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Torus interconnect -- as used in supercomputers


Framing Cognitive Space for Higher Order Coherence (Part #2)

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The pattern inspiring the following exploration has been the torus interconnect fundamental to one approach to memory organization in what are generically now known as high performance computers. The array of possibilities for such computation is usefully presented in the following accessible texts:

With respect to the high degree of competition in this rapidly evolving arena, the torus interconnect has been central to the development of the Fujitsu initiative, of which the K supercomputer has been ranked as the world's fastest, although recently superseded. The K version (Tofu1) has itself been superseded by the TofuD version, as variously indicated in the following.

Torus fusion: "Tofu" stands for "torus fusion" -- a feature central to the followings argument. Such development necessitates a level of operational coherence now framed as six-dimensional. As described in 2012, Tofu is an interconnect for massive parallel computers, connecting more than 80 000 nodes with scalability beyond 100,000 nodes. The network topology is a highly scalable six-dimensional mesh/torus.with node communicating in four directions simultaneously.

The image on the left below is a schematic from Wikipedia of the principle underlying torus interconnect a 3D torus network as often used by high performance computing systems.

Torus interconnect schematic
(in cubic array) 		3D reconstruction of schematic on left
(animation with indicative cube)
Torus interconnect schematic in Tofu supercomputer Animation in 3D of torus interconnect schematic in Tofu supercomputer
Reproduced from Wikipedia  

The images above suggest the manner in which the array of nodes can be extended from 2x2x2 (8 nodes) to 16 nodes, with those below showing completion of the torus interconnection process with the addition of further nodes to 24. Given the original cubic array, it is useful to note how colour coding is used in the 3D variants to distinguish x-axis (blue), y-axis (red) and z-axis (green). The design artifice used in the virtual reality application orients the plane of each torus above towards the centre. Given the requirement to stretch each torus to encompass the increasing number of nodes, in those below a further artifice was used, namely slightly flattening the cross-sections rather then using toroidal ellipses. A variety of improvements and alternatives could of course be envisaged. The node colouring is arbitrary to clarify and increasingly complex structure. Note that each loop of toruses of similar colour frames a "pathway" (below right) which is irrelevant to the supercomputer metaphor but is discussed further below.

Indication of progressive increase and interlinking of nodes
Interlinking of 16 nodes
(only partially unlinked) 		Addition of a further set of nodes
(only partially unlinked) 		Interlinking of a 3x3x3 set of 24 nodes
(each linking 3 orthogonal loops)
Addition of nodes to 3D torus interconnect schematic in Fujitsu supercomputer Addition of nodes to 3D torus interconnect schematic in Fujitsu supercomputer Animation of additional nodes in torus interconnect schematic in Fujitsu supercomputer
     

Scalability and dimensionality: The pattern of "torus fusion" is necessarily developed much further in a supercomputer. The image on the left of the Fujitsu conceptual model of Tofu shows the 6 coordinate axes through which 6-dimensionality is achieved. Each node has a 12-fold 3D pattern embedded within it. The X-Y-Z axes vary in size according to the system configuration; the A-B-C axes are fixed at 2x3x2 as shown. Each pair of adjacent nodes in then connected by a pattern of 12 links, as shown below right

Whereas the conceptual model of Fujitsu, as indicated below, necessarily emphasizes a rectilinear matrix and its potential for scalability, the reconstruction of that model in 3D emphasizes a degree of spherical organization in relation to the centre of the cube. This implies that scalability is better understood, for the purposes of this argument with respect to comprehension, as spherically scalable. Aspects of the argument for the merits of such organization are presented separately (Spherical Accounting: using geometry to embody developmental integrity, 2004).

The higher dimensionality is considered below in terms of nesting.

Conceptual model of Tofu supercomputer memory organization
Overview Detail
Details from depiction of supercomputer conceptual model of Fujitsu
Details from copyrighted presentations by Fujitsu (above)

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