户实测 dagger/诊断吃满 24 GB 显存）：本模型 1936 条胶囊 / 491 组 / 67256 粗对 / 104.7 万细对。
    # 显存有两段峰值，都随点数线性涨：
    #   粗筛段 cc[:,cp_a]-cc[:,cp_b] 的广播中间量 ≈ 36 B × 点数 × 粗对数（4096 点实测 9.3 GiB，与 cap 无关）；
    #   精算段 ≈ 每对几百字节 × 幸存细对数（4096 点 cap 40 幸存 2.4 亿对；旧版不分块实测 36.9 GiB）。
    # 所以先按 COARSE_ENTRIES 把点切块（粗筛每块 ≤ ~1 GiB），块内再按幸存细对数 PAIR_BUDGET 切（精算每块 ≤ ~1 GiB）。
    # 两段不同时存在，峰值与调用方 batch 大小无关。结果与不分块逐位一致（梯度经 cat 保留）。
    COARSE_ENTRIES = 30_000_000
    PAIR_BUDGET = 2_000_000

    @staticmethod
    def _cat_gaps(parts, starts):
        out = {'gm': torch.cat([p.pop('gm') for p in parts], 0)}
        if 'b' in parts[0]:
            # 非 in-place：b 会被 autograd 的索引反向图引用（APG 的碰撞铰链梯度路径），+= 会让 backward 报 version 错
            for p, s in zip(parts, starts): p['b'] = p['b'] + s
            for k in ('b', 'i', 'j', 'gap'): out[k] = torch.cat([p.pop(k) for p in parts])   # 逐键拼、拼完即释放
        return out

    def gaps(self, q, cap=40.0, xf=None, max_pairs=None, pairs=False):
        """返回 dict：
             gm  [B,49]：组对最小间隙 min(gap, cap)（gA*7+gB，gA<gB；其余为 cap）
             pairs=True 时另有 b, i, j, gap：幸存胶囊对（gap 可微；只有 APG 的 hinge 与 check_parity 需要）
           2026-10-19（用户实测 4096 点 cap 40 峰值 4.46 GiB 全在拼接 8.6e7 对的 b/i/j/gap）：
             默认只返回 gm，每块算完就丢掉胶囊对，峰值只剩单块。
        """
        xf = self._checked_xf(q, xf)
        Rs, Ts = xf
        B = q.shape[0]
        step = max(1, self.COARSE_ENTRIES // int(self.cp_a.shape[0]))
        if B <= step:
            return self._gaps_split(q, cap, xf, pairs)
        st = list(range(0, B, step))
        return self._cat_gaps([self._gaps_split(q[s:s + step], cap, (Rs[s:s + step], Ts[s:s + step]), pairs) for s in st], st)

    def _coarse(self, q, cap, xf):
        Rs, Ts = xf
        cc = torch.einsum('bkij,kj->bki', Rs[:, self.cl_g], self.cl_c.to(q.dtype)) + Ts[:, self.cl_g]
        d2 = (cc[:, self.cp_a] - cc[:, self.cp_b]).pow(2).sum(-1)          # [B,M]
        del cc
        return d2 <= (self.cp_lim + cap).pow(2)

    def _gaps_split(self, q, cap, xf, pairs):
        """粗筛已在显存预算内：按幸存细对数再切块做精算"""
        Rs, Ts = xf
        B = q.shape[0]
        with torch.no_grad():
            per = (self._coarse(q, cap, xf).long() * self.cp_cnt).sum(1)    # [B] 每点幸存细对数
            if B <= 1 or int(per.sum()) <= self.PAIR_BUDGET:
                bounds = [0, B]
            else:
                cs = torch.cumsum(per, 0).tolist(); bounds = [0]; base = 0
                for k, c in enumerate(cs):
                    if c - base > self.PAIR_BUDGET and k > bounds[-1]:
                        bounds.append(k); base = cs[k - 1]
                bounds.append(B)
            del per
        if len(bounds) == 2:
            return self._gaps_one(q, cap, xf, pairs)
        return self._cat_gaps([self._gaps_one(q[s:e], cap, (Rs[s:e], Ts[s:e]), pairs) for s, e in zip(bounds[:-1], bounds[1:])], bounds[:-1])

    def _gaps_one(self, q, cap, xf, pairs):
        Rs, Ts = xf
        B = q.shape[0]
        with torch.no_grad():
            keep = self._coarse(q, cap, xf)
            bb, mm = keep.nonzero(as_tuple=True)
            del keep
            cnt = self.cp_cnt[mm]
            rep_b = torch.repeat_interleave(bb, cnt)
            off = torch.repeat_interleave(self.cp_start[mm] - torch.cumsum(cnt, 0) + cnt, cnt) + torch.arange(int(cnt.sum()), device=q.device)
            pidx = off
        a, b = self.caps_world(q, xf)
        with torch.no_grad():
            pi, pj = self.pi[pidx], self.pj[pidx]
            mid = 0.5 * (a[rep_b, pi] + b[rep_b, pi] - a[rep_b, pj] - b[rep_b, pj])
            k2 = mid.pow(2).sum(-1) <= (self.pair_bl[pidx] + cap).pow(2)
            rep_b, pidx, pi, pj = rep_b[k2], pidx[k2], pi[k2], pj[k2]
        d = seg_seg_dist(a[rep_b, pi], b[rep_b, pi], a[rep_b, pj], b[rep_b, pj])
        gap = d - self.pair_need[pidx].to(q.dtype)
        gm = torch.full((B * 49,), float(cap), dtype=q.dtype, device=q.device)
        gm = gm.scatter_reduce(0, rep_b * 49 + self.pair_gp[pidx], gap.clamp(max=cap), reduce='amin', include_self=True)
        if not pairs: return {'gm': gm.view(B, 49)}
        return {'gm': gm.view(B, 49), 'b': rep_b, 'i': pi, 'j': pj, 'gap': gap}

    def gm_groups(self, q, gp, cap=40.0, xf=None):
        """只算指定组对 gp=[(a,b),...] 的最小间隙 [B,len(gp)]（特征用，避免 49 组全量）。
        数值与 gaps(q,cap)['gm'][:, a*7+b] 一致；组对在碰撞粗对里不存在时返回 cap。
        xf 可传入调用者已算好的 cum_xf(q)，避免同一姿态重复算 FK（特征路径每周期省一次）。"""
        key = tuple(gp)
        if getattr(self, '_gp_key', None) != key:
            m = torch.full((49,), -1, dtype=torch.long, device=q.device)
            for i, (a_, b_) in enumerate(gp): m[min(a_, b_) * 7 + max(a_, b_)] = i
            ga, gb = self.cl_g[self.cp_a], self.cl_g[self.cp_b]
            cg = torch.minimum(ga, gb) * 7 + torch.maximum(ga, gb)   # 簇对 → 7 连杆组对
            sel = torch.isin(cg, torch.tensor([min(a, b) * 7 + max(a, b) for a, b in gp], device=q.device))
            self._gp = (m, sel, sel.nonzero(as_tuple=True)[0]); self._gp_key = key
        self._gp49, sel, idx = self._gp
        xf = self._checked_xf(q, xf); Rs, Ts = xf; B = q.shape[0]
        with torch.no_grad():
            cc = torch.einsum('bkij,kj->bki', Rs[:, self.cl_g], self.cl_c.to(q.dtype)) + Ts[:, self.cl_g]
            d2 = (cc[:, self.cp_a[idx]] - cc[:, self.cp_b[idx]]).pow(2).sum(-1)
            keep = d2 <= (self.cp_lim[idx] + cap).pow(2)
            bb, mm = keep.nonzero(as_tuple=True)
            del keep, d2, cc
            cnt = self.cp_cnt[idx][mm]
            rep_b = torch.repeat_interleave(bb, cnt)
            off = torch.repeat_interleave(self.cp_start[idx][mm] - torch.cumsum(cnt, 0) + cnt, cnt) + torch.arange(int(cnt.sum()), device=q.device)
            pidx = off
        a, b = self.caps_world(q, xf)
        with torch.no_grad():
            pi, pj = self.pi[pidx], self.pj[pidx]
            mid = 0.5 * (a[rep_b, pi] + b[rep_b, pi] - a[rep_b, pj] - b[rep_b, pj])
            k2 = mid.pow(2).sum(-1) <= (self.pair_bl[pidx] + cap).pow(2)
            rep_b, pidx, pi, pj = rep_b[k2], pidx[k2], pi[k2], pj[k2]
        d = seg_seg_dist(a[rep_b, pi], b[rep_b, pi], a[rep_b, pj], b[rep_b, pj])
        gap = d - self.pair_need[pidx].to(q.dtype)
        gm = torch.full((B * len(gp),), float(cap), dtype=q.dtype, device=q.device)
        gm = gm.scatter_reduce(0, rep_b * len(gp) + self._gp49[self.pair_gp[pidx]], gap.clamp(max=cap), reduce='amin', include_self=True)
        return gm.view(B, len(gp))

    @torch.no_grad()
    def certify_segments(self, a, b, max_queries=32, max_depth=12, eps=1e-4, cap=20.0):
        """逐层二分认证：每根段独立查询预算，未知（超预算/超深度/非有限/越界）一律拒绝。

        判据对每条组对：子段两端间隙之和 > 该子段位移界 + 2eps（间隙取 min(gap,cap)，钳制只会更保守）。
        cap 必须 ≥ 该层子段界 + 2eps 才不会挡住本可通过的判定，故不做自适应收紧——同批其他段会改变
        钳制程度、让结果随批次而变（实测也无耗时收益，见探索日志轮次 31）。
        """
        if self.dtype != torch.float64 or a.dtype != torch.float64 or b.dtype != torch.float64:
            raise ValueError('segment certification requires float64')
        if a.shape != b.shape or a.ndim != 2 or a.shape[1] != 6:
            raise ValueError('a and b must be [count,6] with identical shape')
        # 预算给成张量时 max_depth + 1 会在 uint8 这类窄类型上回绕成 0，循环整个跳过，把碰撞段当安全返回。
        if type(max_queries) is not int or type(max_depth) is not int:
            raise ValueError('certification budgets must be plain ints')
        if max_queries < 2 or max_depth < 0 or eps <= 0 or cap <= eps:
            raise ValueError('invalid certification budget or tolerance')
        count = a.shape[0]
        status = torch.zeros(count, dtype=torch.long, device=a.device)
        inside = (((a >= self.lo) & (a <= self.hi) & (b >= self.lo) & (b <= self.hi)) | self.cont).all(-1)
        status[~inside] = 3
        root = torch.arange(count, device=a.device)
        gaps = self.gaps(torch.cat([a, b]), cap)['gm'][:, self.cert_groups]
        ga, gb = gaps[:count], gaps[count:]
        queries = torch.full((count,), 2, dtype=torch.long, device=a.device)
        bound = (b - a).abs() @ self.cert_lever.T
        for depth in range(max_depth + 1):
            finite = torch.isfinite(ga).all(-1) & torch.isfinite(gb).all(-1)
            collision = (ga <= 0).any(-1) | (gb <= 0).any(-1)
            status[root[~finite]] = 2
            status[root[collision]] = 1
            positive = (ga > eps).all(-1) & (gb > eps).all(-1)
            proven = positive & (ga + gb > bound + 2 * eps).all(-1)
            pending = (status[root] == 0) & ~proven
            if not bool(pending.any()):
                break
            a, b, ga, gb, root, bound = a[pending], b[pending], ga[pending], gb[pending], root[pending], bound[pending]
            if depth == max_depth:
                status[root] = 2
                break
            requested = torch.bincount(root, minlength=count)
            status[(status == 0) & (queries + requested > max_queries)] = 2
            keep = status[root] == 0
            a, b, ga, gb, root, bound = (t[keep] for t in (a, b, ga, gb, root, bound))
            if not root.numel():
                break
            mid = a + 0.5 * (b - a)
            gm = self.gaps(mid, cap)['gm'][:, self.cert_groups]
            queries += torch.bincount(root, minlength=count)
            a, b = torch.cat([a, mid]), torch.cat([mid, b])
            ga, gb = torch.cat([ga, gm]), torch.cat([gm, gb])
            root = torch.cat([root, root])
            bound = torch.cat([bound, bound]) / 2
        return {'safe': status == 0, 'collision': status == 1, 'unresolved': status == 2,
                'outside_box': status == 3, 'queries': queries}

    @torch.no_grad()
    def certify_uniform(self, a, b, n=64, eps=1e-4, cap=None):
        """固定层数的均匀细分认证：n 个子段只需一次 gaps 调用（n+1 个点），没有逐层依赖的往返。

        判据与 certify_segments 完全相同；界对 Δq 线性，所以子段界 = 整段界 / n。未通过即 unproven
        （拒绝），不存在“未知当安全”。cap=None 时取“最小不挡住可通过判定的宽相位”= 最大子段界 + 2eps：
        小于它钳制会把本可证明的子段压成不可证（偏保守），大于它只是多算对（偏慢），不改正确性。
        """
        if self.dtype != torch.float64 or a.dtype != torch.float64 or b.dtype != torch.float64:
            raise ValueError('segment certification requires float64')
        if type(n) is not int or n < 1 or eps <= 0 or (cap is not None and cap <= eps):
            raise ValueError('invalid subdivision count or tolerance')
        if a.shape != b.shape or a.ndim != 2 or a.shape[1] != 6:
            raise ValueError('a and b must be [count,6] with identical shape')
        count = a.shape[0]
        inside = (((a >= self.lo) & (a <= self.hi) & (b >= self.lo) & (b <= self.hi)) | self.cont).all(-1)
        bound = (b - a).abs() @ self.cert_lever.T / n                       # [count,15] 子段界
        required = float(bound.max()) + 2 * eps if count else 2 * eps
        qc = required if cap is None else cap
        alpha = torch.arange(n + 1, dtype=self.dtype, device=a.device) / n
        points = (a[:, None] + (b - a)[:, None] * alpha[None, :, None]).reshape(-1, 6)
        gm = self.gaps(points, qc)['gm'][:, self.cert_groups].view(count, n + 1, -1)
        adjacent = gm[:, :-1] + gm[:, 1:] > bound[:, None, :] + 2 * eps
        collision = (gm <= 0).any((1, 2))
        safe = inside & (gm > eps).all((1, 2)) & adjacent.all((1, 2)) & ~collision
        return {'safe': safe, 'collision': collision, 'unproven': (~safe & ~collision & inside),
                'outside_box': ~inside, 'points': n + 1, 'queries': n + 1,
                'cap_required_mm': required, 'cap_used_mm': qc}

    def min_gap(self, q, cap=40.0):
        return self.gaps(q, cap)['gm'].min(-1).values

    def unwrap_to(self, a, b):
        """连续轴取离 a 最近的等价角（与 JS unwrapTo 同口径）"""
        d = b - a
        dw = torch.remainder(d + 180.0, 360.0) - 180.0
        return torch.where(self.cont, a + dw, b)

    def clamp_box(self, q):
        return torch.where(self.cont, q, torch.maximum(torch.minimum(q, self.hi), self.lo))