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A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system. IntroductionIn geometry, a torus is created by revolving a circle about an axis coplanar to the circle. While this is a general definition in geometry, the topological properties of this type of shape describes the network topology in its essence. Geometry illustrationIn the representations below, the first is a one dimension torus, a simple circle. The second is a two dimension torus, in the shape of a 'doughnut'. The animation illustrates how a two dimension torus is generated from a rectangle by connecting its two pairs of opposite edges. At one dimension, a torus topology is equivalent to a ring interconnect network, in the shape of a circle. At two dimensions, it becomes equivalent to a two dimension mesh, but with extra connection at the edge nodes.
Torus network topologyA torus interconnect is a switch-less topology that can be seen as a mesh interconnect with nodes arranged in a rectilinear array of N = 2, 3, or more dimensions, with processors connected to their nearest neighbors, and corresponding processors on opposite edges of the array connected.[1] In this lattice, each node has 2N connections. This topology is named for the lattice formed in this way, which is topologically homogeneous to an N-dimensional torus. VisualizationThe first 3 dimensions of torus network topology are easier to visualize and are described below:
Higher-dimensional arrays are difficult to visualize. The above ruleset shows that each higher dimension adds another pair of nearest neighbor connections to each node. PerformanceA number of supercomputers on the TOP500 list use three-dimensional torus networks, e.g. IBM's Blue Gene/L and Blue Gene/P, and the Cray XT3.[1] IBM's Blue Gene/Q uses a five-dimensional torus network. Fujitsu's K computer and the PRIMEHPC FX10 use a proprietary three-dimensional torus 3D mesh interconnect called Tofu.[2] 3D Torus performance simulationSandeep Palur and Dr. Ioan Raicu from Illinois Institute of Technology conducted experiments to simulate 3D torus performance. Their experiments ran on a computer with 250GB RAM, 48 cores and x86_64 architecture. The simulator they used was ROSS (Rensselaer’s Optimistic Simulation System). They mainly focused on three aspects:
They concluded that throughput decreases with the increase of servers and network size. Otherwise, throughput increases with the increase of message size.[3] 6D Torus product performanceMain article: Torus fusion
Fujitsu Limited developed a 6D torus computer model called "Tofu". In their model, a 6D torus can achieve 100 GB/s off-chip bandwidth, 12 times higher scalability than a 3D torus, and high fault tolerance. The model is used in the K computer and Fugaku.[4] CostWhile long wrap-around links may be the easiest way to visualize the connection topology, in practice, restrictions on cable lengths often make long wrap-around links impractical. Instead, directly connected nodes—including nodes that the above visualization places on opposite edges of a grid, connected by a long wrap-around link—are physically placed nearly adjacent to each other in a folded torus network.[5][6] Every link in the folded torus network is very short—almost as short as the nearest-neighbor links in a simple grid interconnect—and therefore low-latency.[7] See alsoReferences
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