Improve numerical stability of binomial_logit, add tests

stan/math/prim/prob/binomial_logit_lpmf.hpp

@@ -3,14 +3,11 @@
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
-#include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
-#include <stan/math/prim/fun/as_array_or_scalar.hpp>
 #include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
 #include <stan/math/prim/fun/binomial_coefficient_log.hpp>
-#include <stan/math/prim/fun/inc_beta.hpp>
-#include <stan/math/prim/fun/inv_logit.hpp>
-#include <stan/math/prim/fun/lbeta.hpp>
-#include <stan/math/prim/fun/log.hpp>
+#include <stan/math/prim/fun/log_inv_logit.hpp>
+#include <stan/math/prim/fun/log1m_inv_logit.hpp>
+#include <stan/math/prim/fun/exp.hpp>
 #include <stan/math/prim/fun/max_size.hpp>
 #include <stan/math/prim/fun/size.hpp>
 #include <stan/math/prim/fun/size_zero.hpp>
@@ -66,33 +63,22 @@ return_type_t<T_prob> binomial_logit_lpmf(const T_n& n, const T_N& N,
   if (!include_summand<propto, T_prob>::value) {
     return 0.0;
   }
-  const auto& inv_logit_alpha
-      = to_ref_if<!is_constant_all<T_prob>::value>(inv_logit(alpha_val));
-  const auto& inv_logit_neg_alpha
-      = to_ref_if<!is_constant_all<T_prob>::value>(inv_logit(-alpha_val));
+  const auto& log_inv_logit_alpha
+      = to_ref_if<!is_constant_all<T_prob>::value>(log_inv_logit(alpha_val));
+  const auto& log1m_inv_logit_alpha
+      = to_ref_if<!is_constant_all<T_prob>::value>(log1m_inv_logit(alpha_val));
 
   size_t maximum_size = max_size(n, N, alpha);
-  const auto& log_inv_logit_alpha = log(inv_logit_alpha);
-  const auto& log_inv_logit_neg_alpha = log(inv_logit_neg_alpha);
   T_partials_return logp = sum(n_val * log_inv_logit_alpha
-                               + (N_val - n_val) * log_inv_logit_neg_alpha);
+                               + (N_val - n_val) * log1m_inv_logit_alpha);
   if (include_summand<propto, T_n, T_N>::value) {
     logp += sum(binomial_coefficient_log(N_val, n_val)) * maximum_size
             / max_size(n, N);
   }
 
   auto ops_partials = make_partials_propagator(alpha_ref);
   if (!is_constant_all<T_prob>::value) {
-    if (is_vector<T_prob>::value) {
-      edge<0>(ops_partials).partials_
-          = n_val * inv_logit_neg_alpha - (N_val - n_val) * inv_logit_alpha;
-    } else {
-      T_partials_return sum_n = sum(n_val) * maximum_size / math::size(n);
-      partials<0>(ops_partials)[0] = forward_as<T_partials_return>(
-          sum_n * inv_logit_neg_alpha
-          - (sum(N_val) * maximum_size / math::size(N) - sum_n)
-                * inv_logit_alpha);
-    }
+    edge<0>(ops_partials).partials_ = n_val - N_val * exp(log_inv_logit_alpha);
   }
 
   return ops_partials.build(logp);

test/unit/math/mix/prob/binomial_logit_lpmf_test.cpp

@@ -0,0 +1,22 @@
+#include <stan/math/mix.hpp>
+#include <test/unit/math/test_ad.hpp>
+
+TEST(mathMixScalFun, binomial_logit_lpmf) {
+  auto f = [](const auto n, const auto N) {
+    return [=](const auto& alpha) {
+      return stan::math::binomial_logit_lpmf(n, N, alpha);
+    };
+  };
+
+  Eigen::VectorXd alpha = Eigen::VectorXd::Random(3);
+  std::vector<int> n_arr{1, 4, 5};
+  std::vector<int> N_arr{10, 45, 25};
+
+  stan::test::expect_ad(f(5, 25), 2.11);
+  stan::test::expect_ad(f(5, 25), alpha);
+  stan::test::expect_ad(f(n_arr, 25), alpha);
+  stan::test::expect_ad(f(n_arr, N_arr), alpha);
+  stan::test::expect_ad(f(n_arr, 10), 2.11);
+  stan::test::expect_ad(f(n_arr, N_arr), 2.11);
+  stan::test::expect_ad(f(5, N_arr), 2.11);
+}