Methods and apparatus for signal flow graph pipelining that reduce storage of temporary variables

A network of nodes organized in stages according to dimensions of a row (R) by column (C) by plane (P) matrix that forms an R×C×P array having connectivity according to adjacency of connections between elements in corresponding dimensions of the R×C×P array which includes wrap around adjacent elements, the connectivity within the stages includes connections between nodes in the same position, the network comprising:

• p planes of R×C arrays of Ar,c,p nodes and p planes of R×C arrays of Rr,c,p nodes having a different p that is the same for an R×C array of Ar,c,p nodes and a corresponding R×C array of Rr,c,p nodes, p ∈ {0, 1, . . . , P−1}, each R×C array of Ar,c,p nodes and each R×C array of Rr,c,p nodes having a different r that is the same for each row r, r ∈ {0, 1, . . . , R−1}, and for each row r, c varies as the column number c ∈ {0, 1, . . . , C−1}, each Ar,c,p node in each plane p is operable to output a data value, and each R×C array of Rr,c,p nodes is directly coupled to a corresponding R×C array of Ar,c,p nodes according to a 1 to N adjacency of nodes in a first dimension, N a positive odd integer, and R≧N and C≧N, wherein each Rr,c,p node is operable to select a data value solely from directly coupled nodes Ar,c−└N/2┘,p, . . . , Ar,c−2,p, Ar,c−1,p, Ar,c,p, Ar,c+1,p, Ar,c−2,p, . . . , Ar,c+└N/2┘,p and to output the Rr,c,p node selected data value, wherein for a selected value of N, the Ar,c−└N/2┘,p, . . . , Ar,c−2,p, Ar,c−1,p sequence of nodes has └N/2┘ nodes and for N>1 the last node is Ar,c−└N/2┘,p and the Ar,c+1,p, Ar,c+2,p, . . . , Ar,c+└N/2┘,p sequence of nodes has └N/2┘ nodes and for N>1 the last node is Ar,c+└N/2┘,p, wherein └N/2┘ is the floor of N/2 which is the largest integer less than N/2;
• p planes of R×C arrays of Sr,c,p nodes having a different p that is the same for an R×C array of Rr,c,p nodes and a corresponding R×C array of Sr,c,p nodes, p ∈ {0, 1, . . . , P−1}, each R×C array of Sr,c,p nodes having a different r that is the same for each row r, r ∈ {0, 1, . . . , R−1}, and for each row r, c varies as the column number c ∈ {0, 1, . . . , C−1}, each R×C array of Sr,c,p nodes in each plane p is directly coupled to a corresponding R×C array of Rr,c,p nodes according to a 1 to M adjacency of nodes in a second dimension, M a positive odd integer, and R≧M and C≧M, wherein each Sr,c,p node is operable to select a data value solely from directly coupled nodes Rr−└M/2┘,c,p, . . . , Rr−2,c,p, Rr−1,c,p, Rr,c,p, Rr+1,c,p, Rr+2,c,p, . . . , Rr+└M/2┘,c,p and to output the Sr,c,p node selected data value, wherein for the selected value of M, the Rr−└M/2┘,c,p, . . . , Rr−2,c,p, Rr−1,c,p sequence of nodes has └M/2┘ nodes and for M>1 the last node is Rr−└M/2┘,c,p, the Rr+1,c,p, Rr+2,c,p, . . . , Rr+└M/2┘,c,p sequence of nodes has └M/2┘ nodes and for M>1 the last node is Rr+└M/2┘,c,p, wherein └M/2┘ is the floor of M/2 which is the largest integer less than M/2;
• and
• p planes of R×C arrays of Vr,c,p nodes having a different p that is the same for an R×C array of Sr,c,p nodes and a corresponding R×C array of Vr,c,p nodes, p ∈ {0, 1, . . . , P−1}, each R×C array of Vr,c,p nodes having a different r that is the same for each row r, r ∈ {0, 1, . . . , R−1}, and for each row r, c varies as the column number c ∈ {0, 1, . . . , C−1}, and each Vr,c,p node is directly coupled to P Sr,c,p nodes having the same r and c as the Vr,c,p node, p ∈ {0, 1, . . . , P−1}, wherein each Vr,c,p node is operable to select a data value from directly coupled P Sr,c,p nodes and to output the Vr,c,p node selected data value.