"""
Robot–environment convex collision in **xy** (ground plane).

For an **axis-aligned robot footprint** vs. a **single convex obstacle triangle**, a
**separating-axis test (SAT)** gives the same **intersection predicate** as **GJK** in
2D, with a compact fully batched reference. A fused device kernel often implements
**GJK (+ EPA for penetration depth)** for arbitrary 3D polyhedra; this problem is
the canonical 2D footprint special case.
"""

import torch
import torch.nn as nn

# Default ModelNew is PyTorch-only. run_and_check: use check_kernel=False with backend=cuda


def _rect_corners_xy(robot_min: torch.Tensor, robot_max: torch.Tensor) -> torch.Tensor:
    """(B, 4, 2) corners of axis-aligned rectangles."""
    x0, x1 = robot_min[:, 0], robot_max[:, 0]
    y0, y1 = robot_min[:, 1], robot_max[:, 1]
    return torch.stack(
        (
            torch.stack((x0, y0), dim=-1),
            torch.stack((x1, y0), dim=-1),
            torch.stack((x1, y1), dim=-1),
            torch.stack((x0, y1), dim=-1),
        ),
        dim=1,
    )


def _project_min_max(points: torch.Tensor, axis: torch.Tensor) -> tuple[torch.Tensor, torch.Tensor]:
    """points (B, K, 2), axis (B, 2) or (2,) broadcast → (B,) min and max projections."""
    if axis.dim() == 1:
        axis = axis.view(1, 2).expand(points.shape[0], -1)
    proj = (points * axis.unsqueeze(1)).sum(dim=-1)
    return proj.min(dim=-1).values, proj.max(dim=-1).values


def _batched_sat_rect_triangle(
    robot_min: torch.Tensor,
    robot_max: torch.Tensor,
    env_triangle: torch.Tensor,
    eps: float,
) -> torch.Tensor:
    """
    Separating-axis test: AABB vs triangle in 2D, fully vectorized over batch.
    Returns (B,) float 1.0 if overlapping else 0.0.
    """
    B = robot_min.shape[0]
    corners = _rect_corners_xy(robot_min, robot_max)
    hit = torch.ones(B, device=robot_min.device, dtype=robot_min.dtype)

    # World axes (rectangle is AABB)
    for ax in (
        torch.tensor([1.0, 0.0], device=robot_min.device, dtype=robot_min.dtype),
        torch.tensor([0.0, 1.0], device=robot_min.device, dtype=robot_min.dtype),
    ):
        r0, r1 = _project_min_max(corners, ax)
        t0, t1 = _project_min_max(env_triangle, ax)
        separated = (r1 < t0 - eps) | (t1 < r0 - eps)
        hit = hit * (~separated).to(hit.dtype)

    # Triangle edge normals (per batch)
    for i in range(3):
        e = env_triangle[:, (i + 1) % 3] - env_triangle[:, i]
        n = torch.stack((-e[:, 1], e[:, 0]), dim=-1)
        n = n / (n.norm(dim=-1, keepdim=True) + 1e-8)
        r0, r1 = _project_min_max(corners, n)
        t0, t1 = _project_min_max(env_triangle, n)
        separated = (r1 < t0 - eps) | (t1 < r0 - eps)
        hit = hit * (~separated).to(hit.dtype)

    return hit


class Model(nn.Module):
    """
    **Batched robot footprint vs. environment triangle** intersection in **xy**.

    Robot: axis-aligned box ``[robot_min, robot_max]`` per batch element.
    Environment: one **triangle** ``(B, 3, 2)``.

    Reference: **vectorized SAT** (5 axis tests). Fused-kernel target: same
    predicate via **GJK/EPA** or specialized SAT SIMD for planning loops.
    """

    def __init__(self, eps: float = 1e-6):
        super().__init__()
        self.eps = eps

    def forward(
        self,
        robot_min: torch.Tensor,
        robot_max: torch.Tensor,
        env_triangle: torch.Tensor,
    ) -> torch.Tensor:
        """
        Args:
            robot_min: (B, 2), robot_max: (B, 2) with max >= min componentwise.
            env_triangle: (B, 3, 2) obstacle vertices in order (any consistent winding).
        Returns:
            (B, 1) float in ``{0.0, 1.0}`` — **1** if the sets intersect.
        """
        B = robot_min.shape[0]
        assert robot_max.shape == (B, 2) and env_triangle.shape == (B, 3, 2)
        h = _batched_sat_rect_triangle(robot_min, robot_max, env_triangle, self.eps)
        return h.unsqueeze(-1)


class ModelNew(nn.Module):
    """KernelBench candidate entry point; default delegates to ``Model``."""

    def __init__(self, eps: float = 1e-6):
        super().__init__()
        self._impl = Model(eps=eps)

    def forward(
        self,
        robot_min: torch.Tensor,
        robot_max: torch.Tensor,
        env_triangle: torch.Tensor,
    ) -> torch.Tensor:
        return self._impl(robot_min, robot_max, env_triangle)


batch_size = 16


def get_inputs():
    bs = popcorn_pri.jitter_int(batch_size)
    robot_min = torch.empty(bs, 2).uniform_(-1.0, 0.5)
    robot_max = robot_min + torch.empty(bs, 2).uniform_(0.2, 0.8)
    env_triangle = torch.empty(bs, 3, 2).uniform_(-0.8, 0.8)
    return [robot_min, robot_max, env_triangle]


def get_init_inputs():
    return []

import torch
import torch.nn as nn
from torch.utils.cpp_extension import load_inline

_cpp_src = r'''
#include <torch/extension.h>

torch::Tensor sat_forward_cuda(torch::Tensor robot_min, torch::Tensor robot_max, torch::Tensor env_triangle, double eps);

torch::Tensor sat_forward(torch::Tensor robot_min, torch::Tensor robot_max, torch::Tensor env_triangle, double eps) {
    return sat_forward_cuda(robot_min, robot_max, env_triangle, eps);
}
'''

_cuda_src = r'''
#include <torch/extension.h>
#include <ATen/cuda/CUDAContext.h>
#include <cuda_runtime.h>

__device__ __forceinline__ bool sep_axis(float rmin, float rmax, float tmin, float tmax, float eps) {
    return (rmax < tmin - eps) || (tmax < rmin - eps);
}

__global__ void sat_kernel(const float* __restrict__ rminp,
                           const float* __restrict__ rmaxp,
                           const float* __restrict__ trip,
                           float* __restrict__ out,
                           int B,
                           float eps) {
    int b = blockIdx.x * blockDim.x + threadIdx.x;
    if (b >= B) return;

    float x0 = rminp[b*2 + 0];
    float y0 = rminp[b*2 + 1];
    float x1 = rmaxp[b*2 + 0];
    float y1 = rmaxp[b*2 + 1];

    const float* tri = trip + b*6;
    float ax = tri[0], ay = tri[1];
    float bx = tri[2], by = tri[3];
    float cx = tri[4], cy = tri[5];

    float tminx = fminf(ax, fminf(bx, cx));
    float tmaxx = fmaxf(ax, fmaxf(bx, cx));
    float tminy = fminf(ay, fminf(by, cy));
    float tmaxy = fmaxf(ay, fmaxf(by, cy));

    bool hit = true;
    if (sep_axis(x0, x1, tminx, tmaxx, eps) || sep_axis(y0, y1, tminy, tmaxy, eps)) {
        hit = false;
    } else {
        #pragma unroll
        for (int i = 0; i < 3; ++i) {
            float px, py, qx, qy;
            if (i == 0) { px = ax; py = ay; qx = bx; qy = by; }
            else if (i == 1) { px = bx; py = by; qx = cx; qy = cy; }
            else { px = cx; py = cy; qx = ax; qy = ay; }
            float ex = qx - px;
            float ey = qy - py;
            float inv = 1.0f / (sqrtf(ex*ex + ey*ey) + 1.0e-8f);
            float nx = -ey * inv;
            float ny =  ex * inv;

            float rx_a = x0 * nx;
            float rx_b = x1 * nx;
            float ry_a = y0 * ny;
            float ry_b = y1 * ny;
            float rlo = fminf(rx_a, rx_b) + fminf(ry_a, ry_b);
            float rhi = fmaxf(rx_a, rx_b) + fmaxf(ry_a, ry_b);

            float pa = ax*nx + ay*ny;
            float pb = bx*nx + by*ny;
            float pc = cx*nx + cy*ny;
            float tlo = fminf(pa, fminf(pb, pc));
            float thi = fmaxf(pa, fmaxf(pb, pc));

            if (sep_axis(rlo, rhi, tlo, thi, eps)) { hit = false; break; }
        }
    }
    out[b] = hit ? 1.0f : 0.0f;
}

torch::Tensor sat_forward_cuda(torch::Tensor robot_min, torch::Tensor robot_max, torch::Tensor env_triangle, double eps) {
    const int B = (int)robot_min.size(0);
    auto out = torch::empty({B, 1}, robot_min.options());
    if (B > 0) {
        const int threads = 32;
        const int blocks = (B + threads - 1) / threads;
        sat_kernel<<<blocks, threads, 0, at::cuda::getCurrentCUDAStream()>>>(
            robot_min.data_ptr<float>(), robot_max.data_ptr<float>(), env_triangle.data_ptr<float>(),
            out.data_ptr<float>(), B, (float)eps);
    }
    return out;
}
'''

_ext = load_inline(
    name='sat_rect_tri_ext_final',
    cpp_sources=[_cpp_src],
    cuda_sources=[_cuda_src],
    functions=['sat_forward'],
    extra_cflags=['-O3'],
    extra_cuda_cflags=['-O3', '--use_fast_math'],
    verbose=False,
)

class ModelNew(nn.Module):
    def __init__(self, eps: float = 1e-6):
        super().__init__()
        self.eps = float(eps)

    def forward(self, robot_min: torch.Tensor, robot_max: torch.Tensor, env_triangle: torch.Tensor) -> torch.Tensor:
        return _ext.sat_forward(robot_min, robot_max, env_triangle, self.eps)