Generalized normal distribution

[jachymb]

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Summary

This is my take on the request #3133 I created a while ago.

The Generalized normal distribution a.k.a. exponential power distribution generalizes the normal, Laplace (double exponential) and in limit also uniform distribution. This makes it an interesting prior choice as it generalizes the corresponding MAP regularization coefficient to L_p norm and can also be interesting to model noise in regression problems for basically the same reasons.

This is my first attempt at implementing a distribution to STAN, I tried to follow the guide https://mc-stan.org/math/md_doxygen_2contributor__help__pages_2adding__new__distributions.html but there are likely some problems, so I welcome any comments.

So far I implemented only the lpdf, if other files like lcdf etc are strictly required, please let me know.

Tests

I added one test file analogical to the one for normal distribution.

Side Effects

I included some very minor code polishing to the related normal and double exponential distributions (I used those as a starting point) which shouldn't do anything and can be discarded if undesired.

Release notes

Added generalized_normal_lpdf

Checklist

• [x] Copyright holder: Me

  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses: - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause) - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• [x] the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• [x] the code is written in idiomatic C++ and changes are documented in the doxygen

• [x] the new changes are tested

[andrjohns]

Thanks for this! Can you remove the changes to the normal and double_exponential if they're unrelated? Feel free to open a separate PR for them afterwards though!

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.46	0.44	1.04	3.47% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.07	6.3% faster
gp_regr/gen_gp_data.stan	0.03	0.03	1.03	2.55% faster
gp_regr/gp_regr.stan	0.11	0.11	1.05	4.91% faster
sir/sir.stan	80.75	78.51	1.03	2.76% faster
irt_2pl/irt_2pl.stan	5.32	4.88	1.09	8.26% faster
eight_schools/eight_schools.stan	0.06	0.06	1.03	3.26% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.28	0.29	0.96	-4.31% slower
pkpd/one_comp_mm_elim_abs.stan	21.42	21.52	1.0	-0.47% slower
garch/garch.stan	0.61	0.55	1.12	10.83% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	3.03	3.14	0.96	-3.7% slower
arK/arK.stan	2.02	2.01	1.01	0.77% faster
gp_pois_regr/gp_pois_regr.stan	3.2	3.11	1.03	2.74% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	10.02	9.49	1.06	5.22% faster
performance.compilation	208.8	212.05	0.98	-1.56% slower
Mean result: 1.0299123921756848

---

Jenkins Console Log Blue Ocean Commit hash: 0f8dd4fc4b9973d67f612f68473daae100089e5c

---

Machine information

No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian Address sizes: 46 bits physical, 48 bits virtual CPU(s): 80 On-line CPU(s) list: 0-79 Thread(s) per core: 2 Core(s) per socket: 20 Socket(s): 2 NUMA node(s): 2 Vendor ID: GenuineIntel CPU family: 6 Model: 85 Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz Stepping: 4 CPU MHz: 2400.000 CPU max MHz: 3700.0000 CPU min MHz: 1000.0000 BogoMIPS: 4800.00 Virtualization: VT-x L1d cache: 1.3 MiB L1i cache: 1.3 MiB L2 cache: 40 MiB L3 cache: 55 MiB NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78 NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79 Vulnerability Gather data sampling: Mitigation; Microcode Vulnerability Itlb multihit: KVM: Mitigation: VMX disabled Vulnerability L1tf: Mitigation; PTE Inversion; VMX conditional cache flushes, SMT vulnerable Vulnerability Mds: Mitigation; Clear CPU buffers; SMT vulnerable Vulnerability Meltdown: Mitigation; PTI Vulnerability Mmio stale data: Mitigation; Clear CPU buffers; SMT vulnerable Vulnerability Reg file data sampling: Not affected Vulnerability Retbleed: Mitigation; IBRS Vulnerability Spec rstack overflow: Not affected Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; IBRS; IBPB conditional; STIBP conditional; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT vulnerable Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++: g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang: clang version 10.0.0-4ubuntu1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin

[jachymb]

I discarded any changes to the existing distributions

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.38	0.37	1.05	4.89% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.08	7.17% faster
gp_regr/gen_gp_data.stan	0.03	0.02	1.06	5.24% faster
gp_regr/gp_regr.stan	0.1	0.09	1.05	4.92% faster
sir/sir.stan	71.8	72.4	0.99	-0.84% slower
irt_2pl/irt_2pl.stan	4.26	4.71	0.9	-10.64% slower
eight_schools/eight_schools.stan	0.06	0.06	0.99	-0.62% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.26	0.27	0.95	-5.82% slower
pkpd/one_comp_mm_elim_abs.stan	19.62	20.31	0.97	-3.53% slower
garch/garch.stan	0.45	0.49	0.92	-9.18% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.73	2.88	0.95	-5.67% slower
arK/arK.stan	1.82	1.92	0.95	-5.27% slower
gp_pois_regr/gp_pois_regr.stan	2.88	2.99	0.96	-3.79% slower
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	9.92	9.15	1.08	7.8% faster
performance.compilation	187.0	189.61	0.99	-1.39% slower
Mean result: 0.9921627173252643

---

Jenkins Console Log Blue Ocean Commit hash: 0f8dd4fc4b9973d67f612f68473daae100089e5c

---

Machine information

No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian Address sizes: 46 bits physical, 48 bits virtual CPU(s): 80 On-line CPU(s) list: 0-79 Thread(s) per core: 2 Core(s) per socket: 20 Socket(s): 2 NUMA node(s): 2 Vendor ID: GenuineIntel CPU family: 6 Model: 85 Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz Stepping: 4 CPU MHz: 2400.000 CPU max MHz: 3700.0000 CPU min MHz: 1000.0000 BogoMIPS: 4800.00 Virtualization: VT-x L1d cache: 1.3 MiB L1i cache: 1.3 MiB L2 cache: 40 MiB L3 cache: 55 MiB NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78 NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79 Vulnerability Gather data sampling: Mitigation; Microcode Vulnerability Itlb multihit: KVM: Mitigation: VMX disabled Vulnerability L1tf: Mitigation; PTE Inversion; VMX conditional cache flushes, SMT vulnerable Vulnerability Mds: Mitigation; Clear CPU buffers; SMT vulnerable Vulnerability Meltdown: Mitigation; PTI Vulnerability Mmio stale data: Mitigation; Clear CPU buffers; SMT vulnerable Vulnerability Reg file data sampling: Not affected Vulnerability Retbleed: Mitigation; IBRS Vulnerability Spec rstack overflow: Not affected Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; IBRS; IBPB conditional; STIBP conditional; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT vulnerable Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++: g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang: clang version 10.0.0-4ubuntu1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin

[jachymb]

Sorry for a broken PR, I believed the tests pass, but apparently I made some mistake when running the tests locally.

Would appreciate any help deciphering the error messages, it doesn't seem very understandable what the problem is exactly to me. But apparently it somehow has to do with the distribution being possibly non-differentiable at mu=y.

The suspect line is:

sign(diff) * beta_val * pow(scaled_abs_diff, beta_val - 1) * inv_alpha

In case when mu=y, we get:

sign(0) * beta_val * pow(0, beta_val - 1) * inv_alpha

which I think should evaluate to 0, and also when beta=1

sign(0) * 1 * pow(0, 0) * inv_alpha

should also evaluate to 0 I would expect? Is pow(0,0) actually undefined in STAN math? And what would be the recommended technique for special-case handling?

[WardBrian]

Sorry for a broken PR, I believed the tests pass, but apparently I made some mistake when running the tests locally.

No worries! It's often quite a miracle when these things pass first try.

You can run the exact test that is given issues locally by running python runTests.py -j4 test/prob/generalized_normal/generalized_normal_0*_test.cpp

Is pow(0,0) actually undefined in STAN math?

It's defined (https://github.com/stan-dev/math/issues/3031), but it's not twice differentiable: https://github.com/stan-dev/math/issues/2993#issuecomment-1871732573, which I believe is the problem here. This second comment is by @andrjohns who can probably also give you suggestions about what to do in this case.

It's possible that what you're doing in the code is fine and you just need to have the test call it somewhere else where it will be better behaved

[jachymb]

OK, so it may be just a testing problem. But this relates to something else: The case when beta=1 where the tests are apparently breaking is maybe just a tip of the iceberg: when beta<1, I write in the code comments the partials are undefined when y=mu, because we then get pow(0, negative_number). This is because the limit can diverge to both positive and negative infinity depending on whether we approach from y>mu or y<mu. I left this undefined intentionally, but is that actually an OK behavior for STAN? Or do we need to use some technique to e.g. artificially set the partial to 0 in theses cases (like sign(0)=0 is defined to be the mathematically non-existent derivative of abs(0))

[jachymb]

Some notes on the distribution (I made some mistakes in the #3133 comments but here should be corrected):

We have the density:

$f(y|\mu,\alpha,\beta) \propto \exp\left(-\left(\frac{|y-\mu|}{\alpha}\right)^{\beta}\right)$ with normalization constant $\frac{1}{2\alpha\Gamma(1 + \frac{1}{\beta})} = \int_{-\infty}^{\infty} \exp\left(-\left(\frac{|y-\mu|}{\alpha}\right)^{\beta}\right) \mathrm{d}y$ (note: can set $\mu = 0$ WLOG to evaluate the integral)

The parameters $\alpha, \beta$ must be positive.

The log-likelihood is then:

$\log f(y|\mu,\alpha,\beta) = -\left(\frac{|y-\mu|}{\alpha}\right)^{\beta} - \log(2) -\log(\alpha) - \log\Gamma(1 + \frac{1}{\beta})$

Wolfram Mathematica outputs the following partials:

$\frac{\partial \log f(y|\mu,\alpha,\beta)}{\partial \mu} = \alpha^{-\beta}\beta|y-\mu|^{\beta-1} \mathrm{sign}\left(y-\mu\right)$

$\frac{\partial \log f(y|\mu,\alpha,\beta)}{\partial y} = -\alpha^{-\beta}\beta|y-\mu|^{\beta-1} \mathrm{sign}\left(y-\mu\right) = -\frac{\partial \log f(y|\mu,\alpha,\beta)}{\partial \mu}$

Using algebraic manipulations I change this to the form:

$\frac{\partial \log f(y|\mu,\alpha,\beta)}{\partial \mu} = \alpha^{-1}\beta \left(\frac{|y-\mu|}{\alpha}\right)^{\beta-1} \mathrm{sign}\left(y-\mu\right)$

This is where I believe the test errors are comming from when testing the case $\beta = 1, y = 0, \mu=0$. The lpdf is defined, the first derivative is by convention 0 (since pow(0,0)=1 and sign(0)=0), but the second derivative undefined. And I am not even testing the case when $\beta < 1$ which I kept undefined for $y = \mu$ as the there is negative power of zero.

The $\beta$ partial is:

$\frac{\partial \log f(y|\mu,\alpha,\beta)}{\partial \beta} = \frac{\mathrm{digamma}(1 + \frac{1}{\beta})}{\beta^2} - \left(\frac{|y-\mu|}{\alpha}\right)^{\beta} \log(\frac{|y-\mu|}{\alpha})$

this one has a also potential boundary problem when $y=\mu$ because we get $\log(0)$ but then the limit goes to 0 and this should be solved by using multiply_log. Not sure about second derivatives tho, do they need to be considered here?

The $\alpha$ partial I think is not problematic but just for completeness, I also used wolfram plus some algebra to obtain:

$\frac{\partial \log f(y|\mu,\alpha,\beta)}{\partial \alpha} = \alpha^{-1}(\beta \left(\frac{|y-\mu|}{\alpha}\right)^{\beta} - 1 )$

I tend to believe that @WardBrian is right that this is perhaps a problem with testing the distribution at these boundaries, but idk what a good approach to this is.

PDF plot from wikipedia for $\mu = 0, \alpha = 1$ illustrates the non-differentiability at $y=0$ for $\beta \le 1$:

[jachymb]

Incorporated changes requested by @SteveBronder although that doesn't solve the test errors. I think those are more like just performance+stylistic improvements. See the notes and discussion above.

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.32	0.3	1.05	4.83% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.08	7.4% faster
gp_regr/gen_gp_data.stan	0.02	0.02	1.07	6.22% faster
gp_regr/gp_regr.stan	0.09	0.1	0.98	-1.65% slower
sir/sir.stan	69.21	68.64	1.01	0.82% faster
irt_2pl/irt_2pl.stan	4.29	4.09	1.05	4.73% faster
eight_schools/eight_schools.stan	0.06	0.05	1.03	3.13% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.25	0.25	1.01	1.36% faster
pkpd/one_comp_mm_elim_abs.stan	19.31	19.43	0.99	-0.61% slower
garch/garch.stan	0.43	0.45	0.96	-4.69% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.7	2.62	1.03	2.93% faster
arK/arK.stan	1.79	1.74	1.03	3.15% faster
gp_pois_regr/gp_pois_regr.stan	2.86	2.74	1.04	4.16% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.72	8.39	1.04	3.76% faster
performance.compilation	181.14	184.12	0.98	-1.65% slower
Mean result: 1.0242034654627605

---

Jenkins Console Log Blue Ocean Commit hash: fa89f3f2eeace783e24dc5d33e94f737d6e7f2f7

---

Machine information

No LSB modules are available. Distributor ID: Ubuntu Description: Ubuntu 20.04.3 LTS Release: 20.04 Codename: focal

CPU: Architecture: x86_64 CPU op-mode(s): 32-bit, 64-bit Byte Order: Little Endian Address sizes: 46 bits physical, 48 bits virtual CPU(s): 80 On-line CPU(s) list: 0-79 Thread(s) per core: 2 Core(s) per socket: 20 Socket(s): 2 NUMA node(s): 2 Vendor ID: GenuineIntel CPU family: 6 Model: 85 Model name: Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz Stepping: 4 CPU MHz: 2400.000 CPU max MHz: 3700.0000 CPU min MHz: 1000.0000 BogoMIPS: 4800.00 Virtualization: VT-x L1d cache: 1.3 MiB L1i cache: 1.3 MiB L2 cache: 40 MiB L3 cache: 55 MiB NUMA node0 CPU(s): 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78 NUMA node1 CPU(s): 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51,53,55,57,59,61,63,65,67,69,71,73,75,77,79 Vulnerability Gather data sampling: Mitigation; Microcode Vulnerability Itlb multihit: KVM: Mitigation: VMX disabled Vulnerability L1tf: Mitigation; PTE Inversion; VMX conditional cache flushes, SMT vulnerable Vulnerability Mds: Mitigation; Clear CPU buffers; SMT vulnerable Vulnerability Meltdown: Mitigation; PTI Vulnerability Mmio stale data: Mitigation; Clear CPU buffers; SMT vulnerable Vulnerability Reg file data sampling: Not affected Vulnerability Retbleed: Mitigation; IBRS Vulnerability Spec rstack overflow: Not affected Vulnerability Spec store bypass: Mitigation; Speculative Store Bypass disabled via prctl Vulnerability Spectre v1: Mitigation; usercopy/swapgs barriers and __user pointer sanitization Vulnerability Spectre v2: Mitigation; IBRS; IBPB conditional; STIBP conditional; RSB filling; PBRSB-eIBRS Not affected; BHI Not affected Vulnerability Srbds: Not affected Vulnerability Tsx async abort: Mitigation; Clear CPU buffers; SMT vulnerable Flags: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe syscall nx pdpe1gb rdtscp lm constant_tsc art arch_perfmon pebs bts rep_good nopl xtopology nonstop_tsc cpuid aperfmperf pni pclmulqdq dtes64 monitor ds_cpl vmx smx est tm2 ssse3 sdbg fma cx16 xtpr pdcm pcid dca sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand lahf_lm abm 3dnowprefetch cpuid_fault epb cat_l3 cdp_l3 invpcid_single pti intel_ppin ssbd mba ibrs ibpb stibp tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm cqm mpx rdt_a avx512f avx512dq rdseed adx smap clflushopt clwb intel_pt avx512cd avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves cqm_llc cqm_occup_llc cqm_mbm_total cqm_mbm_local dtherm ida arat pln pts hwp hwp_act_window hwp_epp hwp_pkg_req pku ospke md_clear flush_l1d arch_capabilities

G++: g++ (Ubuntu 9.4.0-1ubuntu1~20.04) 9.4.0 Copyright (C) 2019 Free Software Foundation, Inc. This is free software; see the source for copying conditions. There is NO warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Clang: clang version 10.0.0-4ubuntu1 Target: x86_64-pc-linux-gnu Thread model: posix InstalledDir: /usr/bin

[jachymb]

Hi, @andrjohns! Could you please go through the above comments and provide me with any feedback on how to properly test this or resolve some other way?