TParallelArray Sort Performance...

Steve Maughan · September 12

The new TParallelArray<T> seems like a drop-in replacement for TArray<T>.

I tested the performance of the parallel sort algorithm on my Intel i9-12900HK laptop. This has 6 performance cores (with hyperthreading) and 8 efficient cores. Here are the results:

One Billion Double Values:

TArray<>: 183.8 seconds

TParallelArray<>: 34.8 seconds

Speed-up: x5.3

Five Million Double Values:

TArray<>: 692 ms

TParallelArray<>: 122 ms

Speed-up: x5.7

500k Double Values:

TArray<>: 65 ms

TParallelArray<>: 18 ms

Speed-up: x3.6

This speed up seems quite good to me.

— Steve

Edited September 12 by Steve Maughan

Anders Melander · September 12

There's something fishy with those numbers.

I would have expected the 500K test to have better throughput than the 5M and 1B tests since the 500K array can fit in the 24Mb cache while the 5M and 1B arrays cannot.

Did you do a warm-up run before the benchmark to get the thread pool spun up?

How many iterations did you do on each test?

Steve Maughan · September 12

I've just repeated the 500k test and there is indeed quite a bit of variation across the parallel times. They range from 10 ms to 25 ms. The single core times are quite consistent at 63 ms to 65 ms.

— Steve

Anders Melander · September 12

You didn't answer any of my questions...

Regardless, would you care to publish your test code so we can see how the sausages got made?

DelphiUdIT · September 12

I try this test (changing the lengths of the array) with an Intel I9-14900HX:

{$APPTYPE CONSOLE}
{$R *.res}
uses System.SysUtils, System.Classes, System.Generics.Collections, System.Threading,
     System.Diagnostics, WinApi.MMSystem;
var SSortArray, PSortArray: TArray<double>;
	I: Integer;
	T: TStopwatch;
begin
  try
    SetLength(SSortArray, 1_000_000_000);
    SetLength(PSortArray, 1_000_000_000);
    Writeln('Fill array (double), elements count: ', Length(SSortArray).ToString);
    for I := Low(SSortArray) to High(SSortArray) do
      begin
        SSortArray[I] := Random(MaxInt);
        PSortArray[I] := SSortArray[I];
      end;
    // Boot up t. pool
    TTask.Create(
      procedure
        begin
          ;
        end).Start;
    Writeln('Start sorting ...');
    // Serial sorting
    T := TStopwatch.StartNew;
    TArray.Sort<double>(SSortArray);
    T.Stop;
    Writeln('TArray.Sort (ms.): ', T.ElapsedMilliseconds.ToString);
    //Insertion of timeBegin... / timeEnd... make the parallel process more fast (10% more)
    //timeBeginPeriod(1);
    // Parallel sorting
    T := TStopwatch.StartNew;
    TParallelArray.Sort<double>(PSortArray);
    T.Stop;
    Writeln('TParallelArray.Sort (ms.): ', T.ElapsedMilliseconds.ToString);
    //timeEndPeriod(1);
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
  SetLength(SSortArray, 0);
  SetLength(PSortArray, 0);
  Readln;

image.png.08dba92a073a968ca8c4b24b7b981eef.png image.png.81cca4ec5f95f20c2bab32e2679dae37.png image.png.391897027034917bfbc11dca845cfbc8.png

Stefan Glienke · September 13

5 hours ago, Anders Melander said:

I would have expected the 500K test to have better throughput than the 5M and 1B tests since the 500K array can fit in the 24Mb cache while the 5M and 1B arrays cannot.

Quicksort with comparer calls compiled by a mediocre compiler operates far below L3 cache speed.

Anders Melander · September 13

12 minutes ago, Stefan Glienke said:

Quicksort with comparer calls compiled by a mediocre compiler operates far below L3 cache speed.

Yes but that's the same for all three tests. The smaller array should still benefit the most from the cache.

To me the posted results indicate that there's a lot of per-sort overhead somewhere.

Stefan Glienke · September 13

I am not commenting on benchmark results without seeing the code - I have seen too many flawed benchmarks in my life.

If you look into the implementation you see that it is using the most simple parallel quicksort imaginable - that means the first run over the entire array which arranges the elements according to the pivot (as in the TArray.Sort the most simple pivot selection - take the middle) runs single threaded.

Only then the processing of left and right is being passed to the PPL.

Anyone who has researched a bit into sorting algorithms in the past 20 years knows that a pure quicksort is hardly anything good enough to be used as general purpose sorting algo in a runtime - other languages using hybrids for years, .NET and some C++ runtimes use IntroSort, Python uses Timsort, so does Java for objects and some special version of QuickSort for primitive types, lately some languages such as Go adapted PDQSort as their default sorting algorithm.

I'd argue that some of these better algorithms running single-threaded outperform parallel quicksort on certain and not so uncommon data patterns.

Edited September 13 by Stefan Glienke

Tommi Prami · September 13

4 hours ago, Stefan Glienke said:

Anyone who has researched a bit into sorting algorithms in the past 20 years knows that a pure quicksort is hardly anything good enough to be used as general purpose sorting algo in a runtime

Average case has most likely very small amount of items to sort. I think I saw somewhere that Bubble Sort would be faster than QuickSort on very small item counts. Not sure tough.

But better is always better and faster is faster, PDQSort was quite interesting, quick look had interesting cases when it is very fast. Seems that it has no really bad worst cases either.

Did not find very good comparison against many other algorithms. Anyhow getting better default sort algorithms to RTL most likely would not hurt much 🙂

-Tee-

Eric Grange · September 13

@Stefan Glienke I've been testing Introsort and other variants as well, they're more resilient to edge cases, but in the typical case, I've found them to be quite underwhelming tbh in Delphi.
In C++ that's different, templates vs generics + loop unrolling give a definitive edge.

On a slower processor (i7-1165G7), for 5 millions values:
- TArray.Sort: 641 ms
- TArray.IntroSort: 673 ms
- Quicksort (non generic, single-thread): 450 ms
- TParallelArray.Sort: 176 ms

So 3.6x speedup over TArray.Sort for a quad-core, which is fair. Overhead of generics is about 40%.

On larger array sizes (like 1T), timing ratios are similar, but the whole machine became unusably slow during the TParallelArray.Sort run, so that's something to keep in mind (don't use it to sort large arrays in a GUI app where you need to keep things snappy)

Edited September 13 by Eric Grange

Stefan Glienke · September 13

Depends on your IntroSort implementation - the one in Spring is usually faster than RTL quicksort. (*)

But this also is a result of it using branchless comparers as far as possible.

Also, there is a reason why usually benchmarks for sorting algorithms don't only test on complete random data but also on several patterns. Because in reality, you often deal with things such as mostly sorted with a few unsorted elements at the end or reversed sorted.

(*) here are the benchmark results for RTL QuickSort vs RTL QuickSort with Spring4d Comparer vs Spring4d IntroSort for several data patterns - you can easily see how the branchless compare affects the performance quite significantly

--------------------------------------------------------------------------------------
Benchmark                                            Time             CPU   Iterations
--------------------------------------------------------------------------------------
random/QuickSort/count:100                        2463 ns         2435 ns          100
random/QuickSort2/count:100                       1802 ns         1782 ns          100
random/IntroSort/count:100                        1420 ns         1395 ns          100
random/QuickSort/count:1000                      50209 ns        50189 ns          100
random/QuickSort2/count:1000                     27645 ns        27612 ns          100
random/IntroSort/count:1000                      18489 ns        18468 ns          100
random/QuickSort/count:10000                    836172 ns       835798 ns          100
random/QuickSort2/count:10000                   728400 ns       727977 ns          100
random/IntroSort/count:10000                    523833 ns       523565 ns          100
random/QuickSort/count:100000                  9855657 ns      9850263 ns          100
random/QuickSort2/count:100000                 8918812 ns      8912401 ns          100
random/IntroSort/count:100000                  6839316 ns      6829126 ns          100
random/QuickSort/count:1000000               119455635 ns    119330369 ns          100
random/QuickSort2/count:1000000              104800849 ns    104696480 ns          100
random/IntroSort/count:1000000                81749401 ns     81660293 ns          100
few_unique/QuickSort/count:100                    2249 ns         2251 ns          100
few_unique/QuickSort2/count:100                   1632 ns         1593 ns          100
few_unique/IntroSort/count:100                    1231 ns         1202 ns          100
few_unique/QuickSort/count:1000                  35486 ns        35454 ns          100
few_unique/QuickSort2/count:1000                 25086 ns        25038 ns          100
few_unique/IntroSort/count:1000                  13094 ns        13071 ns          100
few_unique/QuickSort/count:10000                515193 ns       514924 ns          100
few_unique/QuickSort2/count:10000               371173 ns       370283 ns          100
few_unique/IntroSort/count:10000                285188 ns       285036 ns          100
few_unique/QuickSort/count:100000              5664379 ns      5657759 ns          100
few_unique/QuickSort2/count:100000             4348078 ns      4341859 ns          100
few_unique/IntroSort/count:100000              3164370 ns      3162498 ns          100
few_unique/QuickSort/count:1000000            63121983 ns     63076941 ns          100
few_unique/QuickSort2/count:1000000           43872122 ns     43809752 ns          100
few_unique/IntroSort/count:1000000            30719211 ns     30651572 ns          100
two_values/QuickSort/count:100                    1538 ns         1514 ns          100
two_values/QuickSort2/count:100                   1205 ns         1181 ns          100
two_values/IntroSort/count:100                     781 ns          768 ns          100
two_values/QuickSort/count:1000                  19267 ns        19242 ns          100
two_values/QuickSort2/count:1000                 15309 ns        15261 ns          100
two_values/IntroSort/count:1000                   9174 ns         9146 ns          100
two_values/QuickSort/count:10000                281462 ns       276065 ns          100
two_values/QuickSort2/count:10000               206943 ns       206818 ns          100
two_values/IntroSort/count:10000                150871 ns       150572 ns          100
two_values/QuickSort/count:100000              3483592 ns      3467751 ns          100
two_values/QuickSort2/count:100000             2574497 ns      2555053 ns          100
two_values/IntroSort/count:100000              1947766 ns      1943228 ns          100
two_values/QuickSort/count:1000000            39543461 ns     39439575 ns          100
two_values/QuickSort2/count:1000000           29565091 ns     29524866 ns          100
two_values/IntroSort/count:1000000            22888036 ns     22847673 ns          100
all_equal/QuickSort/count:100                     1453 ns         1424 ns          100
all_equal/QuickSort2/count:100                    1152 ns         1135 ns          100
all_equal/IntroSort/count:100                      735 ns          718 ns          100
all_equal/QuickSort/count:1000                   16442 ns        16424 ns          100
all_equal/QuickSort2/count:1000                  12609 ns        12588 ns          100
all_equal/IntroSort/count:1000                    8274 ns         8253 ns          100
all_equal/QuickSort/count:10000                 214083 ns       213979 ns          100
all_equal/QuickSort2/count:10000                164971 ns       164921 ns          100
all_equal/IntroSort/count:10000                 125590 ns       125514 ns          100
all_equal/QuickSort/count:100000               2819341 ns      2815702 ns          100
all_equal/QuickSort2/count:100000              2120029 ns      2117072 ns          100
all_equal/IntroSort/count:100000               1563758 ns      1560929 ns          100
all_equal/QuickSort/count:1000000             32668228 ns     32563853 ns          100
all_equal/QuickSort2/count:1000000            24450182 ns     24411351 ns          100
all_equal/IntroSort/count:1000000             18799427 ns     18758084 ns          100
ascending/QuickSort/count:100                     1238 ns         1208 ns          100
ascending/QuickSort2/count:100                     989 ns          962 ns          100
ascending/IntroSort/count:100                      723 ns          700 ns          100
ascending/QuickSort/count:1000                   15109 ns        15088 ns          100
ascending/QuickSort2/count:1000                  11357 ns        11335 ns          100
ascending/IntroSort/count:1000                    7988 ns         7969 ns          100
ascending/QuickSort/count:10000                 187903 ns       187573 ns          100
ascending/QuickSort2/count:10000                140454 ns       140400 ns          100
ascending/IntroSort/count:10000                 119619 ns       119090 ns          100
ascending/QuickSort/count:100000               2250330 ns      2249079 ns          100
ascending/QuickSort2/count:100000              1700410 ns      1699408 ns          100
ascending/IntroSort/count:100000               1470538 ns      1467097 ns          100
ascending/QuickSort/count:1000000             28118193 ns     28071460 ns          100
ascending/QuickSort2/count:1000000            20655432 ns     20619601 ns          100
ascending/IntroSort/count:1000000             17387674 ns     17366389 ns          100
slightly_scrambled/QuickSort/count:100            1260 ns         1221 ns          100
slightly_scrambled/QuickSort2/count:100            992 ns          976 ns          100
slightly_scrambled/IntroSort/count:100             760 ns          729 ns          100
slightly_scrambled/QuickSort/count:1000          16685 ns        16664 ns          100
slightly_scrambled/QuickSort2/count:1000         12477 ns        12462 ns          100
slightly_scrambled/IntroSort/count:1000           9125 ns         9105 ns          100
slightly_scrambled/QuickSort/count:10000        247135 ns       246653 ns          100
slightly_scrambled/QuickSort2/count:10000       183518 ns       183063 ns          100
slightly_scrambled/IntroSort/count:10000        158241 ns       157415 ns          100
slightly_scrambled/QuickSort/count:100000      2975025 ns      2964542 ns          100
slightly_scrambled/QuickSort2/count:100000     2393465 ns      2389448 ns          100
slightly_scrambled/IntroSort/count:100000      2140478 ns      2137574 ns          100
slightly_scrambled/QuickSort/count:1000000    36245900 ns     36023047 ns          100
slightly_scrambled/QuickSort2/count:1000000   29002166 ns     28920883 ns          100
slightly_scrambled/IntroSort/count:1000000    25116044 ns     25034741 ns          100
sorted_blocks/QuickSort/count:100                 1588 ns         1557 ns          100
sorted_blocks/QuickSort2/count:100                1377 ns         1369 ns          100
sorted_blocks/IntroSort/count:100                 1195 ns         1171 ns          100
sorted_blocks/QuickSort/count:1000               25010 ns        24969 ns          100
sorted_blocks/QuickSort2/count:1000              19958 ns        19927 ns          100
sorted_blocks/IntroSort/count:1000               13229 ns        13200 ns          100
sorted_blocks/QuickSort/count:10000             296620 ns       295986 ns          100
sorted_blocks/QuickSort2/count:10000            246763 ns       246503 ns          100
sorted_blocks/IntroSort/count:10000             173911 ns       173822 ns          100
sorted_blocks/QuickSort/count:100000           4510684 ns      4474993 ns          100
sorted_blocks/QuickSort2/count:100000          3492714 ns      3479751 ns          100
sorted_blocks/IntroSort/count:100000           2468243 ns      2466781 ns          100
sorted_blocks/QuickSort/count:1000000         51631011 ns     51470454 ns          100
sorted_blocks/QuickSort2/count:1000000        41472336 ns     41323492 ns          100
sorted_blocks/IntroSort/count:1000000         29948990 ns     29886920 ns          100
single_big_swap/QuickSort/count:100               1408 ns         1378 ns          100
single_big_swap/QuickSort2/count:100              1124 ns         1097 ns          100
single_big_swap/IntroSort/count:100               1096 ns         1067 ns          100
single_big_swap/QuickSort/count:1000             16770 ns        16747 ns          100
single_big_swap/QuickSort2/count:1000            12769 ns        12753 ns          100
single_big_swap/IntroSort/count:1000             14975 ns        14945 ns          100
single_big_swap/QuickSort/count:10000           205373 ns       204738 ns          100
single_big_swap/QuickSort2/count:10000          153375 ns       153290 ns          100
single_big_swap/IntroSort/count:10000           211204 ns       210621 ns          100
single_big_swap/QuickSort/count:100000         2427136 ns      2416559 ns          100
single_big_swap/QuickSort2/count:100000        1853420 ns      1851812 ns          100
single_big_swap/IntroSort/count:100000         2900139 ns      2884030 ns          100
single_big_swap/QuickSort/count:1000000       29680453 ns     29600956 ns          100
single_big_swap/QuickSort2/count:1000000      22054106 ns     21979630 ns          100
single_big_swap/IntroSort/count:1000000       35043829 ns     34961055 ns          100
descending/QuickSort/count:100                    1225 ns         1205 ns          100
descending/QuickSort2/count:100                    979 ns          955 ns          100
descending/IntroSort/count:100                     726 ns          703 ns          100
descending/QuickSort/count:1000                  15322 ns        15138 ns          100
descending/QuickSort2/count:1000                 11398 ns        11374 ns          100
descending/IntroSort/count:1000                   8001 ns         7982 ns          100
descending/QuickSort/count:10000                187287 ns       187230 ns          100
descending/QuickSort2/count:10000               140713 ns       139754 ns          100
descending/IntroSort/count:10000                119207 ns       119157 ns          100
descending/QuickSort/count:100000              2251193 ns      2250138 ns          100
descending/QuickSort2/count:100000             1697955 ns      1697229 ns          100
descending/IntroSort/count:100000              1468175 ns      1467358 ns          100
descending/QuickSort/count:1000000            28025499 ns     27991254 ns          100
descending/QuickSort2/count:1000000           20643835 ns     20610794 ns          100
descending/IntroSort/count:1000000            17434312 ns     17380960 ns          100
pipe_organ/QuickSort/count:100                    1347 ns         1325 ns          100
pipe_organ/QuickSort2/count:100                   1068 ns         1052 ns          100
pipe_organ/IntroSort/count:100                     712 ns          690 ns          100
pipe_organ/QuickSort/count:1000                  15772 ns        15749 ns          100
pipe_organ/QuickSort2/count:1000                 11923 ns        11899 ns          100
pipe_organ/IntroSort/count:1000                   8073 ns         8059 ns          100
pipe_organ/QuickSort/count:10000                200075 ns       200011 ns          100
pipe_organ/QuickSort2/count:10000               153828 ns       153583 ns          100
pipe_organ/IntroSort/count:10000                121821 ns       121781 ns          100
pipe_organ/QuickSort/count:100000              2564621 ns      2558463 ns          100
pipe_organ/QuickSort2/count:100000             1958687 ns      1951100 ns          100
pipe_organ/IntroSort/count:100000              1516152 ns      1511432 ns          100
pipe_organ/QuickSort/count:1000000            30322479 ns     30281379 ns          100
pipe_organ/QuickSort2/count:1000000           23019458 ns     22963220 ns          100
pipe_organ/IntroSort/count:1000000            18033541 ns     17998660 ns          100
push_front/QuickSort/count:100                    1657 ns         1627 ns          100
push_front/QuickSort2/count:100                   1208 ns         1193 ns          100
push_front/IntroSort/count:100                    1173 ns         1150 ns          100
push_front/QuickSort/count:1000                  18850 ns        18774 ns          100
push_front/QuickSort2/count:1000                 13694 ns        13669 ns          100
push_front/IntroSort/count:1000                  15505 ns        15491 ns          100
push_front/QuickSort/count:10000                232070 ns       231695 ns          100
push_front/QuickSort2/count:10000               164370 ns       164085 ns          100
push_front/IntroSort/count:10000                223185 ns       223119 ns          100
push_front/QuickSort/count:100000              2786631 ns      2780806 ns          100
push_front/QuickSort2/count:100000             1981209 ns      1977728 ns          100
push_front/IntroSort/count:100000              2986261 ns      2979247 ns          100
push_front/QuickSort/count:1000000            32337658 ns     32237857 ns          100
push_front/QuickSort2/count:1000000           22995000 ns     22948793 ns          100
push_front/IntroSort/count:1000000            35586468 ns     35516490 ns          100
push_middle/QuickSort/count:100                   1445 ns         1416 ns          100
push_middle/QuickSort2/count:100                  1088 ns         1069 ns          100
push_middle/IntroSort/count:100                    893 ns          868 ns          100
push_middle/QuickSort/count:1000                 17087 ns        17063 ns          100
push_middle/QuickSort2/count:1000                27199 ns        12531 ns          100
push_middle/IntroSort/count:1000                 11300 ns        11284 ns          100
push_middle/QuickSort/count:10000               210365 ns       210271 ns          100
push_middle/QuickSort2/count:10000              152367 ns       152240 ns          100
push_middle/IntroSort/count:10000               166248 ns       166154 ns          100
push_middle/QuickSort/count:100000             2529640 ns      2526924 ns          100
push_middle/QuickSort2/count:100000            1844729 ns      1842635 ns          100
push_middle/IntroSort/count:100000             2160489 ns      2158998 ns          100
push_middle/QuickSort/count:1000000           30219881 ns     30136359 ns          100
push_middle/QuickSort2/count:1000000          21940150 ns     21867966 ns          100
push_middle/IntroSort/count:1000000           25940856 ns     25884546 ns          100

Edited September 13 by Stefan Glienke

Stefan Glienke · September 13

TParallelArray.Sort is broken by the way - try this:

uses
  System.Threading,
  System.SysUtils;

procedure Main;
begin
  var data: TArray<Integer>;
  SetLength(data, 1000000);
  for var i := 0 to High(data) do
    data[i] := Random(16);
  TParallelArray.Sort<Integer>(data);
end;

begin
  try
    Main;
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
  Writeln('done');
  Readln;
end.

Lajos Juhász · September 13

Stefan you should give at least 48 hours to a new version before you break it. It does handle array of 100_000 integers. Maybe for a larger arrays you have to buy a special SKU for sorting.

Eric Grange · September 13

I actually used an Introsort implementation you had posted sometime ago, but with the RTL comparare 🙂

However I can't really reproduce your benchmark advantage with latest Spring4D from your repository: in the same conditions as above, Spring4D's sort clocks at 609 ms for 5 million values, just 7% faster than RTL.

.
The code really goes in the IntroSort_Double methods and the Compare_Double comparer (I checked with the debugger), is there some option or setting required ?

When the array is pre-sorted instead of random, the timings are:
- RTL TArray.Sort : 265 ms
- Spring4D IntroSort : 238 ms
- non-generic QuickSort : 78 ms
- TParallelArray.Sort: 100 ms

So Spring4d gets somewhat faster compared to RTL, but not as a massively as the non-generic Quicksort.

The other edge case is an array of 5 millions times the same value:
- RTL TArray.Sort : 248 ms
- Spring4D IntroSort : 229 ms
- non-generic QuickSort : 102 ms
- TParallelArray.Sort: CRASH with Stack Overflow !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Ok, this one looks like a death blow to the new parallel sort 😕

For reference, this is the non-generic QuickSort copy-pasta

{$R-} {$O+} {$Q-}
type
   TDoubleArray = array [0..MaxInt div 8 - 1] of Double;
   PDoubleArray = ^TDoubleArray;
procedure QuickSort(pArray : PDoubleArray; minIndex, maxIndex : NativeInt);
var
   i, j, p : NativeInt;
begin
   repeat
      i := minIndex;
      j := maxIndex;
      p := (i+j) shr 1;
      repeat
         var pv := pArray[p];
         while pArray[i] > pv do Inc(i);
         while pArray[j] < pv do Dec(j);
         if i <= j then begin
            var buf := pArray[i];
            pArray[i] := pArray[j];
            pArray[j] := buf;
            if p = i then p := j else if p = j then p := i;
            Inc(i);
            Dec(j);
         end;
      until i > j;
      if minIndex < j then
         QuickSort(pArray, minIndex, j);
      minIndex := i;
   until i >= maxIndex;
end;

Eric Grange · September 13

Looks like parallel sort largest non-crash single value array size is somewhere between 10000 and 15000 actually at @Lajos Juhász
Stefan actually went easy at it with a Random(16) 😉

Anders Melander · September 13

49 minutes ago, Stefan Glienke said:

here are the benchmark results [...]

How do you get the benchmark results ordered by parameters rather than method?

The way I use spring.benchmark I get the results ordered by method and then parameters which makes it hard to compare the different methods:

procedure Benchmark(BenchmarkFunc: TFunction; const Name: string);
begin
  Spring.Benchmark.Benchmark(BenchmarkFunc, Name).RangeMultiplier(4).Ranges([Range(1024+1, 8192+13), Range(128, 5120)]).TimeUnit(kMillisecond);
end;

//------------------------------------------------------------------------------

begin
  Benchmark(BenchmarkNoTranspose32, 'MemCopy (no transpose)');
  Benchmark(BenchmarkReferenceTranspose32, 'ReferenceTranspose32');
  Benchmark(BenchmarkCacheObliviousTranspose32, 'CacheObliviousTranspose32');
  Benchmark(BenchmarkCacheObliviousTransposeEx32, 'CacheObliviousTransposeEx32');
  Benchmark(BenchmarkSuperDuperTranspose32, 'SuperDuperTranspose32');

  Spring.Benchmark.Benchmark_Main;
end.

------------------------------------------------------------------------------------------------
Benchmark                                      Time             CPU   Iterations UserCounters...
------------------------------------------------------------------------------------------------
MemCopy (no transpose)/1025/128            0,028 ms        0,025 ms        26353 Rate=5.26859G/s
MemCopy (no transpose)/4096/128            0,153 ms        0,143 ms         4480 Rate=3.66644G/s
MemCopy (no transpose)/8205/128            0,616 ms        0,578 ms         1000 Rate=1.81663G/s
MemCopy (no transpose)/1025/256            0,064 ms        0,049 ms        11200 Rate=5.37395G/s
MemCopy (no transpose)/4096/256            0,596 ms        0,502 ms         1120 Rate=2.08783G/s
MemCopy (no transpose)/8205/256             1,30 ms         1,03 ms          560 Rate=2.03463G/s
MemCopy (no transpose)/1025/1024           0,590 ms        0,558 ms         1120 Rate=1.88088G/s
MemCopy (no transpose)/4096/1024            2,56 ms         2,25 ms          299 Rate=1.86656G/s
MemCopy (no transpose)/8205/1024            5,48 ms         4,26 ms          154 Rate=1.97165G/s
MemCopy (no transpose)/1025/4096            2,63 ms         2,08 ms          345 Rate=2.01523G/s
MemCopy (no transpose)/4096/4096            10,9 ms         10,0 ms           64 Rate=1.67608G/s
MemCopy (no transpose)/8205/4096            23,6 ms         22,6 ms           29 Rate=1.48514G/s
MemCopy (no transpose)/1025/5120            3,36 ms         2,85 ms          236 Rate=1.84339G/s
MemCopy (no transpose)/4096/5120            14,3 ms         12,3 ms           56 Rate=1.70823G/s
MemCopy (no transpose)/8205/5120            29,3 ms         23,8 ms           21 Rate=1.7644G/s
ReferenceTranspose32/1025/128              0,345 ms        0,322 ms         2036 Rate=407.045M/s
ReferenceTranspose32/4096/128               1,49 ms         1,35 ms          498 Rate=388.607M/s
ReferenceTranspose32/8205/128               3,84 ms         3,07 ms          224 Rate=342.187M/s
ReferenceTranspose32/1025/256              0,806 ms        0,628 ms         1120 Rate=417.974M/s
ReferenceTranspose32/4096/256               3,91 ms         3,23 ms          213 Rate=324.868M/s
ReferenceTranspose32/8205/256               28,4 ms         25,7 ms           28 Rate=81.8274M/s
ReferenceTranspose32/1025/1024              7,00 ms         6,77 ms           90 Rate=155.018M/s
ReferenceTranspose32/4096/1024              97,6 ms         93,8 ms            7 Rate=44.7392M/s
ReferenceTranspose32/8205/1024               184 ms          168 ms            4 Rate=50.0207M/s
ReferenceTranspose32/1025/4096              33,4 ms         32,8 ms           20 Rate=127.951M/s
ReferenceTranspose32/4096/4096               367 ms          336 ms            2 Rate=49.9415M/s
ReferenceTranspose32/8205/4096               720 ms          656 ms            1 Rate=51.2117M/s
ReferenceTranspose32/1025/5120              44,2 ms         41,4 ms           17 Rate=126.885M/s
ReferenceTranspose32/4096/5120               459 ms          391 ms            2 Rate=53.6871M/s
ReferenceTranspose32/8205/5120               969 ms          781 ms            1 Rate=53.7723M/s
CacheObliviousTranspose32/1025/128         0,326 ms        0,285 ms         2800 Rate=461.001M/s
CacheObliviousTranspose32/4096/128          1,37 ms         1,34 ms          560 Rate=391.468M/s
[...]

Anders Melander · September 13

9 minutes ago, Eric Grange said:

TParallelArray.Sort: CRASH with Stack Overflow

But it crashed faster and fast is better, right? Right?

If only there was some easy way of getting stuff like this tested before release... I mean, come on, we all make bugs but this is simply not acceptable.

Stefan Glienke · September 13

This is the benchmark code - previous results I posted were with TTestType = Integer, but using Double shows similar results (I ran the benchmark as 64bit release)

program SortBench;

{$APPTYPE CONSOLE}

uses
  System.Generics.Collections,
  Spring,
  Spring.Comparers,
  Spring.Benchmark,
  System.SysUtils;

type
  TTestType = Double;

  TDistFunc = function(size: Integer): TArray<TTestType>;
  TSortFunc = procedure(var values: array of TTestType);

function IntToTestType(i: Integer): TTestType;
begin
  Result := i;
end;

function Equals(const left, right: TTestType): Boolean; inline;
begin
  Result := left = right;
end;

function Shuffled(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to size - 1 do
    Result[i] := IntToTestType(i);
  Spring.TArray.Shuffle<TTestType>(Result);
end;

function Shuffled_16Values(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to size - 1 do
    Result[i] := IntToTestType(Random(16));
end;

function TwoValues(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to size - 1 do
    Result[i] := IntToTestType(Random(2));
end;

function AllEqual(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to size - 1 do
    Result[i] := IntToTestType(0);
end;

function Ascending(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to size - 1 do
    Result[i] := IntToTestType(i);
end;

function SlightlyScrambled(size: Integer): TArray<TTestType>;
const
  scramblePercentage = 5;
var
  i, idx1, idx2: Integer;
  temp: TTestType;
  scrambleCount: Integer;
begin
  SetLength(Result, size);
  for i := 0 to size - 1 do
    Result[i] := IntToTestType(i);
  scrambleCount := size * scramblePercentage div 100;
  for i := 1 to scrambleCount do
  begin
    idx1 := Random(size);
    idx2 := Random(size);
    temp := Result[idx1];
    Result[idx1] := Result[idx2];
    Result[idx2] := temp;
  end;
end;

function SortedBlocks(size: Integer): TArray<TTestType>;
type
  TBlock100 = array[1..100] of TTestType;
  TBlock10  = array[1..10] of TTestType;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to size - 1 do
    Result[i] := IntToTestType(i);
  if size > 100 then
    Spring.TArray.Shuffle<TBlock100>(Pointer(Result), (size div (SizeOf(TBlock100) div SizeOf(TTestType))) - 1)
  else
    Spring.TArray.Shuffle<TBlock10>(Pointer(Result), (size div (SizeOf(TBlock10) div SizeOf(TTestType))) - 1);
end;

function SingleBigSwap(size: Integer): TArray<TTestType>;
var
  i: Integer;
  halfSize: Integer;
begin
  SetLength(Result, size);
  halfSize := size div 2;
  for i := 0 to halfSize - 1 do
    Result[i] := IntToTestType(i + halfSize);
  for i := halfSize to size -1 do
    Result[i] := IntToTestType(i - halfSize);
end;

function Descending(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := size-1 downto 0 do
    Result[i] := IntToTestType(i);
end;

function PipeOrgan(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to (size div 2) - 1 do
    Result[i] := IntToTestType(i);
  for i := size div 2 to size -1 do
    Result[i] := IntToTestType(size - 1);
end;

function PushFront(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 1 to size - 1 do
    Result[i - 1] := IntToTestType(i);
  Result[size - 1] := IntToTestType(0);
end;

function PushMiddle(size: Integer): TArray<TTestType>;
var
  i: Integer;
begin
  SetLength(Result, size);
  for i := 0 to (size div 2) - 1 do
    Result[i] := IntToTestType(i);
  for i := (size div 2) + 1 to size -1 do
    Result[i - 1] := IntToTestType(i);
  Result[size - 1] := IntToTestType(size div 2);
end;

procedure QuickSort(var values: array of TTestType);
begin
  System.Generics.Collections.TArray.Sort<TTestType>(values);
end;

procedure QuickSort_SpringComparer(var values: array of TTestType);
begin
  System.Generics.Collections.TArray.Sort<TTestType>(values
    , Spring.Comparers.TComparer<TTestType>.Default
    );
end;

procedure IntroSort(var values: array of TTestType);
begin
  Spring.TArray.Sort<TTestType>(values);
end;

const
  Distributions: array[0..11] of record name: string; func: TDistFunc end = (
    (name: 'random'; func: Shuffled),
    (name: 'few_unique'; func: Shuffled_16Values),
    (name: 'two_values'; func: TwoValues),
    (name: 'all_equal'; func: AllEqual),
    (name: 'ascending'; func: Ascending),
    (name: 'slightly_scrambled'; func: SlightlyScrambled),
    (name: 'sorted_blocks'; func: SortedBlocks),
    (name: 'single_big_swap'; func: SingleBigSwap),
    (name: 'descending'; func: Descending),
    (name: 'pipe_organ'; func: PipeOrgan),
    (name: 'push_front'; func: PushFront),
    (name: 'push_middle'; func: PushMiddle)
  );

  Sorts: array[0..2] of record name: string; func: TSortFunc end = (
    (name: 'QuickSort'; func: QuickSort)
    ,(name: 'QuickSort2'; func: QuickSort_SpringComparer)
    ,(name: 'IntroSort'; func: IntroSort)
  );

  Sizes: array of Integer = [100, 1000, 10000, 100000, 1000000];

procedure BenchSort(const state: TState);
begin
  var distIdx := state[0];
  var sortIdx := state[1];
  var size := state[2];

  var distribution: TDistFunc := Distributions[distIdx].func;
  var sort: TSortFunc := Sorts[sortIdx].func;
  var data := distribution(size);
  var copy: TArray<TTestType>;
  SetLength(copy, size);

  for var _ in state do
  begin
    state.PauseTiming;
    if IsManagedType(TTestType) then
      MoveManaged(data, copy, TypeInfo(TTestType), size)
    else
      Move(data[0], copy[0], size * SizeOf(TTestType));
    state.ResumeTiming;
    sort(copy);
  end;
  QuickSort(data);
  for var i := 0 to high(copy) do
    Assert(Equals(copy[i], data[i]), Distributions[distIdx].Name + '/' + Sorts[sortIdx].Name + '/' + size.ToString);
end;

procedure Main;
begin
  benchmark_format_args := False;

  for var distIdx := Low(distributions) to High(Distributions) do
  for var size in Sizes do
  for var sortIdx := Low(Sorts) to High(Sorts) do
  begin
    var bm := Benchmark(BenchSort, Distributions[distIdx].name + '/' + Sorts[sortIdx].name + '/count:' + size.ToString)
      .Args([distIdx, sortIdx, size]);
    bm.Iterations(100);
  end;
  Benchmark_Main;
end;

begin
  try
    Main;
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
  Readln;
end.

Edited September 13 by Stefan Glienke

DelphiUdIT · September 13

I do test with 1 bilions of elements, and there were no issue, but the test that Stefan (the first post, not the last) did was with limited value (only 16 values in 1 milions of elements).

There are sure an issue with recursive and stack allocation (or may be the algorithm in the ICompare method).

Try to modify the maximum stack allocation and vary the Random value to 24 (Random(24)) and all is running.

Of course this is anyway an issue

Stefan Glienke · September 13

Just now, DelphiUdIT said:

There are sure an issue with recursive and stack allocation (or may be the algorithm in the ICompare method).

The issue is that in the Parallel implementation there is no mitigation against QuickSorts well known worst case.

DelphiUdIT · September 13

13 minutes ago, Stefan Glienke said:

The issue is that in the Parallel implementation there is no mitigation against QuickSorts well known worst case.

If this is so known and clear, Embarcadero was very "light" in proposing such a solution ... let's hope they propose another solution because the times with parallel processing are definitely interesting.

Edited September 13 by DelphiUdIT

Stefan Glienke · September 13

1 hour ago, DelphiUdIT said:

the times with parallel processing are definitely interesting.

To me they are not - if you have some backend server code that is already doing multiple things in parallel it won't get any better if you then do parallel sort.

Eric Grange · September 13

@Stefan Glienke could you try reproducing by invoking your sort calls directly in the minimalistic benchmark code posted in the thread beginning ?

Stefan Glienke · September 13

Benchmark code:

{$APPTYPE CONSOLE}

uses
  System.Diagnostics,
  System.Generics.Collections,
  System.SysUtils,
  Spring;

procedure Test(count: NativeInt);
var
  SSortArray, PSortArray: TArray<double>;
  I: Integer;
  T: TStopwatch;
begin
  try
    SetLength(SSortArray, count);
    SetLength(PSortArray, count);
    Writeln('Fill array (double), elements count: ', count);
    for I := Low(SSortArray) to High(SSortArray) do
      begin
        SSortArray[I] := Random(MaxInt);
        PSortArray[I] := SSortArray[I];
      end;
    Writeln('Start sorting ...');

    T := TStopwatch.StartNew;
    System.Generics.Collections.TArray.Sort<double>(SSortArray);
    T.Stop;
    Writeln('RTL TArray.Sort (ms.): ', T.ElapsedMilliseconds.ToString);

    T := TStopwatch.StartNew;
    Spring.TArray.Sort<double>(PSortArray);
    T.Stop;
    Writeln('Spring TArray.Sort (ms.): ', T.ElapsedMilliseconds.ToString);
  except
    on E: Exception do
      Writeln(E.ClassName, ': ', E.Message);
  end;
  Writeln;
end;
begin
  Test(500_000);
  Test(5_000_000);
  Test(100_000_000);
  Readln;
end.

Results (win64 release) on i7-12700:

Fill array (double), elements count: 500000
Start sorting ...
RTL TArray.Sort (ms.): 49
Spring TArray.Sort (ms.): 33

Fill array (double), elements count: 5000000
Start sorting ...
RTL TArray.Sort (ms.): 560
Spring TArray.Sort (ms.): 393

Fill array (double), elements count: 100000000
Start sorting ...
RTL TArray.Sort (ms.): 13053
Spring TArray.Sort (ms.): 9351

Edited September 13 by Stefan Glienke

Stefan Glienke · September 13

Here is something else to tease you all a bit - PDQSort is using comparer, PDQSort2 does not - others as before QuickSort2 is using the Spring Comparer - test type is Double:

Looks like I am getting twice the speed at worst and 50 times at best. For faster to compare types such as Integer the gain goes up to almost 100 times.

--------------------------------------------------------------------------------------
Benchmark                                            Time             CPU   Iterations
--------------------------------------------------------------------------------------
random/QuickSort/count:100                        2917 ns         2886 ns          100
random/QuickSort2/count:100                       2301 ns         2284 ns          100
random/IntroSort/count:100                        1582 ns         1566 ns          100
random/PDQSort/count:100                          1519 ns         1504 ns          100
random/PDQSort2/count:100                          759 ns          746 ns          100
random/QuickSort/count:1000                      48127 ns        47750 ns          100
random/QuickSort2/count:1000                     26820 ns        26615 ns          100
random/IntroSort/count:1000                      16349 ns        16157 ns          100
random/PDQSort/count:1000                        24101 ns        23928 ns          100
random/PDQSort2/count:1000                        6485 ns         6442 ns          100
random/QuickSort/count:10000                    686240 ns       685846 ns          100
random/QuickSort2/count:10000                   621977 ns       618258 ns          100
random/IntroSort/count:10000                    426604 ns       426023 ns          100
random/PDQSort/count:10000                      445646 ns       443871 ns          100
random/PDQSort2/count:10000                     338404 ns       336588 ns          100
random/QuickSort/count:100000                  8252128 ns      8220957 ns          100
random/QuickSort2/count:100000                 7492506 ns      7371508 ns          100
random/IntroSort/count:100000                  5723208 ns      5578393 ns          100
random/PDQSort/count:100000                    5675312 ns      5650503 ns          100
random/PDQSort2/count:100000                   4504745 ns      4482480 ns          100
random/QuickSort/count:1000000                98163494 ns     97011011 ns          100
random/QuickSort2/count:1000000               88461390 ns     87306397 ns          100
random/IntroSort/count:1000000                67687293 ns     66648855 ns          100
random/PDQSort/count:1000000                  69019337 ns     68147235 ns          100
random/PDQSort2/count:1000000                 55628991 ns     54791149 ns          100
few_unique/QuickSort/count:100                    2356 ns         2314 ns          100
few_unique/QuickSort2/count:100                   1540 ns         1500 ns          100
few_unique/IntroSort/count:100                    1291 ns         1275 ns          100
few_unique/PDQSort/count:100                      1559 ns         1483 ns          100
few_unique/PDQSort2/count:100                      689 ns          674 ns          100
few_unique/QuickSort/count:1000                  29073 ns        29009 ns          100
few_unique/QuickSort2/count:1000                 16086 ns        16026 ns          100
few_unique/IntroSort/count:1000                  11084 ns        11031 ns          100
few_unique/PDQSort/count:1000                     8022 ns         7984 ns          100
few_unique/PDQSort2/count:1000                    4015 ns         3983 ns          100
few_unique/QuickSort/count:10000                424766 ns       424046 ns          100
few_unique/QuickSort2/count:10000               292291 ns       288395 ns          100
few_unique/IntroSort/count:10000                224547 ns       222666 ns          100
few_unique/PDQSort/count:10000                  145437 ns       144788 ns          100
few_unique/PDQSort2/count:10000                 102878 ns       102414 ns          100
few_unique/QuickSort/count:100000              4654357 ns      4640420 ns          100
few_unique/QuickSort2/count:100000             3436405 ns      3421938 ns          100
few_unique/IntroSort/count:100000              2649901 ns      2639618 ns          100
few_unique/PDQSort/count:100000                1487662 ns      1479095 ns          100
few_unique/PDQSort2/count:100000               1172432 ns      1167015 ns          100
few_unique/QuickSort/count:1000000            51130249 ns     50537573 ns          100
few_unique/QuickSort2/count:1000000           38627555 ns     38033922 ns          100
few_unique/IntroSort/count:1000000            30907231 ns     30808893 ns          100
few_unique/PDQSort/count:1000000              14733627 ns     14572366 ns          100
few_unique/PDQSort2/count:1000000             12287426 ns     12233176 ns          100
two_values/QuickSort/count:100                    2115 ns         2099 ns          100
two_values/QuickSort2/count:100                   1601 ns         1558 ns          100
two_values/IntroSort/count:100                    1058 ns         1037 ns          100
two_values/PDQSort/count:100                       714 ns          699 ns          100
two_values/PDQSort2/count:100                      395 ns          377 ns          100
two_values/QuickSort/count:1000                  18838 ns        18787 ns          100
two_values/QuickSort2/count:1000                 15509 ns        15468 ns          100
two_values/IntroSort/count:1000                  10009 ns         9971 ns          100
two_values/PDQSort/count:1000                     3434 ns         3397 ns          100
two_values/PDQSort2/count:1000                    1715 ns         1673 ns          100
two_values/QuickSort/count:10000                310630 ns       306744 ns          100
two_values/QuickSort2/count:10000               221981 ns       214977 ns          100
two_values/IntroSort/count:10000                148667 ns       148595 ns          100
two_values/PDQSort/count:10000                   42702 ns        42577 ns          100
two_values/PDQSort2/count:10000                  24225 ns        24032 ns          100
two_values/QuickSort/count:100000              3353827 ns      3342019 ns          100
two_values/QuickSort2/count:100000             2487005 ns      2476672 ns          100
two_values/IntroSort/count:100000              1870906 ns      1863767 ns          100
two_values/PDQSort/count:100000                 541802 ns       540355 ns          100
two_values/PDQSort2/count:100000                378254 ns       378023 ns          100
two_values/QuickSort/count:1000000            40114855 ns     39440910 ns          100
two_values/QuickSort2/count:1000000           29158407 ns     28744654 ns          100
two_values/IntroSort/count:1000000            23100678 ns     22744457 ns          100
two_values/PDQSort/count:1000000               5633201 ns      5601282 ns          100
two_values/PDQSort2/count:1000000              3762100 ns      3740864 ns          100
all_equal/QuickSort/count:100                     2151 ns         2136 ns          100
all_equal/QuickSort2/count:100                    1647 ns         1618 ns          100
all_equal/IntroSort/count:100                     1058 ns         1040 ns          100
all_equal/PDQSort/count:100                        570 ns          526 ns          100
all_equal/PDQSort2/count:100                       326 ns          310 ns          100
all_equal/QuickSort/count:1000                   17604 ns        17531 ns          100
all_equal/QuickSort2/count:1000                  12558 ns        12503 ns          100
all_equal/IntroSort/count:1000                    8658 ns         8607 ns          100
all_equal/PDQSort/count:1000                      2501 ns         2517 ns          100
all_equal/PDQSort2/count:1000                     1211 ns         1200 ns          100
all_equal/QuickSort/count:10000                 229287 ns       228053 ns          100
all_equal/QuickSort2/count:10000                168158 ns       167545 ns          100
all_equal/IntroSort/count:10000                 123868 ns       122653 ns          100
all_equal/PDQSort/count:10000                    17648 ns        17566 ns          100
all_equal/PDQSort2/count:10000                    6898 ns         6844 ns          100
all_equal/QuickSort/count:100000               3089106 ns      2839190 ns          100
all_equal/QuickSort2/count:100000              1991645 ns      1983108 ns          100
all_equal/IntroSort/count:100000               1517401 ns      1509352 ns          100
all_equal/PDQSort/count:100000                  168092 ns       167526 ns          100
all_equal/PDQSort2/count:100000                  64056 ns        63376 ns          100
all_equal/QuickSort/count:1000000             31780316 ns     31401768 ns          100
all_equal/QuickSort2/count:1000000            23670745 ns     23308078 ns          100
all_equal/IntroSort/count:1000000             18492352 ns     18165700 ns          100
all_equal/PDQSort/count:1000000                1693063 ns      1685270 ns          100
all_equal/PDQSort2/count:1000000                667052 ns       665049 ns          100
ascending/QuickSort/count:100                     1645 ns         1629 ns          100
ascending/QuickSort2/count:100                    1249 ns         1233 ns          100
ascending/IntroSort/count:100                      993 ns          956 ns          100
ascending/PDQSort/count:100                        524 ns          510 ns          100
ascending/PDQSort2/count:100                       290 ns          276 ns          100
ascending/QuickSort/count:1000                   15279 ns        15237 ns          100
ascending/QuickSort2/count:1000                  11455 ns        11389 ns          100
ascending/IntroSort/count:1000                    7931 ns         7802 ns          100
ascending/PDQSort/count:1000                      2618 ns         2572 ns          100
ascending/PDQSort2/count:1000                     1199 ns         1169 ns          100
ascending/QuickSort/count:10000                 186722 ns       185998 ns          100
ascending/QuickSort2/count:10000                134269 ns       134014 ns          100
ascending/IntroSort/count:10000                 106604 ns       106492 ns          100
ascending/PDQSort/count:10000                    19298 ns        19236 ns          100
ascending/PDQSort2/count:10000                    6002 ns         5953 ns          100
ascending/QuickSort/count:100000               2229729 ns      2219903 ns          100
ascending/QuickSort2/count:100000              1655304 ns      1647404 ns          100
ascending/IntroSort/count:100000               1298027 ns      1291995 ns          100
ascending/PDQSort/count:100000                  190239 ns       189988 ns          100
ascending/PDQSort2/count:100000                  53607 ns        53501 ns          100
ascending/QuickSort/count:1000000             27509633 ns     27165759 ns          100
ascending/QuickSort2/count:1000000            19985236 ns     19668315 ns          100
ascending/IntroSort/count:1000000             15326770 ns     15254001 ns          100
ascending/PDQSort/count:1000000                1901178 ns      1890171 ns          100
ascending/PDQSort2/count:1000000                629675 ns       628905 ns          100
slightly_scrambled/QuickSort/count:100            1750 ns         1732 ns          100
slightly_scrambled/QuickSort2/count:100           1373 ns         1343 ns          100
slightly_scrambled/IntroSort/count:100             985 ns          968 ns          100
slightly_scrambled/PDQSort/count:100              1012 ns          997 ns          100
slightly_scrambled/PDQSort2/count:100              471 ns          454 ns          100
slightly_scrambled/QuickSort/count:1000          16791 ns        16735 ns          100
slightly_scrambled/QuickSort2/count:1000         12824 ns        12776 ns          100
slightly_scrambled/IntroSort/count:1000          10458 ns        10399 ns          100
slightly_scrambled/PDQSort/count:1000            16268 ns        15887 ns          100
slightly_scrambled/PDQSort2/count:1000            4547 ns         4494 ns          100
slightly_scrambled/QuickSort/count:10000        235073 ns       233521 ns          100
slightly_scrambled/QuickSort2/count:10000       200321 ns       199399 ns          100
slightly_scrambled/IntroSort/count:10000        151789 ns       151249 ns          100
slightly_scrambled/PDQSort/count:10000          174541 ns       173592 ns          100
slightly_scrambled/PDQSort2/count:10000          89454 ns        89257 ns          100
slightly_scrambled/QuickSort/count:100000      2972211 ns      2964870 ns          100
slightly_scrambled/QuickSort2/count:100000     2376263 ns      2366504 ns          100
slightly_scrambled/IntroSort/count:100000      2305909 ns      2052472 ns          100
slightly_scrambled/PDQSort/count:100000        2093171 ns      2083240 ns          100
slightly_scrambled/PDQSort2/count:100000        982124 ns       978410 ns          100
slightly_scrambled/QuickSort/count:1000000    35292840 ns     34939068 ns          100
slightly_scrambled/QuickSort2/count:1000000   29451877 ns     28875217 ns          100
slightly_scrambled/IntroSort/count:1000000    25058823 ns     24750291 ns          100
slightly_scrambled/PDQSort/count:1000000      25962367 ns     25535252 ns          100
slightly_scrambled/PDQSort2/count:1000000     12483234 ns     12181630 ns          100
sorted_blocks/QuickSort/count:100                 2430 ns         2405 ns          100
sorted_blocks/QuickSort2/count:100                2499 ns         2478 ns          100
sorted_blocks/IntroSort/count:100                 1061 ns         1019 ns          100
sorted_blocks/PDQSort/count:100                   1329 ns         1285 ns          100
sorted_blocks/PDQSort2/count:100                   720 ns          652 ns          100
sorted_blocks/QuickSort/count:1000               16224 ns        16169 ns          100
sorted_blocks/QuickSort2/count:1000              19509 ns        19454 ns          100
sorted_blocks/IntroSort/count:1000               14560 ns        14515 ns          100
sorted_blocks/PDQSort/count:1000                  9479 ns         9313 ns          100
sorted_blocks/PDQSort2/count:1000                 4913 ns         4885 ns          100
sorted_blocks/QuickSort/count:10000             308032 ns       306791 ns          100
sorted_blocks/QuickSort2/count:10000            238446 ns       238183 ns          100
sorted_blocks/IntroSort/count:10000             173146 ns       172243 ns          100
sorted_blocks/PDQSort/count:10000               168365 ns       166934 ns          100
sorted_blocks/PDQSort2/count:10000               65434 ns        65356 ns          100
sorted_blocks/QuickSort/count:100000           4041913 ns      4028550 ns          100
sorted_blocks/QuickSort2/count:100000          3239075 ns      3226690 ns          100
sorted_blocks/IntroSort/count:100000           2578785 ns      2434971 ns          100
sorted_blocks/PDQSort/count:100000             2386599 ns      2375001 ns          100
sorted_blocks/PDQSort2/count:100000             966824 ns       959131 ns          100
sorted_blocks/QuickSort/count:1000000         51596313 ns     50949966 ns          100
sorted_blocks/QuickSort2/count:1000000        39977951 ns     39455223 ns          100
sorted_blocks/IntroSort/count:1000000         29587960 ns     29072445 ns          100
sorted_blocks/PDQSort/count:1000000           29140836 ns     28926711 ns          100
sorted_blocks/PDQSort2/count:1000000          13950878 ns     13703237 ns          100
single_big_swap/QuickSort/count:100               1290 ns         1277 ns          100
single_big_swap/QuickSort2/count:100              1004 ns         1000 ns          100
single_big_swap/IntroSort/count:100               1087 ns         1069 ns          100
single_big_swap/PDQSort/count:100                  633 ns          620 ns          100
single_big_swap/PDQSort2/count:100                 474 ns          456 ns          100
single_big_swap/QuickSort/count:1000             16889 ns        16794 ns          100
single_big_swap/QuickSort2/count:1000            12697 ns        12655 ns          100
single_big_swap/IntroSort/count:1000             14016 ns        13967 ns          100
single_big_swap/PDQSort/count:1000                7008 ns         6939 ns          100
single_big_swap/PDQSort2/count:1000               2342 ns         2339 ns          100
single_big_swap/QuickSort/count:10000           204246 ns       204182 ns          100
single_big_swap/QuickSort2/count:10000          156179 ns       155306 ns          100
single_big_swap/IntroSort/count:10000           192030 ns       190639 ns          100
single_big_swap/PDQSort/count:10000              78781 ns        78285 ns          100
single_big_swap/PDQSort2/count:10000             23238 ns        23145 ns          100
single_big_swap/QuickSort/count:100000         2414905 ns      2395809 ns          100
single_big_swap/QuickSort2/count:100000        1787565 ns      1778945 ns          100
single_big_swap/IntroSort/count:100000         2523279 ns      2517094 ns          100
single_big_swap/PDQSort/count:100000            889865 ns       884869 ns          100
single_big_swap/PDQSort2/count:100000           249087 ns       246596 ns          100
single_big_swap/QuickSort/count:1000000       29262380 ns     28791769 ns          100
single_big_swap/QuickSort2/count:1000000      21306314 ns     20978264 ns          100
single_big_swap/IntroSort/count:1000000       30104774 ns     29736630 ns          100
single_big_swap/PDQSort/count:1000000         10839585 ns     10689165 ns          100
single_big_swap/PDQSort2/count:1000000         3153072 ns      3134668 ns          100
descending/QuickSort/count:100                    1633 ns         1619 ns          100
descending/QuickSort2/count:100                   1324 ns         1245 ns          100
descending/IntroSort/count:100                     915 ns          904 ns          100
descending/PDQSort/count:100                       534 ns          518 ns          100
descending/PDQSort2/count:100                      305 ns          290 ns          100
descending/QuickSort/count:1000                  15212 ns        15109 ns          100
descending/QuickSort2/count:1000                 12131 ns        12071 ns          100
descending/IntroSort/count:1000                   8520 ns         8483 ns          100
descending/PDQSort/count:1000                     2677 ns         2616 ns          100
descending/PDQSort2/count:1000                    1168 ns         1167 ns          100
descending/QuickSort/count:10000                190983 ns       190004 ns          100
descending/QuickSort2/count:10000               142282 ns       141461 ns          100
descending/IntroSort/count:10000                106956 ns       106801 ns          100
descending/PDQSort/count:10000                   22199 ns        22098 ns          100
descending/PDQSort2/count:10000                   7163 ns         6853 ns          100
descending/QuickSort/count:100000              2210157 ns      2201096 ns          100
descending/QuickSort2/count:100000             1639887 ns      1632072 ns          100
descending/IntroSort/count:100000              1308584 ns      1301543 ns          100
descending/PDQSort/count:100000                 186613 ns       185900 ns          100
descending/PDQSort2/count:100000                 56812 ns        56648 ns          100
descending/QuickSort/count:1000000            27759185 ns     27197419 ns          100
descending/QuickSort2/count:1000000           19937923 ns     19733711 ns          100
descending/IntroSort/count:1000000            15222011 ns     15155862 ns          100
descending/PDQSort/count:1000000               2159517 ns      1899555 ns          100
descending/PDQSort2/count:1000000               560522 ns       557461 ns          100
pipe_organ/QuickSort/count:100                    1853 ns         1835 ns          100
pipe_organ/QuickSort2/count:100                   1439 ns         1416 ns          100
pipe_organ/IntroSort/count:100                    1029 ns          950 ns          100
pipe_organ/PDQSort/count:100                       528 ns          517 ns          100
pipe_organ/PDQSort2/count:100                      296 ns          282 ns          100
pipe_organ/QuickSort/count:1000                  15940 ns        15886 ns          100
pipe_organ/QuickSort2/count:1000                 11960 ns        11911 ns          100
pipe_organ/IntroSort/count:1000                   8271 ns         8225 ns          100
pipe_organ/PDQSort/count:1000                     2622 ns         2591 ns          100
pipe_organ/PDQSort2/count:1000                    1192 ns         1172 ns          100
pipe_organ/QuickSort/count:10000                193559 ns       193175 ns          100
pipe_organ/QuickSort2/count:10000               150531 ns       149370 ns          100
pipe_organ/IntroSort/count:10000                115439 ns       115205 ns          100
pipe_organ/PDQSort/count:10000                   19195 ns        19176 ns          100
pipe_organ/PDQSort2/count:10000                   6117 ns         6021 ns          100
pipe_organ/QuickSort/count:100000              2486991 ns      2478769 ns          100
pipe_organ/QuickSort2/count:100000             1819950 ns      1810639 ns          100
pipe_organ/IntroSort/count:100000              1388682 ns      1383509 ns          100
pipe_organ/PDQSort/count:100000                 190331 ns       188891 ns          100
pipe_organ/PDQSort2/count:100000                 52793 ns        52639 ns          100
pipe_organ/QuickSort/count:1000000            29577606 ns     29326755 ns          100
pipe_organ/QuickSort2/count:1000000           21748586 ns     21414611 ns          100
pipe_organ/IntroSort/count:1000000            16696194 ns     16630029 ns          100
pipe_organ/PDQSort/count:1000000               1869925 ns      1864242 ns          100
pipe_organ/PDQSort2/count:1000000               549429 ns       545797 ns          100
push_front/QuickSort/count:100                    2289 ns         2269 ns          100
push_front/QuickSort2/count:100                   1478 ns         1491 ns          100
push_front/IntroSort/count:100                    1605 ns         1561 ns          100
push_front/PDQSort/count:100                      1282 ns         1240 ns          100
push_front/PDQSort2/count:100                      543 ns          523 ns          100
push_front/QuickSort/count:1000                  18117 ns        18055 ns          100
push_front/QuickSort2/count:1000                 15428 ns        15155 ns          100
push_front/IntroSort/count:1000                  14087 ns        13988 ns          100
push_front/PDQSort/count:1000                    12455 ns        12404 ns          100
push_front/PDQSort2/count:1000                    4450 ns         4413 ns          100
push_front/QuickSort/count:10000                229186 ns       227644 ns          100
push_front/QuickSort2/count:10000               160690 ns       160380 ns          100
push_front/IntroSort/count:10000                191233 ns       190610 ns          100
push_front/PDQSort/count:10000                  145472 ns       144255 ns          100
push_front/PDQSort2/count:10000                  41785 ns        41612 ns          100
push_front/QuickSort/count:100000              2922293 ns      2702687 ns          100
push_front/QuickSort2/count:100000             1923425 ns      1917358 ns          100
push_front/IntroSort/count:100000              2488440 ns      2478518 ns          100
push_front/PDQSort/count:100000                1688943 ns      1681909 ns          100
push_front/PDQSort2/count:100000                466741 ns       465112 ns          100
push_front/QuickSort/count:1000000            31411786 ns     31044262 ns          100
push_front/QuickSort2/count:1000000           22438347 ns     22338651 ns          100
push_front/IntroSort/count:1000000            30187199 ns     29784770 ns          100
push_front/PDQSort/count:1000000              19681892 ns     19340073 ns          100
push_front/PDQSort2/count:1000000              5359031 ns      5330950 ns          100
push_middle/QuickSort/count:100                   1986 ns         1972 ns          100
push_middle/QuickSort2/count:100                  1523 ns         1475 ns          100
push_middle/IntroSort/count:100                   1198 ns         1155 ns          100
push_middle/PDQSort/count:100                      982 ns          965 ns          100
push_middle/PDQSort2/count:100                     437 ns          419 ns          100
push_middle/QuickSort/count:1000                 16948 ns        16891 ns          100
push_middle/QuickSort2/count:1000                12581 ns        12432 ns          100
push_middle/IntroSort/count:1000                 10488 ns        10440 ns          100
push_middle/PDQSort/count:1000                    4969 ns         4929 ns          100
push_middle/PDQSort2/count:1000                   2006 ns         1953 ns          100
push_middle/QuickSort/count:10000               206586 ns       206205 ns          100
push_middle/QuickSort2/count:10000              147860 ns       147583 ns          100
push_middle/IntroSort/count:10000               143688 ns       143232 ns          100
push_middle/PDQSort/count:10000                  44343 ns        44226 ns          100
push_middle/PDQSort2/count:10000                 14500 ns        14441 ns          100
push_middle/QuickSort/count:100000             2641267 ns      2493017 ns          100
push_middle/QuickSort2/count:100000            1782662 ns      1775961 ns          100
push_middle/IntroSort/count:100000             1867750 ns      1861113 ns          100
push_middle/PDQSort/count:100000                426423 ns       423756 ns          100
push_middle/PDQSort2/count:100000               121412 ns       120541 ns          100
push_middle/QuickSort/count:1000000           29463664 ns     29094682 ns          100
push_middle/QuickSort2/count:1000000          21699498 ns     21338872 ns          100
push_middle/IntroSort/count:1000000           22344304 ns     21994267 ns          100
push_middle/PDQSort/count:1000000              4514580 ns      4247772 ns          100
push_middle/PDQSort2/count:1000000             1244558 ns      1236921 ns          100

Edited September 13 by Stefan Glienke

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