import torch
import torch.nn as nn
import torch.nn.functional as F

# Default ModelNew is PyTorch-only. run_and_check: use check_kernel=False with backend=cuda
# until the candidate file contains a real CUDA kernel (see kernel_static_checker).


def _quaternion_to_rotation_matrix(q: torch.Tensor) -> torch.Tensor:
    """
    Unit quaternion ``q = (w, x, y, z)`` (scalar-first) to rotation matrix ``R``,
    shape ``(B, 3, 3)``, with ``p' = p @ R.T`` for row vectors ``p`` (``N×3``).
    """
    q = F.normalize(q, dim=-1, eps=1e-8)
    w, x, y, z = q.unbind(dim=-1)

    xx = x * x
    yy = y * y
    zz = z * z
    xy = x * y
    xz = x * z
    yz = y * z
    wx = w * x
    wy = w * y
    wz = w * z

    m00 = 1.0 - 2.0 * (yy + zz)
    m01 = 2.0 * (xy - wz)
    m02 = 2.0 * (xz + wy)
    m10 = 2.0 * (xy + wz)
    m11 = 1.0 - 2.0 * (xx + zz)
    m12 = 2.0 * (yz - wx)
    m20 = 2.0 * (xz - wy)
    m21 = 2.0 * (yz + wx)
    m22 = 1.0 - 2.0 * (xx + yy)

    row0 = torch.stack((m00, m01, m02), dim=-1)
    row1 = torch.stack((m10, m11, m12), dim=-1)
    row2 = torch.stack((m20, m21, m22), dim=-1)
    return torch.stack((row0, row1, row2), dim=-2)


class Model(nn.Module):
    """
    **Fused vectorized pose transform**: rotation from unit quaternion ``q`` and
    translation ``t`` applied to a batch of 3D points.

    One forward fuses **quaternion → ``3×3``** (Hamilton, scalar-first ``w,x,y,z``)
    with **batched matmul** and **broadcast translation**—typical for LiDAR / camera
    extrinsics, hand-eye calibration, and world ↔ body frame changes in VLA stacks.

    ``points' = points @ R.T + t`` with ``points`` row-wise ``(B, N, 3)``.
    """

    def __init__(self):
        super().__init__()

    def forward(
        self,
        points: torch.Tensor,
        quat: torch.Tensor,
        trans: torch.Tensor,
    ) -> torch.Tensor:
        """
        Args:
            points: (B, N, 3) points in the **source** frame.
            quat: (B, 4) unit quaternion ``(w, x, y, z)`` mapping source → target rotation.
            trans: (B, 3) translation in the **target** frame (same convention as ``R``).
        Returns:
            (B, N, 3) points in the **target** frame.
        """
        B, N, _ = points.shape
        assert quat.shape == (B, 4) and trans.shape == (B, 3)

        R = _quaternion_to_rotation_matrix(quat)
        return torch.matmul(points, R.transpose(-1, -2)) + trans.unsqueeze(1)


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

    def __init__(self):
        super().__init__()
        self._impl = Model()

    def forward(
        self,
        points: torch.Tensor,
        quat: torch.Tensor,
        trans: torch.Tensor,
    ) -> torch.Tensor:
        return self._impl(points, quat, trans)


batch_size = 8
num_points = 512


def get_inputs():
    p = popcorn_pri
    points = torch.randn(p.jitter_int(batch_size), p.jitter_int(num_points), 3)
    quat = torch.randn(p.jitter_int(batch_size), 4)
    trans = torch.randn(p.jitter_int(batch_size), 3)
    return [points, quat, trans]


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 pose_transform(torch::Tensor points, torch::Tensor quat, torch::Tensor trans);
'''

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

__global__ void pose_transform_kernel(const float* __restrict__ points,
                                      const float* __restrict__ quat,
                                      const float* __restrict__ trans,
                                      float* __restrict__ out,
                                      int N) {
    __shared__ float s[12];
    int b = blockIdx.x;

    if (threadIdx.x == 0) {
        const float* q = quat + b * 4;
        float w = q[0];
        float x = q[1];
        float y = q[2];
        float z = q[3];

        float ss = w*w + x*x + y*y + z*z;
        float invn = rsqrtf(ss);
        if (ss < 1.0e-16f) invn = 1.0e8f;
        w *= invn;
        x *= invn;
        y *= invn;
        z *= invn;

        float xx = x * x;
        float yy = y * y;
        float zz = z * z;
        float xy = x * y;
        float xz = x * z;
        float yz = y * z;
        float wx = w * x;
        float wy = w * y;
        float wz = w * z;

        s[0] = 1.0f - 2.0f * (yy + zz);
        s[1] = 2.0f * (xy - wz);
        s[2] = 2.0f * (xz + wy);
        s[3] = 2.0f * (xy + wz);
        s[4] = 1.0f - 2.0f * (xx + zz);
        s[5] = 2.0f * (yz - wx);
        s[6] = 2.0f * (xz - wy);
        s[7] = 2.0f * (yz + wx);
        s[8] = 1.0f - 2.0f * (xx + yy);

        const float* t = trans + b * 3;
        s[9] = t[0];
        s[10] = t[1];
        s[11] = t[2];
    }
    __syncthreads();

    int n = blockIdx.y * blockDim.x + threadIdx.x;
    if (n < N) {
        const float* p = points + (b * N + n) * 3;
        float px = p[0];
        float py = p[1];
        float pz = p[2];

        float* o = out + (b * N + n) * 3;
        o[0] = px * s[0] + py * s[1] + pz * s[2] + s[9];
        o[1] = px * s[3] + py * s[4] + pz * s[5] + s[10];
        o[2] = px * s[6] + py * s[7] + pz * s[8] + s[11];
    }
}

torch::Tensor pose_transform(torch::Tensor points, torch::Tensor quat, torch::Tensor trans) {
    auto out = torch::empty_like(points);
    int B = (int)points.size(0);
    int N = (int)points.size(1);
    const int threads = 128;
    dim3 block(threads);
    dim3 grid(B, (N + threads - 1) / threads);
    pose_transform_kernel<<<grid, block>>>(points.data_ptr<float>(), quat.data_ptr<float>(), trans.data_ptr<float>(), out.data_ptr<float>(), N);
    return out;
}
'''

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

class ModelNew(nn.Module):
    def __init__(self):
        super().__init__()

    def forward(self, points: torch.Tensor, quat: torch.Tensor, trans: torch.Tensor) -> torch.Tensor:
        return _ext.pose_transform(points, quat, trans)