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batch: Generate speedup graphs
This commit generates two semi-log graphs that visualize the batch verification speed up over single verification (y-axis) wrt the number of signatures (or tweak checks) in the batch (x-axis). The input data points are taken from the batch verify benchmark. GNU plot was used to generate these graphs (plot.gp file). The instructions to reproduce these graphs (on your local machine) are given in doc/speedup-batch.md file. The value of `STRAUSS_MAX_TERMS_PER_BATCH` was calculated (approx) from the generated graphs. Relevant discussion: siv2r#2 (comment)
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‎doc/speedup-batch.md

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# Schnorrsig Batch Verification Speedup
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![Speedup over single verification](speedup-batch/schnorrsig-speedup-batch.png)
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# Tweak Pubkey Check Batch Verification Speedup
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![Speedup over single verification](speedup-batch/tweakcheck-speedup-batch.png)
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Build steps
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-----------
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To generate the above graphs on your local machine:
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$ cd doc/speedup-batch
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$ make
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$ make speedup-batch.png
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<!-- TODO: add additional notes on the API -->

‎doc/speedup-batch/.gitignore

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*.dat

‎doc/speedup-batch/Makefile

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schnorrsig_data = schnorrsig_batch.dat schnorrsig_single.dat
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tweak_data = tweak_batch.dat tweak_single.dat
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bench_output.txt: bench.sh
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SECP256K1_BENCH_ITERS=500000 ./bench.sh bench_output.txt
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schnorrsig_batch.dat: bench_output.txt
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cat bench_output.txt | grep -v "batchverify_schnorrsigs_1 " | awk '{ gsub(/ /,""); print }' | gawk -F, 'match($$0, /batchverify_schnorrsigs_([0-9]+)/, arr) {print arr[1] " " $$3}' > schnorrsig_batch.dat
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schnorrsig_single.dat: bench_output.txt
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cat bench_output.txt | awk '{ gsub(/ /,""); print }' | awk -F, 'match($$0, /schnorrsig_verify/) {print $$3}' > schnorrsig_single.dat
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tweak_batch.dat: bench_output.txt
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cat bench_output.txt | grep -v "batchverify_tweak_checks_1 " | awk '{ gsub(/ /,""); print }' | gawk -F, 'match($$0, /batchverify_tweak_checks_([0-9]+)/, arr) {print arr[1] " " $$3}' > tweak_batch.dat
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tweak_single.dat: bench_output.txt
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cat bench_output.txt | awk '{ gsub(/ /,""); print }' | awk -F, 'match($$0, /tweak_add_check/) {print $$3}' > tweak_single.dat
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speedup-batch.png: $(schnorrsig_data) $(tweak_data) plot.gp
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gnuplot plot.gp
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clean:
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rm *.log *.txt *.dat *.png

‎doc/speedup-batch/bench.sh

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#!/bin/bash
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output_file=$1
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cur_dir=$(pwd)
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cd ../../
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echo "HEAD: $(git rev-parse --short HEAD)" > "$cur_dir/$output_file.log"
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make clean
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./autogen.sh
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./configure --enable-experimental --enable-module-batch --enable-module-schnorrsig >> "$cur_dir/$output_file.log"
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make
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./bench schnorrsig > "$cur_dir/$output_file"
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./bench extrakeys >> "$cur_dir/$output_file"

‎doc/speedup-batch/bench_output.txt

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Benchmark , Min(us) , Avg(us) , Max(us)
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schnorrsig_sign , 7.57 , 7.60 , 7.64
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schnorrsig_verify , 15.2 , 15.3 , 15.5
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batchverify_schnorrsigs_1 , 17.8 , 17.9 , 18.1
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batchverify_schnorrsigs_2 , 15.6 , 15.8 , 15.9
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batchverify_schnorrsigs_3 , 14.7 , 14.8 , 14.8
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batchverify_schnorrsigs_4 , 14.4 , 14.4 , 14.4
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batchverify_schnorrsigs_5 , 14.1 , 14.1 , 14.2
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batchverify_schnorrsigs_7 , 13.9 , 13.9 , 13.9
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batchverify_schnorrsigs_9 , 13.6 , 13.7 , 13.8
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batchverify_schnorrsigs_11 , 13.7 , 13.8 , 13.8
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batchverify_schnorrsigs_14 , 13.3 , 13.5 , 13.6
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batchverify_schnorrsigs_17 , 13.5 , 13.5 , 13.5
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batchverify_schnorrsigs_21 , 13.4 , 13.4 , 13.5
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batchverify_schnorrsigs_26 , 13.3 , 13.3 , 13.4
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batchverify_schnorrsigs_32 , 13.3 , 13.4 , 13.4
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batchverify_schnorrsigs_39 , 13.3 , 13.3 , 13.4
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batchverify_schnorrsigs_47 , 13.2 , 13.2 , 13.2
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batchverify_schnorrsigs_57 , 13.2 , 13.4 , 13.5
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batchverify_schnorrsigs_69 , 13.2 , 13.3 , 13.4
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batchverify_schnorrsigs_83 , 13.3 , 13.3 , 13.4
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batchverify_schnorrsigs_100 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_121 , 13.2 , 13.3 , 13.5
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batchverify_schnorrsigs_146 , 13.4 , 13.5 , 13.5
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batchverify_schnorrsigs_176 , 13.3 , 13.4 , 13.5
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batchverify_schnorrsigs_212 , 13.2 , 13.3 , 13.5
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batchverify_schnorrsigs_255 , 13.2 , 13.3 , 13.4
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batchverify_schnorrsigs_307 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_369 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_443 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_532 , 13.4 , 13.5 , 13.6
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batchverify_schnorrsigs_639 , 13.5 , 13.6 , 13.6
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batchverify_schnorrsigs_767 , 13.3 , 13.3 , 13.4
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batchverify_schnorrsigs_921 , 13.3 , 13.4 , 13.4
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batchverify_schnorrsigs_1106 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_1328 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_1594 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_1913 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_2296 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_2756 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_3308 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_3970 , 13.3 , 13.6 , 13.8
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batchverify_schnorrsigs_4765 , 13.3 , 13.3 , 13.4
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batchverify_schnorrsigs_5719 , 13.3 , 13.4 , 13.7
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batchverify_schnorrsigs_6863 , 13.4 , 13.5 , 13.7
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batchverify_schnorrsigs_8236 , 13.3 , 13.3 , 13.4
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batchverify_schnorrsigs_9884 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_11861 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_14234 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_17081 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_20498 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_24598 , 13.2 , 13.2 , 13.3
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batchverify_schnorrsigs_29518 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_35422 , 13.2 , 13.2 , 13.3
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batchverify_schnorrsigs_42507 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_51009 , 13.2 , 13.2 , 13.3
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batchverify_schnorrsigs_61211 , 13.2 , 13.2 , 13.2
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batchverify_schnorrsigs_73454 , 13.2 , 13.2 , 13.2
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batchverify_schnorrsigs_88145 , 13.2 , 13.2 , 13.3
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batchverify_schnorrsigs_105775 , 13.2 , 13.2 , 13.2
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batchverify_schnorrsigs_126931 , 13.2 , 13.2 , 13.3
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batchverify_schnorrsigs_152318 , 13.3 , 13.3 , 13.3
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batchverify_schnorrsigs_182782 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_219339 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_263207 , 13.2 , 13.2 , 13.3
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batchverify_schnorrsigs_315849 , 13.2 , 13.3 , 13.3
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batchverify_schnorrsigs_379019 , 13.1 , 13.2 , 13.3
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batchverify_schnorrsigs_454823 , 13.2 , 13.2 , 13.3
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Benchmark , Min(us) , Avg(us) , Max(us)
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tweak_add_check , 11.4 , 11.5 , 11.6
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batchverify_tweak_checks_1 , 12.2 , 12.2 , 12.2
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batchverify_tweak_checks_2 , 10.2 , 10.2 , 10.2
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batchverify_tweak_checks_3 , 9.40 , 9.45 , 9.48
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batchverify_tweak_checks_4 , 9.01 , 9.03 , 9.05
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batchverify_tweak_checks_5 , 8.76 , 8.81 , 8.84
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batchverify_tweak_checks_7 , 8.52 , 8.55 , 8.58
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batchverify_tweak_checks_9 , 8.36 , 8.39 , 8.40
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batchverify_tweak_checks_11 , 8.24 , 8.27 , 8.29
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batchverify_tweak_checks_14 , 8.15 , 8.18 , 8.21
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batchverify_tweak_checks_17 , 8.11 , 8.12 , 8.14
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batchverify_tweak_checks_21 , 8.02 , 8.05 , 8.08
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batchverify_tweak_checks_26 , 7.99 , 8.00 , 8.00
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batchverify_tweak_checks_32 , 7.97 , 8.01 , 8.07
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batchverify_tweak_checks_39 , 7.91 , 7.92 , 7.94
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batchverify_tweak_checks_47 , 7.86 , 7.91 , 7.95
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batchverify_tweak_checks_57 , 7.93 , 7.94 , 7.95
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batchverify_tweak_checks_69 , 7.89 , 7.92 , 7.94
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batchverify_tweak_checks_83 , 7.85 , 7.88 , 7.90
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batchverify_tweak_checks_100 , 7.85 , 7.89 , 7.91
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batchverify_tweak_checks_121 , 7.93 , 7.95 , 7.98
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batchverify_tweak_checks_146 , 7.87 , 7.92 , 7.95
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batchverify_tweak_checks_176 , 7.91 , 7.92 , 7.93
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batchverify_tweak_checks_212 , 7.85 , 7.89 , 7.90
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batchverify_tweak_checks_255 , 7.89 , 7.91 , 7.93
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batchverify_tweak_checks_307 , 7.84 , 7.88 , 7.90
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batchverify_tweak_checks_369 , 7.86 , 7.89 , 7.91
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batchverify_tweak_checks_443 , 7.92 , 7.93 , 7.93
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batchverify_tweak_checks_532 , 7.91 , 7.91 , 7.92
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batchverify_tweak_checks_639 , 7.87 , 7.89 , 7.91
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batchverify_tweak_checks_767 , 7.90 , 7.90 , 7.90
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batchverify_tweak_checks_921 , 7.89 , 7.90 , 7.90
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batchverify_tweak_checks_1106 , 7.86 , 7.88 , 7.89
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batchverify_tweak_checks_1328 , 7.85 , 7.88 , 7.91
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batchverify_tweak_checks_1594 , 7.84 , 7.88 , 7.92
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batchverify_tweak_checks_1913 , 7.90 , 7.91 , 7.92
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batchverify_tweak_checks_2296 , 7.82 , 7.89 , 8.00
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batchverify_tweak_checks_2756 , 7.88 , 7.91 , 7.93
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batchverify_tweak_checks_3308 , 7.93 , 7.94 , 7.97
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batchverify_tweak_checks_3970 , 7.91 , 7.92 , 7.92
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batchverify_tweak_checks_4765 , 7.86 , 7.91 , 7.96
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batchverify_tweak_checks_5719 , 7.94 , 7.99 , 8.02
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batchverify_tweak_checks_6863 , 7.86 , 7.90 , 7.94
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batchverify_tweak_checks_8236 , 7.93 , 7.93 , 7.93
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batchverify_tweak_checks_9884 , 7.91 , 7.94 , 8.01
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batchverify_tweak_checks_11861 , 7.88 , 7.93 , 8.00
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batchverify_tweak_checks_14234 , 7.86 , 7.87 , 7.88
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batchverify_tweak_checks_17081 , 7.90 , 7.91 , 7.92
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batchverify_tweak_checks_20498 , 7.92 , 7.93 , 7.94
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batchverify_tweak_checks_24598 , 7.90 , 7.92 , 7.94
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batchverify_tweak_checks_29518 , 7.88 , 7.93 , 7.96
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batchverify_tweak_checks_35422 , 7.91 , 7.92 , 7.93
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batchverify_tweak_checks_42507 , 7.90 , 7.91 , 7.93
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batchverify_tweak_checks_51009 , 7.90 , 7.91 , 7.92
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batchverify_tweak_checks_61211 , 7.90 , 7.92 , 7.95
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batchverify_tweak_checks_73454 , 7.91 , 7.95 , 7.98
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batchverify_tweak_checks_88145 , 7.91 , 7.95 , 8.02
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batchverify_tweak_checks_105775 , 7.99 , 8.04 , 8.08
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batchverify_tweak_checks_126931 , 7.88 , 7.96 , 8.03
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batchverify_tweak_checks_152318 , 7.92 , 7.96 , 7.99
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batchverify_tweak_checks_182782 , 7.94 , 7.95 , 7.96
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batchverify_tweak_checks_219339 , 7.96 , 8.04 , 8.10
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batchverify_tweak_checks_263207 , 7.94 , 7.97 , 8.00
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batchverify_tweak_checks_315849 , 7.91 , 7.93 , 7.95
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batchverify_tweak_checks_379019 , 7.87 , 7.89 , 7.92
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batchverify_tweak_checks_454823 , 7.81 , 7.88 , 7.92

‎doc/speedup-batch/plot.gp

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set style line 80 lt rgb "#808080"
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set style line 81 lt 0
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set style line 81 lt rgb "#808080"
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set grid back linestyle 81
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set border 3 back linestyle 80
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set xtics nomirror
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set ytics nomirror
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set style line 1 lt rgb "#A00000" lw 2 pt 1
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set style line 2 lt rgb "#00A000" lw 2 pt 6
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set style line 3 lt rgb "#5060D0" lw 2 pt 2
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set style line 4 lt rgb "#F25900" lw 2 pt 9
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set key bottom right
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set autoscale
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unset log
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unset label
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set xtic auto
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set ytic auto
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set title "Batch signature verification in libsecp256k1"
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set xlabel "Number of signatures (logarithmic)"
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set ylabel "Verification time per signature in us"
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set grid
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set logscale x
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set mxtics 10
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# Generate graph of Schnorr signature benchmark
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schnorrsig_single_val=system("cat schnorrsig_single.dat")
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set xrange [1.1:]
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set xtics add ("2" 2)
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set yrange [0.9:]
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set ytics -1,0.1,3
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set ylabel "Speedup over single verification"
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set term png size 800,600
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set output 'schnorrsig-speedup-batch.png'
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plot "schnorrsig_batch.dat" using 1:(schnorrsig_single_val/$2) with points title "" ls 1
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# Generate graph of tweaked x-only pubkey check benchmark
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set title "Batch tweaked x-only pubkey check in libsecp256k1"
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set xlabel "Number of tweak checks (logarithmic)"
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tweak_single_val=system("cat tweak_single.dat")
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set output 'tweakcheck-speedup-batch.png'
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plot "tweak_batch.dat" using 1:(tweak_single_val/$2) with points title "" ls 1

‎doc/speedup-batch/schnorrsig-speedup-batch.png

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‎doc/speedup-batch/tweakcheck-speedup-batch.png

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‎src/modules/batch/main_impl.h

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#include "../../../include/secp256k1_batch.h"
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/* Maximum number of scalar-point pairs on the batch
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* for which `secp256k1_batch_verify` remains efficient */
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#define STRAUSS_MAX_TERMS_PER_BATCH 106
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/* Assume two batch objects (batch1 and batch2) and we call
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* `batch_add_tweak_check` on batch1 and `batch_add_schnorrsig` on batch2.
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* In this case, the same randomizer will be generated if the input bytes to
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secp256k1_batch* batch;
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size_t batch_scratch_size;
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unsigned char zeros[16] = {0};
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/* max number of scalar-point pairs on scratch up to which Strauss multi multiplication is efficient */
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if (max_terms > STRAUSS_MAX_TERMS_PER_BATCH) {
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max_terms = STRAUSS_MAX_TERMS_PER_BATCH;
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}
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VERIFY_CHECK(ctx != NULL);
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ARG_CHECK(max_terms != 0);

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