Intention behind hz.tools It s my sincere hope that my repos help to make Software Defined Radio (SDR) code a bit easier to understand, and serves as an understandable framework to learn with. It s a large codebase, but one that is possible to sit down and understand because, well, it was written by a single person. Frankly, I m also not productive enough in my free time in the middle of the night and on weekends and holidays to create a codebase that s too large to understand, I hope! I remain wary of this project turning into work, so my goal is to be very upfront about my boundaries, and the limits of what classes of contributions i m interested in seeing. Here s some goals of open sourcing these repos:

• I do want this library to be used to learn with. Please go through it all and use it to learn about radios and how software can control them!
• I am interested in bugs if there s a problem you discover. Such bugs are likely a great chance for me to fix something I ve misunderstood or typoed.
• I am interested in PRs fixing bugs you find. I may need a bit of a back and forth to fully understand the problem if I do not understand the bug and fix yet. I hope you may have some grace if it s taking a long time.

Here s a list of some anti-goals of open sourcing these repos.

• I do not want this library to become a critical dependency of an important project, since I do not have the time to deal with the maintenance burden. Putting me in that position is going to make me very uncomfortable.
• I am not interested in feature requests, the features have grown as I ve hit problems, I m not interested in building or maintaining features for features sake. The API surface should be exposed enough to allow others to experiment with such things out-of-tree.
• I m not interested in clever code replacing clear code without a very compelling reason.
• I use GNU/Linux (specifically Debian ), and from time-to-time I ve made sure that my code runs on OpenBSD too. Platforms beyond that will likely not be supported at the expense of either of those two. I ll take fixes for bugs that fix a problem on another platform, but not damage the code to work around issues / lack of features on other platforms (like Windows).

I m not saying all this to be a jerk, I do it to make sure I can continue on my journey to learn about how radios work without my full time job becoming maintaining a radio framework single-handedly for other people to use even if it means I need to close PRs or bugs without merging it or fixing the issue. With all that out of the way, I m very happy to announce that the repos are now public under github.com/hztools.

Should you use this? Probably not. The intent here is not to provide a general purpose Go SDR framework for everyone to build on, although I am keenly aware it looks and feels like it, since that what it is to me. This is a learning project, so for any use beyond joining me in learning should use something like GNU Radio or a similar framework that has a community behind it. In fact, I suspect most contributors ought to be contributing to GNU Radio, and not this project. If I can encourage people to do so, contribute to GNU Radio! Nothing makes me happier than seeing GNU Radio continue to be the go-to, and well supported. Consider donating to GNU Radio!

hz.tools/rf - Frequency types The hz.tools/rf library contains the abstract concept of frequency, and some very basic helpers to interact with frequency ranges (such as helpers to deal with frequency ranges, or frequency range math) as well as frequencies and some very basic conversions (to meters, etc) and parsers (to parse values like 10MHz). This ensures that all the hz.tools libraries have a shared understanding of Frequencies, a standard way of representing ranges of Frequencies, and the ability to handle the IO boundary with things like CLI arguments, JSON or YAML. The git repo can be found at github.com/hztools/go-rf, and is importable as hz.tools/rf.

 // Parse a frequency using hz.tools/rf.ParseHz, and print it to stdout.
 freq := rf.MustParseHz("-10kHz")
fmt.Printf("Frequency: %s\n", freq+rf.MHz)
// Prints: 'Frequency: 990kHz'

// Return the Intersection between two RF ranges, and print
 // it to stdout.
 r1 := rf.Range rf.KHz, rf.MHz 
r2 := rf.Range rf.Hz(10), rf.KHz * 100 
fmt.Printf("Range: %s\n", r1.Intersection(r2))
// Prints: Range: 1000Hz->100kHz

These can be used to represent tons of things - ranges can be used for things like the tunable range of an SDR, the bandpass of a filter or the frequencies that correspond to a bin of an FFT, while frequencies can be used for things such as frequency offsets or the tuned center frequency.

hz.tools/sdr - SDR I/O and IQ Types This is the big one. This library represents the majority of the shared types and bindings, and is likely the most useful place to look at when learning about the IO boundary between a program and an SDR. The git repo can be found at github.com/hztools/go-sdr, and is importable as hz.tools/sdr. This library is designed to look (and in some cases, mirror) the Go io idioms so that this library feels as idiomatic as it can, so that Go builtins interact with IQ in a way that s possible to reason about, and to avoid reinventing the wheel by designing new API surface. While some of the API looks (and is even called) the same thing as a similar function in io, the implementation is usually a lot more naive, and may have unexpected sharp edges such as concurrency issues or performance problems. The following IQ types are implemented using the sdr.Samples interface. The hz.tools/sdr package contains helpers for conversion between types, and some basic manipulation of IQ streams.

IQ Format	hz.tools Name	Underlying Go Type
Interleaved uint8 (rtl-sdr)	sdr.SamplesU8	[][2]uint8
Interleaved int8 (hackrf, uhd)	sdr.SamplesI8	[][2]int8
Interleaved int16 (pluto, uhd)	sdr.SamplesI16	[][2]int16
Interleaved float32 (airspy, uhd)	sdr.SamplesC64	[]complex64

The following SDRs have implemented drivers in-tree.

SDR	Format	RX/TX	State
rtl	u8	RX	Good
HackRF	i8	RX/TX	Good
PlutoSDR	i16	RX/TX	Good
rtl kerberos	u8	RX	Old
uhd	i16/c64/i8	RX/TX	Good
airspyhf	c64	RX	Exp

The following major packages and subpackages exist at the time of writing:

Import	What is it?
hz.tools/sdr	Core IQ types, supporting types and implementations that interact with the byte boundary
hz.tools/sdr/rtl	sdr.Receiver implementation using librtlsdr.
hz.tools/sdr/rtl/kerberos	Helpers to enable coherent RX using the Kerberos SDR.
hz.tools/sdr/rtl/e4k	Helpers to interact with the E4000 RTL-SDR dongle.
hz.tools/sdr/fft	Interfaces for performing an FFT, which are implemented by other packages.
hz.tools/sdr/rtltcp	sdr.Receiver implementation for rtl_tcp servers.
hz.tools/sdr/pluto	sdr.Transceiver implementation for the PlutoSDR using libiio.
hz.tools/sdr/uhd	sdr.Transceiver implementation for UHD radios, specifically the B210 and B200mini
hz.tools/sdr/hackrf	sdr.Transceiver implementation for the HackRF using libhackrf.
hz.tools/sdr/mock	Mock SDR for testing purposes.
hz.tools/sdr/airspyhf	sdr.Receiver implementation for the AirspyHF+ Discovery with libairspyhf.
hz.tools/sdr/internal/simd	SIMD helpers for IQ operations, written in Go ASM. This isn t the best to learn from, and it contains pure go implemtnations alongside.
hz.tools/sdr/stream	Common Reader/Writer helpers that operate on IQ streams.

hz.tools/fftw - hz.tools/sdr/fft implementation The hz.tools/fftw package contains bindings to libfftw3 to implement the hz.tools/sdr/fft.Planner type to transform between the time and frequency domain. The git repo can be found at github.com/hztools/go-fftw, and is importable as hz.tools/fftw. This is the default throughout most of my codebase, although that default is only expressed at the leaf package libraries should not be hardcoding the use of this library in favor of taking an fft.Planner, unless it s used as part of testing. There are a bunch of ways to do an FFT out there, things like clFFT or a pure-go FFT implementation could be plugged in depending on what s being solved for.

hz.tools/ fm,am - analog audio demodulation and modulation The hz.tools/fm and hz.tools/am packages contain demodulators for AM analog radio, and FM analog radio. This code is a bit old, so it has a lot of room for cleanup, but it ll do a very basic demodulation of IQ to audio. The git repos can be found at github.com/hztools/go-fm and github.com/hztools/go-am, and are importable as hz.tools/fm and hz.tools/am. As a bonus, the hz.tools/fm package also contains a modulator, which has been tested on the air and with some of my handheld radios. This code is a bit old, since the hz.tools/fm code is effectively the first IQ processing code I d ever written, but it still runs and I run it from time to time.

 // Basic sketch for playing FM radio using a reader stream from
 // an SDR or other IQ stream.

bandwidth := 150*rf.KHz
reader, err = stream.ConvertReader(reader, sdr.SampleFormatC64)
if err != nil  
...
 
demod, err := fm.Demodulate(reader, fm.DemodulatorConfig 
Deviation: bandwidth / 2,
Downsample: 8, // some value here depending on sample rate
 Planner: fftw.Plan,
 )
if err != nil  
...
 
speaker, err := pulseaudio.NewWriter(pulseaudio.Config 
Format: pulseaudio.SampleFormatFloat32NE,
Rate: demod.SampleRate(),
AppName: "rf",
StreamName: "fm",
Channels: 1,
SinkName: "",
 )
if err != nil  
...
 
buf := make([]float32, 1024*64)
for  
i, err := demod.Read(buf)
if err != nil  
...
 
if i == 0  
panic("...")
 
if err := speaker.Write(buf[:i]); err != nil  
...
 
 

hz.tools/rfcap - byte serialization for IQ data The hz.tools/rfcap package is the reference implementation of the rfcap spec , and is how I store IQ captures locally, and how I send them across a byte boundary. The git repo can be found at github.com/hztools/go-rfcap, and is importable as hz.tools/rfcap. If you re interested in storing IQ in a way others can use, the better approach is to use SigMF rfcap exists for cases like using UNIX pipes to move IQ around, through APIs, or when I send IQ data through an OS socket, to ensure the sample format (and other metadata) is communicated with it. rfcap has a number of limitations, for instance, it can not express a change in frequency or sample rate during the capture, since the header is fixed at the beginning of the file.

% cat /boot/System.map-5.10.0-6-amd64 
ffffffffffffffff B The real System.map is in the linux-image-<version>-dbg package

--cursor-file=FILE      Show entries after cursor in FILE and update FILE
--facility=FACILITY...  Show entries with the specified facilities
--image=IMAGE           Operate on files in filesystem image
--namespace=NAMESPACE   Show journal data from specified namespace
--relinquish-var        Stop logging to disk, log to temporary file system
--smart-relinquish-var  Similar, but NOP if log directory is on root mount

clean UNIT...                       Clean runtime, cache, state, logs or configuration of unit
freeze PATTERN...                   Freeze execution of unit processes
thaw PATTERN...                     Resume execution of a frozen unit
log-level [LEVEL]                   Get/set logging threshold for manager
log-target [TARGET]                 Get/set logging target for manager
service-watchdogs [BOOL]            Get/set service watchdog state
--with-dependencies                 Show unit dependencies with 'status', 'cat', 'list-units', and 'list-unit-files'
 -T --show-transaction              When enqueuing a unit job, show full transaction
 --what=RESOURCES                   Which types of resources to remove
--boot-loader-menu=TIME             Boot into boot loader menu on next boot
--boot-loader-entry=NAME            Boot into a specific boot loader entry on next boot
--timestamp=FORMAT                  Change format of printed timestamps

• systemd-bless-boot.8
• systemd-boot-check-no-failures.8
• systemd-boot-system-token.service.8
• systemd-journald-varlink@.socket.8
• systemd.net-naming-scheme.7
• systemd-network-generator.service.8
• systemd-pstore.service.8
• systemd-udev-settle.service.8
• systemd-user-runtime-dir.5
• systemd-xdg-autostart-generator.8

• ProtectProc
• ProcSubset
• ProtectClock
• ProtectHostname
• ProtectKernelLogs
• RestrictSUIDSGID

systemd now defaults to the unified cgroup hierarchy (i.e. cgroupv2).
This change reflects the fact that cgroups2 support has matured
substantially in both systemd and in the kernel.
All major container tools nowadays should support cgroupv2.
If you run into problems with cgroupv2, you can switch back to the previous,
hybrid setup by adding systemd.unified_cgroup_hierarchy=false to the
kernel command line.
You can read more about the benefits of cgroupv2 at
https://www.kernel.org/doc/html/latest/admin-guide/cgroup-v2.html

• prometheus-elasticsearch-exporter (v1.1.0)
• prometheus-exporter-exporter (v0.4.0-1)
• prometheus-hacluster-exporter (v1.2.1-1)
• prometheus-homeplug-exporter (v0.3.0-2)
• prometheus-ipmi-exporter (v1.2.0)
• prometheus-libvirt-exporter (v0.2.0-1)
• prometheus-mqtt-exporter (v0.1.4-2)
• prometheus-nginx-vts-exporter (v0.10.3)
• prometheus-postfix-exporter (v0.2.0-3)
• prometheus-redis-exporter (v1.16.0-1)
• prometheus-smokeping-prober (v0.4.1-2)
• prometheus-tplink-plug-exporter (v0.2.0)

% apt-cache policy docker-ce
  docker-ce:
    Installed: 5:20.10.6~3-0~debian-buster
    Candidate: 5:20.10.6~3-0~debian-buster
    Version table:
   *** 5:20.10.6~3-0~debian-buster 100
          100 /var/lib/dpkg/status
       5:20.10.6~3-0~debian-bullseye 500
          500 https://download.docker.com/linux/debian bullseye/stable amd64 Packages

% export DEBUGINFOD_PROGRESS=1    # for optional download progress reporting
% export DEBUGINFOD_URLS="https://debuginfod.debian.net"

au CmdLineEnter : let s:incs = &incsearch   set noincsearch
au CmdLineLeave : let &incsearch = s:incs

• --atimes: preserve access (use) times
• --copy-as=USER: specify user (and optionally group) for the copy
• --crtimes/-N: for preserving the file s create time
• --max-alloc=SIZE: change a limit relating to memory allocation
• --mkpath:create the destination s path component
• --open-noatime: avoid changing the atime on opened files
• --stop-after=MINS: stop rsync after MINS minutes have elapsed
• --write-devices: write to devices as files (implies inplace)

• It now defers creation of ~/.ssh until there s something to write (e.g. the known_hosts file), so the good old admin trick to run ssh localhost and cancel immediately to create ~/.ssh with proper permissions no longer works
• v8.2 brought FIDO/U2F + FIDO2 resident keys Support
• The new include sshd_config keyword allows including additional configuration files via glob(3) patterns
• ssh now allows %n to be expanded in ProxyCommand strings.
• The scp and sftp command-lines now accept -J option as an alias to ProxyJump.
• The scp and sftp command-lines allow the -A flag to explicitly enable agent forwarding.

• apt: was updated from version 1.8 to 2.2, apt maintainer Julian Andres Klode wrote something about changes in apt 2.0 and changes in apt 2.2
• e2fsprogs: supports the new ext4 fast_commit feature
• exim: you might be interested being aware of the allow_insecure_tainted_data option, see #987133 + #987924 (Exim 4.94 includes a new tainting-feature)
• glusterfs: was updated from 5.5 to v9.1, there s no direct upgrade path (only v5 towards v8 would be supported), so online migration does not work
• mariadb: no longer runs as /usr/sbin/mysqld, but as /usr/sbin/mariadbd
• python: Python 2.7 (and a few core packages) is still present, but there won t be any security updates for Python 2, see wiki.debian.org/Python/2Removal
• qemu-system-x86: /proc/stat on host does not show guest cpu usage
• rsnapshot is gone (see #986709)

../../../hardwareintegration/client/brcm-egl/qwaylandbrcmeglwindow.cpp: In constructor  QtWaylandClient::QWaylandBrcmEglWindow::QWaylandBrcmEglWindow(QWindow*) :
../../../hardwareintegration/client/brcm-egl/qwaylandbrcmeglwindow.cpp:131:67: error: no matching function for call to  QtWaylandClient::QWaylandWindow::QWaylandWindow(QWindow*&) 
     , m_eventQueue(wl_display_create_queue(mDisplay->wl_display()))
                                                                   ^
In file included from ../../../../include/QtWaylandClient/5.15.0/QtWaylandClient/private/qwaylandwindow_p.h:1,
                 from ../../../hardwareintegration/client/brcm-egl/qwaylandbrcmeglwindow.h:43,
                 from ../../../hardwareintegration/client/brcm-egl/qwaylandbrcmeglwindow.cpp:40:
../../../../include/QtWaylandClient/5.15.0/QtWaylandClient/private/../../../../../src/client/qwaylandwindow_p.h:97:5: note: candidate:  QtWaylandClient::QWaylandWindow::QWaylandWindow(QWindow*, QtWayland
Client::QWaylandDisplay*) 
     QWaylandWindow(QWindow *window, QWaylandDisplay *display);
     ^~~~~~~~~~~~~~
../../../../include/QtWaylandClient/5.15.0/QtWaylandClient/private/../../../../../src/client/qwaylandwindow_p.h:97:5: note:   candidate expects 2 arguments, 1 provided
make[5]: Leaving directory '/home/build/armhf/qt-everywhere-src-5.15.0/qttools/src/qdoc'

Command: /usr/bin/python2 /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/3rdparty/chromium/build/config/linux/pkg-config.py -s /home/build/sysroot/ -a arm -p /usr/bin/arm-linux-gnueabihf-pkg-config --system_libdir lib nss -v -lssl3
Returned 1.
stderr:
Package nss was not found in the pkg-config search path.
Perhaps you should add the directory containing  nss.pc'
to the PKG_CONFIG_PATH environment variable
No package 'nss' found
Traceback (most recent call last):
  File "/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/3rdparty/chromium/build/config/linux/pkg-config.py", line 248, in <module>
    sys.exit(main())
  File "/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/3rdparty/chromium/build/config/linux/pkg-config.py", line 143, in main
    prefix = GetPkgConfigPrefixToStrip(options, args)
  File "/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/3rdparty/chromium/build/config/linux/pkg-config.py", line 82, in GetPkgConfigPrefixToStrip
    "--variable=prefix"] + args, env=os.environ).decode('utf-8')
  File "/usr/lib/python2.7/subprocess.py", line 223, in check_output
    raise CalledProcessError(retcode, cmd, output=output)
subprocess.CalledProcessError: Command '['/usr/bin/arm-linux-gnueabihf-pkg-config', '--variable=prefix', 'nss']' returned non-zero exit status 1
See //build/config/linux/nss/BUILD.gn:15:3: whence it was called.
  pkg_config("system_nss_no_ssl_config")  
  ^---------------------------------------
See //crypto/BUILD.gn:218:25: which caused the file to be included.
    public_configs += [ "//build/config/linux/nss:system_nss_no_ssl_config" ]
                        ^--------------------------------------------------
Project ERROR: GN run error!

--- pkg-config.py.orig  2020-07-16 11:46:21.005373002 +0200
+++ pkg-config.py   2020-07-16 11:46:02.605296967 +0200
@@ -61,6 +61,7 @@
   libdir = sysroot + '/usr/' + options.system_libdir + '/pkgconfig'
   libdir += ':' + sysroot + '/usr/share/pkgconfig'
+  libdir += ':' + sysroot + '/usr/lib/arm-linux-gnueabihf/pkgconfig'
   os.environ['PKG_CONFIG_LIBDIR'] = libdir
   return libdir

/usr/bin/arm-linux-gnueabihf-g++ -MMD -MF obj/skia/skcms/skcms.o.d -DUSE_UDEV -DUSE_AURA=1 -DUSE_NSS_CERTS=1 -DUSE_OZONE=1 -DOFFICIAL_BUILD -DTOOLKIT_QT -D_FILE_OFFSET_BITS=64 -D_LARGEFILE_SOURCE -D_LARGEFILE64_SOURCE -DNO_UNWIND_TABLES -D__STDC_CONSTANT_MACROS -D__STDC_FORMAT_MACROS -DCR_SYSROOT_HASH=76e6068f9f6954e2ab1ff98ce5fa236d3d85bcbd -DNDEBUG -DNVALGRIND -DDYNAMIC_ANNOTATIONS_ENABLED=0 -I../../3rdparty/chromium/third_party/skia/include/third_party/skcms -Igen -I../../3rdparty/chromium -w -std=c11 -mfp16-format=ieee -fno-strict-aliasing --param=ssp-buffer-size=4 -fstack-protector -fno-unwind-tables -fno-asynchronous-unwind-tables -fPIC -pipe -pthread -march=armv7-a -mfloat-abi=hard -mtune=generic-armv7-a -mfpu=vfpv3-d16 -mthumb -Wall -U_FORTIFY_SOURCE -D_FORTIFY_SOURCE=2 -Wno-psabi -Wno-unused-local-typedefs -Wno-maybe-uninitialized -Wno-deprecated-declarations -fno-delete-null-pointer-checks -Wno-comments -Wno-packed-not-aligned -Wno-dangling-else -Wno-missing-field-initializers -Wno-unused-parameter -O2 -fno-ident -fdata-sections -ffunction-sections -fno-omit-frame-pointer -g0 -fvisibility=hidden -std=gnu++14 -Wno-narrowing -Wno-class-memaccess -Wno-attributes -Wno-class-memaccess -Wno-subobject-linkage -Wno-invalid-offsetof -Wno-return-type -Wno-deprecated-copy -fno-exceptions -fno-rtti --sysroot=../../../../../../sysroot/ -fvisibility-inlines-hidden -c ../../3rdparty/chromium/third_party/skia/third_party/skcms/skcms.cc -o obj/skia/skcms/skcms.o
during RTL pass: expand
In file included from ../../3rdparty/chromium/third_party/skia/third_party/skcms/skcms.cc:2053:
../../3rdparty/chromium/third_party/skia/third_party/skcms/src/Transform_inl.h: In function  void baseline::exec_ops(const Op*, const void**, const char*, char*, int) :
../../3rdparty/chromium/third_party/skia/third_party/skcms/src/Transform_inl.h:766:13: internal compiler error: in convert_move, at expr.c:218
 static void exec_ops(const Op* ops, const void** args,
             ^~~~~~~~
Please submit a full bug report,
with preprocessed source if appropriate.
See <file:///usr/share/doc/gcc-8/README.Bugs> for instructions.

/usr/bin/arm-linux-gnueabihf-gcc -MMD -MF obj/third_party/ffmpeg/ffmpeg_internal/opus.o.d -DHAVE_AV_CONFIG_H -D_POSIX_C_SOURCE=200112 -D_XOPEN_SOURCE=600 -DPIC -DFFMPEG_CONFIGURATION=NULL -DCHROMIUM_NO_LOGGING -D_ISOC99_SOURCE -D_LARGEFILE_SOURCE -DUSE_UDEV -DUSE_AURA=1 -DUSE_NSS_CERTS=1 -DUSE_OZONE=1 -DOFFICIAL_BUILD -DTOOLKIT_QT -D_FILE_OFFSET_BITS=64 -D_LARGEFILE_SOURCE -D_LARGEFILE64_SOURCE -DNO_UNWIND_TABLES -DCR_SYSROOT_HASH=76e6068f9f6954e2ab1ff98ce5fa236d3d85bcbd -DNDEBUG -DNVALGRIND -DDYNAMIC_ANNOTATIONS_ENABLED=0 -DOPUS_FIXED_POINT -I../../3rdparty/chromium/third_party/ffmpeg/chromium/config/Chromium/linux/arm -I../../3rdparty/chromium/third_party/ffmpeg -I../../3rdparty/chromium/third_party/ffmpeg/compat/atomics/gcc -Igen -I../../3rdparty/chromium -I../../3rdparty/chromium/third_party/opus/src/include -fPIC -Wno-deprecated-declarations -fomit-frame-pointer -w -std=c99 -pthread -fno-math-errno -fno-signed-zeros -fno-tree-vectorize -fno-strict-aliasing --param=ssp-buffer-size=4 -fstack-protector -fno-unwind-tables -fno-asynchronous-unwind-tables -fPIC -pipe -pthread -march=armv7-a -mfloat-abi=hard -mtune=generic-armv7-a -mfpu=vfpv3-d16 -mthumb -g0 -fvisibility=hidden -Wno-psabi -Wno-unused-local-typedefs -Wno-maybe-uninitialized -Wno-deprecated-declarations -fno-delete-null-pointer-checks -Wno-comments -Wno-packed-not-aligned -Wno-dangling-else -Wno-missing-field-initializers -Wno-unused-parameter -O0 -fno-ident -fdata-sections -ffunction-sections -std=gnu11 --sysroot=../../../../../../sysroot/ -c ../../3rdparty/chromium/third_party/ffmpeg/libavcodec/opus.c -o obj/third_party/ffmpeg/ffmpeg_internal/opus.o
In file included from ../../3rdparty/chromium/third_party/ffmpeg/libavutil/intmath.h:30,
                 from ../../3rdparty/chromium/third_party/ffmpeg/libavutil/common.h:106,
                 from ../../3rdparty/chromium/third_party/ffmpeg/libavutil/avutil.h:296,
                 from ../../3rdparty/chromium/third_party/ffmpeg/libavutil/audio_fifo.h:30,
                 from ../../3rdparty/chromium/third_party/ffmpeg/libavcodec/opus.h:28,
                 from ../../3rdparty/chromium/third_party/ffmpeg/libavcodec/opus_celt.h:29,
                 from ../../3rdparty/chromium/third_party/ffmpeg/libavcodec/opus.c:32:
../../3rdparty/chromium/third_party/ffmpeg/libavcodec/opus.c: In function  ff_celt_quant_bands :
../../3rdparty/chromium/third_party/ffmpeg/libavutil/arm/intmath.h:77:5: error: impossible constraint in  asm 
     __asm__ ("usat %0, %2, %1" : "=r"(x) : "r"(a), "i"(p));
     ^~~~~~~

#pragma GCC push_options
#pragma GCC optimize ("O0")

#pragma GCC pop_options

/usr/bin/g++ -MMD -MF v8_snapshot/obj/v8/torque_base/csa-generator.o.d -DUSE_UDEV -DUSE_AURA=1 -DUSE_NSS_CERTS=1 -DUSE_OZONE=1 -DOFFICIAL_BUILD -DTOOLKIT_QT -D_FILE_OFFSET_BITS=64 -D_LARGEFILE_SOURCE -D_LARGEFILE64_SOURCE -DNO_UNWIND_TABLES -D__STDC_CONSTANT_MACROS -D__STDC_FORMAT_MACROS -DNDEBUG -DNVALGRIND -DDYNAMIC_ANNOTATIONS_ENABLED=0 -DV8_TYPED_ARRAY_MAX_SIZE_IN_HEAP=64 -DENABLE_MINOR_MC -DV8_INTL_SUPPORT -DV8_CONCURRENT_MARKING -DV8_ENABLE_LAZY_SOURCE_POSITIONS -DV8_EMBEDDED_BUILTINS -DV8_SHARED_RO_HEAP -DV8_WIN64_UNWINDING_INFO -DV8_ENABLE_REGEXP_INTERPRETER_THREADED_DISPATCH -DV8_31BIT_SMIS_ON_64BIT_ARCH -DV8_DEPRECATION_WARNINGS -DV8_TARGET_ARCH_ARM -DCAN_USE_ARMV7_INSTRUCTIONS -DCAN_USE_VFP3_INSTRUCTIONS -DUSE_EABI_HARDFLOAT=1 -DV8_HAVE_TARGET_OS -DV8_TARGET_OS_LINUX -DDISABLE_UNTRUSTED_CODE_MITIGATIONS -DV8_31BIT_SMIS_ON_64BIT_ARCH -DV8_DEPRECATION_WARNINGS -Iv8_snapshot/gen -I../../3rdparty/chromium -I../../3rdparty/chromium/v8 -Iv8_snapshot/gen/v8 -fno-strict-aliasing --param=ssp-buffer-size=4 -fstack-protector -fno-unwind-tables -fno-asynchronous-unwind-tables -fPIC -pipe -pthread -m32 -msse2 -mfpmath=sse -mmmx -Wall -U_FORTIFY_SOURCE -D_FORTIFY_SOURCE=2 -Wno-unused-local-typedefs -Wno-maybe-uninitialized -Wno-deprecated-declarations -fno-delete-null-pointer-checks -Wno-comments -Wno-packed-not-aligned -Wno-dangling-else -Wno-missing-field-initializers -Wno-unused-parameter -fno-omit-frame-pointer -g0 -fvisibility=hidden -Wno-strict-overflow -Wno-return-type -O3 -fno-ident -fdata-sections -ffunction-sections -std=gnu++14 -Wno-narrowing -Wno-class-memaccess -Wno-attributes -Wno-class-memaccess -Wno-subobject-linkage -Wno-invalid-offsetof -Wno-return-type -Wno-deprecated-copy -fvisibility-inlines-hidden -fexceptions -frtti -c ../../3rdparty/chromium/v8/src/torque/csa-generator.cc -o v8_snapshot/obj/v8/torque_base/csa-generator.o
In file included from ../../3rdparty/chromium/v8/src/torque/csa-generator.h:8,
                 from ../../3rdparty/chromium/v8/src/torque/csa-generator.cc:5:
/usr/include/c++/8/iostream:38:10: fatal error: bits/c++config.h: No such file or directory
 #include <bits/c++config.h>
          ^~~~~~~~~~~~~~~~~~
compilation terminated.

apt install lib32stdc++-8-dev
apt install libc6-dev-i386
dpkg --add-architecture i386
apt install linux-libc-dev:i386

/usr/bin/arm-linux-gnueabihf-g++ -MMD -MF obj/QtWebEngineCore/gl_ozone_glx_qt.o.d -DCHROMIUM_VERSION=\"80.0.3987.163\" -DUSE_UDEV -DUSE_AURA=1 -DUSE_NSS_CERTS=1 -DUSE_OZONE=1 -DOFFICIAL_BUILD -DTOOLKIT_QT -D_FILE_OFFSET_BITS=64 -D_LARGEFILE_SOURCE -D_LARGEFILE64_SOURCE -DNO_UNWIND_TABLES -D__STDC_CONSTANT_MACROS -D__STDC_FORMAT_MACROS -DCR_SYSROOT_HASH=76e6068f9f6954e2ab1ff98ce5fa236d3d85bcbd -DNDEBUG -DNVALGRIND -DDYNAMIC_ANNOTATIONS_ENABLED=0 -DQT_NO_LINKED_LIST -DQT_NO_KEYWORDS -DQT_USE_QSTRINGBUILDER -DQ_FORWARD_DECLARE_OBJC_CLASS=QT_FORWARD_DECLARE_CLASS -DQTWEBENGINECORE_VERSION_STR=\"5.15.0\" -DQTWEBENGINEPROCESS_NAME=\"QtWebEngineProcess\" -DBUILDING_CHROMIUM -DQTWEBENGINE_EMBEDDED_SWITCHES -DQT_NO_EXCEPTIONS -D_LARGEFILE64_SOURCE -D_LARGEFILE_SOURCE -DQT_NO_DEBUG -DQT_QUICK_LIB -DQT_GUI_LIB -DQT_QMLMODELS_LIB -DQT_WEBCHANNEL_LIB -DQT_QML_LIB -DQT_NETWORK_LIB -DQT_POSITIONING_LIB -DQT_CORE_LIB -DQT_WEBENGINECOREHEADERS_LIB -DVK_NO_PROTOTYPES -DGL_GLEXT_PROTOTYPES -DUSE_GLX -DUSE_EGL -DGOOGLE_PROTOBUF_NO_RTTI -DGOOGLE_PROTOBUF_NO_STATIC_INITIALIZER -DHAVE_PTHREAD -DU_USING_ICU_NAMESPACE=0 -DU_ENABLE_DYLOAD=0 -DUSE_CHROMIUM_ICU=1 -DU_STATIC_IMPLEMENTATION -DICU_UTIL_DATA_IMPL=ICU_UTIL_DATA_FILE -DUCHAR_TYPE=uint16_t -DWEBRTC_NON_STATIC_TRACE_EVENT_HANDLERS=0 -DWEBRTC_CHROMIUM_BUILD -DWEBRTC_POSIX -DWEBRTC_LINUX -DABSL_ALLOCATOR_NOTHROW=1 -DWEBRTC_USE_BUILTIN_ISAC_FIX=1 -DWEBRTC_USE_BUILTIN_ISAC_FLOAT=0 -DHAVE_SCTP -DNO_MAIN_THREAD_WRAPPING -DSK_HAS_PNG_LIBRARY -DSK_HAS_WEBP_LIBRARY -DSK_USER_CONFIG_HEADER=\"../../skia/config/SkUserConfig.h\" -DSK_GL -DSK_HAS_JPEG_LIBRARY -DSK_USE_LIBGIFCODEC -DSK_VULKAN_HEADER=\"../../skia/config/SkVulkanConfig.h\" -DSK_VULKAN=1 -DSK_SUPPORT_GPU=1 -DSK_GPU_WORKAROUNDS_HEADER=\"gpu/config/gpu_driver_bug_workaround_autogen.h\" -DVK_NO_PROTOTYPES -DLEVELDB_PLATFORM_CHROMIUM=1 -DLEVELDB_PLATFORM_CHROMIUM=1 -DV8_31BIT_SMIS_ON_64BIT_ARCH -DV8_DEPRECATION_WARNINGS -I../../3rdparty/chromium/skia/config -I../../3rdparty/chromium/third_party -I../../3rdparty/chromium/third_party/boringssl/src/include -I../../3rdparty/chromium/third_party/skia/include/core -Igen -I../../3rdparty/chromium -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/api -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQuick/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQuick/5.15.0/QtQuick -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtGui/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtGui/5.15.0/QtGui -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQuick -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtGui -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQmlModels/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQmlModels/5.15.0/QtQmlModels -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQml/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQml/5.15.0/QtQml -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtCore/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtCore/5.15.0/QtCore -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQmlModels -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebchannel/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebchannel/include/QtWebChannel -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQml -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtNetwork -I/home/build/armhf/qt-everywhere-src-5.15.0/qtlocation/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtlocation/include/QtPositioning -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtCore -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include/QtWebEngineCore -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include/QtWebEngineCore/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include/QtWebEngineCore/5.15.0/QtWebEngineCore -I.moc -I/home/build/sysroot/opt/vc/include -I/home/build/sysroot/opt/vc/include/interface/vcos/pthreads -I/home/build/sysroot/opt/vc/include/interface/vmcs_host/linux -Igen/.moc -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/mkspecs/devices/linux-rasp-pi2-g++ -Igen -Igen -I../../3rdparty/chromium/third_party/libyuv/include -Igen -I../../3rdparty/chromium/third_party/jsoncpp/source/include -I../../3rdparty/chromium/third_party/jsoncpp/generated -Igen -Igen -I../../3rdparty/chromium/third_party/khronos -I../../3rdparty/chromium/gpu -I../../3rdparty/chromium/third_party/vulkan/include -I../../3rdparty/chromium/third_party/perfetto/include -Igen/third_party/perfetto/build_config -Igen -Igen -Igen/third_party/dawn/src/include -I../../3rdparty/chromium/third_party/dawn/src/include -Igen -I../../3rdparty/chromium/third_party/boringssl/src/include -I../../3rdparty/chromium/third_party/protobuf/src -Igen/protoc_out -I../../3rdparty/chromium/third_party/protobuf/src -I../../3rdparty/chromium/third_party/ced/src -I../../3rdparty/chromium/third_party/icu/source/common -I../../3rdparty/chromium/third_party/icu/source/i18n -I../../3rdparty/chromium/third_party/webrtc_overrides -I../../3rdparty/chromium/third_party/webrtc -Igen/third_party/webrtc -I../../3rdparty/chromium/third_party/abseil-cpp -I../../3rdparty/chromium/third_party/skia -I../../3rdparty/chromium/third_party/libgifcodec -I../../3rdparty/chromium/third_party/vulkan/include -I../../3rdparty/chromium/third_party/skia/third_party/vulkanmemoryallocator -I../../3rdparty/chromium/third_party/vulkan/include -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -I../../3rdparty/chromium/third_party/crashpad/crashpad -I../../3rdparty/chromium/third_party/crashpad/crashpad/compat/non_mac -I../../3rdparty/chromium/third_party/crashpad/crashpad/compat/linux -I../../3rdparty/chromium/third_party/crashpad/crashpad/compat/non_win -I../../3rdparty/chromium/third_party/libwebm/source -I../../3rdparty/chromium/third_party/leveldatabase -I../../3rdparty/chromium/third_party/leveldatabase/src -I../../3rdparty/chromium/third_party/leveldatabase/src/include -I../../3rdparty/chromium/v8/include -Igen/v8/include -I../../3rdparty/chromium/third_party/mesa_headers -fno-strict-aliasing --param=ssp-buffer-size=4 -fstack-protector -fno-unwind-tables -fno-asynchronous-unwind-tables -fPIC -pipe -pthread -march=armv7-a -mfloat-abi=hard -mtune=generic-armv7-a -mfpu=vfpv3-d16 -mthumb -Wall -U_FORTIFY_SOURCE -D_FORTIFY_SOURCE=2 -Wno-psabi -Wno-unused-local-typedefs -Wno-maybe-uninitialized -Wno-deprecated-declarations -fno-delete-null-pointer-checks -Wno-comments -Wno-packed-not-aligned -Wno-dangling-else -Wno-missing-field-initializers -Wno-unused-parameter -O2 -fno-ident -fdata-sections -ffunction-sections -fno-omit-frame-pointer -g0 -fvisibility=hidden -g -O2 -fdebug-prefix-map=/home/build/armhf/qt-everywhere-src-5.15.0=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -O2 -fno-exceptions -Wall -Wextra -D_REENTRANT -I/home/build/sysroot/usr/include/nss -I/home/build/sysroot/usr/include/nspr -std=gnu++14 -Wno-narrowing -Wno-class-memaccess -Wno-attributes -Wno-class-memaccess -Wno-subobject-linkage -Wno-invalid-offsetof -Wno-return-type -Wno-deprecated-copy -fno-exceptions -fno-rtti --sysroot=../../../../../../sysroot/ -fvisibility-inlines-hidden -g -O2 -fdebug-prefix-map=/home/build/armhf/qt-everywhere-src-5.15.0=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -O2 -std=gnu++1y -fno-exceptions -Wall -Wextra -D_REENTRANT -Wno-unused-parameter -Wno-unused-variable -Wno-deprecated-declarations -c /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/ozone/gl_ozone_glx_qt.cpp -o obj/QtWebEngineCore/gl_ozone_glx_qt.o
In file included from ../../3rdparty/chromium/ui/gl/gl_bindings.h:497,
                 from ../../3rdparty/chromium/ui/gl/gl_gl_api_implementation.h:12,
                 from /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/ozone/gl_ozone_glx_qt.cpp:49:
../../3rdparty/chromium/ui/gl/gl_bindings_autogen_egl.h:227:5: error:  EGLSetBlobFuncANDROID  has not been declared
     EGLSetBlobFuncANDROID set,
     ^~~~~~~~~~~~~~~~~~~~~
../../3rdparty/chromium/ui/gl/gl_bindings_autogen_egl.h:228:5: error:  EGLGetBlobFuncANDROID  has not been declared
     EGLGetBlobFuncANDROID get);
     ^~~~~~~~~~~~~~~~~~~~~
../../3rdparty/chromium/ui/gl/gl_bindings_autogen_egl.h:571:46: error:  EGLSetBlobFuncANDROID  has not been declared
                                              EGLSetBlobFuncANDROID set,
                                              ^~~~~~~~~~~~~~~~~~~~~
../../3rdparty/chromium/ui/gl/gl_bindings_autogen_egl.h:572:46: error:  EGLGetBlobFuncANDROID  has not been declared
                                              EGLGetBlobFuncANDROID get) = 0;
                                              ^~~~~~~~~~~~~~~~~~~~~
cc1plus: warning: unrecognized command line option  -Wno-deprecated-copy 

/usr/bin/arm-linux-gnueabihf-g++ -MMD -MF obj/QtWebEngineCore/display_gl_output_surface.o.d -DCHROMIUM_VERSION=\"80.0.3987.163\" -DUSE_UDEV -DUSE_AURA=1 -DUSE_NSS_CERTS=1 -DUSE_OZONE=1 -DOFFICIAL_BUILD -DTOOLKIT_QT -D_FILE_OFFSET_BITS=64 -D_LARGEFILE_SOURCE -D_LARGEFILE64_SOURCE -DNO_UNWIND_TABLES -D__STDC_CONSTANT_MACROS -D__STDC_FORMAT_MACROS -DCR_SYSROOT_HASH=76e6068f9f6954e2ab1ff98ce5fa236d3d85bcbd -DNDEBUG -DNVALGRIND -DDYNAMIC_ANNOTATIONS_ENABLED=0 -DQT_NO_LINKED_LIST -DQT_NO_KEYWORDS -DQT_USE_QSTRINGBUILDER -DQ_FORWARD_DECLARE_OBJC_CLASS=QT_FORWARD_DECLARE_CLASS -DQTWEBENGINECORE_VERSION_STR=\"5.15.0\" -DQTWEBENGINEPROCESS_NAME=\"QtWebEngineProcess\" -DBUILDING_CHROMIUM -DQTWEBENGINE_EMBEDDED_SWITCHES -DQT_NO_EXCEPTIONS -D_LARGEFILE64_SOURCE -D_LARGEFILE_SOURCE -DQT_NO_DEBUG -DQT_QUICK_LIB -DQT_GUI_LIB -DQT_QMLMODELS_LIB -DQT_WEBCHANNEL_LIB -DQT_QML_LIB -DQT_NETWORK_LIB -DQT_POSITIONING_LIB -DQT_CORE_LIB -DQT_WEBENGINECOREHEADERS_LIB -DVK_NO_PROTOTYPES -DGL_GLEXT_PROTOTYPES -DUSE_GLX -DUSE_EGL -DGOOGLE_PROTOBUF_NO_RTTI -DGOOGLE_PROTOBUF_NO_STATIC_INITIALIZER -DHAVE_PTHREAD -DU_USING_ICU_NAMESPACE=0 -DU_ENABLE_DYLOAD=0 -DUSE_CHROMIUM_ICU=1 -DU_STATIC_IMPLEMENTATION -DICU_UTIL_DATA_IMPL=ICU_UTIL_DATA_FILE -DUCHAR_TYPE=uint16_t -DWEBRTC_NON_STATIC_TRACE_EVENT_HANDLERS=0 -DWEBRTC_CHROMIUM_BUILD -DWEBRTC_POSIX -DWEBRTC_LINUX -DABSL_ALLOCATOR_NOTHROW=1 -DWEBRTC_USE_BUILTIN_ISAC_FIX=1 -DWEBRTC_USE_BUILTIN_ISAC_FLOAT=0 -DHAVE_SCTP -DNO_MAIN_THREAD_WRAPPING -DSK_HAS_PNG_LIBRARY -DSK_HAS_WEBP_LIBRARY -DSK_USER_CONFIG_HEADER=\"../../skia/config/SkUserConfig.h\" -DSK_GL -DSK_HAS_JPEG_LIBRARY -DSK_USE_LIBGIFCODEC -DSK_VULKAN_HEADER=\"../../skia/config/SkVulkanConfig.h\" -DSK_VULKAN=1 -DSK_SUPPORT_GPU=1 -DSK_GPU_WORKAROUNDS_HEADER=\"gpu/config/gpu_driver_bug_workaround_autogen.h\" -DVK_NO_PROTOTYPES -DLEVELDB_PLATFORM_CHROMIUM=1 -DLEVELDB_PLATFORM_CHROMIUM=1 -DV8_31BIT_SMIS_ON_64BIT_ARCH -DV8_DEPRECATION_WARNINGS -I../../3rdparty/chromium/skia/config -I../../3rdparty/chromium/third_party -I../../3rdparty/chromium/third_party/boringssl/src/include -I../../3rdparty/chromium/third_party/skia/include/core -Igen -I../../3rdparty/chromium -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/api -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQuick/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQuick/5.15.0/QtQuick -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtGui/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtGui/5.15.0/QtGui -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQuick -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtGui -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQmlModels/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQmlModels/5.15.0/QtQmlModels -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQml/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQml/5.15.0/QtQml -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtCore/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtCore/5.15.0/QtCore -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQmlModels -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebchannel/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebchannel/include/QtWebChannel -I/home/build/armhf/qt-everywhere-src-5.15.0/qtdeclarative/include/QtQml -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtNetwork -I/home/build/armhf/qt-everywhere-src-5.15.0/qtlocation/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtlocation/include/QtPositioning -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/include/QtCore -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include/QtWebEngineCore -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include/QtWebEngineCore/5.15.0 -I/home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/include/QtWebEngineCore/5.15.0/QtWebEngineCore -I.moc -I/home/build/sysroot/opt/vc/include -I/home/build/sysroot/opt/vc/include/interface/vcos/pthreads -I/home/build/sysroot/opt/vc/include/interface/vmcs_host/linux -Igen/.moc -I/home/build/armhf/qt-everywhere-src-5.15.0/qtbase/mkspecs/devices/linux-rasp-pi2-g++ -Igen -Igen -I../../3rdparty/chromium/third_party/libyuv/include -Igen -I../../3rdparty/chromium/third_party/jsoncpp/source/include -I../../3rdparty/chromium/third_party/jsoncpp/generated -Igen -Igen -I../../3rdparty/chromium/third_party/khronos -I../../3rdparty/chromium/gpu -I../../3rdparty/chromium/third_party/vulkan/include -I../../3rdparty/chromium/third_party/perfetto/include -Igen/third_party/perfetto/build_config -Igen -Igen -Igen/third_party/dawn/src/include -I../../3rdparty/chromium/third_party/dawn/src/include -Igen -I../../3rdparty/chromium/third_party/boringssl/src/include -I../../3rdparty/chromium/third_party/protobuf/src -Igen/protoc_out -I../../3rdparty/chromium/third_party/protobuf/src -I../../3rdparty/chromium/third_party/ced/src -I../../3rdparty/chromium/third_party/icu/source/common -I../../3rdparty/chromium/third_party/icu/source/i18n -I../../3rdparty/chromium/third_party/webrtc_overrides -I../../3rdparty/chromium/third_party/webrtc -Igen/third_party/webrtc -I../../3rdparty/chromium/third_party/abseil-cpp -I../../3rdparty/chromium/third_party/skia -I../../3rdparty/chromium/third_party/libgifcodec -I../../3rdparty/chromium/third_party/vulkan/include -I../../3rdparty/chromium/third_party/skia/third_party/vulkanmemoryallocator -I../../3rdparty/chromium/third_party/vulkan/include -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -Igen/third_party/perfetto -I../../3rdparty/chromium/third_party/crashpad/crashpad -I../../3rdparty/chromium/third_party/crashpad/crashpad/compat/non_mac -I../../3rdparty/chromium/third_party/crashpad/crashpad/compat/linux -I../../3rdparty/chromium/third_party/crashpad/crashpad/compat/non_win -I../../3rdparty/chromium/third_party/libwebm/source -I../../3rdparty/chromium/third_party/leveldatabase -I../../3rdparty/chromium/third_party/leveldatabase/src -I../../3rdparty/chromium/third_party/leveldatabase/src/include -I../../3rdparty/chromium/v8/include -Igen/v8/include -I../../3rdparty/chromium/third_party/mesa_headers -fno-strict-aliasing --param=ssp-buffer-size=4 -fstack-protector -fno-unwind-tables -fno-asynchronous-unwind-tables -fPIC -pipe -pthread -march=armv7-a -mfloat-abi=hard -mtune=generic-armv7-a -mfpu=vfpv3-d16 -mthumb -Wall -U_FORTIFY_SOURCE -D_FORTIFY_SOURCE=2 -Wno-psabi -Wno-unused-local-typedefs -Wno-maybe-uninitialized -Wno-deprecated-declarations -fno-delete-null-pointer-checks -Wno-comments -Wno-packed-not-aligned -Wno-dangling-else -Wno-missing-field-initializers -Wno-unused-parameter -O2 -fno-ident -fdata-sections -ffunction-sections -fno-omit-frame-pointer -g0 -fvisibility=hidden -g -O2 -fdebug-prefix-map=/home/build/armhf/qt-everywhere-src-5.15.0=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -O2 -fno-exceptions -Wall -Wextra -D_REENTRANT -I/home/build/sysroot/usr/include/nss -I/home/build/sysroot/usr/include/nspr -std=gnu++14 -Wno-narrowing -Wno-class-memaccess -Wno-attributes -Wno-class-memaccess -Wno-subobject-linkage -Wno-invalid-offsetof -Wno-return-type -Wno-deprecated-copy -fno-exceptions -fno-rtti --sysroot=../../../../../../sysroot/ -fvisibility-inlines-hidden -g -O2 -fdebug-prefix-map=/home/build/armhf/qt-everywhere-src-5.15.0=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -O2 -std=gnu++1y -fno-exceptions -Wall -Wextra -D_REENTRANT -Wno-unused-parameter -Wno-unused-variable -Wno-deprecated-declarations -c /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/compositor/display_gl_output_surface.cpp -o obj/QtWebEngineCore/display_gl_output_surface.o
In file included from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_interface.h:8,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/client_transfer_cache.h:15,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_implementation.h:28,
                 from /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/compositor/display_gl_output_surface.cpp:47:
/home/build/sysroot/opt/vc/include/GLES2/gl2.h:78: warning: "GL_FALSE" redefined
 #define GL_FALSE                          (GLboolean)0
In file included from ../../3rdparty/chromium/gpu/command_buffer/client/client_context_state.h:10,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_implementation.h:27,
                 from /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/compositor/display_gl_output_surface.cpp:47:
../../3rdparty/chromium/third_party/khronos/GLES3/gl3.h:85: note: this is the location of the previous definition
 #define GL_FALSE                          0
In file included from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_interface.h:8,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/client_transfer_cache.h:15,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_implementation.h:28,
                 from /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/compositor/display_gl_output_surface.cpp:47:
/home/build/sysroot/opt/vc/include/GLES2/gl2.h:79: warning: "GL_TRUE" redefined
 #define GL_TRUE                           (GLboolean)1
In file included from ../../3rdparty/chromium/gpu/command_buffer/client/client_context_state.h:10,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_implementation.h:27,
                 from /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/compositor/display_gl_output_surface.cpp:47:
../../3rdparty/chromium/third_party/khronos/GLES3/gl3.h:86: note: this is the location of the previous definition
 #define GL_TRUE                           1
In file included from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_interface.h:8,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/client_transfer_cache.h:15,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_implementation.h:28,
                 from /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/compositor/display_gl_output_surface.cpp:47:
/home/build/sysroot/opt/vc/include/GLES2/gl2.h:600:37: error: conflicting declaration of C function  void glShaderSource(GLuint, GLsizei, const GLchar**, const GLint*) 
 GL_APICALL void         GL_APIENTRY glShaderSource (GLuint shader, GLsizei count, const GLchar** string, const GLint* length);
                                     ^~~~~~~~~~~~~~
In file included from ../../3rdparty/chromium/gpu/command_buffer/client/client_context_state.h:10,
                 from ../../3rdparty/chromium/gpu/command_buffer/client/gles2_implementation.h:27,
                 from /home/build/armhf/qt-everywhere-src-5.15.0/qtwebengine/src/core/compositor/display_gl_output_surface.cpp:47:
../../3rdparty/chromium/third_party/khronos/GLES3/gl3.h:624:29: note: previous declaration  void glShaderSource(GLuint, GLsizei, const GLchar* const*, const GLint*) 
 GL_APICALL void GL_APIENTRY glShaderSource (GLuint shader, GLsizei count, const GLchar *const*string, const GLint *length);
                             ^~~~~~~~~~~~~~
cc1plus: warning: unrecognized command line option  -Wno-deprecated-copy 

Long story short, a fast solution for the issue with EGLSetBlobFuncANDROID is to remove libraspberrypi-dev from your sysroot and do a full rebuild. There will be some changes to the configure results, so please review them - if they are relevant for you - before proceeding with your work.

Outreachy is an organization that provides three-month internships for people from groups traditionally underrepresented in tech. Interns work remotely with mentors from Free and Open Source Software (FOSS) communities on projects ranging from programming, user experience, documentation, illustration and graphical design, to data science.

HOL is a logic of total functions If I have a Isabelle function f :: a b between two types a and b (the function arrow in Isabelle is , not ), then by definition of what it means to be a function in HOL whenever I have a value x :: a, then the expression f x (i.e. f applied to x) is a value of type b. Therefore, and without exception, every Isabelle function is total. In particular, it cannot be that f x does not exist for some x :: a. This is a first difference from Haskell, which does have partial functions like

spin :: Maybe Integer -> Bool
spin (Just n) = spin (Just (n+1))

Here, neither the expression spin Nothing nor the expression spin (Just 42) produce a value of type Bool: The former raises an exception ( incomplete pattern match ), the latter does not terminate. Confusingly, though, both expressions have type Bool. Because every function is total, this confusion cannot arise in Isabelle: If an expression e has type t, then it is a value of type t. This trait is shared with other total systems, including Coq. Did you notice the emphasis I put on the word is here, and how I deliberately did not write evaluates to or returns ? This is because of another big source for confusion:

Isabelle functions do not compute We (i.e., functional programmers) stole the word function from mathematics and repurposed it². But the word function , in the context of Isabelle, refers to the mathematical concept of a function, and it helps to keep that in mind. What is the difference?

• A function a b in functional programming is an algorithm that, given a value of type a, calculates (returns, evaluates to) a value of type b.
• A function a b in math (or Isabelle) associates with each value of type a a value of type b.

For example, the following is a perfectly valid function definition in math (and HOL), but could not be a function in the programming sense:

definition foo :: "(nat   real)   real" where
  "foo seq = (if convergent seq then lim seq else 0)"

This assigns a real number to every sequence, but it does not compute it in any useful sense. From this it follows that

Isabelle functions are specified, not defined Consider this function definition:

fun plus :: "nat   nat   nat"  where
   "plus 0       m = m"
   "plus (Suc n) m = Suc (plus n m)"

To a functional programmer, this reads

plus is a function that analyses its first argument. If that is 0, then it returns the second argument. Otherwise, it calls itself with the predecessor of the first argument and increases the result by one.

which is clearly a description of a computation. But to Isabelle, the above reads

plus is a binary function on natural numbers, and it satisfies the following two equations:

And in fact, it is not so much Isabelle that reads it this way, but rather the fun command, which is external to the Isabelle logic. The fun command analyses the given equations, constructs a non-recursive definition of plus under the hood, passes that to Isabelle and then proves that the given equations hold for plus. One interesting consequence of this is that different specifications can lead to the same functions. In fact, if we would define plus' by recursing on the second argument, we d obtain the the same function (i.e. plus = plus' is a theorem, and there would be no way of telling the two apart).

Termination is a property of specifications, not functions Because a function does not evaluate, it does not make sense to ask if it terminates. The question of termination arises before the function is defined: The fun command can only construct plus in a way that the equations hold if it passes a termination check very much like Fixpoint in Coq. But while the termination check of Fixpoint in Coq is a deep part of the basic logic, in Isabelle it is simply something that this particular command requires for its internal machinery to go through. At no point does a termination proof of the function exist as a theorem inside the logic. And other commands may have other means of defining a function that do not even require such a termination argument! For example, a function specification that is tail-recursive can be turned in to a function, even without a termination proof: The following definition describes a higher-order function that iterates its first argument f on the second argument x until it finds a fixpoint. It is completely polymorphic (the single quote in 'a indicates that this is a type variable):

partial_function (tailrec)
  fixpoint :: "('a   'a)   'a   'a"
where
  "fixpoint f x = (if f x = x then x else fixpoint f (f x))"

We can work with this definition just fine. For example, if we instantiate f with ( x. x-1), we can prove that it will always return 0:

lemma "fixpoint (  n . n - 1) (n::nat) = 0"
  by (induction n) (auto simp add: fixpoint.simps)

Similarly, if we have a function that works within the option monad (i.e. Maybe in Haskell), its specification can always be turned into a function without an explicit termination proof here one that calculates the Collatz sequence:

partial_function (option) collatz :: "nat   nat list option"
 where "collatz n =
        (if n = 1 then Some [n]
         else if even n
           then do   ns <- collatz (n div 2);    Some (n # ns)  
           else do   ns <- collatz (3 * n + 1);  Some (n # ns) )"

Note that lists in Isabelle are finite (like in Coq, unlike in Haskell), so this function returns a list only if the collatz sequence eventually reaches 1. I expect these definitions to make a Coq user very uneasy. How can fixpoint be a total function? What is fixpoint ( n. n+1)? What if we run collatz n for a n where the Collatz sequence does not reach 1?³ We will come back to that question after a little detour

HOL is a logic of non-empty types Another big difference between Isabelle and Coq is that in Isabelle, every type is inhabited. Just like the totality of functions, this is a very fundamental fact about what HOL defines to be a type. Isabelle gets away with that design because in Isabelle, we do not use types for propositions (like we do in Coq), so we do not need empty types to denote false propositions. This design has an important consequence: It allows the existence of a polymorphic expression that inhabits any type, namely

undefined :: 'a

The naming of this term alone has caused a great deal of confusion for Isabelle beginners, or in communication with users of different systems, so I implore you to not read too much into the name. In fact, you will have a better time if you think of it as arbitrary or, even better, unknown. Since undefined can be instantiated at any type, we can instantiate it for example at bool, and we can observe an important fact: undefined is not an extra value besides the usual ones . It is simply some value of that type, which is demonstrated in the following lemma:

lemma "undefined = True   undefined = False" by auto

In fact, if the type has only one value (such as the unit type), then we know the value of undefined for sure:

lemma "undefined = ()" by auto

It is very handy to be able to produce an expression of any type, as we will see as follows

Partial functions are just underspecified functions For example, it allows us to translate incomplete function specifications. Consider this definition, Isabelle s equivalent of Haskell s partial fromJust function:

fun fromSome :: "'a option   'a" where
  "fromSome (Some x) = x"

This definition is accepted by fun (albeit with a warning), and the generated function fromSome behaves exactly as specified: when applied to Some x, it is x. The term fromSome None is also a value of type 'a, we just do not know which one it is, as the specification does not address that. So fromSome None behaves just like undefined above, i.e. we can prove

lemma "fromSome None = False   fromSome None = True" by auto

Here is a small exercise for you: Can you come up with an explanation for the following lemma:

fun constOrId :: "bool   bool" where
  "constOrId True = True"
lemma "constOrId = ( _.True)   constOrId = ( x. x)"
  by (metis (full_types) constOrId.simps)

Overall, this behavior makes sense if we remember that function definitions in Isabelle are not really definitions, but rather specifications. And a partial function definition is simply a underspecification. The resulting function is simply any function hat fulfills the specification, and the two lemmas above underline that observation.

Nonterminating functions are also just underspecified Let us return to the puzzle posed by fixpoint above. Clearly, the function seen as a functional program is not total: When passed the argument ( n. n + 1) or ( b. b) it will loop forever trying to find a fixed point. But Isabelle functions are not functional programs, and the definitions are just specifications. What does the specification say about the case when f has no fixed-point? It states that the equation fixpoint f x = fixpoint f (f x) holds. And this equation has a solution, for example fixpoint f _ = undefined. Or more concretely: The specification of the fixpoint function states that fixpoint ( b. b) True = fixpoint ( b. b) False has to hold, but it does not specify which particular value (True or False) it should denote any is fine.

Not all function specifications are ok At this point you might wonder: Can I just specify any equations for a function f and get a function out of that? But rest assured: That is not the case. For example, no Isabelle command allows you define a function bogus :: () nat with the equation bogus () = Suc (bogus ()), because this equation does not have a solution. We can actually prove that such a function cannot exist:

lemma no_bogus: "  bogus. bogus () = Suc (bogus ())" by simp

(Of course, not_bogus () = not_bogus () is just fine )

You cannot reason about partiality in Isabelle We have seen that there are many ways to define functions that one might consider partial . Given a function, can we prove that it is not partial in that sense? Unfortunately, but unavoidably, no: Since undefined is not a separate, recognizable value, but rather simply an unknown one, there is no way of stating that A function result is not specified . Here is an example that demonstrates this: Two partial functions (one with not all cases specified, the other one with a self-referential specification) are indistinguishable from the total variant:

fun partial1 :: "bool   unit" where
  "partial1 True = ()"
partial_function (tailrec) partial2 :: "bool   unit" where
  "partial2 b = partial2 b"
fun total :: "bool   unit" where
  "total True = ()"
  "total False = ()"
lemma "partial1 = total   partial2 = total" by auto

If you really do want to reason about partiality of functional programs in Isabelle, you should consider implementing them not as plain HOL functions, but rather use HOLCF, where you can give equational specifications of functional programs and obtain continuous functions between domains. In that setting, () and partial2 = total. We have done that to verify some of HLint s equations.

You can still compute with Isabelle functions I hope by this point, I have not scared away anyone who wants to use Isabelle for functional programming, and in fact, you can use it for that. If the equations that you pass to fun are a reasonable definition for a function (in the programming sense), then these equations, used as rewriting rules, will allow you to compute that function quite like you would in Coq or Haskell. Moreover, Isabelle supports code extraction: You can take the equations of your Isabelle functions and have them expored into Ocaml, Haskell, Scala or Standard ML. See Concon for a conference management system with confidentially verified in Isabelle. While these usually are the equations you defined the function with, they don't have to: You can declare other proved equations to be used for code extraction, e.g. to refine your elegant definitions to performant ones. Like with code extraction from Coq to, say, Haskell, the adequacy of the translations rests on a moral reasoning foundation. Unlike extraction from Coq, where you have an (unformalized) guarantee that the resulting Haskell code is terminating, you do not get that guarantee from Isabelle. Conversely, this allows you do reason about and extract non-terminating programs, like fixpoint, which is not possible in Coq. There is currently ongoing work about verified code generation, where the code equations are reflected into a deep embedding of HOL in Isabelle that would allow explicit termination proofs.

Conclusion We have seen how in Isabelle, every function is total. Function declarations have equations, but these do not define the function in an computational sense, but rather specify them. Because in HOL, there are no empty types, many specifications that appear partial (incomplete patterns, non-terminating recursion) have solutions in the space of total functions. Partiality in the specification is no longer visible in the final product.

PS: Axiom undefined in Coq This section is speculative, and an invitation for discussion. Coq already distinguishes between types used in programs (Set) and types used in proofs Prop. Could Coq ensure that every t : Set is non-empty? I imagine this would require additional checks in the Inductive command, similar to the checks that the Isabelle command datatype has to perform⁴, and it would disallow Empty_set. If so, then it would be sound to add the following axiom

Axiom undefined : forall (a : Set), a.

wouldn't it? This axiom does not have any computational meaning, but that seems to be ok for optional Coq axioms, like classical reasoning or function extensionality. With this in place, how much of what I describe above about function definitions in Isabelle could now be done soundly in Coq. Certainly pattern matches would not have to be complete and could sport an implicit case _ undefined. Would it help with non-obviously terminating functions? Would it allow a Coq command Tailrecursive that accepts any tailrecursive function without a termination check?

---

1. Isabelle is a metalogical framework, and other logics, e.g. Isabelle/ZF, behave differently. For the purpose of this blog post, I always mean Isabelle/HOL.
2. Isabelle is a metalogical framework, and other logics, e.g. Isabelle/ZF, behave differently. For the purpose of this blog post, I always mean Isabelle/HOL.
3. Let me know if you find such an n. Besides n = 0.
4. Like fun, the constructions by datatype are not part of the logic, but create a type definition from more primitive notions that is isomorphic to the specified data type.

1. Cheap but sturdy. Total cost will be under $2500. It would probably cost at least twice as much to get a professional install, and the pros might not even want to do such a small install.
2. Learn the roof mount system. I want to be able to add more panels, remove panels when working on the roof, and understand everything.
3. Make every day a sunny day. With my current solar panels, I get around 10x as much power on a sunny day as a cloudy day, and I have plenty of power on sunny days. So 10x the PV capacity should be a good amount of power all the time.

• local delivery (RTN_LOCAL),
• forwarding to a supplied next hop (RTN_UNICAST),
• silent discard (RTN_BLACKHOLE).

Route lookup in a trie Looking up a route in a routing table is to find the most specific prefix matching the requested destination. Let s assume the following routing table:

$ ip route show scope global table 100
default via 203.0.113.5 dev out2
192.0.2.0/25
        nexthop via 203.0.113.7  dev out3 weight 1
        nexthop via 203.0.113.9  dev out4 weight 1
192.0.2.47 via 203.0.113.3 dev out1
192.0.2.48 via 203.0.113.3 dev out1
192.0.2.49 via 203.0.113.3 dev out1
192.0.2.50 via 203.0.113.3 dev out1

Here are some examples of lookups and the associated results:

Destination IP	Next hop
192.0.2.49	203.0.113.3 via out1
192.0.2.50	203.0.113.3 via out1
192.0.2.51	203.0.113.7 via out3 or 203.0.113.9 via out4 (ECMP)
192.0.2.200	203.0.113.5 via out2

A common structure for route lookup is the trie, a tree structure where each node has its parent as prefix.

Lookup with a simple trie The following trie encodes the previous routing table: For each node, the prefix is known by its path from the root node and the prefix length is the current depth. A lookup in such a trie is quite simple: at each step, fetch the n^th bit of the IP address, where n is the current depth. If it is 0, continue with the first child. Otherwise, continue with the second. If a child is missing, backtrack until a routing entry is found. For example, when looking for 192.0.2.50, we will find the result in the corresponding leaf (at depth 32). However for 192.0.2.51, we will reach 192.0.2.50/31 but there is no second child. Therefore, we backtrack until the 192.0.2.0/25 routing entry. Adding and removing routes is quite easy. From a performance point of view, the lookup is done in constant time relative to the number of routes (due to maximum depth being capped to 32). Quagga is an example of routing software still using this simple approach.

Lookup with a path-compressed trie In the previous example, most nodes only have one child. This leads to a lot of unneeded bitwise comparisons and memory is also wasted on many nodes. To overcome this problem, we can use path compression: each node with only one child is removed (except if it also contains a routing entry). Each remaining node gets a new property telling how many input bits should be skipped. Such a trie is also known as a Patricia trie or a radix tree. Here is the path-compressed version of the previous trie: Since some bits have been ignored, on a match, a final check is executed to ensure all bits from the found entry are matching the input IP address. If not, we must act as if the entry wasn t found (and backtrack to find a matching prefix). The following figure shows two IP addresses matching the same leaf: The reduction on the average depth of the tree compensates the necessity to handle those false positives. The insertion and deletion of a routing entry is still easy enough. Many routing systems are using Patricia trees:

• OpenBSD
• NetBSD
• FreeBSD
• GoBGP (through go-radix)
• Linux for IPv6

Lookup with a level-compressed trie In addition to path compression, level compression² detects parts of the trie that are densily populated and replace them with a single node and an associated vector of 2^k children. This node will handle k input bits instead of just one. For example, here is a level-compressed version our previous trie: Such a trie is called LC-trie or LPC-trie and offers higher lookup performances compared to a radix tree. An heuristic is used to decide how many bits a node should handle. On Linux, if the ratio of non-empty children to all children would be above 50% when the node handles an additional bit, the node gets this additional bit. On the other hand, if the current ratio is below 25%, the node loses the responsibility of one bit. Those values are not tunable. Insertion and deletion becomes more complex but lookup times are also improved.

Implementation in Linux The implementation for IPv4 in Linux exists since 2.6.13 (commit 19baf839ff4a) and is enabled by default since 2.6.39 (commit 3630b7c050d9). Here is the representation of our example routing table in memory³: There are several structures involved:

• struct fib_table represents a routing table,
• struct trie represents a complete trie,
• struct key_vector represents either an internal node (when bits is not zero) or a leaf,
• struct fib_info contains the characteristics shared by several routes (like a next-hop gateway and an output interface),
• struct fib_alias is the glue between the leaves and the fib_info structures.

The trie can be retrieved through /proc/net/fib_trie:

$ cat /proc/net/fib_trie
Id 100:
  +-- 0.0.0.0/0 2 0 2
      -- 0.0.0.0
        /0 universe UNICAST
     +-- 192.0.2.0/26 2 0 1
         -- 192.0.2.0
           /25 universe UNICAST
         -- 192.0.2.47
           /32 universe UNICAST
        +-- 192.0.2.48/30 2 0 1
            -- 192.0.2.48
              /32 universe UNICAST
            -- 192.0.2.49
              /32 universe UNICAST
            -- 192.0.2.50
              /32 universe UNICAST
[...]

For internal nodes, the numbers after the prefix are:

1. the number of bits handled by the node,
2. the number of full children (they only handle one bit),
3. the number of empty children.

Moreover, if the kernel was compiled with CONFIG_IP_FIB_TRIE_STATS, some interesting statistics are available in /proc/net/fib_triestat⁴:

$ cat /proc/net/fib_triestat
Basic info: size of leaf: 48 bytes, size of tnode: 40 bytes.
Id 100:
        Aver depth:     2.33
        Max depth:      3
        Leaves:         6
        Prefixes:       6
        Internal nodes: 3
          2: 3
        Pointers: 12
Null ptrs: 4
Total size: 1  kB
[...]

When a routing table is very dense, a node can handle many bits. For example, a densily populated routing table with 1 million entries packed in a /12 can have one internal node handling 20 bits. In this case, route lookup is essentially reduced to a lookup in a vector. The following graph shows the number of internal nodes used relative to the number of routes for different scenarios (routes extracted from an Internet full view, /32 routes spreaded over 4 different subnets with various densities). When routes are densily packed, the number of internal nodes are quite limited.

Performance So how performant is a route lookup? The maximum depth stays low (about 6 for a full view), so a lookup should be quite fast. With the help of a small kernel module, we can accurately benchmark⁵ the fib_lookup() function: The lookup time is loosely tied to the maximum depth. When the routing table is densily populated, the maximum depth is low and the lookup times are fast. When forwarding at 10 Gbps, the time budget for a packet would be about 50 ns. Since this is also the time needed for the route lookup alone in some cases, we wouldn t be able to forward at line rate with only one core. Nonetheless, the results are pretty good and they are expected to scale linearly with the number of cores. The measurements are done with a Linux kernel 4.11 from Debian unstable. I have gathered performance metrics accross kernel versions in Performance progression of IPv4 route lookup on Linux . Another interesting figure is the time it takes to insert all those routes into the kernel. Linux is also quite efficient in this area since you can insert 2 million routes in less than 10 seconds:

Memory usage The memory usage is available directly in /proc/net/fib_triestat. The statistic provided doesn t account for the fib_info structures, but you should only have a handful of them (one for each possible next-hop). As you can see on the graph below, the memory use is linear with the number of routes inserted, whatever the shape of the routes is. The results are quite good. With only 256 MiB, about 2 million routes can be stored!

Routing rules Unless configured without CONFIG_IP_MULTIPLE_TABLES, Linux supports several routing tables and has a system of configurable rules to select the table to use. These rules can be configured with ip rule. By default, there are three of them:

$ ip rule show
0:      from all lookup local
32766:  from all lookup main
32767:  from all lookup default

Linux will first lookup for a match in the local table. If it doesn t find one, it will lookup in the main table and at last resort, the default table.

Builtin tables The local table contains routes for local delivery:

$ ip route show table local
broadcast 127.0.0.0 dev lo proto kernel scope link src 127.0.0.1
local 127.0.0.0/8 dev lo proto kernel scope host src 127.0.0.1
local 127.0.0.1 dev lo proto kernel scope host src 127.0.0.1
broadcast 127.255.255.255 dev lo proto kernel scope link src 127.0.0.1
broadcast 192.168.117.0 dev eno1 proto kernel scope link src 192.168.117.55
local 192.168.117.55 dev eno1 proto kernel scope host src 192.168.117.55
broadcast 192.168.117.63 dev eno1 proto kernel scope link src 192.168.117.55

This table is populated automatically by the kernel when addresses are configured. Let s look at the three last lines. When the IP address 192.168.117.55 was configured on the eno1 interface, the kernel automatically added the appropriate routes:

• a route for 192.168.117.55 for local unicast delivery to the IP address,
• a route for 192.168.117.255 for broadcast delivery to the broadcast address,
• a route for 192.168.117.0 for broadcast delivery to the network address.

When 127.0.0.1 was configured on the loopback interface, the same kind of routes were added to the local table. However, a loopback address receives a special treatment and the kernel also adds the whole subnet to the local table. As a result, you can ping any IP in 127.0.0.0/8:

$ ping -c1 127.42.42.42
PING 127.42.42.42 (127.42.42.42) 56(84) bytes of data.
64 bytes from 127.42.42.42: icmp_seq=1 ttl=64 time=0.039 ms
--- 127.42.42.42 ping statistics ---
1 packets transmitted, 1 received, 0% packet loss, time 0ms
rtt min/avg/max/mdev = 0.039/0.039/0.039/0.000 ms

The main table usually contains all the other routes:

$ ip route show table main
default via 192.168.117.1 dev eno1 proto static metric 100
192.168.117.0/26 dev eno1 proto kernel scope link src 192.168.117.55 metric 100

The default route has been configured by some DHCP daemon. The connected route (scope link) has been automatically added by the kernel (proto kernel) when configuring an IP address on the eno1 interface. The default table is empty and has little use. It has been kept when the current incarnation of advanced routing has been introduced in Linux 2.1.68 after a first tentative using classes in Linux 2.1.15⁶.

Performance Since Linux 4.1 (commit 0ddcf43d5d4a), when the set of rules is left unmodified, the main and local tables are merged and the lookup is done with this single table (and the default table if not empty). Moreover, since Linux 3.0 (commit f4530fa574df), without specific rules, there is no performance hit when enabling the support for multiple routing tables. However, as soon as you add new rules, some CPU cycles will be spent for each datagram to evaluate them. Here is a couple of graphs demonstrating the impact of routing rules on lookup times: For some reason, the relation is linear when the number of rules is between 1 and 100 but the slope increases noticeably past this threshold. The second graph highlights the negative impact of the first rule (about 30 ns). A common use of rules is to create virtual routers: interfaces are segregated into domains and when a datagram enters through an interface from domain A, it should use routing table A:

# ip rule add iif vlan457 table 10
# ip rule add iif vlan457 blackhole
# ip rule add iif vlan458 table 20
# ip rule add iif vlan458 blackhole

The blackhole rules may be removed if you are sure there is a default route in each routing table. For example, we add a blackhole default with a high metric to not override a regular default route:

# ip route add blackhole default metric 9999 table 10
# ip route add blackhole default metric 9999 table 20
# ip rule add iif vlan457 table 10
# ip rule add iif vlan458 table 20

To reduce the impact on performance when many interface-specific rules are used, interfaces can be attached to VRF instances and a single rule can be used to select the appropriate table:

# ip link add vrf-A type vrf table 10
# ip link set dev vrf-A up
# ip link add vrf-B type vrf table 20
# ip link set dev vrf-B up
# ip link set dev vlan457 master vrf-A
# ip link set dev vlan458 master vrf-B
# ip rule show
0:      from all lookup local
1000:   from all lookup [l3mdev-table]
32766:  from all lookup main
32767:  from all lookup default

The special l3mdev-table rule was automatically added when configuring the first VRF interface. This rule will select the routing table associated to the VRF owning the input (or output) interface. VRF was introduced in Linux 4.3 (commit 193125dbd8eb), the performance was greatly enhanced in Linux 4.8 (commit 7889681f4a6c) and the special routing rule was also introduced in Linux 4.8 (commit 96c63fa7393d, commit 1aa6c4f6b8cd). You can find more details about it in the kernel documentation.

Conclusion The takeaways from this article are:

• route lookup times hardly increase with the number of routes,
• densily packed /32 routes lead to amazingly fast route lookups,
• memory use is low (128 MiB par million routes),
• no optimization is done on routing rules.

---

1. The routing cache was subject to reasonably easy to launch denial of service attacks. It was also believed to not be efficient for high volume sites like Google but I have first-hand experience it was not the case for moderately high volume sites.
2. IP-address lookup using LC-tries , IEEE Journal on Selected Areas in Communications, 17(6):1083-1092, June 1999.
3. For internal nodes, the key_vector structure is embedded into a tnode structure. This structure contains information rarely used during lookup, notably the reference to the parent that is usually not needed for backtracking as Linux keeps the nearest candidate in a variable.
4. One leaf can contain several routes (struct fib_alias is a list). The number of prefixes can therefore be greater than the number of leaves. The system also keeps statistics about the distribution of the internal nodes relative to the number of bits they handle. In our example, all the three internal nodes are handling 2 bits.
5. The measurements are done in a virtual machine with one vCPU. The host is an Intel Core i5-4670K running at 3.7 GHz during the experiment (CPU governor was set to performance). The benchmark is single-threaded. It runs a warm-up phase, then executes about 100,000 timed iterations and keeps the median. Timings of individual runs are computed from the TSC.
6. Fun fact: the documentation of this first tentative of more flexible routing is still available in today s kernel tree and explains the usage of the default class .

• Critical: 3 @ 5.2 years average
• High: 44 @ 6.2 years average
• Medium: 404 @ 5.3 years average
• Low: 216 @ 5.5 years average

2016, Kees Cook. This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License.

Patches_linux:
 break-fix: 3a50597de8635cd05133bd12c95681c82fe7b878 23567fd052a9abb6d67fe8e7a9ccdd9800a540f2

• Critical: 2 @ 3.3 years
• High: 34 @ 6.4 years
• Medium: 334 @ 5.2 years
• Low: 186 @ 5.0 years

2016, Kees Cook. This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License.

2016, Kees Cook. This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 License.

Server setup The first thing I did on the server-side is to follow Sean Whitton's advice and configure postfix so that it keeps undelivered emails for 10 days (instead of 5 days, the default):

postconf -e maximal_queue_lifetime=10d

Then I created a new user:

adduser mailq-check

with a password straight out of pwgen -s 32. I gave ssh permission to that user:

adduser mailq-check sshuser

and then authorized my new ssh key (see next section):

sudo -u mailq-check -i
mkdir ~/.ssh/
cat - > ~/.ssh/authorized_keys

Laptop setup On my laptop, the machine from where I monitor the server's mail queue, I first created a new password-less ssh key:

ssh-keygen -t ed25519 -f .ssh/egilsstadir-mailq-check
cat ~/.ssh/egilsstadir-mailq-check.pub

which I then installed on the server. Then I added this cronjob in /etc/cron.d/egilsstadir-mailq-check:

0 2 * * * francois /usr/bin/ssh -i /home/francois/.ssh/egilsstadir-mailq-check mailq-check@egilsstadir mailq   grep -v "Mail queue is empty"

and that's it. I get a (locally delivered) email whenever the mail queue on the server is non-empty. There is a race condition built into this setup since it's possible that the server will want to send an email at 2am. However, all that does is send a spurious warning email in that case and so it's a pretty small price to pay for a dirt simple setup that's unlikely to break.

1. use 2FA on important websites like Github, to improve the security of critical infrastructure (like my Borg backup software)
2. login to remote SSH servers without exposing my password or my private key material on third party computers
3. store OpenPGP key material on the key securely, so that the private key material can never be compromised

• PIV (Personnal Identity Verification): basically to run your own Certificate Authority
• OTP (One Time Password): allows sites to request a OTP from a Yubikey server validator. I haven't explored that mode since it requires a third party server and more modifications on the server side.
• OATH (Initiative for Open Authentication): a purely "offline" and more "traditionnal" approach to OTP. In this mode, you can authenticate with only the token given by the key and a shared secret. Maybe i will follow this OATH tutorial eventually.

Not recommended After experimenting with the device and doing a little more research, I am not sure it was the right decision to buy a Yubikey. I would not recommend buying Yubikey devices because they don't allow changing the firmware, making the device basically proprietary, even in the face of an embarrassing security vulnerability on the Yubikey NEO that came out in 2015. A security device, obviously, should be as open as the protocols it uses, otherwise it's basically impossible to trust that the crypto hasn't been backdoored or compromised, or, in this case, is vulnerable to the simplest drive-by attacks. Furthermore, it turns out that the primary use case that Github was promoting is actually not working as advertised: to use the Yubikey on Github, you actually first need to configure 2FA with another tool, either with your phone's text messages (SMS) or with something like Google Authenticator. After contacting Github support, they explained that the Yubikey is seen as a "backup device", which seems really odd to me, especially considering the promotion and the fact that I don't have a "smart" (aka "Google", it seems these days) phone or the desire to share my personal phone number with Github. Finally, as I mentioned before, the fact that those devices are fairly new and the configuration necessary to make them work at all is completely obtuse, non-standardized or at least not available by default on arbitrary computers makes them basically impossible to use on other computers than your own specially crafted gems.

Plugging it in The Yubikey, when inserted into a USB port, seems to be detected properly. It shows up both as a USB keyboard and a generic device.

d c 14 17:23:26 angela kernel: input: Yubico Yubikey NEO OTP+U2F as /devices/pci0000:00/0000:00:12.0/usb3/3-2/3-2:1.0/0003:1050:0114.0016/input/input127
d c 14 17:23:26 angela kernel: hid-generic 0003:1050:0114.0016: input,hidraw3: USB HID v1.10 Keyboard [Yubico Yubikey NEO OTP+U2F] on usb-0000:00:12.0-2/input0
d c 14 17:23:26 angela kernel: hid-generic 0003:1050:0114.0017: hiddev0,hidraw4: USB HID v1.10 Device [Yubico Yubikey NEO OTP+U2F] on usb-0000:00:12.0-2/input1

We'll be changing this now - we want to to support OTP, U2F and CCID. Don't worry about those acronyms now, but U2F is for the web, CCID is for GPG/SSH, and OTP is for the One Time Passwords stuff mentionned earlier. I am using the Yubikey Personalization tool from stretch because the jessie one is too old, according to Gorzen. Indeed, I found out that the jessie version doesn't ship with the proper udev rules. Also, note that we need to run as sudo otherwise we get a permission denied:

$ sudo apt install yubikey-personalization/stretch
$ sudo ykpersonalize -m86
Firmware version 3.4.3 Touch level 1541 Program sequence 1
The USB mode will be set to: 0x86
Commit? (y/n) [n]: y

To understand better what the above does, see the NEO composite device documentation. The next step is to reconnect the key, for the udev rules to kick in. If you were like me, you enthusiastically plugged in the device before installing the yubikey-personalization package, and the udev rules were not present then.

Configuring a PIN Various operations will require you to enter a PIN when talking to the key. The default PIN is 123456 and the default admin PIN is 12345678. You will want to change that, otherwise someone that gets a hold of your key could do any operation without your consent. For this, you need to use:

$ gpg --card-edit
> passwd
> admin
> passwd

Be sure to remember those passwords! Of course, the key material on the Yubikey can be revoked when you loose the key, but only if you still have control of the master key, or if you have a OpenPGP revocation certification (which you should have).

Configuring GPG To do OpenPGP operations (like decryption, signatures and so on), or SSH operations (like authentication on a remote server), you need to talk with GPG. Yes, OpenPGP keys are RSA keys that can be used to authenticate with SSH servers, that's not new and I have already been doing this with Monkeysphere for a while. Now the challenge is how to make GPG talk with the Yubikey. So the next step is to see if gpg can see the key alright, as described in the Yubikey importing keys howto - you will need first to install scdaemon and pcscd (according to this howto) for gpg-agent to be able to talk with the key:

$ sudo apt install scdaemon gnupg-agent pcscd
$ gpg-connect-agent --hex "scd apdu 00 f1 00 00" /bye
ERR 100663404 Card error <SCD>

Well that failed. At this point, touching the key types a bunch of seemingly random characters wherever my cursor is sitting - fun but totally useless still. That was because I failed to reconnect the key: make sure the udev rules are in place and reconnect the key, the above should work:

$ gpg-connect-agent --hex "scd apdu 00 f1 00 00" /bye
D[0000]  01 00 10 90 00                                     .....
OK

This shows it is running the firmware 1.10, which is not vulnerable to the infamous security issue. (Note: I also happened to install opensc and gpgsm because of this suggestion but I am not sure they are required at all.)

Using SSH To make GPG work with SSH, you need somehow to start gpg-agent with ssh support, for example with:

gpg-agent --daemon --enable-ssh-support bash

Of course, this will work better if it's started with your Xsession. Such an agent should already be started, so you just need to add the ssh emulation to its configuration file and restart your X session.

echo 'enable-ssh-support' >> .gnupg/gpg-agent.conf

In Debian Jessie, the ssh-agent wrapper will not start if it detects that you have already one running (for example from gpg-agent) but if that fails, you can try commenting out use-ssh-agent from /etc/X11/Xsession.options to keep it from starting up in your session. (Thanks to stackexchange for that reference.) Here I assume you have already created an authentication subkey on your PGP key. If you haven't, I suggest trying out simply monkeysphere gen-subkey, which will generate an authentication subkey for you. You can also do it by hand by following one of the OpenPGP/SSH tutorials from Yubikey, especially the more complete one. If you are going to generate a completely new OpenPGP key, you may want to follow this simpler tutorial here. Then you need to move your authentication subkey to the Yubikey. For this, you need to edit the key and use the keytocard command:

$ gpg2 --edit-key anarcat@debian.org
> toggle
> key 2
> keytocard
> save

Here, we use toggle to show the OpenPGP private key material. You should see a key marked with A for Authentication. Mine was the second one so I selected it with key 2 which put a star next to it. The keytocard command moved it to the key and save ensure the key was removed from the local keyring. Obviously, backups are essential before doing this, because it's perfectly possible to loose that key in the process, for example if you destroy or lose the key or forget the password. It's probably better to create a completely different authentication subkey for just this purpose, but that may require reconfiguring all remote SSH hosts, and you may not want to do that. Then SSH should magically talk with the GPG agent and ask you for the PIN! That's pretty much all there is to it - if it doesn't, it means that gpg-agent is not your SSH agent, and obviously things will fail... Also, you should be able to see the key being loaded in the agent when it is:

$ ssh-add -l
2048 23:f3:be:bf:1e:da:e8:ad:4b:c7:f6:60:5e:03:c2:a6 cardno:000603647189 (RSA)

.. that's about it! I have yet to cover 2FA and OpenPGP support, but that got me going for a while and I'll stop geeking around with that thing for now. It was fun, for sure, but not sure it's worth it for now.

Using OATH This is pretty neat: it allows you to add two factor authentication to a lot of things. For example, PAM has such a module, which I will configure here to allow myself to login to my server from untrusted machines. While I will expose my main password to keyloggers, the OTP password will prevent that from being reused. This is a simplified version of this OATH tutorial. We install the PAM module with:

sudo apt install libpam-oath

Then, we can hook it into any PAM consumer, for example with sshd:

--- a/pam.d/sshd
+++ b/pam.d/sshd
@@ -1,5 +1,8 @@
 # PAM configuration for the Secure Shell service
+# for the yubikey
+auth required pam_oath.so usersfile=/etc/users.oath window=5 digits=8
+
 # Standard Un*x authentication.
 @include common-auth

We also needed to allow OTP passwords in sshd explicitely, with:

ChallengeResponseAuthentication yes

This will force the user to enter a valid oath token on the server. Unfortunately, this will affect all users, regardless of whether they are present in the users.oath file. I filed bug #807990 regarding this, with a patch. Also, it means the main password is still exposed on the client machine - you can use the sufficient keyword instead of required to workaround that, but then it means anyone with your key can login to your machine, which is something to keep in mind. The /etc/users.oath file needs to be created with something like:

#type   username        pin     start seed
HOTP    anarcat -   00

00 is obviously a fake, and insecure string. Generate a proper one with:

dd if=/dev/random bs=1k count=1   sha1sum # create a random secret

Then the shared secret needs to be added to the Yubikey:

ykpersonalize -1 -o oath-hotp -o oath-hotp8 -o append-cr -a

You simply paste the random secret you created above, when prompted, and that shared secret will be saved in a Yubikey slot for future use. Next time you login to the SSH server, you will be prompted for a OATH password, you just touch the button on the key and it will be pasted there:

$ ssh -o PubkeyAuthentication=no anarc.at
One-time password (OATH) for  anarcat':
Password:
[... logged in!]

Final note: the centralized file approach makes it hard, if not impossible, for users to update their own secret token.. It would be nice if there would be a user-accessible token file, maybe ~/.oath? Filed feature request #807992 about this as well.

• Catalog tests (e.g. testing the compiled puppet catalog)
• Functional/Acceptance tests in a real environment

• Part 0: Setup your environment
• Part 1: Create a simple calss
• Part 2: Create a more complex class and refactor it
• Part 3: create a custom type and provider