+######################################################################
+
+
+def pscan_diff(X, V, s=1):
+ if X.size(1) == 1:
+ return X, V
+
+ T = 2 * (X.size(1) // 2)
+
+ Xf = X[:, :T].view(X.size(0), X.size(1) // 2, 2, X.size(2))
+ Vf = V[:, :T].view(V.size(0), V.size(1) // 2, 2)
+
+ Xr = X.new(X.size())
+ Vr = V.new(V.size())
+ Xrf = Xr[:, :T].view(Xr.size(0), Xr.size(1) // 2, 2, Xr.size(2))
+ Vrf = Vr[:, :T].view(Vr.size(0), Vr.size(1) // 2, 2)
+
+ # [:, :, 0] < [:, :, 1]
+ dv0 = (Vf[:, :, 0] - Vf[:, :, 0].detach())[:, :, None]
+ dv = (Vf[:, :, 1] - Vf[:, :, 1].detach())[:, :, None]
+ m = (Vf[:, :, 0] - s >= Vf[:, :, 1]).long()
+ Vv = m * (Vf[:, :, 0] - s) + (1 - m) * Vf[:, :, 1]
+ m = m[:, :, None]
+ Xx = m * Xf[:, :, 0] + (1 - m) * (Xf[:, :, 1] * (1 + dv) + Xf[:, :, 0] * dv0)
+
+ Xrf[:, :, 1], Vrf[:, :, 1] = pscan_diff(Xx, Vv, s * 2)
+
+ # [:, :-1, 1] < [:, 1:, 0]
+ dv0 = (Vrf[:, :-1, 1] - Vrf[:, :-1, 1].detach())[:, :, None]
+ dv = (Vf[:, 1:, 0] - Vf[:, 1:, 0].detach())[:, :, None]
+ m = (Vrf[:, :-1, 1] - s >= Vf[:, 1:, 0]).long()
+ Vrf[:, 1:, 0] = m * (Vrf[:, :-1, 1] - s) + (1 - m) * Vf[:, 1:, 0]
+ m = m[:, :, None]
+ Xrf[:, 1:, 0] = m * Xrf[:, :-1, 1] + (1 - m) * (
+ Xf[:, 1:, 0] * (1 + dv) + Xrf[:, :-1, 1] * dv0
+ )
+
+ Xr[:, 0] = X[:, 0]
+ Vr[:, 0] = V[:, 0]
+
+ if T < X.size(1):
+ # [:, -2] < [:, -1]
+ dx = X[:, -2] - X[:, -2].detach()
+ dv = (V[:, -1] - V[:, -1].detach())[:, None]
+ m = (V[:, -2] - s >= V[:, -1]).long()
+ Vr[:, -1] = m * (Vr[:, -2] - s) + (1 - m) * V[:, -1]
+ m = m[:, None]
+ Xr[:, -1] = m * Xr[:, -2] + (1 - m) * (X[:, -1] * (1 + dv) + dx)
+
+ return Xr, Vr
+
+