This updates the underlying gamma distribution in the param function by
invoking the param function on the corresponding member:
 * _M_gd for negative_binomial_distribution, student_t_distribution;
 * _M_gd_x, _M_gd_y for fisher_f_distribution.

The distribution_param.cc test, validates that for all distributions,
constructing or setting params results in equal distribution that
produces same values. The test uses -ffloat-store for -m32, following
chi_squared_distribution test for PR83833 - that is removed, as all
cases are covered in new test.

libstdc++-v3/ChangeLog:

        PR libstdc++/123409
        * include/bits/random.h (negative_binomial_distribution::param)
        (fisher_f_distribution::param, student_t_distribution::param):
        Updated underlying gamma distributions, by calling param.
        (chi_squared_distribution::param): Use type alias and parenthesis
        for consistency.
        * testsuite/26_numerics/random/distribution_param.cc: New test.
        * testsuite/26_numerics/random/chi_squared_distribution/83833.cc: 
Removed,
        covered by above.
---
v2 was written from scratch, as I started with the test for all distributions,
and fixed ones for which they are failing (and I about the patch existing).
Still sending is as v2, so we know that patch was handled.

Tested on x86_64-linux. *random* test passed in all standard modes,
-m32, debug and assertions. OK for trunk, and backports up to 14?


 libstdc++-v3/include/bits/random.h            | 32 ++++++++--
 .../random/chi_squared_distribution/83833.cc  | 41 -------------
 .../26_numerics/random/distribution_param.cc  | 60 +++++++++++++++++++
 3 files changed, 86 insertions(+), 47 deletions(-)
 delete mode 100644 
libstdc++-v3/testsuite/26_numerics/random/chi_squared_distribution/83833.cc
 create mode 100644 
libstdc++-v3/testsuite/26_numerics/random/distribution_param.cc

diff --git a/libstdc++-v3/include/bits/random.h 
b/libstdc++-v3/include/bits/random.h
index cfec087f0cd..1a2900e2b9d 100644
--- a/libstdc++-v3/include/bits/random.h
+++ b/libstdc++-v3/include/bits/random.h
@@ -3559,9 +3559,10 @@ _GLIBCXX_END_INLINE_ABI_NAMESPACE(_V2)
       param(const param_type& __param)
       {
        _M_param = __param;
-       typedef typename std::gamma_distribution<result_type>::param_type
-         param_type;
-       _M_gd.param(param_type{__param.n() / 2});
+
+       using param_type
+         = typename std::gamma_distribution<result_type>::param_type;
+       _M_gd.param(param_type(__param.n() / 2));
       }
 
       /**
@@ -4015,7 +4016,14 @@ _GLIBCXX_END_INLINE_ABI_NAMESPACE(_V2)
        */
       void
       param(const param_type& __param)
-      { _M_param = __param; }
+     {
+       _M_param = __param;
+
+       using param_type
+         = typename std::gamma_distribution<result_type>::param_type;
+       _M_gd_x.param(param_type(__param.m() / 2));
+       _M_gd_y.param(param_type(__param.n() / 2));
+      }
 
       /**
        * @brief Returns the greatest lower bound value of the distribution.
@@ -4244,7 +4252,13 @@ _GLIBCXX_END_INLINE_ABI_NAMESPACE(_V2)
        */
       void
       param(const param_type& __param)
-      { _M_param = __param; }
+      {
+       _M_param = __param;
+
+       using param_type
+         = typename std::gamma_distribution<result_type>::param_type;
+       _M_gd.param(param_type(__param.n() / 2, 2));
+      }
 
       /**
        * @brief Returns the greatest lower bound value of the distribution.
@@ -5175,7 +5189,13 @@ _GLIBCXX_END_INLINE_ABI_NAMESPACE(_V2)
        */
       void
       param(const param_type& __param)
-      { _M_param = __param; }
+      {
+       _M_param = __param;
+
+       using param_type
+         = typename std::gamma_distribution<double>::param_type;
+       _M_gd.param(param_type(__param.k(), (1.0 - __param.p()) / __param.p()));
+      }
 
       /**
        * @brief Returns the greatest lower bound value of the distribution.
diff --git 
a/libstdc++-v3/testsuite/26_numerics/random/chi_squared_distribution/83833.cc 
b/libstdc++-v3/testsuite/26_numerics/random/chi_squared_distribution/83833.cc
deleted file mode 100644
index 4008f7db89c..00000000000
--- 
a/libstdc++-v3/testsuite/26_numerics/random/chi_squared_distribution/83833.cc
+++ /dev/null
@@ -1,41 +0,0 @@
-// Copyright (C) 2018-2026 Free Software Foundation, Inc.
-//
-// This file is part of the GNU ISO C++ Library.  This library is free
-// software; you can redistribute it and/or modify it under the
-// terms of the GNU General Public License as published by the
-// Free Software Foundation; either version 3, or (at your option)
-// any later version.
-
-// This library is distributed in the hope that it will be useful,
-// but WITHOUT ANY WARRANTY; without even the implied warranty of
-// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-// GNU General Public License for more details.
-
-// You should have received a copy of the GNU General Public License along
-// with this library; see the file COPYING3.  If not see
-// <http://www.gnu.org/licenses/>.
-
-// { dg-do run { target c++11 } }
-// { dg-additional-options "-ffloat-store" { target { m68*-*-* || ia32 } } }
-// { dg-require-cstdint "" }
-
-#include <random>
-#include <testsuite_hooks.h>
-
-void
-test01()
-{
-  std::default_random_engine r1, r2;
-  using chi = std::chi_squared_distribution<double>;
-  chi::param_type p(5);
-  chi d1(p);
-  chi d2;
-  d2.param(p);
-  VERIFY( d1(r1) == d2(r2) ); // PR libstdc++/83833
-}
-
-int
-main()
-{
-  test01();
-}
diff --git a/libstdc++-v3/testsuite/26_numerics/random/distribution_param.cc 
b/libstdc++-v3/testsuite/26_numerics/random/distribution_param.cc
new file mode 100644
index 00000000000..d6c06766233
--- /dev/null
+++ b/libstdc++-v3/testsuite/26_numerics/random/distribution_param.cc
@@ -0,0 +1,60 @@
+// { dg-do run { target c++11 } }
+// { dg-additional-options "-ffloat-store" { target { m68*-*-* || ia32 } } }
+// { dg-require-cstdint "" }
+
+#include <random>
+#include <testsuite_hooks.h>
+
+template<typename Distribution>
+void
+validate(Distribution&& source)
+{
+  const auto& params = source.param();
+
+  Distribution constr(params);
+  VERIFY( constr == source );
+
+  Distribution setter;
+  setter.param(params);
+  VERIFY( setter == source );
+
+  std::mt19937_64 e1(0x19650809ull), e2 = e1, e3 = e1;
+  for (int i = 0; i < 10; ++i)
+  {
+    const auto expected = source(e1);
+    VERIFY( constr(e2) == expected );
+    VERIFY( setter(e3) == expected );
+  }
+}
+
+int main()
+{
+  // PR83833, PR123409
+  validate(std::uniform_int_distribution<>(13, 22));
+  validate(std::uniform_real_distribution<>(1.0, 9.0));
+
+  validate(std::bernoulli_distribution(0.478));
+  validate(std::binomial_distribution<>(7, 0.334));
+  validate(std::negative_binomial_distribution<>(726, 0.65));
+  validate(std::geometric_distribution<>(0.545));
+
+  validate(std::poisson_distribution<>(6));
+  validate(std::exponential_distribution<>(3));
+  validate(std::gamma_distribution<>(1.1, 2.2));
+  validate(std::weibull_distribution<>(1.7, 3.0));
+  validate(std::extreme_value_distribution<>(-1.628, 1.628));
+
+  validate(std::normal_distribution<>(5.0, 2.0));
+  validate(std::lognormal_distribution<>(1.67, 0.25));
+  validate(std::chi_squared_distribution<>(5));
+  validate(std::cauchy_distribution<>(-3, 0.25));
+  validate(std::fisher_f_distribution<>(26.0, 7.0));
+  validate(std::student_t_distribution<>(65.0));
+
+  const auto wf = [](double x) { return 1 + x; };
+  validate(std::discrete_distribution<>(4, 1.2, 4.5, wf));
+  validate(std::piecewise_constant_distribution<>(5, 0.5, 9, wf));
+  validate(std::piecewise_linear_distribution<>(3, 1.2, 3.4, wf));
+
+  return 0;
+}
-- 
2.55.0

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