From 2a9394a655ee94c4c6c680561cd1b64b59387166 Mon Sep 17 00:00:00 2001
From: Jacob Hass <jacobhass8@gmail.com>
Date: Thu, 12 Feb 2026 11:18:34 -0800
Subject: [PATCH] Reverted nc=0 condition and changed relaxed test conditions

---
 .../math/distributions/non_central_f.hpp      | 21 +++++++++++--------
 test/test_nc_f.cpp                            |  2 +-
 2 files changed, 13 insertions(+), 10 deletions(-)

diff --git a/include/boost/math/distributions/non_central_f.hpp b/include/boost/math/distributions/non_central_f.hpp
index c0acc8225..0fd33e6da 100644
--- a/include/boost/math/distributions/non_central_f.hpp
+++ b/include/boost/math/distributions/non_central_f.hpp
@@ -46,8 +46,7 @@ namespace boost
          };
          
          template <class RealType, class Policy>
-         BOOST_MATH_GPU_ENABLED RealType find_non_centrality_f(const RealType x, const RealType v1, const RealType v2, const RealType p, const RealType q, const Policy& pol)         
-         {
+         BOOST_MATH_GPU_ENABLED RealType find_non_centrality_f(const RealType x, const RealType v1, const RealType v2, const RealType p, const RealType q, const RealType p_q_precision, const Policy& pol)         {
             constexpr auto function = "non_central_f<%1%>::find_non_centrality";
 
             if ( p == 0 || q == 0) {
@@ -55,14 +54,16 @@ namespace boost
                   RealType(boost::math::numeric_limits<RealType>::quiet_NaN()), Policy()); // LCOV_EXCL_LINE
             }
 
-            non_centrality_finder_f<RealType, Policy> f(x, v1, v2, p < q ? p : q, p < q ? false : true);
-
             // Check if nc = 0 (which is just the F-distribution)
-            // When the relative difference between the cdf with nc=0
-            // and p drops below 1e-6, the function f becomes 
-            // numerically unstable. Thus, we can't find nc below this point. 
-            // See PR 1345 for more details. 
-            if (abs(f(tools::min_value<RealType>()) / p) <= 1e-6){
+            non_centrality_finder_f<RealType, Policy> f(x, v1, v2, p < q ? p : q, p < q ? false : true);
+            // This occurs when the root finder would need to find a result smaller than
+            // tools::min_value (which it cannot do).  Note that we have to add in a small
+            // amount of "tolerance" since the subtraction in our termination condition
+            // implies a small amount of wobble in the result which should be of the
+            // order p * eps (note not q * eps, since q is calculated as 1-p).
+            // Also note that p_q_precision is passed down from our caller as the
+            // epsilon of the original called values, and not after possible promotion.
+            if (f(tools::min_value<RealType>()) <= 20 * p_q_precision * p){
                return 0;
             }
 
@@ -135,6 +136,7 @@ namespace boost
                static_cast<eval_type>(v2),
                static_cast<eval_type>(p),
                static_cast<eval_type>(1-p),
+               static_cast<eval_type>(tools::epsilon<RealType>()),
                forwarding_policy());
             return policies::checked_narrowing_cast<RealType, forwarding_policy>(
                result,
@@ -157,6 +159,7 @@ namespace boost
                static_cast<eval_type>(c.param2),
                static_cast<eval_type>(1-c.param3),
                static_cast<eval_type>(c.param3),
+               static_cast<eval_type>(tools::epsilon<RealType>()),
                forwarding_policy());
             return policies::checked_narrowing_cast<RealType, forwarding_policy>(
                result,
diff --git a/test/test_nc_f.cpp b/test/test_nc_f.cpp
index 5a1cd4da6..6b7c2347a 100644
--- a/test/test_nc_f.cpp
+++ b/test/test_nc_f.cpp
@@ -336,7 +336,7 @@ void test_spots(RealType, const char* name = nullptr)
    for (RealType x : x_vals)
    {
       RealType P = cdf(dist_no_centrality, x);
-      BOOST_CHECK_LE(dist.find_non_centrality(x, a, b, P), boost::math::tools::min_value<RealType>() * 10);
+      BOOST_CHECK_LE(dist.find_non_centrality(x, a, b, P), tolerance);
    }
    // Case when P=1 or P=0 
    BOOST_MATH_CHECK_THROW(dist.find_non_centrality(x, a, b, 1), std::domain_error);