def _s2_fft(x, for_grad, b_in, b_out):
'''
:param x: [batch, beta, alpha, complex] (nbatch, 2 * b_in, 2 * b_in, 2)
:return: [l * m, batch, complex] (b_out**2, nbatch, 2)
'''
nspec = b_out**2
nbatch = x.size(0)
wigner = _setup_wigner(b_in,
nl=b_out,
weighted=not for_grad,
device_type=x.device.type,
device_index=x.device.index)
cuda_kernel = _setup_s2fft_cuda_kernel(b=b_in, nspec=nspec, nbatch=nbatch)
x = torch.fft(x, 1) # [batch, beta, m, complex]
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
output = x.new_empty((nspec, nbatch, 2))
cuda_kernel(block=(1024, 1, 1),
grid=(cuda_utils.get_blocks(nspec * nbatch, 1024), 1, 1),
args=[
x.contiguous().data_ptr(),
wigner.contiguous().data_ptr(),
output.data_ptr()
],
stream=stream)
# [l * m, batch, complex]
return output
def _s2_ifft(x, for_grad, b_in, b_out):
'''
:param x: [l * m, batch, complex] (b_in**2, nbatch, 2)
:return: [batch, beta, alpha, complex] (nbatch, 2 b_out, 2 * b_out, 2)
'''
nbatch = x.size(1)
wigner = _setup_wigner(
b_out,
nl=b_in,
weighted=for_grad,
device_type=x.device.type,
device_index=x.device.index) # [beta, l * m] (2 * b_out - 1, nspec)
cuda_kernel = _setup_s2ifft_cuda_kernel(b=b_out, nl=b_in, nbatch=nbatch)
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
output = x.new_empty((nbatch, 2 * b_out, 2 * b_out, 2))
cuda_kernel(block=(1024, 1, 1),
grid=(cuda_utils.get_blocks(nbatch * (2 * b_out)**2,
1024), 1, 1),
args=[x.data_ptr(),
wigner.data_ptr(),
output.data_ptr()],
stream=stream)
# [batch, beta, m, complex] (nbatch, 2 * b_out, 2 * b_out, 2)
output = torch.ifft(output, 1) * output.size(
-2) # [batch, beta, alpha, complex]
return output
def backward(self, gradz): # pylint: disable=W
x, y = self.saved_tensors
nl = round(x.size(0)**0.5)
nbatch = x.size(1)
nfeature_in = x.size(2)
nfeature_out = y.size(2)
nspec = (4 * nl**2 - 1) * nl // 3
gradx_cuda_kernel = _setup_s2mm_gradx_cuda_kernel(nbatch=nbatch, nspec=nspec, nl=nl, nfeature_in=nfeature_in, nfeature_out=nfeature_out)
grady_cuda_kernel = _setup_s2mm_grady_cuda_kernel(nbatch=nbatch, nspec=nspec, nl=nl, nfeature_in=nfeature_in, nfeature_out=nfeature_out)
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
gradx = grady = None
if self.needs_input_grad[0]:
gradx = gradz.new_empty((nl**2, nbatch, nfeature_in, 2))
gradx_cuda_kernel(block=(cuda_utils.CUDA_NUM_THREADS, 1, 1),
grid=(cuda_utils.get_blocks(nl**2 * nbatch * nfeature_in, 1024), 1, 1),
args=[gradz.contiguous().data_ptr(), y.contiguous().data_ptr(), gradx.data_ptr()],
stream=stream)
if self.needs_input_grad[1]:
grady = gradz.new_empty((nl**2, nfeature_in, nfeature_out, 2))
grady_cuda_kernel(block=(cuda_utils.CUDA_NUM_THREADS, 1, 1),
grid=(cuda_utils.get_blocks(nl**2 * nfeature_in * nfeature_out, 1024), 1, 1),
args=[gradz.contiguous().data_ptr(), x.contiguous().data_ptr(), grady.data_ptr()],
stream=stream)
return gradx, grady
def s2_mm(x, y):
'''
:param x: [l * m, batch, feature_in, complex]
:param y: [l * m, feature_in, feature_out, complex]
:return: [l * m * n, batch, feature_out, complex]
'''
assert x.is_cuda and x.dtype == torch.float32
assert y.is_cuda and y.dtype == torch.float32
assert y.size(3) == 2
assert x.size(3) == 2
nbatch = x.size(1)
nfeature_in = x.size(2)
nfeature_out = y.size(2)
assert y.size(1) == nfeature_in
assert y.size(0) == x.size(0)
nl = round(x.size(0)**0.5)
nspec = (4 * nl**2 - 1) * nl // 3
assert x.size(0) == nl ** 2
assert y.size(0) == nl ** 2
cuda_kernel = _setup_s2mm_cuda_kernel(nbatch=nbatch, nspec=nspec, nfeature_in=nfeature_in, nfeature_out=nfeature_out)
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
output = x.new_empty((nspec, nbatch, nfeature_out, 2))
cuda_kernel(block=(cuda_utils.CUDA_NUM_THREADS, 1, 1),
grid=(cuda_utils.get_blocks(nspec * nbatch * nfeature_out, 1024), 1, 1),
args=[x.contiguous().data_ptr(), y.contiguous().data_ptr(), output.data_ptr()],
stream=stream)
# [l * m * n, batch, feature_out, complex]
return output
def s2_fft(x, for_grad=False, b_out=None):
'''
:param x: [..., beta, alpha, complex]
:return: [l * m, ..., complex]
'''
assert x.size(-1) == 2
b_in = x.size(-2) // 2
assert x.size(-2) == 2 * b_in
assert x.size(-3) == 2 * b_in
if b_out is None:
b_out = b_in
assert b_out <= b_in
batch_size = x.size()[:-3]
x = x.view(-1, 2 * b_in, 2 * b_in, 2) # [batch, beta, alpha, complex]
'''
:param x: [batch, beta, alpha, complex] (nbatch, 2 * b_in, 2 * b_in, 2)
:return: [l * m, batch, complex] (b_out**2, nbatch, 2)
'''
nspec = b_out**2
nbatch = x.size(0)
wigner = _setup_wigner(b_in,
nl=b_out,
weighted=not for_grad,
device=x.device)
wigner = wigner.view(2 * b_in, -1) # [beta, l * m] (2 * b_in, nspec)
x = torch.view_as_real(torch.fft.fft(
torch.view_as_complex(x))) # [batch, beta, m, complex]
output = x.new_empty((nspec, nbatch, 2))
if x.is_cuda and x.dtype == torch.float32:
import s2cnn.utils.cuda as cuda_utils
cuda_kernel = _setup_s2fft_cuda_kernel(b=b_in,
nspec=nspec,
nbatch=nbatch,
device=x.device.index)
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
cuda_kernel(block=(1024, 1, 1),
grid=(cuda_utils.get_blocks(nspec * nbatch, 1024), 1, 1),
args=[
x.contiguous().data_ptr(),
wigner.contiguous().data_ptr(),
output.data_ptr()
],
stream=stream)
# [l * m, batch, complex]
else:
for l in range(b_out):
s = slice(l**2, l**2 + 2 * l + 1)
xx = torch.cat(
(x[:, :,
-l:], x[:, :, :l + 1]), dim=2) if l > 0 else x[:, :, :1]
output[s] = torch.einsum("bm,zbmc->mzc", (wigner[:, s], xx))
output = output.view(-1, *batch_size,
2) # [l * m, ..., complex] (nspec, ..., 2)
return output
def s2_ifft(x, for_grad=False, b_out=None):
'''
:param x: [l * m, ..., complex]
'''
assert x.size(-1) == 2
nspec = x.size(0)
b_in = round(nspec**0.5)
assert nspec == b_in**2
if b_out is None:
b_out = b_in
assert b_out >= b_in
batch_size = x.size()[1:-1]
x = x.view(nspec, -1, 2) # [l * m, batch, complex] (nspec, nbatch, 2)
'''
:param x: [l * m, batch, complex] (b_in**2, nbatch, 2)
:return: [batch, beta, alpha, complex] (nbatch, 2 b_out, 2 * b_out, 2)
'''
nbatch = x.size(1)
wigner = _setup_wigner(b_out, nl=b_in, weighted=for_grad, device=x.device)
wigner = wigner.view(2 * b_out, -1) # [beta, l * m] (2 * b_out, nspec)
if x.is_cuda and x.dtype == torch.float32:
import s2cnn.utils.cuda as cuda_utils
cuda_kernel = _setup_s2ifft_cuda_kernel(b=b_out,
nl=b_in,
nbatch=nbatch,
device=x.device.index)
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
output = x.new_empty((nbatch, 2 * b_out, 2 * b_out, 2))
cuda_kernel(block=(1024, 1, 1),
grid=(cuda_utils.get_blocks(nbatch * (2 * b_out)**2,
1024), 1, 1),
args=[x.data_ptr(),
wigner.data_ptr(),
output.data_ptr()],
stream=stream)
# [batch, beta, m, complex] (nbatch, 2 * b_out, 2 * b_out, 2)
else:
output = x.new_zeros((nbatch, 2 * b_out, 2 * b_out, 2))
for l in range(b_in):
s = slice(l**2, l**2 + 2 * l + 1)
out = torch.einsum("mzc,bm->zbmc", (x[s], wigner[:, s]))
output[:, :, :l + 1] += out[:, :, -l - 1:]
if l > 0:
output[:, :, -l:] += out[:, :, :l]
output = torch.view_as_real(torch.fft.ifft(
torch.view_as_complex(output))) * output.size(
-2) # [batch, beta, alpha, complex]
output = output.view(*batch_size, 2 * b_out, 2 * b_out, 2)
return output
def _s2_fft(x, for_grad, b_in, b_out):
'''
:param x: [batch, beta, alpha, complex] (nbatch, 2 * b_in, 2 * b_in, 2)
:return: [l * m, batch, complex] (b_out**2, nbatch, 2)
'''
nspec = b_out**2
nbatch = x.size(0)
wigner = _setup_wigner(b_in,
nl=b_out,
weighted=not for_grad,
device_type=x.device.type,
device_index=x.device.index)
wigner = wigner.view(2 * b_in, -1) # [beta, l * m] (2 * b_in, nspec)
x = torch.fft(x, 1) # [batch, beta, m, complex]
output = x.new_empty((nspec, nbatch, 2))
if x.is_cuda and x.dtype == torch.float32:
import s2cnn.utils.cuda as cuda_utils
device = torch.cuda.current_device()
cuda_kernel = _setup_s2fft_cuda_kernel(b=b_in,
nspec=nspec,
nbatch=nbatch,
device=device)
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
cuda_kernel(block=(1024, 1, 1),
grid=(cuda_utils.get_blocks(nspec * nbatch, 1024), 1, 1),
args=[
x.contiguous().data_ptr(),
wigner.contiguous().data_ptr(),
output.data_ptr()
],
stream=stream)
# [l * m, batch, complex]
else:
for l in range(b_out):
s = slice(l**2, l**2 + 2 * l + 1)
xx = torch.cat(
(x[:, :,
-l:], x[:, :, :l + 1]), dim=2) if l > 0 else x[:, :, :1]
output[s] = torch.einsum("bm,zbmc->mzc", (wigner[:, s], xx))
return output
def _s2_ifft(x, for_grad, b_in, b_out):
'''
:param x: [l * m, batch, complex] (b_in**2, nbatch, 2)
:return: [batch, beta, alpha, complex] (nbatch, 2 b_out, 2 * b_out, 2)
'''
nbatch = x.size(1)
wigner = _setup_wigner(b_out,
nl=b_in,
weighted=for_grad,
device_type=x.device.type,
device_index=x.device.index)
wigner = wigner.view(2 * b_out, -1) # [beta, l * m] (2 * b_out, nspec)
if x.is_cuda and x.dtype == torch.float32:
import s2cnn.utils.cuda as cuda_utils
device = torch.cuda.current_device()
cuda_kernel = _setup_s2ifft_cuda_kernel(b=b_out,
nl=b_in,
nbatch=nbatch,
device=device)
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
output = x.new_empty((nbatch, 2 * b_out, 2 * b_out, 2))
cuda_kernel(block=(1024, 1, 1),
grid=(cuda_utils.get_blocks(nbatch * (2 * b_out)**2,
1024), 1, 1),
args=[x.data_ptr(),
wigner.data_ptr(),
output.data_ptr()],
stream=stream)
# [batch, beta, m, complex] (nbatch, 2 * b_out, 2 * b_out, 2)
else:
output = x.new_zeros((nbatch, 2 * b_out, 2 * b_out, 2))
for l in range(b_in):
s = slice(l**2, l**2 + 2 * l + 1)
out = torch.einsum("mzc,bm->zbmc", (x[s], wigner[:, s]))
output[:, :, :l + 1] += out[:, :, -l - 1:]
if l > 0:
output[:, :, -l:] += out[:, :, :l]
output = torch.ifft(output, 1) * output.size(
-2) # [batch, beta, alpha, complex]
return output
def _setup_so3ifft_cuda_kernel(b_in, b_out, nbatch, real_output, device=0):
kernel = '''
#define B_IN {}
#define B_OUT {}
#define NSPEC {}
#define NBATCH {}
'''.format(b_in, b_out, b_in * (4 * b_in ** 2 - 1) // 3, nbatch)
if real_output:
kernel += '''
#define REAL_OUT
'''
kernel += '''
#define MOD(i, n) (((i) + (n)) % (n))
#define MAX(x, y) ((x) < (y) ? (y) : (x))
#define CEIL_DIV(x, y) (((x) + (y) - 1) / (y))
extern "C"
__global__ void main_(const float* in, const float* wig, float* out)
{
int m = (blockIdx.z / (2 * B_OUT - 1)) - (B_OUT - 1);
int n = (blockIdx.z % (2 * B_OUT - 1)) - (B_OUT - 1);
#ifdef REAL_OUT
if (n < 0 || (n == 0 && m < 0)) {
return; // note: this return does not depend on threadIdx
}
#endif
int l_min = MAX(abs(m), abs(n));
int batch = blockIdx.y * 32 + threadIdx.y;
float sum_re = 0.0;
float sum_im = 0.0;
for (int tile = 0; tile < CEIL_DIV(B_IN - l_min, 32); ++tile) {
__shared__ float tileA[2][32][32];
__shared__ float tileB[32][32+1];
int l = l_min + tile * 32 + threadIdx.x;
int lmn = (4 * l*l - 1) * l / 3 + (l+m) * (2 * l + 1) + (l+n);
int i = (lmn * NBATCH + batch) * 2;
tileA[0][threadIdx.y][threadIdx.x] = l < B_IN && batch < NBATCH ? in[i + 0] : 0.0;
tileA[1][threadIdx.y][threadIdx.x] = l < B_IN && batch < NBATCH ? in[i + 1] : 0.0;
int beta = blockIdx.x * 32 + threadIdx.y;
tileB[threadIdx.x][threadIdx.y] = l < B_IN && beta < 2*B_OUT ? wig[beta * NSPEC + lmn] : 0.0;
__syncthreads();
for (int l = 0; l < 32; ++l) {
sum_re += tileA[0][threadIdx.y][l] * tileB[l][threadIdx.x];
sum_im += tileA[1][threadIdx.y][l] * tileB[l][threadIdx.x];
}
__syncthreads();
}
int beta = blockIdx.x * 32 + threadIdx.x;
if (beta < 2*B_OUT && batch < NBATCH) {
int i = (((batch * 2*B_OUT + beta) * 2*B_OUT + MOD(m, 2*B_OUT)) * 2*B_OUT + MOD(n, 2*B_OUT)) * 2;
out[i + 0] = sum_re;
out[i + 1] = sum_im;
#ifdef REAL_OUT
i = (((batch * 2*B_OUT + beta) * 2*B_OUT + MOD(-m, 2*B_OUT)) * 2*B_OUT + MOD(-n, 2*B_OUT)) * 2;
out[i + 0] = sum_re;
out[i + 1] = -sum_im;
#endif
}
}
'''
import s2cnn.utils.cuda as cuda_utils
kernel = cuda_utils.compile_kernel(kernel, 'so3ifft.cu', 'main_')
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
def fun(x, wigner, output):
output[:] = 0
kernel(block=(32, 32, 1),
grid=(math.ceil(2 * b_out / 32), math.ceil(nbatch / 32), (2 * b_out - 1) ** 2),
args=[x.data_ptr(), wigner.data_ptr(), output.data_ptr()],
stream=stream)
return fun
def _setup_so3fft_cuda_kernel(b_in, b_out, nbatch, real_input, device=0):
kernel = '''
#define B_IN {}
#define B_OUT {}
#define NSPEC {}
#define NBATCH {}
'''.format(b_in, b_out, b_out * (4 * b_out ** 2 - 1) // 3, nbatch)
if real_input:
kernel += '''
#define REAL_IN
'''
kernel += '''
#define MOD(i, n) (((i) + (n)) % (n))
#define MAX(x, y) ((x) < (y) ? (y) : (x))
#define CEIL_DIV(x, y) (((x) + (y) - 1) / (y))
extern "C"
__global__ void main_(const float* in, const float* wig, float* out)
{
// blockIdx = (l, batch, mn)
// blockDim = (32, 32, 1)
// threadIdx = (sub l, sub batch, 0)
// gridDim = (b / 32, nbatch / 32, (2b-1)**2)
int m = (blockIdx.z / (2 * B_OUT - 1)) - (B_OUT - 1);
int n = (blockIdx.z % (2 * B_OUT - 1)) - (B_OUT - 1);
int l_min = MAX(abs(m), abs(n));
if (blockIdx.x * 32 + 31 < l_min) {
// for blocks fully out of l-range
return; // note: this return does not depend on threadIdx
}
#ifdef REAL_IN
if (n < 0 || (n == 0 && m < 0)) {
return; // note: this return does not depend on threadIdx
}
#endif
int batch = blockIdx.y * 32 + threadIdx.y;
int l = blockIdx.x * 32 + threadIdx.x;
int lmn = (4 * l*l - 1) * l / 3 + (l+m) * (2 * l + 1) + (l+n);
float sum_re = 0.0;
float sum_im = 0.0;
for (int tile = 0; tile < CEIL_DIV(2 * B_IN, 32); ++tile) {
__shared__ float tileA[32][32][2];
__shared__ float tileB[32][32];
int beta = tile * 32 + threadIdx.x;
#ifdef REAL_IN
// `in` shape is (NBATCH, 2 * B_IN, 2 * B_IN, B_IN + 1, 2)
// http://www.fftw.org/fftw3_doc/Multi_002dDimensional-DFTs-of-Real-Data.html
int i = (((batch * 2*B_IN + beta) * 2*B_IN + MOD(m, 2*B_IN)) * (B_IN + 1) + n) * 2;
#else
int i = (((batch * 2*B_IN + beta) * 2*B_IN + MOD(m, 2*B_IN)) * 2*B_IN + MOD(n, 2*B_IN)) * 2;
#endif
tileA[threadIdx.y][threadIdx.x][0] = beta < 2*B_IN && batch < NBATCH ? in[i + 0] : 0.0;
tileA[threadIdx.y][threadIdx.x][1] = beta < 2*B_IN && batch < NBATCH ? in[i + 1] : 0.0;
beta = tile * 32 + threadIdx.y;
tileB[threadIdx.y][threadIdx.x] = beta < 2*B_IN && l_min <= l && l < B_OUT ? wig[beta * NSPEC + lmn] : 0.0;
__syncthreads();
for (int beta = 0; beta < 32; ++beta) {
sum_re += tileA[threadIdx.y][beta][0] * tileB[beta][threadIdx.x];
sum_im += tileA[threadIdx.y][beta][1] * tileB[beta][threadIdx.x];
}
__syncthreads();
}
// About this if: some blocks are used to compute but not to save the results
if (l_min <= l && l < B_OUT && batch < NBATCH) {
out[(lmn * NBATCH + batch) * 2 + 0] = sum_re;
out[(lmn * NBATCH + batch) * 2 + 1] = sum_im;
#ifdef REAL_IN
lmn = (4 * l*l - 1) * l / 3 + (l-m) * (2 * l + 1) + (l-n);
float fudge = (m - n) % 2 == 0 ? 1.0 : -1.0;
out[(lmn * NBATCH + batch) * 2 + 0] = fudge * sum_re;
out[(lmn * NBATCH + batch) * 2 + 1] = -fudge * sum_im;
#endif
}
}
'''
import s2cnn.utils.cuda as cuda_utils
kernel = cuda_utils.compile_kernel(kernel, 'so3fft.cu', 'main_')
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
def fun(x, wigner, output):
assert output.is_contiguous()
kernel(block=(32, 32, 1),
grid=(math.ceil(b_out / 32), math.ceil(nbatch / 32), (2 * b_out - 1) ** 2),
args=[x.contiguous().data_ptr(), wigner.contiguous().data_ptr(), output.data_ptr()],
stream=stream)
return fun
def _setup_so3mm_cuda_kernel(nl,
ni,
nj,
nk,
conj_x=False,
conj_y=False,
trans_x_spec=False,
trans_x_feature=False,
trans_y_spec=False,
trans_y_feature=False,
trans_out_feature=False,
device=0):
'''
return a function that computes
out[l*m*n, i, j] = sum_k sum_p x[l*m*p, i, k] y[l*p*n, k, j]
where out, x, y are complex valued
if conj_x is set to True, x is conjugated
if conj_y is set to True, y is conjugated
if trans_x_spec is set to True m and p are permuted in x[...]
if trans_y_spec is set to True p and n are permuted in y[...]
if trans_x_feature is set to True i and k are permuted in x[...]
if trans_y_feature is set to True k and j are permuted in y[...]
if trans_out_feature is set to True i and j are permuted in out[...]
'''
kernel = '''
#define NI {}
#define NJ {}
#define NK {}
'''.format(ni, nj, nk)
if not trans_x_spec and not trans_x_feature:
kernel += '#define INDEX_X (((L0 + m * L + p) * NI + i) * NK + k)\n'
if not trans_x_spec and trans_x_feature:
kernel += '#define INDEX_X (((L0 + m * L + p) * NK + k) * NI + i)\n'
if trans_x_spec and not trans_x_feature:
kernel += '#define INDEX_X (((L0 + p * L + m) * NI + i) * NK + k)\n'
if trans_x_spec and trans_x_feature:
kernel += '#define INDEX_X (((L0 + p * L + m) * NK + k) * NI + i)\n'
if not trans_y_spec and not trans_y_feature:
kernel += '#define INDEX_Y (((L0 + p * L + n) * NK + k) * NJ + j)\n'
if not trans_y_spec and trans_y_feature:
kernel += '#define INDEX_Y (((L0 + p * L + n) * NJ + j) * NK + k)\n'
if trans_y_spec and not trans_y_feature:
kernel += '#define INDEX_Y (((L0 + n * L + p) * NK + k) * NJ + j)\n'
if trans_y_spec and trans_y_feature:
kernel += '#define INDEX_Y (((L0 + n * L + p) * NJ + j) * NK + k)\n'
if not trans_out_feature:
kernel += '#define INDEX_OUT (((L0 + m * L + n) * NI + i) * NJ + j)\n'
if trans_out_feature:
kernel += '#define INDEX_OUT (((L0 + m * L + n) * NJ + j) * NI + i)\n'
kernel += '''
#define CONJ_X {}
#define CONJ_Y {}
'''.format("x_im = -x_im;" if conj_x else ";",
"y_im = -y_im;" if conj_y else ";")
kernel += '''
#define CEIL_DIV(x, y) (((x) + (y) - 1) / (y))
extern "C"
__global__ void main_(const float* in_x, const float* in_y, float* out)
{
// start of thread independant code
int l = blockIdx.z;
int L = 2 * l + 1;
int L0 = (4 * l*l - 1) * l / 3;
if (blockIdx.y * 32 >= L * NI || blockIdx.x * 32 >= L * NJ) {
return;
}
int ntile = CEIL_DIV(L * NK, 32);
// end of thread independant code
int mi = blockIdx.y * 32 + threadIdx.y;
int m = mi / NI;
int i = mi % NI;
int nj = blockIdx.x * 32 + threadIdx.x;
int n = nj / NJ;
int j = nj % NJ;
float sum_re = 0.0;
float sum_im = 0.0;
for (int tile = 0; tile < ntile; ++tile) {
__shared__ float tileX[2][32][32];
__shared__ float tileY[2][32][32];
int pk = tile * 32 + threadIdx.x;
int p = pk / NK;
int k = pk % NK;
int index = INDEX_X * 2;
tileX[0][threadIdx.y][threadIdx.x] = m < L && p < L ? in_x[index + 0] : 0.0;
tileX[1][threadIdx.y][threadIdx.x] = m < L && p < L ? in_x[index + 1] : 0.0;
pk = tile * 32 + threadIdx.y;
p = pk / NK;
k = pk % NK;
index = INDEX_Y * 2;
tileY[0][threadIdx.y][threadIdx.x] = p < L && n < L ? in_y[index + 0] : 0.0;
tileY[1][threadIdx.y][threadIdx.x] = p < L && n < L ? in_y[index + 1] : 0.0;
__syncthreads();
for (int any = 0; any < 32; ++any) {
float x_re = tileX[0][threadIdx.y][any];
float x_im = tileX[1][threadIdx.y][any];
float y_re = tileY[0][any][threadIdx.x];
float y_im = tileY[1][any][threadIdx.x];
CONJ_X
CONJ_Y
sum_re += x_re * y_re - x_im * y_im;
sum_im += x_re * y_im + x_im * y_re;
}
__syncthreads();
}
if (m < L && n < L) {
int index = INDEX_OUT * 2;
out[index + 0] = sum_re;
out[index + 1] = sum_im;
}
}
'''
import s2cnn.utils.cuda as cuda_utils
kernel = cuda_utils.compile_kernel(kernel, b'so3_mm.cu', 'main_')
stream = cuda_utils.Stream(ptr=torch.cuda.current_stream().cuda_stream)
def fun(x, y, output):
assert output.is_contiguous()
kernel(block=(32, 32, 1),
grid=(math.ceil(
(2 * nl - 1) * nj / 32), math.ceil(
(2 * nl - 1) * ni / 32), nl),
args=[
x.contiguous().data_ptr(),
y.contiguous().data_ptr(),
output.data_ptr()
],
stream=stream)
return fun
