Fixed Point Numbers
In a fixed point number system, each number has
exactly the same number of
digits, and the point is always in the same place.
Examples from the decimal
number system would be 0.23,
HYPERCUBES AND THEIR ALGORITHMS
261
13.1. DEFINITION AND MAIN PROPERTIES
The origins of the hypercube architecture can be traced back to the early 1960s [Squi63].
Subsequently, both the direct (single
9
Sorting on a 2D
Mesh or Torus
There are good reasons for beginning our discussion of 2D mesh and torus
architectures through algorithms for the seemingly difficult sorting problem. First,
sorting on
NUMERICAL 2D MESH ALGORITHMS
231
If each of the two merge phases can be done in O( )steps, then the running time of the
algorithm will be T ( n ) = T ( n/4) + O( ) = O( ). Take the horizontal merge ph
INTRODUCTION TO PARALLEL PROCESSING
216
Figure 11.5. Lower/upper triangular square matrix.
.
.
.
Such a triangular system of linear equations can be easily solved by back substitution.
Compute x0 from
ROUTING ON A 2D MESH OR TORUS
201
Figure 10.7. Demonstrating the worst-case buffer requirement with row-first routing.
highest speed with a constant buffer space per node. This, while possible, leads
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INTRODUCTION TO PARALLEL PROCESSING
Figure 12.10. Some processor states in a reconfigurable mesh.
logarithmic time combining phase in Column 0 then yields the final result. In fact, we can
do bett
16
A Sampler of Other
Networks
In this chapter, we study several other classes of interconnection architectures,
focusing in particular on hybrid or hierarchical schemes that combine features
from two
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INTRODUCTION TO PARALLEL PROCESSING
b.
c.
Extend the result of part (a) by showing that any p -node h -D mesh is a subgraph of the
(log2 p +h 1)-cube.
Show that the result of part (b) is in genera
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INTRODUCTION TO PARALLEL PROCESSING
that are (sub)logarithmic in terms of their sizes p' and p', the product graph G will also have
a (sub)logarithmic node degree or diameter in terms of its size
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INTRODUCTION TO PARALLEL PROCESSING
Figure 15.5. Butterfly network with permuted dimensions.
fat tree is a treelike network specifically designed to remedy this problem. In a fat tree, the
link mu
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291
The bit-reversal permutation is an example of a bad routing problem for dimension-order
routing. Bit-reversal permutation routing is when each Node x = x q1 x q2.