Implement logit function

include/boost/math/special_functions/logit.hpp

@@ -0,0 +1,54 @@
+// Copyright Matt Borland 2025.
+// 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)
+
+#ifndef BOOST_MATH_SF_LOGIT_HPP
+#define BOOST_MATH_SF_LOGIT_HPP
+
+#include <boost/math/tools/config.hpp>
+#include <boost/math/policies/policy.hpp>
+#include <cmath>
+#include <cfenv>
+
+namespace boost {
+namespace math {
+
+template <typename RealType, typename Policy>
+RealType logit(RealType p, const Policy&)
+{
+    BOOST_MATH_STD_USING
+
+    using promoted_real_type = typename policies::evaluation<RealType, Policy>::type;
+
+    std::fexcept_t flags;
+    std::fegetexceptflag(&flags, FE_ALL_EXCEPT);
+
+    static const RealType crossover {RealType{1}/4};
+    const auto promoted_p {static_cast<promoted_real_type>(p)};
+    RealType result {};
+    if (p > crossover)
+    {
+        result = 2 * atanh(2 * promoted_p - 1);
+    }
+    else
+    {
+        result = log((1 - promoted_p) / promoted_p);
+    }
+
+    std::fesetexceptflag(&flags, FE_ALL_EXCEPT);
+
+    return result;
+}
+
+template <typename RealType>
+RealType logit(RealType p)
+{
+    return logit(p, policies::policy<>());
+}
+
+} // namespace math
+} // namespace boost
+
+#endif // BOOST_MATH_SF_LOGIT_HPP