Closed jywangx closed 1 year ago
Should we clean our git log and open a pull request?😀
@jywangx Congratulations on winning the competition!! Thanks for your efforts! We have reduce-scatter(sharp_coll_do_reduce_scatter_nb) feature implications in lisharp in the upcoming October HPCX release. we will use this API directly in UCC
@jywangx Congratulations on winning the competition!! Thanks for your efforts! We have reduce-scatter(sharp_coll_do_reduce_scatter_nb) feature implications in lisharp in the upcoming October HPCX release. we will use this API directly in UCC
Hi bureddy, thanks for your congratulations. We are excited to see the reduce-scatter (sharp_coll_do_reduce_scatter_nb) feature being implemented in the upcoming HPCX release. If there's anything we can do to help, we're more than willing to contribute our efforts to further enhance SHARP and UCC.
Best regrads.
Hello, in this branch we implement reduce-scatter by SHARP APIs and we would like to inquire wether our modifications are acceptable.
We are three winner teams in the 11th RDMA Competition held by HPC-AI Advisory Council. We have further improved and organized the code developed by our three teams during the competition and conducted testing. Our SHARP-based implementation exhibits excellent communication performance compared to UCP's reduce-scatter.
We are very willing to make contributions to the UCC repository, but we lack experience in participating in open-source communities. Please do not hesitate to contact us if our code or Git records need improvement.
Implementation
We implement a
sharp_coll_do_allreduce_nb
based reduce-scatter and asharp_coll_do_reduce_nb
based one. Since thesharp_coll_do_reduce_nb
API of the SHARP can only support messages with size >= 16K by default (this threshold can be configured). Thus, when the message size is small (total array size / number of nodes < 16K), the scatter-reduce is done based on thesharp_coll_do_allreduce_nb
API of SHARP, when the message size is large (total array size / number of nodes >= 16K), the scatter-reduce is done based on thesharp_coll_do_reduce_nb
API.Allreduce-Wrapped Reduce-Scatter
In the allreduce-wrapped reduce-scatter, we perform an allreduce operation on the send buffer for reduce-scatter, after which each process retrieves its data and places it into the receive buffer. If the IN_PLACE flag is not set, we need to allocate a temporary buffer to store the result of the allreduce operation.
N-Reduce Reduce-Scatter
In the n-reduce reduce-scatter, we conduct n (the size of the UCC group) parallel reductions on the send buffer. During the reduction of the ith data, processer i serves as the root of this particular reduction.
Evaluation
We conducted an evaluation of our reduce-scatter operation using the ucc_perftest benchmark on the Thor Cluster, which is provided by the HPC-AI Advisory Council. The hardware configuration of the Thor cluster is as follows:
We utilized 16 nodes of the cluster and did not employ any BlueField DPU nodes. As demonstrated by the experimental results below, using Sharp significantly improves the performance of the reduce-scatter operation in all tested cases, compared to the current TL/UCP components.
In the following figures:
We observed that the
sharp_coll_do_reduce
function is worked only for streaming-aggregation tree when the message size is greater than or equal to 256B. Therefore, the n-reduce reduce-scatter is used on these message sizes.4 nodes:
![gnode4](https://redblog.oss-cn-chengdu.aliyuncs.com/picgo/gnode4.png)8 nodes:
![gnode8](https://redblog.oss-cn-chengdu.aliyuncs.com/picgo/gnode8.png)16 nodes:
![gnode16](https://redblog.oss-cn-chengdu.aliyuncs.com/picgo/gnode16.png)Test python script:
```python import subprocess import sys import nums_from_string as ns import pandas as pd if len(sys.argv) < 2 : sys.stderr.write("Usage: python "+sys.argv[0]+"Raw data:
| count | msg_size | avg | min | maximum | nnode | ppn | cl | sharp | | -------- | -------- | -------- | -------- | -------- | ----- | ---- | ----- | -------- | | 1 | 4 | 6.19 | 6.12 | 6.26 | 4 | 1 | basic | no-sharp | | 2 | 8 | 7.44 | 7.37 | 7.48 | 4 | 1 | basic | no-sharp | | 4 | 16 | 7.43 | 7.35 | 7.48 | 4 | 1 | basic | no-sharp | | 8 | 32 | 7.46 | 7.43 | 7.5 | 4 | 1 | basic | no-sharp | | 16 | 64 | 7.86 | 7.84 | 7.9 | 4 | 1 | basic | no-sharp | | 32 | 128 | 8.3 | 8.26 | 8.35 | 4 | 1 | basic | no-sharp | | 64 | 256 | 10.51 | 10.49 | 10.56 | 4 | 1 | basic | no-sharp | | 128 | 512 | 11.11 | 11.06 | 11.2 | 4 | 1 | basic | no-sharp | | 256 | 1024 | 11.35 | 11.3 | 11.39 | 4 | 1 | basic | no-sharp | | 512 | 2048 | 12.33 | 12.3 | 12.36 | 4 | 1 | basic | no-sharp | | 1024 | 4096 | 14.1 | 14.05 | 14.14 | 4 | 1 | basic | no-sharp | | 2048 | 8192 | 18.95 | 18.9 | 19.02 | 4 | 1 | basic | no-sharp | | 4096 | 16384 | 25.43 | 25.3 | 25.59 | 4 | 1 | basic | no-sharp | | 8192 | 32768 | 38.85 | 38.74 | 39.09 | 4 | 1 | basic | no-sharp | | 16384 | 65536 | 66.03 | 65.17 | 66.81 | 4 | 1 | basic | no-sharp | | 32768 | 131072 | 114.58 | 114.23 | 115.2 | 4 | 1 | basic | no-sharp | | 65536 | 262144 | 208.13 | 207.31 | 208.63 | 4 | 1 | basic | no-sharp | | 131072 | 524288 | 404.05 | 401.44 | 406.25 | 4 | 1 | basic | no-sharp | | 262144 | 1048576 | 776.91 | 771.95 | 780.08 | 4 | 1 | basic | no-sharp | | 524288 | 2097152 | 1531.19 | 1511.4 | 1553.23 | 4 | 1 | basic | no-sharp | | 1048576 | 4194304 | 3055.65 | 3037.47 | 3083.75 | 4 | 1 | basic | no-sharp | | 2097152 | 8388608 | 8276.69 | 8244.52 | 8294.44 | 4 | 1 | basic | no-sharp | | 4194304 | 16777216 | 26968.41 | 26677.17 | 27346.57 | 4 | 1 | basic | no-sharp | | 8388608 | 33554432 | 53883.55 | 53193.68 | 54437.43 | 4 | 1 | basic | no-sharp | | 16777216 | 67108864 | 107077.3 | 106020.6 | 108183.4 | 4 | 1 | basic | no-sharp | | 1 | 4 | 2.7 | 2.68 | 2.73 | 4 | 1 | basic | llt-arw | | 2 | 8 | 2.74 | 2.73 | 2.75 | 4 | 1 | basic | llt-arw | | 4 | 16 | 2.76 | 2.75 | 2.78 | 4 | 1 | basic | llt-arw | | 8 | 32 | 2.87 | 2.86 | 2.88 | 4 | 1 | basic | llt-arw | | 16 | 64 | 3.42 | 3.38 | 3.48 | 4 | 1 | basic | llt-arw | | 32 | 128 | 3.86 | 3.84 | 3.9 | 4 | 1 | basic | llt-arw | | 64 | 256 | 4.18 | 4.16 | 4.21 | 4 | 1 | basic | llt-arw | | 128 | 512 | 5.02 | 5 | 5.04 | 4 | 1 | basic | llt-arw | | 256 | 1024 | 6.09 | 6.06 | 6.13 | 4 | 1 | basic | llt-arw | | 512 | 2048 | 8.03 | 7.97 | 8.06 | 4 | 1 | basic | llt-arw | | 1024 | 4096 | 15.55 | 15.53 | 15.56 | 4 | 1 | basic | llt-arw | | 2048 | 8192 | 29.19 | 29.17 | 29.2 | 4 | 1 | basic | llt-arw | | 4096 | 16384 | 56.37 | 56.33 | 56.39 | 4 | 1 | basic | llt-arw | | 8192 | 32768 | 109.17 | 108.96 | 109.39 | 4 | 1 | basic | llt-arw | | 16384 | 65536 | 214.74 | 213.79 | 215.12 | 4 | 1 | basic | llt-arw | | 32768 | 131072 | 425.95 | 424.76 | 426.51 | 4 | 1 | basic | llt-arw | | 65536 | 262144 | 850.26 | 850.13 | 850.43 | 4 | 1 | basic | llt-arw | | 131072 | 524288 | 1686.25 | 1686.13 | 1686.34 | 4 | 1 | basic | llt-arw | | 262144 | 1048576 | 3368.88 | 3368.66 | 3369.07 | 4 | 1 | basic | llt-arw | | 524288 | 2097152 | 6721.53 | 6721.09 | 6721.74 | 4 | 1 | basic | llt-arw | | 1048576 | 4194304 | 13473.55 | 13473 | 13474.7 | 4 | 1 | basic | llt-arw | | 2097152 | 8388608 | 29787.6 | 29785.33 | 29789.51 | 4 | 1 | basic | llt-arw | | 4194304 | 16777216 | 69329.36 | 69019.25 | 69635 | 4 | 1 | basic | llt-arw | | 8388608 | 33554432 | 144770.5 | 143827.5 | 145128 | 4 | 1 | basic | llt-arw | | 16777216 | 67108864 | 291667.9 | 291595.6 | 291788.5 | 4 | 1 | basic | llt-arw | | 1 | 4 | 2.69 | 2.67 | 2.71 | 4 | 1 | basic | sat-nr | | 2 | 8 | 2.74 | 2.72 | 2.76 | 4 | 1 | basic | sat-nr | | 4 | 16 | 2.74 | 2.73 | 2.75 | 4 | 1 | basic | sat-nr | | 8 | 32 | 2.86 | 2.82 | 2.88 | 4 | 1 | basic | sat-nr | | 16 | 64 | 5.17 | 5.16 | 5.22 | 4 | 1 | basic | sat-nr | | 32 | 128 | 5.23 | 5.2 | 5.24 | 4 | 1 | basic | sat-nr | | 64 | 256 | 5.88 | 5.14 | 6.55 | 4 | 1 | basic | sat-nr | | 128 | 512 | 6.02 | 5.28 | 6.7 | 4 | 1 | basic | sat-nr | | 256 | 1024 | 6.13 | 5.49 | 6.43 | 4 | 1 | basic | sat-nr | | 512 | 2048 | 6.81 | 5.97 | 7.18 | 4 | 1 | basic | sat-nr | | 1024 | 4096 | 7.18 | 6.05 | 7.79 | 4 | 1 | basic | sat-nr | | 2048 | 8192 | 8.17 | 7.18 | 9.14 | 4 | 1 | basic | sat-nr | | 4096 | 16384 | 10.46 | 9.81 | 11.69 | 4 | 1 | basic | sat-nr | | 8192 | 32768 | 15.88 | 15.12 | 17.21 | 4 | 1 | basic | sat-nr | | 16384 | 65536 | 27.53 | 26.84 | 29.18 | 4 | 1 | basic | sat-nr | | 32768 | 131072 | 51.06 | 50.34 | 52.43 | 4 | 1 | basic | sat-nr | | 65536 | 262144 | 97.85 | 97.13 | 99.52 | 4 | 1 | basic | sat-nr | | 131072 | 524288 | 220.13 | 219.58 | 221.6 | 4 | 1 | basic | sat-nr | | 262144 | 1048576 | 438.77 | 438.14 | 440.52 | 4 | 1 | basic | sat-nr | | 524288 | 2097152 | 882.82 | 882.07 | 884.84 | 4 | 1 | basic | sat-nr | | 1048576 | 4194304 | 1787.73 | 1786.91 | 1789.97 | 4 | 1 | basic | sat-nr | | 2097152 | 8388608 | 3652.78 | 3651.66 | 3655.79 | 4 | 1 | basic | sat-nr | | 4194304 | 16777216 | 7468.75 | 7467.69 | 7471.2 | 4 | 1 | basic | sat-nr | | 8388608 | 33554432 | 15137.65 | 15136.63 | 15140 | 4 | 1 | basic | sat-nr | | 16777216 | 67108864 | 30557.61 | 30556.8 | 30559.8 | 4 | 1 | basic | sat-nr | | 1 | 4 | 2.71 | 2.68 | 2.74 | 4 | 1 | basic | sat-arw | | 2 | 8 | 2.73 | 2.71 | 2.75 | 4 | 1 | basic | sat-arw | | 4 | 16 | 2.75 | 2.73 | 2.77 | 4 | 1 | basic | sat-arw | | 8 | 32 | 2.86 | 2.85 | 2.87 | 4 | 1 | basic | sat-arw | | 16 | 64 | 3.45 | 3.39 | 3.5 | 4 | 1 | basic | sat-arw | | 32 | 128 | 3.86 | 3.83 | 3.9 | 4 | 1 | basic | sat-arw | | 64 | 256 | 4.22 | 4.2 | 4.25 | 4 | 1 | basic | sat-arw | | 128 | 512 | 5 | 4.97 | 5.03 | 4 | 1 | basic | sat-arw | | 256 | 1024 | 6.09 | 6.08 | 6.11 | 4 | 1 | basic | sat-arw | | 512 | 2048 | 8.02 | 7.99 | 8.06 | 4 | 1 | basic | sat-arw | | 1024 | 4096 | 7.66 | 7.65 | 7.68 | 4 | 1 | basic | sat-arw | | 2048 | 8192 | 9.28 | 9.27 | 9.31 | 4 | 1 | basic | sat-arw | | 4096 | 16384 | 14.03 | 14.02 | 14.05 | 4 | 1 | basic | sat-arw | | 8192 | 32768 | 21.15 | 21.06 | 21.23 | 4 | 1 | basic | sat-arw | | 16384 | 65536 | 37.22 | 37.06 | 37.35 | 4 | 1 | basic | sat-arw | | 32768 | 131072 | 69.88 | 69.79 | 69.98 | 4 | 1 | basic | sat-arw | | 65536 | 262144 | 136.56 | 136.47 | 136.69 | 4 | 1 | basic | sat-arw | | 131072 | 524288 | 299.29 | 298.88 | 299.7 | 4 | 1 | basic | sat-arw | | 262144 | 1048576 | 571.52 | 570 | 573.22 | 4 | 1 | basic | sat-arw | | 524288 | 2097152 | 1155.31 | 1144.31 | 1166.91 | 4 | 1 | basic | sat-arw | | 1048576 | 4194304 | 2356.19 | 2332.09 | 2368.01 | 4 | 1 | basic | sat-arw | | 2097152 | 8388608 | 11591.81 | 11568.47 | 11607.25 | 4 | 1 | basic | sat-arw | | 4194304 | 16777216 | 25487.22 | 25450.08 | 25510.96 | 4 | 1 | basic | sat-arw | | 8388608 | 33554432 | 50639.96 | 50629.19 | 50655.21 | 4 | 1 | basic | sat-arw | | 16777216 | 67108864 | 101170.4 | 101140 | 101197 | 4 | 1 | basic | sat-arw | | 1 | 4 | 13.43 | 13.32 | 13.6 | 8 | 1 | basic | no-sharp | | 2 | 8 | 17.3 | 17.15 | 17.48 | 8 | 1 | basic | no-sharp | | 4 | 16 | 17.27 | 17.13 | 17.36 | 8 | 1 | basic | no-sharp | | 8 | 32 | 17.2 | 17.08 | 17.32 | 8 | 1 | basic | no-sharp | | 16 | 64 | 18.28 | 18.2 | 18.34 | 8 | 1 | basic | no-sharp | | 32 | 128 | 19.13 | 19.02 | 19.24 | 8 | 1 | basic | no-sharp | | 64 | 256 | 23.58 | 23.38 | 23.73 | 8 | 1 | basic | no-sharp | | 128 | 512 | 24.71 | 24.57 | 24.83 | 8 | 1 | basic | no-sharp | | 256 | 1024 | 25.45 | 25.38 | 25.54 | 8 | 1 | basic | no-sharp | | 512 | 2048 | 27.6 | 27.47 | 27.77 | 8 | 1 | basic | no-sharp | | 1024 | 4096 | 31.72 | 31.58 | 31.91 | 8 | 1 | basic | no-sharp | | 2048 | 8192 | 42.33 | 42.1 | 42.55 | 8 | 1 | basic | no-sharp | | 4096 | 16384 | 57.1 | 56.93 | 57.29 | 8 | 1 | basic | no-sharp | | 8192 | 32768 | 88.38 | 87.95 | 88.97 | 8 | 1 | basic | no-sharp | | 16384 | 65536 | 153.79 | 153.04 | 154.57 | 8 | 1 | basic | no-sharp | | 32768 | 131072 | 265.07 | 264.42 | 265.71 | 8 | 1 | basic | no-sharp | | 65536 | 262144 | 500.05 | 497.11 | 504.41 | 8 | 1 | basic | no-sharp | | 131072 | 524288 | 921.76 | 917.62 | 924.64 | 8 | 1 | basic | no-sharp | | 262144 | 1048576 | 1803.02 | 1794.68 | 1810.59 | 8 | 1 | basic | no-sharp | | 524288 | 2097152 | 3532.39 | 3521.74 | 3545.42 | 8 | 1 | basic | no-sharp | | 1048576 | 4194304 | 8078.49 | 8021.24 | 8150.99 | 8 | 1 | basic | no-sharp | | 2097152 | 8388608 | 19526.98 | 19458.55 | 19597.24 | 8 | 1 | basic | no-sharp | | 4194304 | 16777216 | 52539.24 | 52182.83 | 52916.2 | 8 | 1 | basic | no-sharp | | 8388608 | 33554432 | 106060.2 | 105554.3 | 106625.8 | 8 | 1 | basic | no-sharp | | 16777216 | 67108864 | 211120.6 | 209923.6 | 212278.3 | 8 | 1 | basic | no-sharp | | 1 | 4 | 2.84 | 2.77 | 2.88 | 8 | 1 | basic | llt-arw | | 2 | 8 | 2.84 | 2.82 | 2.89 | 8 | 1 | basic | llt-arw | | 4 | 16 | 2.94 | 2.93 | 2.98 | 8 | 1 | basic | llt-arw | | 8 | 32 | 3.58 | 3.52 | 3.62 | 8 | 1 | basic | llt-arw | | 16 | 64 | 4.04 | 3.98 | 4.1 | 8 | 1 | basic | llt-arw | | 32 | 128 | 4.59 | 4.48 | 4.69 | 8 | 1 | basic | llt-arw | | 64 | 256 | 5.39 | 5.3 | 5.46 | 8 | 1 | basic | llt-arw | | 128 | 512 | 6.86 | 6.72 | 6.96 | 8 | 1 | basic | llt-arw | | 256 | 1024 | 9.26 | 9.1 | 9.37 | 8 | 1 | basic | llt-arw | | 512 | 2048 | 16.76 | 16.65 | 16.86 | 8 | 1 | basic | llt-arw | | 1024 | 4096 | 30.31 | 30.22 | 30.42 | 8 | 1 | basic | llt-arw | | 2048 | 8192 | 57.95 | 57.83 | 58.05 | 8 | 1 | basic | llt-arw | | 4096 | 16384 | 112.52 | 112.41 | 112.74 | 8 | 1 | basic | llt-arw | | 8192 | 32768 | 222.68 | 221.76 | 223.04 | 8 | 1 | basic | llt-arw | | 16384 | 65536 | 446.37 | 445.19 | 446.79 | 8 | 1 | basic | llt-arw | | 32768 | 131072 | 869.17 | 868.01 | 869.42 | 8 | 1 | basic | llt-arw | | 65536 | 262144 | 1737.31 | 1737.15 | 1737.46 | 8 | 1 | basic | llt-arw | | 131072 | 524288 | 3459.48 | 3459.25 | 3459.61 | 8 | 1 | basic | llt-arw | | 262144 | 1048576 | 6893.13 | 6892.53 | 6893.43 | 8 | 1 | basic | llt-arw | | 524288 | 2097152 | 13778.56 | 13777.59 | 13778.99 | 8 | 1 | basic | llt-arw | | 1048576 | 4194304 | 30467.59 | 30464.71 | 30468.94 | 8 | 1 | basic | llt-arw | | 2097152 | 8388608 | 69980.45 | 69815.62 | 70170.11 | 8 | 1 | basic | llt-arw | | 4194304 | 16777216 | 146219.4 | 145721.4 | 146409.1 | 8 | 1 | basic | llt-arw | | 8388608 | 33554432 | 297550.2 | 296459.5 | 297781.8 | 8 | 1 | basic | llt-arw | | 16777216 | 67108864 | 598079.1 | 597995.3 | 598157.5 | 8 | 1 | basic | llt-arw | | 1 | 4 | 2.82 | 2.8 | 2.84 | 8 | 1 | basic | sat-nr | | 2 | 8 | 2.83 | 2.81 | 2.87 | 8 | 1 | basic | sat-nr | | 4 | 16 | 2.93 | 2.9 | 2.96 | 8 | 1 | basic | sat-nr | | 8 | 32 | 5.3 | 5.25 | 5.35 | 8 | 1 | basic | sat-nr | | 16 | 64 | 5.47 | 5.42 | 5.52 | 8 | 1 | basic | sat-nr | | 32 | 128 | 5.64 | 5.54 | 5.68 | 8 | 1 | basic | sat-nr | | 64 | 256 | 6.94 | 5.98 | 7.91 | 8 | 1 | basic | sat-nr | | 128 | 512 | 7.01 | 6.01 | 7.99 | 8 | 1 | basic | sat-nr | | 256 | 1024 | 7.26 | 6.36 | 8.47 | 8 | 1 | basic | sat-nr | | 512 | 2048 | 7.88 | 6.66 | 8.85 | 8 | 1 | basic | sat-nr | | 1024 | 4096 | 8.78 | 7.63 | 10.11 | 8 | 1 | basic | sat-nr | | 2048 | 8192 | 10.93 | 10.01 | 12.76 | 8 | 1 | basic | sat-nr | | 4096 | 16384 | 16.5 | 15.83 | 18.62 | 8 | 1 | basic | sat-nr | | 8192 | 32768 | 27.54 | 26.99 | 29.39 | 8 | 1 | basic | sat-nr | | 16384 | 65536 | 50.75 | 50.16 | 52.9 | 8 | 1 | basic | sat-nr | | 32768 | 131072 | 97.8 | 97.25 | 99.69 | 8 | 1 | basic | sat-nr | | 65536 | 262144 | 220.3 | 219.77 | 221.9 | 8 | 1 | basic | sat-nr | | 131072 | 524288 | 436.89 | 436.31 | 438.75 | 8 | 1 | basic | sat-nr | | 262144 | 1048576 | 874.98 | 873.88 | 878.62 | 8 | 1 | basic | sat-nr | | 524288 | 2097152 | 1765.57 | 1765.04 | 1767.97 | 8 | 1 | basic | sat-nr | | 1048576 | 4194304 | 3613.11 | 3612.26 | 3615.26 | 8 | 1 | basic | sat-nr | | 2097152 | 8388608 | 7470 | 7469.32 | 7472.62 | 8 | 1 | basic | sat-nr | | 4194304 | 16777216 | 15264.72 | 15264.07 | 15267.5 | 8 | 1 | basic | sat-nr | | 8388608 | 33554432 | 30652.23 | 30651.58 | 30654.92 | 8 | 1 | basic | sat-nr | | 16777216 | 67108864 | 61581.56 | 61581 | 61584.29 | 8 | 1 | basic | sat-nr | | 1 | 4 | 2.81 | 2.79 | 2.83 | 8 | 1 | basic | sat-arw | | 2 | 8 | 2.78 | 2.76 | 2.8 | 8 | 1 | basic | sat-arw | | 4 | 16 | 2.93 | 2.91 | 2.97 | 8 | 1 | basic | sat-arw | | 8 | 32 | 3.6 | 3.54 | 3.63 | 8 | 1 | basic | sat-arw | | 16 | 64 | 4.02 | 3.99 | 4.07 | 8 | 1 | basic | sat-arw | | 32 | 128 | 4.6 | 4.48 | 4.7 | 8 | 1 | basic | sat-arw | | 64 | 256 | 5.37 | 5.26 | 5.49 | 8 | 1 | basic | sat-arw | | 128 | 512 | 6.8 | 6.64 | 6.93 | 8 | 1 | basic | sat-arw | | 256 | 1024 | 9.25 | 9.12 | 9.35 | 8 | 1 | basic | sat-arw | | 512 | 2048 | 7.53 | 7.47 | 7.57 | 8 | 1 | basic | sat-arw | | 1024 | 4096 | 8.85 | 8.8 | 8.93 | 8 | 1 | basic | sat-arw | | 2048 | 8192 | 13.07 | 13.03 | 13.12 | 8 | 1 | basic | sat-arw | | 4096 | 16384 | 19.25 | 19.18 | 19.35 | 8 | 1 | basic | sat-arw | | 8192 | 32768 | 33.2 | 33.07 | 33.26 | 8 | 1 | basic | sat-arw | | 16384 | 65536 | 61.51 | 61.37 | 61.81 | 8 | 1 | basic | sat-arw | | 32768 | 131072 | 118.47 | 118.25 | 118.67 | 8 | 1 | basic | sat-arw | | 65536 | 262144 | 264.26 | 263.82 | 264.96 | 8 | 1 | basic | sat-arw | | 131072 | 524288 | 529.61 | 528.04 | 531.62 | 8 | 1 | basic | sat-arw | | 262144 | 1048576 | 1042.82 | 1034.3 | 1050.54 | 8 | 1 | basic | sat-arw | | 524288 | 2097152 | 2132.34 | 2117.91 | 2141.33 | 8 | 1 | basic | sat-arw | | 1048576 | 4194304 | 11800.51 | 11776.94 | 11807.43 | 8 | 1 | basic | sat-arw | | 2097152 | 8388608 | 24546.88 | 24508.03 | 24561.12 | 8 | 1 | basic | sat-arw | | 4194304 | 16777216 | 49004.82 | 48967.96 | 49023.43 | 8 | 1 | basic | sat-arw | | 8388608 | 33554432 | 97557.92 | 97508.9 | 97593.09 | 8 | 1 | basic | sat-arw | | 16777216 | 67108864 | 197282.7 | 197184.7 | 197332.2 | 8 | 1 | basic | sat-arw | | 1 | 4 | 28.09 | 28 | 28.2 | 16 | 1 | basic | no-sharp | | 2 | 8 | 37.06 | 36.9 | 37.32 | 16 | 1 | basic | no-sharp | | 4 | 16 | 36.65 | 36.45 | 36.81 | 16 | 1 | basic | no-sharp | | 8 | 32 | 36.57 | 36.41 | 36.74 | 16 | 1 | basic | no-sharp | | 16 | 64 | 39.26 | 39 | 39.36 | 16 | 1 | basic | no-sharp | | 32 | 128 | 40.71 | 40.57 | 40.85 | 16 | 1 | basic | no-sharp | | 64 | 256 | 49.87 | 49.72 | 49.98 | 16 | 1 | basic | no-sharp | | 128 | 512 | 52.58 | 52.32 | 53.03 | 16 | 1 | basic | no-sharp | | 256 | 1024 | 53.91 | 53.73 | 54.04 | 16 | 1 | basic | no-sharp | | 512 | 2048 | 58.54 | 58.38 | 58.71 | 16 | 1 | basic | no-sharp | | 1024 | 4096 | 68.42 | 67.91 | 68.81 | 16 | 1 | basic | no-sharp | | 2048 | 8192 | 90.78 | 89.42 | 91.59 | 16 | 1 | basic | no-sharp | | 4096 | 16384 | 118.82 | 118.54 | 119.02 | 16 | 1 | basic | no-sharp | | 8192 | 32768 | 186.22 | 185.7 | 186.6 | 16 | 1 | basic | no-sharp | | 16384 | 65536 | 340.6 | 338.13 | 342.54 | 16 | 1 | basic | no-sharp | | 32768 | 131072 | 565.27 | 564.46 | 566.37 | 16 | 1 | basic | no-sharp | | 65536 | 262144 | 1028.68 | 1026.96 | 1031.7 | 16 | 1 | basic | no-sharp | | 131072 | 524288 | 1985.03 | 1977 | 1993.01 | 16 | 1 | basic | no-sharp | | 262144 | 1048576 | 3846.01 | 3834.95 | 3854.68 | 16 | 1 | basic | no-sharp | | 524288 | 2097152 | 7816.11 | 7786.75 | 7864.7 | 16 | 1 | basic | no-sharp | | 1048576 | 4194304 | 19832.7 | 19782.93 | 19873.64 | 16 | 1 | basic | no-sharp | | 2097152 | 8388608 | 40917.34 | 40865.79 | 40989.82 | 16 | 1 | basic | no-sharp | | 4194304 | 16777216 | 99975.54 | 99930.16 | 100036.9 | 16 | 1 | basic | no-sharp | | 8388608 | 33554432 | 204123.8 | 203641.8 | 204790.1 | 16 | 1 | basic | no-sharp | | 16777216 | 67108864 | 408446.7 | 407499.9 | 408887.6 | 16 | 1 | basic | no-sharp | | 1 | 4 | 2.88 | 2.85 | 2.89 | 16 | 1 | basic | llt-arw | | 2 | 8 | 3.04 | 3 | 3.07 | 16 | 1 | basic | llt-arw | | 4 | 16 | 3.67 | 3.64 | 3.71 | 16 | 1 | basic | llt-arw | | 8 | 32 | 4.48 | 4.35 | 4.59 | 16 | 1 | basic | llt-arw | | 16 | 64 | 5.26 | 4.99 | 5.51 | 16 | 1 | basic | llt-arw | | 32 | 128 | 6.46 | 6.18 | 6.71 | 16 | 1 | basic | llt-arw | | 64 | 256 | 9.04 | 8.78 | 9.29 | 16 | 1 | basic | llt-arw | | 128 | 512 | 13.46 | 13.19 | 13.73 | 16 | 1 | basic | llt-arw | | 256 | 1024 | 21.92 | 21.64 | 22.19 | 16 | 1 | basic | llt-arw | | 512 | 2048 | 39.49 | 39.2 | 39.76 | 16 | 1 | basic | llt-arw | | 1024 | 4096 | 75.01 | 74.71 | 75.28 | 16 | 1 | basic | llt-arw | | 2048 | 8192 | 145.03 | 144.72 | 145.28 | 16 | 1 | basic | llt-arw | | 4096 | 16384 | 294.23 | 293.36 | 294.57 | 16 | 1 | basic | llt-arw | | 8192 | 32768 | 570.01 | 569.43 | 570.38 | 16 | 1 | basic | llt-arw | | 16384 | 65536 | 1126.69 | 1125.35 | 1127.16 | 16 | 1 | basic | llt-arw | | 32768 | 131072 | 2262.68 | 2260.92 | 2263.07 | 16 | 1 | basic | llt-arw | | 65536 | 262144 | 4510.45 | 4509.98 | 4510.95 | 16 | 1 | basic | llt-arw | | 131072 | 524288 | 8998.83 | 8998.5 | 8999.07 | 16 | 1 | basic | llt-arw | | 262144 | 1048576 | 17976.99 | 17975.99 | 17977.78 | 16 | 1 | basic | llt-arw | | 524288 | 2097152 | 38830.95 | 38827.66 | 38834.83 | 16 | 1 | basic | llt-arw | | 1048576 | 4194304 | 83524.61 | 83446.13 | 83628.15 | 16 | 1 | basic | llt-arw | | 2097152 | 8388608 | 172213.1 | 171953.2 | 172341.7 | 16 | 1 | basic | llt-arw | | 4194304 | 16777216 | 352505.2 | 351913.5 | 352617 | 16 | 1 | basic | llt-arw | | 8388608 | 33554432 | 705229.2 | 704044.3 | 705372.6 | 16 | 1 | basic | llt-arw | | 16777216 | 67108864 | 1419763 | 1419658 | 1419840 | 16 | 1 | basic | llt-arw | | 1 | 4 | 2.96 | 2.93 | 3 | 16 | 1 | basic | sat-nr | | 2 | 8 | 2.97 | 2.94 | 3.01 | 16 | 1 | basic | sat-nr | | 4 | 16 | 5.36 | 5.32 | 5.41 | 16 | 1 | basic | sat-nr | | 8 | 32 | 5.39 | 5.35 | 5.42 | 16 | 1 | basic | sat-nr | | 16 | 64 | 5.62 | 5.57 | 5.68 | 16 | 1 | basic | sat-nr | | 32 | 128 | 6.23 | 6.15 | 6.28 | 16 | 1 | basic | sat-nr | | 64 | 256 | 9.01 | 8.22 | 10.71 | 16 | 1 | basic | sat-nr | | 128 | 512 | 9.1 | 8.35 | 10.61 | 16 | 1 | basic | sat-nr | | 256 | 1024 | 9.53 | 8.81 | 11.15 | 16 | 1 | basic | sat-nr | | 512 | 2048 | 10.36 | 9.44 | 12.22 | 16 | 1 | basic | sat-nr | | 1024 | 4096 | 12.12 | 11.26 | 14 | 16 | 1 | basic | sat-nr | | 2048 | 8192 | 17.4 | 16.87 | 19.67 | 16 | 1 | basic | sat-nr | | 4096 | 16384 | 28.67 | 28.19 | 31.04 | 16 | 1 | basic | sat-nr | | 8192 | 32768 | 51.2 | 50.86 | 53.24 | 16 | 1 | basic | sat-nr | | 16384 | 65536 | 97.51 | 96.84 | 100.19 | 16 | 1 | basic | sat-nr | | 32768 | 131072 | 220.17 | 219.51 | 221.91 | 16 | 1 | basic | sat-nr | | 65536 | 262144 | 436.54 | 435.8 | 438.58 | 16 | 1 | basic | sat-nr | | 131072 | 524288 | 872.29 | 870.18 | 874.93 | 16 | 1 | basic | sat-nr | | 262144 | 1048576 | 1750.65 | 1749.74 | 1752.98 | 16 | 1 | basic | sat-nr | | 524288 | 2097152 | 3580.16 | 3579.45 | 3582.62 | 16 | 1 | basic | sat-nr | | 1048576 | 4194304 | 7389.65 | 7388.82 | 7392.82 | 16 | 1 | basic | sat-nr | | 2097152 | 8388608 | 15245.23 | 15244.39 | 15248.67 | 16 | 1 | basic | sat-nr | | 4194304 | 16777216 | 30918.23 | 30917.32 | 30921.83 | 16 | 1 | basic | sat-nr | | 8388608 | 33554432 | 61645.29 | 61644.59 | 61648.8 | 16 | 1 | basic | sat-nr | | 16777216 | 67108864 | 123365.5 | 123364.5 | 123368.7 | 16 | 1 | basic | sat-nr | | 1 | 4 | 2.91 | 2.89 | 2.94 | 16 | 1 | basic | sat-arw | | 2 | 8 | 2.93 | 2.9 | 2.95 | 16 | 1 | basic | sat-arw | | 4 | 16 | 3.61 | 3.56 | 3.66 | 16 | 1 | basic | sat-arw | | 8 | 32 | 4.4 | 4.27 | 4.5 | 16 | 1 | basic | sat-arw | | 16 | 64 | 5.27 | 4.99 | 5.49 | 16 | 1 | basic | sat-arw | | 32 | 128 | 6.36 | 6.12 | 6.58 | 16 | 1 | basic | sat-arw | | 64 | 256 | 8.88 | 8.6 | 9.16 | 16 | 1 | basic | sat-arw | | 128 | 512 | 13.11 | 12.85 | 13.35 | 16 | 1 | basic | sat-arw | | 256 | 1024 | 7.4 | 7.34 | 7.47 | 16 | 1 | basic | sat-arw | | 512 | 2048 | 8.67 | 8.58 | 8.77 | 16 | 1 | basic | sat-arw | | 1024 | 4096 | 12.57 | 12.52 | 12.62 | 16 | 1 | basic | sat-arw | | 2048 | 8192 | 18.32 | 18.2 | 18.4 | 16 | 1 | basic | sat-arw | | 4096 | 16384 | 31.27 | 31.22 | 31.36 | 16 | 1 | basic | sat-arw | | 8192 | 32768 | 57.26 | 57.17 | 57.36 | 16 | 1 | basic | sat-arw | | 16384 | 65536 | 109.79 | 109.65 | 109.94 | 16 | 1 | basic | sat-arw | | 32768 | 131072 | 246.16 | 245.76 | 246.53 | 16 | 1 | basic | sat-arw | | 65536 | 262144 | 494.95 | 494 | 495.77 | 16 | 1 | basic | sat-arw | | 131072 | 524288 | 997.77 | 994.1 | 1002.34 | 16 | 1 | basic | sat-arw | | 262144 | 1048576 | 2013.23 | 2001.89 | 2019.63 | 16 | 1 | basic | sat-arw | | 524288 | 2097152 | 11931.21 | 11913.41 | 11937.93 | 16 | 1 | basic | sat-arw | | 1048576 | 4194304 | 24107.37 | 24075.58 | 24123.03 | 16 | 1 | basic | sat-arw | | 2097152 | 8388608 | 48147.2 | 48092.65 | 48171.82 | 16 | 1 | basic | sat-arw | | 4194304 | 16777216 | 95934.55 | 95887.15 | 95954.49 | 16 | 1 | basic | sat-arw | | 8388608 | 33554432 | 193929.4 | 193893 | 193972.7 | 16 | 1 | basic | sat-arw | | 16777216 | 67108864 | 408847.9 | 408792.2 | 408926 | 16 | 1 | basic | sat-arw |