Fix the MSVC warning and the no-exceptions link error in mode_has_nan

doc/statistics/univariate_statistics.qbk

@@ -392,6 +392,7 @@ Compute the mode(s) of a data set:
 
 /Nota bene/: The input data must be sorted in order to pass a forward iterator. If data is not sorted random access iterators are required for a call to `std::sort`.
 Data containing a NaN have no mode, and a `std::domain_error` is thrown.
+If exceptions are disabled, no mode is written.
 
 [heading References]
 

include/boost/math/statistics/detail/single_pass.hpp

@@ -369,12 +369,14 @@ template<typename ForwardIterator>
 bool mode_has_nan(ForwardIterator first, ForwardIterator last)
 {
     using Z = typename std::iterator_traits<ForwardIterator>::value_type;
-    if (std::any_of(first, last, [](const Z& z) { return !(z == z); }))
+    const bool has_nan = std::any_of(first, last, [](const Z& z) { return !(z == z); });
+#ifndef BOOST_MATH_NO_EXCEPTIONS
+    if (has_nan)
     {
         BOOST_MATH_THROW_EXCEPTION(std::domain_error("The mode is undefined for data containing a NaN."))
-        return true;
     }
-    return false;
+#endif
+    return has_nan;
 }
 
 template<typename ForwardIterator, typename OutputIterator>

test/Jamfile.v2

@@ -1117,6 +1117,7 @@ test-suite misc :
        /boost/test//boost_unit_test_framework ]
    [ run test_ulp.cpp /boost/test//boost_unit_test_framework ]
    [ run git_issue_1419.cpp ]
+   [ run git_issue_1621.cpp ]
    [ compile-fail git_issue_1421.cpp ]
 
 #   [ run __temporary_test.cpp test_instances//test_instances : : : <test-info>always_show_run_output <pch>off ]
@@ -2004,6 +2005,7 @@ alias no_eh_tests :
    #test_tools_ulps_plot_incl
    #test_tools_ulps_heatmap_incl
    test_tools_workaround_incl
+   git_issue_1621
 ;
 
 explicit no_eh_tests ;

test/git_issue_1621.cpp

@@ -0,0 +1,29 @@
+//  Copyright 2026 Shen-Ta Hsieh
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+//  See: https://github.com/boostorg/math/issues/1621
+
+#include <boost/math/statistics/univariate_statistics.hpp>
+#include <boost/core/lightweight_test.hpp>
+#include <iterator>
+#include <limits>
+#include <stdexcept>
+#include <vector>
+
+int main()
+{
+    std::vector<double> v {1.0, 2.0, 2.0, std::numeric_limits<double>::quiet_NaN()};
+    std::vector<double> modes;
+
+    // Without exceptions, data that contain a NaN give no mode, and boost::throw_exception is not called
+#ifndef BOOST_MATH_NO_EXCEPTIONS
+    BOOST_TEST_THROWS(boost::math::statistics::mode(v.begin(), v.end(), std::back_inserter(modes)), std::domain_error);
+#else
+    boost::math::statistics::mode(v.begin(), v.end(), std::back_inserter(modes));
+#endif
+    BOOST_TEST(modes.empty());
+
+    return boost::report_errors();
+}