This change takes the observation that previous dbm.IsKeyInDomain
which searches for [start, end) was performing too many byteslice
comparisons. Instead we start off by sorting all the values in the
store.unsortedCache, and then apply a modified binary search to
look for values that fall within the domain [start, end)
The procedure involves:
* iterating over all items to build a list of all keys -- O(n)
* invoking sort.Strings immediately, of which
we anyways eventually invoke sort.Slice(unsorted, ...) which uses
Quicksort -- O(nlog(n)) or O(n^2) worst case
* invoking modified binary search which is O(log(n)) * 2 ~ O(log(n))
to search for the [start, end) range indices
for a total approximate complexity of:
Best case: O(n) + O(n(log(n))) + O(log(n)) ~= O(nlog(n))
Worst case: O(n) + O(n^2) + O(log(n)) ~= O(n^2)
instead of previously:
* iterating over all the unsorted items and invoking dbm.IsKeyInDomain:
bytes.Compare ~ O(n) + O(n*s*e) where s -- len(start), e -- len(end)
for overall complexity of O(n*s*e)
* invoking sort.Slice(unsorted, ...) which uses
Quicksort -- O(nlog(n)) or O(n^2) worst case
for a total approximate complexity of:
Best case: O(n) + O(n*s*e) + O(nlog(n)) ~= O(n*s*e) ~ O(n^2)
Worst case: O(n) + O(n*s*e) + O(n^2) ~= O(n*s*e) ~ O(n^2)
Ordinarily we'd combine the n*s*e to be n*m, but really the comparisons
between (start & key, end & key) are profound that it makes sense to
keep them as factors. The overall benchmark results vindicate our choice
of isolating the factors (n*s*e)
The benchmarks show that as the number of keys to iterate grows, the
new code grows gracefully in a somewhat linear growth, notice for
CAcheKVStoreIterator*, when we go from:
* 1,000 to 10,000 keys: 120us->1,600us (13X) old vs 95us->900us (9.47X) new
* 50,000 to 100,000 keys: 19ms->100ms (5.3X) old vs 5.5ms->17ms (3X) new
```shell
time/op
GetValidator-8 5.8ms ± 2% 4.7ms ± 1% -17.69% (p=0.000 n=10+10)
OneBankSendTxPerBlock-8 3.2ms ± 2% 2.8ms ± 1% -10.80% (p=0.000 n=7+10)
OneBankMultiSendTxPerBlock-8 3.1ms ± 3% 2.9ms ± 2% -8.36% (p=0.000 n=10+10)
AccountMapperSetAccount-8 8.6µs ± 1% 7.8µs ± 1% -9.74% (p=0.000 n=10+10)
CacheKVStoreIterator500-8 64µs ± 6% 51µs ± 6% -19.22% (p=0.000 n=10+9)
CacheKVStoreIterator1000-8 0.12ms ± 4% 95µs ± 4% -19.55% (p=0.000 n=10+10)
CacheKVStoreIterator10000-8 1.6ms ± 4% 0.90ms ± 1% -42.11% (p=0.000 n=10+10)
CacheKVStoreIterator50000-8 19ms ± 5% 5.5ms ± 1% -71.35% (p=0.000 n=10+10)
CacheKVStoreIterator100000-8 0.10s ± 23% 17ms ± 7% -83.44% (p=0.000 n=10+10)
CacheKVStoreGetNoKeyFound-8 1.3µs ± 6% 0.90µs ± 3% -31.19% (p=0.000 n=9+9)
CacheKVStoreGetKeyFound-8 0.66µs ± 6% 0.56µs ± 2% -14.81% (p=0.000 n=10+9)
alloc/op
B/op
BlockProvision-8 0.11kB ± 0% 0.10kB ± 0% -7.14% (p=0.000 n=10+10)
CacheKVStoreIterator50000-8 0.89MB ± 6% 0.53MB ± 1% -40.85% (p=0.000 n=10+10)
CacheKVStoreIterator100000-8 6.3MB ± 23% 1.6MB ± 6% -74.17% (p=0.000 n=10+10)
CacheKVStoreGetNoKeyFound-8 0.26kB ± 0% 0.23kB ± 1% -11.53% (p=0.000 n=10+8)
allocs/op (count)
AccountMapperSetAccount-8 42 ± 0% 38 ± 0% -9.52% (p=0.000 n=10+10)
BlockProvision-8 6.0 ± 0% 5.0 ± 0% -16.67% (p=0.000 n=10+10)
CacheKVStoreIterator1000-8 14 ± 0% 13 ± 0% -7.14% (p=0.002 n=8+10)
CacheKVStoreIterator10000-8 0.15k ± 2% 76 ± 1% -49.00% (p=0.000 n=7+10)
CacheKVStoreIterator50000-8 8.9k ± 11% 2.0k ± 2% -77.60% (p=0.000 n=10+10)
CacheKVStoreIterator100000-8 0.10M ± 26% 13k ± 12% -86.89% (p=0.000 n=10+10)
CacheKVStoreGetNoKeyFound-8 5.0 ± 0% 4.0 ± 0% -20.00% (p=0.000 n=10+10)
```
Note: Purposefully using a commit off master that doesn't
include the buggy code that caused x/bank.BenchmarkOneBank* to fail
per issue https://github.com/cosmos/cosmos-sdk/issues/10023
Updates #9876
/cc @cuonglm @kirbyquerby
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Emmanuel T Odeke