1-
FiGURE 5. I
Suppose the quantity of interest is a function called
of temperature or charge distribution. It is to be computed over the surface of a
slab by means of solving a differential equation. If the equation were exactly
soluble l CP (XI y) could be determined for any point on the slab. However l in many
instances l the equation is not exactly soluable. One mustl therefore l use a finite
approximation to the differential equation and be content with computing the finite
equivalent ct> (II J) at a finite number of points on the slab.
7
~~~ ~~~~~~~~~~~~~~~~~~~~~BURROUGHSSCIENTIFICPROCESSOR
Two points should be understood about the computer solution of the cl>(I, J) on a
sequential computer. First, all
the total amount of computation tim e is proportional to the number of grid points
and to the solution time per grid point.
However, in many instances there is nothing in the mathematics which dictates
that the cl> (I, J) be computed one at a time. In fact, many models have the
property that ~ (I+1, J) depends only on
performance (Figure 6).
1-
FIGURE 6. I
Simultaneous computation suggests parallelism. Parallel or simultaneous com-
putation in turn suggests that there may be an entity more suitable to an architec-
ture based on parallel technology than the single operand which is associated
(conceptually, at least), with a sequential or serial architecture.
The basic quantity susceptible to parallelism is the linear vector. In this context, a
vector is defined as a set of operands upon which some sequence of arithmetic
opera tions is to be performed. A linear vector is a vector whose elements are
mapped into the memory of a computer in a linear fashion, i. e., the addresses
of the elements differ by a constant (Figure 7).
Simple manipulations of linear vectors correspond to looping structures in
FORTRAN. For example, if A and B are defined as vectors with 100 elements
each, then the vector statement:
C=A+B
is equivalent to: DO 10 I = 1, 100 (1)
10 C(I) = A(I) + B(I).
8
BSP ------------------ - BURROUGHS SCIENTIFIC PROCESSOR
LINEAR VECTORS
4 X 5 ARRAY
r
A A A A A
11 12 13 14 15
A A A A A
21 22 23 24 25
N <
A A A A A
31 32 33 34 35
A A A A A
41 42 43 44 45
"-
STANDARD FORTRAN COLUMNWISE MAPPI NG
ARRAY A A A A A A A A A A A A A A A A A A A A
ELEMENTS 11 21 31 41 12 22 32 42 13 23 33 43 14 24 34 44 15 25 35 45
MEMORY
ADDRESS
o 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
=J!...
LINEAR VECTOR COMPONENTS SEPARATED BY A CONSTANT INCREMENT .s!
COLUMNS .Q. = 1
ROWS Q= N
FORWARD DIAGONALS .s! = Nt 1
FIGlJR