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Add some more discussion surrounding cmov
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@chriselrod
chriselrod committed Jan 26, 2024
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Sample results using `-Cnative,-prefer-256-bit` on an AVX512 capable laptop:
```julia
julia> @benchmark findbench(FindFirstFunctions.findfirstequal, $x, $perm)
BenchmarkTools.Trial: 9219 samples with 1 evaluation.
Range (min … max): 107.094 μs … 137.850 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 107.376 μs ┊ GC (median): 0.00%
Time (mean ± σ): 107.577 μs ± 1.175 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
BenchmarkTools.Trial: 6794 samples with 1 evaluation.
Range (min … max): 141.489 μs … 190.383 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 145.892 μs ┊ GC (median): 0.00%
Time (mean ± σ): 145.978 μs ± 4.697 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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107 μs Histogram: frequency by time 110 μs <
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141 μs Histogram: log(frequency) by time 163 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->findfirst(==(x), v), $x, $perm)
BenchmarkTools.Trial: 2144 samples with 1 evaluation.
Range (min … max): 462.442 μs … 584.795 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 464.638 μs ┊ GC (median): 0.00%
Time (mean ± σ): 465.686 μs ± 5.534 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
BenchmarkTools.Trial: 1765 samples with 1 evaluation.
Range (min … max): 547.812 μs … 663.534 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 564.245 μs ┊ GC (median): 0.00%
Time (mean ± σ): 565.600 μs ± 14.561 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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462 μs Histogram: log(frequency) by time 486 μs <
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548 μs Histogram: log(frequency) by time 628 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench(FindFirstFunctions.findfirstsortedequal, $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 46.256 μs … 88.446 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 48.048 μs ┊ GC (median): 0.00%
Time (mean ± σ): 48.702 μs ± 2.079 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
Range (min … max): 75.857 μs … 125.111 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 85.811 μs ┊ GC (median): 0.00%
Time (mean ± σ): 86.135 μs ± 3.217 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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46.3 μs Histogram: frequency by time 56 μs <
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75.9 μs Histogram: frequency by time 101 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->searchsortedfirst(v, x), $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 77.387 μs … 108.634 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 79.305 μs ┊ GC (median): 0.00%
Time (mean ± σ): 81.398 μs ± 4.536 μs ┊ GC (mean ± σ): 0.00% ± 0.00%
BenchmarkTools.Trial: 8741 samples with 1 evaluation.
Range (min … max): 108.941 μs … 152.368 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 113.026 μs ┊ GC (median): 0.00%
Time (mean ± σ): 113.282 μs ± 3.812 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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77.4 μs Histogram: frequency by time 92.6 μs <
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109 μs Histogram: frequency by time 130 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> versioninfo()
Julia Version 1.10.0
Commit 3120989f39* (2023-12-25 18:01 UTC)
Commit 3120989f39 (2023-12-25 18:01 UTC)
Build Info:

Note: This is an unofficial build, please report bugs to the project
Expand All @@ -128,14 +128,130 @@ Build Info:

Platform Info:
OS: Linux (x86_64-redhat-linux)
CPU: 8 × 11th Gen Intel(R) Core(TM) i7-1165G7 @ 2.80GHz
CPU: 36 × Intel(R) Core(TM) i9-7980XE CPU @ 2.60GHz
WORD_SIZE: 64
LIBM: libopenlibm
LLVM: libLLVM-15.0.7 (ORCJIT, tigerlake)
Threads: 11 on 8 virtual cores
LLVM: libLLVM-15.0.7 (ORCJIT, skylake-avx512)
Threads: 1 on 36 virtual cores
Environment:
JULIA_PATH = @.
LD_LIBRARY_PATH = /usr/local/lib/x86_64-unknown-linux-gnu/:/usr/local/lib/:/usr/local/lib/x86_64-unknown-linux-gnu/:/usr/local/lib/
JULIA_NUM_THREADS = 8
JULIA_NUM_THREADS = 36
LD_UN_PATH = /usr/local/lib/x86_64-unknown-linux-gnu/:/usr/local/lib/
```


Note, if you're searching sorted collections and on an x86 CPU, it is worth setting the `ENV` variable `JULIA_LLVM_ARGS="-x86-cmov-converter=false"` before starting Julia, e.g. on an AVX512 capable CPU, you may wish to start Julia from the commad line using
```sh
JULIA_LLVM_ARGS="-x86-cmov-converter=false" julia -Cnative,-prefer-256-bit
```
With this, benchmark results are
```julia
julia> @benchmark findbench(FindFirstFunctions.findfirstequal, $x, $perm)
BenchmarkTools.Trial: 6623 samples with 1 evaluation.
Range (min … max): 141.304 μs … 473.786 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 145.581 μs ┊ GC (median): 0.00%
Time (mean ± σ): 149.690 μs ± 28.577 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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141 μs Histogram: log(frequency) by time 302 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->findfirst(==(x), v), $x, $perm)
BenchmarkTools.Trial: 1784 samples with 1 evaluation.
Range (min … max): 546.395 μs … 660.254 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 560.513 μs ┊ GC (median): 0.00%
Time (mean ± σ): 559.546 μs ± 14.138 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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546 μs Histogram: log(frequency) by time 625 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench(FindFirstFunctions.findfirstsortedequal, $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 45.969 μs … 73.354 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 47.674 μs ┊ GC (median): 0.00%
Time (mean ± σ): 47.675 μs ± 1.999 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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46 μs Histogram: log(frequency) by time 58.1 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->searchsortedfirst(v, x), $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 35.988 μs … 224.353 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 37.807 μs ┊ GC (median): 0.00%
Time (mean ± σ): 38.966 μs ± 7.905 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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36 μs Histogram: log(frequency) by time 57 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->FindFirstFunctions.findfirstsortedequal(x,v,Val(64)), $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 43.709 μs … 182.914 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 45.227 μs ┊ GC (median): 0.00%
Time (mean ± σ): 45.954 μs ± 5.377 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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43.7 μs Histogram: log(frequency) by time 61.4 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->FindFirstFunctions.findfirstsortedequal(x,v,Val(32)), $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 42.482 μs … 172.067 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 44.422 μs ┊ GC (median): 0.00%
Time (mean ± σ): 45.765 μs ± 8.329 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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42.5 μs Histogram: log(frequency) by time 83.3 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->FindFirstFunctions.findfirstsortedequal(x,v,Val(16)), $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 36.870 μs … 154.299 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 39.764 μs ┊ GC (median): 0.00%
Time (mean ± σ): 40.400 μs ± 2.552 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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36.9 μs Histogram: log(frequency) by time 53 μs <

Memory estimate: 0 bytes, allocs estimate: 0.

julia> @benchmark findbench((x,v)->FindFirstFunctions.findfirstsortedequal(x,v,Val(8)), $s, $perm)
BenchmarkTools.Trial: 10000 samples with 1 evaluation.
Range (min … max): 26.011 μs … 48.109 μs ┊ GC (min … max): 0.00% … 0.00%
Time (median): 26.954 μs ┊ GC (median): 0.00%
Time (mean ± σ): 27.046 μs ± 1.677 μs ┊ GC (mean ± σ): 0.00% ± 0.00%

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26 μs Histogram: log(frequency) by time 37.9 μs <

Memory estimate: 0 bytes, allocs estimate: 0.
```
The branches in a binary search are unpredicable, thus disabling the conversion of `cmov` into branches results in a substantial performance increase.
Additionally, enablig `cmov` (i.e., disabling `cmov` conversion) greatly reduces the optimal base case size for `FindFirstFunctions.findfirstsortedequal`. Without `cmov`, we need a very large base case to avoid too many branches, scanning large swaths contiguously.
With `cmov`, we can reduce the base case size to `8`, taking several additional binary search steps without incurring heavy branch prediction penalties.

However, we default to a large base case size, under the assumptions users are not setting this `ENV` variable; we assume that an expert user concerned about binary search performace who sets this variable will also be able to choose their own basecase size.

Take care when benchmarking `JULIA_LLVM_ARGS="-x86-cmov-converter=false"`: your CPU's branch predictor can probably memorize a sequece of hundreds of perfectly random branches. Branch predcitors are great at defeating microbenchmarks.
Thus, you need a very long unpredictable sequece (which I tried to do in the above benchmark) to prevent the branch predictor from memorizing it.
In "real world" workloads, your branch predictor isn't going to be able to memorize a sequence of left vs right bisections in your binary search, as you won't be performing the same searches over and over again!
Without making your benchmark realistic, the default setting of converting `cmov` into branches will look unrealistically good.

If you actually are, memoize. If you're looking for close answers, look for something like `bracketstrictlymontonic`'s `guess` API.

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