fix standalone gqs rng seed

[avehtari]

Fixes #3401.

The fix and PR message were assisted by Claude

Submission Checklist

• Run unit tests: ./runTests.py src/test/unit
• Run cpplint: make cpplint
• Declare copyright holder and open-source license: see below

Summary

Neither overload of standalone_generate could use a
chain id, because neither accepted one:

• the single-chain overload seeded with create_rng(seed, 1), a
  hard-coded 1;
• the multi-chain overload seeded chain i with
  create_rng(seed, i + 1), where i is the chain's index within the
  current process, so it restarts from 0 in every process.

When chains run as separate processes — what CmdStanR and CmdStanPy do
for parallel_chains — both forms give every chain the same stream, and
every chain returns identical *_rng draws.

This PR adds a chain id parameter to each overload, named as in the
sampler services (hmc_nuts_diag_e_adapt et al.), and seeds with it:

create_rng(seed, chain)                 // single-chain overload
create_rng(seed, init_chain_id + i)     // chain i, multi-chain overload

Both parameters are trailing and default to 1, so existing calls
compile unchanged and keep their current behaviour.

The fix has no user-visible effect until CmdStan forwards its id
argument, which requires another PR (to be submitted soon)

Intended Effect

Standalone generated quantities launched as one process per chain — what
CmdStanR and CmdStanPy do for parallel_chains — get independent random
number streams, instead of every chain repeating stream 1.

How to Verify

./runTests.py src/test/unit/services/sample/standalone_gqs_parallel_test.cpp

Two new tests:

• genDraws_bernoulli_chain_id_rng — the same draws generated with
  chain = 1 and chain = 2 must differ, and generating twice with
  chain = 1 must give identical output;
• genDraws_bernoulli_init_chain_id_offset — a two-chain run with
  init_chain_id = 3 must reproduce chains 3 and 4 of a four-chain run
  with init_chain_id = 1.

End-to-end verification is in the CmdStan PR (id=1 vs id=2 on the
command line), because that is where id is parsed.

Side Effects

No API break: both parameters are trailing with a default of 1, so
every existing call compiles and behaves exactly as before.

The sampler services take chain / init_chain_id as required parameters, and matching that
would be more consistent, but that would have broke building CmdStan and RStan. With the default, nothing
breaks. CmdStan needs a patch anyway to get the correct behavior.

Documentation

None needed; the parameter is documented in the comments

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company):

Aki Vehtari

By submitting this pull request, the copyright holder is agreeing to 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/)

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
gp_regr/gp_regr.stan	0.11	0.11	1.01	0.82% faster
gp_regr/gen_gp_data.stan	0.02	0.02	1.03	2.73% faster
arK/arK.stan	1.63	1.58	1.03	2.85% faster
eight_schools/eight_schools.stan	0.06	0.06	1.02	1.61% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.7	8.49	1.02	2.39% faster
pkpd/one_comp_mm_elim_abs.stan	19.78	19.18	1.03	3.06% faster
pkpd/sim_one_comp_mm_elim_abs.stan	0.26	0.27	0.97	-3.49% slower
sir/sir.stan	70.96	70.15	1.01	1.14% faster
gp_pois_regr/gp_pois_regr.stan	2.42	2.34	1.04	3.4% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.88	2.69	1.07	6.41% faster
irt_2pl/irt_2pl.stan	5.2	4.93	1.05	5.15% faster
arma/arma.stan	0.31	0.28	1.08	7.61% faster
garch/garch.stan	0.47	0.44	1.07	6.56% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.09	8.22% faster
performance.compilation	276.6	262.72	1.05	5.02% faster
Mean result: 1.0379243919756296

---

Jenkins Console Log
Blue Ocean
Commit hash: 07501d859c49af3d678c3b786da70a7e77d8e698

---

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: 3099.999
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: Split huge pages
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
Vulnerability Vmscape: Mitigation; IBPB before exit to userspace
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