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Predicate locking in hash indexes.

Browse Source 
Hash index searches acquire predicate locks on the primary
page of a bucket. It acquires a lock on both the old and new buckets
for scans that happen concurrently with page splits. During a bucket
split, a predicate lock is copied from the primary page of an old
bucket to the primary page of a new bucket.

Author: Shubham Barai, Amit Kapila
Reviewed by: Amit Kapila, Alexander Korotkov, Thomas Munro
Discussion: https://www.postgresql.org/message-id/flat/CALxAEPvNsM2GTiXdRgaaZ1Pjd1bs+sxfFsf7Ytr+iq+5JJoYXA@mail.gmail.com
This commit is contained in:
Teodor Sigaev
2018-04-07 16:59:14 +03:00
parent 971d7ddbe1
commit b508a56f2f
8 changed files with 802 additions and 1 deletions
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659
src/test/isolation/expected/predicate-hash.out Normal file
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@ -0,0 +1,659 @@
Parsed test spec with 2 sessions
starting permutation: rxy1 wx1 c1 rxy2 wy2 c2
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c1: commit;
step rxy2: select sum(p) from hash_tbl where p=30;
sum
600
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c2: commit;
starting permutation: rxy2 wy2 c2 rxy1 wx1 c1
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c2: commit;
step rxy1: select sum(p) from hash_tbl where p=20;
sum
400
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c1: commit;
starting permutation: rxy3 wx3 c1 rxy4 wy4 c2
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
starting permutation: rxy4 wy4 c2 rxy3 wx3 c1
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
starting permutation: rxy1 wx1 rxy2 c1 wy2 c2
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step c1: commit;
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
ERROR: could not serialize access due to read/write dependencies among transactions
step c2: commit;
starting permutation: rxy1 wx1 rxy2 wy2 c1 c2
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c1: commit;
step c2: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy1 wx1 rxy2 wy2 c2 c1
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c2: commit;
step c1: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy1 rxy2 wx1 c1 wy2 c2
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c1: commit;
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
ERROR: could not serialize access due to read/write dependencies among transactions
step c2: commit;
starting permutation: rxy1 rxy2 wx1 wy2 c1 c2
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c1: commit;
step c2: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy1 rxy2 wx1 wy2 c2 c1
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c2: commit;
step c1: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy1 rxy2 wy2 wx1 c1 c2
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c1: commit;
step c2: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy1 rxy2 wy2 wx1 c2 c1
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c2: commit;
step c1: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy1 rxy2 wy2 c2 wx1 c1
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c2: commit;
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
ERROR: could not serialize access due to read/write dependencies among transactions
step c1: commit;
starting permutation: rxy2 rxy1 wx1 c1 wy2 c2
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c1: commit;
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
ERROR: could not serialize access due to read/write dependencies among transactions
step c2: commit;
starting permutation: rxy2 rxy1 wx1 wy2 c1 c2
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c1: commit;
step c2: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy2 rxy1 wx1 wy2 c2 c1
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c2: commit;
step c1: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy2 rxy1 wy2 wx1 c1 c2
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c1: commit;
step c2: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy2 rxy1 wy2 wx1 c2 c1
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c2: commit;
step c1: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy2 rxy1 wy2 c2 wx1 c1
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step c2: commit;
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
ERROR: could not serialize access due to read/write dependencies among transactions
step c1: commit;
starting permutation: rxy2 wy2 rxy1 wx1 c1 c2
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c1: commit;
step c2: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy2 wy2 rxy1 wx1 c2 c1
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
step c2: commit;
step c1: commit;
ERROR: could not serialize access due to read/write dependencies among transactions
starting permutation: rxy2 wy2 rxy1 c2 wx1 c1
step rxy2: select sum(p) from hash_tbl where p=30;
sum
300
step wy2: insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g;
step rxy1: select sum(p) from hash_tbl where p=20;
sum
200
step c2: commit;
step wx1: insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g;
ERROR: could not serialize access due to read/write dependencies among transactions
step c1: commit;
starting permutation: rxy3 wx3 rxy4 c1 wy4 c2
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step c1: commit;
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
starting permutation: rxy3 wx3 rxy4 wy4 c1 c2
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c1: commit;
step c2: commit;
starting permutation: rxy3 wx3 rxy4 wy4 c2 c1
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
step c1: commit;
starting permutation: rxy3 rxy4 wx3 c1 wy4 c2
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
starting permutation: rxy3 rxy4 wx3 wy4 c1 c2
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c1: commit;
step c2: commit;
starting permutation: rxy3 rxy4 wx3 wy4 c2 c1
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
step c1: commit;
starting permutation: rxy3 rxy4 wy4 wx3 c1 c2
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
step c2: commit;
starting permutation: rxy3 rxy4 wy4 wx3 c2 c1
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c2: commit;
step c1: commit;
starting permutation: rxy3 rxy4 wy4 c2 wx3 c1
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
starting permutation: rxy4 rxy3 wx3 c1 wy4 c2
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
starting permutation: rxy4 rxy3 wx3 wy4 c1 c2
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c1: commit;
step c2: commit;
starting permutation: rxy4 rxy3 wx3 wy4 c2 c1
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
step c1: commit;
starting permutation: rxy4 rxy3 wy4 wx3 c1 c2
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
step c2: commit;
starting permutation: rxy4 rxy3 wy4 wx3 c2 c1
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c2: commit;
step c1: commit;
starting permutation: rxy4 rxy3 wy4 c2 wx3 c1
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step c2: commit;
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
starting permutation: rxy4 wy4 rxy3 wx3 c1 c2
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;
step c2: commit;
starting permutation: rxy4 wy4 rxy3 wx3 c2 c1
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c2: commit;
step c1: commit;
starting permutation: rxy4 wy4 rxy3 c2 wx3 c1
step rxy4: select sum(p) from hash_tbl where p=30;
sum
300
step wy4: insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g;
step rxy3: select sum(p) from hash_tbl where p=20;
sum
200
step c2: commit;
step wx3: insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g;
step c1: commit;

1
src/test/isolation/isolation_schedule
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@ -70,6 +70,7 @@ test: async-notify
test: vacuum-reltuples
test: timeouts
test: vacuum-concurrent-drop
test: predicate-hash
test: predicate-gist
test: predicate-gin
# The checksum_enable suite will enable checksums for the cluster so should

122
src/test/isolation/specs/predicate-hash.spec Normal file
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@ -0,0 +1,122 @@
# Test for page level predicate locking in hash index
#
# Test to verify serialization failures and to check reduced false positives
#
# To verify serialization failures, queries and permutations are written in such
# a way that an index scan (from one transaction) and an index insert (from
# another transaction) will try to access the same bucket of the index
# whereas to check reduced false positives, they will try to access different
# buckets of the index.
setup
{
create table hash_tbl(id int4, p integer);
create index hash_idx on hash_tbl using hash(p);
insert into hash_tbl (id, p)
select g, 10 from generate_series(1, 10) g;
insert into hash_tbl (id, p)
select g, 20 from generate_series(11, 20) g;
insert into hash_tbl (id, p)
select g, 30 from generate_series(21, 30) g;
insert into hash_tbl (id, p)
select g, 40 from generate_series(31, 40) g;
}
teardown
{
drop table hash_tbl;
}
session "s1"
setup
{
begin isolation level serializable;
set enable_seqscan=off;
set enable_bitmapscan=off;
set enable_indexonlyscan=on;
}
step "rxy1" { select sum(p) from hash_tbl where p=20; }
step "wx1" { insert into hash_tbl (id, p)
select g, 30 from generate_series(41, 50) g; }
step "rxy3" { select sum(p) from hash_tbl where p=20; }
step "wx3" { insert into hash_tbl (id, p)
select g, 50 from generate_series(41, 50) g; }
step "c1" { commit; }
session "s2"
setup
{
begin isolation level serializable;
set enable_seqscan=off;
set enable_bitmapscan=off;
set enable_indexonlyscan=on;
}
step "rxy2" { select sum(p) from hash_tbl where p=30; }
step "wy2" { insert into hash_tbl (id, p)
select g, 20 from generate_series(51, 60) g; }
step "rxy4" { select sum(p) from hash_tbl where p=30; }
step "wy4" { insert into hash_tbl (id, p)
select g, 60 from generate_series(51, 60) g; }
step "c2" { commit; }
# An index scan (from one transaction) and an index insert (from another
# transaction) try to access the same bucket of the index but one transaction
# commits before other transaction begins so no r-w conflict.
permutation "rxy1" "wx1" "c1" "rxy2" "wy2" "c2"
permutation "rxy2" "wy2" "c2" "rxy1" "wx1" "c1"
# An index scan (from one transaction) and an index insert (from another
# transaction) try to access different buckets of the index and also one
# transaction commits before other transaction begins, so no r-w conflict.
permutation "rxy3" "wx3" "c1" "rxy4" "wy4" "c2"
permutation "rxy4" "wy4" "c2" "rxy3" "wx3" "c1"
# An index scan (from one transaction) and an index insert (from another
# transaction) try to access the same bucket of the index and one transaction
# begins before other transaction commits so there is a r-w conflict.
permutation "rxy1" "wx1" "rxy2" "c1" "wy2" "c2"
permutation "rxy1" "wx1" "rxy2" "wy2" "c1" "c2"
permutation "rxy1" "wx1" "rxy2" "wy2" "c2" "c1"
permutation "rxy1" "rxy2" "wx1" "c1" "wy2" "c2"
permutation "rxy1" "rxy2" "wx1" "wy2" "c1" "c2"
permutation "rxy1" "rxy2" "wx1" "wy2" "c2" "c1"
permutation "rxy1" "rxy2" "wy2" "wx1" "c1" "c2"
permutation "rxy1" "rxy2" "wy2" "wx1" "c2" "c1"
permutation "rxy1" "rxy2" "wy2" "c2" "wx1" "c1"
permutation "rxy2" "rxy1" "wx1" "c1" "wy2" "c2"
permutation "rxy2" "rxy1" "wx1" "wy2" "c1" "c2"
permutation "rxy2" "rxy1" "wx1" "wy2" "c2" "c1"
permutation "rxy2" "rxy1" "wy2" "wx1" "c1" "c2"
permutation "rxy2" "rxy1" "wy2" "wx1" "c2" "c1"
permutation "rxy2" "rxy1" "wy2" "c2" "wx1" "c1"
permutation "rxy2" "wy2" "rxy1" "wx1" "c1" "c2"
permutation "rxy2" "wy2" "rxy1" "wx1" "c2" "c1"
permutation "rxy2" "wy2" "rxy1" "c2" "wx1" "c1"
# An index scan (from one transaction) and an index insert (from another
# transaction) try to access different buckets of the index so no r-w conflict.
permutation "rxy3" "wx3" "rxy4" "c1" "wy4" "c2"
permutation "rxy3" "wx3" "rxy4" "wy4" "c1" "c2"
permutation "rxy3" "wx3" "rxy4" "wy4" "c2" "c1"
permutation "rxy3" "rxy4" "wx3" "c1" "wy4" "c2"
permutation "rxy3" "rxy4" "wx3" "wy4" "c1" "c2"
permutation "rxy3" "rxy4" "wx3" "wy4" "c2" "c1"
permutation "rxy3" "rxy4" "wy4" "wx3" "c1" "c2"
permutation "rxy3" "rxy4" "wy4" "wx3" "c2" "c1"
permutation "rxy3" "rxy4" "wy4" "c2" "wx3" "c1"
permutation "rxy4" "rxy3" "wx3" "c1" "wy4" "c2"
permutation "rxy4" "rxy3" "wx3" "wy4" "c1" "c2"
permutation "rxy4" "rxy3" "wx3" "wy4" "c2" "c1"
permutation "rxy4" "rxy3" "wy4" "wx3" "c1" "c2"
permutation "rxy4" "rxy3" "wy4" "wx3" "c2" "c1"
permutation "rxy4" "rxy3" "wy4" "c2" "wx3" "c1"
permutation "rxy4" "wy4" "rxy3" "wx3" "c1" "c2"
permutation "rxy4" "wy4" "rxy3" "wx3" "c2" "c1"
permutation "rxy4" "wy4" "rxy3" "c2" "wx3" "c1"