Schwartz’s Algorithm
In essence: don’t assume unbounded parallelism
1
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Schwartz's Algorithm and Generalized Reduce & Scan, Study notes of Computer Science
Schwartz's algorithm, a parallel reduction technique, and its extension, generalized reduce and scan. The algorithms are presented with examples and templates for various data types. Schwartz's algorithm assumes bounded parallelism, while generalized reduce and scan can handle an associative, commutative operation that isn't built-in.
Typology: Study notes
Pre 2010
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Schwartz’s Algorithm
In essence: don’t assume unbounded parallelism
Schwartz’s Algorithm
int nodeval'[t
];
forall(index
in (0..t
int tally;tally = ... + ...;for (int stride = 1; stride < t
;^ stride
*=^
2)^ {
if (index % (2 * stride) == 0)
tally += nodeval'[index + stride];} else {nodeval'[index] = tally;break;}
Generalized Reduce
What if you have an associate, commutative
〈op〉
that isn’t built in?• Implement Schwartz’s algorithm yourself, or• Use a
generalized reduce
template
5-
Generalized Reduce
data_t
array
[n]; result_t
result
tally_t
nodeval'[t
];
forall(index
in^ (0..t
tally_t
tally; tally
=^ localTally(mySize(array
,^ 0),
localize(array
for^ (int stride
=^ 1;
stride
<^ t;
stride
*=^ 2)
if^ (index
%^ (
*^ stride)
==^
0)^ {
tally
=^ combine
(tally,
nodeval'[index
+^ stride]);
}^ else
nodeval'[index]
=^ tally;
break;} } if^ (index
result
=^ reduceGen
(tally);
Generalized Reduce
You provide:•^ data_t
— type of input data
•^ tally_t
— type of intermediate data
•^ result_t
— type of result data
•^ tally_t
init
()^ — initialize local
•^ tally_t
accum
(tally_t, int, data_t[])
— local
•^ tally_t
combine
(tally_t, tally_t)
— global
•^ result_t
reduceGen
(tally_t)
— post-process
Generalized Reduce
Generalized Scan
data_t
array
[n];^
result_t
result
[n];
tally_t
nodeval'[t
],^ pval'[t
];
forall(index
in^ (0..t
-1))^
{
tally_t
tally
=^ localTally(mySize(array
,^ 0), localize(array
));
for^ (int
stride
=^ 1;
stride
<^ t;
stride
*=^ 2) {
if^ (index
%^ (
*^ stride)
==^ 0)
{
pval'[index+stride]
=^ tally;
/*^ left
total to right child */
tally
=^ combine
(tally,
nodeval'[index
- stride]);
}^ else
{ nodeval'[index]
=^ tally;
break;} } tally_t^ ptally
=^ propagateParentTally(index);
localScanGen(ptally,
mySize(array
,^ 0),
localize(array
),^ localize(result
));
}
Generalized Scan
tally_t
propagateParentTally(int
index)
{ tally_t
ptally; if^ (index
==^
ptally
=^ init
else/* Parent
supplies
left
total
then
parent
ptally
=^ combine
(pval'[index],
pval'[index]);
/*^ Propagate
total
from
parent
to^ right
children
for^ (int stride
=^ 1;
stride
<^ t ;^ stride
*=^
2)^ {
if^ (index
%^ (
*^ stride)
==^ 0)
pval'[index+stride]
=^ ptally;
elsebreak;} return^
ptally; }