pointer-chasing

Utilities to measure read access times of caches, memory, and hardware prefetches for simple and fused operations

Summary

This package provides the following three utilities:

random-chase: measure average read access times of all cache levels and main memory
linear-chase: measure read access times for a linear access pattern with a constant stride
fused-linear-chase: like linear-chase but for an interleaved access pattern of multiple linear sequences, all with the same stride

All of them work with memory buffers that are organized as an array of pointers where

all pointers point into the very same buffer, and where
beginning from any pointer all other pointers can be reached following the pointer chain, and where
all locations are reached.

Once such a memory buffer has been set up, we measure the time of

void** p = (void**) memory[0];
while (count-- > 0) {
   p = (void**) *p;
}

The p = (void**) *p construct enforces all memory accesses to be serialized, i.e. the next access can only be scheduled by the processor when the previous fetch has been finished. To defeat optimizers who tend to optimize the loop away when the result isn't used, the last pointer value is assigned to a volatile global variable which is otherwise unused.

In case of fused-linear-chase multiple such buffers are configured in dependence of the fuse factor.

For the sake of simplicity, all utilities are parameterized through preprocessor macros.

The idea of pointer chasing is not new, in fact there exist quite a number of papers and other utilities related to it.

random-chase

Following preprocessor macros allow to configure this utility:

MIN_SIZE: Minimal buffer size in bytes which should be small enough to fit comfortably into the L1 cache.
MAX_SIZE: Maximal buffer size in bytes which should be larger than the L3 cache.
GRANULARITY: All powers of two between MIN_SIZE and MAX_SIZE are tested. The granularity specifies how many sizes are tested in-between. For a granularity of n > 0 we get 2^{n-1} sizes in-between.

The output consists of a header line and then a line for each tested buffer size from MIN_SIZE to MAX_SIZE where the memory size and the measured access time in nanoseconds is given.

This is the sample output for an Intel Xeon 5650 with three caches (L1: 32 KiB, L2: 256 KiB, L3: 12 MiB) with default parameters, i.e. MIN_SIZE = 1024, MAX_SIZE = 32 MiB, and GRANULARITY = 1:

  memsize  time in ns
     1024     1.36904
     1536     1.35973
     2048     1.36904
     3072     1.35973
     4096     1.35973
     6144     1.36904
     8192     1.35973
    12288     1.35973
    16384     1.35973
    24576     1.37836
    32768     1.36904
    49152     2.06754
    65536     2.43075
    98304     2.79397
   131072     2.97092
   196608     3.14787
   262144     3.29688
   393216     8.37259
   524288    10.85922
   786432    13.20615
  1048576    14.38893
  1572864    15.59965
  2097152    16.23295
  3145728    18.08628
  4194304    18.34705
  6291456    19.79060
  8388608    22.66839
 12582912    31.55321
 16777216    43.27856
 25165824    59.39975
 33554432    64.04705

A gnuplot script may be helpful to visualize this:

set terminal png size 900, 500
set output "random-chase.png"
set xlabel "memory area in bytes"
set logscale x
set ylabel "avg access time in ns"
set title "Access times in dependence of memory area"
set key out
set pointsize 0.5

# determine maximal y value by plotting to a dummy terminal
set terminal push
set terminal unknown
plot "random-chase.out" using 2
set terminal pop

# mark L1, L2, and L3:
maxy = GPVAL_Y_MAX
l1 = 32
l2 = 256
l3 = 12288
set arrow from l1*1024,0 to l1*1024,maxy nohead lc rgb 'blue';
set arrow from l2*1024,0 to l2*1024,maxy nohead lc rgb 'blue';
set arrow from l3*1024,0 to l3*1024,maxy nohead lc rgb 'blue';

plot "random-chase.out" using 1:2 with linespoints lt 2 title "Intel Xeon 5650"

Result:

linear-chase

Following preprocessor macros configure this utility:

MIN_STRIDE: Minimal stride value. By default, sizeof(void*) is taken.
MAX_STRIDE: Maximal stride value.

The output consists of a header line and then a line for each tested stride value from MIN_STRIDE to MAX_STRIDE in steps of sizeof(void*) and the measured acess time in nanoseconds.

This is a sample output for the same Intel Xeon 5650 compiled for an 32-bit address space, i.e. sizeof(void*) == 4 which has been shortened for brevity:

   stride  time in ns
        4     1.30385
        8     1.31316
       12     1.31316
       ...
     1188    13.57868
     1192    13.10371
     1196    13.52280
     1200    13.58800

A gnuplot script may be helpful as before:

set terminal png size 900, 500
set output "linear-chase.png"
set xlabel "stride in bytes"
set ylabel "avg access time in ns"
set title "Access times in dependence of stride"
set key out
set pointsize 0.5

plot "linear-chase.out" using 1:2 with linespoints lt 2 title "Intel Xeon 5650"

Result:

fused-linear-chase

Like linear-chase, the macro parameters MIN_STRIDE and MAX_STRIDE are supported. The range of tested fuse factors extends from 1 to 8. This test allows to analyze how many interleaved access patterns with a constant stride are supported by the hardware prefetch.

The output is a table with a column for each fuse factor from 1 to 8 and a line for each stride value tested between MIN_STRIDE and MAX_STRIDE. For each combination the aggregated data access speed in GiB/s is given. There are three header lines.

This is a sample output for the very same Intel Xeon 5650 as above:

                                          data access speeds in GiB/s
     fuse           1           2           3           4           5           6           7           8
    stride
        4     2.81690     5.71429     7.50000    10.06289    10.63830     9.26641     6.42202     6.47773
        8     2.83688     5.63380     7.27273     9.03955     9.85222     8.79121     6.23608     5.98131
       12     2.85714     5.55556     6.81818     8.24742     9.30233     7.97342     5.85774     5.89319
       16     2.83688     5.55556     6.31579     7.51174     5.79710     5.56845     4.00000     3.65714
       20     2.39521     4.73373     5.74163     4.73373     4.90196     5.02092     4.95575     4.87062
       24     2.07254     4.04040     3.77358     3.85542     4.21941     4.30108     4.20420     4.18301
       28     1.90476     3.75587     3.32410     3.48584     3.68324     3.75000     3.66492     3.76471
       32     1.63934     3.38983     2.94118     3.07102     3.18979     3.23015     3.05344     2.96571
       36     1.54440     2.36686     2.63158     2.76339     2.86123     3.00375     2.96610     2.99345
       40     1.45985     2.14477     2.38569     2.50784     2.67023     2.72109     2.73171     2.74914
       44     1.40351     1.95122     2.17786     2.29555     2.43902     2.49480     2.44541     2.51572
       48     1.33333     1.80180     1.99336     2.11640     2.17155     2.18182     2.14559     2.14909
       52     1.25786     1.69851     1.85759     1.96802     2.08551     2.13144     2.13090     2.16802
       56     1.20482     1.59681     1.72166     1.83276     1.94553     1.97694     1.98020     2.00501
       60     1.15274     1.49533     1.61725     1.72043     1.82482     1.86335     1.84941     1.89798
       64     1.08992     1.40351     1.51324     1.60804     1.64339     1.63154     1.63075     1.65889
       68     1.00503     1.37694     1.47059     1.58730     1.68209     1.75439     1.76879     1.79574
       72     0.93240     1.33556     1.42518     1.55039     1.62866     1.68658     1.68980     1.71306
       76     0.90909     1.29450     1.38090     1.49953     1.58479     1.64948     1.67164     1.69223
       80     0.89888     1.26582     1.35135     1.47738     1.50038     1.49254     1.47446     1.48285
       84     0.88300     1.23267     1.32013     1.47194     1.56617     1.67131     1.68370     1.70758
       88     0.87912     1.21581     1.30293     1.46119     1.49477     1.59893     1.59817     1.62025
       92     0.85106     1.17820     1.26449     1.40105     1.48038     1.59151     1.59091     1.63016
       96     0.83333     1.13636     1.24224     1.43498     1.43885     1.41260     1.39651     1.44993
      100     0.82816     1.11888     1.20846     1.36519     1.46520     1.57274     1.56863     1.60966
      104     0.79051     1.06809     1.16959     1.38289     1.54440     1.62712     1.61570     1.62850
      108     0.74906     1.04439     1.13422     1.35021     1.47384     1.55440     1.56337     1.64271
      112     0.74488     1.03896     1.11008     1.31796     1.29955     1.25720     1.24611     1.31201
      116     0.68376     1.02828     1.07431     1.34567     1.47820     1.55039     1.55729     1.63850
      120     0.66116     1.02960     1.08794     1.41970     1.47601     1.55039     1.54525     1.56479

This can be visualized using a gnuplot script:

set terminal png size 1500, 900
set output "fused-linear-chase.png"
set xlabel "stride in bytes"
set ylabel "data access speed in GiB/s"
set title "Data access speeds in dependence of stride and fuse (on Intel Xeon 5650)"
set pointsize 0.5
plot \
   "fused-linear-chase.out" every ::3::32 using 1:2 title "fuse 1" with linespoints lt 2, \
   "fused-linear-chase.out" every ::3::32 using 1:3 title "fuse 2" with linespoints lt 3, \
   "fused-linear-chase.out" every ::3::32 using 1:4 title "fuse 3" with linespoints lt 4, \
   "fused-linear-chase.out" every ::3::32 using 1:5 title "fuse 4" with linespoints lt 5, \
   "fused-linear-chase.out" every ::3::32 using 1:6 title "fuse 5" with linespoints lt 1, \
   "fused-linear-chase.out" every ::3::32 using 1:7 title "fuse 6" with linespoints lt 7, \
   "fused-linear-chase.out" every ::3::32 using 1:8 title "fuse 7" with linespoints lt 8, \
   "fused-linear-chase.out" every ::3::32 using 1:9 title "fuse 8" with linespoints lt 9

Result:

Downloading and testing

If you want to clone this project, you should do this recursively:

git clone --recursive https://github.com/afborchert/pointer-chasing.git

To build it, just invoke make. You need g++ supporting C++11 and GNU make for this to work.

License

afborchert/pointer-chasing

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