Differential state compression encodes a state's transitions as the
difference between the state and its default state (the state it is
relative too).
This reduces the number of transitions that need to be stored in the
transition table, hence reducing the size of the dfa. There is a
trade off in that a single input character may have to traverse more
than one state. This is somewhat offset by reduced table sizes providing
better locality and caching properties.
With carefully encoding we can still make constant match time guarentees.
This patch guarentees that a state that is differentially encoded will do at
most 3m state traversal to match an input of length m (as opposed to a
non-differentially compressed dfa doing exactly m state traversals).
In practice the actually number of extra traversals is less than this becaus
we selectively choose which states are differentially encoded.
In addition to reducing the size of the dfa by reducing the number of
transitions that have to be stored. Differential encoding reduces the
number of transitions that need to be considered by comb compression,
which can result in tighter packing, due to a reduction in sparseness, and
also reduces the time spent in comb compression which currently uses an
O(n^2) algorithm.
Differential encoding will always result in a DFA that is smaller or equal
in size to the encoded DFA, and will usually improve compilation times,
with the performance improvements increasing as the DFA gets larger.
Eg. Given a example DFA that created 8991 states after minimization.
* If only comb compression (current default) is used
52057 transitions are packed into a table of 69591 entries. Achieving an
efficiency of about 75% (an average of about 7.74 table entries per state).
With a resulting compressed dfa16 size of 404238 bytes and a run time for
the dfa compilation of
real 0m9.037s
user 0m8.893s
sys 0m0.036s
* If differential encoding + comb compression is used, 8292 of the 8991
states are differentially encoded, with 31557 trans removed. Resulting in
20500 transitions are packed into a table of 20675 entries. Acheiving an
efficiency of about 99.2% (an average of about 2.3 table entries per state
With a resulting compressed dfa16 size of 207874 bytes (about 48.6%
reduction) and a run time for the dfa compilation of
real 0m5.416s (about 40% faster)
user 0m5.280s
sys 0m0.040s
Repeating with a larger DFA that has 17033 states after minimization.
* If only comb compression (current default) is used
102992 transitions are packed into a table of 137987 entries. Achieving
an efficiency of about 75% (an average of about 8.10 entries per state).
With a resultant compressed dfa16 size of 790410 bytes and a run time for d
compilation of
real 0m28.153s
user 0m27.634s
sys 0m0.120s
* with differential encoding
39374 transition are packed into a table of 39594 entries. Achieving an
efficiency of about 99.4% (an average of about 2.32 entries per state).
With a resultant compressed dfa16 size of 396838 bytes (about 50% reduction
and a run time for dfa compilation of
real 0m11.804s (about 58% faster)
user 0m11.657s
sys 0m0.084s
Signed-off-by: John Johansen <john.johansen@canonical.com>
Acked-by: Seth Arnold <seth.arnold@canonical.com>
commits were made (as well as a few other minor warnings elsewhere).
The Makefile change is to avoid passing -Wstrict-prototypes and
-Wnested-externs to the C++ compiler, which the compiler yells about and
then ignores.
Since we compile with -Wmissing-field-initializers I dropped the
unreferenced zero-width fields in the header structs, and then explicitly
initialized the remaining fields.
I tagged several unused function parameters to silence those warnings.
And finally, I dropped the unused filter_escapes() too.
