A torus interconnect is a switch-less network topology for connecting processing nodes in a parallel computer system.
In 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.
In 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.
A 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.
The 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.
A 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]
Sandeep 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]
Main 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]