Next: Sample Codes
Up: The Benchmarks: A
Previous: The Eight Benchmark
In order to give the reader a flavor of the problem descriptions in
[6], a detailed definition will be given for the first
problem, the ``embarrassingly parallel'' benchmark:
Set 
and 
. Generate the pseudorandom
floating point values 
in the interval (0, 1) for 
using the scheme described below. Then for 
set
and 
. Thus 
and 
are uniformly distributed on the interval 
.
Next set 
, and beginning with 
, test to see if 
. If not, reject this pair and proceed to the
next 
. If this inequality holds, then set 
and 
, where 
denotes the natural logarithm. Then 
and 
are independent Gaussian deviates with mean zero and
variance one. Approximately 
pairs will be constructed in
this manner.
Finally, for 
tabulate 
as the count of the
pairs 
that lie in the square annulus 
, and output the ten counts.
Each of the ten counts must agree exactly with reference values.
The 
uniform pseudorandom numbers mentioned above are to be
generated according to the following scheme: Set 
and let
be the specified initial ``seed''. Generate the integers
for 
using the linear congruential recursion
and return the numbers 
as the results. Observe
that 
and the 
are very nearly uniformly distributed
on the unit interval.
An important feature of this pseudorandom number generator is that any
particular value of the sequence can be computed directly from
the initial seed 
by using the binary algorithm for exponentiation,
taking remainders modulo 
after each multiplication. The
importance of this property for parallel processing is that numerous
separate segments of a single, reproducible sequence can be generated
on separate processors of a multiprocessor system. Many other widely
used schemes for pseudorandom number generation do not possess this
important property.
Additional information and references for this benchmark problem are
given in [6].
Next: Sample Codes
Up: The Benchmarks: A
Previous: The Eight Benchmark