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import torch
import torch.nn.functional as F
def npo2(len):
return 2 ** math.ceil(math.log2(len))
def pad_npo2(X):
len_npo2 = npo2(X.size(1))
pad_tuple = (0, 0, 0, 0, 0, len_npo2 - X.size(1))
return F.pad(X, pad_tuple, "constant", 0)
class PScan(torch.autograd.Function):
@staticmethod
def pscan(A, X):
B, D, L, _ = A.size()
num_steps = int(math.log2(L))
Aa = A
Xa = X
for _ in range(num_steps-2):
T = Xa.size(2)
Aa = Aa.view(B, D, T//2, 2, -1)
Xa = Xa.view(B, D, T//2, 2, -1)
Xa[:, :, :, 1].add_(Aa[:, :, :, 1].mul(Xa[:, :, :, 0]))
Aa[:, :, :, 1].mul_(Aa[:, :, :, 0])
Aa = Aa[:, :, :, 1]
Xa = Xa[:, :, :, 1]
if Xa.size(2) == 4:
Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 0]))
Aa[:, :, 1].mul_(Aa[:, :, 0])
Xa[:, :, 3].add_(Aa[:, :, 3].mul(Xa[:, :, 2] + Aa[:, :, 2].mul(Xa[:, :, 1])))
elif Xa.size(2) == 2:
Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 0]))
return
else:
return
Aa = A[:, :, 2**(num_steps-2)-1:L:2**(num_steps-2)]
Xa = X[:, :, 2**(num_steps-2)-1:L:2**(num_steps-2)]
Xa[:, :, 2].add_(Aa[:, :, 2].mul(Xa[:, :, 1]))
Aa[:, :, 2].mul_(Aa[:, :, 1])
for k in range(num_steps-3, -1, -1):
Aa = A[:, :, 2**k-1:L:2**k]
Xa = X[:, :, 2**k-1:L:2**k]
T = Xa.size(2)
Aa = Aa.view(B, D, T//2, 2, -1)
Xa = Xa.view(B, D, T//2, 2, -1)
Xa[:, :, 1:, 0].add_(Aa[:, :, 1:, 0].mul(Xa[:, :, :-1, 1]))
Aa[:, :, 1:, 0].mul_(Aa[:, :, :-1, 1])
@staticmethod
def pscan_rev(A, X):
B, D, L, _ = A.size()
num_steps = int(math.log2(L))
Aa = A
Xa = X
for _ in range(num_steps-2):
T = Xa.size(2)
Aa = Aa.view(B, D, T//2, 2, -1)
Xa = Xa.view(B, D, T//2, 2, -1)
Xa[:, :, :, 0].add_(Aa[:, :, :, 0].mul(Xa[:, :, :, 1]))
Aa[:, :, :, 0].mul_(Aa[:, :, :, 1])
Aa = Aa[:, :, :, 0]
Xa = Xa[:, :, :, 0]
if Xa.size(2) == 4:
Xa[:, :, 2].add_(Aa[:, :, 2].mul(Xa[:, :, 3]))
Aa[:, :, 2].mul_(Aa[:, :, 3])
Xa[:, :, 0].add_(Aa[:, :, 0].mul(Xa[:, :, 1].add(Aa[:, :, 1].mul(Xa[:, :, 2]))))
elif Xa.size(2) == 2:
Xa[:, :, 0].add_(Aa[:, :, 0].mul(Xa[:, :, 1]))
return
else:
return
Aa = A[:, :, 0:L:2**(num_steps-2)]
Xa = X[:, :, 0:L:2**(num_steps-2)]
Xa[:, :, 1].add_(Aa[:, :, 1].mul(Xa[:, :, 2]))
Aa[:, :, 1].mul_(Aa[:, :, 2])
for k in range(num_steps-3, -1, -1):
Aa = A[:, :, 0:L:2**k]
Xa = X[:, :, 0:L:2**k]
T = Xa.size(2)
Aa = Aa.view(B, D, T//2, 2, -1)
Xa = Xa.view(B, D, T//2, 2, -1)
Xa[:, :, :-1, 1].add_(Aa[:, :, :-1, 1].mul(Xa[:, :, 1:, 0]))
Aa[:, :, :-1, 1].mul_(Aa[:, :, 1:, 0])
@staticmethod
def forward(ctx, A_in, X_in):
L = X_in.size(1)
if L == npo2(L):
A = A_in.clone()
X = X_in.clone()
else:
A = pad_npo2(A_in)
X = pad_npo2(X_in)
A = A.transpose(2, 1)
X = X.transpose(2, 1)
PScan.pscan(A, X)
ctx.save_for_backward(A_in, X)
return X.transpose(2, 1)[:, :L]
@staticmethod
def backward(ctx, grad_output_in):
A_in, X = ctx.saved_tensors
L = grad_output_in.size(1)
if L == npo2(L):
grad_output = grad_output_in.clone()
else:
grad_output = pad_npo2(grad_output_in)
A_in = pad_npo2(A_in)
grad_output = grad_output.transpose(2, 1)
A_in = A_in.transpose(2, 1)
A = torch.nn.functional.pad(A_in[:, :, 1:], (0, 0, 0, 1))
PScan.pscan_rev(A, grad_output)
Q = torch.zeros_like(X)
Q[:, :, 1:].add_(X[:, :, :-1] * grad_output[:, :, 1:])
return Q.transpose(2, 1)[:, :L], grad_output.transpose(2, 1)[:, :L]
pscan = PScan.apply
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