"""
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


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

__device__ __forceinline__ bool sep_interval(float r0, float r1, float t0, float t1, float eps) {
    return (r1 < t0 - eps) || (t1 < r0 - eps);
}

__global__ void sat_rect_tri_kernel(const float* __restrict__ robot_min,
                                    const float* __restrict__ robot_max,
                                    const float* __restrict__ tri,
                                    float* __restrict__ out,
                                    int B,
                                    float eps) {
    int b = blockIdx.x * blockDim.x + threadIdx.x;
    if (b >= B) return;

    const float xmin = robot_min[b*2 + 0];
    const float ymin = robot_min[b*2 + 1];
    const float xmax = robot_max[b*2 + 0];
    const float ymax = robot_max[b*2 + 1];

    const float x0 = tri[b*6 + 0];
    const float y0 = tri[b*6 + 1];
    const float x1 = tri[b*6 + 2];
    const float y1 = tri[b*6 + 3];
    const float x2 = tri[b*6 + 4];
    const float y2 = tri[b*6 + 5];

    bool hit = true;

    // Axis (1,0)
    float txmin = fminf(x0, fminf(x1, x2));
    float txmax = fmaxf(x0, fmaxf(x1, x2));
    if (sep_interval(xmin, xmax, txmin, txmax, eps)) hit = false;

    // Axis (0,1)
    float tymin = fminf(y0, fminf(y1, y2));
    float tymax = fmaxf(y0, fmaxf(y1, y2));
    if (sep_interval(ymin, ymax, tymin, tymax, eps)) hit = false;

    // Triangle edge normal axes.  The PyTorch reference normalizes by
    // (norm + 1e-8); equivalently scale the epsilon by that denominator.
    #pragma unroll
    for (int i = 0; i < 3; ++i) {
        float ax, ay, bx, by;
        if (i == 0) { ax = x0; ay = y0; bx = x1; by = y1; }
        else if (i == 1) { ax = x1; ay = y1; bx = x2; by = y2; }
        else { ax = x2; ay = y2; bx = x0; by = y0; }

        float ex = bx - ax;
        float ey = by - ay;
        float nx = -ey;
        float ny = ex;
        float eps_scaled = eps * (sqrtf(ex*ex + ey*ey) + 1.0e-8f);

        // Project AABB without materializing corners.
        float r0 = (nx >= 0.0f ? xmin * nx : xmax * nx) + (ny >= 0.0f ? ymin * ny : ymax * ny);
        float r1 = (nx >= 0.0f ? xmax * nx : xmin * nx) + (ny >= 0.0f ? ymax * ny : ymin * ny);

        float p0 = x0 * nx + y0 * ny;
        float p1 = x1 * nx + y1 * ny;
        float p2 = x2 * nx + y2 * ny;
        float tmin = fminf(p0, fminf(p1, p2));
        float tmax = fmaxf(p0, fmaxf(p1, p2));

        if (sep_interval(r0, r1, tmin, tmax, eps_scaled)) hit = false;
    }

    out[b] = hit ? 1.0f : 0.0f;
}

torch::Tensor sat_forward(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());
    const int threads = 128;
    const int blocks = (B + threads - 1) / threads;
    sat_rect_tri_kernel<<<blocks, threads>>>(
        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',
    cpp_sources='',
    cuda_sources=_cuda_src,
    functions=['sat_forward'],
    extra_cuda_cflags=['-O3', '--use_fast_math'],
    extra_cflags=['-O3'],
    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)