# AOT ID: ['0_inference']
from ctypes import c_void_p, c_long, c_int
import torch
import math
import random
import os
import tempfile
from math import inf, nan
from torch._inductor.hooks import run_intermediate_hooks
from torch._inductor.utils import maybe_profile
from torch._inductor.codegen.memory_planning import _align as align
from torch import device, empty_strided
from torch._inductor.async_compile import AsyncCompile
from torch._inductor.select_algorithm import extern_kernels
from torch._inductor.codegen.multi_kernel import MultiKernelCall
import triton
import triton.language as tl
from torch._inductor.runtime.triton_heuristics import grid, split_scan_grid, grid_combo_kernels, start_graph, end_graph
from torch._C import _cuda_getCurrentRawStream as get_raw_stream

aten = torch.ops.aten
inductor_ops = torch.ops.inductor
_quantized = torch.ops._quantized
assert_size_stride = torch._C._dynamo.guards.assert_size_stride
empty_strided_cpu = torch._C._dynamo.guards._empty_strided_cpu
empty_strided_cuda = torch._C._dynamo.guards._empty_strided_cuda
empty_strided_xpu = torch._C._dynamo.guards._empty_strided_xpu
reinterpret_tensor = torch._C._dynamo.guards._reinterpret_tensor
alloc_from_pool = torch.ops.inductor._alloc_from_pool
async_compile = AsyncCompile()


# kernel path: runs/run_shard_4/inductor_cache/vc/cvcidhupkzamyjt4mabzbt7uoyuumdlftgbce2nvckckmvjwsvcw.py
# Topologically Sorted Source Nodes: [theta_sq, abs_1, small_inds, large_inds], Original ATen: [aten.pow, aten.abs, aten.lt, aten.eq]
# Source node to ATen node mapping:
#   abs_1 => abs_1
#   large_inds => eq
#   small_inds => lt
#   theta_sq => pow_1
# Graph fragment:
#   %pow_1 : [num_users=1] = call_function[target=torch.ops.aten.pow.Tensor_Scalar](args = (%arg0_1, 2), kwargs = {})
#   %abs_1 : [num_users=1] = call_function[target=torch.ops.aten.abs.default](args = (%arg0_1,), kwargs = {})
#   %lt : [num_users=2] = call_function[target=torch.ops.aten.lt.Scalar](args = (%abs_1, 0.001), kwargs = {})
#   %eq : [num_users=1] = call_function[target=torch.ops.aten.eq.Scalar](args = (%lt, 0), kwargs = {})
triton_poi_fused_abs_eq_lt_pow_0 = async_compile.triton('triton_poi_fused_abs_eq_lt_pow_0', '''
import triton
import triton.language as tl
from triton.compiler.compiler import AttrsDescriptor

from torch._inductor.runtime import triton_helpers, triton_heuristics
from torch._inductor.runtime.triton_helpers import libdevice, math as tl_math
from torch._inductor.runtime.hints import AutotuneHint, ReductionHint, TileHint, instance_descriptor, DeviceProperties

@triton_heuristics.pointwise(
    size_hints=[256], 
    filename=__file__,
    triton_meta={'signature': {0: '*fp32', 1: '*fp32', 2: '*i1', 3: '*i1', 4: 'i32'}, 'device': DeviceProperties(type='cuda', index=0, cc=80, major=8, regs_per_multiprocessor=65536, max_threads_per_multi_processor=2048, multi_processor_count=108), 'constants': {}, 'configs': [AttrsDescriptor(divisible_by_16=(0, 1, 2, 3, 4), equal_to_1=())]},
    inductor_meta={'autotune_hints': set(), 'kernel_name': 'triton_poi_fused_abs_eq_lt_pow_0', 'mutated_arg_names': [], 'no_x_dim': False, 'num_load': 1, 'num_reduction': 0, 'backend_hash': 'A9C866B4A14FD3277824029365D703C2427B2E685E54EC9B3EF4ADC8D1EEAC1D', 'are_deterministic_algorithms_enabled': False, 'assert_indirect_indexing': True, 'autotune_local_cache': True, 'autotune_pointwise': True, 'autotune_remote_cache': None, 'force_disable_caches': False, 'dynamic_scale_rblock': True, 'max_autotune': False, 'max_autotune_pointwise': False, 'min_split_scan_rblock': 256, 'spill_threshold': 16, 'store_cubin': False},
    min_elem_per_thread=0
)
@triton.jit
def triton_poi_fused_abs_eq_lt_pow_0(in_ptr0, out_ptr0, out_ptr1, out_ptr2, xnumel, XBLOCK : tl.constexpr):
    xnumel = 256
    xoffset = tl.program_id(0) * XBLOCK
    xindex = xoffset + tl.arange(0, XBLOCK)[:]
    xmask = xindex < xnumel
    x0 = xindex
    tmp0 = tl.load(in_ptr0 + (x0), xmask)
    tmp1 = tmp0 * tmp0
    tmp2 = tl_math.abs(tmp0)
    tmp3 = 0.001
    tmp4 = tmp2 < tmp3
    tmp5 = tmp4.to(tl.int64)
    tmp6 = tl.full([1], 0, tl.int64)
    tmp7 = tmp5 == tmp6
    tl.store(out_ptr0 + (x0), tmp1, xmask)
    tl.store(out_ptr1 + (x0), tmp4, xmask)
    tl.store(out_ptr2 + (x0), tmp7, xmask)
''', device_str='cuda')


# kernel path: runs/run_shard_4/inductor_cache/yx/cyx33b4cuc5wetqcfqkvlznxkkeck5wuib3zqzten6pdyhb3nib2.py
# Topologically Sorted Source Nodes: [result], Original ATen: [aten.zeros_like]
# Source node to ATen node mapping:
#   result => full_default
# Graph fragment:
#   %full_default : [num_users=1] = call_function[target=torch.ops.aten.full.default](args = ([4, 4, 4, 4], 0), kwargs = {dtype: torch.float32, layout: torch.strided, device: cuda:0, pin_memory: False})
triton_poi_fused_zeros_like_1 = async_compile.triton('triton_poi_fused_zeros_like_1', '''
import triton
import triton.language as tl
from triton.compiler.compiler import AttrsDescriptor

from torch._inductor.runtime import triton_helpers, triton_heuristics
from torch._inductor.runtime.triton_helpers import libdevice, math as tl_math
from torch._inductor.runtime.hints import AutotuneHint, ReductionHint, TileHint, instance_descriptor, DeviceProperties

@triton_heuristics.pointwise(
    size_hints=[256], 
    filename=__file__,
    triton_meta={'signature': {0: '*fp32', 1: 'i32'}, 'device': DeviceProperties(type='cuda', index=0, cc=80, major=8, regs_per_multiprocessor=65536, max_threads_per_multi_processor=2048, multi_processor_count=108), 'constants': {}, 'configs': [AttrsDescriptor(divisible_by_16=(0, 1), equal_to_1=())]},
    inductor_meta={'autotune_hints': set(), 'kernel_name': 'triton_poi_fused_zeros_like_1', 'mutated_arg_names': [], 'no_x_dim': False, 'num_load': 0, 'num_reduction': 0, 'backend_hash': 'A9C866B4A14FD3277824029365D703C2427B2E685E54EC9B3EF4ADC8D1EEAC1D', 'are_deterministic_algorithms_enabled': False, 'assert_indirect_indexing': True, 'autotune_local_cache': True, 'autotune_pointwise': True, 'autotune_remote_cache': None, 'force_disable_caches': False, 'dynamic_scale_rblock': True, 'max_autotune': False, 'max_autotune_pointwise': False, 'min_split_scan_rblock': 256, 'spill_threshold': 16, 'store_cubin': False},
    min_elem_per_thread=0
)
@triton.jit
def triton_poi_fused_zeros_like_1(out_ptr0, xnumel, XBLOCK : tl.constexpr):
    xnumel = 256
    xoffset = tl.program_id(0) * XBLOCK
    xindex = xoffset + tl.arange(0, XBLOCK)[:]
    xmask = xindex < xnumel
    x0 = xindex
    tmp0 = 0.0
    tl.store(out_ptr0 + (x0), tmp0, xmask)
''', device_str='cuda')


async_compile.wait(globals())
del async_compile

def call(args):
    arg0_1, = args
    args.clear()
    assert_size_stride(arg0_1, (4, 4, 4, 4), (64, 16, 4, 1))
    with torch.cuda._DeviceGuard(0):
        torch.cuda.set_device(0)
        buf0 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        buf2 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.bool)
        buf3 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.bool)
        # Topologically Sorted Source Nodes: [theta_sq, abs_1, small_inds, large_inds], Original ATen: [aten.pow, aten.abs, aten.lt, aten.eq]
        stream0 = get_raw_stream(0)
        triton_poi_fused_abs_eq_lt_pow_0.run(arg0_1, buf0, buf2, buf3, 256, grid=grid(256), stream=stream0)
        del arg0_1
        buf1 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        # Topologically Sorted Source Nodes: [result], Original ATen: [aten.zeros_like]
        triton_poi_fused_zeros_like_1.run(buf1, 256, grid=grid(256), stream=stream0)
    return (buf0, buf2, buf1, buf3, )


def benchmark_compiled_module(times=10, repeat=10):
    from torch._dynamo.testing import rand_strided
    from torch._inductor.utils import print_performance
    arg0_1 = rand_strided((4, 4, 4, 4), (64, 16, 4, 1), device='cuda:0', dtype=torch.float32)
    fn = lambda: call([arg0_1])
    return print_performance(fn, times=times, repeat=repeat)


if __name__ == "__main__":
    from torch._inductor.wrapper_benchmark import compiled_module_main
    compiled_module_main('None', benchmark_compiled_module)

import torch
from torch import cos
from torch import sin


def get_small_and_large_angle_inds(theta: 'torch.Tensor', eps: 'float'=0.001):
    """Returns the indices of small and non-small (large) angles, given
    a tensor of angles, and the threshold below (exclusive) which angles
    are considered 'small'.

    Args:
        theta (torch.Tensor): Angle (magnitude of axis-angle vector).
        eps (float): Threshold (exclusive) below which an angle is
            considered 'small'.
    """
    small_inds = torch.abs(theta) < eps
    large_inds = small_inds == 0
    return small_inds, large_inds


def grad_one_minus_cos_theta_by_theta_sq(theta: 'torch.Tensor', eps:
    'float'=0.001):
    """Computes :math:`\\frac{\\partial}{\\partial \\theta}\\frac{1 - cos \\theta}{\\theta^2}`.

    Args:
        theta (torch.Tensor): Angle (magnitude of axis-angle vector).
        eps (float): Threshold (exclusive) below which an angle is
            considered 'small'.

    """
    result = torch.zeros_like(theta)
    s, l = get_small_and_large_angle_inds(theta, eps)
    theta_sq = theta ** 2
    result[s] = -theta[s] / 12 * (1 - theta_sq[s] / 5 * (1 / 3 - theta_sq[s
        ] / 56 * (1 / 2 - theta_sq[s] / 135)))
    result[l] = sin(theta[l]) / theta_sq[l] - 2 * (1 - cos(theta[l])) / (
        theta_sq[l] * theta[l])
    return result


def one_minus_cos_theta_by_theta_sq(theta: 'torch.Tensor', eps: 'float'=0.001):
    """Computes :math:`\\frac{1 - cos \\theta}{\\theta^2}`. 

    Args:
        theta (torch.Tensor): Angle (magnitude of axis-angle vector).
        eps (float): Threshold (exclusive) below which an angle is
            considered 'small'.

    """
    result = torch.zeros_like(theta)
    s, l = get_small_and_large_angle_inds(theta, eps)
    theta_sq = theta ** 2
    result[s] = 1 / 2 * (1 - theta_sq[s] / 12 * (1 - theta_sq[s] / 30 * (1 -
        theta_sq[s] / 56)))
    result[l] = (1 - cos(theta[l])) / theta_sq[l]
    return result


class OneMinusCosThetaByThetaSq_Function(torch.autograd.Function):

    @staticmethod
    def forward(ctx, theta):
        ctx.save_for_backward(theta)
        return one_minus_cos_theta_by_theta_sq(theta)

    @staticmethod
    def backward(ctx, grad_output):
        theta, = ctx.saved_tensors
        grad_theta = None
        if ctx.needs_input_grad[0]:
            grad_theta = grad_output * grad_one_minus_cos_theta_by_theta_sq(
                theta)
        return grad_theta


class OneMinusCosThetaByThetaSq(torch.nn.Module):

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

    def forward(self, x):
        return OneMinusCosThetaByThetaSq_Function.apply(x)


def get_inputs():
    return [torch.rand([4, 4, 4, 4])]


def get_init_inputs():
    return [[], {}]

import torch
import triton
import triton.language as tl
from torch._inductor.runtime.triton_heuristics import grid
from torch._C import _cuda_getCurrentRawStream as get_raw_stream
from torch._inductor.runtime.triton_helpers import math as tl_math
from torch import cos
from torch import sin
assert_size_stride = torch._C._dynamo.guards.assert_size_stride
empty_strided_cuda = torch._C._dynamo.guards._empty_strided_cuda


@triton.jit
def triton_poi_fused_abs_eq_lt_pow_0(in_ptr0, out_ptr0, out_ptr1, out_ptr2,
    xnumel, XBLOCK: tl.constexpr):
    xnumel = 256
    xoffset = tl.program_id(0) * XBLOCK
    xindex = xoffset + tl.arange(0, XBLOCK)[:]
    xmask = xindex < xnumel
    x0 = xindex
    tmp0 = tl.load(in_ptr0 + x0, xmask)
    tmp1 = tmp0 * tmp0
    tmp2 = tl_math.abs(tmp0)
    tmp3 = 0.001
    tmp4 = tmp2 < tmp3
    tmp5 = tmp4.to(tl.int64)
    tmp6 = tl.full([1], 0, tl.int64)
    tmp7 = tmp5 == tmp6
    tl.store(out_ptr0 + x0, tmp1, xmask)
    tl.store(out_ptr1 + x0, tmp4, xmask)
    tl.store(out_ptr2 + x0, tmp7, xmask)


@triton.jit
def triton_poi_fused_zeros_like_1(out_ptr0, xnumel, XBLOCK: tl.constexpr):
    xnumel = 256
    xoffset = tl.program_id(0) * XBLOCK
    xindex = xoffset + tl.arange(0, XBLOCK)[:]
    xmask = xindex < xnumel
    x0 = xindex
    tmp0 = 0.0
    tl.store(out_ptr0 + x0, tmp0, xmask)


def call(args):
    arg0_1, = args
    args.clear()
    assert_size_stride(arg0_1, (4, 4, 4, 4), (64, 16, 4, 1))
    with torch.cuda._DeviceGuard(0):
        torch.cuda.set_device(0)
        buf0 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        buf2 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.bool)
        buf3 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.bool)
        get_raw_stream(0)
        triton_poi_fused_abs_eq_lt_pow_0[grid(256)](arg0_1, buf0, buf2,
            buf3, 256, XBLOCK=256, num_warps=4, num_stages=1)
        del arg0_1
        buf1 = empty_strided_cuda((4, 4, 4, 4), (64, 16, 4, 1), torch.float32)
        triton_poi_fused_zeros_like_1[grid(256)](buf1, 256, XBLOCK=256,
            num_warps=4, num_stages=1)
    return buf0, buf2, buf1, buf3


def get_small_and_large_angle_inds(theta: 'torch.Tensor', eps: 'float'=0.001):
    """Returns the indices of small and non-small (large) angles, given
    a tensor of angles, and the threshold below (exclusive) which angles
    are considered 'small'.

    Args:
        theta (torch.Tensor): Angle (magnitude of axis-angle vector).
        eps (float): Threshold (exclusive) below which an angle is
            considered 'small'.
    """
    small_inds = torch.abs(theta) < eps
    large_inds = small_inds == 0
    return small_inds, large_inds


def grad_one_minus_cos_theta_by_theta_sq(theta: 'torch.Tensor', eps:
    'float'=0.001):
    """Computes :math:`\\frac{\\partial}{\\partial \\theta}\\frac{1 - cos \\theta}{\\theta^2}`.

    Args:
        theta (torch.Tensor): Angle (magnitude of axis-angle vector).
        eps (float): Threshold (exclusive) below which an angle is
            considered 'small'.

    """
    result = torch.zeros_like(theta)
    s, l = get_small_and_large_angle_inds(theta, eps)
    theta_sq = theta ** 2
    result[s] = -theta[s] / 12 * (1 - theta_sq[s] / 5 * (1 / 3 - theta_sq[s
        ] / 56 * (1 / 2 - theta_sq[s] / 135)))
    result[l] = sin(theta[l]) / theta_sq[l] - 2 * (1 - cos(theta[l])) / (
        theta_sq[l] * theta[l])
    return result


def one_minus_cos_theta_by_theta_sq(theta: 'torch.Tensor', eps: 'float'=0.001):
    """Computes :math:`\\frac{1 - cos \\theta}{\\theta^2}`. 

    Args:
        theta (torch.Tensor): Angle (magnitude of axis-angle vector).
        eps (float): Threshold (exclusive) below which an angle is
            considered 'small'.

    """
    result = torch.zeros_like(theta)
    s, l = get_small_and_large_angle_inds(theta, eps)
    theta_sq = theta ** 2
    result[s] = 1 / 2 * (1 - theta_sq[s] / 12 * (1 - theta_sq[s] / 30 * (1 -
        theta_sq[s] / 56)))
    result[l] = (1 - cos(theta[l])) / theta_sq[l]
    return result


class OneMinusCosThetaByThetaSq_Function(torch.autograd.Function):

    @staticmethod
    def forward(ctx, theta):
        ctx.save_for_backward(theta)
        return one_minus_cos_theta_by_theta_sq(theta)

    @staticmethod
    def backward(ctx, grad_output):
        theta, = ctx.saved_tensors
        grad_theta = None
        if ctx.needs_input_grad[0]:
            grad_theta = grad_output * grad_one_minus_cos_theta_by_theta_sq(
                theta)
        return grad_theta


class OneMinusCosThetaByThetaSqNew(torch.nn.Module):

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

    def forward(self, input_0):
        arg0_1 = input_0
        output = call([arg0_1])
        return output[0]
