update bessel so that reverse mode is chosen over the perfect forward…

[SteveBronder]

Summary

This fixes bessel_second_kind so that the reverse mode specialization is chosen over the perfect forwarding version of the function we use for the vectorized prim function.

Tests

Added tests for bessel_second_kind that uses reverse mode autodiff for std::vector<int> and std::vector<std::vector<int>> as the lhs.

Side Effects

@WardBrian can we run the stanc3 tests on this to make sure this fixes the issue?

Release notes

Checklist

• Copyright holder: Steve Bronder

  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/)

• 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)

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

• the new changes are tested

[WardBrian]

Running here: https://jenkins.flatironinstitute.org/blue/organizations/jenkins/Stan%2FStanc3/detail/PR-1527/9/pipeline

[WardBrian]

Closer but still errors @SteveBronder

../../test/integration/good/function-signatures/math/matrix/bessel_second_kind.hpp:1751:9: error: call to 'bessel_second_kind' is ambiguous
        stan::math::bessel_second_kind(d_int_array, transformed_param_real),
        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
../../test/integration/good/function-signatures/math/matrix/bessel_second_kind.hpp:2784:12: note: in instantiation of function template specialization 'bessel_second_kind_model_namespace::bessel_second_kind_model::log_prob_impl<false, false, Eigen::Matrix<stan::math::var_value<double, void>, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, nullptr, nullptr, nullptr>' requested here
    return log_prob_impl<propto__, jacobian__>(params_r, params_i, pstream);
           ^
/home/jenkins/workspace/Stan_Stanc3_PR-1527@2/compile-good-O1/performance-tests-cmdstan/cmdstan/stan/src/stan/model/model_base_crtp.hpp:98:50: note: in instantiation of function template specialization 'bessel_second_kind_model_namespace::bessel_second_kind_model::log_prob<false, false, stan::math::var_value<double, void> >' requested here
    return static_cast<const M*>(this)->template log_prob<false, false>(theta,
                                                 ^
../../test/integration/good/function-signatures/math/matrix/bessel_second_kind.hpp:280:3: note: in instantiation of member function 'stan::model::model_base_crtp<bessel_second_kind_model_namespace::bessel_second_kind_model>::log_prob' requested here
  ~bessel_second_kind_model() {}
  ^
/home/jenkins/workspace/Stan_Stanc3_PR-1527@2/compile-good-O1/performance-tests-cmdstan/cmdstan/stan/lib/stan_math/stan/math/prim/fun/bessel_second_kind.hpp:57:13: note: candidate function [with T1 = const std::vector<int, std::allocator<int> > &, T2 = stan::math::var_value<double, void> &, $2 = nullptr, $3 = nullptr]
inline auto bessel_second_kind(T1&& a, T2&& b) {
            ^
/home/jenkins/workspace/Stan_Stanc3_PR-1527@2/compile-good-O1/performance-tests-cmdstan/cmdstan/stan/lib/stan_math/stan/math/rev/fun/bessel_second_kind.hpp:13:13: note: candidate function [with T1 = const std::vector<int, std::allocator<int> > &, T2 = stan::math::var_value<double, void> &, $2 = nullptr, $3 = nullptr]
inline auto bessel_second_kind(T1&& v, T2&& a) {
            ^
../../test/integration/good/function-signatures/math/matrix/bessel_second_kind.hpp:1760:9: error: call to 'bessel_second_kind' is ambiguous
        stan::math::bessel_second_kind(d_int_array_2d, transformed_param_real),
        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/jenkins/workspace/Stan_Stanc3_PR-1527@2/compile-good-O1/performance-tests-cmdstan/cmdstan/stan/lib/stan_math/stan/math/prim/fun/bessel_second_kind.hpp:57:13: note: candidate function [with T1 = const std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > &, T2 = stan::math::var_value<double, void> &, $2 = nullptr, $3 = nullptr]
inline auto bessel_second_kind(T1&& a, T2&& b) {
            ^
/home/jenkins/workspace/Stan_Stanc3_PR-1527@2/compile-good-O1/performance-tests-cmdstan/cmdstan/stan/lib/stan_math/stan/math/rev/fun/bessel_second_kind.hpp:13:13: note: candidate function [with T1 = const std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > &, T2 = stan::math::var_value<double, void> &, $2 = nullptr, $3 = nullptr]
inline auto bessel_second_kind(T1&& v, T2&& a) {
            ^
../../test/integration/good/function-signatures/math/matrix/bessel_second_kind.hpp:1769:9: error: call to 'bessel_second_kind' is ambiguous
        stan::math::bessel_second_kind(d_int_array_3d, transformed_param_real),
        ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/home/jenkins/workspace/Stan_Stanc3_PR-1527@2/compile-good-O1/performance-tests-cmdstan/cmdstan/stan/lib/stan_math/stan/math/prim/fun/bessel_second_kind.hpp:57:13: note: candidate function [with T1 = const std::vector<std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >, std::allocator<std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > > > &, T2 = stan::math::var_value<double, void> &, $2 = nullptr, $3 = nullptr]
inline auto bessel_second_kind(T1&& a, T2&& b) {
            ^
/home/jenkins/workspace/Stan_Stanc3_PR-1527@2/compile-good-O1/performance-tests-cmdstan/cmdstan/stan/lib/stan_math/stan/math/rev/fun/bessel_second_kind.hpp:13:13: note: candidate function [with T1 = const std::vector<std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >, std::allocator<std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > > > &, T2 = stan::math::var_value<double, void> &, $2 = nullptr, $3 = nullptr]
inline auto bessel_second_kind(T1&& v, T2&& a) {

[WardBrian]

Latest push passed over in stan-dev/stanc3#1540

[stan-buildbot]

---

Name	Old Result	New Result	Ratio	Performance change( 1 - new / old )
arma/arma.stan	0.31	0.3	1.02	1.67% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan	0.01	0.01	1.03	2.57% faster
gp_regr/gen_gp_data.stan	0.02	0.02	1.03	3.27% faster
gp_regr/gp_regr.stan	0.09	0.09	1.01	1.36% faster
sir/sir.stan	68.7	67.34	1.02	1.97% faster
irt_2pl/irt_2pl.stan	3.93	3.97	0.99	-0.98% slower
eight_schools/eight_schools.stan	0.05	0.06	0.93	-7.52% slower
pkpd/sim_one_comp_mm_elim_abs.stan	0.24	0.24	1.01	0.86% faster
pkpd/one_comp_mm_elim_abs.stan	18.87	18.51	1.02	1.92% faster
garch/garch.stan	0.41	0.4	1.02	1.78% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan	2.7	2.62	1.03	2.97% faster
arK/arK.stan	1.79	1.72	1.05	4.37% faster
gp_pois_regr/gp_pois_regr.stan	2.84	2.68	1.06	5.53% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan	8.67	8.35	1.04	3.64% faster
performance.compilation	173.57	177.46	0.98	-2.24% slower
Mean result: 1.0152456205193936

---

Jenkins Console Log
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Commit hash: a534e266df6d111101436ad27c8924a8af101e00

---

Machine information

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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

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