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Merge pull request #3 from AFLplusplus/stable
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AFL Stable merge
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Sumit Lahiri authored Feb 22, 2024
2 parents 61e27c6 + 775861e commit 621f784
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10 changes: 4 additions & 6 deletions .github/workflows/ci.yml
Original file line number Diff line number Diff line change
Expand Up @@ -20,20 +20,18 @@ jobs:
AFL_I_DONT_CARE_ABOUT_MISSING_CRASHES: 1
steps:
- uses: actions/checkout@v3
- name: update
run: sudo apt-get update && sudo apt-get upgrade -y
- name: debug
run: apt-cache search plugin-dev | grep gcc-; echo; apt-cache search clang-format- | grep clang-format-
- name: update
run: sudo apt-get update
# && sudo apt-get upgrade -y
- name: install packages
#run: sudo apt-get install -y -m -f --install-suggests build-essential git libtool libtool-bin automake bison libglib2.0-0 clang llvm-dev libc++-dev findutils libcmocka-dev python3-dev python3-setuptools ninja-build python3-pip
run: sudo apt-get install -y -m -f build-essential git libtool libtool-bin automake flex bison libglib2.0-0 clang llvm-dev libc++-dev findutils libcmocka-dev python3-dev python3-setuptools ninja-build python3-pip
run: sudo apt-get install -y -m -f build-essential gcc-10 g++-10 git libtool libtool-bin automake flex bison libglib2.0-0 clang-12 llvm-12-dev libc++-dev findutils libcmocka-dev python3-dev python3-setuptools ninja-build python3-pip gcc-10-plugin-dev
- name: compiler installed
run: gcc -v; echo; clang -v
- name: install gcc plugin
run: sudo apt-get install -y -m -f --install-suggests $(readlink /usr/bin/gcc)-plugin-dev
- name: build afl++
run: make distrib ASAN_BUILD=1 NO_NYX=1
run: export NO_NYX=1; export ASAN_BUILD=1; export LLVM_CONFIG=llvm-config-12; make ASAN_BUILD=1 NO_NYX=1 LLVM_CONFIG=llvm-config-12 distrib
- name: run tests
run: sudo -E ./afl-system-config; make tests
# macos:
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6 changes: 3 additions & 3 deletions .gitmodules
Original file line number Diff line number Diff line change
Expand Up @@ -19,9 +19,9 @@
[submodule "nyx_mode/libnyx"]
path = nyx_mode/libnyx
url = https://github.com/nyx-fuzz/libnyx.git
[submodule "nyx_mode/QEMU-Nyx"]
path = nyx_mode/QEMU-Nyx
url = https://github.com/nyx-fuzz/qemu-nyx.git
[submodule "nyx_mode/packer"]
path = nyx_mode/packer
url = https://github.com/nyx-fuzz/packer.git
[submodule "nyx_mode/QEMU-Nyx"]
path = nyx_mode/QEMU-Nyx
url = https://github.com/nyx-fuzz/QEMU-Nyx
6 changes: 3 additions & 3 deletions Dockerfile
Original file line number Diff line number Diff line change
Expand Up @@ -16,8 +16,8 @@ ENV NO_CORESIGHT=1
ENV NO_NYX=1

### Only change these if you know what you are doing:
# LLVM 15 does not look good so we stay at 14 to still have LTO
ENV LLVM_VERSION=14
# Current recommended LLVM version is 16
ENV LLVM_VERSION=16
# GCC 12 is producing compile errors for some targets so we stay at GCC 11
ENV GCC_VERSION=11

Expand Down Expand Up @@ -88,7 +88,7 @@ ARG TEST_BUILD

RUN sed -i.bak 's/^ -/ /g' GNUmakefile && \
make clean && make distrib && \
([ "${TEST_BUILD}" ] || (make install && make clean)) && \
([ "${TEST_BUILD}" ] || (make install)) && \
mv GNUmakefile.bak GNUmakefile

RUN echo "set encoding=utf-8" > /root/.vimrc && \
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27 changes: 16 additions & 11 deletions GNUmakefile
Original file line number Diff line number Diff line change
Expand Up @@ -66,6 +66,10 @@ ifdef MSAN_BUILD
override LDFLAGS += -fsanitize=memory
endif

ifdef CODE_COVERAGE
override CFLAGS += -D__AFL_CODE_COVERAGE=1
endif

ifeq "$(findstring android, $(shell $(CC) --version 2>/dev/null))" ""
ifeq "$(shell echo 'int main() {return 0; }' | $(CC) $(CFLAGS) -Werror -x c - -flto=full -o .test 2>/dev/null && echo 1 || echo 0 ; rm -f .test )" "1"
CFLAGS_FLTO ?= -flto=full
Expand Down Expand Up @@ -395,7 +399,7 @@ help:
@echo INTROSPECTION - compile afl-fuzz with mutation introspection
@echo NO_PYTHON - disable python support
@echo NO_SPLICING - disables splicing mutation in afl-fuzz, not recommended for normal fuzzing
@echo NO_UTF - do not use UTF-8 for line rendering in status screen (fallback to G1 box drawing, of vanilla AFL)
@echo "NO_UTF - do not use UTF-8 for line rendering in status screen (fallback to G1 box drawing, of vanilla AFL)"
@echo NO_NYX - disable building nyx mode dependencies
@echo "NO_CORESIGHT - disable building coresight (arm64 only)"
@echo NO_UNICORN_ARM64 - disable building unicorn on arm64
Expand Down Expand Up @@ -649,16 +653,16 @@ endif
# -$(MAKE) -C utils/plot_ui
-$(MAKE) -C frida_mode
ifneq "$(SYS)" "Darwin"
ifeq "$(ARCH)" "aarch64"
ifndef NO_CORESIGHT
ifeq "$(ARCH)" "aarch64"
ifndef NO_CORESIGHT
-$(MAKE) -C coresight_mode
endif
endif
ifeq "$(SYS)" "Linux"
ifndef NO_NYX
endif
ifeq "$(SYS)" "Linux"
ifndef NO_NYX
-cd nyx_mode && ./build_nyx_support.sh
endif
endif
endif
endif
-cd qemu_mode && sh ./build_qemu_support.sh
ifeq "$(ARCH)" "aarch64"
ifndef NO_UNICORN_ARM64
Expand Down Expand Up @@ -782,7 +786,7 @@ install: all $(MANPAGES)
@rm -f $${DESTDIR}$(BIN_PATH)/afl-plot.sh
@rm -f $${DESTDIR}$(BIN_PATH)/afl-as
@rm -f $${DESTDIR}$(HELPER_PATH)/afl-llvm-rt.o $${DESTDIR}$(HELPER_PATH)/afl-llvm-rt-32.o $${DESTDIR}$(HELPER_PATH)/afl-llvm-rt-64.o $${DESTDIR}$(HELPER_PATH)/afl-gcc-rt.o
@for i in afl-llvm-dict2file.so afl-llvm-lto-instrumentlist.so afl-llvm-pass.so cmplog-instructions-pass.so cmplog-routines-pass.so cmplog-switches-pass.so compare-transform-pass.so libcompcov.so libdislocator.so libnyx.so libqasan.so libtokencap.so SanitizerCoverageLTO.so SanitizerCoveragePCGUARD.so split-compares-pass.so split-switches-pass.so; do echo rm -fv $${DESTDIR}$(HELPER_PATH)/$${i}; done
@for i in afl-llvm-dict2file.so afl-llvm-lto-instrumentlist.so afl-llvm-pass.so cmplog-instructions-pass.so cmplog-routines-pass.so cmplog-switches-pass.so compare-transform-pass.so libcompcov.so libdislocator.so libnyx.so libqasan.so libtokencap.so SanitizerCoverageLTO.so SanitizerCoveragePCGUARD.so split-compares-pass.so split-switches-pass.so injection-pass.so; do echo rm -fv $${DESTDIR}$(HELPER_PATH)/$${i}; done
install -m 755 $(PROGS) $(SH_PROGS) $${DESTDIR}$(BIN_PATH)
@if [ -f afl-qemu-trace ]; then install -m 755 afl-qemu-trace $${DESTDIR}$(BIN_PATH); fi
@if [ -f utils/plot_ui/afl-plot-ui ]; then install -m 755 utils/plot_ui/afl-plot-ui $${DESTDIR}$(BIN_PATH); fi
Expand Down Expand Up @@ -813,11 +817,12 @@ endif
install -m 644 docs/*.md $${DESTDIR}$(DOC_PATH)
cp -r testcases/ $${DESTDIR}$(MISC_PATH)
cp -r dictionaries/ $${DESTDIR}$(MISC_PATH)
cp injections.dic $${DESTDIR}$(MISC_PATH)

.PHONY: uninstall
uninstall:
-cd $${DESTDIR}$(BIN_PATH) && rm -f $(PROGS) $(SH_PROGS) afl-cs-proxy afl-qemu-trace afl-plot-ui afl-fuzz-document afl-network-server afl-g* afl-plot.sh afl-as afl-ld-lto afl-c* afl-lto*
-cd $${DESTDIR}$(HELPER_PATH) && rm -f afl-g*.*o afl-llvm-*.*o afl-compiler-*.*o libdislocator.so libtokencap.so libcompcov.so libqasan.so afl-frida-trace.so libnyx.so socketfuzz*.so argvfuzz*.so libAFLDriver.a libAFLQemuDriver.a as afl-as SanitizerCoverage*.so compare-transform-pass.so cmplog-*-pass.so split-*-pass.so dynamic_list.txt
-cd $${DESTDIR}$(BIN_PATH) && rm -f $(PROGS) $(SH_PROGS) afl-cs-proxy afl-qemu-trace afl-plot-ui afl-fuzz-document afl-network-client afl-network-server afl-g* afl-plot.sh afl-as afl-ld-lto afl-c* afl-lto*
-cd $${DESTDIR}$(HELPER_PATH) && rm -f afl-g*.*o afl-llvm-*.*o afl-compiler-*.*o libdislocator.so libtokencap.so libcompcov.so libqasan.so afl-frida-trace.so libnyx.so socketfuzz*.so argvfuzz*.so libAFLDriver.a libAFLQemuDriver.a as afl-as SanitizerCoverage*.so compare-transform-pass.so cmplog-*-pass.so split-*-pass.so dynamic_list.txt injections.dic
-rm -rf $${DESTDIR}$(MISC_PATH)/testcases $${DESTDIR}$(MISC_PATH)/dictionaries
-sh -c "ls docs/*.md | sed 's|^docs/|$${DESTDIR}$(DOC_PATH)/|' | xargs rm -f"
-cd $${DESTDIR}$(MAN_PATH) && rm -f $(MANPAGES)
Expand Down
2 changes: 1 addition & 1 deletion GNUmakefile.gcc_plugin
Original file line number Diff line number Diff line change
Expand Up @@ -11,7 +11,7 @@
# from Laszlo Szekeres.
#
# Copyright 2015 Google Inc. All rights reserved.
# Copyright 2019-2023 AFLplusplus Project. All rights reserved.
# Copyright 2019-2024 AFLplusplus Project. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
Expand Down
13 changes: 8 additions & 5 deletions GNUmakefile.llvm
Original file line number Diff line number Diff line change
Expand Up @@ -45,13 +45,13 @@ endif
LLVMVER = $(shell $(LLVM_CONFIG) --version 2>/dev/null | sed 's/git//' | sed 's/svn//' )
LLVM_MAJOR = $(shell $(LLVM_CONFIG) --version 2>/dev/null | sed 's/\..*//' )
LLVM_MINOR = $(shell $(LLVM_CONFIG) --version 2>/dev/null | sed 's/.*\.//' | sed 's/git//' | sed 's/svn//' | sed 's/ .*//' )
LLVM_UNSUPPORTED = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^[0-2]\.|^3.[0-7]\.' && echo 1 || echo 0 )
LLVM_UNSUPPORTED = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^[0-2]\.|^3.[0-8]\.' && echo 1 || echo 0 )
LLVM_TOO_NEW = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^1[8-9]|^2[0-9]' && echo 1 || echo 0 )
LLVM_TOO_OLD = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^[1-9]\.|^1[012]\.' && echo 1 || echo 0 )
LLVM_NEW_API = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^1[0-9]' && echo 1 || echo 0 )
LLVM_NEWER_API = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^1[6-9]' && echo 1 || echo 0 )
LLVM_13_OK = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^1[3-9]' && echo 1 || echo 0 )
LLVM_HAVE_LTO = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^1[1-9]' && echo 1 || echo 0 )
LLVM_HAVE_LTO = $(shell $(LLVM_CONFIG) --version 2>/dev/null | grep -E -q '^1[2-9]' && echo 1 || echo 0 )
LLVM_BINDIR = $(shell $(LLVM_CONFIG) --bindir 2>/dev/null)
LLVM_LIBDIR = $(shell $(LLVM_CONFIG) --libdir 2>/dev/null)
LLVM_STDCXX = gnu++11
Expand Down Expand Up @@ -95,12 +95,12 @@ ifeq "$(LLVM_NEWER_API)" "1"
endif

ifeq "$(LLVM_HAVE_LTO)" "1"
$(info [+] llvm_mode detected llvm 11+, enabling afl-lto LTO implementation)
$(info [+] llvm_mode detected llvm 12+, enabling afl-lto LTO implementation)
LLVM_LTO = 1
endif

ifeq "$(LLVM_LTO)" "0"
$(info [+] llvm_mode detected llvm < 11, afl-lto LTO will not be build.)
$(info [+] llvm_mode detected llvm < 12, afl-lto LTO will not be build.)
endif

ifeq "$(LLVM_APPLE_XCODE)" "1"
Expand Down Expand Up @@ -341,7 +341,7 @@ ifeq "$(TEST_MMAP)" "1"
endif

PROGS_ALWAYS = ./afl-cc ./afl-compiler-rt.o ./afl-compiler-rt-32.o ./afl-compiler-rt-64.o
PROGS = $(PROGS_ALWAYS) ./afl-llvm-pass.so ./SanitizerCoveragePCGUARD.so ./split-compares-pass.so ./split-switches-pass.so ./cmplog-routines-pass.so ./cmplog-instructions-pass.so ./cmplog-switches-pass.so ./afl-llvm-dict2file.so ./compare-transform-pass.so ./afl-ld-lto ./afl-llvm-lto-instrumentlist.so ./SanitizerCoverageLTO.so
PROGS = $(PROGS_ALWAYS) ./afl-llvm-pass.so ./SanitizerCoveragePCGUARD.so ./split-compares-pass.so ./split-switches-pass.so ./cmplog-routines-pass.so ./cmplog-instructions-pass.so ./cmplog-switches-pass.so ./afl-llvm-dict2file.so ./compare-transform-pass.so ./afl-ld-lto ./afl-llvm-lto-instrumentlist.so ./SanitizerCoverageLTO.so ./injection-pass.so

# If prerequisites are not given, warn, do not build anything, and exit with code 0
ifeq "$(LLVMVER)" ""
Expand Down Expand Up @@ -469,6 +469,9 @@ endif
afl-llvm-dict2file.so: instrumentation/afl-llvm-dict2file.so.cc instrumentation/afl-llvm-common.o | test_deps
$(CXX) $(CLANG_CPPFL) -shared $< -o $@ $(CLANG_LFL) instrumentation/afl-llvm-common.o

./injection-pass.so: instrumentation/injection-pass.cc instrumentation/afl-llvm-common.o | test_deps
$(CXX) $(CLANG_CPPFL) -shared $< -o $@ $(CLANG_LFL) instrumentation/afl-llvm-common.o

.PHONY: document
document:
$(CLANG_BIN) -D_AFL_DOCUMENT_MUTATIONS $(CFLAGS_SAFE) $(CPPFLAGS) $(CLANG_CFL) -O3 -Wno-unused-result -fPIC -c instrumentation/afl-compiler-rt.o.c -o ./afl-compiler-rt.o
Expand Down
4 changes: 2 additions & 2 deletions README.md
Original file line number Diff line number Diff line change
Expand Up @@ -2,9 +2,9 @@

<img align="right" src="https://raw.githubusercontent.com/AFLplusplus/Website/main/static/aflpp_bg.svg" alt="AFL++ logo" width="250" heigh="250">

Release version: [4.08c](https://github.com/AFLplusplus/AFLplusplus/releases)
Release version: [4.10c](https://github.com/AFLplusplus/AFLplusplus/releases)

GitHub version: 4.09a
GitHub version: 4.10c

Repository:
[https://github.com/AFLplusplus/AFLplusplus](https://github.com/AFLplusplus/AFLplusplus)
Expand Down
12 changes: 9 additions & 3 deletions TODO.md
Original file line number Diff line number Diff line change
Expand Up @@ -2,15 +2,21 @@

## Must

- UI revamp
- hardened_usercopy=0 page_alloc.shuffle=0
- add value_profile but only enable after 15 minutes without finds
- cmplog max len, cmplog max items envs?
- adapt MOpt to new mutation engine
- Update afl->pending_not_fuzzed for MOpt
- cmplog rtn sanity check on fixed length? + no length 1
- Update afl->pending_not_fuzzed for MOpt
- cmplog rtn sanity check on fixed length? currently we ignore the length
- afl-showmap -f support
- afl-fuzz multicore wrapper script
- when trimming then perform crash detection
- problem: either -L0 and/or -p mmopt results in zero new coverage


## Should

- add value_profile but only enable after 15 minutes without finds?
- afl-crash-analysis
- support persistent and deferred fork server in afl-showmap?
- better autodetection of shifting runtime timeout values
Expand Down
6 changes: 5 additions & 1 deletion afl-cmin
Original file line number Diff line number Diff line change
@@ -1,11 +1,15 @@
#!/usr/bin/env sh
SYS=$(uname -s)
test "$SYS" = "Darwin" && {
echo Error: afl-cmin does not work on Apple currently. please use afl-cmin.bash instead.
exit 1
}
export AFL_QUIET=1
export ASAN_OPTIONS=detect_leaks=0
THISPATH=`dirname ${0}`
export PATH="${THISPATH}:$PATH"
awk -f - -- ${@+"$@"} <<'EOF'
#!/usr/bin/awk -f
# awk script to minimize a test corpus of input files
#
# based on afl-cmin bash script written by Michal Zalewski
Expand Down
2 changes: 1 addition & 1 deletion afl-cmin.bash
Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@
#
# Copyright 2014, 2015 Google Inc. All rights reserved.
#
# Copyright 2019-2023 AFLplusplus
# Copyright 2019-2024 AFLplusplus
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
Expand Down
8 changes: 8 additions & 0 deletions afl-persistent-config
Original file line number Diff line number Diff line change
Expand Up @@ -38,6 +38,7 @@ fi

echo
PLATFORM=`uname -s`
ARCH=`uname -m`

# check that we're on Mac
if [[ "$PLATFORM" = "Darwin" ]] ; then
Expand Down Expand Up @@ -87,6 +88,13 @@ if [[ "$PLATFORM" = "Darwin" ]] ; then
</plist>
EOF

if [[ "$ARCH" = "x86_64" ]]; then
echo "Disabling ASLR system wide"
nvram boot-args="no_aslr=1"
else
echo NOTICE: on ARM64 we do not know currently how to disable system wide ASLR, please report if you know how.
fi

echo
echo "Reboot and enjoy your fuzzing"
exit 0
Expand Down
1 change: 1 addition & 0 deletions afl-system-config
Original file line number Diff line number Diff line change
Expand Up @@ -25,6 +25,7 @@ echo "WARNING: this reduces the security of the system!"
echo
if [ '!' "$EUID" = 0 ] && [ '!' `id -u` = 0 ] ; then
echo "Warning: you need to be root to run this!"
sleep 1
# we do not exit as other mechanisms exist that allows to do this than
# being root. let the errors speak for themselves.
fi
Expand Down
2 changes: 1 addition & 1 deletion afl-whatsup
Original file line number Diff line number Diff line change
Expand Up @@ -6,7 +6,7 @@
# Originally written by Michal Zalewski
#
# Copyright 2015 Google Inc. All rights reserved.
# Copyright 2019-2023 AFLplusplus Project. All rights reserved.
# Copyright 2019-2024 AFLplusplus Project. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
Expand Down
4 changes: 0 additions & 4 deletions benchmark/COMPARISON

This file was deleted.

9 changes: 9 additions & 0 deletions benchmark/COMPARISON.md
Original file line number Diff line number Diff line change
@@ -0,0 +1,9 @@
CPU | MHz | threads | singlecore | multicore | afl-*-config |
====================================================|=======|=========|============|===========|==============|
Raspberry Pi 5 | 2400 | 4 | 25786 | 101114 | both |
AMD EPYC 7282 16-Core Processor | 3194 | 32 | 87199 | 769001 | both |
AMD Ryzen 5 PRO 4650G with Radeon Graphics | 3700 | 12 | 95356 | 704840 | both |
Intel(R) Core(TM) i9-9900K CPU @ 3.60GHz | 4995 | 16 | 120064 | 1168943 | both |
12th Gen Intel(R) Core(TM) i7-1270P | 4761 | 16 | 149778 | 641219 | both |
AMD Ryzen 9 5950X 16-Core Processor | 4792 | 32 | 161690 | 2339763 | both |
Apple Mac Studio M2 Ultra 2023, Linux VM guest | 3500 | 16 | 163570 | 1157465 | both |
59 changes: 59 additions & 0 deletions benchmark/README.md
Original file line number Diff line number Diff line change
@@ -0,0 +1,59 @@
# American Fuzzy Lop plus plus (AFL++)

## benchmarking

This directory contains benchmarking tools that allow you to compare one machine
with another in terms of raw ability to execute a fuzzing target repeatedly.

To achieve this, we use a sample program ("test-instr.c") where each path is
equally likely, supply it a single seed, and tell AFL to exit after one run of
deterministic mutations against that seed.

**Note that this is not a real-world scenario!**
Because the target does basically nothing this is rather a stress test on
Kernel I/O / context switching.
For this reason you will not see a difference if you run the multicore test
with 20 or 40 threads - or even see the performance decline the more threads
(`-f` parameter) you use. In a real-world scenario you can expect to gain
exec/s until 40-60 threads (if you have that many available on your CPU).

Usage example:

```
cd aflplusplus/benchmark
python3 benchmark.py
[*] Ready, starting benchmark...
[*] Compiling the test-instr-persist-shmem fuzzing harness for the benchmark to use.
[*] singlecore test-instr-persist-shmem run 1 of 2, execs/s: 124883.62
[*] singlecore test-instr-persist-shmem run 2 of 2, execs/s: 126704.93
[*] Average execs/sec for this test across all runs was: 125794.28
[*] Using 16 fuzzers for multicore fuzzing (use --fuzzers to override).
[*] multicore test-instr-persist-shmem run 1 of 2, execs/s: 1179822.66
[*] multicore test-instr-persist-shmem run 2 of 2, execs/s: 1175584.09
[*] Average execs/sec for this test across all runs was: 1177703.38
[*] Results have been written to the benchmark-results.jsonl file.
[*] Results have been written to the COMPARISON.md file.
```

By default, the script will use a number of parallel fuzzers equal to your
available CPUs/threads (change with `--fuzzers`), and will perform each test
three times and average the result (change with `--runs`).

The script will use multicore fuzzing instead of singlecore by default (change
with `--mode singlecore`) and use a persistent-mode shared memory harness for
optimal speed (change with `--target test-instr`).

Feel free to submit the resulting line for your CPU added to the COMPARISON.md
and benchmark-results.jsonl files back to AFL++ in a pull request.

Each run writes results to [benchmark-results.jsonl](benchmark-results.jsonl)
in [JSON Lines](https://jsonlines.org/) format, ready to be pulled in to other
tools such as [jq -cs](https://jqlang.github.io/jq/) or
[pandas](https://pandas.pydata.org/) for analysis.

## Data analysis

There is sample data in [benchmark-results.jsonl](benchmark-results.jsonl), and
a Jupyter notebook for exploring the results and suggesting their meaning at
[benchmark.ipynb](benchmark.ipynb).

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