Multiple level minimum logic network

Description of equivalent WO 9704399 A2

MULTIPLE LEVEL MINIMUM LOGIC NETWORK

FIELD OF INVENTION

The present invention relates to interconnection structures for computing and communication systems. More specifically, the present invention relates to multiple level interconnection structures in which control and logic circuits are minimized.

BACKGROUND OF THE INVENTION

Many advanced computing systems, including supercomputers for example, utilize multiple computational units to improve performance in what is called a parallel system. The system of interconnections among parallel computational units is an important characteristic for determining performance. One technique for interconnecting parallel computational units involves construction of a communication network similar to a telephone network in which groups of network elements are connected to switching systems. The switching systems are interconnected in a hierarchical manner so that any switching station manages a workable number of connections.

One disadvantage of a network connection is an increase in the latency of access to another computational unit since transmission of a message traverses several stages of a network. Typically, periods of peak activity occur in which the network is saturated with numerous messages so that many messages simultaneously contend for the use of a switching station. Various network types have been devised with goals of reducing congestion, improving transmission speed and achieving a reasonable cost. These goals are typically attained by rapidly communicating between nodes and minimizing the number of interconnections that a node must support.

One conventional interconnection scheme is a ring of nodes with each node connected to two other nodes so that the line of interconnections forms a circle. The definition of a ring, in accordance with a standard definition of a ring network in the art of computing (IBM Dictionary of Computing. McDaniel G. ed., McGraw-Hill, Inc., 1994, p. 584) is a network configuration in which devices are connected by unidirectional transmission links to form a closed path. Another simple conventional scheme is a mesh in which each node is connected to its four nearest neighbors. The ring and mesh techniques advantageously limit the number of interconnections supported by a node. Unfortunately, the ring and mesh networks typically are plagued by lengthy delays in message communication since the number of nodes traversed in sending a message from one node to another may be quite large. These lengthy delays commonly cause a computational unit to remain idle awaiting a message in transit to the unit.

The earliest networks, generally beginning with telephone networks, utilize circuit switching in which each message is routed through the network along a dedicated path that is reserved for the duration of the communication analogous to a direct connection via a single circuit between the communicating parties. Circuit switching disadvantageously requires a lengthy setup time. Such delays are intolerable during the short and quick exchanges that take place between different computational units. Furthermore, a dedicated pathway is very wasteful of system bandwidth. One technique for solving the problems arising using circuit switching is called packet switching in which messages sent from one computational unit to another does not travel in a continuous stream to a dedicated circuit. Instead, each computational unit is connected to a node that subdivides messages into a sequence of data packets. A message contains an arbitrary sequence of binary digits that are preceded by addressing information. The length of the entire message is limited to a defined maximum length. A "header" containing at least the destination address and a sequence number is attached to each packet, and the packets are sent across the network. Addresses are read and packets are delivered within a fraction of a second. No circuit setup delay is imposed because no circuit is set up. System bandwidth is not wasted since there is no individual connection between two computational units. However, a small portion of the communication capacity is used for routing information, headers and other control information. When communication advances in isolated, short bursts, packet switching more efficiently utilizes network capacity. Because no transmission capacity is specifically reserved for an individual computational unit, time gaps between packets are filled with packets from other users. Packet switching implements a type of distributed multiplexing system by enabling all users to share lines on the network continuously.

Advances in technology result in improvement in computer system performance. However, the manner in which these technological advances are implemented will greatly determine the extent of improvement in performance. For example, performance improvements arising from completely optical computing strongly depend on an interconnection scheme that best exploits the advantages of optical technology.

SUMMARY OF THE INVENTION

In accordance with the present invention, a multiple level minimum logic network interconnect structure has a very high bandwidth and low latency. Control of interconnect structure switching is distributed throughout multiple nodes in the structure so that a supervisory controller providing a global control function is not necessary. A global control function is eliminated and complex logic structures are avoided by a novel data flow technique that is based on timing and positioning of messages communicating through the interconnect structure. Furthermore, the interconnect structure implements a "deflection" or "hot potato" design in which processing and storage overhead at each node is minimized by routing a message packet through an additional output port rather than holding the packet until a desired output port is available. Accordingly, the usage of buffers at the nodes is eliminated. Elimination of a global controller and buffering at the nodes greatly reduces the amount of control and logic structures in the interconnect structure, simplifying overall control components and network interconnect components, improving speed performance of message communication and potentially reducing interconnection costs substantially. Implementation of the interconnect structure is highly flexible so that fully electronic, fully optical and mixed electronic-optical embodiments are achieved. An implementation using all optical switches is facilitated by nodes exploiting uniquely simple logic and elimination of buffering at the nodes.

The multiple level minimum logic network interconnect architecture is used for various purposes. For example, in some embodiments the architecture is used as an interconnect strucmre for a massively parallel computer such as a supercomputer. In other exemplary embodiments, the architecture forms an interconnect structure linking a group of workstations, computers, terminals, ATM machines, elements of a national flight control system and the like. Another usage is an interconnect structure in various telecommunications applications or an interconnect strucmre for numerous schedulers operating in a business main frame.

In accordance with one aspect of the present invention, an interconnect apparams includes a plurality of nodes and a plurality of interconnect lines selectively connecting the nodes in a multiple level strucmre in which the levels include a richly interconnected collection of rings. The multiple level strucmre includes a plurality of J+l levels in a hierarchy of levels and a plurality of 2^JK nodes at each level. If integer K is an odd number, the nodes on a level M are situated on 2^{J M} rings with each ring including 2^MK nodes. Message data leaves the interconnect structure from nodes on a level zero. Each node has multiple communication terminals. Some are message data input and output terminals. Others are control input and output terminals. For example, a node A on level 0, the innermost level, receives message data from a node B on level 0 and also receives message data from a node C on level 1. Node A sends message data to a node D on level 0 and also sends message data to a device E that is typically outside the interconnect strucmre. One example of a device E is an input buffer of a computational unit. Node A receives a control input signal from a device F which is commonly outside the interconnect strucmre. An example of a device F is an output buffer of a computational unit. Node A sends a control signal to a node G on level 1.

All message data enters the interconnect strucmre on an outermost level J.

For example, a node A on level J, the outermost level, receives message data from a node B on level J and also receives message data from a device C that is outside the interconnect strucmre. One example of device C is an output buffer of a computational unit. Node A sends message data to a node D on level J and also sends message data to a node E on level J-1. Node A receives a control input signal from a node F on level J-1. Node A sends a control signal to a device G that is typically outside the interconnect strucmre. An example of a device G is an output buffer of a computational unit.

Nodes between the innermost level 0 and the outermost level J communicate message data and control signals among other nodes. For example, a node A on a level T that is neither level 0 or level J receives message data from a node B on level T and also receives message data from a node C on level T+l. Node A sends message data to a node D on level T and also sends message data to a node E on level T-l. Node A receives a control input signal from a node F on level T-l. Node A sends a control signal to a node G on level T+ l.

Level M has 2^J"M rings, each containing 2^MK nodes for a total of 2^JK nodes on level M. Specifically: Level 0 has 2^J rings, each containing 2°K = K nodes for a total of 2^JK nodes on level 0.

Level 1 has 2^{J 1} rings, each containing 2'K = 2K nodes for a total of 2^JK nodes on level 1. Level 2 has 2^J~2 rings, each containing 2²K = 4K nodes for a total of 2^JK nodes on level M.

Level J-2 has 2^J"(J"2) = 4 rings, each containing 2^(J"2)K nodes for a total of 2^JK nodes on level J-2.

Level J-1 has 2^{J J 1)} = 2 rings, each containing 2^{(J 1)}K nodes for a total of 2^JK nodes on level J-1.

Level J has 2^J"J = 1 ring containing 2 ^{, 1)}K nodes for a total of 2^JK nodes on level J.

For a ring R_τ on a level T which is not the outermost level J, then one ring R_τ+1 on level T+l exists such that each node A on ring R_τ receives data from a node B on ring R_τ and a node C on ring R_τ+1. For a ring R_τ on a level T which is not the innermost level 0, then there exist exactly two rings Rlχ-ι and R2_T__j on level T-l such that a node A on ring R_τ sends message data to a node D on ring R_τ and a node E on either ring Rl_τ._j or ring R2_T._J. A message on any level M of the interconnect strucmre can travel to two of the rings on level M-l and is eventually able to travel to 2^M of the rings on level 0.

In the following discussion a "predecessor" of a node sends message data to that node. An "immediate predecessor" sends message data to a node on the same ring. A "successor" of a node receives message data from that node. An "immediate successor" receives message data to a node on the same ring. For a node A_RT on ring R_τ on level T, there are nodes B_RT and D_RT on ring R_τ of level T such that node B_RT is an immediate predecessor of node A_RT and node D_RT is an immediate successor of node A_RT. Node A_RT receives message data from node B_RT and sends message data to node D_RT. Node A_RT receives message data from a device C that is not on the ring R_τ and sends data to a device E that is not on ring R_τ. If the level is not the innermost level 0, then device E is a node on level T-l and there is an immediate predecessor node F on the same ring as device E. Node A_RT receives control information from device F. If node A_RT is on node T equal to zero, then device E is outside the interconnect structure and device E sends control information to node A_RT. For example, if device E is an input buffer of a computational unit, then the control information from device E to node A_RT indicates to node A_RT whether device E is ready to receive message data from node A_RT. Node D_RT receives message data from a device G that is not on ring R_τ. Node A_RT sends a control signal to device G.

Control information is conveyed to resolve data transmission conflicts in the interconnect strucmre. Each node is a successor to a node on the adjacent outer level and an immediate successor to a node on the same level. Message data from the immediate successor has priority. Control information is send from nodes on a level to nodes on the adjacent outer level to warn of impending conflicts.

When the levels are evenly spaced and the nodes on each ring and each level are evenly spaced, the interconnect strucmre forms a three-dimensional cylindrical strucmre. The interconnect strucmre is fully defined by designating the interconnections for each node A of each level T to devices or nodes B, C, D, E, F and G. Each node or device has a location designated in three-dimensional cylindrical coordinates (r, θ, z) where radius r is an integer which specifies the cylinder number from 0 to J, angle θ is an integer multiple of 2π/K, which specifies the spacing of nodes around the circular cross-section of a cylinder from 0 to K-l, and height z is a binary integer which specifies distance along the z-axis from 0 to 2^J-1. Height z is expressed as a binary number because the interconnection between nodes in the z-dimension is most easily described as a binary digit manipulation. On the innermost level 0, one ring is spanned in one pass through the angles 0 from 0 to K-l and each height z designates a ring. On level 1, one ring is spanned in two passes through the angles 0 and two heights z are used to designate one ring. The ring strucmre proceeds in this manner through the outermost ring J in which one ring is spanned in all 2^J heights along the z-axis.

Node A on a ring R receives message data from a node B, which is an immediate predecessor of node A on ring R. For a node A located at a node position N(r,0,z), node B is positioned at N(r,(0-l)mod K,H_r(z)) on level r. (0- l)mod K is equal K when 0 is equal to 0 and equal to 0-1 otherwise. The conversion of z to H_r(z) on a level r is described for z = [Z_J._J, Z_j_₂, . . , z-, z_rΛ, . . , 2>₂, Z_j, Z_Q] by reversing the order of low-order z bits from z,_Λ to ZrJ into the form z = [z ._j, Z_j_₂, . . , Z-, z₀, Z_j, z₂, . ., z_r._j], subtracting one (modulus 2¹) and reversing back the modified low-order z bits.

Node A also receives message data from a device C which is not on level r. If node A is positioned on the outermost level r= J, then device C is outside of the interconnect strucmre. If node A is not positioned on the outermost level, then device C is a node located at position N(r+ l,(0-l)mod K,z) on level r+ 1.

Node A sends message data to a node D, which is an immediate successor to node A on ring R. Node D is located at node position N(r,(0+l)mod K,h-(z)) on level r. (0+l)mod K is equal 0 when 0 is equal to K-l and equal to 0+1 otherwise. The conversion of z to h_(z) on a level r is described for z = [Z_j.j, z,_₂, . . , z-, z_r_j, . . , Z , Zj, Z_Q] by reversing the order of low-order z bits from z_xΛ to ZQ] into the form z = [z_J , Z_j_₂, . . , z-, z₀, z_x, z₂, . ., z ], adding one (modulus 2¹) and reversing back the low-order z bits. Node A also sends message data to a device E that is not on the same level r as node A. If node A is on the innermost level r=0, node A(r,0,z) is interconnected with a device (e.g. a computational unit) outside of the interconnect strucmre. Otherwise, node A is interconnected to send message data to device E, which is a node located at node position N(r-l,(0+l)mod K,z) on level r-l.

Node A receives control information from a device F. If node A is on the innermost level r=0, the device F is the same as device E. If node A is not on the innermost level, device F is a node which is distinct from the device E. Node F is located at node position N(r-l,0,H (z)) on level r-l.

Node A sends control information to a device G. If node A is on the outermost level r=J, then device G is positioned outside of the interconnect strucmre. Device G is a device, for example a computational unit, that sends message data to node D. If node A is not positioned on level r=J, then device G is a node which is located at node position N(r+ l,0,h_r+1(z)) on level r+1 and device G sends message data to node D.

In accordance with a second aspect of the present invention, a method is shown of transmitting a message from a node N to a target destination in a first, a second and a third dimension of three dimensions in an interconnect strucmre arranged as a plurality of nodes in a topology of d e three dimensions. The method includes the steps of determimng whether a node en route to the target destination in the first and second dimensions and advancing one level toward the destination level of the third dimension is blocked by another message, advancing the message one level toward the destination level of the third dimension when the en route node is not blocked and moving the message in the first and second dimensions along a constant level in the third dimension otherwise. This method further includes the step of specifying the third dimension to describe a plurality of levels and specifying the first and second dimensions to described a plurality of nodes on each level. A control signal is sent from the node en route to the node N on a level q in the third dimension, the control signal specifying whether the node en route is blocked. Transmission of a message is timed using a global clock specifying timing intervals to keep integral time modulus the number of nodes at a particular cylindrical height, the global clock time interval being equal to the second time interval and the first time interval being smaller than the global time interval. A first time interval a is set for moving the message in only the first and second dimensions. A second time interval - β is set for advancing the message one level toward the destination level. A third time interval is set for sending the control signal from the node en route to the node N, the third time interval being equal to β.

In accordance with a third aspect of the present invention, a method is shown of transmitting a message from an input device to an output device through an interconnect strucmre. The message travels through the interconnect strucmre connecting a plurality of nodes in a three dimensional strucmre. The message has a target destination corresponding to a target ring on level 0 of the interconnect strucmre. A message M at a node N on level T en route to a target ring on level 0 advances to a node N' on level T-l so long as the target ring is accessible from node N' and no other higher priority message is progressing to node N' to block the progress of message M. Whether the target ring is accessible from node N' is typically efficiently determined by testing a single bit of a binary code designating the target ring. Whether a higher priority message is blocking the progress of message M is efficiently determined using timed control signals. If a message is blocked at a time t, the message is in position to progress to the next level at time t+2. If a message is blocked by a message M' on level T-l, then a limited time duration will transpire before the message M' is able to block message M again.

A global clock controls traffic flow in the interconnect strucmre. Data flow follows rules that allow much of the control information to be "hidden" in system timing so that, rather than encoding all control information in a message packet header, timing considerations convey some information. For example, the target ring is encoded in the message packet header but, in some embodiments of the interconnect strucmre, designation of the target computational unit is determined by the timing of arrival of a message with respect to time on the global clock.

The disclosed multiple level interconnect strucmre has many advantages.

One advantage is that the strucmre is simple, highly ordered and achieves fast and efficient communication for systems having a wide range of sizes, from small systems to enormous systems.

In addition, the interconnect structure is highly advantageous for many reasons. The interconnect strucmre resolves contention among messages directed toward the same node and ensures that a message that is blocked makes a complete tour of the messages on a level before any message is in position to block again. In this manner, a message inherently moves to cover all possible paths to the next level. A blocking message typically proceeds to subsequent levels so that overlying messages are not blocked for long.

BRIEF DESCRIPTION OF THE DRAWINGS

The feamres of the invention believed to be novel are specifically set forth in the appended claims. However, the invention itself, both as to its strucmre and method of operation, may best be understood by referring to the following description and accompanying drawings.

Figures IA, IB, IC and ID are abstract three-dimensional pictorial illustrations of the strucmre of an embodiment of a multiple level minimum logic interconnect apparams.

Figure 2 is a schematic diagram of a node, node terminals and interconnection lines connected to the terminals. Figures 3A, 3B and 3C are schematic block diagrams that illustrate interconnections of nodes on various levels of the interconnect structure.

Figure 4 is an abstract schematic pictorial diagram showing the topology of levels of an interconnect strucmre.

Figure 5 is an abstract schematic pictorial diagram showing the topology of nodes of an interconnect strucmre.

Figure 6 is an abstract schematic pictorial diagram which illustrates the manner in which nodes of the rings on a particular cylindrical level are interconnected.

Figure 7 illustrates interconnections of a node on level zero.

Figure 8 depicts interconnections of a node on level one.

Figure 9 depicts interconnections of a node on level two.

Figure 10 depicts interconnections of a node on level three.

Figure 11 is an abstract schematic pictorial diagram which illustrates interconnections between devices and nodes of a ring on the low level cylinder.

Figure 12 is an abstract schematic pictorial diagram which illustrates interconnections among nodes of two adjacent cylindrical levels.

Figure 13 is an abstract schematic pictorial diagram showing interconnections of nodes on cylindrical level one. -13-

Figure 14 is an abstract schematic pictorial diagram showing interconnections of nodes on cylindrical level two.

Figure 15 is an abstract schematic pictorial diagram showing interconnections of nodes on cylindrical level three.

Figure 16 is an abstract schematic pictorial diagram illustrating the interaction of messages on adjacent levels of an embodiment of the interconnection strucmre.

Figure 17 is a timing diagram which illustrates timing of message communication in the described interconnect strucmre.

Figure 18 is a pictorial representation illustrating the format of a message packet including a header and payload.

Figure 19 is a pictorial diagram which illustrates the operation of a lithium niobate node, a first exemplary node strucmre.

Figure 20 is a pictorial diagram which illustrates the operation of a nonlinear optical loop mirror (NOLM), a second exemplary node strucmre.

Figure 21 is a pictorial diagram which illustrates the operation of a terahertz optical asymmetrical demultiplexer (TOAD) switch, a third exemplary node strucmre.

Figure 22 is a pictorial diagram showing the operation of a regenerator utilizing a lithium niobate gate. Figure 23 is an abstract schematic pictorial diagram illustrating an alternative embodiment of an interconnect strucmre in which devices issue message packets to multiple nodes.

Figure 24 is an abstract schematic pictorial diagram illustrating an alternative embodiment of an interconnect strucmre in which devices receive message packets from multiple nodes.

Figure 25 is an abstract schematic pictorial diagram illustrating an alternative embodiment of an interconnect strucmre in which devices issue message packets to nodes at various interconnect levels.

DETAILED DESCRIPTION

Referring to Figures IA, IB, IC and ID, an embodiment of a multiple level minimum logic interconnect apparams 100 includes multiple nodes 102 which are connected in a multiple level interconnect strucmre by interconnect lines 104.

The multiple level interconnect strucmre is shown illustratively as a three- dimensional structure to facilitate understanding.

The nodes 102 in the multiple level interconnect strucmre are arranged to include multiple levels 110, each level 110 having a hierarchical significance so that, after a message is initiated in the strucmre, the messages generally move from an initial level 112 to a final level 114 in the direction of levels of a previous hierarchical sigmficance 116 to levels of a subsequent hierarchical sigmficance 118. Illustratively, each level 110 includes multiple strucmres which are called rings 120. Each ring 120 includes multiple nodes 102. The term "rings" is used merely to facilitate understanding of the strucmre of a network in the abstract in which visualization of the strucmre as a collection of concentric cylindrical levels 110 is useful. The different Figures IA, IB, IC and ID are included to more easily visualize and understand the interconnections between nodes. Figure IA illustrates message data transmission interconnections between nodes 102 on the various cylindrical levels 110. Figure IB adds a depiction of message data transmission interconnections between nodes 102 and devices 130 to the interconnections illustrated in Figure IA. Figure IC further shows message data interconnections between nodes 102 on different levels. Figure ID cumulatively shows the interconnections shown in Figures IA, IB and IC in addition to control interconnections between the nodes 102.

The acmal physical geometry of an interconnect strucmre is not to be limited to a cylindrical strucmre. What is important is that multiple nodes are arranged in a first class of groups and the first class of groups are arranged into a second class of groups. Reference to the first class of groups as rings and the second class of groups as levels is meant to be instructive but not limiting.

The illustrative interconnect apparams 100 has a strucmre which includes a plurality of J+ l levels 110. Each level 110 includes a plurality of 2^JK nodes 102. Each level M contains 2^J"M rings 120, each containing 2^MK nodes 102. The total number of nodes 102 in the entire strucmre is (J+ 1)2^JK. The interconnect apparams 100 also includes a plurality 2^JK devices 130. In the illustrative embodiment, each device of the 2^JK devices 130 is connected to a data output port of each of the K nodes 102 in each ring of the 2^J rings of the final level 114. Typically, in an interconnect structure of a computer a device 130 is a computational unit such as a processor-memory unit or a cluster of processor- memory units and input and output buffers.

Referring to Figure 2, an interconnect strucmre 200 of a node 102 has three input terminals and three output terminals. The input terminals include a first data input terminal 210, a second data input terminal 212 and a control input terminal 214. The output terminals include a first data output terminal 220, a second data output terminal 222 and a control output terminal 224. The data input and output terminals of a node communicate message data with other nodes. The control terminals communicate control bits with other nodes for controlling transmission of message data. The number of control bits for controlling message transmission is efficiently reduced since much of the logic throughout the interconnect strucmre 200 is determined by timing of the receipt of control bits and message data in a manner to be detailed hereinafter. Only one control bit enters a node and only one control bit leaves at a given time step. Messages are communicated by generating a clock signal for timing time units. Message transmission is controlled so that, during one time unit, any node 102 receives message data from only one input terminal of the data input terminals 212 and 214. Since, a node 202 does not have a buffer, only one of the node's ouφut ports is active in one time unit.

Referring to Figures 3 through 16, the topology of an interconnect strucmre 300 is illustrated. To facilitate understanding, the strucmre 300 is illustrated as a collection of concentric cylinders in three dimensions r, 0 and z. Each node or device has a location designated (r, 0, z) which relates to a position (r, 2x0/K, z) in three-dimensional cylindrical coordinates where radius r is an integer which specifies the cylinder number from 0 to J, angle 0 is an integer which specifies the spacing of nodes around the circular cross-section of a cylinder from 0 to K-l, and height z is a binary integer which specifies distance along the z-axis from 0 to 2^J-1. Height z is expressed as a binary number because the interconnection between nodes in the z-dimension is most easily described as a manipulation of binary digits. Accordingly, an interconnect strucmre 300 is defined with respect to two design parameters J and K.

Figures 3A, 3B and 3C are schematic block diagrams that show interconnections of nodes on various levels of the interconnect strucmre. Figure 3A shows a node A_jy 320 on a ring R of outermost level J and the interconnections of node A_RJ 320 to node BR, 322, device C 324, node DR, 326, node E_j^y._j) 328, node Fj ._j) 330 and device G 332. Figure 3B shows a node A_RT 340 on a ring R of a level J and the interconnections of node A_RT 340 to node B_RT 342, node C_R(T+1) 344, node D_RT 346, node E_R^-.^ 348, node FR^.^ 350 and node G_R(T+1) 352. Figure 3C shows a node A_R0 360 on a ring R of innermost level 0 and the interconnections of node A_R0 360 to node B_R0 362, node C_R1 364, node D_R0 366, device E 368 and node G_R1 372.

In Figures 3 A, 3B and 3C interconnections are shown with solid lines with arrows indicating the direction of message data flow and dashed lines with arrows indicating the direction of control message flow. In summary, for nodes A, B and D and nodes or devices C, E, F, G:

(1) A is on level T.

(2) B and C send data to A.

(3) D and E receive data from A. (4) F sends a control signal to A.

(5) G receives a control signal from A.

(6) B and D are on level T.

(7) B is the immediate predecessor of A.

(8) D is the immediate successor to A. (9) C, E, F and G are not on level T.

The positions in three-dimensional cylindrical notation of the various nodes and devices is as follows:

(10) A is positioned at node N(r, 0, z).

(11) B is positioned at node N(r, 0-1, H_τ(z)). (12) C is either positioned at node N(r+1, 0-1, z) or is outside the interconnect strucmre.

(13) D is positioned at node N(r, 0+1, hτ(z)).

(14) E is either positioned at node N(r-1, 0+1, z) or is outside the interconnect strucmre and the same as device F. (15) F is either positioned at node N(r-1, 0, H_τ._j(z)) or is outside the interconnect strucmre and the same as device E.

(16) G is either positioned at node N(r+1, 0, h_τ(z)) or is outside the interconnect strucmre.

In this notation, (ø-l)mod K is equal K when 0 is equal to 0 and equal to

0-1 otherwise. The conversion of z to H_r(z) on a level r is described for z = [z_j._j, Z_j_₂, . . , z-, z , . . , Z₂, Z_j, Z_Q] by reversing the order of low-order z bits from z-.j to Z_Q] into the form z = [z , Zj_₂. • • , Z-, z₀, z_lt z^, . ., z.^], subtracting (modulus 2¹ and reversing back the low-order z bits. Similarly, (0+l)mod K is equal 0 when 0 is equal to K-l and equal to 0+1 otherwise. The conversion of z to h_r(z) on a level r is described for z = [Z_J._J, Z_j_₂, . . , -.-, z_r._j, . . , z^, z_{l 5} Z_Q] by reversing the order of low-order z bits from z_r to Z_Q] into the form z = [z , Z_j.₂, . . , Z-, z₀, Zj, z₂, . ., Z-. , adding (modulus 2¹ and reversing back the low- order z bits.

Referring to Figure 4, concentric cylindrical levels zero 310, one 312, two

314 and three 316 are shown for a J=3 interconnect strucmre 300 where level 0 refers to the innermost cylindrical level, progressing outward and numerically to the outermost cylindrical level 3. A node 102 on a level T is called a level T node.

An interconnect strucmre has J+l levels and 2^JK nodes on each level.

Referring to Figure 5, the design parameter K is set equal to 5 so that the interconnect strucmre 300 has four levels (J+ l = 3 + 1 = 4) with 40 (2^JK = (2³)5 = 40) nodes on each level.

Referring to Figure 6, the interconnect strucmre is fully defined by designating the interconnections for each node A 530 of each level T to devices or nodes B 532, C 534, D 536, E 538, F 540 and G 542. Node A(r,0,z) 530 is interconnected with an immediate predecessor node B(r,(0-l)mod K,H_r(z)) 532 on level r. If node A(r,0,z) 530 is on the outermost level r=J, node A(r,0,z) 530 is interconnected with a device (e.g. a computational unit of a computer) outside ofthe interconnect strucmre. Otherwise, node A(r,0,z) 530 is interconnected with a predecessor node C(r+l,(0-l)mod K,z) 534 on level r+1.

Node A(r,0,z) 530 is interconnected with an immediate successor node D(r,(0+ l)mod K,h-(z)) 536 on level r. If node A(r,0,z) 530 is on the innermost level r=0, node A(r,0,z) 530 is interconnected with a device (e.g. a computational unit) outside of the interconnect strucmre. Otherwise, node A(r,0,z) 530 is interconnected with a successor node E(r-l,(0+l)mod K,z) 538 on level r-l to send message data.

If node A(r,0,z) 530 is on the innermost level r=0, node A(r,0,z) 530 is interconnected with a device (e.g. a computational unit) outside ofthe interconnect strucmre. Otherwise, node A(r,0,z) 530 is interconnected with a node F(r- l,0,H_r(z)) 540 on level r-l to receive a control input signal.

If node A(r,0,z) 530 is on the outermost level r=J, node A(r,0,z) 530 is interconnected with a device (e.g. a computational unit) outside of the interconnect strucmre. Otherwise, node A(r,0,z) 530 is interconnected with a node G(r+ l,0,h_r+1(z)) 542 on level r+1 to send a control output signal.

Specifically, the interconnections of a node A for the example of an interconnect strucmre with interconnect design parameters J=3 and K=5 are defined for all nodes on a ring. Every ring is unidirectional and forms a closed curve so that the entire strucmre is defined by designating for each node A, a node D that receives data from node A. Referring to Figure 7 in conjunction with Figure 6, interconnections of a node A on level zero are shown. Node A(0,0,z) 530 is interconnected to receive message data from immediate predecessor node B(0,(0-l)mod 5,z) 532 on level 0 and to send message data to immediate successor node D(0,(0+l)mod 5,z) 536 on level 0. Although the interconnection term in the second dimension for nodes B and D is previously defined as H_r(z) and h_r(z), respectively, on level zero, H_r(z) and h_r(z) are equal to z. Node A(0,0,z) 530 is also interconnected to receive message data from predecessor node C(l,(0-l)mod 5,z) 534 on level 1 and to send message data to a device E(0,z) 538. Node A(0,0,z) 530 is interconnected to receive a control input signal from a device F((0-l)mod 5,z) 540 and to send a control output signal to node G(l,0,h_j(z)) 542 on level 1.

Referring to Figure 8 in conjunction with Figure 6, interconnections of a node A on level one are shown. Node A(l,0,z) 530 is interconnected to receive message data from immediate predecessor node B(l,(0-l)mod 5,H_j(z)) 532 on level 1 and to send message data to immediate successor node D(l,(0+l)mod 5,1-^)) 536 on level 1. Height z is expressed as a binary number (base 2) having the form [Z^Z_I.Z_Q]. For level one, when z is [z_.,Z_j,0] then h_j(z) and H^z) are both fø.Zi. l]. When z is [Z₂,z_l5l] then h,(z) and H_j(z) are both <img file="WO9704399A2_D0001.tif" /> Node A(l,0,z) 530 is also interconnected to receive message data from predecessor node C(2,(0-l)mod 5,z) 534 on level 2 and to send message data to successor node E(0,(0+ l)mod 5,z) 538 on level 0. Node A(l,0,z) 530 is interconnected to receive a control input signal from a node F(0,0,Hι(z)) 540 on level zero and to send a control output signal to node G(2,0,h₂(z)) 542 on level 2.

Referring to Figure 9 in conjunction with Figure 6, interconnections of a node A on level two are shown. Node A(2,0,z) 530 is interconnected to receive message data from immediate predecessor node B(2,(0-l)mod 5,H₂(z)) 532 on level 2 and to send message data to immediate successor node D(2,(0+l)mod

5,h₂(z)) 536 on level 2. Height z is expressed as a binary number (base 2) having the form [Z^Z^Z_Q]. For level two, when z is [2^,0,0] then h₂(z) is [z_.,l,0] and H₂(z) is [--₂,1,1]. When z is [z₂,0,l] then h₂(z) is [-^,1,1] and H₂(z) is [z₂,l,0]. When z is ^,1,0] then h₂(z) is ^,0,1] and H₂(z) is [z^O.O]. When z is [--₂,1,1] then h₂(z) is [Z₂,0,0] and H₂(z) is fø_.O.l]. Node A(2,0,z) 530 is also interconnected to receive message data from predecessor node C(3,(0-l)mod 5,z) 534 on level 3 and to send message data to successor node E(1,(0+ l)mod 5,z) 538 on level 1. Node A(2,0,z) 530 is interconnected to receive a control input signal from a node F(l,0,H₂(z)) 540 on level 1 and to send a control output signal to node G(3,0,h₃(z)) 542 on level 3.

Referring to Figure 10 in conjunction with Figure 6, interconnections of a node A on level three are shown. Node A(3,0,z) 530 is interconnected to receive message data from immediate predecessor node B(3,(0-l)mod 5,H₃(z)) 532 on level 3 and to send message data to immediate successor node D(3,(0+l)mod 5,h₃(z)) 536 on level 3. For level three, when z is [0,0,0] then h₃(z) is [1,0,0] and H₃(z) is [1,1,1]. When z is [0,0,1] then h₃(z) is [1,0,1] and H₃(z) is [1,1,0]. When z is [0,1,0] then h₃(z) is [1,1,0] and H₃(z) is [1,0,0]. When z is [0,1,1] then h₃(z) is [1,1,1] and H₃(z) is [1,0,1]. When z is [1,0,0] then h₃(z) is [0,1,0] and H₃(z) is [0,0,0]. When z is [1,0,1] then h₃(z) is [0,1,1] and H₃(z) is [0,0,1]. When z is [1,1,0] then h₃(z) is [0,0,1] and H₃(z) is [0,1,0]. When z is [1,1,1] then h₃(z) is [0,0,0] and H₃(z) is [0,1,1]. Node A(3,0,z) 530 is also interconnected to receive message data from predecessor node C(4,(0-l)mod 5,z) 534 on level 4 and to send message data to successor node E(2,(0+ l)mod 5,z) 538 on level 2. Node A(3,0,z) 530 is interconnected to receive a control input signal from a node F(2,0,H₃(z)) 540 on level 2 and to send a control output signal to node G(4,0,h₄(z)) 542 on level 4.

Figure 11 illustrates interconnections between devices 130 and nodes 102 of a ring 120 on the cylindrical level zero 110. In accordance with the description of the interconnect strucmre 200 of a node 102 discussed with respect to Figure 2, a node 102 has three input terminals and three output terminals, including two data input terminals and one control input terminal and two data output terminals and one control output terminal. In a simple embodiment, a device 130 has one data input terminal 402, one control bit input terminal 404, one data output terminal 406 and one control bit output terminal 408.

Referring to Figure 11, nodes 102 at the lowest cylindrical level 110, specifically nodes N(0,0,z), are connected to devices CU(0,z). In particular, the data input terminal 402 of devices CU(0,z) are connected to the second data output terminal 222 of nodes N(0,0,z). The control bit output terminal 408 of devices CU(0,z) are connected to the control input terminal 214 of nodes N(0,0,z).

The devices CU(0,z) are also connected to nodes N(J,0,z) at the outermost cylinder level. In particular, the data output terminal 406 of devices CU(0,z) are connected to the second data input terminal 212 of nodes N(J,0,z). The control bit input terminal 404 of devices CU(0,z) are connected to the control output terminal 224 of nodes N(0,0,z). Messages are communicated from devices CU(0,z) to nodes N(J,0,z) at the outermost cylindrical level J. Then messages move sequentially inward from the outermost cylindrical level J to level J-1, level J-2 and so forth unit the messages reach level 0 and then enter a device. Messages on the outermost cylinder J can reach any of the 2^J rings at level zero. Generally, messages on any cylindrical level T can reach a node on 2^T rings on level zero.

Figure 12 illustrates interconnections among nodes 102 of two adjacent cylindrical levels 110. Referring to Figure 12 in conjunction with Figure 2, nodes 102 at the T cylindrical level 110, specifically nodes N(T,0,z) 450, have terminals connected to nodes on the T level, the T+l level and the T-l level. These connections are such that the nodes N(T,0,z) 450 have one data input terminal connected to a node on the same level T and one data input terminal connected to another source, usually a node on the next outer level T+l but for nodes on the outermost level J, a device is a source. In particular, nodes N(T,0,z) 450 have a first data input terminal 210 which is connected to a first data output terminal 220 of nodes N(T+l,0-l,z) 452. Also, nodes N(T,0,z) 450 have a first data output terminal 220 which is connected to a first data input terminal 210 of nodes N(T- l,0+ l,z) 454.

The nodes N(T,0,z) 450 also have a second data input terminal 212 and a second data output terminal 222 which are connected to nodes 102 on the same level T. The second data input terminal 212 of nodes N(T,0,z) 450 are connected to the second data output terminal 222 of nodes N(T,0-l,h_T(z)) 456. The second data output terminal 222 of nodes N(T,0,z) 450 are connected to the second data input terminal 212 of nodes N(T,0 + 1 ,H_τ(z)) 458. The cylinder height designation H_τ(z) is determined using an inverse operation of the technique for determining height designation h_τ(z). The interconnection of nodes from cylindrical height to height (height z to height H_τ(z) and height h_τ(z) to height z) on the same level T is precisely defined according to a height transformation technique and depends on the particular level T within which messages are communicated. Specifically in accordance with the height transformation technique, the height position z is put into binary form where z = Zj.^^"1 + Z_j.₂2^J"2 + . . . + z-.2^T + z^ 2 + . . . + Zj2^! + ^2°. A next height position hr(z) is determined using a process including three steps. First, binary coefficients starting with coefficient Z_Q, up to and but not including coefficient Zη- are reversed in order while coefficients z^ and above are kept the same. Thus, after the first step the height position becomes Z_j. j2 + z,-₂2^J-² + . . . + Zτ2^τ + Zo2° + Z_j2^! + . . . + Z_T.₂2^T-² + z^ 2^τ . Second, an odd number modulus 2^T, for example one, is added to the height position after inversion. Third, circularity of the height position is enforced by limiting the inverted and incremented height position by modulus 2^T. Fourth, the first step is repeated, again inverting ti e binary coefficients below the z^J coefficient of the previously inverted, incremented and limited height position. The inverse operation for deriving height descriptor H_τ(z) is determined in the same manner except that, rather than adding the odd number modulus 2^T to the order-inverted bit string, the same odd number modulus 2^T is added to the order- inverted bit string.

The interconnection between nodes 102 on the same level is notable and highly advantageous for many reasons. For example, the interconnection strucmre resolves contention among messages directed toward the same node. Also, the interconnection strucmre ensures that a message on a particular level that is blocked by messages on the next level makes a complete tour of the messages on that level before any message is in position to block again. Thus a message inherently moves to cover all possible paths to the next level. Furthermore, a blocking message must cycle through all rings of a level to block a message twice. Consequently, every message is diverted to avoid continuously blocking other messages. In addition, blocking messages typically proceed to subsequent levels so that overlying messages are not blocked for long.

When messages are sent from second data output terminal 222 of a node N(T,0,z) 450 to a second data input terminal 212 of a node N(T,0+l,h_T(z)), a control code is also sent from a control output terminal 224 of the node N(T,0,z) 450 to a control input terminal 214 of a node N(T+ l,0,h_T+1(z)), the node on level T+l that has a data output terminal connected to a data input terminal of node N(T,0+ l,h_T(z)). This control code prohibits node N(T+l,0,h_T+1(z)) from sending a message to node N(T,0+l,h_T+1(z)) at the time node N(T,0,z) 450 is sending a message to node N(T,0+l,h_T+1(z)). When node N(T+l,0,h_T+1(z)) is blocked from sending a message to node <img file="WO9704399A2_D0002.tif" /> the message is deflected to a node on level T+l. Thus, messages communicated on the same level have priority over messages communicated from another level.

The second data output terminal 222 of nodes N(T,0-1 ,H_τ(z)) are connected to a second data input terminal 212 of nodes N(T,0,z) 450 so that nodes N(T,0,z) 450 receive messages from nodes N(T,0-l,H_T(z)) that are blocked from transmission to nodes N(T-l,0,H_T(z)). Also, the control output terminal 224 of nodes N(T-l,0,H_T(z)) to the control input terminal 214 of nodes N(T,0,z) 450 to warn of a blocked node and to inform nodes N(T,0,z) 450 not to send data at this time since no node receives data from two sources at the same time.

Referring to Figure 13, interconnections of nodes 102 on cylindrical level one exemplify the described interconnections and demonstrate characteristics and advantages that arise from the general interconnection technique. In this example, the number of nodes K at a cylindrical height is five and the number of heights 2^J is 2², or 4, for a three level (J+ l) interconnect strucmre 500. Nodes N(l ,0,z) 510 have: (1) a first data input terminal 210 connected to a first data output terminal 220 of nodes N(2,0-l,z) 512, (2) a control output terminal 224 connected to control input terminal 214 of nodes N(2,0,h₂(z)) 512, (3) a first data output terminal 220 connected to a first data input terminal 210 of nodes N(0,0+ l,z) 516, (4) a control input terminal 214 connected to a control ouφut terminal 224 of nodes N(0,0,H_r(z)) 516, (5) a second data input terminal 212 connected to the second data output terminal 222 of nodes NQ.ø-l.H^z)) 520, and (6) a second data output terminal 222 connected to the second data input terminal 212 of nodes N(l,0+ l,h_!(z)) 522. For nodes N(l,0,z) 510 on level one, height z differs from height hj(z) and height H_j(z) only in the final bit position.

Messages are communicated through the interconnect strucmre 500 in discrete time steps. A global clock (not shown) generates timing signals in discrete time steps modulus the number of nodes K at a cylindrical height z of a cylindrical level r. When messages traverse the interconnect structure 500 on the same level (for example, level one) because nodes on an inner level are blocked, messages are communicated from node to node in the discrete time steps. For the interconnect strucmre 500 with an odd number (K=5) of nodes at a cylindrical level, if data traverses level one for 2K time steps, then the message packet visits 2K different nodes. On time step 2K+ 1, message packets will begin repeating nodes following the sequential order of the first node traversal. Because the global clock generates the discrete time steps integral time modulus K, if a message packet on level one is over the target ring of that packet at a time T=0 (modulus K) and is deflected by a message on level zero, the message will be over the target ring also at a time T=0 (modulus K) to make another attempt to enter the target ring. In various embodiments, this timing characteristic is consistent throughout the interconnect strucmre so that, if a message packet is in a position to descend to the next level at a time T=0 (modulus K), the packet will once again be in a position to descend at a subsequent time T=0 (modulus K).

Referring to Figure 14 in conjunction with Figure 13, interconnections of nodes 102 on cylindrical level two further exemplify described interconnections.

In Figure 14, a level two message path 620 is shown overlying the paths 610 and

612 of messages moving on level one. The number of nodes K at a cylindrical level is five and the number of levels 2^J is 2², or 4, for a three level (J+l) interconnect strucmre 500. Same-level interconnections of nodes N(2,0,z) include: (1) a second data input terminal 212 connected to the second data output terminal

222 of nodes N(2,0-l,h₂(z)) and (2) a second data output terminal 222 connected to the second data input terminal 212 of nodes N(2,0+l,H₂(z)). For nodes

N(2,0,z) on level two, height z differs from height .^(z) and height H₂(z) only in the final two bit positions. Generally stated in binary form for any suitable number of nodes K at a height and number of heights 2^J in a level, bits z and h₂(z) on cylindrical level two are related as follows:

-^zj-i_'^zj-2' ^{• •} •' ^z2' "&gt; vl ⁼ ι^zj-i' ^zj-2' • • •&gt; ^z2&gt; 1&gt; 0];

[^Zj-l- ^zj-2&gt; • ^{• •}» ^Z2&gt; 1» "I' ⁼ -^ZM&gt; ^zJ-2&gt; • • •' ^z2» 0' l]i

[ZJ._J, Z_J_₂, . . ., Z_J, 0, 1]' = [Z_J._J, Z_J_₂, . . . , Z_j, 1, 1]; and [Z , Zj_₂, . . ., Zj, 1, 1]' = [Z_J._J, Z_J._J. • . ., Z_J, 0, 0].

A second advantage of this interconnection technique for nodes on the same level is that blocked messages are directed to avoid subsequent blocking. Figure 14 illustrates a message blocking condition and its resolution. On level one, a message π-o 610 is shown at node ^'N_00i and a message m_j 612 at node N_ou. A message M 620 on level two at node N^ i targeted for ring zero. At a time zero, message M 620 is blocked and deflected by message m_j 612 to node N_{1 2} at time one. Assuming that messages π-o and m_j are also deflected and traversing level one, at a time one message π-o 610 is at node N_ιπ and message m_j 612 at node N₁₀₁. At a time two, message M 620 moves to node N₂₁₂, message π-o 610 to node N₂₀₁ and message m_j 612 to node N₂₁₁. Thus, at time two, message M 620 is deflected by message π-o 610. At time four, message M 620 is again blocked by message m_j 612. This alternating blocking of message M 620 by messages π-o 610 and mj 612 continues indefinitely as long as messages π-o 610 and m_j 612 are also blocked. This characteristic is pervasive throughout the interconnect strucmre so that a single message on an inner level cannot continue to block a message on an outer level. Because a single message packet cannot block another packet and blocking packets continually proceed through the levels, blocking does not persist. Referring to Figure 15, interconnections of nodes 102 on cylindrical level three show additional examples of previously described interconnections. A level three message path 720 is shown overlying the paths 710, 712 and 714 of messages moving on level two. The number of nodes K at a cylindrical height is seven and the number of heights 2^J is 2³ (8), for a four level (J+l) interconnect strucmre. Same-level interconnections of nodes N(3,0,z) include: (1) a second data input terminal 212 connected to the second data output terminal 222 of nodes N(3,0-l,h₃(z)) and (2) a second data output terminal 222 connected to the second data input terminal 212 of nodes N(3,0+l,H₃(z)). For nodes N(3,0,z) on level three, height z differs from height h₃(z) and height H₃(z) only in the final three bit positions. Generally stated in binary form for any suitable number of nodes K at a cylindrical height and number of heights 2¹ in a level, bits z and h₃(z) on cylindrical level three are related as follows:

[ZJ._J, Z_J_₂, . . , Z₃, 0, 0, 0]' = [Z_J._J, ZJ_₂, . ., Z-,, 1, 0, 0];

[Z_J._J , Z_j.₂, . ., z₃, 1, 0, 0]' = [z_j._j, Z_j_₂, . ., z₃, 0, 1, 0]; [Zj-j, Zj.₂, . ., z₃, 0, 1, 0]' = [Z_J._J, Z_j.₂, . . , z₃, 1, 1, 0];

[Z_j._j, Z_j_₂, . ., z₃, 1, 1, 0] = [Z_J._J , Z_J_₂, . ., z₃, 0, 0, 1]; -^ZJ-1» ^zJ-2&gt; • •' ^z3&gt; 0» ^. *J ⁼ -^ZJ-1' ^zJ-2' ^• •' ^z3&gt; 1» 0» IJϊ [Zj-1. ^zj-2&gt; • •' ^z3' 1» 0» 1]' ⁼ -^ZJ-1&gt; ^zJ-2&gt; • •» ^z3» 0' 1&gt; l]^j

[ZJ.J , ZJ_₂, • ., z₃, 0, 1, 1]' = [ZJ.J , Z_j.₂, . ., z₃, 1, 1, 1]; and [Z_j._j, Z_j_₂, . ., z₃, 1, 1, 1] = [ZJ.J , Zj.₂, . ., z₃, 0, 0, 0].

Figure 15 illustrates another example of a message blocking condition and its resolution. On level two, a message π_o 710 is shown at node N^, a message m_j 712 at node N₀₁₂, a message m₂ 714 at node N₀₂₂ and a message m₃ 716 at node N₀₃₂- A message M 720 on level three at node N^ is targeted for ring zero. At a time zero, message M 720 is blocked and deflected by message m₃ 716 to node N₁₇₃ at time one. Assuming that messages TΪΪ_Q, m , m₂ and m₃ are also deflected and traversing level two, at a time one message π-o 710 is at node N₁₃₂, message m_j 712 at node N₁₂₂, message m₂ 714 at node N₁₀₂ and message m₃ 716 at node N₁₁₂. At a time two, message M 720 moves to node N₂₃₃, message π-o 710 to node N₂₁₂, message _l 712 to node N₂₀₂, message m₂ 714 to node N₂₃₂ and message m₃ 716 to node N₂₂₂. Thus, at time two, message M 720 is deflected by message m_j 712. At time four, message M 720 is blocked by message m₂ 714. At time six, message M 720 is blocked by message π-o 710. At time eight, message M 720 is again blocked by message m₃ 716. This alternating blocking of message M 720 by messages π-o 710, m_j 712, m₂ 714 and m₃ 716 continues indefinitely as long as messages π-o 710, m_j 712, m₂ 714 and m₃ 716 are also blocked.

This analysis illustrates the facility by which the described interconnect strucmre avoids blocking at any level. Thus, "hot spots" of congestion in the strucmre are minimized. This characteristic is maintained at all levels in the strucmre.

The described interconnect strucmre provides that every node N(0,0,z) on level zero is accessible by any node N(J,0,z) on outermost level J. However, only half of the nodes N(0,0,z) on level zero are accessible by a node N(J-l,0,z) on the level once removed from the outermost level. Data at a node N(l,0,z) on level one can access any node N(0,0,z) on level zero so long as the binary representation of height z of level one and the binary representation of ring r of level zero differ only in the last bit. Similarly, data at a node N(2,0,z) on level two can access any node N(0,0,z) on level zero so long as the binary representation of height z of level two and the binary representation of ring r of level zero differ only in the last two bits. A general rule is that, data at a node N(T,0,z) on level T can access any node N(0,0,z) on level zero so long as the binary representation of height z of level T and the binary representation of ring r of level zero differ only in the last T bits. Accordingly, moving from the outermost level J to level J-1 fixes the most significant bit of the address of the target ring. Moving from level J-1 to level J-2 fixes the next most significant bit of the address of the target ring and so forth. At level zero, no bits are left to be fixed so that no header bit is tested and a message is always passed to a device. In some embodiments, an additional header bit is included and tested at a level zero node. This final bit may be used for various purposes, such as for directing message data to a particular buffer of a device when the device accepts the message data. An advantage of including an additional bit in the header and performing a bit test at the final node is that all the nodes at all levels of the interconnect strucmre operate consistently.

In some embodiments of an interconnect strucmre, an additional header bit is included in a message packet. This bit indicates that a message packet is being transmitted. Another purpose for such an additional bit in the header is to identify which bit in the header is the control bit.

A message packet moves from a level T to the next inner level T-l so long as two conditions are met, as follows: (1) the target ring of the message packet is accessible from level T-l, and (2) the message packet is not blocked by a message on the level T-l . One significant aspect of this strucmre is that any message packet at a node

N(T,0,z) on a level T that can access its target ring can also access the target ring from a node N(T-l,0+l,z) only if the bit T-l of the address ring is the same as bit T-l of the target ring. Therefore, analysis of only a single bit yields all information for determining a correct routing decision.

Referring to Figure 16, a general relationship between message packets on two adjacent levels T and T+l is described. In this example, a message packet M at a node N₄₅₀ on level four, which is targeted for ring two, is potentially blocked by eight message packets π-o 810, m_j 811, m₂ 812, m₃ 813, m₄ 814, m₅ 815, π-g 816 and m₇ 817 at nodes N_3i0 residing on each of the heights 0 to 7 on level three. Although the behavior of the interconnect strucmre is analyzed with respect to levels three and four for purposes of illustration, the analysis is applicable to any arbitrary adjacent levels. At an arbitrary time step, illustratively called time step zero, the message M moves from node N₄₅₀ on level four to node N₃₅₁ on level three unless a control code is send to node N₄₅₀ from a level three node having a data output terminal connected to node N₃₅₁. In this example, node N₃jo has a data output terminal connected to node N₃₅₁ and, at time step zero, message mj resides at node N₃j₀. Accordingly, node N_3j0 sends a control code, in this example a single bit code, to node N₄₅₀, causing deflection of message M to node N_4D1 (where D is a hexadecimal designation of 13) on an interconnection line. A bit line illustratively shows the control connection from node N₃₁₀ to node N₄₅₀. At a time step one, message M moves from node N_4Dj to node N₄₃₂ on interconnection line regardless of whether a node N_3D2 is blocked because ring two is not accessible from node N_3D2. At a time step two, message M moves from node N₄₃₂ to node N₃₃₃ unless a control blocking code is sent from node N₃₅₂ to node N₄₃₂ where node N₃₅₂ is the node on level three that has a data output terminal connected to a data input terminal of node N₃₃₃. However, the message M is blocked from accessing node N₃₃₃ because message 11 currently resides at node N₃₅₂ at time step two. A deflection control code is sent from node N₃₅₂ to node N₄₃₂ on control bit line 822. Furthermore, assuming that none of the message packets m_j progresses to level two and beyond, at time step four, message M is blocked by message m₂ via a control code sent on control bit line. At time six, message M is blocked by message π^ though a blocking control code on control bit line.

This example, illustrates various advantages ofthe disclosed interconnection strucmre. First, deflections of the message M completely tour all of the heights on a level T if messages m_j on level T-l continue to block progression to the level T-l for all levels T. Accordingly, a message M on a level T is blocked for a complete tour of the heights only if 2^T messages are in position on level T-l to block message M. In general, a message m_j on a level T-l must remain on the level T-l for 2^T+1 time steps to block the same message M on level T twice.

The description exemplifies an interconnect strucmre in which messages descend from an outer level to devices at a core inner layer by advancing one level when the height dimension matches the destination ring location and traversing the rings when the ring location does not match the height designation. In other embodiments, the messages may move from an inner level to an outer level. In some embodiments, the heights may be traversed as the level changes and the height held constant as the level remains stationary. In these embodiments, the progression of messages through nodes is substantially equivalent to the disclosed interconnect strucmre. However, the advantage of the disclosed network that avoids blocking of messages is negated.

Referring to Figure 17, a timing diagram illustrates timing of message communication in the described interconnect strucmre. In various embodiments of the interconnect strucmre, control of message communication is determined by timing of message arrival at a node. A message packet, such as a packet 900 shown in Figure 18, includes a header 910 and a payload 920. The header 910 includes a series of bits 912 designating the target ring in a binary form. When a source device CU(0j,Zj) at an angle _j and height z_x sends a message packet M to a destination device CU(0₂,z₂) at an angle 0₂ and height z₂, the bits 912 of header 910 are set to the binary representation of height z^

A global clock servicing an entire interconnect strucmre keeps integral time modulus K where, again, K designates the number of nodes n at a cylinder height z. There are two constants and β such that the duration of exceeds the duration of β and the following five conditions are met. First, the amount of time for a message M to exit a node N(T,0+l,h_T(z)) on level T after exiting a node N(T,0,z) also on level T is α. Second, the amount of time for a message M to exit a node N(T-l,0+l,z) on level T-l after exiting a node N(T,0,z) on level T is a - β. Third, the amount of time for a message to travel from a device CU to a node N(r,0,z) is a - β. Fourth, when a message M moves from a node N(r,0,z) to a node N(r,0+l,h_r(z)) in time duration CK, the message M also causes a control code to be sent from node N(r,0,z) to a node N(r+ l,0+ l,h-(z)) to deflect messages on the outer level r+ 1. The time that elapses from the time that message M enters node N(r,0,z) until the control bit arrives at node N(r + 1 , 0 + 1 , h_{r +} (z)) is time duration β . The aforementioned fourth condition also is applicable when a message M moves from a node N(J,0,z) to a node N(J,0+ 1 ,h_j(z)) at the outermost level J so that the message M also causes a control code to be sent from node N(J,0,z) to a device CU(0,z). The time that elapses from the time that message M enters node N(r,0,z) until the control bit arrives at device CU(0,z) is time duration β. Fifth, the global clock generates timing pulses at a rate of a.

When the source device CU(0j,Z_j) sends a message packet M to the destination device CU(0₂,z ), the message packet M is sent from a data output terminal of device CU(0j,Z_j) to a data input terminal of node N(J,0_j,Z_j) at the outermost level J. Message packets and control bits enter nodes N(T,0,z) on a level T at times having the form na + Lβ where n is a positive integer. The message M from device CU(0_j,Zj) is sent to the data input terminal of node N(J,0j,Zj) at a time X_Q - β and is inserted into the data input terminal of node N(J,0j,Z_j) at time to so long as the node N(J,0_j,Z_j) is not blocked by a control bit resulting from a message traversing on the level J. Time to has the form (0₂-0_j)o- +JjS. Similarly, there is a time of the form (0₂-0_j)o! +J/3 at which a data input terminal of node N(J,0_j,Z_j) is receptive to a message packet from device CU(0_j,Z_j).

Nodes N(r,0,z) include logic that controls routing of messages based on the target address of a message packet M and timing signals from other nodes. A first logic switch (not shown) of node N(r,0,z) determines whether the message packet M is to proceed to a node N(T-l,0+ l,z) on the next level T-l or whether the node N(T-1,0+ l,z) is blocked. The first logic switch of node N(r,0,z) is set according to whether a single-bit blocking control code sent from node N(T-l,0,H_T(z)) arrives at node N(r,0,z) at a time to- For example, in some embodiments the first logic switch takes a logic 1 value when a node N(T-l,0+l,z) is blocked and a logic 0 value otherwise. A second logic switch (not shown) of node N(r,0,z) determines whether the message packet M is to proceed to a node N(T-l,0+l,z) on the next level T-l or whether the node N(T-l,0+l,z) is not in a suitable path for accessing the destination device CU(0₂,Z₂) of the message packet M. The message packet M includes the binary representation of destination height Z_j (z^_j), _-₂₍j-i₎, . . , -^_(T), . . , Z₂₍j₎, z₂₍o₎. The node N(T,0,z) on level T includes a single- bit designation Zj of the height designation z (z_}, z _Λ, . . , z^, . . , z_x, Z_Q). In this embodiment, when the first logic switch has a logic 0 value and the bit designation -^_(X) of the destination height is equal to the height designation r, then the message packet M proceeds to the next level at node N(T-l,0+l,z) and the destination height bit z^^ is stripped from the header of message packet M. Otherwise, the message packet M traverses on the same level T to node N(T,0+ l,h_T(z)). If message packet M proceeds to node N(T-l,0+ l,z), then message packet M arrives at a time tς, + ( - β) which is equal to a time ( ^ - z + l)α + (J - \)β. If message packet M traverses to node N(T,0+l,h_T(z)), then message packet M arrives at a time to + , which is equal to a time (Z₂ - Z + l)α + Jβ. As message packet M is sent from node N(r,0,z) to node N(T,0+l,h_T(z)), a single-bit control code is sent to node N(T+l,0+l,H_T+j(z)) (or device CU(0,z) which arrives at time ^ + β. This timing scheme is continued throughout the interconnect strucmre, maintaining synchrony as message packets are advanced and deflected.

The message packet M reaches level zero at the designated destination height ∑₂. Furthermore, the message packet M reaches the targeted destination device CU(0₂,Z₂) at a time zero modulus K (the number of nodes at a height z). If the targeted destination device CU( ₂,Z₂) is ready to accept the message packet M, an input port is activated at time zero modulus K to accept the packet. Advantageously, all routing control operations are achieved by comparing two bits, without ever comparing two multiple-bit values. Further advantageously, at the exit point of the interconnect strucmre as message packets proceed from the nodes to the devices, there is no comparison logic. If a device is prepared to accept a message, the message enters the device via a clock-controlled gate.

Many advantages arise as a consequence of the disclosed timing and interconnect scheme. In an optical implementation, rather than an electronic implementation, of the interconnect strucmre, signals that encode bits ofthe header typical have a longer duration than bits that encode the payload. Header bits are extended in duration because, as messages communicate through the interconnect structure, timing becomes slightly skewed. Longer duration header bits allow for accurate reading of the bits even when the message is skewed. In contrast, payload bits encode data that is not read during communication through the interconnect strucmre. The disclosed timing scheme is advantageous because the number of header bits in a message is greatly reduced. Furthermore, in some embodiments the number of header bits is decremented as bits are used for control purposes at each level then discarded while messages pass from level to level in the interconnect strucmre. In embodiments that discard a control bit for each level of the interconnect strucmre, logic at each node is simplified since the control bit at each level is located at the same position throughout the interconnect strucmre. That messages communicated on the same level have priority over messages communicated from another level is similarly advantageous because message contention is resolved without carrying priority information in the message header. Message contention is otherwise typically resolved by giving priority to messages that have been in an interconnect strucmre the longest or to predetermined prioritization. These techniques use information stored in the header to resolve contention.

Although it is advantageous that the interconnect strucmre and message communication method determines message transmission routing using self-routing decision-making which is local to the nodes and depends on message timing, in some embodiments of the control strucmre, both local and global communication control is employed. For example, one embodiment of an interconnect strucmre uses local control which is based on timing to control transmission of message packets in a first transmission mode and alternatively uses global control via a scheduler to administer cornmunication of lengthy strings of message data in a second mode. In the global mode, the usage of a scheduler makes the usage of control bit input and output terminals unnecessary.

One consequence of self-routing of message packets is that the ordering of message packet receipt at a target device may be variable. In some embodiments, the correct order of message segments is ordered by sending ordering information in the message header. Other embodiments employ an optical sorter to order message packets.

Although many advantages are realized through a control strucmre and communication method which utilizes timing characteristics, rather than control bits in the header, to control message routing, some interconnect node technologies more suitably operate in a routing system utilizing no timing component. Thus in these technologies, instead of introducing a message at predetermined time so that the message arrives at a preset destination at a designated, routing information is contained in additional header bits. Accordingly, a designated target device position is included in header bits, for example bits following the designated target ring position.

In one embodiment, the label of a target device is represented as a single logic one in a string of logic zeros. Thus, when a message arrives at a device N, the device samples the Nth bit of the device element of the header (as distinguished from the ring element) and accepts the message if the Nth bit is a logic one. This technique is highly suitable for optical node implementations.

Nodes

The nodes N(r,0,z) have been described in generic terms to refer to various data communication switches for directing data to alternative data paths. Node strucmres which are presently available include electronic nodes, optical nodes and mixed optical/electronic nodes. What is claimed include, for example, interconnect and timing methods, an interconnect apparams and an interconnect topology. These methods and apparati involve nodes in a generic sense. Thus, the scope of the claims is not limited by the particular type of node described herein and is to extend to any node known now or in the future, which performs the function of the nodes described herein.

One example of a node 1300 is shown, referring to Figure 19, which includes a lithium niobate (LiNbO3) gate 1302. The lithium niobate gate 1302 has two data input terminals 1310 and 1312, two data output terminals 1320 and 1322 and one control input terminal 1330. Various control circuitry 1340 is added to the lithium niobate gate 1302 to form a control output terminal 1332 of the node 1300. Node 1300 also includes optical to electronic converters 1354, 1356 and 1358. The lithium niobate gate 1302 is forms a 2x2 crossbar. Data paths 1342 and 1344 are optical and the control of the node 1300 is electronic. The lithium niobate gate 1302 is combined with a photodetectors 1350 and 1352 and a few electronic logic components to form a node 1300 for various embodiments of an interconnect strucmre.

In operation, as a message packet 1360 approaches the node 1300, part of the message packet signal 1360 is split off and an appropriate bit of the message packet header (not shown) designating a bit of the binary representation of destination ring in accordance with the discussion hereinbefore, is read by the photodetector 1350. This bit is converted from optical form to an electronic signal. This bit, a bit designating the cylinder height upon which the node 1300 lies and a bit designating whether a destination node on the next level is blocked are processed electronically and a result of the logical tests of these bits is directed to the control input terminal 1330 of the lithium niobate gate 1302. In a first type of lithium niobate gate technology, if the result signal is a logic zero, the gate switches in the cross state. In a second type of lithium niobate gate technology, a logic zero result signal switches the gate in a bar (straight through) state.

Referring to Figure 20, an additional example of a node 1400 is shown.

Node 1400 uses a nonlinear optical loop mirror (NOLM) 1410 to perform a switching function. A nonlinear optical loop mirror is a device that makes use of the refractive index of a material to form a completely optical switch that is extremely fast. One example of a NOLM switch includes a data input terminal 1412 and a control input terminal 1414. Depending upon the signal at the control input terminal 1414, data either leaves the NOLM 1410 through the same data input terminal 1412 from which the data entered (hence the term mirror) or the data exits through a data output terminal 1416. Data is polarized and split into two signal "halves" of equal intensity. In the absence of a control pulse, the two halves of the signal recombine and leave the NOLM 1410 through the data input terminal 1414. When a control pulse is applied to the control input terminal 1414, the control pulse is polarized at right angles to the data pulse and inserted into the NOLM 1410 so that the control pulse travels with one half of the data pulse. The control pulse is more intense than the data pulse and the combined first half of the data pulse and the control pulse quickly pass the second half of the data pulse so that the second half of the data pulse is only minimally accelerated. Thus, the two halves of the data pulse travel with slightly different velocities and are 180° out of phase when the two halves are recombined. This phase difference causes the combined data pulse signal to pass through the data output terminal 1416. One disadvantage of the NOLM 1410 is that switching is operational only when a long optical transmission loop is employed, thus latency is a problem.

Referring to Figure 21, another example of a node 1500 is shown which uses a terahertz optical asymmetrical demultiplexer (TOAD) switch 1510. The TOAD switch 1510 is a variation of the NOLM switch 1410. The TOAD 1510 includes an optical fiber loop 1512 and a semiconductor element 1514, a nonlinear element (NLE) or a semiconductor optical amplifier for example. The TOAD switch 1510 has an input data terminal 1520 which also serves as an output data port under some conditions. The TOAD switch 1510 also has a separate second output data terminal 1522. The semiconductor element 1514 is placed asymmetrically with respect to the center 1516 of the fiber optic loop 1512. A distance 1518 from the semiconductor element 1514 to the center 1516 of the fiber optic loop 1512 is the distance to transmit one bit of data. The TOAD 1510 functions by removing a single bit from a signal having a high data rate. The TOAD 1510 is switched by passing a constant electrical current through the semiconductor element 1514. An optical signal entering the semiconductor material causes the index of refraction of the material to immediately change. After the optical signal terminates, the index of refraction slowly (a time span of several bits) drifts back to the level previous to application of the optical signal. A control pulse is an optical signal having an intensity higher than that of an optical data signal and polarization at right angles to the optical data signal. An optical data input signal is polarized and split into two signal "halves" of equal intensity. The control pulse is injected in a manner to move through the fiber optic loop 1512 directly over the bit that is to be removed. Because the distance 1518 is exactly one bit long, one half of the split optical data signal corresponding to a bit leaves the semiconductor element 1514 just as the other half of the bit enters the semiconductor element 1514. The control pulse only combines with one half of the optical data signal bit so that the velocity of the two halves differs. The combined data and control signal bit exits the TOAD 1510 at the input data terminal 1520. Thus, this first bit is removed from the data path. A next optical signal bit is split and a first half and second half, moving in opposite directions, are delayed approximately the same amount as the index of refraction of the semiconductor element 1514 gradually changes so that this bit is not removed. After a few bits have passes through the semiconductor element 1514, the semiconductor material relaxes and another bit is ready to be multiplexed from the optical data signal. Advantageously, the TOAD 1510 has a very short optical transmission loop 1512.

Regenerators

It is a characteristic of certain nodes that messages lose strength and pick up noise as they propagate through the nodes. Using various other nodes, message signals do not lose strength but noise accumulates during message transmission. Accordingly, in various embodiments of the interconnect strucmre, signal regenerators or amplifiers are used to improve message signal fidelity after messages have passed through a number of nodes.

Referring to Figure 22, one embodiment of a regenerator 1600 is shown which is constructed using a lithium niobate gate 1602. A lithium niobate gate 1602 regenerates message data having a transmission speed of the order of 2.5 gigabits. The lithium niobate gate 1602 detects and converts an optical message signal to an electronic signal which drives an electronic input port 1604 of the lithium niobate gate 1602. The lithium niobate gate 1602 is clocked using a clock signal which is applied to one of two optical data ports 1606 and 1608 of the gate 1602. The clock signal is switched by the electronic control pulses and a high fidelity regenerated signal is emitted from the lithium niobate gate 1602.

Typically, an interconnect strucmre utilizing a lithium niobate gate 1602 in a regenerator 1600 also uses lithium niobate gates to construct nodes. One large power laser (not shown) supplies high fidelity timing pulses to all of the regenerators in an interconnect strucmre. The illustrative regenerator 1600 and node 1650 combination includes an optical coupler 1620 which has a first data input connection to a node on the same level C as the node 1650 and a second data input connection to a node on the overlying level C + 1. The illustrative regenerator 1600 also includes a photodetector 1622 connected to an output terminal of the optical coupler 1620, optical to electronic converter 1624 which has an input terminal connected to the optical coupler 1620 through the photodetector 1622 and an output terminal which is connected to the lithium niobate gate 1602. An output terminal of the lithium niobate gate 1602 is connected to a second lithium niobate gate (not shown) of a node (not shown). Two signal lines of the lithium niobate gate (not shown) are combined, regenerated and switched.

When regenerators or amplifiers are incorporated to improve signal fidelity and if the time expended by a regenerator or amplifier to recondition a message signal exceeds the time - β, then the regenerator or amplifier is placed prior to the input terminal of the node and timing is modified to accommodate the delay.

Other Embodiments

The interconnect strucmre shown in Figures 1 through 16 is a simplified strucmre, meant to easily convey understanding of the principles of the invention.

Numerous variations to the basic strucmre are possible. Various examples of alternative interconnect strucmres are discussed hereinafter, along with advantages achieved by these alternative strucmres. Referring to Figure 23, an alternative embodiment of an interconnect strucmre 1000 includes devices 1030 which issue message packets to multiple nodes 1002 of the outermost level J. In the interconnect apparams 100 shown in Figures 1 through 16, a device CU(0,z) initiates a message transmission operation by sending a message packet to a node N(J,0,z). In the alternative interconnect strucmre 1000, the device CU(0,z) initiates a message transmission operation by sending a message packet to node N(J,0,z) but, in addition, also includes interconnections to additional multiple nodes N(J,0,z) where z designates cylinder heights selected from heights 0 to 2^J of the outermost level J and 0 designates node angles selected from angles 0 to K of the heights z. In the case that a device sends messages to more than one node in the outermost level, the disclosed timing scheme maintains the characteristic that messages arrive at the target node at time zero modulus K.

Devices are connected to many nodes in the outermost level J to avoid congestion upon entry into the interconnect strucmre caused by multiple devices sending a series of messages at a high rate to nodes having converging data paths. In some embodiments, the nodes to which a device is connected are selected at random. In other embodiments, the multiple interconnection of a device to several nodes is selected in a predetermined manner. An additional advantage arising from the connection of a device to several nodes increases the input bandwidth of a communication network.

Referring to Figure 24, an alternative embodiment of an interconnect strucmre 1100 includes devices 1130 which receive message packets from multiple nodes 1102 of the innermost level 0. In this example, the number of nodes K at a particular height z is nine and each device 1130 is connected to receive message from three nodes on level zero. The interconnect strucmre 1100 is advantageous for improving network exit bandwidth when the number of nodes K on at a particular height is large. In the example in which the number of nodes K on a height z is nine and each device receives messages from three nodes on level zero, each node on ring zero is connected to a buffer that has three levels. At time 0, message data is injected into the level zero buffer. At time three, data is injected into the level one buffer. At time 6, data is injected into the level two buffer. A device CU(0,0) reads from the level zero buffer at node N(0,0,0), from the level one buffer at node N(0,(0+3)mod 9,0), and from the level two buffer at node N(0,(0+6)mod 9,0). This reading of message data is accomplished in a synchronous or nonsynchronous manner. If in the synchronous mode, a time t is expended to transfer data from the buffer to the device. In this case, the device CU(0,0) reads from the level zero buffer at time t, reads from the level three buffer at time 3+t, and reads from the level six buffer at time 6+t. In an asynchronous mode, device CU(0,0) interconnects to the three buffers as described hereinbefore and reads message data whenever a buffer signals that data is available.

Referring to Figure 25, an alternative embodiment of an interconnect strucmre 1200 includes devices 1230 which issue message packets to multiple nodes 1202, not only in the outermost level J but also in other levels. In the alternative interconnect strucmre 1200, the device CU(0,z) initiates a message transmission operation by sending a message packet to node N(J,0,z) but, in addition, also includes interconnections to additional multiple nodes N(T,θ,z) where T designates levels of the interconnect strucmre 1200, z designates cylinder heights selected from heights 0 to 2^J of the outermost level J and 0 designates node angles selected from angles 0 to K of the heights z. In the case that a device sends messages to nodes in more than level, message communication is controlled according to a priority, as follows. First, messages entering a node N(r,0,z) from the same level T have a first priority. Second, messages entering a node N(r,0,z) from a higher level T+l have a second priority. Messages entering a node N(r,0,z) from a device CU(0,z) have last priority. The alternative embodiment of interconnect strucmre 1200 allows a device to send messages to neighboring devices more rapidly. The disclosed timing scheme maintains the characteristic that messages arrive at the node designated in the message header at time zero modulus K.

In these various embodiments, devices accept data from level zero nodes using one of various predetermined techniques. Some embodiments rely exclusively on timing to determine when the devices accept data so that devices accept data at time zero modulus K. Some embodiments include devices that accept message data at various predetermined times with respect to modulus K timing. Still other embodiments have devices that accept data whenever a buffer is ready to accept data.

Wave Division Multiplexing Embodiment

In another embodiment of an interconnect strucmre, message signal bandwidth is increased using wave division multiplexing. A plurality of K colors are defined and generated in a message signal that is transmitted using an interconnect strucmre having K devices at a cylinder height. Accordingly, each device is assigned a particular color. Message packets travel to a preselected target ring in the manner described hereinbefore for a single wavelength interconnect system. Message packets pass from level zero to the appropriate device depending on the color assigned to the message packet.

A message includes a header and a payload. The header and payload are distinguished by having different colors. Similarly, the payload is multiplexed using different colors, which are also different from the color of the header. Message bandwidth is also increased by combining different messages of different colors for simultaneous transmission of the messages. Furthermore, different messages of different colors are bound on a same target ring, combined an transmitted simultaneously. All messages are not demultiplexed at all of the nodes but, rather, are demultiplexed at input buffers to the devices. Variable Base r⁷ Height Structure Embodiment

In a further additional embodiment, an interconnect strucmre has i^J cylindrical heights on a level for each of J+l levels, where i is a suitable integer number such as 2 (the previously described embodiment), 3, 4 or more. As was described previously, each height contains K nodes, and each node has two data input terminals, two data output terminals, one control input terminal and one control output terminal.

For example, an interconnect strucmre may have 3^J heights per level. On level one, message data is communicated to one of three level zero heights. On level two, message data is communicated to one of nine level zero heights and so forth. This result is achieved as follows. First, the two output data terminals of a node N(r,0,z) are connected to input data terminals of a node N(T-1,0+ l,z) and a node N(T,0+l,h_T(z)), in the manner previously discussed. However in this further embodiment, a third height transformation h_τ(h_τ(h_τ(z))) rather than a second height transformation h_τ(h_τ(z)) is equal to the original height designation z. With the nodes interconnected in this manner, the target ring is accessible to message data on every third step on level one. In an interconnect strucmre having this form, although nodes having two output data terminals are suitable, advantages are gained by increasing the number of output data terminals to three. Thus, one data output terminal of a node on a given level is connected to two nodes on that level and to one node on a successive level. Accordingly, each level has 3^J heights and a message packet and a message can descend to a lower level every other step.

In this manner, many different interconnect strucmres are formed by utilizing i^J heights per level for various numbers i. Where i is equal to 4, the fourth height transformation h_τ(h_τ(h_τ(h_τ(z)))) is equal to the original height designation z. If i is 5, the fifth height transformation -^(^(^(^(^(z))))) is the same as the original height z, and so forth. In the variable base i^J height strucmre embodiment, whether the target ring is accessible from a particular node is determined by testing a more than one bit of a code designating the target ring.

Variable Base Transformation Technique Embodiment

In a still further embodiment of an interconnect strucmre, the height transformation technique outlined hereinbefore is modified as follows. In this embodiment, a base three notation height transform technique is utilized rather than the binary height transformation technique discussed previously. In the base three transformation technique, a target ring is designated by a sequence of base three numbers. Thus, one a level n, the n low-order base three numbers of the height designation are reversed in order, the low-order-bit-reversed height designation is incremented by one, and the n low-order base three numbers are reversed back again. An exemplary interconnect strucmre has four levels (J=3 plus one), nine heights (3^J = 3³) per level and five nodes (K=5) per height. In accordance with the base three height transformation technique, node N_2(20j)3 on level 2 has a first data input terminal connected to a data output terminal of node N_3(20j)2 on level 3, a second data input terminal connected to a data output terminal of node N_2(22θ)₂^on l^evel ^two- Node N₂₍₂oi)₃ also has a first data output terminal connected to a data input terminal of node N₁₍₂o_₎ on level one and a second data output terminal connected to a data input terminal of node N_2(211)4. Node N_{2 20}i₎₃ also has a control input bit connected to a control output bit of node N₁₍₂oo₎₃ and a control output bit connected to a control input bit of node N_3(2U)3. In this embodiment, the header includes a synch bit followed by the address of a target ring in base three. For example, the base three numbers are symbolized in binary form as 00, 01 and 10 or using three bits in the form 001, 010 and 100.

Further additional height transformation techniques are possible using various numeric bases, such as base 5 or base 7 arithmetic, and employing the number reversal, increment and reversal back method discussed previously. Multiple Level Step Embodiment

In another embodiment, an interconnect structure of the nodes have ten terminals, including five input terminals and five output terminals. The input terminals include three data input terminals and two control input terminals. The output terminals include three data output terminals and two control output terminals. In this interconnect strucmre, nodes are generally connected among five adjacent cylindrical levels. Specifically, nodes N(T,0,z) at the T cylindrical level have terminals connected to nodes on the T, T+ l, T+2, T-l and T-2 levels. These connections are such that the nodes N(T,0,z) have data input terminals connected to nodes on the same level T, the next outer level T+l and the previous outer level T+2. In particular, nodes N(T,0,z) have data input terminals connected to data output terminals of nodes N(T,0-l,h_T(z)), N(T+l,0-l,z) and N(T+2,0-l,z). Nodes N(T,0,z) also have control output terminals, which correspond to data input terminals, connected to nodes on the next outer level T+l and the previous outer level T+2. Nodes N(T,0,z) have control output terminals connected to control input terminals of nodes N(T+l,0-l,z) and N(T+2,0-l,z). Nodes N(T,0,z) also have data output terminals connected to nodes on the same level T, the next inner level T-l and the subsequent inner level T-2. In particular, nodes N(T,0,z) have data output terminals connected to data output terminals of nodes N(T,0+ l,H_T(z)), N(T-l,0+l,z) and N(T-2,0+l,z). Nodes N(T,0,z) also have control input terminals, which correspond to data output terminals, connected to nodes on the next inner level T-l and the subsequent inner level T-2. Nodes N(T,0,z) have control input terminals connected to control output terminals of nodes N(T-l,0+l,z) and N(T-2,0+ l,z).

This ten-terminal strucmre applies only to nodes at the intermediate levels

2 to J-2 since nodes at the outer levels J and J-1 and at the inner levels 1 and 0 have the same connections as the standard six-terminal nodes. This ten-terminal strucmre allows messages to skip past levels when possible and thereby pass through fewer nodes at the cost of increasing logic at the nodes. Only one message is allowed to enter a node at one time. The priority of message access to a node is that a message on the same level has top priority, a message from a node one level removed has second priority and a message from a node two levels away has last priority. Messages descend two levels whenever possible. The timing rules for an interconnect strucmre using the six-terminal nodes. Advantages of the ten-terminal node interconnect strucmre are that messages pass more quickly through the levels.

Other interconnect strucmre embodiments include nodes having more than ten terminals so that data and control terminals are connected to additional nodes on additional levels. For example, various nodes N(T,0,z) also have associated control input terminals and data output terminals, which are connected to nodes on inner levels T-3, T-4 and so on. In other examples, various nodes N(T,0,z) also have associated control output terminals and data input terminals, which are connected to nodes on outer levels T+3, T+4 and so on. In various interconnect strucmre embodiments, nodes may be connected among all levels or selected levels.

Multiple Interconnections to the Same Level Embodiment

Additional interconnect strucmre embodiments utilize additional interconnections among nodes on the same level. Specifically, nodes N(T,0,z) on the level T have interconnections in addition to the connections of (1) an output data terminal connected to an input data terminal of nodes N(T,0+ 1 ,h_τ(z)) and (2) an input data terminal connected to an output data terminal of nodes N(T,0- l,H_τ(z)). Thus nodes N(T,0,z) on the level T have interconnections including a connection of (1) an output data terminal connected to an input data terminal of nodes N(T,0+l,g_T(z)) and (2) an input data terminal connected to an output data terminal of nodes N(T,0-l,hτ(z)). Like cylinder height h_τ(z), height g_τ(z) is on the half of the interconnect structure of level T that is opposite to the position of height z (meaning bit T of the binary code describing height h_τ(z) and g_τ(z) is complementary to bit T of height z).

Multiple Interconnections to a Next Level Embodiment

A multiple interconnections to a next level embodiment is similar to the multiple interconnections to the same level embodiment except that node N(T,0,z) has one output data terminal connected to one node N(T,0+ l,h_τ(z)) on level T and two output data terminals connected to two nodes N(T-l,0+l,z) and N(T- l,0+l,g_T._j(z)) on level T-l. Thus one data output interconnection traverses the same level, a second interconnection progresses one level and a third interconnection both progresses one level and traverses. Like height hτ(z), height g_τ(z) is on the half of the interconnect strucmre of level T that is opposite to the position of height z. Conflicts between node access are resolved by applying a first priority to messages moving on the same level, a second priority to messages progressing one level and a third priority to messages both progressing one level and traversing.

The description of certain embodiments of this invention is intended to be illustrative and not limiting. Numerous other embodiments will be apparent to those skilled in the art, all of which are included within the broad scope of this invention. For example, many different types of devices may be connected using the interconnect strucmre including, but not limited to, workstations, computers, terminals, ATM machines, elements of a national flight control system and the like. Also, other interconnection transformations other than h_τ and H_τ may be implemented to describe the interconnections between nodes.

The description and claims occasionally make reference to an interconnect strucmre which is arranged in multiple dimensions. This reference to dimensions is useful for understanding the interconnect strucmre topology. However, these dimensions are not limited to spatial dimensions but generally refer to groups of nodes which are interconnected in a particular manner.