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Fix gamma lccdf#3275

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syclik wants to merge 3 commits intodevelopfrom
fix-gamma-lccdf-v3
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Fix gamma lccdf#3275
syclik wants to merge 3 commits intodevelopfrom
fix-gamma-lccdf-v3

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@syclik syclik commented Feb 5, 2026

Summary

This pr closes #3257. The gamma_lccdf experiences numerical instability for alpha approximately greater than 30. It’s due to gamma_q or grad_reg_inc_gamma. This pr rewrites the code to use gamma_p and grad_reg_lower_inc_gamma, which avoids potential instability in a tgamma(alpha) and digamma(alpha) call. It seems to sample a bit faster than just wrapping gamma_lcdf with log1m_exp.

This fixes the reverted PR: #3272.

cc: @spinkney

Tests

New probability tests in the problematic regime.

Release notes

The gamma_lccdf is made more robust for alpha values. The issue was overflow in the derivatives when alpha was greater than 30.

Checklist

  • Copyright holder: Publicis Groupe, Daniel Lee
    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

@syclik syclik requested a review from spinkney February 5, 2026 15:32
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spinkney commented Feb 5, 2026

thanks! I'll take a look tomorrow and then we'll probably want @SteveBronder to look it over too

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Name Old Result New Result Ratio Performance change( 1 - new / old )
gp_regr/gp_regr.stan 0.09 0.09 1.01 0.61% faster
gp_regr/gen_gp_data.stan 0.02 0.02 0.99 -0.96% slower
arK/arK.stan 1.72 1.71 1.01 0.62% faster
eight_schools/eight_schools.stan 0.05 0.05 0.99 -0.76% slower
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan 8.35 8.33 1.0 0.19% faster
pkpd/one_comp_mm_elim_abs.stan 18.52 18.56 1.0 -0.22% slower
pkpd/sim_one_comp_mm_elim_abs.stan 0.24 0.24 1.0 -0.18% slower
sir/sir.stan 67.43 67.52 1.0 -0.13% slower
gp_pois_regr/gp_pois_regr.stan 2.72 2.72 1.0 -0.32% slower
low_dim_gauss_mix/low_dim_gauss_mix.stan 2.59 2.61 0.99 -0.87% slower
irt_2pl/irt_2pl.stan 3.93 3.9 1.01 0.81% faster
arma/arma.stan 0.27 0.27 1.01 0.76% faster
garch/garch.stan 0.41 0.4 1.02 1.49% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan 0.01 0.01 1.04 3.77% faster
performance.compilation 216.05 216.44 1.0 -0.18% slower
Mean result: 1.0032247855384595

Jenkins Console Log
Blue Ocean
Commit hash: 1b337025e3b7d081640d4cabb20b61b24aa7a46a


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
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

@SteveBronder
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@spinkney have you had a change to look yet?

@SteveBronder
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@syclik I made a good number of cleanup changes in the branch below. Feel free to take a look and merge what you would like
https://github.com/stan-dev/math/tree/fix/gamma-lccdf-v3-review
(diff)
https://github.com/stan-dev/math/compare/fix-gamma-lccdf-v3...fix/gamma-lccdf-v3-review?expand=1

spinkney
spinkney previously approved these changes Mar 10, 2026
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@syclik or @spinkney can one of yinz have a look at the changes I made below? imo I think it would be nice to clean this a bit before merge.

https://github.com/stan-dev/math/tree/fix/gamma-lccdf-v3-review
(diff)
https://github.com/stan-dev/math/compare/fix-gamma-lccdf-v3...fix/gamma-lccdf-v3-review?expand=1

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@syclik or @spinkney can one of yinz have a look at the changes I made below? imo I think it would be nice to clean this a bit before merge.

https://github.com/stan-dev/math/tree/fix/gamma-lccdf-v3-review (diff) https://github.com/stan-dev/math/compare/fix-gamma-lccdf-v3...fix/gamma-lccdf-v3-review?expand=1

That looks good for what I understand. I still don't have a good grasp of decay_t or why (un)likely helps (maybe we can meet for 30 min and you can describe it to me). I like the .first/second and switch to y_val, I feel like I should've written it as the latter to begin with!

On the auto decs, I know @syclik prefers to declare the exact type if possible. I'll let him weigh in if he's OK with those.

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syclik commented Mar 11, 2026

On the auto decs, I know @syclik prefers to declare the exact type if possible. I'll let him weigh in if he's OK with those.

I absolutely prefer the more explicit types. While there's a lot of benefit to auto, right now we're still relying on human devs to read and understand the code. The explicit types make it a lot easier to track what's going on.

Otherwise, nice changes! Should we try to open a PR against this branch and we can merge most of it?

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SteveBronder commented Mar 11, 2026

Just opened a PR here!

#3292

Feel free to add or remove what you like.

That looks good for what I understand. I still don't have a good grasp of decay_t or why (un)likely helps (maybe we can meet for 30 min and you can describe it to me).

std::decay_t is used on a type to remove any const or reference & it may have. So if your type is const double& and you do using ret = std::decay_t<const double&> then the type of ret is double. C++'s type system treats const and & as modifying the type T and is a separate type than T. That means that if a type trait expects only plain types and we give it a const T then the type trait would not produce the answer we expect.

The godbolt below has an example that may be easier to understand than my description above.
https://godbolt.org/z/961d5E4nP

(unlikely) is a compiler hint for which side of an if statement is (un)likely to happen. So if we tell the compiler which side of an if statement is most likely than it will arrange the assembly to expect to go through the more likely side with a jump for the unlikely side.

In the godbolt below, the top left program has unlikely and the bottom program has likely. You can see that for the likely it puts the first branch inline and then has a jump for going to the now unlikely else branch. In the second program that has unlikely, the else branch is put inline and the first branch is instead put behind a jmp. So unlikely is nice to use for conditions like if (is_na(x)) because we don't expect that route to happen very often. So we use if (unlikely(is_na(x))) to tell the compiler this is unlikely to happen so that it puts the inside of the if statement behind a jmp instruction.

https://godbolt.org/z/ocThfc8fK

Also happy to jump on a call to chat!

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Name Old Result New Result Ratio Performance change( 1 - new / old )
gp_regr/gp_regr.stan 0.12 0.09 1.28 21.58% faster
gp_regr/gen_gp_data.stan 0.02 0.02 1.03 2.54% faster
arK/arK.stan 1.76 1.7 1.03 3.35% faster
eight_schools/eight_schools.stan 0.05 0.05 1.02 2.15% faster
low_dim_gauss_mix_collapse/low_dim_gauss_mix_collapse.stan 8.57 8.39 1.02 2.11% faster
pkpd/one_comp_mm_elim_abs.stan 19.13 18.65 1.03 2.54% faster
pkpd/sim_one_comp_mm_elim_abs.stan 0.26 0.25 1.06 5.71% faster
sir/sir.stan 67.46 65.96 1.02 2.22% faster
gp_pois_regr/gp_pois_regr.stan 2.81 2.74 1.03 2.5% faster
low_dim_gauss_mix/low_dim_gauss_mix.stan 2.62 2.56 1.02 2.08% faster
irt_2pl/irt_2pl.stan 4.03 3.89 1.03 3.36% faster
arma/arma.stan 0.28 0.27 1.02 1.73% faster
garch/garch.stan 0.41 0.4 1.04 3.43% faster
low_dim_corr_gauss/low_dim_corr_gauss.stan 0.01 0.01 1.04 3.85% faster
performance.compilation 217.77 215.21 1.01 1.17% faster
Mean result: 1.0450235956538003

Jenkins Console Log
Blue Ocean
Commit hash: e54f8430358b51f678186c551d8b7ce3a19d9c1c


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: 3465.967
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
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

@SteveBronder
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Ping me when tests pass and I'll approve

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@SteveBronder thank you for those godbolts! That's super helpful!

Also, do we need to restart the tests?

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syclik commented Mar 12, 2026

I might have messed up some of the types. Let me check into it first, @spinkney

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syclik commented Mar 13, 2026

@SteveBronder, the proposed changes that you made didn't actually work. I went back to your last commit: 3fb810f.

The updates I made to the branch didn't solve the problem.

Here's the reproducible way to get the error:

git clean -d -x -f
make generate-tests
make test/prob/gamma/gamma_ccdf_log_00000_generated_ffv_test

At commit 3fb810f, the compiler error looks like:

$ make test/prob/gamma/gamma_ccdf_log_00000_generated_ffv_test
clang++ -std=c++17 -Wno-unknown-warning-option -Wno-tautological-compare -Wno-sign-compare -D_REENTRANT -ffp-contract=off -Wno-ignored-attributes      -I lib/tbb_2020.3/include    -O3  -I . -I lib/eigen_3.4.0 -I lib/boost_1.87.0 -I lib/sundials_6.1.1/include -I lib/sundials_6.1.1/src/sundials -I lib/benchmark_1.5.1/googletest/googletest/include -I lib/benchmark_1.5.1/googletest/googletest -I lib/benchmark_1.5.1/googletest/googletest/include -I lib/benchmark_1.5.1/googletest/googletest      -DBOOST_DISABLE_ASSERTS            -c -o test/prob/gamma/gamma_ccdf_log_00000_generated_ffv_test.o test/prob/gamma/gamma_ccdf_log_00000_generated_ffv_test.cpp
In file included from test/prob/gamma/gamma_ccdf_log_00000_generated_ffv_test.cpp:3:
In file included from ./test/prob/test_fixture_distr.hpp:4:
In file included from ./stan/math/mix.hpp:31:
In file included from ./stan/math/prim.hpp:18:
In file included from ./stan/math/prim/prob.hpp:107:
In file included from ./stan/math/prim/prob/gamma_ccdf_log.hpp:5:
In file included from ./stan/math/prim/prob/gamma_lccdf.hpp:22:
./stan/math/prim/fun/log_gamma_q_dgamma.hpp:51:11: error: assigning to 'double' from incompatible type 'fvar<var_value<double, void>>'
   51 |     D = b + an * D;
      |         ~~^~~~~~~~
./stan/math/prim/prob/gamma_lccdf.hpp:46:25: note: in instantiation of function template specialization 'stan::math::internal::log_q_gamma_cf<double, stan::math::fvar<stan::math::var_value<double>>>' requested here
   46 |     ret_t out{internal::log_q_gamma_cf(alpha, beta_y), 0.0};
      |                         ^
./stan/math/prim/prob/gamma_ccdf_log.hpp:16:10: note: in instantiation of function template specialization 'stan::math::gamma_lccdf<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>>' requested here
   16 |   return gamma_lccdf<T_y, T_shape, T_inv_scale>(y, alpha, beta);
      |          ^
./test/prob/gamma/gamma_ccdf_log_test.hpp:87:24: note: in instantiation of function template specialization 'stan::math::gamma_ccdf_log<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>>' requested here
   87 |     return stan::math::gamma_ccdf_log(y, alpha, beta);
      |                        ^
./test/prob/test_fixture_ccdf_log.hpp:105:26: note: in instantiation of function template specialization 'AgradCcdfLogGamma::ccdf_log<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>, empty, empty, empty>' requested here
  105 |       TestClass.template ccdf_log<T0, T1, T2, T3, T4, T5>(p0, p1, p2, p3, p4,
      |                          ^
./test/prob/test_fixture_ccdf_log.hpp:828:9: note: in instantiation of member function 'AgradCcdfLogTestFixture<std::tuple<AgradCcdfLogGamma, std::tuple<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>, empty, empty, empty>>>::call_all_versions' requested here
  828 |   this->call_all_versions();
      |         ^
lib/benchmark_1.5.1/googletest/googletest/include/gtest/internal/gtest-internal.h:472:44: note: in instantiation of member function 'gtest_suite_AgradCcdfLogTestFixture_::CallAllVersions<std::tuple<AgradCcdfLogGamma, std::tuple<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>, empty, empty, empty>>>::TestBody' requested here
  472 |   Test* CreateTest() override { return new TestClass; }
      |                                            ^
lib/benchmark_1.5.1/googletest/googletest/include/gtest/internal/gtest-internal.h:730:13: note: in instantiation of member function 'testing::internal::TestFactoryImpl<gtest_suite_AgradCcdfLogTestFixture_::CallAllVersions<std::tuple<AgradCcdfLogGamma, std::tuple<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>, empty, empty, empty>>>>::CreateTest' requested here
  730 |         new TestFactoryImpl<TestClass>);
      |             ^
lib/benchmark_1.5.1/googletest/googletest/include/gtest/internal/gtest-internal.h:789:50: note: in instantiation of member function 'testing::internal::TypeParameterizedTest<AgradCcdfLogTestFixture, testing::internal::TemplateSel<gtest_suite_AgradCcdfLogTestFixture_::CallAllVersions>, testing::internal::Types<std::tuple<AgradCcdfLogGamma, std::tuple<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>, empty, empty, empty>>>>::Register' requested here
  789 |     TypeParameterizedTest<Fixture, Head, Types>::Register(
      |                                                  ^
test/prob/gamma/gamma_ccdf_log_00000_generated_ffv_test.cpp:211:1: note: in instantiation of member function 'testing::internal::TypeParameterizedTestSuite<AgradCcdfLogTestFixture, testing::internal::Templates<gtest_suite_AgradCcdfLogTestFixture_::CallAllVersions, gtest_suite_AgradCcdfLogTestFixture_::ValidValues, gtest_suite_AgradCcdfLogTestFixture_::InvalidValues, gtest_suite_AgradCcdfLogTestFixture_::FiniteDiff, gtest_suite_AgradCcdfLogTestFixture_::Function, gtest_suite_AgradCcdfLogTestFixture_::RepeatAsVector, gtest_suite_AgradCcdfLogTestFixture_::LowerBound, gtest_suite_AgradCcdfLogTestFixture_::UpperBound, gtest_suite_AgradCcdfLogTestFixture_::AsScalarsVsAsVector, gtest_suite_AgradCcdfLogTestFixture_::Length0Vector>, testing::internal::Types<std::tuple<AgradCcdfLogGamma, std::tuple<double, double, stan::math::fvar<stan::math::fvar<stan::math::var_value<double>>>, empty, empty, empty>>>>::Register' requested here
  211 | INSTANTIATE_TYPED_TEST_SUITE_P(AgradCcdfLogGamma_ffv_0, AgradCcdfLogTestFixture, AgradCcdfLogGamma_ffv_0);
      | ^

and it keeps going.

I didn't delete the proposed branch, so what I'll do is reset this branch back to the last working commit.

@syclik syclik force-pushed the fix-gamma-lccdf-v3 branch from e4240a7 to 86ac561 Compare March 13, 2026 00:16
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syclik commented Mar 13, 2026

@SteveBronder, this branch was reset back to 86ac561 (the last commit before the fix/gamma-lccdf-v3-review branch).

Do you want to reset the other branch back to 3fb810f and work through the test?

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Fix gamma_lccdf actually

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