From d95e37718fbd61868a2c811b7324d07b96932e03 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 9 Dec 2019 18:17:58 +0100
Subject: [PATCH 01/82] Failing test for cutoff when delegate neg_binomial_2 to
 poisson

---
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    |  7 +++++-
 .../prim/scal/prob/neg_binomial_2_test.cpp    | 24 +++++++++++++++++++
 2 files changed, 30 insertions(+), 1 deletion(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 10c7ff708ae..c3769982c37 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -16,6 +16,11 @@
 namespace stan {
 namespace math {
 
+namespace internal {
+  //Exposing to let me us this in tests
+  constexpr double neg_binomial_2_phi_cutoff = 1e5;
+}
+
 // NegBinomial(n|mu, phi)  [mu >= 0; phi > 0;  n >= 0]
 template <bool propto, typename T_n, typename T_location, typename T_precision>
 return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
@@ -95,7 +100,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     }
 
     // if phi is large we probably overflow, defer to Poisson:
-    if (phi__[i] > 1e5) {
+    if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
       logp = poisson_lpmf(n_vec[i], mu__[i]);
     }
 
diff --git a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
index 00192dd81cb..20ebb48aa51 100644
--- a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
@@ -214,3 +214,27 @@ TEST(ProbDistributionsNegBinomial, extreme_values) {
     EXPECT_LT(logp, 0);
   }
 }
+
+TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
+  std::array<double, 5> mu_to_test = {0.1, 13, 150, 1621, 18432 };
+  std::array<unsigned int, 7> y_to_test = {0, 3, 16, 24, 181, 2132, 121358 };
+  constexpr double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  for(auto mu_iter = mu_to_test.begin(); 
+    mu_iter != mu_to_test.end(); ++mu_iter) {
+    for(auto y_iter = y_to_test.begin(); 
+      y_iter != y_to_test.end(); ++y_iter) {
+        unsigned int y = *y_iter;
+        double mu = *mu_iter;
+
+        double before_cutoff = 
+          stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff - 1e-8);
+        double after_cutoff = 
+          stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff + 1e-8);
+        double diff_at_cutoff = before_cutoff - after_cutoff;
+        EXPECT_NEAR(diff_at_cutoff, 0, 1e-8) << 
+          "neg_binomial_2_lpmf changes too much around phi cutoff for y = " <<
+          y << ", mu = " << mu << " value at cutoff - 1e-8: " << 
+          before_cutoff << ", value at cutoff + 1e-8: " << after_cutoff;
+    }
+  }  
+}

From 25b8ebe9fbad12ab6ff99a7f9ad8ed78f1351c7d Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 9 Dec 2019 18:37:10 +0100
Subject: [PATCH 02/82] Failing test for vectors needing cutoff

---
 .../unit/math/prim/mat/prob/neg_binomial_2_test.cpp | 13 +++++++++++++
 1 file changed, 13 insertions(+)

diff --git a/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
index b51719abf6f..2d854325692 100644
--- a/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
@@ -34,3 +34,16 @@ TEST(ProbDistributionsNegativeBinomial2, errorCheck) {
 TEST(ProbDistributionsNegativeBinomial2, distributionCheck) {
   check_counts_real_real(NegativeBinomial2TestRig());
 }
+
+TEST(ProbDistributionsNegativeBinomial2, vectorAroundCutoff) {
+  int y = 10;
+  double mu = 9.36;
+  std::vector<double> phi;
+  phi.push_back(1);
+  phi.push_back(stan::math::internal::neg_binomial_2_phi_cutoff + 1);
+  double vector_value = stan::math::neg_binomial_2_lpmf(y, mu, phi);
+  double scalar_value = stan::math::neg_binomial_2_lpmf(y, mu, phi[0]) +
+    stan::math::neg_binomial_2_lpmf(y, mu, phi[1]);
+  
+  EXPECT_FLOAT_EQ(vector_value, scalar_value);
+}
\ No newline at end of file

From e47d5d792d59de4c6c75f3f72b6d69221d2aa444 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 9 Dec 2019 18:45:55 +0100
Subject: [PATCH 03/82] Phi cutoff no longer overrides logp accumulator

---
 stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp | 11 ++++++-----
 1 file changed, 6 insertions(+), 5 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index c3769982c37..c5bb8890445 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -83,6 +83,12 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   }
 
   for (size_t i = 0; i < size; i++) {
+    // if phi is large we probably overflow, defer to Poisson:
+    if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
+      logp += poisson_lpmf(n_vec[i], mu__[i]);
+      continue;
+    }
+
     if (include_summand<propto>::value) {
       logp -= lgamma(n_vec[i] + 1.0);
     }
@@ -99,11 +105,6 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       logp += lgamma(n_plus_phi[i]);
     }
 
-    // if phi is large we probably overflow, defer to Poisson:
-    if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
-      logp = poisson_lpmf(n_vec[i], mu__[i]);
-    }
-
     if (!is_constant_all<T_location>::value) {
       ops_partials.edge1_.partials_[i]
           += n_vec[i] / mu__[i] - (n_vec[i] + phi__[i]) / (mu__[i] + phi__[i]);

From 6f76adfef4098490c3f75feece3433a0d0942fbd Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 9 Dec 2019 19:03:49 +0100
Subject: [PATCH 04/82] Failing test for propto conservation around the cutoff

---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 19 ++++++++++++++++++-
 1 file changed, 18 insertions(+), 1 deletion(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index e4d49b3f753..e168660f70f 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -38,9 +38,26 @@ TEST(ProbDistributionsNegBinomial, derivatives) {
     finite_diffs.push_back(dphi * inv2e);
 
     for (int i = 0; i < 2; ++i) {
-      EXPECT_NEAR(gradients[i], finite_diffs[i], 1.0);
+      EXPECT_NEAR(gradients[i], finite_diffs[i], 1.0) << 
+        "for mu = " << mu_dbl << "  +/- epsilon, phi = " << phi_dbl <<
+        " +/- epsilon";
     }
 
     phi_dbl *= 10;
   }
 }
+
+TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
+  using stan::math::neg_binomial_2_lpmf;
+  using stan::math::var;
+  using stan::math::internal::neg_binomial_2_phi_cutoff;
+
+  var mu_var(10);
+  int y = 11.8;
+  var value_before_cutoff = neg_binomial_2_lpmf<true, int, var, double>(
+    y, mu_var, neg_binomial_2_phi_cutoff - 1e-8);
+  var value_after_cutoff = neg_binomial_2_lpmf<true, int, var, double>(
+    y, mu_var, neg_binomial_2_phi_cutoff + 1e-8);
+
+  EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);  
+}

From b43aa0d98d6a1ddb2eb5e581528269be4c1ccd5c Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 9 Dec 2019 15:13:15 -0500
Subject: [PATCH 05/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    |  6 +--
 .../prim/mat/prob/neg_binomial_2_test.cpp     |  6 +--
 .../prim/scal/prob/neg_binomial_2_test.cpp    | 38 +++++++++----------
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 14 +++----
 4 files changed, 32 insertions(+), 32 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index c5bb8890445..72296f25f0f 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -17,9 +17,9 @@ namespace stan {
 namespace math {
 
 namespace internal {
-  //Exposing to let me us this in tests
-  constexpr double neg_binomial_2_phi_cutoff = 1e5;
-}
+// Exposing to let me us this in tests
+constexpr double neg_binomial_2_phi_cutoff = 1e5;
+}  // namespace internal
 
 // NegBinomial(n|mu, phi)  [mu >= 0; phi > 0;  n >= 0]
 template <bool propto, typename T_n, typename T_location, typename T_precision>
diff --git a/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
index 2d854325692..deabf8c9fae 100644
--- a/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
@@ -42,8 +42,8 @@ TEST(ProbDistributionsNegativeBinomial2, vectorAroundCutoff) {
   phi.push_back(1);
   phi.push_back(stan::math::internal::neg_binomial_2_phi_cutoff + 1);
   double vector_value = stan::math::neg_binomial_2_lpmf(y, mu, phi);
-  double scalar_value = stan::math::neg_binomial_2_lpmf(y, mu, phi[0]) +
-    stan::math::neg_binomial_2_lpmf(y, mu, phi[1]);
-  
+  double scalar_value = stan::math::neg_binomial_2_lpmf(y, mu, phi[0])
+                        + stan::math::neg_binomial_2_lpmf(y, mu, phi[1]);
+
   EXPECT_FLOAT_EQ(vector_value, scalar_value);
 }
\ No newline at end of file
diff --git a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
index 20ebb48aa51..ddbf1dd0b0e 100644
--- a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
@@ -216,25 +216,25 @@ TEST(ProbDistributionsNegBinomial, extreme_values) {
 }
 
 TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
-  std::array<double, 5> mu_to_test = {0.1, 13, 150, 1621, 18432 };
-  std::array<unsigned int, 7> y_to_test = {0, 3, 16, 24, 181, 2132, 121358 };
+  std::array<double, 5> mu_to_test = {0.1, 13, 150, 1621, 18432};
+  std::array<unsigned int, 7> y_to_test = {0, 3, 16, 24, 181, 2132, 121358};
   constexpr double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  for(auto mu_iter = mu_to_test.begin(); 
-    mu_iter != mu_to_test.end(); ++mu_iter) {
-    for(auto y_iter = y_to_test.begin(); 
-      y_iter != y_to_test.end(); ++y_iter) {
-        unsigned int y = *y_iter;
-        double mu = *mu_iter;
-
-        double before_cutoff = 
-          stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff - 1e-8);
-        double after_cutoff = 
-          stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff + 1e-8);
-        double diff_at_cutoff = before_cutoff - after_cutoff;
-        EXPECT_NEAR(diff_at_cutoff, 0, 1e-8) << 
-          "neg_binomial_2_lpmf changes too much around phi cutoff for y = " <<
-          y << ", mu = " << mu << " value at cutoff - 1e-8: " << 
-          before_cutoff << ", value at cutoff + 1e-8: " << after_cutoff;
+  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
+       ++mu_iter) {
+    for (auto y_iter = y_to_test.begin(); y_iter != y_to_test.end(); ++y_iter) {
+      unsigned int y = *y_iter;
+      double mu = *mu_iter;
+
+      double before_cutoff
+          = stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff - 1e-8);
+      double after_cutoff
+          = stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff + 1e-8);
+      double diff_at_cutoff = before_cutoff - after_cutoff;
+      EXPECT_NEAR(diff_at_cutoff, 0, 1e-8)
+          << "neg_binomial_2_lpmf changes too much around phi cutoff for y = "
+          << y << ", mu = " << mu
+          << " value at cutoff - 1e-8: " << before_cutoff
+          << ", value at cutoff + 1e-8: " << after_cutoff;
     }
-  }  
+  }
 }
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index e168660f70f..00f26e74a65 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -38,9 +38,9 @@ TEST(ProbDistributionsNegBinomial, derivatives) {
     finite_diffs.push_back(dphi * inv2e);
 
     for (int i = 0; i < 2; ++i) {
-      EXPECT_NEAR(gradients[i], finite_diffs[i], 1.0) << 
-        "for mu = " << mu_dbl << "  +/- epsilon, phi = " << phi_dbl <<
-        " +/- epsilon";
+      EXPECT_NEAR(gradients[i], finite_diffs[i], 1.0)
+          << "for mu = " << mu_dbl << "  +/- epsilon, phi = " << phi_dbl
+          << " +/- epsilon";
     }
 
     phi_dbl *= 10;
@@ -48,16 +48,16 @@ TEST(ProbDistributionsNegBinomial, derivatives) {
 }
 
 TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
+  using stan::math::internal::neg_binomial_2_phi_cutoff;
   using stan::math::neg_binomial_2_lpmf;
   using stan::math::var;
-  using stan::math::internal::neg_binomial_2_phi_cutoff;
 
   var mu_var(10);
   int y = 11.8;
   var value_before_cutoff = neg_binomial_2_lpmf<true, int, var, double>(
-    y, mu_var, neg_binomial_2_phi_cutoff - 1e-8);
+      y, mu_var, neg_binomial_2_phi_cutoff - 1e-8);
   var value_after_cutoff = neg_binomial_2_lpmf<true, int, var, double>(
-    y, mu_var, neg_binomial_2_phi_cutoff + 1e-8);
+      y, mu_var, neg_binomial_2_phi_cutoff + 1e-8);
 
-  EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);  
+  EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
 }

From 8bcd8b46f58e4160030c695aade4fa0930d55f39 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Tue, 10 Dec 2019 15:33:21 +0100
Subject: [PATCH 06/82] Using binomial_coefficient_log, better Poisson defer,
 further tests

---
 stan/math/prim/scal/fun/lgamma.hpp            |  11 ++
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    |  94 +++++++----
 .../prim/scal/prob/neg_binomial_2_test.cpp    |  73 +++++----
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 146 +++++++++++++++---
 4 files changed, 241 insertions(+), 83 deletions(-)

diff --git a/stan/math/prim/scal/fun/lgamma.hpp b/stan/math/prim/scal/fun/lgamma.hpp
index 43d74f1b684..6b5794855a5 100644
--- a/stan/math/prim/scal/fun/lgamma.hpp
+++ b/stan/math/prim/scal/fun/lgamma.hpp
@@ -89,6 +89,17 @@ inline double lgamma(int x) {
 #endif
 }
 
+inline double lgamma(unsigned int x) {
+#if !__MINGW32__
+  int sign = 1;
+  return ::lgamma_r(x, &sign);
+#else
+  if (unlikely(x == 0.0))
+    return std::numeric_limits<double>::infinity();
+  return boost::math::lgamma(x, boost_policy_t());
+#endif
+}
+
 }  // namespace math
 }  // namespace stan
 #endif
diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 72296f25f0f..cb4cd46520a 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -9,6 +9,7 @@
 #include <stan/math/prim/scal/fun/multiply_log.hpp>
 #include <stan/math/prim/scal/fun/digamma.hpp>
 #include <stan/math/prim/scal/fun/lgamma.hpp>
+#include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
 #include <stan/math/prim/scal/fun/value_of.hpp>
 #include <stan/math/prim/scal/prob/poisson_lpmf.hpp>
 #include <cmath>
@@ -17,9 +18,11 @@ namespace stan {
 namespace math {
 
 namespace internal {
-// Exposing to let me us this in tests
-constexpr double neg_binomial_2_phi_cutoff = 1e5;
-}  // namespace internal
+  //Exposing to let me us this in tests
+  //The current tests fail when the cutoff is 1e8 and pass with 1e9, 
+  //setting 1e10 to be safe
+  constexpr double neg_binomial_2_phi_cutoff = 1e10;
+}
 
 // NegBinomial(n|mu, phi)  [mu >= 0; phi > 0;  n >= 0]
 template <bool propto, typename T_n, typename T_location, typename T_precision>
@@ -83,36 +86,61 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   }
 
   for (size_t i = 0; i < size; i++) {
-    // if phi is large we probably overflow, defer to Poisson:
-    if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
-      logp += poisson_lpmf(n_vec[i], mu__[i]);
-      continue;
-    }
-
-    if (include_summand<propto>::value) {
-      logp -= lgamma(n_vec[i] + 1.0);
-    }
-    if (include_summand<propto, T_precision>::value) {
-      logp += multiply_log(phi__[i], phi__[i]) - lgamma(phi__[i]);
-    }
-    if (include_summand<propto, T_location, T_precision>::value) {
-      logp -= (n_plus_phi[i]) * log_mu_plus_phi[i];
-    }
-    if (include_summand<propto, T_location>::value) {
-      logp += multiply_log(n_vec[i], mu__[i]);
-    }
-    if (include_summand<propto, T_precision>::value) {
-      logp += lgamma(n_plus_phi[i]);
-    }
-
-    if (!is_constant_all<T_location>::value) {
-      ops_partials.edge1_.partials_[i]
-          += n_vec[i] / mu__[i] - (n_vec[i] + phi__[i]) / (mu__[i] + phi__[i]);
-    }
-    if (!is_constant_all<T_precision>::value) {
-      ops_partials.edge2_.partials_[i]
-          += 1.0 - n_plus_phi[i] / (mu__[i] + phi__[i]) + log_phi[i]
-             - log_mu_plus_phi[i] - digamma(phi__[i]) + digamma(n_plus_phi[i]);
+    if(phi__[i] > internal::neg_binomial_2_phi_cutoff) {
+      //Phi is large, deferring to Poisson. 
+      //Copying the code here as just calling
+      //poisson_lpmf does not preserve propto logic correctly
+      if (include_summand<propto>::value) {
+        logp -= lgamma(n_vec[i] + 1.0);
+      }
+      if (include_summand<propto, T_location>::value) {
+        logp += multiply_log(n_vec[i], mu__[i]) - mu__[i];
+      }
+
+      // if (include_summand<propto, T_location, T_precision>::value) {
+      //   logp += (mu__[i] * (mu__[i] - 2 * n_vec[i]) +
+      //     n_vec[i] * (n_vec[i] - 1)) / ( 2 * phi__[i] ); 
+      //   // logp += (mu__[i] * mu__[i] - n_vec[i] - 
+      //   //   2 * mu__[i] * n_vec[i] + n_vec[i] * n_vec[i])/phi
+      // }
+
+      if (!is_constant_all<T_location>::value) {
+        //This is the Taylor series of the full derivative for phi -> Inf
+        //Obtained in Mathematica via 
+        //Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
+        ops_partials.edge1_.partials_[i]
+            += n_vec[i] / mu__[i]  + (mu__[i] - n_vec[i]) / phi__[i] - 1;              
+      }
+      
+      //The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2)      
+      //So ignoring here
+      //Obtained in Mathematica via
+      //Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] - 
+      //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 1}]
+
+    } else {
+      if (include_summand<propto, T_precision>::value) {
+        logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
+      }
+      if (include_summand<propto, T_precision>::value) {
+        logp += multiply_log(phi__[i], phi__[i]);
+      }
+      if (include_summand<propto, T_location, T_precision>::value) {
+        logp -= (n_plus_phi[i]) * log_mu_plus_phi[i];
+      }
+      if (include_summand<propto, T_location>::value) {
+        logp += multiply_log(n_vec[i], mu__[i]);
+      }
+
+      if (!is_constant_all<T_location>::value) {
+        ops_partials.edge1_.partials_[i]
+            += n_vec[i] / mu__[i] - (n_vec[i] + phi__[i]) / (mu__[i] + phi__[i]);
+      }
+      if (!is_constant_all<T_precision>::value) {
+        ops_partials.edge2_.partials_[i]
+            += 1.0 - n_plus_phi[i] / (mu__[i] + phi__[i]) + log_phi[i]
+              - log_mu_plus_phi[i] - digamma(phi__[i]) + digamma(n_plus_phi[i]);
+      }    
     }
   }
   return ops_partials.build(logp);
diff --git a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
index ddbf1dd0b0e..63f9a4eaf34 100644
--- a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
@@ -205,36 +205,57 @@ TEST(ProbDistributionsNegBinomial, chiSquareGoodnessFitTest4) {
 }
 
 TEST(ProbDistributionsNegBinomial, extreme_values) {
-  int N = 100;
-  double mu = 8;
-  double phi = 1e12;
-  for (int n = 0; n < 10; ++n) {
-    phi *= 10;
-    double logp = stan::math::neg_binomial_2_log<false>(N, mu, phi);
-    EXPECT_LT(logp, 0);
+  std::array<unsigned int, 5> n_to_test = {1, 5, 100, 12985, 1968422};
+  std::array<double, 6> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054 };
+  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  for(auto mu_iter = mu_to_test.begin(); 
+      mu_iter != mu_to_test.end(); ++mu_iter) {
+    for(auto n_iter = n_to_test.begin(); 
+        n_iter != n_to_test.end(); ++n_iter) {
+      double mu = *mu_iter;
+      unsigned int n = *n_iter;
+      //Test just before cutoff
+      double logp = stan::math::neg_binomial_2_log<false>(
+          n, mu, phi_cutoff - 1e-8);
+        EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << 
+          mu << ", phi = " << (phi_cutoff - 1e-8);
+
+
+      //Test across a range of phi
+      double phi = 1e12;
+      for (int i = 0; i < 10; ++i) {
+        phi *= 10;
+        double logp = stan::math::neg_binomial_2_log<false>(n, mu, phi);
+        EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << 
+          mu << ", phi = " << phi;
+      }
+    }
   }
 }
 
 TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
-  std::array<double, 5> mu_to_test = {0.1, 13, 150, 1621, 18432};
-  std::array<unsigned int, 7> y_to_test = {0, 3, 16, 24, 181, 2132, 121358};
-  constexpr double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
-       ++mu_iter) {
-    for (auto y_iter = y_to_test.begin(); y_iter != y_to_test.end(); ++y_iter) {
-      unsigned int y = *y_iter;
-      double mu = *mu_iter;
-
-      double before_cutoff
-          = stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff - 1e-8);
-      double after_cutoff
-          = stan::math::neg_binomial_2_lpmf(y, mu, phi_cutoff + 1e-8);
-      double diff_at_cutoff = before_cutoff - after_cutoff;
-      EXPECT_NEAR(diff_at_cutoff, 0, 1e-8)
-          << "neg_binomial_2_lpmf changes too much around phi cutoff for y = "
-          << y << ", mu = " << mu
-          << " value at cutoff - 1e-8: " << before_cutoff
-          << ", value at cutoff + 1e-8: " << after_cutoff;
+  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  std::array<double, 7> mu_to_test = 
+    {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345 };
+  std::array<unsigned int, 8> n_to_test = 
+    {0, 3, 16, 24, 181, 2132, 121358, 865422242 };
+  for(auto mu_iter = mu_to_test.begin(); 
+      mu_iter != mu_to_test.end(); ++mu_iter) {
+    double mu = *mu_iter;
+    for(auto n_iter = n_to_test.begin(); 
+        n_iter != n_to_test.end(); ++n_iter) {
+      unsigned int n = *n_iter;
+
+      double before_cutoff = 
+        stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff - 1e-8);
+      double after_cutoff = 
+        stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff + 1e-8);
+      double relative_error_at_cutoff = log(before_cutoff / after_cutoff);
+      EXPECT_NEAR(relative_error_at_cutoff, 0, 1e-8) << 
+        "neg_binomial_2_lpmf changes too much around phi cutoff for n = " <<
+        n << ", mu = " << mu << ", cutoff = " << phi_cutoff << 
+        " value at cutoff - 1e-8: " << 
+        before_cutoff << ", value at cutoff + 1e-8: " << after_cutoff;
     }
   }
 }
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 00f26e74a65..a0964ba894a 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -2,19 +2,62 @@
 #include <gtest/gtest.h>
 #include <vector>
 
-TEST(ProbDistributionsNegBinomial, derivatives) {
+struct TestValue {
+  unsigned int n;
+  double mu;
+  double phi;
+  double value;
+  double grad_mu;
+  double grad_phi;
+
+  TestValue(unsigned int _n, double _mu, double _phi, double _value, double _grad_mu, double _grad_phi)
+      : n(_n), mu(_mu), phi(_phi), value(_value), grad_mu(_grad_mu), grad_phi(_grad_phi) {}
+};
+
+//Test data generated in Mathematica (Wolfram Cloud) via
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi ]+ 
+//   n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
+// nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
+// nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
+// out = OpenWrite["nb_test.txt"]
+// mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
+//  phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
+// ns = {0,6,14,1525,10233};
+//  WriteString[out, "std::array<TestValue, ", 
+//      Length[mus]*Length[phis]*Length[ns], "> testValues = {"];
+//    Block[{$MaxPrecision = 80, $MinPrecision = 40}, {
+//      For[i = 1, i <= Length[mus], i++, {
+//        For[j = 1, j <= Length[phis], j++, {
+//        For[k = 1, k <= Length[ns], k++, {
+//          cmu = mus[[i]];
+//          cphi = phis[[j]];
+//     cn=ns[[k]];
+//          val = N[nb2[cn,cmu,cphi]];
+//     ddmu= N[nb2dmu[cn,cmu,cphi]];
+//     ddphi= N[nb2dphi[cn,cmu,cphi]];
+//          WriteString[out,"  TestValue(",CForm[cn],",",CForm[cmu],",",
+//            CForm[cphi],",", CForm[val],","CForm[ddmu],",",CForm[ddphi],"),"]
+//        }]
+//      }]
+//   }]
+//    }];
+//  WriteString[out,"};"];
+//  Close[out];
+//  FilePrint[%]
+std::array<TestValue, 175> testValues = {  TestValue(0,0.0000256,0.0004,-0.000024814156367780882, -0.9398496240601504,-0.0018850149796021398),  TestValue(6,0.0000256,0.0004,-26.480362597222488, 220276.31578947368,-11595.463497838708),  TestValue(14,0.0000256,0.0004,-49.814562438358635, 513979.32330827066,-30391.559221530802),  TestValue(1525,0.0000256,0.0004,-4301.784727467015, 5.5987134868421055e7,-3.580668787634408e6),  TestValue(10233,0.0000256,0.0004,-28781.07085289515, 3.7568285855263156e8,-2.4041193199521683e7),  TestValue(0,0.0000256,0.065,-0.000025594960092480967, -0.9996063088998794,-7.751668684718993e-8),  TestValue(6,0.0000256,0.065,-51.41938813644809, 234281.72904210034,-74.69380754597304),  TestValue(14,0.0000256,0.065,-114.92817109028836, 546658.7005733127,-196.83239209326592),  TestValue(1525,0.0000256,0.065,-11965.467128123484, 5.954685919853104e7,-23429.11268911477),  TestValue(10233,0.0000256,0.065,-80237.4790550341, 3.995691927102557e8,-157343.697098361),  TestValue(0,0.0000256,4.42,-0.000025599925864390194, -0.9999942081783417,-1.677258332222209e-11),  TestValue(6,0.0000256,4.42,-67.52038137511191, 234372.6425475907,-0.4312559247584902),  TestValue(14,0.0000256,4.42,-161.64931287705224, 546870.8326033225,-1.650128690902025),  TestValue(1525,0.0000256,4.42,-18367.34289180058, 5.956996647937967e7,-339.0570825343945),  TestValue(10233,0.0000256,4.42,-123371.16336416776, 3.997242463550437e8,-2307.279979293951),  TestValue(0,0.0000256,800,-0.00002559999998652529, -0.999999968000001,-8.881784197001252e-16),  TestValue(6,0.0000256,800,-69.9980790657431, 234373.99250003224,-0.000023330384471442756),  TestValue(14,0.0000256,800,-173.09898662779824, 546873.9825000325,-0.00014060727924558591),  TestValue(1525,0.0000256,800,-24826.22813563853, 5.957030959375009e7,-0.8389762876176414),  TestValue(10233,0.0000256,800,-173733.65594636812, 3.997265487087504e8,-10.166635446653597),  TestValue(0,0.0000256,15324,-0.000025599996959613236, -0.9999999983294179,0.),  TestValue(6,0.0000256,15324,-70.01580732128963, 234373.99960845898,-6.386142814562845e-8),  TestValue(14,0.0000256,15324,-173.20616504262574, 546873.9990864021,-3.872936886750722e-7),  TestValue(1525,0.0000256,15324,-25707.717028801628, 5.957031140048291e7,-0.004643062913324059),  TestValue(10233,0.0000256,15324,-189611.39394380094, 3.9972656083222395e8,-0.15627194690990365),  TestValue(0,0.314,0.0004,-0.002666782716971683, -0.001272264631043257,-5.66822905706025),  TestValue(6,0.314,0.0004,-9.625197494412376, 0.023038524497171847,2477.530549555817),  TestValue(14,0.314,0.0004,-10.482321240387563, 0.05545291000145865,2452.982014445862),  TestValue(1525,0.314,0.0004,-17.094738795518424, 6.1777199721236284,-2348.2711549792057),  TestValue(10233,0.314,0.0004,-30.083534640958533, 41.460778593539814,-30043.568270589793),  TestValue(0,0.314,0.065,-0.11460468078714132, -0.17150395778364116,-0.9346528929704305),  TestValue(6,0.314,0.065,-5.6231627412658, 3.1056417323496293,0.8117566646875254),  TestValue(14,0.314,0.065,-7.917539720426937, 7.4751693191939905,-19.40653851445296),  TestValue(1525,0.314,0.065,-296.58556828610017, 832.7696922844226,-4001.4921811261693),  TestValue(10233,0.314,0.065,-1936.716591758479, 5589.00047056451,-26975.841613138524),  TestValue(0,0.314,4.42,-0.30334820230965986, -0.9336713138994508,-0.00230212890163628),  TestValue(6,0.314,4.42,-11.748118636048988, 16.90718181793719,-0.3435269754367143),  TestValue(14,0.314,4.42,-31.109603016060397, 40.69498599371937,-1.4423583039713965),  TestValue(1525,0.314,4.42,-4115.10160678526, 4533.61649969458,-316.1764856190919),  TestValue(10233,0.314,4.42,-27734.55588693275, 30426.641345033488,-2153.7342775414127),  TestValue(0,0.314,800,-0.31393839362010567, -0.9996076539958066,-7.698783210940974e-8),  TestValue(6,0.314,800,-13.827010724886122, 18.101175543376296,-0.000020465017271042996),  TestValue(14,0.314,800,-41.61461010763844, 43.568886473205765,-0.00013381877200302483),  TestValue(1525,0.314,800,-10469.94267675256, 4853.782788344746,-0.8382285160349765),  TestValue(10233,0.314,800,-77398.83453431107, 32575.386135464123,-10.16161733713528),  TestValue(0,0.314,15324,-0.31399678298770084, -0.9999795096863716,-2.099280749234822e-10),  TestValue(6,0.314,15324,-13.842565956968983, 18.10790921043538,-5.6049177743489054e-8),  TestValue(14,0.314,15324,-41.71664028188991, 43.58509417059771,-3.687852014877535e-7),  TestValue(1525,0.314,15324,-11350.864477542971, 4855.588403521258,-0.004641024152967077),  TestValue(10233,0.314,15324,-93272.76691554434, 32587.50423265796,-0.15625826529496223),  TestValue(0,1.5,0.0004,-0.003291911100032755, -0.00026659557451346307,-7.230044345656401),  TestValue(6,1.5,0.0004,-9.619783961619232, 0.0007997867235403892,2491.0537701151675),  TestValue(14,1.5,0.0004,-10.468856159359483, 0.002221629787612192,2486.6186161358087),  TestValue(1525,1.5,0.0004,-15.560537541616213, 0.270772238514174,1484.280307752038),  TestValue(10233,1.5,0.0004,-19.785223133323598, 1.8184484137563317,-4317.601447204935),  TestValue(0,1.5,0.065,-0.2067814991501101, -0.04153354632587859,-2.2227873794044952),  TestValue(6,1.5,0.065,-4.841004539887443, 0.12460063897763578,11.520890928200775),  TestValue(14,1.5,0.065,-5.969601492726813, 0.34611288604898827,7.298954082323366),  TestValue(1525,1.5,0.065,-74.45092758687497, 42.184238551650694,-953.4745083343279),  TestValue(10233,1.5,0.065,-445.630392408013, 283.3003194888179,-6515.787894589817),  TestValue(0,1.5,4.42,-1.2915096474038796, -0.7466216216216216,-0.03881837442792935),  TestValue(6,1.5,4.42,-4.694711300875651, 2.239864864864865,-0.12612961153608993),  TestValue(14,1.5,4.42,-13.334103973863655, 6.221846846846847,-0.8864094608348823),  TestValue(1525,1.5,4.42,-2072.1910365790172, 758.3186936936937,-251.67662613527665),  TestValue(10233,1.5,4.42,-14020.648493631525, 5092.706081081081,-1720.7211329093311),  TestValue(0,1.5,800,-1.4985955053447242, -0.9981285090455396,-1.7534272203079126e-6),  TestValue(6,1.5,800,-5.63758835785638, 2.9943855271366187,-0.00001104786953298742),  TestValue(14,1.5,800,-20.926415102269573, 8.317737575379496,-0.00010961017476240897),  TestValue(1525,1.5,800,-8088.548799680884, 1013.7658556872531,-0.8354105724129193),  TestValue(10233,1.5,800,-61412.52664040723, 6808.234560199626,-10.142698900729565),  TestValue(0,1.5,15324,-1.499926590534038, -0.9999021239111285,-4.790177143831897e-9),  TestValue(6,1.5,15324,-5.645995699555982, 2.9997063717333856,-3.032959305926397e-8),  TestValue(14,1.5,15324,-21.010069937864472, 8.332517699259403,-3.0266583905813604e-7),  TestValue(1525,1.5,15324,-8967.33164084002, 1015.5672571857361,-0.004633327525485953),  TestValue(10233,1.5,15324,-77272.09898456372, 6820.332387197807,-0.15620659350885369),  TestValue(0,3,0.0004,-0.003569116649587855, -0.0001333155579256099,-7.922924939527562),  TestValue(6,3,0.0004,-9.619261327135609, 0.0001333155579256099,2492.360089770114),  TestValue(14,3,0.0004,-10.467267071498288, 0.0004888237123939031,2490.5905361225123),  TestValue(1525,3,0.0004,-15.357522072066786, 0.06763542638759276,1991.7174903993568),  TestValue(10233,3,0.0004,-18.421373162287637, 0.4546060525263298,-908.6583034400528),  TestValue(0,3,0.065,-0.25047201260085383, -0.021207177814029365,-2.874622756288704),  TestValue(6,3,0.065,-4.758782442354863, 0.021207177814029365,12.74533572164111),  TestValue(14,3,0.065,-5.719495913883133, 0.07775965198477433,11.025105769529759),  TestValue(1525,3,0.065,-42.491829475397026, 10.75910821098423,-477.2384670870571),  TestValue(10233,3,0.065,-230.9301248894044, 72.31647634584013,-3316.4438994781904),  TestValue(0,3,4.42,-2.2897339760163957, -0.5956873315363881,-0.11372669262607049),  TestValue(6,3,4.42,-2.889108195828742, 0.5956873315363881,0.003850246852058703),  TestValue(14,3,4.42,-7.790064290604171, 2.18418688230009,-0.4832453669983474),  TestValue(1525,3,4.42,-1360.5497881858591, 302.2120395327942,-199.67578957112616),  TestValue(10233,3,4.42,-9239.719029853994, 2031.2938005390836,-1371.3592560596119),  TestValue(0,3,800,-2.994389023067612, -0.9962640099626401,-6.996241475043519e-6),  TestValue(6,3,800,-2.9857172436025223, 0.9962640099626401,-2.3069406651643476e-6),  TestValue(14,3,800,-12.744324478713366, 3.65296803652968,-0.00008222425506509978),  TestValue(1525,3,800,-7035.84649923785, 505.4379410543794,-0.8318616138503963),  TestValue(10233,3,800,-54340.180404088605, 3397.2602739726026,-10.118854869649681),  TestValue(0,3,15324,-2.999706381300726, -0.9998042669798395,-1.9158207464897714e-8),  TestValue(6,3,15324,-2.9874796347589054, 0.9998042669798395,-6.3824572293924575e-9),  TestValue(14,3,15324,-12.807159398982407, 3.665948978926078,-2.2763181739549054e-7),  TestValue(1525,3,15324,-7911.931224008331, 507.2340314477719,-0.004623603455756964),  TestValue(10233,3,15324,-70181.6251826905, 3409.332550401253,-0.15614126136305728),  TestValue(0,180,0.0004,-0.0052068020335865025, -2.2222172839615914e-6,-12.01700730618354),  TestValue(6,180,0.0004,-9.62011239916672, -2.148143374496205e-6,2490.2324075130828),  TestValue(14,180,0.0004,-10.467069325725546, -2.04937816187569e-6,2491.084720678314),  TestValue(1525,180,0.0004,-15.159228863591125, 0.000016604901371824113,2487.4167692289852),  TestValue(10233,180,0.0004,-17.08144177432405, 0.00012411083530925487,2440.94300115826),  TestValue(0,180,0.065,-0.5152345838836883, -0.00036098075694887956,-6.927046886659846),  TestValue(6,180,0.065,-4.897099604874426, -0.0003489480650505836,10.617175935000475),  TestValue(14,180,0.065,-5.689219198051667, -0.0003329044758528556,11.4626317745298),  TestValue(1525,180,0.065,-10.618383986015033, 0.0026973284338680167,7.7929628140754765),  TestValue(10233,180,0.065,-15.542242814932251, 0.020160775275594924,-38.6634853761835),  TestValue(0,180,4.42,-16.491356225074536, -0.023967031775295522,-2.755043100796684),  TestValue(6,180,4.42,-11.802883319144515, -0.023168130716119003,-1.8613752566654882),  TestValue(14,180,4.42,-9.653376579596795, -0.022102929303883648,-1.313682997645138),  TestValue(1525,180,4.42,-30.756932642065294, 0.1790869874320693,-5.0606677133089075),  TestValue(10233,180,4.42,-235.49737914944126, 1.3385587246502548,-50.37753458197702),  TestValue(0,180,800,-162.35267519735217, -0.8163265306122449,-0.01926737460893513),  TestValue(6,180,800,-138.9731231908616, -0.7891156462585034,-0.017913154212997107),  TestValue(14,180,800,-117.57055678993851, -0.7528344671201814,-0.016193696733894036),  TestValue(1525,180,800,-1255.1060610431614, 6.099773242630386,-0.5081161722061651),  TestValue(10233,180,800,-14640.50246307096, 45.59183673469388,-7.836489965276398),  TestValue(0,180,15324,-178.95104102256036, -0.9883900928792569,-0.00006792118926490787),  TestValue(6,180,15324,-154.44163935947577, -0.9554437564499484,-0.00006343927721985665),  TestValue(14,180,15324,-131.5984192349756, -0.911515307877537,-0.000057701678183974536),  TestValue(1525,180,15324,-1861.5172673616398, 7.38547041623667,-0.0035556000115217756),  TestValue(10233,180,15324,-28577.644697168085, 55.2015866873065,-0.14858705144088802),  TestValue(0,1123,0.0004,-0.005939122128713381, -3.5618865318302646e-7,-13.847805677972104),  TestValue(6,1123,0.0004,-9.620833523075628, -3.5428559715533445e-7,2488.429599570756),  TestValue(14,1123,0.0004,-10.467775521386166, -3.517481891184117e-7,2489.3192333086026),  TestValue(1525,1123,0.0004,-15.157115486355906, 1.2750475385536657e-7,2492.70020501204),  TestValue(10233,1123,0.0004,-17.063078998820856, 2.8894734020457448e-6,2486.849880233364),  TestValue(0,1123,0.065,-0.6342170147837343, -0.000057877326779839104,-8.75724272015346),  TestValue(6,1123,0.065,-5.014263034227778, -0.000057568097963562137,8.814958879676311),  TestValue(14,1123,0.065,-5.803957292009425, -0.000057155792875192846,9.697719756764902),  TestValue(1525,1123,0.065,-10.275036857130544, 0.000020718330690556827,13.074039765317043),  TestValue(10233,1123,0.065,-12.558918107941281, 0.0004695124193805291,7.224124958319663),  TestValue(0,1123,4.42,-24.493639593452325, -0.00392045555338738,-4.545467874886493),  TestValue(6,1123,4.42,-19.68318216630322, -0.003899509219175159,-3.624587483847729),  TestValue(14,1123,4.42,-17.37102939846337, -0.003871580773558864,-3.040611828950623),  TestValue(1525,1123,4.42,-7.7548168672583415, 0.0014034043922188128,0.0654298516080507),  TestValue(10233,1123,4.42,-35.45506157865748, 0.031803517445555686,-5.756960605210265),  TestValue(0,1123,800,-701.6240143366822, -0.4160166406656266,-0.29304665858647905),  TestValue(6,1123,800,-671.3041847506472, -0.4137939337698174,-0.28869011401594236),  TestValue(14,1123,800,-640.6479149103316, -0.4108303245754051,-0.2829675576373729),  TestValue(1525,1123,800,-30.39018204828426, 0.14892136201921807,-0.018804728472968435),  TestValue(10233,1123,800,-3343.1303902972795, 3.3748099701370067,-2.9898053694742615),  TestValue(0,1123,15324,-1083.757151397245, -0.9317200705295798,-0.002442933450309326),  TestValue(6,1123,15324,-1048.6172073187354, -0.9267420470004815,-0.002416262805940761),  TestValue(14,1123,15324,-1011.5999306403351, -0.920104682295017,-0.00238094023047708),  TestValue(1525,1123,15324,-64.3938471491183, 0.33352757644959136,-0.00029097614079454104),  TestValue(10233,1123,15324,-11352.060718035325, 7.558299058347705,-0.11311918072723515),  TestValue(0,10586,0.0004,-0.006836533480423993, -3.778575334268833e-8,-16.091333738845734),  TestValue(6,10586,0.0004,-9.621729024009568, -3.776433689454398e-8,2486.19084755338),  TestValue(14,10586,0.0004,-10.468668475096411, -3.7735781630351504e-8,2487.0868493492235),  TestValue(1525,10586,0.0004,-15.157527333190956, -3.234240610599839e-8,2491.6705880068075),  TestValue(10233,10586,0.0004,-17.060718192660715, -1.2600010324928188e-9,2492.7518943576556),  TestValue(0,10586,0.065,-0.7800430171085975, -6.1401474485561915e-6,-11.00066794181818),  TestValue(6,10586,0.065,-5.159778603540011, -6.1366672969700086e-6,6.57630939764217),  TestValue(14,10586,0.065,-5.949058950638154, -6.132027094855097e-6,7.465437927571536),  TestValue(1525,10586,0.065,-10.34196113541293, -5.255608920401252e-6,12.044448366424728),  TestValue(10233,10586,0.065,-12.175300607224926, -2.047489183204549e-7,13.125723676609066),  TestValue(0,10586,4.42,-34.3945190758502, -0.0004173583295091224,-6.781982760105572),  TestValue(6,10586,4.42,-29.562997357281894, -0.00041712177651676886,-5.856347033468785),  TestValue(14,10586,4.42,-27.2227588675498, -0.0004168063725269641,-5.266030931107645),  TestValue(1525,10586,4.42,-12.301855613945008, -0.0003572344439525938,-0.9624372357797295),  TestValue(10233,10586,4.42,-9.430792045634007, -0.00001391720105013416,0.11674937200192481),  TestValue(0,10586,800,-2124.4224654744803, -0.07026172492534692,-1.7257898067684474),  TestValue(6,10586,800,-2091.312452085902, -0.07022190154073024,-1.7188401003298583),  TestValue(14,10586,800,-2056.9359371755286, -0.07016880369457469,-1.7096599947938858),  TestValue(1525,10586,800,-744.0169167062886, -0.060139948001942986,-0.7924525685250288),  TestValue(10233,10586,800,-7.2703661972227565, -0.0023429424616141564,0.00008904830662359586),  TestValue(0,10586,15324,-8048.29915678056, -0.5914318795831726,-0.11664064731878732),  TestValue(6,10586,15324,-8002.424955944863, -0.5910966640836922,-0.11648073932479441),  TestValue(14,10586,15324,-7951.095336923546, -0.590649710084385,-0.11626776694982688),  TestValue(1525,10586,15324,-4300.645593413912, -0.506231273465249,-0.08062419697917278),  TestValue(10233,10586,15324,-9.327824035135563, -0.019721845219427537,-0.00008059480749977865)};
+
+TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
+  using stan::math::value_of;
 
-  int N = 100;
-  double mu_dbl = 8;
-  double phi_dbl = 1.5;
-
-  for (int k = 0; k < 20; ++k) {
-    var mu(mu_dbl);
-    var phi(phi_dbl);
-    var val = neg_binomial_2_log(N, mu, phi);
+  for(auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
+    TestValue t = *iter;  
+    unsigned int n = t.n;
+    var mu(t.mu);
+    var phi(t.phi);
+    var val = neg_binomial_2_log(n, mu, phi);
 
     std::vector<var> x;
     x.push_back(mu);
@@ -27,23 +70,75 @@ TEST(ProbDistributionsNegBinomial, derivatives) {
       EXPECT_FALSE(is_nan(gradients[i]));
     }
 
-    std::vector<double> finite_diffs;
-    double eps = 1e-10;
-    double inv2e = 0.5 / eps;
-    double dmu = neg_binomial_2_log(N, mu_dbl + eps, phi_dbl)
-                 - neg_binomial_2_log(N, mu_dbl - eps, phi_dbl);
-    double dphi = neg_binomial_2_log(N, mu_dbl, phi_dbl + eps)
-                  - neg_binomial_2_log(N, mu_dbl, phi_dbl - eps);
-    finite_diffs.push_back(dmu * inv2e);
-    finite_diffs.push_back(dphi * inv2e);
+    EXPECT_NEAR(value_of(val), t.value, fabs(t.value * 1e-8)) << 
+      "value n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
+    EXPECT_NEAR(gradients[0], t.grad_mu, fabs(t.grad_mu * 1e-8)) << 
+      "grad_mu n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
+    EXPECT_NEAR(gradients[1], t.grad_phi, fabs(t.grad_phi * 1e-8)) << 
+      "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
+
+  }
+}
 
-    for (int i = 0; i < 2; ++i) {
-      EXPECT_NEAR(gradients[i], finite_diffs[i], 1.0)
-          << "for mu = " << mu_dbl << "  +/- epsilon, phi = " << phi_dbl
-          << " +/- epsilon";
-    }
 
-    phi_dbl *= 10;
+TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
+  using stan::math::is_nan;
+  using stan::math::neg_binomial_2_log;
+  using stan::math::var;
+
+  //The range of values tested has to be quite conservative to let the test
+  //pass
+  std::array<unsigned int, 1> n_to_test = {100};
+  std::array<double, 1> mu_to_test = {8};
+  // std::array<unsigned int, 3> n_to_test = {7, 100, 835};
+  // std::array<double, 2> mu_to_test = {8, 24};
+  // std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835};
+  // std::array<double, 6> mu_to_test = {0.8, 8, 24, 271};
+  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  for(auto mu_iter = mu_to_test.begin(); 
+      mu_iter != mu_to_test.end(); ++mu_iter) {
+    for(auto n_iter = n_to_test.begin(); 
+        n_iter != n_to_test.end(); ++n_iter) {
+      double mu_dbl = *mu_iter;
+      unsigned int n = *n_iter;
+      double phi_dbl = 1.5;
+
+      for (int k = 0; k < 20; ++k) {
+        var mu(mu_dbl);
+        var phi(phi_dbl);
+        var val = neg_binomial_2_log(n, mu, phi);
+
+        std::vector<var> x;
+        x.push_back(mu);
+        x.push_back(phi);
+
+        std::vector<double> gradients;
+        val.grad(x, gradients);
+
+        for (int i = 0; i < 2; ++i) {
+          EXPECT_FALSE(is_nan(gradients[i]));
+        }
+
+        std::vector<double> finite_diffs;
+        double eps = 1e-10;
+        double inv2e = 0.5 / eps;
+        double dmu = neg_binomial_2_log(n, mu_dbl + eps, phi_dbl)
+                    - neg_binomial_2_log(n, mu_dbl - eps, phi_dbl);
+        double dphi = neg_binomial_2_log(n, mu_dbl, phi_dbl + eps)
+                      - neg_binomial_2_log(n, mu_dbl, phi_dbl - eps);
+        finite_diffs.push_back(dmu * inv2e);
+        finite_diffs.push_back(dphi * inv2e);
+
+        for (int i = 0; i < 2; ++i) {
+          EXPECT_NEAR(gradients[i], finite_diffs[i], 
+            std::max(1.0, gradients[i] * 1e-4)) << 
+            "for i = " << i << ", n = " << n << ", mu = " << mu_dbl << 
+            "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon";
+        }
+
+        phi_dbl *= 10;
+      }
+    }
   }
 }
 
@@ -61,3 +156,6 @@ TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
 
   EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
 }
+
+
+//TODO test continuity of derivatives at cutoff
\ No newline at end of file

From c96d9d81bac54dc4fd8b936b60e987b7464c885c Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Tue, 10 Dec 2019 09:34:08 -0500
Subject: [PATCH 07/82] [Jenkins] auto-formatting by clang-format version
 5.0.2-svn328729-1~exp1~20180509124008.99 (branches/release_50)

---
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    |  48 +-
 .../prim/scal/prob/neg_binomial_2_test.cpp    |  59 ++-
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 412 ++++++++++++++++--
 3 files changed, 435 insertions(+), 84 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index cb4cd46520a..96b17de1589 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -18,11 +18,11 @@ namespace stan {
 namespace math {
 
 namespace internal {
-  //Exposing to let me us this in tests
-  //The current tests fail when the cutoff is 1e8 and pass with 1e9, 
-  //setting 1e10 to be safe
-  constexpr double neg_binomial_2_phi_cutoff = 1e10;
-}
+// Exposing to let me us this in tests
+// The current tests fail when the cutoff is 1e8 and pass with 1e9,
+// setting 1e10 to be safe
+constexpr double neg_binomial_2_phi_cutoff = 1e10;
+}  // namespace internal
 
 // NegBinomial(n|mu, phi)  [mu >= 0; phi > 0;  n >= 0]
 template <bool propto, typename T_n, typename T_location, typename T_precision>
@@ -86,10 +86,10 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   }
 
   for (size_t i = 0; i < size; i++) {
-    if(phi__[i] > internal::neg_binomial_2_phi_cutoff) {
-      //Phi is large, deferring to Poisson. 
-      //Copying the code here as just calling
-      //poisson_lpmf does not preserve propto logic correctly
+    if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
+      // Phi is large, deferring to Poisson.
+      // Copying the code here as just calling
+      // poisson_lpmf does not preserve propto logic correctly
       if (include_summand<propto>::value) {
         logp -= lgamma(n_vec[i] + 1.0);
       }
@@ -99,23 +99,23 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
 
       // if (include_summand<propto, T_location, T_precision>::value) {
       //   logp += (mu__[i] * (mu__[i] - 2 * n_vec[i]) +
-      //     n_vec[i] * (n_vec[i] - 1)) / ( 2 * phi__[i] ); 
-      //   // logp += (mu__[i] * mu__[i] - n_vec[i] - 
+      //     n_vec[i] * (n_vec[i] - 1)) / ( 2 * phi__[i] );
+      //   // logp += (mu__[i] * mu__[i] - n_vec[i] -
       //   //   2 * mu__[i] * n_vec[i] + n_vec[i] * n_vec[i])/phi
       // }
 
       if (!is_constant_all<T_location>::value) {
-        //This is the Taylor series of the full derivative for phi -> Inf
-        //Obtained in Mathematica via 
-        //Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
+        // This is the Taylor series of the full derivative for phi -> Inf
+        // Obtained in Mathematica via
+        // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
         ops_partials.edge1_.partials_[i]
-            += n_vec[i] / mu__[i]  + (mu__[i] - n_vec[i]) / phi__[i] - 1;              
+            += n_vec[i] / mu__[i] + (mu__[i] - n_vec[i]) / phi__[i] - 1;
       }
-      
-      //The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2)      
-      //So ignoring here
-      //Obtained in Mathematica via
-      //Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] - 
+
+      // The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2)
+      // So ignoring here
+      // Obtained in Mathematica via
+      // Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] -
       //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 1}]
 
     } else {
@@ -134,13 +134,15 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
 
       if (!is_constant_all<T_location>::value) {
         ops_partials.edge1_.partials_[i]
-            += n_vec[i] / mu__[i] - (n_vec[i] + phi__[i]) / (mu__[i] + phi__[i]);
+            += n_vec[i] / mu__[i]
+               - (n_vec[i] + phi__[i]) / (mu__[i] + phi__[i]);
       }
       if (!is_constant_all<T_precision>::value) {
         ops_partials.edge2_.partials_[i]
             += 1.0 - n_plus_phi[i] / (mu__[i] + phi__[i]) + log_phi[i]
-              - log_mu_plus_phi[i] - digamma(phi__[i]) + digamma(n_plus_phi[i]);
-      }    
+               - log_mu_plus_phi[i] - digamma(phi__[i])
+               + digamma(n_plus_phi[i]);
+      }
     }
   }
   return ops_partials.build(logp);
diff --git a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
index 63f9a4eaf34..56572e2d91f 100644
--- a/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/scal/prob/neg_binomial_2_test.cpp
@@ -206,28 +206,26 @@ TEST(ProbDistributionsNegBinomial, chiSquareGoodnessFitTest4) {
 
 TEST(ProbDistributionsNegBinomial, extreme_values) {
   std::array<unsigned int, 5> n_to_test = {1, 5, 100, 12985, 1968422};
-  std::array<double, 6> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054 };
+  std::array<double, 6> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  for(auto mu_iter = mu_to_test.begin(); 
-      mu_iter != mu_to_test.end(); ++mu_iter) {
-    for(auto n_iter = n_to_test.begin(); 
-        n_iter != n_to_test.end(); ++n_iter) {
+  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
+       ++mu_iter) {
+    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
       double mu = *mu_iter;
       unsigned int n = *n_iter;
-      //Test just before cutoff
-      double logp = stan::math::neg_binomial_2_log<false>(
-          n, mu, phi_cutoff - 1e-8);
-        EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << 
-          mu << ", phi = " << (phi_cutoff - 1e-8);
+      // Test just before cutoff
+      double logp
+          = stan::math::neg_binomial_2_log<false>(n, mu, phi_cutoff - 1e-8);
+      EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << mu
+                         << ", phi = " << (phi_cutoff - 1e-8);
 
-
-      //Test across a range of phi
+      // Test across a range of phi
       double phi = 1e12;
       for (int i = 0; i < 10; ++i) {
         phi *= 10;
         double logp = stan::math::neg_binomial_2_log<false>(n, mu, phi);
-        EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << 
-          mu << ", phi = " << phi;
+        EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << mu
+                           << ", phi = " << phi;
       }
     }
   }
@@ -235,27 +233,26 @@ TEST(ProbDistributionsNegBinomial, extreme_values) {
 
 TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  std::array<double, 7> mu_to_test = 
-    {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345 };
-  std::array<unsigned int, 8> n_to_test = 
-    {0, 3, 16, 24, 181, 2132, 121358, 865422242 };
-  for(auto mu_iter = mu_to_test.begin(); 
-      mu_iter != mu_to_test.end(); ++mu_iter) {
+  std::array<double, 7> mu_to_test
+      = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
+  std::array<unsigned int, 8> n_to_test
+      = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
+  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
+       ++mu_iter) {
     double mu = *mu_iter;
-    for(auto n_iter = n_to_test.begin(); 
-        n_iter != n_to_test.end(); ++n_iter) {
+    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
       unsigned int n = *n_iter;
 
-      double before_cutoff = 
-        stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff - 1e-8);
-      double after_cutoff = 
-        stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff + 1e-8);
+      double before_cutoff
+          = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff - 1e-8);
+      double after_cutoff
+          = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff + 1e-8);
       double relative_error_at_cutoff = log(before_cutoff / after_cutoff);
-      EXPECT_NEAR(relative_error_at_cutoff, 0, 1e-8) << 
-        "neg_binomial_2_lpmf changes too much around phi cutoff for n = " <<
-        n << ", mu = " << mu << ", cutoff = " << phi_cutoff << 
-        " value at cutoff - 1e-8: " << 
-        before_cutoff << ", value at cutoff + 1e-8: " << after_cutoff;
+      EXPECT_NEAR(relative_error_at_cutoff, 0, 1e-8)
+          << "neg_binomial_2_lpmf changes too much around phi cutoff for n = "
+          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+          << " value at cutoff - 1e-8: " << before_cutoff
+          << ", value at cutoff + 1e-8: " << after_cutoff;
     }
   }
 }
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index a0964ba894a..841ffe2679b 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -10,12 +10,18 @@ struct TestValue {
   double grad_mu;
   double grad_phi;
 
-  TestValue(unsigned int _n, double _mu, double _phi, double _value, double _grad_mu, double _grad_phi)
-      : n(_n), mu(_mu), phi(_phi), value(_value), grad_mu(_grad_mu), grad_phi(_grad_phi) {}
+  TestValue(unsigned int _n, double _mu, double _phi, double _value,
+            double _grad_mu, double _grad_phi)
+      : n(_n),
+        mu(_mu),
+        phi(_phi),
+        value(_value),
+        grad_mu(_grad_mu),
+        grad_phi(_grad_phi) {}
 };
 
-//Test data generated in Mathematica (Wolfram Cloud) via
-// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi ]+ 
+// Test data generated in Mathematica (Wolfram Cloud) via
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi ]+
 //   n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
 // nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
 // nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
@@ -23,7 +29,7 @@ struct TestValue {
 // mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
 //  phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
 // ns = {0,6,14,1525,10233};
-//  WriteString[out, "std::array<TestValue, ", 
+//  WriteString[out, "std::array<TestValue, ",
 //      Length[mus]*Length[phis]*Length[ns], "> testValues = {"];
 //    Block[{$MaxPrecision = 80, $MinPrecision = 40}, {
 //      For[i = 1, i <= Length[mus], i++, {
@@ -44,16 +50,366 @@ struct TestValue {
 //  WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::array<TestValue, 175> testValues = {  TestValue(0,0.0000256,0.0004,-0.000024814156367780882, -0.9398496240601504,-0.0018850149796021398),  TestValue(6,0.0000256,0.0004,-26.480362597222488, 220276.31578947368,-11595.463497838708),  TestValue(14,0.0000256,0.0004,-49.814562438358635, 513979.32330827066,-30391.559221530802),  TestValue(1525,0.0000256,0.0004,-4301.784727467015, 5.5987134868421055e7,-3.580668787634408e6),  TestValue(10233,0.0000256,0.0004,-28781.07085289515, 3.7568285855263156e8,-2.4041193199521683e7),  TestValue(0,0.0000256,0.065,-0.000025594960092480967, -0.9996063088998794,-7.751668684718993e-8),  TestValue(6,0.0000256,0.065,-51.41938813644809, 234281.72904210034,-74.69380754597304),  TestValue(14,0.0000256,0.065,-114.92817109028836, 546658.7005733127,-196.83239209326592),  TestValue(1525,0.0000256,0.065,-11965.467128123484, 5.954685919853104e7,-23429.11268911477),  TestValue(10233,0.0000256,0.065,-80237.4790550341, 3.995691927102557e8,-157343.697098361),  TestValue(0,0.0000256,4.42,-0.000025599925864390194, -0.9999942081783417,-1.677258332222209e-11),  TestValue(6,0.0000256,4.42,-67.52038137511191, 234372.6425475907,-0.4312559247584902),  TestValue(14,0.0000256,4.42,-161.64931287705224, 546870.8326033225,-1.650128690902025),  TestValue(1525,0.0000256,4.42,-18367.34289180058, 5.956996647937967e7,-339.0570825343945),  TestValue(10233,0.0000256,4.42,-123371.16336416776, 3.997242463550437e8,-2307.279979293951),  TestValue(0,0.0000256,800,-0.00002559999998652529, -0.999999968000001,-8.881784197001252e-16),  TestValue(6,0.0000256,800,-69.9980790657431, 234373.99250003224,-0.000023330384471442756),  TestValue(14,0.0000256,800,-173.09898662779824, 546873.9825000325,-0.00014060727924558591),  TestValue(1525,0.0000256,800,-24826.22813563853, 5.957030959375009e7,-0.8389762876176414),  TestValue(10233,0.0000256,800,-173733.65594636812, 3.997265487087504e8,-10.166635446653597),  TestValue(0,0.0000256,15324,-0.000025599996959613236, -0.9999999983294179,0.),  TestValue(6,0.0000256,15324,-70.01580732128963, 234373.99960845898,-6.386142814562845e-8),  TestValue(14,0.0000256,15324,-173.20616504262574, 546873.9990864021,-3.872936886750722e-7),  TestValue(1525,0.0000256,15324,-25707.717028801628, 5.957031140048291e7,-0.004643062913324059),  TestValue(10233,0.0000256,15324,-189611.39394380094, 3.9972656083222395e8,-0.15627194690990365),  TestValue(0,0.314,0.0004,-0.002666782716971683, -0.001272264631043257,-5.66822905706025),  TestValue(6,0.314,0.0004,-9.625197494412376, 0.023038524497171847,2477.530549555817),  TestValue(14,0.314,0.0004,-10.482321240387563, 0.05545291000145865,2452.982014445862),  TestValue(1525,0.314,0.0004,-17.094738795518424, 6.1777199721236284,-2348.2711549792057),  TestValue(10233,0.314,0.0004,-30.083534640958533, 41.460778593539814,-30043.568270589793),  TestValue(0,0.314,0.065,-0.11460468078714132, -0.17150395778364116,-0.9346528929704305),  TestValue(6,0.314,0.065,-5.6231627412658, 3.1056417323496293,0.8117566646875254),  TestValue(14,0.314,0.065,-7.917539720426937, 7.4751693191939905,-19.40653851445296),  TestValue(1525,0.314,0.065,-296.58556828610017, 832.7696922844226,-4001.4921811261693),  TestValue(10233,0.314,0.065,-1936.716591758479, 5589.00047056451,-26975.841613138524),  TestValue(0,0.314,4.42,-0.30334820230965986, -0.9336713138994508,-0.00230212890163628),  TestValue(6,0.314,4.42,-11.748118636048988, 16.90718181793719,-0.3435269754367143),  TestValue(14,0.314,4.42,-31.109603016060397, 40.69498599371937,-1.4423583039713965),  TestValue(1525,0.314,4.42,-4115.10160678526, 4533.61649969458,-316.1764856190919),  TestValue(10233,0.314,4.42,-27734.55588693275, 30426.641345033488,-2153.7342775414127),  TestValue(0,0.314,800,-0.31393839362010567, -0.9996076539958066,-7.698783210940974e-8),  TestValue(6,0.314,800,-13.827010724886122, 18.101175543376296,-0.000020465017271042996),  TestValue(14,0.314,800,-41.61461010763844, 43.568886473205765,-0.00013381877200302483),  TestValue(1525,0.314,800,-10469.94267675256, 4853.782788344746,-0.8382285160349765),  TestValue(10233,0.314,800,-77398.83453431107, 32575.386135464123,-10.16161733713528),  TestValue(0,0.314,15324,-0.31399678298770084, -0.9999795096863716,-2.099280749234822e-10),  TestValue(6,0.314,15324,-13.842565956968983, 18.10790921043538,-5.6049177743489054e-8),  TestValue(14,0.314,15324,-41.71664028188991, 43.58509417059771,-3.687852014877535e-7),  TestValue(1525,0.314,15324,-11350.864477542971, 4855.588403521258,-0.004641024152967077),  TestValue(10233,0.314,15324,-93272.76691554434, 32587.50423265796,-0.15625826529496223),  TestValue(0,1.5,0.0004,-0.003291911100032755, -0.00026659557451346307,-7.230044345656401),  TestValue(6,1.5,0.0004,-9.619783961619232, 0.0007997867235403892,2491.0537701151675),  TestValue(14,1.5,0.0004,-10.468856159359483, 0.002221629787612192,2486.6186161358087),  TestValue(1525,1.5,0.0004,-15.560537541616213, 0.270772238514174,1484.280307752038),  TestValue(10233,1.5,0.0004,-19.785223133323598, 1.8184484137563317,-4317.601447204935),  TestValue(0,1.5,0.065,-0.2067814991501101, -0.04153354632587859,-2.2227873794044952),  TestValue(6,1.5,0.065,-4.841004539887443, 0.12460063897763578,11.520890928200775),  TestValue(14,1.5,0.065,-5.969601492726813, 0.34611288604898827,7.298954082323366),  TestValue(1525,1.5,0.065,-74.45092758687497, 42.184238551650694,-953.4745083343279),  TestValue(10233,1.5,0.065,-445.630392408013, 283.3003194888179,-6515.787894589817),  TestValue(0,1.5,4.42,-1.2915096474038796, -0.7466216216216216,-0.03881837442792935),  TestValue(6,1.5,4.42,-4.694711300875651, 2.239864864864865,-0.12612961153608993),  TestValue(14,1.5,4.42,-13.334103973863655, 6.221846846846847,-0.8864094608348823),  TestValue(1525,1.5,4.42,-2072.1910365790172, 758.3186936936937,-251.67662613527665),  TestValue(10233,1.5,4.42,-14020.648493631525, 5092.706081081081,-1720.7211329093311),  TestValue(0,1.5,800,-1.4985955053447242, -0.9981285090455396,-1.7534272203079126e-6),  TestValue(6,1.5,800,-5.63758835785638, 2.9943855271366187,-0.00001104786953298742),  TestValue(14,1.5,800,-20.926415102269573, 8.317737575379496,-0.00010961017476240897),  TestValue(1525,1.5,800,-8088.548799680884, 1013.7658556872531,-0.8354105724129193),  TestValue(10233,1.5,800,-61412.52664040723, 6808.234560199626,-10.142698900729565),  TestValue(0,1.5,15324,-1.499926590534038, -0.9999021239111285,-4.790177143831897e-9),  TestValue(6,1.5,15324,-5.645995699555982, 2.9997063717333856,-3.032959305926397e-8),  TestValue(14,1.5,15324,-21.010069937864472, 8.332517699259403,-3.0266583905813604e-7),  TestValue(1525,1.5,15324,-8967.33164084002, 1015.5672571857361,-0.004633327525485953),  TestValue(10233,1.5,15324,-77272.09898456372, 6820.332387197807,-0.15620659350885369),  TestValue(0,3,0.0004,-0.003569116649587855, -0.0001333155579256099,-7.922924939527562),  TestValue(6,3,0.0004,-9.619261327135609, 0.0001333155579256099,2492.360089770114),  TestValue(14,3,0.0004,-10.467267071498288, 0.0004888237123939031,2490.5905361225123),  TestValue(1525,3,0.0004,-15.357522072066786, 0.06763542638759276,1991.7174903993568),  TestValue(10233,3,0.0004,-18.421373162287637, 0.4546060525263298,-908.6583034400528),  TestValue(0,3,0.065,-0.25047201260085383, -0.021207177814029365,-2.874622756288704),  TestValue(6,3,0.065,-4.758782442354863, 0.021207177814029365,12.74533572164111),  TestValue(14,3,0.065,-5.719495913883133, 0.07775965198477433,11.025105769529759),  TestValue(1525,3,0.065,-42.491829475397026, 10.75910821098423,-477.2384670870571),  TestValue(10233,3,0.065,-230.9301248894044, 72.31647634584013,-3316.4438994781904),  TestValue(0,3,4.42,-2.2897339760163957, -0.5956873315363881,-0.11372669262607049),  TestValue(6,3,4.42,-2.889108195828742, 0.5956873315363881,0.003850246852058703),  TestValue(14,3,4.42,-7.790064290604171, 2.18418688230009,-0.4832453669983474),  TestValue(1525,3,4.42,-1360.5497881858591, 302.2120395327942,-199.67578957112616),  TestValue(10233,3,4.42,-9239.719029853994, 2031.2938005390836,-1371.3592560596119),  TestValue(0,3,800,-2.994389023067612, -0.9962640099626401,-6.996241475043519e-6),  TestValue(6,3,800,-2.9857172436025223, 0.9962640099626401,-2.3069406651643476e-6),  TestValue(14,3,800,-12.744324478713366, 3.65296803652968,-0.00008222425506509978),  TestValue(1525,3,800,-7035.84649923785, 505.4379410543794,-0.8318616138503963),  TestValue(10233,3,800,-54340.180404088605, 3397.2602739726026,-10.118854869649681),  TestValue(0,3,15324,-2.999706381300726, -0.9998042669798395,-1.9158207464897714e-8),  TestValue(6,3,15324,-2.9874796347589054, 0.9998042669798395,-6.3824572293924575e-9),  TestValue(14,3,15324,-12.807159398982407, 3.665948978926078,-2.2763181739549054e-7),  TestValue(1525,3,15324,-7911.931224008331, 507.2340314477719,-0.004623603455756964),  TestValue(10233,3,15324,-70181.6251826905, 3409.332550401253,-0.15614126136305728),  TestValue(0,180,0.0004,-0.0052068020335865025, -2.2222172839615914e-6,-12.01700730618354),  TestValue(6,180,0.0004,-9.62011239916672, -2.148143374496205e-6,2490.2324075130828),  TestValue(14,180,0.0004,-10.467069325725546, -2.04937816187569e-6,2491.084720678314),  TestValue(1525,180,0.0004,-15.159228863591125, 0.000016604901371824113,2487.4167692289852),  TestValue(10233,180,0.0004,-17.08144177432405, 0.00012411083530925487,2440.94300115826),  TestValue(0,180,0.065,-0.5152345838836883, -0.00036098075694887956,-6.927046886659846),  TestValue(6,180,0.065,-4.897099604874426, -0.0003489480650505836,10.617175935000475),  TestValue(14,180,0.065,-5.689219198051667, -0.0003329044758528556,11.4626317745298),  TestValue(1525,180,0.065,-10.618383986015033, 0.0026973284338680167,7.7929628140754765),  TestValue(10233,180,0.065,-15.542242814932251, 0.020160775275594924,-38.6634853761835),  TestValue(0,180,4.42,-16.491356225074536, -0.023967031775295522,-2.755043100796684),  TestValue(6,180,4.42,-11.802883319144515, -0.023168130716119003,-1.8613752566654882),  TestValue(14,180,4.42,-9.653376579596795, -0.022102929303883648,-1.313682997645138),  TestValue(1525,180,4.42,-30.756932642065294, 0.1790869874320693,-5.0606677133089075),  TestValue(10233,180,4.42,-235.49737914944126, 1.3385587246502548,-50.37753458197702),  TestValue(0,180,800,-162.35267519735217, -0.8163265306122449,-0.01926737460893513),  TestValue(6,180,800,-138.9731231908616, -0.7891156462585034,-0.017913154212997107),  TestValue(14,180,800,-117.57055678993851, -0.7528344671201814,-0.016193696733894036),  TestValue(1525,180,800,-1255.1060610431614, 6.099773242630386,-0.5081161722061651),  TestValue(10233,180,800,-14640.50246307096, 45.59183673469388,-7.836489965276398),  TestValue(0,180,15324,-178.95104102256036, -0.9883900928792569,-0.00006792118926490787),  TestValue(6,180,15324,-154.44163935947577, -0.9554437564499484,-0.00006343927721985665),  TestValue(14,180,15324,-131.5984192349756, -0.911515307877537,-0.000057701678183974536),  TestValue(1525,180,15324,-1861.5172673616398, 7.38547041623667,-0.0035556000115217756),  TestValue(10233,180,15324,-28577.644697168085, 55.2015866873065,-0.14858705144088802),  TestValue(0,1123,0.0004,-0.005939122128713381, -3.5618865318302646e-7,-13.847805677972104),  TestValue(6,1123,0.0004,-9.620833523075628, -3.5428559715533445e-7,2488.429599570756),  TestValue(14,1123,0.0004,-10.467775521386166, -3.517481891184117e-7,2489.3192333086026),  TestValue(1525,1123,0.0004,-15.157115486355906, 1.2750475385536657e-7,2492.70020501204),  TestValue(10233,1123,0.0004,-17.063078998820856, 2.8894734020457448e-6,2486.849880233364),  TestValue(0,1123,0.065,-0.6342170147837343, -0.000057877326779839104,-8.75724272015346),  TestValue(6,1123,0.065,-5.014263034227778, -0.000057568097963562137,8.814958879676311),  TestValue(14,1123,0.065,-5.803957292009425, -0.000057155792875192846,9.697719756764902),  TestValue(1525,1123,0.065,-10.275036857130544, 0.000020718330690556827,13.074039765317043),  TestValue(10233,1123,0.065,-12.558918107941281, 0.0004695124193805291,7.224124958319663),  TestValue(0,1123,4.42,-24.493639593452325, -0.00392045555338738,-4.545467874886493),  TestValue(6,1123,4.42,-19.68318216630322, -0.003899509219175159,-3.624587483847729),  TestValue(14,1123,4.42,-17.37102939846337, -0.003871580773558864,-3.040611828950623),  TestValue(1525,1123,4.42,-7.7548168672583415, 0.0014034043922188128,0.0654298516080507),  TestValue(10233,1123,4.42,-35.45506157865748, 0.031803517445555686,-5.756960605210265),  TestValue(0,1123,800,-701.6240143366822, -0.4160166406656266,-0.29304665858647905),  TestValue(6,1123,800,-671.3041847506472, -0.4137939337698174,-0.28869011401594236),  TestValue(14,1123,800,-640.6479149103316, -0.4108303245754051,-0.2829675576373729),  TestValue(1525,1123,800,-30.39018204828426, 0.14892136201921807,-0.018804728472968435),  TestValue(10233,1123,800,-3343.1303902972795, 3.3748099701370067,-2.9898053694742615),  TestValue(0,1123,15324,-1083.757151397245, -0.9317200705295798,-0.002442933450309326),  TestValue(6,1123,15324,-1048.6172073187354, -0.9267420470004815,-0.002416262805940761),  TestValue(14,1123,15324,-1011.5999306403351, -0.920104682295017,-0.00238094023047708),  TestValue(1525,1123,15324,-64.3938471491183, 0.33352757644959136,-0.00029097614079454104),  TestValue(10233,1123,15324,-11352.060718035325, 7.558299058347705,-0.11311918072723515),  TestValue(0,10586,0.0004,-0.006836533480423993, -3.778575334268833e-8,-16.091333738845734),  TestValue(6,10586,0.0004,-9.621729024009568, -3.776433689454398e-8,2486.19084755338),  TestValue(14,10586,0.0004,-10.468668475096411, -3.7735781630351504e-8,2487.0868493492235),  TestValue(1525,10586,0.0004,-15.157527333190956, -3.234240610599839e-8,2491.6705880068075),  TestValue(10233,10586,0.0004,-17.060718192660715, -1.2600010324928188e-9,2492.7518943576556),  TestValue(0,10586,0.065,-0.7800430171085975, -6.1401474485561915e-6,-11.00066794181818),  TestValue(6,10586,0.065,-5.159778603540011, -6.1366672969700086e-6,6.57630939764217),  TestValue(14,10586,0.065,-5.949058950638154, -6.132027094855097e-6,7.465437927571536),  TestValue(1525,10586,0.065,-10.34196113541293, -5.255608920401252e-6,12.044448366424728),  TestValue(10233,10586,0.065,-12.175300607224926, -2.047489183204549e-7,13.125723676609066),  TestValue(0,10586,4.42,-34.3945190758502, -0.0004173583295091224,-6.781982760105572),  TestValue(6,10586,4.42,-29.562997357281894, -0.00041712177651676886,-5.856347033468785),  TestValue(14,10586,4.42,-27.2227588675498, -0.0004168063725269641,-5.266030931107645),  TestValue(1525,10586,4.42,-12.301855613945008, -0.0003572344439525938,-0.9624372357797295),  TestValue(10233,10586,4.42,-9.430792045634007, -0.00001391720105013416,0.11674937200192481),  TestValue(0,10586,800,-2124.4224654744803, -0.07026172492534692,-1.7257898067684474),  TestValue(6,10586,800,-2091.312452085902, -0.07022190154073024,-1.7188401003298583),  TestValue(14,10586,800,-2056.9359371755286, -0.07016880369457469,-1.7096599947938858),  TestValue(1525,10586,800,-744.0169167062886, -0.060139948001942986,-0.7924525685250288),  TestValue(10233,10586,800,-7.2703661972227565, -0.0023429424616141564,0.00008904830662359586),  TestValue(0,10586,15324,-8048.29915678056, -0.5914318795831726,-0.11664064731878732),  TestValue(6,10586,15324,-8002.424955944863, -0.5910966640836922,-0.11648073932479441),  TestValue(14,10586,15324,-7951.095336923546, -0.590649710084385,-0.11626776694982688),  TestValue(1525,10586,15324,-4300.645593413912, -0.506231273465249,-0.08062419697917278),  TestValue(10233,10586,15324,-9.327824035135563, -0.019721845219427537,-0.00008059480749977865)};
+std::array<TestValue, 175> testValues
+    = {TestValue(0, 0.0000256, 0.0004, -0.000024814156367780882,
+                 -0.9398496240601504, -0.0018850149796021398),
+       TestValue(6, 0.0000256, 0.0004, -26.480362597222488, 220276.31578947368,
+                 -11595.463497838708),
+       TestValue(14, 0.0000256, 0.0004, -49.814562438358635, 513979.32330827066,
+                 -30391.559221530802),
+       TestValue(1525, 0.0000256, 0.0004, -4301.784727467015,
+                 5.5987134868421055e7, -3.580668787634408e6),
+       TestValue(10233, 0.0000256, 0.0004, -28781.07085289515,
+                 3.7568285855263156e8, -2.4041193199521683e7),
+       TestValue(0, 0.0000256, 0.065, -0.000025594960092480967,
+                 -0.9996063088998794, -7.751668684718993e-8),
+       TestValue(6, 0.0000256, 0.065, -51.41938813644809, 234281.72904210034,
+                 -74.69380754597304),
+       TestValue(14, 0.0000256, 0.065, -114.92817109028836, 546658.7005733127,
+                 -196.83239209326592),
+       TestValue(1525, 0.0000256, 0.065, -11965.467128123484,
+                 5.954685919853104e7, -23429.11268911477),
+       TestValue(10233, 0.0000256, 0.065, -80237.4790550341,
+                 3.995691927102557e8, -157343.697098361),
+       TestValue(0, 0.0000256, 4.42, -0.000025599925864390194,
+                 -0.9999942081783417, -1.677258332222209e-11),
+       TestValue(6, 0.0000256, 4.42, -67.52038137511191, 234372.6425475907,
+                 -0.4312559247584902),
+       TestValue(14, 0.0000256, 4.42, -161.64931287705224, 546870.8326033225,
+                 -1.650128690902025),
+       TestValue(1525, 0.0000256, 4.42, -18367.34289180058, 5.956996647937967e7,
+                 -339.0570825343945),
+       TestValue(10233, 0.0000256, 4.42, -123371.16336416776,
+                 3.997242463550437e8, -2307.279979293951),
+       TestValue(0, 0.0000256, 800, -0.00002559999998652529, -0.999999968000001,
+                 -8.881784197001252e-16),
+       TestValue(6, 0.0000256, 800, -69.9980790657431, 234373.99250003224,
+                 -0.000023330384471442756),
+       TestValue(14, 0.0000256, 800, -173.09898662779824, 546873.9825000325,
+                 -0.00014060727924558591),
+       TestValue(1525, 0.0000256, 800, -24826.22813563853, 5.957030959375009e7,
+                 -0.8389762876176414),
+       TestValue(10233, 0.0000256, 800, -173733.65594636812,
+                 3.997265487087504e8, -10.166635446653597),
+       TestValue(0, 0.0000256, 15324, -0.000025599996959613236,
+                 -0.9999999983294179, 0.),
+       TestValue(6, 0.0000256, 15324, -70.01580732128963, 234373.99960845898,
+                 -6.386142814562845e-8),
+       TestValue(14, 0.0000256, 15324, -173.20616504262574, 546873.9990864021,
+                 -3.872936886750722e-7),
+       TestValue(1525, 0.0000256, 15324, -25707.717028801628,
+                 5.957031140048291e7, -0.004643062913324059),
+       TestValue(10233, 0.0000256, 15324, -189611.39394380094,
+                 3.9972656083222395e8, -0.15627194690990365),
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+       TestValue(6, 0.314, 0.0004, -9.625197494412376, 0.023038524497171847,
+                 2477.530549555817),
+       TestValue(14, 0.314, 0.0004, -10.482321240387563, 0.05545291000145865,
+                 2452.982014445862),
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+                 -2348.2711549792057),
+       TestValue(10233, 0.314, 0.0004, -30.083534640958533, 41.460778593539814,
+                 -30043.568270589793),
+       TestValue(0, 0.314, 0.065, -0.11460468078714132, -0.17150395778364116,
+                 -0.9346528929704305),
+       TestValue(6, 0.314, 0.065, -5.6231627412658, 3.1056417323496293,
+                 0.8117566646875254),
+       TestValue(14, 0.314, 0.065, -7.917539720426937, 7.4751693191939905,
+                 -19.40653851445296),
+       TestValue(1525, 0.314, 0.065, -296.58556828610017, 832.7696922844226,
+                 -4001.4921811261693),
+       TestValue(10233, 0.314, 0.065, -1936.716591758479, 5589.00047056451,
+                 -26975.841613138524),
+       TestValue(0, 0.314, 4.42, -0.30334820230965986, -0.9336713138994508,
+                 -0.00230212890163628),
+       TestValue(6, 0.314, 4.42, -11.748118636048988, 16.90718181793719,
+                 -0.3435269754367143),
+       TestValue(14, 0.314, 4.42, -31.109603016060397, 40.69498599371937,
+                 -1.4423583039713965),
+       TestValue(1525, 0.314, 4.42, -4115.10160678526, 4533.61649969458,
+                 -316.1764856190919),
+       TestValue(10233, 0.314, 4.42, -27734.55588693275, 30426.641345033488,
+                 -2153.7342775414127),
+       TestValue(0, 0.314, 800, -0.31393839362010567, -0.9996076539958066,
+                 -7.698783210940974e-8),
+       TestValue(6, 0.314, 800, -13.827010724886122, 18.101175543376296,
+                 -0.000020465017271042996),
+       TestValue(14, 0.314, 800, -41.61461010763844, 43.568886473205765,
+                 -0.00013381877200302483),
+       TestValue(1525, 0.314, 800, -10469.94267675256, 4853.782788344746,
+                 -0.8382285160349765),
+       TestValue(10233, 0.314, 800, -77398.83453431107, 32575.386135464123,
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+       TestValue(0, 0.314, 15324, -0.31399678298770084, -0.9999795096863716,
+                 -2.099280749234822e-10),
+       TestValue(6, 0.314, 15324, -13.842565956968983, 18.10790921043538,
+                 -5.6049177743489054e-8),
+       TestValue(14, 0.314, 15324, -41.71664028188991, 43.58509417059771,
+                 -3.687852014877535e-7),
+       TestValue(1525, 0.314, 15324, -11350.864477542971, 4855.588403521258,
+                 -0.004641024152967077),
+       TestValue(10233, 0.314, 15324, -93272.76691554434, 32587.50423265796,
+                 -0.15625826529496223),
+       TestValue(0, 1.5, 0.0004, -0.003291911100032755, -0.00026659557451346307,
+                 -7.230044345656401),
+       TestValue(6, 1.5, 0.0004, -9.619783961619232, 0.0007997867235403892,
+                 2491.0537701151675),
+       TestValue(14, 1.5, 0.0004, -10.468856159359483, 0.002221629787612192,
+                 2486.6186161358087),
+       TestValue(1525, 1.5, 0.0004, -15.560537541616213, 0.270772238514174,
+                 1484.280307752038),
+       TestValue(10233, 1.5, 0.0004, -19.785223133323598, 1.8184484137563317,
+                 -4317.601447204935),
+       TestValue(0, 1.5, 0.065, -0.2067814991501101, -0.04153354632587859,
+                 -2.2227873794044952),
+       TestValue(6, 1.5, 0.065, -4.841004539887443, 0.12460063897763578,
+                 11.520890928200775),
+       TestValue(14, 1.5, 0.065, -5.969601492726813, 0.34611288604898827,
+                 7.298954082323366),
+       TestValue(1525, 1.5, 0.065, -74.45092758687497, 42.184238551650694,
+                 -953.4745083343279),
+       TestValue(10233, 1.5, 0.065, -445.630392408013, 283.3003194888179,
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+                 -0.03881837442792935),
+       TestValue(6, 1.5, 4.42, -4.694711300875651, 2.239864864864865,
+                 -0.12612961153608993),
+       TestValue(14, 1.5, 4.42, -13.334103973863655, 6.221846846846847,
+                 -0.8864094608348823),
+       TestValue(1525, 1.5, 4.42, -2072.1910365790172, 758.3186936936937,
+                 -251.67662613527665),
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+                 -1.7534272203079126e-6),
+       TestValue(6, 1.5, 800, -5.63758835785638, 2.9943855271366187,
+                 -0.00001104786953298742),
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+                 -0.00010961017476240897),
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+                 -0.8354105724129193),
+       TestValue(10233, 1.5, 800, -61412.52664040723, 6808.234560199626,
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+                 -4.790177143831897e-9),
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+                 -3.032959305926397e-8),
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+                 -3.0266583905813604e-7),
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+                 1991.7174903993568),
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+       TestValue(14, 180, 15324, -131.5984192349756, -0.911515307877537,
+                 -0.000057701678183974536),
+       TestValue(1525, 180, 15324, -1861.5172673616398, 7.38547041623667,
+                 -0.0035556000115217756),
+       TestValue(10233, 180, 15324, -28577.644697168085, 55.2015866873065,
+                 -0.14858705144088802),
+       TestValue(0, 1123, 0.0004, -0.005939122128713381, -3.5618865318302646e-7,
+                 -13.847805677972104),
+       TestValue(6, 1123, 0.0004, -9.620833523075628, -3.5428559715533445e-7,
+                 2488.429599570756),
+       TestValue(14, 1123, 0.0004, -10.467775521386166, -3.517481891184117e-7,
+                 2489.3192333086026),
+       TestValue(1525, 1123, 0.0004, -15.157115486355906, 1.2750475385536657e-7,
+                 2492.70020501204),
+       TestValue(10233, 1123, 0.0004, -17.063078998820856,
+                 2.8894734020457448e-6, 2486.849880233364),
+       TestValue(0, 1123, 0.065, -0.6342170147837343, -0.000057877326779839104,
+                 -8.75724272015346),
+       TestValue(6, 1123, 0.065, -5.014263034227778, -0.000057568097963562137,
+                 8.814958879676311),
+       TestValue(14, 1123, 0.065, -5.803957292009425, -0.000057155792875192846,
+                 9.697719756764902),
+       TestValue(1525, 1123, 0.065, -10.275036857130544,
+                 0.000020718330690556827, 13.074039765317043),
+       TestValue(10233, 1123, 0.065, -12.558918107941281, 0.0004695124193805291,
+                 7.224124958319663),
+       TestValue(0, 1123, 4.42, -24.493639593452325, -0.00392045555338738,
+                 -4.545467874886493),
+       TestValue(6, 1123, 4.42, -19.68318216630322, -0.003899509219175159,
+                 -3.624587483847729),
+       TestValue(14, 1123, 4.42, -17.37102939846337, -0.003871580773558864,
+                 -3.040611828950623),
+       TestValue(1525, 1123, 4.42, -7.7548168672583415, 0.0014034043922188128,
+                 0.0654298516080507),
+       TestValue(10233, 1123, 4.42, -35.45506157865748, 0.031803517445555686,
+                 -5.756960605210265),
+       TestValue(0, 1123, 800, -701.6240143366822, -0.4160166406656266,
+                 -0.29304665858647905),
+       TestValue(6, 1123, 800, -671.3041847506472, -0.4137939337698174,
+                 -0.28869011401594236),
+       TestValue(14, 1123, 800, -640.6479149103316, -0.4108303245754051,
+                 -0.2829675576373729),
+       TestValue(1525, 1123, 800, -30.39018204828426, 0.14892136201921807,
+                 -0.018804728472968435),
+       TestValue(10233, 1123, 800, -3343.1303902972795, 3.3748099701370067,
+                 -2.9898053694742615),
+       TestValue(0, 1123, 15324, -1083.757151397245, -0.9317200705295798,
+                 -0.002442933450309326),
+       TestValue(6, 1123, 15324, -1048.6172073187354, -0.9267420470004815,
+                 -0.002416262805940761),
+       TestValue(14, 1123, 15324, -1011.5999306403351, -0.920104682295017,
+                 -0.00238094023047708),
+       TestValue(1525, 1123, 15324, -64.3938471491183, 0.33352757644959136,
+                 -0.00029097614079454104),
+       TestValue(10233, 1123, 15324, -11352.060718035325, 7.558299058347705,
+                 -0.11311918072723515),
+       TestValue(0, 10586, 0.0004, -0.006836533480423993, -3.778575334268833e-8,
+                 -16.091333738845734),
+       TestValue(6, 10586, 0.0004, -9.621729024009568, -3.776433689454398e-8,
+                 2486.19084755338),
+       TestValue(14, 10586, 0.0004, -10.468668475096411, -3.7735781630351504e-8,
+                 2487.0868493492235),
+       TestValue(1525, 10586, 0.0004, -15.157527333190956,
+                 -3.234240610599839e-8, 2491.6705880068075),
+       TestValue(10233, 10586, 0.0004, -17.060718192660715,
+                 -1.2600010324928188e-9, 2492.7518943576556),
+       TestValue(0, 10586, 0.065, -0.7800430171085975, -6.1401474485561915e-6,
+                 -11.00066794181818),
+       TestValue(6, 10586, 0.065, -5.159778603540011, -6.1366672969700086e-6,
+                 6.57630939764217),
+       TestValue(14, 10586, 0.065, -5.949058950638154, -6.132027094855097e-6,
+                 7.465437927571536),
+       TestValue(1525, 10586, 0.065, -10.34196113541293, -5.255608920401252e-6,
+                 12.044448366424728),
+       TestValue(10233, 10586, 0.065, -12.175300607224926,
+                 -2.047489183204549e-7, 13.125723676609066),
+       TestValue(0, 10586, 4.42, -34.3945190758502, -0.0004173583295091224,
+                 -6.781982760105572),
+       TestValue(6, 10586, 4.42, -29.562997357281894, -0.00041712177651676886,
+                 -5.856347033468785),
+       TestValue(14, 10586, 4.42, -27.2227588675498, -0.0004168063725269641,
+                 -5.266030931107645),
+       TestValue(1525, 10586, 4.42, -12.301855613945008, -0.0003572344439525938,
+                 -0.9624372357797295),
+       TestValue(10233, 10586, 4.42, -9.430792045634007,
+                 -0.00001391720105013416, 0.11674937200192481),
+       TestValue(0, 10586, 800, -2124.4224654744803, -0.07026172492534692,
+                 -1.7257898067684474),
+       TestValue(6, 10586, 800, -2091.312452085902, -0.07022190154073024,
+                 -1.7188401003298583),
+       TestValue(14, 10586, 800, -2056.9359371755286, -0.07016880369457469,
+                 -1.7096599947938858),
+       TestValue(1525, 10586, 800, -744.0169167062886, -0.060139948001942986,
+                 -0.7924525685250288),
+       TestValue(10233, 10586, 800, -7.2703661972227565, -0.0023429424616141564,
+                 0.00008904830662359586),
+       TestValue(0, 10586, 15324, -8048.29915678056, -0.5914318795831726,
+                 -0.11664064731878732),
+       TestValue(6, 10586, 15324, -8002.424955944863, -0.5910966640836922,
+                 -0.11648073932479441),
+       TestValue(14, 10586, 15324, -7951.095336923546, -0.590649710084385,
+                 -0.11626776694982688),
+       TestValue(1525, 10586, 15324, -4300.645593413912, -0.506231273465249,
+                 -0.08062419697917278),
+       TestValue(10233, 10586, 15324, -9.327824035135563, -0.019721845219427537,
+                 -0.00008059480749977865)};
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
-  using stan::math::var;
   using stan::math::value_of;
+  using stan::math::var;
 
-  for(auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
-    TestValue t = *iter;  
+  for (auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
+    TestValue t = *iter;
     unsigned int n = t.n;
     var mu(t.mu);
     var phi(t.phi);
@@ -70,24 +426,22 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
       EXPECT_FALSE(is_nan(gradients[i]));
     }
 
-    EXPECT_NEAR(value_of(val), t.value, fabs(t.value * 1e-8)) << 
-      "value n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
-    EXPECT_NEAR(gradients[0], t.grad_mu, fabs(t.grad_mu * 1e-8)) << 
-      "grad_mu n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
-    EXPECT_NEAR(gradients[1], t.grad_phi, fabs(t.grad_phi * 1e-8)) << 
-      "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
-
+    EXPECT_NEAR(value_of(val), t.value, fabs(t.value * 1e-8))
+        << "value n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
+    EXPECT_NEAR(gradients[0], t.grad_mu, fabs(t.grad_mu * 1e-8))
+        << "grad_mu n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
+    EXPECT_NEAR(gradients[1], t.grad_phi, fabs(t.grad_phi * 1e-8))
+        << "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
   }
 }
 
-
 TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
 
-  //The range of values tested has to be quite conservative to let the test
-  //pass
+  // The range of values tested has to be quite conservative to let the test
+  // pass
   std::array<unsigned int, 1> n_to_test = {100};
   std::array<double, 1> mu_to_test = {8};
   // std::array<unsigned int, 3> n_to_test = {7, 100, 835};
@@ -95,10 +449,9 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
   // std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835};
   // std::array<double, 6> mu_to_test = {0.8, 8, 24, 271};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  for(auto mu_iter = mu_to_test.begin(); 
-      mu_iter != mu_to_test.end(); ++mu_iter) {
-    for(auto n_iter = n_to_test.begin(); 
-        n_iter != n_to_test.end(); ++n_iter) {
+  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
+       ++mu_iter) {
+    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
       double mu_dbl = *mu_iter;
       unsigned int n = *n_iter;
       double phi_dbl = 1.5;
@@ -123,17 +476,17 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
         double eps = 1e-10;
         double inv2e = 0.5 / eps;
         double dmu = neg_binomial_2_log(n, mu_dbl + eps, phi_dbl)
-                    - neg_binomial_2_log(n, mu_dbl - eps, phi_dbl);
+                     - neg_binomial_2_log(n, mu_dbl - eps, phi_dbl);
         double dphi = neg_binomial_2_log(n, mu_dbl, phi_dbl + eps)
                       - neg_binomial_2_log(n, mu_dbl, phi_dbl - eps);
         finite_diffs.push_back(dmu * inv2e);
         finite_diffs.push_back(dphi * inv2e);
 
         for (int i = 0; i < 2; ++i) {
-          EXPECT_NEAR(gradients[i], finite_diffs[i], 
-            std::max(1.0, gradients[i] * 1e-4)) << 
-            "for i = " << i << ", n = " << n << ", mu = " << mu_dbl << 
-            "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon";
+          EXPECT_NEAR(gradients[i], finite_diffs[i],
+                      std::max(1.0, gradients[i] * 1e-4))
+              << "for i = " << i << ", n = " << n << ", mu = " << mu_dbl
+              << "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon";
         }
 
         phi_dbl *= 10;
@@ -157,5 +510,4 @@ TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
   EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
 }
 
-
-//TODO test continuity of derivatives at cutoff
\ No newline at end of file
+// TODO test continuity of derivatives at cutoff
\ No newline at end of file

From 7b992e9bc3534a876cea6b182fd25edb8b18d805 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Tue, 10 Dec 2019 17:21:39 +0100
Subject: [PATCH 08/82] Fixed formatting issues

---
 test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp | 2 +-
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 3 ++-
 2 files changed, 3 insertions(+), 2 deletions(-)

diff --git a/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
index deabf8c9fae..d6a5ce6c0b0 100644
--- a/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/mat/prob/neg_binomial_2_test.cpp
@@ -46,4 +46,4 @@ TEST(ProbDistributionsNegativeBinomial2, vectorAroundCutoff) {
                         + stan::math::neg_binomial_2_lpmf(y, mu, phi[1]);
 
   EXPECT_FLOAT_EQ(vector_value, scalar_value);
-}
\ No newline at end of file
+}
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 841ffe2679b..dec12cf5fd1 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -1,6 +1,7 @@
 #include <stan/math/rev/scal.hpp>
 #include <gtest/gtest.h>
 #include <vector>
+#include <algorithm>
 
 struct TestValue {
   unsigned int n;
@@ -510,4 +511,4 @@ TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
   EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
 }
 
-// TODO test continuity of derivatives at cutoff
\ No newline at end of file
+// TODO(martinmodrak) test continuity of derivatives at cutoff

From 64e034fe2ca815d7dd84ba942d1f17a1241229ff Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 09:02:38 +0100
Subject: [PATCH 09/82] Improved tests and their reporting

---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 381 +-----------------
 1 file changed, 17 insertions(+), 364 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index dec12cf5fd1..50bc6b3861f 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -51,357 +51,7 @@ struct TestValue {
 //  WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::array<TestValue, 175> testValues
-    = {TestValue(0, 0.0000256, 0.0004, -0.000024814156367780882,
-                 -0.9398496240601504, -0.0018850149796021398),
-       TestValue(6, 0.0000256, 0.0004, -26.480362597222488, 220276.31578947368,
-                 -11595.463497838708),
-       TestValue(14, 0.0000256, 0.0004, -49.814562438358635, 513979.32330827066,
-                 -30391.559221530802),
-       TestValue(1525, 0.0000256, 0.0004, -4301.784727467015,
-                 5.5987134868421055e7, -3.580668787634408e6),
-       TestValue(10233, 0.0000256, 0.0004, -28781.07085289515,
-                 3.7568285855263156e8, -2.4041193199521683e7),
-       TestValue(0, 0.0000256, 0.065, -0.000025594960092480967,
-                 -0.9996063088998794, -7.751668684718993e-8),
-       TestValue(6, 0.0000256, 0.065, -51.41938813644809, 234281.72904210034,
-                 -74.69380754597304),
-       TestValue(14, 0.0000256, 0.065, -114.92817109028836, 546658.7005733127,
-                 -196.83239209326592),
-       TestValue(1525, 0.0000256, 0.065, -11965.467128123484,
-                 5.954685919853104e7, -23429.11268911477),
-       TestValue(10233, 0.0000256, 0.065, -80237.4790550341,
-                 3.995691927102557e8, -157343.697098361),
-       TestValue(0, 0.0000256, 4.42, -0.000025599925864390194,
-                 -0.9999942081783417, -1.677258332222209e-11),
-       TestValue(6, 0.0000256, 4.42, -67.52038137511191, 234372.6425475907,
-                 -0.4312559247584902),
-       TestValue(14, 0.0000256, 4.42, -161.64931287705224, 546870.8326033225,
-                 -1.650128690902025),
-       TestValue(1525, 0.0000256, 4.42, -18367.34289180058, 5.956996647937967e7,
-                 -339.0570825343945),
-       TestValue(10233, 0.0000256, 4.42, -123371.16336416776,
-                 3.997242463550437e8, -2307.279979293951),
-       TestValue(0, 0.0000256, 800, -0.00002559999998652529, -0.999999968000001,
-                 -8.881784197001252e-16),
-       TestValue(6, 0.0000256, 800, -69.9980790657431, 234373.99250003224,
-                 -0.000023330384471442756),
-       TestValue(14, 0.0000256, 800, -173.09898662779824, 546873.9825000325,
-                 -0.00014060727924558591),
-       TestValue(1525, 0.0000256, 800, -24826.22813563853, 5.957030959375009e7,
-                 -0.8389762876176414),
-       TestValue(10233, 0.0000256, 800, -173733.65594636812,
-                 3.997265487087504e8, -10.166635446653597),
-       TestValue(0, 0.0000256, 15324, -0.000025599996959613236,
-                 -0.9999999983294179, 0.),
-       TestValue(6, 0.0000256, 15324, -70.01580732128963, 234373.99960845898,
-                 -6.386142814562845e-8),
-       TestValue(14, 0.0000256, 15324, -173.20616504262574, 546873.9990864021,
-                 -3.872936886750722e-7),
-       TestValue(1525, 0.0000256, 15324, -25707.717028801628,
-                 5.957031140048291e7, -0.004643062913324059),
-       TestValue(10233, 0.0000256, 15324, -189611.39394380094,
-                 3.9972656083222395e8, -0.15627194690990365),
-       TestValue(0, 0.314, 0.0004, -0.002666782716971683, -0.001272264631043257,
-                 -5.66822905706025),
-       TestValue(6, 0.314, 0.0004, -9.625197494412376, 0.023038524497171847,
-                 2477.530549555817),
-       TestValue(14, 0.314, 0.0004, -10.482321240387563, 0.05545291000145865,
-                 2452.982014445862),
-       TestValue(1525, 0.314, 0.0004, -17.094738795518424, 6.1777199721236284,
-                 -2348.2711549792057),
-       TestValue(10233, 0.314, 0.0004, -30.083534640958533, 41.460778593539814,
-                 -30043.568270589793),
-       TestValue(0, 0.314, 0.065, -0.11460468078714132, -0.17150395778364116,
-                 -0.9346528929704305),
-       TestValue(6, 0.314, 0.065, -5.6231627412658, 3.1056417323496293,
-                 0.8117566646875254),
-       TestValue(14, 0.314, 0.065, -7.917539720426937, 7.4751693191939905,
-                 -19.40653851445296),
-       TestValue(1525, 0.314, 0.065, -296.58556828610017, 832.7696922844226,
-                 -4001.4921811261693),
-       TestValue(10233, 0.314, 0.065, -1936.716591758479, 5589.00047056451,
-                 -26975.841613138524),
-       TestValue(0, 0.314, 4.42, -0.30334820230965986, -0.9336713138994508,
-                 -0.00230212890163628),
-       TestValue(6, 0.314, 4.42, -11.748118636048988, 16.90718181793719,
-                 -0.3435269754367143),
-       TestValue(14, 0.314, 4.42, -31.109603016060397, 40.69498599371937,
-                 -1.4423583039713965),
-       TestValue(1525, 0.314, 4.42, -4115.10160678526, 4533.61649969458,
-                 -316.1764856190919),
-       TestValue(10233, 0.314, 4.42, -27734.55588693275, 30426.641345033488,
-                 -2153.7342775414127),
-       TestValue(0, 0.314, 800, -0.31393839362010567, -0.9996076539958066,
-                 -7.698783210940974e-8),
-       TestValue(6, 0.314, 800, -13.827010724886122, 18.101175543376296,
-                 -0.000020465017271042996),
-       TestValue(14, 0.314, 800, -41.61461010763844, 43.568886473205765,
-                 -0.00013381877200302483),
-       TestValue(1525, 0.314, 800, -10469.94267675256, 4853.782788344746,
-                 -0.8382285160349765),
-       TestValue(10233, 0.314, 800, -77398.83453431107, 32575.386135464123,
-                 -10.16161733713528),
-       TestValue(0, 0.314, 15324, -0.31399678298770084, -0.9999795096863716,
-                 -2.099280749234822e-10),
-       TestValue(6, 0.314, 15324, -13.842565956968983, 18.10790921043538,
-                 -5.6049177743489054e-8),
-       TestValue(14, 0.314, 15324, -41.71664028188991, 43.58509417059771,
-                 -3.687852014877535e-7),
-       TestValue(1525, 0.314, 15324, -11350.864477542971, 4855.588403521258,
-                 -0.004641024152967077),
-       TestValue(10233, 0.314, 15324, -93272.76691554434, 32587.50423265796,
-                 -0.15625826529496223),
-       TestValue(0, 1.5, 0.0004, -0.003291911100032755, -0.00026659557451346307,
-                 -7.230044345656401),
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TestValue(14,10586,800,-2056.9359371755286,-0.07016880369457469,-1.7096599947938858),  TestValue(1525,10586,800,-744.0169167062886,-0.060139948001942986,-0.7924525685250288),  TestValue(10233,10586,800,-7.2703661972227565,-0.0023429424616141564,0.00008904830662359586),  TestValue(0,10586,15324,-8048.29915678056,-0.5914318795831726,-0.11664064731878732),  TestValue(6,10586,15324,-8002.424955944863,-0.5910966640836922,-0.11648073932479441),  TestValue(14,10586,15324,-7951.095336923546,-0.590649710084385,-0.11626776694982688),  TestValue(1525,10586,15324,-4300.645593413912,-0.506231273465249,-0.08062419697917278),  TestValue(10233,10586,15324,-9.327824035135563,-0.019721845219427537,-0.00008059480749977865),  TestValue(0,10586,162345,-10255.166530843997,-0.9387848332571951,-0.0019538038497231014),  TestValue(6,10586,162345,-10206.520977570348,-0.93825274285482,-0.001951542008541196),  TestValue(14,10586,162345,-10151.499529961993,-0.9375432889849864,-0.0019485283448990032),  TestValue(1525,10586,162345,-5869.2020812217015,-0.8035451893201818,-0.0014225911704155436),  TestValue(10233,10586,162345,-11.157754570856923,-0.03130465200640373,-1.9036241010184085e-6),};
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::is_nan;
@@ -441,12 +91,8 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
 
-  // The range of values tested has to be quite conservative to let the test
-  // pass
-  std::array<unsigned int, 1> n_to_test = {100};
-  std::array<double, 1> mu_to_test = {8};
-  // std::array<unsigned int, 3> n_to_test = {7, 100, 835};
-  // std::array<double, 2> mu_to_test = {8, 24};
+  std::array<unsigned int, 3> n_to_test = {7, 100, 835};
+  std::array<double, 2> mu_to_test = {8, 24};
   // std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835};
   // std::array<double, 6> mu_to_test = {0.8, 8, 24, 271};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
@@ -469,6 +115,9 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
         std::vector<double> gradients;
         val.grad(x, gradients);
 
+        EXPECT_TRUE(value_of(val) < 0)  << "for n = " << n << ", mu = " <<
+          mu_dbl << ", phi = " << phi_dbl; 
+
         for (int i = 0; i < 2; ++i) {
           EXPECT_FALSE(is_nan(gradients[i]));
         }
@@ -483,12 +132,16 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
         finite_diffs.push_back(dmu * inv2e);
         finite_diffs.push_back(dphi * inv2e);
 
-        for (int i = 0; i < 2; ++i) {
-          EXPECT_NEAR(gradients[i], finite_diffs[i],
-                      std::max(1.0, gradients[i] * 1e-4))
-              << "for i = " << i << ", n = " << n << ", mu = " << mu_dbl
-              << "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon";
-        }
+        EXPECT_NEAR(gradients[0], finite_diffs[0],
+                    std::max(1.0, gradients[0] * 1e-4))
+            << "grad_mu, n = " << n << ", mu = " << mu_dbl
+            << "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon, dmu = " << 
+            dmu;
+        EXPECT_NEAR(gradients[1], finite_diffs[1],
+                    std::max(1.0, gradients[1] * 1e-4))
+            << "grad_phi, n = " << n << ", mu = " << mu_dbl
+            << "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon, dphi = " << 
+            dphi;
 
         phi_dbl *= 10;
       }
@@ -502,7 +155,7 @@ TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
   using stan::math::var;
 
   var mu_var(10);
-  int y = 11.8;
+  int y = 11;
   var value_before_cutoff = neg_binomial_2_lpmf<true, int, var, double>(
       y, mu_var, neg_binomial_2_phi_cutoff - 1e-8);
   var value_after_cutoff = neg_binomial_2_lpmf<true, int, var, double>(

From a6eccc83c9b90afc1a3f8a9662e15595621abe6e Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Wed, 11 Dec 2019 08:03:19 +0000
Subject: [PATCH 10/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 435 +++++++++++++++++-
 1 file changed, 428 insertions(+), 7 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 50bc6b3861f..fd01952f017 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -51,7 +51,428 @@ struct TestValue {
 //  WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::array<TestValue, 210> testValues = {  TestValue(0,0.0000256,0.0004,-0.000024814156367780882,-0.9398496240601504,-0.0018850149796021398),  TestValue(6,0.0000256,0.0004,-26.480362597222488,220276.31578947368,-11595.463497838708),  TestValue(14,0.0000256,0.0004,-49.814562438358635,513979.32330827066,-30391.559221530802),  TestValue(1525,0.0000256,0.0004,-4301.784727467015,5.5987134868421055e7,-3.580668787634408e6),  TestValue(10233,0.0000256,0.0004,-28781.07085289515,3.7568285855263156e8,-2.4041193199521683e7),  TestValue(0,0.0000256,0.065,-0.000025594960092480967,-0.9996063088998794,-7.751668684718993e-8),  TestValue(6,0.0000256,0.065,-51.41938813644809,234281.72904210034,-74.69380754597304),  TestValue(14,0.0000256,0.065,-114.92817109028836,546658.7005733127,-196.83239209326592),  TestValue(1525,0.0000256,0.065,-11965.467128123484,5.954685919853104e7,-23429.11268911477),  TestValue(10233,0.0000256,0.065,-80237.4790550341,3.995691927102557e8,-157343.697098361),  TestValue(0,0.0000256,4.42,-0.000025599925864390194,-0.9999942081783417,-1.677258332222209e-11),  TestValue(6,0.0000256,4.42,-67.52038137511191,234372.6425475907,-0.4312559247584902),  TestValue(14,0.0000256,4.42,-161.64931287705224,546870.8326033225,-1.650128690902025),  TestValue(1525,0.0000256,4.42,-18367.34289180058,5.956996647937967e7,-339.0570825343945),  TestValue(10233,0.0000256,4.42,-123371.16336416776,3.997242463550437e8,-2307.279979293951),  TestValue(0,0.0000256,800,-0.00002559999998652529,-0.999999968000001,-8.881784197001252e-16),  TestValue(6,0.0000256,800,-69.9980790657431,234373.99250003224,-0.000023330384471442756),  TestValue(14,0.0000256,800,-173.09898662779824,546873.9825000325,-0.00014060727924558591),  TestValue(1525,0.0000256,800,-24826.22813563853,5.957030959375009e7,-0.8389762876176414),  TestValue(10233,0.0000256,800,-173733.65594636812,3.997265487087504e8,-10.166635446653597),  TestValue(0,0.0000256,15324,-0.000025599996959613236,-0.9999999983294179,0.),  TestValue(6,0.0000256,15324,-70.01580732128963,234373.99960845898,-6.386142814562845e-8),  TestValue(14,0.0000256,15324,-173.20616504262574,546873.9990864021,-3.872936886750722e-7),  TestValue(1525,0.0000256,15324,-25707.717028801628,5.957031140048291e7,-0.004643062913324059),  TestValue(10233,0.0000256,15324,-189611.39394380094,3.9972656083222395e8,-0.15627194690990365),  TestValue(0,0.0000256,162345,-0.00002560001632012643,-0.9999999998423111,0.),  TestValue(6,0.0000256,162345,-70.01669365713798,234373.99996304183,-5.691145332775704e-10),  TestValue(14,0.0000256,162345,-173.21154115647926,546873.9999137641,-3.452532482128845e-9),  TestValue(1525,0.0000256,162345,-25774.016830882043,5.957031149060642e7,-0.00004381660427021927),  TestValue(10233,0.0000256,162345,-192134.409728957,3.9972656143696755e8,-0.001906640534274473),  TestValue(0,0.314,0.0004,-0.002666782716971683,-0.001272264631043257,-5.66822905706025),  TestValue(6,0.314,0.0004,-9.625197494412376,0.023038524497171847,2477.530549555817),  TestValue(14,0.314,0.0004,-10.482321240387563,0.05545291000145865,2452.982014445862),  TestValue(1525,0.314,0.0004,-17.094738795518424,6.1777199721236284,-2348.2711549792057),  TestValue(10233,0.314,0.0004,-30.083534640958533,41.460778593539814,-30043.568270589793),  TestValue(0,0.314,0.065,-0.11460468078714132,-0.17150395778364116,-0.9346528929704305),  TestValue(6,0.314,0.065,-5.6231627412658,3.1056417323496293,0.8117566646875254),  TestValue(14,0.314,0.065,-7.917539720426937,7.4751693191939905,-19.40653851445296),  TestValue(1525,0.314,0.065,-296.58556828610017,832.7696922844226,-4001.4921811261693),  TestValue(10233,0.314,0.065,-1936.716591758479,5589.00047056451,-26975.841613138524),  TestValue(0,0.314,4.42,-0.30334820230965986,-0.9336713138994508,-0.00230212890163628),  TestValue(6,0.314,4.42,-11.748118636048988,16.90718181793719,-0.3435269754367143),  TestValue(14,0.314,4.42,-31.109603016060397,40.69498599371937,-1.4423583039713965),  TestValue(1525,0.314,4.42,-4115.10160678526,4533.61649969458,-316.1764856190919),  TestValue(10233,0.314,4.42,-27734.55588693275,30426.641345033488,-2153.7342775414127),  TestValue(0,0.314,800,-0.31393839362010567,-0.9996076539958066,-7.698783210940974e-8),  TestValue(6,0.314,800,-13.827010724886122,18.101175543376296,-0.000020465017271042996),  TestValue(14,0.314,800,-41.61461010763844,43.568886473205765,-0.00013381877200302483),  TestValue(1525,0.314,800,-10469.94267675256,4853.782788344746,-0.8382285160349765),  TestValue(10233,0.314,800,-77398.83453431107,32575.386135464123,-10.16161733713528),  TestValue(0,0.314,15324,-0.31399678298770084,-0.9999795096863716,-2.099280749234822e-10),  TestValue(6,0.314,15324,-13.842565956968983,18.10790921043538,-5.6049177743489054e-8),  TestValue(14,0.314,15324,-41.71664028188991,43.58509417059771,-3.687852014877535e-7),  TestValue(1525,0.314,15324,-11350.864477542971,4855.588403521258,-0.004641024152967077),  TestValue(10233,0.314,15324,-93272.76691554434,32587.50423265796,-0.15625826529496223),  TestValue(0,0.314,162345,-0.31399969611972445,-0.9999980658511647,-1.8687273950490635e-12),  TestValue(6,0.314,162345,-13.843343876770248,18.108245230667904,-4.995062141688322e-10),  TestValue(14,0.314,162345,-41.72175954081669,43.58590295936,-3.2876226185862834e-9),  TestValue(1525,0.314,162345,-11417.135986375062,4855.678506466079,-0.0000437984390462276),  TestValue(10233,0.314,162345,-95795.59283173154,32588.10894414742,-0.001906518631979992),  TestValue(0,1.5,0.0004,-0.003291911100032755,-0.00026659557451346307,-7.230044345656401),  TestValue(6,1.5,0.0004,-9.619783961619232,0.0007997867235403892,2491.0537701151675),  TestValue(14,1.5,0.0004,-10.468856159359483,0.002221629787612192,2486.6186161358087),  TestValue(1525,1.5,0.0004,-15.560537541616213,0.270772238514174,1484.280307752038),  TestValue(10233,1.5,0.0004,-19.785223133323598,1.8184484137563317,-4317.601447204935),  TestValue(0,1.5,0.065,-0.2067814991501101,-0.04153354632587859,-2.2227873794044952),  TestValue(6,1.5,0.065,-4.841004539887443,0.12460063897763578,11.520890928200775),  TestValue(14,1.5,0.065,-5.969601492726813,0.34611288604898827,7.298954082323366),  TestValue(1525,1.5,0.065,-74.45092758687497,42.184238551650694,-953.4745083343279),  TestValue(10233,1.5,0.065,-445.630392408013,283.3003194888179,-6515.787894589817),  TestValue(0,1.5,4.42,-1.2915096474038796,-0.7466216216216216,-0.03881837442792935),  TestValue(6,1.5,4.42,-4.694711300875651,2.239864864864865,-0.12612961153608993),  TestValue(14,1.5,4.42,-13.334103973863655,6.221846846846847,-0.8864094608348823),  TestValue(1525,1.5,4.42,-2072.1910365790172,758.3186936936937,-251.67662613527665),  TestValue(10233,1.5,4.42,-14020.648493631525,5092.706081081081,-1720.7211329093311),  TestValue(0,1.5,800,-1.4985955053447242,-0.9981285090455396,-1.7534272203079126e-6),  TestValue(6,1.5,800,-5.63758835785638,2.9943855271366187,-0.00001104786953298742),  TestValue(14,1.5,800,-20.926415102269573,8.317737575379496,-0.00010961017476240897),  TestValue(1525,1.5,800,-8088.548799680884,1013.7658556872531,-0.8354105724129193),  TestValue(10233,1.5,800,-61412.52664040723,6808.234560199626,-10.142698900729565),  TestValue(0,1.5,15324,-1.499926590534038,-0.9999021239111285,-4.790177143831897e-9),  TestValue(6,1.5,15324,-5.645995699555982,2.9997063717333856,-3.032959305926397e-8),  TestValue(14,1.5,15324,-21.010069937864472,8.332517699259403,-3.0266583905813604e-7),  TestValue(1525,1.5,15324,-8967.33164084002,1015.5672571857361,-0.004633327525485953),  TestValue(10233,1.5,15324,-77272.09898456372,6820.332387197807,-0.15620659350885369),  TestValue(0,1.5,162345,-1.4999930703617181,-0.9999907605029982,-4.268407849394862e-11),  TestValue(6,1.5,162345,-5.646416676253864,2.999972281508995,-2.703277601767695e-10),  TestValue(14,1.5,162345,-21.01427157395574,8.333256337524984,-2.698453016591884e-9),  TestValue(1525,1.5,162345,-9033.49633366488,1015.6572824175452,-0.000043729856523455624),  TestValue(10233,1.5,162345,-79794.20778485533,6820.936977390951,-0.0019060581989425174),  TestValue(0,3,0.0004,-0.003569116649587855,-0.0001333155579256099,-7.922924939527562),  TestValue(6,3,0.0004,-9.619261327135609,0.0001333155579256099,2492.360089770114),  TestValue(14,3,0.0004,-10.467267071498288,0.0004888237123939031,2490.5905361225123),  TestValue(1525,3,0.0004,-15.357522072066786,0.06763542638759276,1991.7174903993568),  TestValue(10233,3,0.0004,-18.421373162287637,0.4546060525263298,-908.6583034400528),  TestValue(0,3,0.065,-0.25047201260085383,-0.021207177814029365,-2.874622756288704),  TestValue(6,3,0.065,-4.758782442354863,0.021207177814029365,12.74533572164111),  TestValue(14,3,0.065,-5.719495913883133,0.07775965198477433,11.025105769529759),  TestValue(1525,3,0.065,-42.491829475397026,10.75910821098423,-477.2384670870571),  TestValue(10233,3,0.065,-230.9301248894044,72.31647634584013,-3316.4438994781904),  TestValue(0,3,4.42,-2.2897339760163957,-0.5956873315363881,-0.11372669262607049),  TestValue(6,3,4.42,-2.889108195828742,0.5956873315363881,0.003850246852058703),  TestValue(14,3,4.42,-7.790064290604171,2.18418688230009,-0.4832453669983474),  TestValue(1525,3,4.42,-1360.5497881858591,302.2120395327942,-199.67578957112616),  TestValue(10233,3,4.42,-9239.719029853994,2031.2938005390836,-1371.3592560596119),  TestValue(0,3,800,-2.994389023067612,-0.9962640099626401,-6.996241475043519e-6),  TestValue(6,3,800,-2.9857172436025223,0.9962640099626401,-2.3069406651643476e-6),  TestValue(14,3,800,-12.744324478713366,3.65296803652968,-0.00008222425506509978),  TestValue(1525,3,800,-7035.84649923785,505.4379410543794,-0.8318616138503963),  TestValue(10233,3,800,-54340.180404088605,3397.2602739726026,-10.118854869649681),  TestValue(0,3,15324,-2.999706381300726,-0.9998042669798395,-1.9158207464897714e-8),  TestValue(6,3,15324,-2.9874796347589054,0.9998042669798395,-6.3824572293924575e-9),  TestValue(14,3,15324,-12.807159398982407,3.665948978926078,-2.2763181739549054e-7),  TestValue(1525,3,15324,-7911.931224008331,507.2340314477719,-0.004623603455756964),  TestValue(10233,3,15324,-70181.6251826905,3409.332550401253,-0.15614126136305728),  TestValue(0,3,162345,-2.99997228162999,-0.9999815211767314,-1.7073631397579447e-10),  TestValue(6,3,162345,-2.987568240888365,0.9999815211767314,-5.6909144063865824e-11),  TestValue(14,3,162345,-12.810319609745221,3.6665989109813486,-2.029739931685981e-9),  TestValue(1525,3,162345,-7977.960952690064,507.32395841032843,-0.00004364319426564123),  TestValue(10233,3,162345,-72702.82721273272,3409.9369872126545,-0.0019054759497976193),  TestValue(0,180,0.0004,-0.0052068020335865025,-2.2222172839615914e-6,-12.01700730618354),  TestValue(6,180,0.0004,-9.62011239916672,-2.148143374496205e-6,2490.2324075130828),  TestValue(14,180,0.0004,-10.467069325725546,-2.04937816187569e-6,2491.084720678314),  TestValue(1525,180,0.0004,-15.159228863591125,0.000016604901371824113,2487.4167692289852),  TestValue(10233,180,0.0004,-17.08144177432405,0.00012411083530925487,2440.94300115826),  TestValue(0,180,0.065,-0.5152345838836883,-0.00036098075694887956,-6.927046886659846),  TestValue(6,180,0.065,-4.897099604874426,-0.0003489480650505836,10.617175935000475),  TestValue(14,180,0.065,-5.689219198051667,-0.0003329044758528556,11.4626317745298),  TestValue(1525,180,0.065,-10.618383986015033,0.0026973284338680167,7.7929628140754765),  TestValue(10233,180,0.065,-15.542242814932251,0.020160775275594924,-38.6634853761835),  TestValue(0,180,4.42,-16.491356225074536,-0.023967031775295522,-2.755043100796684),  TestValue(6,180,4.42,-11.802883319144515,-0.023168130716119003,-1.8613752566654882),  TestValue(14,180,4.42,-9.653376579596795,-0.022102929303883648,-1.313682997645138),  TestValue(1525,180,4.42,-30.756932642065294,0.1790869874320693,-5.0606677133089075),  TestValue(10233,180,4.42,-235.49737914944126,1.3385587246502548,-50.37753458197702),  TestValue(0,180,800,-162.35267519735217,-0.8163265306122449,-0.01926737460893513),  TestValue(6,180,800,-138.9731231908616,-0.7891156462585034,-0.017913154212997107),  TestValue(14,180,800,-117.57055678993851,-0.7528344671201814,-0.016193696733894036),  TestValue(1525,180,800,-1255.1060610431614,6.099773242630386,-0.5081161722061651),  TestValue(10233,180,800,-14640.50246307096,45.59183673469388,-7.836489965276398),  TestValue(0,180,15324,-178.95104102256036,-0.9883900928792569,-0.00006792118926490787),  TestValue(6,180,15324,-154.44163935947577,-0.9554437564499484,-0.00006343927721985665),  TestValue(14,180,15324,-131.5984192349756,-0.911515307877537,-0.000057701678183974536),  TestValue(1525,180,15324,-1861.5172673616398,7.38547041623667,-0.0035556000115217756),  TestValue(10233,180,15324,-28577.644697168085,55.2015866873065,-0.14858705144088802),  TestValue(0,180,162345,-179.90028620870413,-0.9988924780802954,-6.137556081142748e-7),  TestValue(6,180,162345,-155.32835273471773,-0.9655960621442855,-5.733925689810349e-7),  TestValue(14,180,162345,-132.40506485924828,-0.9212008408962724,-5.216997802648393e-7),  TestValue(1525,180,162345,-1912.647535667431,7.4639465723222065,-0.00003402677068820026),  TestValue(10233,180,162345,-30993.45007826088,55.788144900784495,-0.0018374445009108342),  TestValue(0,1123,0.0004,-0.005939122128713381,-3.5618865318302646e-7,-13.847805677972104),  TestValue(6,1123,0.0004,-9.620833523075628,-3.5428559715533445e-7,2488.429599570756),  TestValue(14,1123,0.0004,-10.467775521386166,-3.517481891184117e-7,2489.3192333086026),  TestValue(1525,1123,0.0004,-15.157115486355906,1.2750475385536657e-7,2492.70020501204),  TestValue(10233,1123,0.0004,-17.063078998820856,2.8894734020457448e-6,2486.849880233364),  TestValue(0,1123,0.065,-0.6342170147837343,-0.000057877326779839104,-8.75724272015346),  TestValue(6,1123,0.065,-5.014263034227778,-0.000057568097963562137,8.814958879676311),  TestValue(14,1123,0.065,-5.803957292009425,-0.000057155792875192846,9.697719756764902),  TestValue(1525,1123,0.065,-10.275036857130544,0.000020718330690556827,13.074039765317043),  TestValue(10233,1123,0.065,-12.558918107941281,0.0004695124193805291,7.224124958319663),  TestValue(0,1123,4.42,-24.493639593452325,-0.00392045555338738,-4.545467874886493),  TestValue(6,1123,4.42,-19.68318216630322,-0.003899509219175159,-3.624587483847729),  TestValue(14,1123,4.42,-17.37102939846337,-0.003871580773558864,-3.040611828950623),  TestValue(1525,1123,4.42,-7.7548168672583415,0.0014034043922188128,0.0654298516080507),  TestValue(10233,1123,4.42,-35.45506157865748,0.031803517445555686,-5.756960605210265),  TestValue(0,1123,800,-701.6240143366822,-0.4160166406656266,-0.29304665858647905),  TestValue(6,1123,800,-671.3041847506472,-0.4137939337698174,-0.28869011401594236),  TestValue(14,1123,800,-640.6479149103316,-0.4108303245754051,-0.2829675576373729),  TestValue(1525,1123,800,-30.39018204828426,0.14892136201921807,-0.018804728472968435),  TestValue(10233,1123,800,-3343.1303902972795,3.3748099701370067,-2.9898053694742615),  TestValue(0,1123,15324,-1083.757151397245,-0.9317200705295798,-0.002442933450309326),  TestValue(6,1123,15324,-1048.6172073187354,-0.9267420470004815,-0.002416262805940761),  TestValue(14,1123,15324,-1011.5999306403351,-0.920104682295017,-0.00238094023047708),  TestValue(1525,1123,15324,-64.3938471491183,0.33352757644959136,-0.00029097614079454104),  TestValue(10233,1123,15324,-11352.060718035325,7.558299058347705,-0.11311918072723515),  TestValue(0,1123,162345,-1119.133717664517,-0.9931301539139159,-0.000023706026173186956),  TestValue(6,1123,162345,-1083.611684066063,-0.9878240266445628,-0.00002345269725800847),  TestValue(14,1123,162345,-1046.088262691303,-0.9807491902854254,-0.000023117049972043446),  TestValue(1525,1123,162345,-68.73051882103027,0.35551052704665553,-2.9902146572169386e-6),  TestValue(10233,1123,162345,-13257.287747436989,8.056469903967741,-0.0014973234714386052),  TestValue(0,10586,0.0004,-0.006836533480423993,-3.778575334268833e-8,-16.091333738845734),  TestValue(6,10586,0.0004,-9.621729024009568,-3.776433689454398e-8,2486.19084755338),  TestValue(14,10586,0.0004,-10.468668475096411,-3.7735781630351504e-8,2487.0868493492235),  TestValue(1525,10586,0.0004,-15.157527333190956,-3.234240610599839e-8,2491.6705880068075),  TestValue(10233,10586,0.0004,-17.060718192660715,-1.2600010324928188e-9,2492.7518943576556),  TestValue(0,10586,0.065,-0.7800430171085975,-6.1401474485561915e-6,-11.00066794181818),  TestValue(6,10586,0.065,-5.159778603540011,-6.1366672969700086e-6,6.57630939764217),  TestValue(14,10586,0.065,-5.949058950638154,-6.132027094855097e-6,7.465437927571536),  TestValue(1525,10586,0.065,-10.34196113541293,-5.255608920401252e-6,12.044448366424728),  TestValue(10233,10586,0.065,-12.175300607224926,-2.047489183204549e-7,13.125723676609066),  TestValue(0,10586,4.42,-34.3945190758502,-0.0004173583295091224,-6.781982760105572),  TestValue(6,10586,4.42,-29.562997357281894,-0.00041712177651676886,-5.856347033468785),  TestValue(14,10586,4.42,-27.2227588675498,-0.0004168063725269641,-5.266030931107645),  TestValue(1525,10586,4.42,-12.301855613945008,-0.0003572344439525938,-0.9624372357797295),  TestValue(10233,10586,4.42,-9.430792045634007,-0.00001391720105013416,0.11674937200192481),  TestValue(0,10586,800,-2124.4224654744803,-0.07026172492534692,-1.7257898067684474),  TestValue(6,10586,800,-2091.312452085902,-0.07022190154073024,-1.7188401003298583),  TestValue(14,10586,800,-2056.9359371755286,-0.07016880369457469,-1.7096599947938858),  TestValue(1525,10586,800,-744.0169167062886,-0.060139948001942986,-0.7924525685250288),  TestValue(10233,10586,800,-7.2703661972227565,-0.0023429424616141564,0.00008904830662359586),  TestValue(0,10586,15324,-8048.29915678056,-0.5914318795831726,-0.11664064731878732),  TestValue(6,10586,15324,-8002.424955944863,-0.5910966640836922,-0.11648073932479441),  TestValue(14,10586,15324,-7951.095336923546,-0.590649710084385,-0.11626776694982688),  TestValue(1525,10586,15324,-4300.645593413912,-0.506231273465249,-0.08062419697917278),  TestValue(10233,10586,15324,-9.327824035135563,-0.019721845219427537,-0.00008059480749977865),  TestValue(0,10586,162345,-10255.166530843997,-0.9387848332571951,-0.0019538038497231014),  TestValue(6,10586,162345,-10206.520977570348,-0.93825274285482,-0.001951542008541196),  TestValue(14,10586,162345,-10151.499529961993,-0.9375432889849864,-0.0019485283448990032),  TestValue(1525,10586,162345,-5869.2020812217015,-0.8035451893201818,-0.0014225911704155436),  TestValue(10233,10586,162345,-11.157754570856923,-0.03130465200640373,-1.9036241010184085e-6),};
+std::array<TestValue, 210> testValues = {
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+    TestValue(14, 0.0000256, 0.0004, -49.814562438358635, 513979.32330827066,
+              -30391.559221530802),
+    TestValue(1525, 0.0000256, 0.0004, -4301.784727467015, 5.5987134868421055e7,
+              -3.580668787634408e6),
+    TestValue(10233, 0.0000256, 0.0004, -28781.07085289515,
+              3.7568285855263156e8, -2.4041193199521683e7),
+    TestValue(0, 0.0000256, 0.065, -0.000025594960092480967,
+              -0.9996063088998794, -7.751668684718993e-8),
+    TestValue(6, 0.0000256, 0.065, -51.41938813644809, 234281.72904210034,
+              -74.69380754597304),
+    TestValue(14, 0.0000256, 0.065, -114.92817109028836, 546658.7005733127,
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+    TestValue(1525, 0.0000256, 0.065, -11965.467128123484, 5.954685919853104e7,
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+    TestValue(10233, 0.0000256, 0.065, -80237.4790550341, 3.995691927102557e8,
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+    TestValue(0, 0.0000256, 4.42, -0.000025599925864390194, -0.9999942081783417,
+              -1.677258332222209e-11),
+    TestValue(6, 0.0000256, 4.42, -67.52038137511191, 234372.6425475907,
+              -0.4312559247584902),
+    TestValue(14, 0.0000256, 4.42, -161.64931287705224, 546870.8326033225,
+              -1.650128690902025),
+    TestValue(1525, 0.0000256, 4.42, -18367.34289180058, 5.956996647937967e7,
+              -339.0570825343945),
+    TestValue(10233, 0.0000256, 4.42, -123371.16336416776, 3.997242463550437e8,
+              -2307.279979293951),
+    TestValue(0, 0.0000256, 800, -0.00002559999998652529, -0.999999968000001,
+              -8.881784197001252e-16),
+    TestValue(6, 0.0000256, 800, -69.9980790657431, 234373.99250003224,
+              -0.000023330384471442756),
+    TestValue(14, 0.0000256, 800, -173.09898662779824, 546873.9825000325,
+              -0.00014060727924558591),
+    TestValue(1525, 0.0000256, 800, -24826.22813563853, 5.957030959375009e7,
+              -0.8389762876176414),
+    TestValue(10233, 0.0000256, 800, -173733.65594636812, 3.997265487087504e8,
+              -10.166635446653597),
+    TestValue(0, 0.0000256, 15324, -0.000025599996959613236,
+              -0.9999999983294179, 0.),
+    TestValue(6, 0.0000256, 15324, -70.01580732128963, 234373.99960845898,
+              -6.386142814562845e-8),
+    TestValue(14, 0.0000256, 15324, -173.20616504262574, 546873.9990864021,
+              -3.872936886750722e-7),
+    TestValue(1525, 0.0000256, 15324, -25707.717028801628, 5.957031140048291e7,
+              -0.004643062913324059),
+    TestValue(10233, 0.0000256, 15324, -189611.39394380094,
+              3.9972656083222395e8, -0.15627194690990365),
+    TestValue(0, 0.0000256, 162345, -0.00002560001632012643,
+              -0.9999999998423111, 0.),
+    TestValue(6, 0.0000256, 162345, -70.01669365713798, 234373.99996304183,
+              -5.691145332775704e-10),
+    TestValue(14, 0.0000256, 162345, -173.21154115647926, 546873.9999137641,
+              -3.452532482128845e-9),
+    TestValue(1525, 0.0000256, 162345, -25774.016830882043, 5.957031149060642e7,
+              -0.00004381660427021927),
+    TestValue(10233, 0.0000256, 162345, -192134.409728957, 3.9972656143696755e8,
+              -0.001906640534274473),
+    TestValue(0, 0.314, 0.0004, -0.002666782716971683, -0.001272264631043257,
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+    TestValue(6, 0.314, 0.0004, -9.625197494412376, 0.023038524497171847,
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+    TestValue(14, 0.314, 0.0004, -10.482321240387563, 0.05545291000145865,
+              2452.982014445862),
+    TestValue(1525, 0.314, 0.0004, -17.094738795518424, 6.1777199721236284,
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+    TestValue(10233, 0.314, 0.0004, -30.083534640958533, 41.460778593539814,
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+    TestValue(0, 0.314, 0.065, -0.11460468078714132, -0.17150395778364116,
+              -0.9346528929704305),
+    TestValue(6, 0.314, 0.065, -5.6231627412658, 3.1056417323496293,
+              0.8117566646875254),
+    TestValue(14, 0.314, 0.065, -7.917539720426937, 7.4751693191939905,
+              -19.40653851445296),
+    TestValue(1525, 0.314, 0.065, -296.58556828610017, 832.7696922844226,
+              -4001.4921811261693),
+    TestValue(10233, 0.314, 0.065, -1936.716591758479, 5589.00047056451,
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+    TestValue(6, 0.314, 4.42, -11.748118636048988, 16.90718181793719,
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+    TestValue(14, 0.314, 4.42, -31.109603016060397, 40.69498599371937,
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+    TestValue(1525, 0.314, 4.42, -4115.10160678526, 4533.61649969458,
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+    TestValue(10233, 0.314, 4.42, -27734.55588693275, 30426.641345033488,
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+              -7.698783210940974e-8),
+    TestValue(6, 0.314, 800, -13.827010724886122, 18.101175543376296,
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+    TestValue(14, 0.314, 800, -41.61461010763844, 43.568886473205765,
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+    TestValue(10233, 0.314, 800, -77398.83453431107, 32575.386135464123,
+              -10.16161733713528),
+    TestValue(0, 0.314, 15324, -0.31399678298770084, -0.9999795096863716,
+              -2.099280749234822e-10),
+    TestValue(6, 0.314, 15324, -13.842565956968983, 18.10790921043538,
+              -5.6049177743489054e-8),
+    TestValue(14, 0.314, 15324, -41.71664028188991, 43.58509417059771,
+              -3.687852014877535e-7),
+    TestValue(1525, 0.314, 15324, -11350.864477542971, 4855.588403521258,
+              -0.004641024152967077),
+    TestValue(10233, 0.314, 15324, -93272.76691554434, 32587.50423265796,
+              -0.15625826529496223),
+    TestValue(0, 0.314, 162345, -0.31399969611972445, -0.9999980658511647,
+              -1.8687273950490635e-12),
+    TestValue(6, 0.314, 162345, -13.843343876770248, 18.108245230667904,
+              -4.995062141688322e-10),
+    TestValue(14, 0.314, 162345, -41.72175954081669, 43.58590295936,
+              -3.2876226185862834e-9),
+    TestValue(1525, 0.314, 162345, -11417.135986375062, 4855.678506466079,
+              -0.0000437984390462276),
+    TestValue(10233, 0.314, 162345, -95795.59283173154, 32588.10894414742,
+              -0.001906518631979992),
+    TestValue(0, 1.5, 0.0004, -0.003291911100032755, -0.00026659557451346307,
+              -7.230044345656401),
+    TestValue(6, 1.5, 0.0004, -9.619783961619232, 0.0007997867235403892,
+              2491.0537701151675),
+    TestValue(14, 1.5, 0.0004, -10.468856159359483, 0.002221629787612192,
+              2486.6186161358087),
+    TestValue(1525, 1.5, 0.0004, -15.560537541616213, 0.270772238514174,
+              1484.280307752038),
+    TestValue(10233, 1.5, 0.0004, -19.785223133323598, 1.8184484137563317,
+              -4317.601447204935),
+    TestValue(0, 1.5, 0.065, -0.2067814991501101, -0.04153354632587859,
+              -2.2227873794044952),
+    TestValue(6, 1.5, 0.065, -4.841004539887443, 0.12460063897763578,
+              11.520890928200775),
+    TestValue(14, 1.5, 0.065, -5.969601492726813, 0.34611288604898827,
+              7.298954082323366),
+    TestValue(1525, 1.5, 0.065, -74.45092758687497, 42.184238551650694,
+              -953.4745083343279),
+    TestValue(10233, 1.5, 0.065, -445.630392408013, 283.3003194888179,
+              -6515.787894589817),
+    TestValue(0, 1.5, 4.42, -1.2915096474038796, -0.7466216216216216,
+              -0.03881837442792935),
+    TestValue(6, 1.5, 4.42, -4.694711300875651, 2.239864864864865,
+              -0.12612961153608993),
+    TestValue(14, 1.5, 4.42, -13.334103973863655, 6.221846846846847,
+              -0.8864094608348823),
+    TestValue(1525, 1.5, 4.42, -2072.1910365790172, 758.3186936936937,
+              -251.67662613527665),
+    TestValue(10233, 1.5, 4.42, -14020.648493631525, 5092.706081081081,
+              -1720.7211329093311),
+    TestValue(0, 1.5, 800, -1.4985955053447242, -0.9981285090455396,
+              -1.7534272203079126e-6),
+    TestValue(6, 1.5, 800, -5.63758835785638, 2.9943855271366187,
+              -0.00001104786953298742),
+    TestValue(14, 1.5, 800, -20.926415102269573, 8.317737575379496,
+              -0.00010961017476240897),
+    TestValue(1525, 1.5, 800, -8088.548799680884, 1013.7658556872531,
+              -0.8354105724129193),
+    TestValue(10233, 1.5, 800, -61412.52664040723, 6808.234560199626,
+              -10.142698900729565),
+    TestValue(0, 1.5, 15324, -1.499926590534038, -0.9999021239111285,
+              -4.790177143831897e-9),
+    TestValue(6, 1.5, 15324, -5.645995699555982, 2.9997063717333856,
+              -3.032959305926397e-8),
+    TestValue(14, 1.5, 15324, -21.010069937864472, 8.332517699259403,
+              -3.0266583905813604e-7),
+    TestValue(1525, 1.5, 15324, -8967.33164084002, 1015.5672571857361,
+              -0.004633327525485953),
+    TestValue(10233, 1.5, 15324, -77272.09898456372, 6820.332387197807,
+              -0.15620659350885369),
+    TestValue(0, 1.5, 162345, -1.4999930703617181, -0.9999907605029982,
+              -4.268407849394862e-11),
+    TestValue(6, 1.5, 162345, -5.646416676253864, 2.999972281508995,
+              -2.703277601767695e-10),
+    TestValue(14, 1.5, 162345, -21.01427157395574, 8.333256337524984,
+              -2.698453016591884e-9),
+    TestValue(1525, 1.5, 162345, -9033.49633366488, 1015.6572824175452,
+              -0.000043729856523455624),
+    TestValue(10233, 1.5, 162345, -79794.20778485533, 6820.936977390951,
+              -0.0019060581989425174),
+    TestValue(0, 3, 0.0004, -0.003569116649587855, -0.0001333155579256099,
+              -7.922924939527562),
+    TestValue(6, 3, 0.0004, -9.619261327135609, 0.0001333155579256099,
+              2492.360089770114),
+    TestValue(14, 3, 0.0004, -10.467267071498288, 0.0004888237123939031,
+              2490.5905361225123),
+    TestValue(1525, 3, 0.0004, -15.357522072066786, 0.06763542638759276,
+              1991.7174903993568),
+    TestValue(10233, 3, 0.0004, -18.421373162287637, 0.4546060525263298,
+              -908.6583034400528),
+    TestValue(0, 3, 0.065, -0.25047201260085383, -0.021207177814029365,
+              -2.874622756288704),
+    TestValue(6, 3, 0.065, -4.758782442354863, 0.021207177814029365,
+              12.74533572164111),
+    TestValue(14, 3, 0.065, -5.719495913883133, 0.07775965198477433,
+              11.025105769529759),
+    TestValue(1525, 3, 0.065, -42.491829475397026, 10.75910821098423,
+              -477.2384670870571),
+    TestValue(10233, 3, 0.065, -230.9301248894044, 72.31647634584013,
+              -3316.4438994781904),
+    TestValue(0, 3, 4.42, -2.2897339760163957, -0.5956873315363881,
+              -0.11372669262607049),
+    TestValue(6, 3, 4.42, -2.889108195828742, 0.5956873315363881,
+              0.003850246852058703),
+    TestValue(14, 3, 4.42, -7.790064290604171, 2.18418688230009,
+              -0.4832453669983474),
+    TestValue(1525, 3, 4.42, -1360.5497881858591, 302.2120395327942,
+              -199.67578957112616),
+    TestValue(10233, 3, 4.42, -9239.719029853994, 2031.2938005390836,
+              -1371.3592560596119),
+    TestValue(0, 3, 800, -2.994389023067612, -0.9962640099626401,
+              -6.996241475043519e-6),
+    TestValue(6, 3, 800, -2.9857172436025223, 0.9962640099626401,
+              -2.3069406651643476e-6),
+    TestValue(14, 3, 800, -12.744324478713366, 3.65296803652968,
+              -0.00008222425506509978),
+    TestValue(1525, 3, 800, -7035.84649923785, 505.4379410543794,
+              -0.8318616138503963),
+    TestValue(10233, 3, 800, -54340.180404088605, 3397.2602739726026,
+              -10.118854869649681),
+    TestValue(0, 3, 15324, -2.999706381300726, -0.9998042669798395,
+              -1.9158207464897714e-8),
+    TestValue(6, 3, 15324, -2.9874796347589054, 0.9998042669798395,
+              -6.3824572293924575e-9),
+    TestValue(14, 3, 15324, -12.807159398982407, 3.665948978926078,
+              -2.2763181739549054e-7),
+    TestValue(1525, 3, 15324, -7911.931224008331, 507.2340314477719,
+              -0.004623603455756964),
+    TestValue(10233, 3, 15324, -70181.6251826905, 3409.332550401253,
+              -0.15614126136305728),
+    TestValue(0, 3, 162345, -2.99997228162999, -0.9999815211767314,
+              -1.7073631397579447e-10),
+    TestValue(6, 3, 162345, -2.987568240888365, 0.9999815211767314,
+              -5.6909144063865824e-11),
+    TestValue(14, 3, 162345, -12.810319609745221, 3.6665989109813486,
+              -2.029739931685981e-9),
+    TestValue(1525, 3, 162345, -7977.960952690064, 507.32395841032843,
+              -0.00004364319426564123),
+    TestValue(10233, 3, 162345, -72702.82721273272, 3409.9369872126545,
+              -0.0019054759497976193),
+    TestValue(0, 180, 0.0004, -0.0052068020335865025, -2.2222172839615914e-6,
+              -12.01700730618354),
+    TestValue(6, 180, 0.0004, -9.62011239916672, -2.148143374496205e-6,
+              2490.2324075130828),
+    TestValue(14, 180, 0.0004, -10.467069325725546, -2.04937816187569e-6,
+              2491.084720678314),
+    TestValue(1525, 180, 0.0004, -15.159228863591125, 0.000016604901371824113,
+              2487.4167692289852),
+    TestValue(10233, 180, 0.0004, -17.08144177432405, 0.00012411083530925487,
+              2440.94300115826),
+    TestValue(0, 180, 0.065, -0.5152345838836883, -0.00036098075694887956,
+              -6.927046886659846),
+    TestValue(6, 180, 0.065, -4.897099604874426, -0.0003489480650505836,
+              10.617175935000475),
+    TestValue(14, 180, 0.065, -5.689219198051667, -0.0003329044758528556,
+              11.4626317745298),
+    TestValue(1525, 180, 0.065, -10.618383986015033, 0.0026973284338680167,
+              7.7929628140754765),
+    TestValue(10233, 180, 0.065, -15.542242814932251, 0.020160775275594924,
+              -38.6634853761835),
+    TestValue(0, 180, 4.42, -16.491356225074536, -0.023967031775295522,
+              -2.755043100796684),
+    TestValue(6, 180, 4.42, -11.802883319144515, -0.023168130716119003,
+              -1.8613752566654882),
+    TestValue(14, 180, 4.42, -9.653376579596795, -0.022102929303883648,
+              -1.313682997645138),
+    TestValue(1525, 180, 4.42, -30.756932642065294, 0.1790869874320693,
+              -5.0606677133089075),
+    TestValue(10233, 180, 4.42, -235.49737914944126, 1.3385587246502548,
+              -50.37753458197702),
+    TestValue(0, 180, 800, -162.35267519735217, -0.8163265306122449,
+              -0.01926737460893513),
+    TestValue(6, 180, 800, -138.9731231908616, -0.7891156462585034,
+              -0.017913154212997107),
+    TestValue(14, 180, 800, -117.57055678993851, -0.7528344671201814,
+              -0.016193696733894036),
+    TestValue(1525, 180, 800, -1255.1060610431614, 6.099773242630386,
+              -0.5081161722061651),
+    TestValue(10233, 180, 800, -14640.50246307096, 45.59183673469388,
+              -7.836489965276398),
+    TestValue(0, 180, 15324, -178.95104102256036, -0.9883900928792569,
+              -0.00006792118926490787),
+    TestValue(6, 180, 15324, -154.44163935947577, -0.9554437564499484,
+              -0.00006343927721985665),
+    TestValue(14, 180, 15324, -131.5984192349756, -0.911515307877537,
+              -0.000057701678183974536),
+    TestValue(1525, 180, 15324, -1861.5172673616398, 7.38547041623667,
+              -0.0035556000115217756),
+    TestValue(10233, 180, 15324, -28577.644697168085, 55.2015866873065,
+              -0.14858705144088802),
+    TestValue(0, 180, 162345, -179.90028620870413, -0.9988924780802954,
+              -6.137556081142748e-7),
+    TestValue(6, 180, 162345, -155.32835273471773, -0.9655960621442855,
+              -5.733925689810349e-7),
+    TestValue(14, 180, 162345, -132.40506485924828, -0.9212008408962724,
+              -5.216997802648393e-7),
+    TestValue(1525, 180, 162345, -1912.647535667431, 7.4639465723222065,
+              -0.00003402677068820026),
+    TestValue(10233, 180, 162345, -30993.45007826088, 55.788144900784495,
+              -0.0018374445009108342),
+    TestValue(0, 1123, 0.0004, -0.005939122128713381, -3.5618865318302646e-7,
+              -13.847805677972104),
+    TestValue(6, 1123, 0.0004, -9.620833523075628, -3.5428559715533445e-7,
+              2488.429599570756),
+    TestValue(14, 1123, 0.0004, -10.467775521386166, -3.517481891184117e-7,
+              2489.3192333086026),
+    TestValue(1525, 1123, 0.0004, -15.157115486355906, 1.2750475385536657e-7,
+              2492.70020501204),
+    TestValue(10233, 1123, 0.0004, -17.063078998820856, 2.8894734020457448e-6,
+              2486.849880233364),
+    TestValue(0, 1123, 0.065, -0.6342170147837343, -0.000057877326779839104,
+              -8.75724272015346),
+    TestValue(6, 1123, 0.065, -5.014263034227778, -0.000057568097963562137,
+              8.814958879676311),
+    TestValue(14, 1123, 0.065, -5.803957292009425, -0.000057155792875192846,
+              9.697719756764902),
+    TestValue(1525, 1123, 0.065, -10.275036857130544, 0.000020718330690556827,
+              13.074039765317043),
+    TestValue(10233, 1123, 0.065, -12.558918107941281, 0.0004695124193805291,
+              7.224124958319663),
+    TestValue(0, 1123, 4.42, -24.493639593452325, -0.00392045555338738,
+              -4.545467874886493),
+    TestValue(6, 1123, 4.42, -19.68318216630322, -0.003899509219175159,
+              -3.624587483847729),
+    TestValue(14, 1123, 4.42, -17.37102939846337, -0.003871580773558864,
+              -3.040611828950623),
+    TestValue(1525, 1123, 4.42, -7.7548168672583415, 0.0014034043922188128,
+              0.0654298516080507),
+    TestValue(10233, 1123, 4.42, -35.45506157865748, 0.031803517445555686,
+              -5.756960605210265),
+    TestValue(0, 1123, 800, -701.6240143366822, -0.4160166406656266,
+              -0.29304665858647905),
+    TestValue(6, 1123, 800, -671.3041847506472, -0.4137939337698174,
+              -0.28869011401594236),
+    TestValue(14, 1123, 800, -640.6479149103316, -0.4108303245754051,
+              -0.2829675576373729),
+    TestValue(1525, 1123, 800, -30.39018204828426, 0.14892136201921807,
+              -0.018804728472968435),
+    TestValue(10233, 1123, 800, -3343.1303902972795, 3.3748099701370067,
+              -2.9898053694742615),
+    TestValue(0, 1123, 15324, -1083.757151397245, -0.9317200705295798,
+              -0.002442933450309326),
+    TestValue(6, 1123, 15324, -1048.6172073187354, -0.9267420470004815,
+              -0.002416262805940761),
+    TestValue(14, 1123, 15324, -1011.5999306403351, -0.920104682295017,
+              -0.00238094023047708),
+    TestValue(1525, 1123, 15324, -64.3938471491183, 0.33352757644959136,
+              -0.00029097614079454104),
+    TestValue(10233, 1123, 15324, -11352.060718035325, 7.558299058347705,
+              -0.11311918072723515),
+    TestValue(0, 1123, 162345, -1119.133717664517, -0.9931301539139159,
+              -0.000023706026173186956),
+    TestValue(6, 1123, 162345, -1083.611684066063, -0.9878240266445628,
+              -0.00002345269725800847),
+    TestValue(14, 1123, 162345, -1046.088262691303, -0.9807491902854254,
+              -0.000023117049972043446),
+    TestValue(1525, 1123, 162345, -68.73051882103027, 0.35551052704665553,
+              -2.9902146572169386e-6),
+    TestValue(10233, 1123, 162345, -13257.287747436989, 8.056469903967741,
+              -0.0014973234714386052),
+    TestValue(0, 10586, 0.0004, -0.006836533480423993, -3.778575334268833e-8,
+              -16.091333738845734),
+    TestValue(6, 10586, 0.0004, -9.621729024009568, -3.776433689454398e-8,
+              2486.19084755338),
+    TestValue(14, 10586, 0.0004, -10.468668475096411, -3.7735781630351504e-8,
+              2487.0868493492235),
+    TestValue(1525, 10586, 0.0004, -15.157527333190956, -3.234240610599839e-8,
+              2491.6705880068075),
+    TestValue(10233, 10586, 0.0004, -17.060718192660715, -1.2600010324928188e-9,
+              2492.7518943576556),
+    TestValue(0, 10586, 0.065, -0.7800430171085975, -6.1401474485561915e-6,
+              -11.00066794181818),
+    TestValue(6, 10586, 0.065, -5.159778603540011, -6.1366672969700086e-6,
+              6.57630939764217),
+    TestValue(14, 10586, 0.065, -5.949058950638154, -6.132027094855097e-6,
+              7.465437927571536),
+    TestValue(1525, 10586, 0.065, -10.34196113541293, -5.255608920401252e-6,
+              12.044448366424728),
+    TestValue(10233, 10586, 0.065, -12.175300607224926, -2.047489183204549e-7,
+              13.125723676609066),
+    TestValue(0, 10586, 4.42, -34.3945190758502, -0.0004173583295091224,
+              -6.781982760105572),
+    TestValue(6, 10586, 4.42, -29.562997357281894, -0.00041712177651676886,
+              -5.856347033468785),
+    TestValue(14, 10586, 4.42, -27.2227588675498, -0.0004168063725269641,
+              -5.266030931107645),
+    TestValue(1525, 10586, 4.42, -12.301855613945008, -0.0003572344439525938,
+              -0.9624372357797295),
+    TestValue(10233, 10586, 4.42, -9.430792045634007, -0.00001391720105013416,
+              0.11674937200192481),
+    TestValue(0, 10586, 800, -2124.4224654744803, -0.07026172492534692,
+              -1.7257898067684474),
+    TestValue(6, 10586, 800, -2091.312452085902, -0.07022190154073024,
+              -1.7188401003298583),
+    TestValue(14, 10586, 800, -2056.9359371755286, -0.07016880369457469,
+              -1.7096599947938858),
+    TestValue(1525, 10586, 800, -744.0169167062886, -0.060139948001942986,
+              -0.7924525685250288),
+    TestValue(10233, 10586, 800, -7.2703661972227565, -0.0023429424616141564,
+              0.00008904830662359586),
+    TestValue(0, 10586, 15324, -8048.29915678056, -0.5914318795831726,
+              -0.11664064731878732),
+    TestValue(6, 10586, 15324, -8002.424955944863, -0.5910966640836922,
+              -0.11648073932479441),
+    TestValue(14, 10586, 15324, -7951.095336923546, -0.590649710084385,
+              -0.11626776694982688),
+    TestValue(1525, 10586, 15324, -4300.645593413912, -0.506231273465249,
+              -0.08062419697917278),
+    TestValue(10233, 10586, 15324, -9.327824035135563, -0.019721845219427537,
+              -0.00008059480749977865),
+    TestValue(0, 10586, 162345, -10255.166530843997, -0.9387848332571951,
+              -0.0019538038497231014),
+    TestValue(6, 10586, 162345, -10206.520977570348, -0.93825274285482,
+              -0.001951542008541196),
+    TestValue(14, 10586, 162345, -10151.499529961993, -0.9375432889849864,
+              -0.0019485283448990032),
+    TestValue(1525, 10586, 162345, -5869.2020812217015, -0.8035451893201818,
+              -0.0014225911704155436),
+    TestValue(10233, 10586, 162345, -11.157754570856923, -0.03130465200640373,
+              -1.9036241010184085e-6),
+};
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::is_nan;
@@ -115,8 +536,8 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
         std::vector<double> gradients;
         val.grad(x, gradients);
 
-        EXPECT_TRUE(value_of(val) < 0)  << "for n = " << n << ", mu = " <<
-          mu_dbl << ", phi = " << phi_dbl; 
+        EXPECT_TRUE(value_of(val) < 0)
+            << "for n = " << n << ", mu = " << mu_dbl << ", phi = " << phi_dbl;
 
         for (int i = 0; i < 2; ++i) {
           EXPECT_FALSE(is_nan(gradients[i]));
@@ -135,13 +556,13 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
         EXPECT_NEAR(gradients[0], finite_diffs[0],
                     std::max(1.0, gradients[0] * 1e-4))
             << "grad_mu, n = " << n << ", mu = " << mu_dbl
-            << "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon, dmu = " << 
-            dmu;
+            << "  +/- epsilon, phi = " << phi_dbl
+            << " +/- epsilon, dmu = " << dmu;
         EXPECT_NEAR(gradients[1], finite_diffs[1],
                     std::max(1.0, gradients[1] * 1e-4))
             << "grad_phi, n = " << n << ", mu = " << mu_dbl
-            << "  +/- epsilon, phi = " << phi_dbl << " +/- epsilon, dphi = " << 
-            dphi;
+            << "  +/- epsilon, phi = " << phi_dbl
+            << " +/- epsilon, dphi = " << dphi;
 
         phi_dbl *= 10;
       }

From 50653afd67092d03ba53e490f6889e3bb515a0c9 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 09:14:10 +0100
Subject: [PATCH 11/82] Updated precomputed test values

---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 633 ++++++------------
 1 file changed, 211 insertions(+), 422 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index fd01952f017..cdfbf394855 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -51,428 +51,217 @@ struct TestValue {
 //  WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::array<TestValue, 210> testValues = {
-    TestValue(0, 0.0000256, 0.0004, -0.000024814156367780882,
-              -0.9398496240601504, -0.0018850149796021398),
-    TestValue(6, 0.0000256, 0.0004, -26.480362597222488, 220276.31578947368,
-              -11595.463497838708),
-    TestValue(14, 0.0000256, 0.0004, -49.814562438358635, 513979.32330827066,
-              -30391.559221530802),
-    TestValue(1525, 0.0000256, 0.0004, -4301.784727467015, 5.5987134868421055e7,
-              -3.580668787634408e6),
-    TestValue(10233, 0.0000256, 0.0004, -28781.07085289515,
-              3.7568285855263156e8, -2.4041193199521683e7),
-    TestValue(0, 0.0000256, 0.065, -0.000025594960092480967,
-              -0.9996063088998794, -7.751668684718993e-8),
-    TestValue(6, 0.0000256, 0.065, -51.41938813644809, 234281.72904210034,
-              -74.69380754597304),
-    TestValue(14, 0.0000256, 0.065, -114.92817109028836, 546658.7005733127,
-              -196.83239209326592),
-    TestValue(1525, 0.0000256, 0.065, -11965.467128123484, 5.954685919853104e7,
-              -23429.11268911477),
-    TestValue(10233, 0.0000256, 0.065, -80237.4790550341, 3.995691927102557e8,
-              -157343.697098361),
-    TestValue(0, 0.0000256, 4.42, -0.000025599925864390194, -0.9999942081783417,
-              -1.677258332222209e-11),
-    TestValue(6, 0.0000256, 4.42, -67.52038137511191, 234372.6425475907,
-              -0.4312559247584902),
-    TestValue(14, 0.0000256, 4.42, -161.64931287705224, 546870.8326033225,
-              -1.650128690902025),
-    TestValue(1525, 0.0000256, 4.42, -18367.34289180058, 5.956996647937967e7,
-              -339.0570825343945),
-    TestValue(10233, 0.0000256, 4.42, -123371.16336416776, 3.997242463550437e8,
-              -2307.279979293951),
-    TestValue(0, 0.0000256, 800, -0.00002559999998652529, -0.999999968000001,
-              -8.881784197001252e-16),
-    TestValue(6, 0.0000256, 800, -69.9980790657431, 234373.99250003224,
-              -0.000023330384471442756),
-    TestValue(14, 0.0000256, 800, -173.09898662779824, 546873.9825000325,
-              -0.00014060727924558591),
-    TestValue(1525, 0.0000256, 800, -24826.22813563853, 5.957030959375009e7,
-              -0.8389762876176414),
-    TestValue(10233, 0.0000256, 800, -173733.65594636812, 3.997265487087504e8,
-              -10.166635446653597),
-    TestValue(0, 0.0000256, 15324, -0.000025599996959613236,
-              -0.9999999983294179, 0.),
-    TestValue(6, 0.0000256, 15324, -70.01580732128963, 234373.99960845898,
-              -6.386142814562845e-8),
-    TestValue(14, 0.0000256, 15324, -173.20616504262574, 546873.9990864021,
-              -3.872936886750722e-7),
-    TestValue(1525, 0.0000256, 15324, -25707.717028801628, 5.957031140048291e7,
-              -0.004643062913324059),
-    TestValue(10233, 0.0000256, 15324, -189611.39394380094,
-              3.9972656083222395e8, -0.15627194690990365),
-    TestValue(0, 0.0000256, 162345, -0.00002560001632012643,
-              -0.9999999998423111, 0.),
-    TestValue(6, 0.0000256, 162345, -70.01669365713798, 234373.99996304183,
-              -5.691145332775704e-10),
-    TestValue(14, 0.0000256, 162345, -173.21154115647926, 546873.9999137641,
-              -3.452532482128845e-9),
-    TestValue(1525, 0.0000256, 162345, -25774.016830882043, 5.957031149060642e7,
-              -0.00004381660427021927),
-    TestValue(10233, 0.0000256, 162345, -192134.409728957, 3.9972656143696755e8,
-              -0.001906640534274473),
-    TestValue(0, 0.314, 0.0004, -0.002666782716971683, -0.001272264631043257,
-              -5.66822905706025),
-    TestValue(6, 0.314, 0.0004, -9.625197494412376, 0.023038524497171847,
-              2477.530549555817),
-    TestValue(14, 0.314, 0.0004, -10.482321240387563, 0.05545291000145865,
-              2452.982014445862),
-    TestValue(1525, 0.314, 0.0004, -17.094738795518424, 6.1777199721236284,
-              -2348.2711549792057),
-    TestValue(10233, 0.314, 0.0004, -30.083534640958533, 41.460778593539814,
-              -30043.568270589793),
-    TestValue(0, 0.314, 0.065, -0.11460468078714132, -0.17150395778364116,
-              -0.9346528929704305),
-    TestValue(6, 0.314, 0.065, -5.6231627412658, 3.1056417323496293,
-              0.8117566646875254),
-    TestValue(14, 0.314, 0.065, -7.917539720426937, 7.4751693191939905,
-              -19.40653851445296),
-    TestValue(1525, 0.314, 0.065, -296.58556828610017, 832.7696922844226,
-              -4001.4921811261693),
-    TestValue(10233, 0.314, 0.065, -1936.716591758479, 5589.00047056451,
-              -26975.841613138524),
-    TestValue(0, 0.314, 4.42, -0.30334820230965986, -0.9336713138994508,
-              -0.00230212890163628),
-    TestValue(6, 0.314, 4.42, -11.748118636048988, 16.90718181793719,
-              -0.3435269754367143),
-    TestValue(14, 0.314, 4.42, -31.109603016060397, 40.69498599371937,
-              -1.4423583039713965),
-    TestValue(1525, 0.314, 4.42, -4115.10160678526, 4533.61649969458,
-              -316.1764856190919),
-    TestValue(10233, 0.314, 4.42, -27734.55588693275, 30426.641345033488,
-              -2153.7342775414127),
-    TestValue(0, 0.314, 800, -0.31393839362010567, -0.9996076539958066,
-              -7.698783210940974e-8),
-    TestValue(6, 0.314, 800, -13.827010724886122, 18.101175543376296,
-              -0.000020465017271042996),
-    TestValue(14, 0.314, 800, -41.61461010763844, 43.568886473205765,
-              -0.00013381877200302483),
-    TestValue(1525, 0.314, 800, -10469.94267675256, 4853.782788344746,
-              -0.8382285160349765),
-    TestValue(10233, 0.314, 800, -77398.83453431107, 32575.386135464123,
-              -10.16161733713528),
-    TestValue(0, 0.314, 15324, -0.31399678298770084, -0.9999795096863716,
-              -2.099280749234822e-10),
-    TestValue(6, 0.314, 15324, -13.842565956968983, 18.10790921043538,
-              -5.6049177743489054e-8),
-    TestValue(14, 0.314, 15324, -41.71664028188991, 43.58509417059771,
-              -3.687852014877535e-7),
-    TestValue(1525, 0.314, 15324, -11350.864477542971, 4855.588403521258,
-              -0.004641024152967077),
-    TestValue(10233, 0.314, 15324, -93272.76691554434, 32587.50423265796,
-              -0.15625826529496223),
-    TestValue(0, 0.314, 162345, -0.31399969611972445, -0.9999980658511647,
-              -1.8687273950490635e-12),
-    TestValue(6, 0.314, 162345, -13.843343876770248, 18.108245230667904,
-              -4.995062141688322e-10),
-    TestValue(14, 0.314, 162345, -41.72175954081669, 43.58590295936,
-              -3.2876226185862834e-9),
-    TestValue(1525, 0.314, 162345, -11417.135986375062, 4855.678506466079,
-              -0.0000437984390462276),
-    TestValue(10233, 0.314, 162345, -95795.59283173154, 32588.10894414742,
-              -0.001906518631979992),
-    TestValue(0, 1.5, 0.0004, -0.003291911100032755, -0.00026659557451346307,
-              -7.230044345656401),
-    TestValue(6, 1.5, 0.0004, -9.619783961619232, 0.0007997867235403892,
-              2491.0537701151675),
-    TestValue(14, 1.5, 0.0004, -10.468856159359483, 0.002221629787612192,
-              2486.6186161358087),
-    TestValue(1525, 1.5, 0.0004, -15.560537541616213, 0.270772238514174,
-              1484.280307752038),
-    TestValue(10233, 1.5, 0.0004, -19.785223133323598, 1.8184484137563317,
-              -4317.601447204935),
-    TestValue(0, 1.5, 0.065, -0.2067814991501101, -0.04153354632587859,
-              -2.2227873794044952),
-    TestValue(6, 1.5, 0.065, -4.841004539887443, 0.12460063897763578,
-              11.520890928200775),
-    TestValue(14, 1.5, 0.065, -5.969601492726813, 0.34611288604898827,
-              7.298954082323366),
-    TestValue(1525, 1.5, 0.065, -74.45092758687497, 42.184238551650694,
-              -953.4745083343279),
-    TestValue(10233, 1.5, 0.065, -445.630392408013, 283.3003194888179,
-              -6515.787894589817),
-    TestValue(0, 1.5, 4.42, -1.2915096474038796, -0.7466216216216216,
-              -0.03881837442792935),
-    TestValue(6, 1.5, 4.42, -4.694711300875651, 2.239864864864865,
-              -0.12612961153608993),
-    TestValue(14, 1.5, 4.42, -13.334103973863655, 6.221846846846847,
-              -0.8864094608348823),
-    TestValue(1525, 1.5, 4.42, -2072.1910365790172, 758.3186936936937,
-              -251.67662613527665),
-    TestValue(10233, 1.5, 4.42, -14020.648493631525, 5092.706081081081,
-              -1720.7211329093311),
-    TestValue(0, 1.5, 800, -1.4985955053447242, -0.9981285090455396,
-              -1.7534272203079126e-6),
-    TestValue(6, 1.5, 800, -5.63758835785638, 2.9943855271366187,
-              -0.00001104786953298742),
-    TestValue(14, 1.5, 800, -20.926415102269573, 8.317737575379496,
-              -0.00010961017476240897),
-    TestValue(1525, 1.5, 800, -8088.548799680884, 1013.7658556872531,
-              -0.8354105724129193),
-    TestValue(10233, 1.5, 800, -61412.52664040723, 6808.234560199626,
-              -10.142698900729565),
-    TestValue(0, 1.5, 15324, -1.499926590534038, -0.9999021239111285,
-              -4.790177143831897e-9),
-    TestValue(6, 1.5, 15324, -5.645995699555982, 2.9997063717333856,
-              -3.032959305926397e-8),
-    TestValue(14, 1.5, 15324, -21.010069937864472, 8.332517699259403,
-              -3.0266583905813604e-7),
-    TestValue(1525, 1.5, 15324, -8967.33164084002, 1015.5672571857361,
-              -0.004633327525485953),
-    TestValue(10233, 1.5, 15324, -77272.09898456372, 6820.332387197807,
-              -0.15620659350885369),
-    TestValue(0, 1.5, 162345, -1.4999930703617181, -0.9999907605029982,
-              -4.268407849394862e-11),
-    TestValue(6, 1.5, 162345, -5.646416676253864, 2.999972281508995,
-              -2.703277601767695e-10),
-    TestValue(14, 1.5, 162345, -21.01427157395574, 8.333256337524984,
-              -2.698453016591884e-9),
-    TestValue(1525, 1.5, 162345, -9033.49633366488, 1015.6572824175452,
-              -0.000043729856523455624),
-    TestValue(10233, 1.5, 162345, -79794.20778485533, 6820.936977390951,
-              -0.0019060581989425174),
-    TestValue(0, 3, 0.0004, -0.003569116649587855, -0.0001333155579256099,
-              -7.922924939527562),
-    TestValue(6, 3, 0.0004, -9.619261327135609, 0.0001333155579256099,
-              2492.360089770114),
-    TestValue(14, 3, 0.0004, -10.467267071498288, 0.0004888237123939031,
-              2490.5905361225123),
-    TestValue(1525, 3, 0.0004, -15.357522072066786, 0.06763542638759276,
-              1991.7174903993568),
-    TestValue(10233, 3, 0.0004, -18.421373162287637, 0.4546060525263298,
-              -908.6583034400528),
-    TestValue(0, 3, 0.065, -0.25047201260085383, -0.021207177814029365,
-              -2.874622756288704),
-    TestValue(6, 3, 0.065, -4.758782442354863, 0.021207177814029365,
-              12.74533572164111),
-    TestValue(14, 3, 0.065, -5.719495913883133, 0.07775965198477433,
-              11.025105769529759),
-    TestValue(1525, 3, 0.065, -42.491829475397026, 10.75910821098423,
-              -477.2384670870571),
-    TestValue(10233, 3, 0.065, -230.9301248894044, 72.31647634584013,
-              -3316.4438994781904),
-    TestValue(0, 3, 4.42, -2.2897339760163957, -0.5956873315363881,
-              -0.11372669262607049),
-    TestValue(6, 3, 4.42, -2.889108195828742, 0.5956873315363881,
-              0.003850246852058703),
-    TestValue(14, 3, 4.42, -7.790064290604171, 2.18418688230009,
-              -0.4832453669983474),
-    TestValue(1525, 3, 4.42, -1360.5497881858591, 302.2120395327942,
-              -199.67578957112616),
-    TestValue(10233, 3, 4.42, -9239.719029853994, 2031.2938005390836,
-              -1371.3592560596119),
-    TestValue(0, 3, 800, -2.994389023067612, -0.9962640099626401,
-              -6.996241475043519e-6),
-    TestValue(6, 3, 800, -2.9857172436025223, 0.9962640099626401,
-              -2.3069406651643476e-6),
-    TestValue(14, 3, 800, -12.744324478713366, 3.65296803652968,
-              -0.00008222425506509978),
-    TestValue(1525, 3, 800, -7035.84649923785, 505.4379410543794,
-              -0.8318616138503963),
-    TestValue(10233, 3, 800, -54340.180404088605, 3397.2602739726026,
-              -10.118854869649681),
-    TestValue(0, 3, 15324, -2.999706381300726, -0.9998042669798395,
-              -1.9158207464897714e-8),
-    TestValue(6, 3, 15324, -2.9874796347589054, 0.9998042669798395,
-              -6.3824572293924575e-9),
-    TestValue(14, 3, 15324, -12.807159398982407, 3.665948978926078,
-              -2.2763181739549054e-7),
-    TestValue(1525, 3, 15324, -7911.931224008331, 507.2340314477719,
-              -0.004623603455756964),
-    TestValue(10233, 3, 15324, -70181.6251826905, 3409.332550401253,
-              -0.15614126136305728),
-    TestValue(0, 3, 162345, -2.99997228162999, -0.9999815211767314,
-              -1.7073631397579447e-10),
-    TestValue(6, 3, 162345, -2.987568240888365, 0.9999815211767314,
-              -5.6909144063865824e-11),
-    TestValue(14, 3, 162345, -12.810319609745221, 3.6665989109813486,
-              -2.029739931685981e-9),
-    TestValue(1525, 3, 162345, -7977.960952690064, 507.32395841032843,
-              -0.00004364319426564123),
-    TestValue(10233, 3, 162345, -72702.82721273272, 3409.9369872126545,
-              -0.0019054759497976193),
-    TestValue(0, 180, 0.0004, -0.0052068020335865025, -2.2222172839615914e-6,
-              -12.01700730618354),
-    TestValue(6, 180, 0.0004, -9.62011239916672, -2.148143374496205e-6,
-              2490.2324075130828),
-    TestValue(14, 180, 0.0004, -10.467069325725546, -2.04937816187569e-6,
-              2491.084720678314),
-    TestValue(1525, 180, 0.0004, -15.159228863591125, 0.000016604901371824113,
-              2487.4167692289852),
-    TestValue(10233, 180, 0.0004, -17.08144177432405, 0.00012411083530925487,
-              2440.94300115826),
-    TestValue(0, 180, 0.065, -0.5152345838836883, -0.00036098075694887956,
-              -6.927046886659846),
-    TestValue(6, 180, 0.065, -4.897099604874426, -0.0003489480650505836,
-              10.617175935000475),
-    TestValue(14, 180, 0.065, -5.689219198051667, -0.0003329044758528556,
-              11.4626317745298),
-    TestValue(1525, 180, 0.065, -10.618383986015033, 0.0026973284338680167,
-              7.7929628140754765),
-    TestValue(10233, 180, 0.065, -15.542242814932251, 0.020160775275594924,
-              -38.6634853761835),
-    TestValue(0, 180, 4.42, -16.491356225074536, -0.023967031775295522,
-              -2.755043100796684),
-    TestValue(6, 180, 4.42, -11.802883319144515, -0.023168130716119003,
-              -1.8613752566654882),
-    TestValue(14, 180, 4.42, -9.653376579596795, -0.022102929303883648,
-              -1.313682997645138),
-    TestValue(1525, 180, 4.42, -30.756932642065294, 0.1790869874320693,
-              -5.0606677133089075),
-    TestValue(10233, 180, 4.42, -235.49737914944126, 1.3385587246502548,
-              -50.37753458197702),
-    TestValue(0, 180, 800, -162.35267519735217, -0.8163265306122449,
-              -0.01926737460893513),
-    TestValue(6, 180, 800, -138.9731231908616, -0.7891156462585034,
-              -0.017913154212997107),
-    TestValue(14, 180, 800, -117.57055678993851, -0.7528344671201814,
-              -0.016193696733894036),
-    TestValue(1525, 180, 800, -1255.1060610431614, 6.099773242630386,
-              -0.5081161722061651),
-    TestValue(10233, 180, 800, -14640.50246307096, 45.59183673469388,
-              -7.836489965276398),
-    TestValue(0, 180, 15324, -178.95104102256036, -0.9883900928792569,
-              -0.00006792118926490787),
-    TestValue(6, 180, 15324, -154.44163935947577, -0.9554437564499484,
-              -0.00006343927721985665),
-    TestValue(14, 180, 15324, -131.5984192349756, -0.911515307877537,
-              -0.000057701678183974536),
-    TestValue(1525, 180, 15324, -1861.5172673616398, 7.38547041623667,
-              -0.0035556000115217756),
-    TestValue(10233, 180, 15324, -28577.644697168085, 55.2015866873065,
-              -0.14858705144088802),
-    TestValue(0, 180, 162345, -179.90028620870413, -0.9988924780802954,
-              -6.137556081142748e-7),
-    TestValue(6, 180, 162345, -155.32835273471773, -0.9655960621442855,
-              -5.733925689810349e-7),
-    TestValue(14, 180, 162345, -132.40506485924828, -0.9212008408962724,
-              -5.216997802648393e-7),
-    TestValue(1525, 180, 162345, -1912.647535667431, 7.4639465723222065,
-              -0.00003402677068820026),
-    TestValue(10233, 180, 162345, -30993.45007826088, 55.788144900784495,
-              -0.0018374445009108342),
-    TestValue(0, 1123, 0.0004, -0.005939122128713381, -3.5618865318302646e-7,
-              -13.847805677972104),
-    TestValue(6, 1123, 0.0004, -9.620833523075628, -3.5428559715533445e-7,
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+TestValue(14,180,15324,-131.5984192349756,-0.911515307877537,-0.000057701678183974536),  
+TestValue(14,180,150000,-132.39809487222743,-0.9211168819638655,-6.110279944238073e-7),  
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+TestValue(14,1123,800,-640.6479149103316,-0.4108303245754051,-0.2829675576373729),  
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+TestValue(14,10586,0.0004,-10.468668475096411,-3.7735781630351504e-8,2487.0868493492235),  
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+TestValue(14,10586,15324,-7951.095336923546,-0.590649710084385,-0.11626776694982688),  
+TestValue(14,10586,150000,-10125.552885388513,-0.9328436151809941,-0.002267117824567677),  
+TestValue(1525,0.0000256,0.0004,-4301.784727467015,5.5987134868421055e7,-3.580668787634408e6),  
+TestValue(1525,0.0000256,0.065,-11965.467128123484,5.954685919853104e7,-23429.11268911477),  
+TestValue(1525,0.0000256,4.42,-18367.34289180058,5.956996647937967e7,-339.0570825343945),  
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+TestValue(1525,0.314,15324,-11350.864477542971,4855.588403521258,-0.004641024152967077),  
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+TestValue(1525,8,0.0004,-15.230842685268726,0.00948077596120194,2308.3869231549475),  
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+TestValue(1525,8,15324,-6421.662226247852,189.52605661361858,-0.004591272777291877),  
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+TestValue(1525,180,800,-1255.1060610431614,6.099773242630386,-0.5081161722061651),  
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+TestValue(1525,180,150000,-1912.1930479564326,7.463266302659031,-0.00003983284968711587),  
+TestValue(1525,1123,0.0004,-15.157115486355906,1.2750475385536657e-7,2492.70020501204),  
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+TestValue(1525,1123,150000,-68.69059192176792,0.3553096391221344,-3.4982159551333325e-6),  
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+TestValue(1525,10586,0.065,-10.34196113541293,-5.255608920401252e-6,12.044448366424728),  
+TestValue(1525,10586,4.42,-12.301855613945008,-0.0003572344439525938,-0.9624372357797295),  
+TestValue(1525,10586,800,-744.0169167062886,-0.060139948001942986,-0.7924525685250288),  
+TestValue(1525,10586,15324,-4300.645593413912,-0.506231273465249,-0.08062419697917278),  
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+TestValue(10233,0.0000256,0.0004,-28781.07085289515,3.7568285855263156e8,-2.4041193199521683e7),  
+TestValue(10233,0.0000256,0.065,-80237.4790550341,3.995691927102557e8,-157343.697098361),  
+TestValue(10233,0.0000256,4.42,-123371.16336416776,3.997242463550437e8,-2307.279979293951),  
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+TestValue(10233,0.0000256,15324,-189611.39394380094,3.9972656083222395e8,-0.15627194690990365),  
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+TestValue(10233,1.5,800,-61412.52664040723,6808.234560199626,-10.142698900729565),  
+TestValue(10233,1.5,15324,-77272.09898456372,6820.332387197807,-0.15620659350885369),  
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+TestValue(10233,8,0.065,-94.45295843966596,10.30106943583385,-1247.5517925303861),  
+TestValue(10233,8,4.42,-4476.485408813824,454.85607890499193,-816.4371067130297),  
+TestValue(10233,8,800,-44371.840290708235,1265.470297029703,-10.040039157123783),  
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+TestValue(10233,8,150000,-62645.92507437721,1278.056836968695,-0.002222438504382751),  
+TestValue(10233,180,0.0004,-17.08144177432405,0.00012411083530925487,2440.94300115826),  
+TestValue(10233,180,0.065,-15.542242814932251,0.020160775275594924,-38.6634853761835),  
+TestValue(10233,180,4.42,-235.49737914944126,1.3385587246502548,-50.37753458197702),  
+TestValue(10233,180,800,-14640.50246307096,45.59183673469388,-7.836489965276398),  
+TestValue(10233,180,15324,-28577.644697168085,55.2015866873065,-0.14858705144088802),  
+TestValue(10233,180,150000,-30968.941707557387,55.78306032760687,-0.0021450282568338253),  
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+TestValue(10233,1123,4.42,-35.45506157865748,0.031803517445555686,-5.756960605210265),  
+TestValue(10233,1123,800,-3343.1303902972795,3.3748099701370067,-2.9898053694742615),  
+TestValue(10233,1123,15324,-11352.060718035325,7.558299058347705,-0.11311918072723515),  
+TestValue(10233,1123,150000,-13237.322258064814,8.051917443787673,-0.0017468778907598903),  
+TestValue(10233,10586,0.0004,-17.060718192660715,-1.2600010324928188e-9,2492.7518943576556),  
+TestValue(10233,10586,0.065,-12.175300607224926,-2.047489183204549e-7,13.125723676609066),  
+TestValue(10233,10586,4.42,-9.430792045634007,-0.00001391720105013416,0.11674937200192481),  
+TestValue(10233,10586,800,-7.2703661972227565,-0.0023429424616141564,0.00008904830662359586),  
+TestValue(10233,10586,15324,-9.327824035135563,-0.019721845219427537,-0.00008059480749977865),  
+TestValue(10233,10586,150000,-11.132452601363184,-0.031147729489111892,-2.2067081495436014e-6),};
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::is_nan;

From 02865a9cbe6a45f4b3a3f85ee4fc8d5e9ab7c7fd Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Wed, 11 Dec 2019 08:14:45 +0000
Subject: [PATCH 12/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 633 ++++++++++++------
 1 file changed, 422 insertions(+), 211 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index cdfbf394855..50b917c30aa 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -51,217 +51,428 @@ struct TestValue {
 //  WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::array<TestValue, 210> testValues = {  
-TestValue(0,0.0000256,0.0004,-0.000024814156367780882,-0.9398496240601504,-0.0018850149796021398),  
-TestValue(0,0.0000256,0.065,-0.000025594960092480967,-0.9996063088998794,-7.751668684718993e-8),  
-TestValue(0,0.0000256,4.42,-0.000025599925864390194,-0.9999942081783417,-1.677258332222209e-11),  
-TestValue(0,0.0000256,800,-0.00002559999998652529,-0.999999968000001,-8.881784197001252e-16),  
-TestValue(0,0.0000256,15324,-0.000025599996959613236,-0.9999999983294179,0.),  
-TestValue(0,0.0000256,150000,-0.00002560005540885868,-0.9999999998293333,0.),  
-TestValue(0,0.314,0.0004,-0.002666782716971683,-0.001272264631043257,-5.66822905706025),  
-TestValue(0,0.314,0.065,-0.11460468078714132,-0.17150395778364116,-0.9346528929704305),  
-TestValue(0,0.314,4.42,-0.30334820230965986,-0.9336713138994508,-0.00230212890163628),  
-TestValue(0,0.314,800,-0.31393839362010567,-0.9996076539958066,-7.698783210940974e-8),  
-TestValue(0,0.314,15324,-0.31399678298770084,-0.9999795096863716,-2.099280749234822e-10),  
-TestValue(0,0.314,150000,-0.3139996713308335,-0.9999979066710487,-2.190247982980509e-12),  
-TestValue(0,1.5,0.0004,-0.003291911100032755,-0.00026659557451346307,-7.230044345656401),  
-TestValue(0,1.5,0.065,-0.2067814991501101,-0.04153354632587859,-2.2227873794044952),  
-TestValue(0,1.5,4.42,-1.2915096474038796,-0.7466216216216216,-0.03881837442792935),  
-TestValue(0,1.5,800,-1.4985955053447242,-0.9981285090455396,-1.7534272203079126e-6),  
-TestValue(0,1.5,15324,-1.499926590534038,-0.9999021239111285,-4.790177143831897e-9),  
-TestValue(0,1.5,150000,-1.4999925000758196,-0.999990000099999,-4.999911595859885e-11),  
-TestValue(0,8,0.0004,-0.003961415020514468,-0.00004999750012499375,-8.903587548786295),  
-TestValue(0,8,0.065,-0.3133586118431387,-0.008059516429014259,-3.8289612370926864),  
-TestValue(0,8,4.42,-4.566604241437509,-0.355877616747182,-0.3890459971629081),  
-TestValue(0,8,800,-7.9602646825343015,-0.9900990099009901,-0.000049340754157967126),  
-TestValue(0,8,15324,-7.99791249886043,-0.9994782154969998,-1.361769044194716e-7),  
-TestValue(0,8,150000,-7.999786674428577,-0.9999466695109595,-1.4221228639144101e-9),  
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-TestValue(0,180,0.065,-0.5152345838836883,-0.00036098075694887956,-6.927046886659846),  
-TestValue(0,180,4.42,-16.491356225074536,-0.023967031775295522,-2.755043100796684),  
-TestValue(0,180,800,-162.35267519735217,-0.8163265306122449,-0.01926737460893513),  
-TestValue(0,180,15324,-178.95104102256036,-0.9883900928792569,-0.00006792118926490787),  
-TestValue(0,180,150000,-179.8920863223863,-0.9988014382740711,-7.188495541043949e-7),  
-TestValue(0,1123,0.0004,-0.005939122128713381,-3.5618865318302646e-7,-13.847805677972104),  
-TestValue(0,1123,0.065,-0.6342170147837343,-0.000057877326779839104,-8.75724272015346),  
-TestValue(0,1123,4.42,-24.493639593452325,-0.00392045555338738,-4.545467874886493),  
-TestValue(0,1123,800,-701.6240143366822,-0.4160166406656266,-0.29304665858647905),  
-TestValue(0,1123,15324,-1083.757151397245,-0.9317200705295798,-0.002442933450309326),  
-TestValue(0,1123,150000,-1118.817101006986,-0.9925689670003904,-0.000027747673771116865),  
-TestValue(0,10586,0.0004,-0.006836533480423993,-3.778575334268833e-8,-16.091333738845734),  
-TestValue(0,10586,0.065,-0.7800430171085975,-6.1401474485561915e-6,-11.00066794181818),  
-TestValue(0,10586,4.42,-34.3945190758502,-0.0004173583295091224,-6.781982760105572),  
-TestValue(0,10586,800,-2124.4224654744803,-0.07026172492534692,-1.7257898067684474),  
-TestValue(0,10586,15324,-8048.29915678056,-0.5914318795831726,-0.11664064731878732),  
-TestValue(0,10586,150000,-10229.149577360897,-0.9340789358972762,-0.0022732664130149516),  
-TestValue(7,0.0000256,0.0004,-29.445354199147125,256989.1917293233,-13944.92090243279),  
-TestValue(7,0.0000256,0.065,-59.40270770911646,273328.85048350185,-89.90748568276743),  
-TestValue(7,0.0000256,4.42,-79.18162818224879,273434.9163045572,-0.5615296684557465),  
-TestValue(7,0.0000256,800,-82.50943543843826,273436.49125003227,-0.00003263555538968177),  
-TestValue(7,0.0000256,15324,-82.5342442124603,273436.4995432019,-8.94022633701752e-8),  
-TestValue(7,0.0000256,150000,-82.53547440969385,273436.4999533335,-9.33299659777731e-10),  
-TestValue(7,0.314,0.0004,-9.780554584441889,0.027090322685207696,2474.516543534505),  
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-TestValue(7,0.314,4.42,-14.063434552944763,19.880657339909963,-0.4587955394328642),  
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-TestValue(7,1.5,0.0004,-9.774134608119379,0.0009775171065493646,2490.5539367351803),  
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-TestValue(7,1.5,800,-7.172434628346302,3.6598045331669784,-0.000018013716757359077),  
-TestValue(7,1.5,15324,-7.186147155348181,3.6663077876741377,-4.948342535726624e-8),  
-TestValue(7,1.5,150000,-7.1868281060611565,3.666630000366663,-5.166445049553658e-10),  
-TestValue(7,8,0.0004,-9.773287685468139,-6.249687515624219e-6,2492.6708598338487),  
-TestValue(7,8,0.065,-4.893078153217412,-0.0010074395536267824,13.045515423749752),  
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-TestValue(7,8,15324,-1.9692663072788577,-0.12493477693712497,1.277112104958178e-8),  
-TestValue(7,8,150000,-1.9690905691403486,-0.12499333368886993,1.333280152948646e-10),  
-TestValue(7,180,0.0004,-9.774198636769189,-2.1357977229186406e-6,2490.3935075261693),  
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+    TestValue(10233, 8, 4.42, -4476.485408813824, 454.85607890499193,
+              -816.4371067130297),
+    TestValue(10233, 8, 800, -44371.840290708235, 1265.470297029703,
+              -10.040039157123783),
+    TestValue(10233, 8, 15324, -60153.13532501529, 1277.4580941821027,
+              -0.15592364901449507),
+    TestValue(10233, 8, 150000, -62645.92507437721, 1278.056836968695,
+              -0.002222438504382751),
+    TestValue(10233, 180, 0.0004, -17.08144177432405, 0.00012411083530925487,
+              2440.94300115826),
+    TestValue(10233, 180, 0.065, -15.542242814932251, 0.020160775275594924,
+              -38.6634853761835),
+    TestValue(10233, 180, 4.42, -235.49737914944126, 1.3385587246502548,
+              -50.37753458197702),
+    TestValue(10233, 180, 800, -14640.50246307096, 45.59183673469388,
+              -7.836489965276398),
+    TestValue(10233, 180, 15324, -28577.644697168085, 55.2015866873065,
+              -0.14858705144088802),
+    TestValue(10233, 180, 150000, -30968.941707557387, 55.78306032760687,
+              -0.0021450282568338253),
+    TestValue(10233, 1123, 0.0004, -17.063078998820856, 2.8894734020457448e-6,
+              2486.849880233364),
+    TestValue(10233, 1123, 0.065, -12.558918107941281, 0.0004695124193805291,
+              7.224124958319663),
+    TestValue(10233, 1123, 4.42, -35.45506157865748, 0.031803517445555686,
+              -5.756960605210265),
+    TestValue(10233, 1123, 800, -3343.1303902972795, 3.3748099701370067,
+              -2.9898053694742615),
+    TestValue(10233, 1123, 15324, -11352.060718035325, 7.558299058347705,
+              -0.11311918072723515),
+    TestValue(10233, 1123, 150000, -13237.322258064814, 8.051917443787673,
+              -0.0017468778907598903),
+    TestValue(10233, 10586, 0.0004, -17.060718192660715, -1.2600010324928188e-9,
+              2492.7518943576556),
+    TestValue(10233, 10586, 0.065, -12.175300607224926, -2.047489183204549e-7,
+              13.125723676609066),
+    TestValue(10233, 10586, 4.42, -9.430792045634007, -0.00001391720105013416,
+              0.11674937200192481),
+    TestValue(10233, 10586, 800, -7.2703661972227565, -0.0023429424616141564,
+              0.00008904830662359586),
+    TestValue(10233, 10586, 15324, -9.327824035135563, -0.019721845219427537,
+              -0.00008059480749977865),
+    TestValue(10233, 10586, 150000, -11.132452601363184, -0.031147729489111892,
+              -2.2067081495436014e-6),
+};
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::is_nan;

From abc6858009ebe0c4cf4f87062f78d701b5a9627c Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 13:08:59 +0100
Subject: [PATCH 13/82] Changing order of operations, passing precomputed test

---
 stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp   |  6 ++----
 .../scal/fun/binomial_coefficient_log_test.cpp     |  3 +++
 .../math/rev/scal/prob/neg_binomial_2_test.cpp     | 14 ++++++++++----
 3 files changed, 15 insertions(+), 8 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 96b17de1589..1df8b2aa0e1 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -122,11 +122,9 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       if (include_summand<propto, T_precision>::value) {
         logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
       }
-      if (include_summand<propto, T_precision>::value) {
-        logp += multiply_log(phi__[i], phi__[i]);
-      }
       if (include_summand<propto, T_location, T_precision>::value) {
-        logp -= (n_plus_phi[i]) * log_mu_plus_phi[i];
+        logp += phi__[i] *  (log(phi__[i]) - log(mu__[i]  + phi__[i]))
+          - (n_vec[i]) * log_mu_plus_phi[i];
       }
       if (include_summand<propto, T_location>::value) {
         logp += multiply_log(n_vec[i], mu__[i]);
diff --git a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
index 2bc50f0d4a9..554cd0b743a 100644
--- a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
@@ -20,6 +20,9 @@ TEST(MathFunctions, binomial_coefficient_log) {
 
   EXPECT_FLOAT_EQ(29979.16, binomial_coefficient_log(100000, 91116));
 
+  EXPECT_EQ(binomial_coefficient_log(50, 0), 0);
+  EXPECT_EQ(binomial_coefficient_log(10000, 0), 0);
+
   for (int n = 0; n < 1010; ++n) {
     test_binom_coefficient(1010, n);
     test_binom_coefficient(1010.0, n);
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 50b917c30aa..4bbdd8982f2 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -479,6 +479,7 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
   using stan::math::var;
+  using stan::math::digamma;
 
   for (auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
     TestValue t = *iter;
@@ -498,12 +499,17 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
       EXPECT_FALSE(is_nan(gradients[i]));
     }
 
-    EXPECT_NEAR(value_of(val), t.value, fabs(t.value * 1e-8))
+    auto tolerance = [](double x) { 
+      return std::max(fabs(x * 1e-8), 1e-14);
+    };
+
+    EXPECT_NEAR(value_of(val), t.value, tolerance(t.value))
         << "value n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
-    EXPECT_NEAR(gradients[0], t.grad_mu, fabs(t.grad_mu * 1e-8))
+    EXPECT_NEAR(gradients[0], t.grad_mu, tolerance(t.grad_mu))
         << "grad_mu n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
-    EXPECT_NEAR(gradients[1], t.grad_phi, fabs(t.grad_phi * 1e-8))
-        << "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
+    EXPECT_NEAR(gradients[1], t.grad_phi, tolerance(t.grad_phi))
+        << "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi <<
+        ", digamma = " << digamma(t.phi) << ", " << digamma(t.n + t.phi);
   }
 }
 

From 2dcbb82b48e712ec655b94b4eee662363569a7ec Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Wed, 11 Dec 2019 07:09:54 -0500
Subject: [PATCH 14/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp     |  4 ++--
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 10 ++++------
 2 files changed, 6 insertions(+), 8 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 1df8b2aa0e1..46a1aa68ac5 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -123,8 +123,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
         logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
       }
       if (include_summand<propto, T_location, T_precision>::value) {
-        logp += phi__[i] *  (log(phi__[i]) - log(mu__[i]  + phi__[i]))
-          - (n_vec[i]) * log_mu_plus_phi[i];
+        logp += phi__[i] * (log(phi__[i]) - log(mu__[i] + phi__[i]))
+                - (n_vec[i]) * log_mu_plus_phi[i];
       }
       if (include_summand<propto, T_location>::value) {
         logp += multiply_log(n_vec[i], mu__[i]);
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 4bbdd8982f2..1b4a63638f9 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -475,11 +475,11 @@ std::array<TestValue, 210> testValues = {
 };
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
+  using stan::math::digamma;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
   using stan::math::var;
-  using stan::math::digamma;
 
   for (auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
     TestValue t = *iter;
@@ -499,17 +499,15 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
       EXPECT_FALSE(is_nan(gradients[i]));
     }
 
-    auto tolerance = [](double x) { 
-      return std::max(fabs(x * 1e-8), 1e-14);
-    };
+    auto tolerance = [](double x) { return std::max(fabs(x * 1e-8), 1e-14); };
 
     EXPECT_NEAR(value_of(val), t.value, tolerance(t.value))
         << "value n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
     EXPECT_NEAR(gradients[0], t.grad_mu, tolerance(t.grad_mu))
         << "grad_mu n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
     EXPECT_NEAR(gradients[1], t.grad_phi, tolerance(t.grad_phi))
-        << "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi <<
-        ", digamma = " << digamma(t.phi) << ", " << digamma(t.n + t.phi);
+        << "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi
+        << ", digamma = " << digamma(t.phi) << ", " << digamma(t.n + t.phi);
   }
 }
 

From b6bf80c7435e8b2866590ee1686de8675ad66885 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 13:11:01 +0100
Subject: [PATCH 15/82] Removed unnecessary debug info

---
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 1b4a63638f9..c1d064f5140 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -475,7 +475,6 @@ std::array<TestValue, 210> testValues = {
 };
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
-  using stan::math::digamma;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
@@ -506,8 +505,7 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
     EXPECT_NEAR(gradients[0], t.grad_mu, tolerance(t.grad_mu))
         << "grad_mu n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
     EXPECT_NEAR(gradients[1], t.grad_phi, tolerance(t.grad_phi))
-        << "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi
-        << ", digamma = " << digamma(t.phi) << ", " << digamma(t.n + t.phi);
+        << "grad_phi n = " << n << ", mu = " << t.mu << ", phi = " << t.phi;
   }
 }
 

From 85059fd15dd33c1c8b92393ea2073703be5be865 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 13:22:54 +0100
Subject: [PATCH 16/82] Use precomputed values

---
 stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 46a1aa68ac5..0928d8503d8 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -123,7 +123,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
         logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
       }
       if (include_summand<propto, T_location, T_precision>::value) {
-        logp += phi__[i] * (log(phi__[i]) - log(mu__[i] + phi__[i]))
+        logp += phi__[i] * (log_phi[i] - log_mu_plus_phi[i])
                 - (n_vec[i]) * log_mu_plus_phi[i];
       }
       if (include_summand<propto, T_location>::value) {

From 788c894d7a0e53d53883b12a4bd9c9aeeafdebf9 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 14:16:53 +0100
Subject: [PATCH 17/82] Test for continuity of gradients at cutoff

Implemented gradient wrt. phi for Poisson approximation to make the test pass
---
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    | 18 ++++--
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 64 ++++++++++++++++++-
 2 files changed, 76 insertions(+), 6 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 0928d8503d8..d834e56ee1b 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -8,6 +8,7 @@
 #include <stan/math/prim/scal/fun/size_zero.hpp>
 #include <stan/math/prim/scal/fun/multiply_log.hpp>
 #include <stan/math/prim/scal/fun/digamma.hpp>
+#include <stan/math/prim/scal/fun/square.hpp>
 #include <stan/math/prim/scal/fun/lgamma.hpp>
 #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
 #include <stan/math/prim/scal/fun/value_of.hpp>
@@ -108,15 +109,22 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
         // This is the Taylor series of the full derivative for phi -> Inf
         // Obtained in Mathematica via
         // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
+        // Currently ignoring the term (mu__[i] - n_vec[i]) / phi__[i]
         ops_partials.edge1_.partials_[i]
-            += n_vec[i] / mu__[i] + (mu__[i] - n_vec[i]) / phi__[i] - 1;
+            += n_vec[i] / mu__[i] - 1;
       }
 
-      // The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2)
-      // So ignoring here
-      // Obtained in Mathematica via
+      // The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2),
+      // But the quadratic term is big enough to warrant inclusion here
+      // (can be around 1e-6 at cutoff).
+      // Expansion obtained in Mathematica via
       // Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] -
-      //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 1}]
+      //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 2}]
+      if (!is_constant_all<T_precision>::value) {
+        ops_partials.edge2_.partials_[i]
+          += (mu__[i] * (-mu__[i] + 2 * n_vec[i]) + n_vec[i] * (1 - n_vec[i]) ) 
+            / (2 * square(phi__[i]));
+      }
 
     } else {
       if (include_summand<propto, T_precision>::value) {
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index c1d064f5140..0a8c78ccc63 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -587,4 +587,66 @@ TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
   EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
 }
 
-// TODO(martinmodrak) test continuity of derivatives at cutoff
+
+TEST(ProbDistributionsNegBinomial, derivativesAtCutoff) {
+  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  using stan::math::is_nan;
+  using stan::math::var;
+
+  std::array<double, 7> mu_to_test
+      = {9.3e-6, 0.0028252, 4, 11, 8522, 984256, 5036842};
+  std::array<unsigned int, 8> n_to_test
+      = {0, 1, 5, 48, 1158, 224582, 48235842, 20314458};
+  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
+       ++mu_iter) {
+    double mu = *mu_iter;
+    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
+      unsigned int n = *n_iter;
+      var mu_before(mu);
+      var phi_before(phi_cutoff - 1e-8);
+      var value_before = neg_binomial_2_lpmf(n, mu_before, phi_before);
+      std::vector<var> x_before;
+      x_before.push_back(mu_before);
+      x_before.push_back(phi_before);
+
+      std::vector<double> gradients_before;
+      value_before.grad(x_before, gradients_before);
+
+      var mu_after(mu);
+      var phi_after(phi_cutoff + 1e-8);
+      var value_after = neg_binomial_2_lpmf(n, mu_after, phi_after);
+      std::vector<var> x_after;
+      x_after.push_back(mu_after);
+      x_after.push_back(phi_after);
+
+      std::vector<double> gradients_after;
+      value_after.grad(x_after, gradients_after);
+
+
+      for (int i = 0; i < 2; ++i) {
+        EXPECT_FALSE(is_nan(gradients_before[i]));
+        EXPECT_FALSE(is_nan(gradients_after[i]));
+      }
+
+      EXPECT_NEAR(value_of(value_before), value_of(value_after), 
+        1e-8 * fabs(value_of(value_after)))
+          << "value changes too much around phi cutoff for n = "
+          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+          << " value at cutoff - 1e-8: " << value_of(value_before)
+          << ", value at cutoff + 1e-8: " << value_of(value_after);
+      EXPECT_NEAR(gradients_before[0], gradients_after[0], 
+        1e-8 * fabs(gradients_before[0]))
+          << "grad_mu changes too much around phi cutoff for n = "
+          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+          << " grad_mu at cutoff - 1e-8: " << gradients_before[0]
+          << ", grad_mu at cutoff + 1e-8: " << gradients_after[0];
+
+      EXPECT_NEAR(gradients_before[1], gradients_after[1], 
+        1e-8 * fabs(gradients_before[1]))
+          << "grad_phi changes too much around phi cutoff for n = "
+          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+          << " grad_phi at cutoff - 1e-8: " << gradients_before[1]
+          << ", grad_phi at cutoff + 1e-8: " << gradients_after[1];      
+    }
+  }
+}

From 8ec6a37cb73ac4d05945e846b2bc3cfae2633c69 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Wed, 11 Dec 2019 08:17:47 -0500
Subject: [PATCH 18/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    |  7 ++---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 28 +++++++++----------
 2 files changed, 16 insertions(+), 19 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index d834e56ee1b..c2fa67dcbd3 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -110,8 +110,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
         // Obtained in Mathematica via
         // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
         // Currently ignoring the term (mu__[i] - n_vec[i]) / phi__[i]
-        ops_partials.edge1_.partials_[i]
-            += n_vec[i] / mu__[i] - 1;
+        ops_partials.edge1_.partials_[i] += n_vec[i] / mu__[i] - 1;
       }
 
       // The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2),
@@ -122,8 +121,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 2}]
       if (!is_constant_all<T_precision>::value) {
         ops_partials.edge2_.partials_[i]
-          += (mu__[i] * (-mu__[i] + 2 * n_vec[i]) + n_vec[i] * (1 - n_vec[i]) ) 
-            / (2 * square(phi__[i]));
+            += (mu__[i] * (-mu__[i] + 2 * n_vec[i]) + n_vec[i] * (1 - n_vec[i]))
+               / (2 * square(phi__[i]));
       }
 
     } else {
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 0a8c78ccc63..d6f75e40d40 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -587,7 +587,6 @@ TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
   EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
 }
 
-
 TEST(ProbDistributionsNegBinomial, derivativesAtCutoff) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   using stan::math::is_nan;
@@ -622,31 +621,30 @@ TEST(ProbDistributionsNegBinomial, derivativesAtCutoff) {
       std::vector<double> gradients_after;
       value_after.grad(x_after, gradients_after);
 
-
       for (int i = 0; i < 2; ++i) {
         EXPECT_FALSE(is_nan(gradients_before[i]));
         EXPECT_FALSE(is_nan(gradients_after[i]));
       }
 
-      EXPECT_NEAR(value_of(value_before), value_of(value_after), 
-        1e-8 * fabs(value_of(value_after)))
-          << "value changes too much around phi cutoff for n = "
-          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+      EXPECT_NEAR(value_of(value_before), value_of(value_after),
+                  1e-8 * fabs(value_of(value_after)))
+          << "value changes too much around phi cutoff for n = " << n
+          << ", mu = " << mu << ", cutoff = " << phi_cutoff
           << " value at cutoff - 1e-8: " << value_of(value_before)
           << ", value at cutoff + 1e-8: " << value_of(value_after);
-      EXPECT_NEAR(gradients_before[0], gradients_after[0], 
-        1e-8 * fabs(gradients_before[0]))
-          << "grad_mu changes too much around phi cutoff for n = "
-          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+      EXPECT_NEAR(gradients_before[0], gradients_after[0],
+                  1e-8 * fabs(gradients_before[0]))
+          << "grad_mu changes too much around phi cutoff for n = " << n
+          << ", mu = " << mu << ", cutoff = " << phi_cutoff
           << " grad_mu at cutoff - 1e-8: " << gradients_before[0]
           << ", grad_mu at cutoff + 1e-8: " << gradients_after[0];
 
-      EXPECT_NEAR(gradients_before[1], gradients_after[1], 
-        1e-8 * fabs(gradients_before[1]))
-          << "grad_phi changes too much around phi cutoff for n = "
-          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+      EXPECT_NEAR(gradients_before[1], gradients_after[1],
+                  1e-8 * fabs(gradients_before[1]))
+          << "grad_phi changes too much around phi cutoff for n = " << n
+          << ", mu = " << mu << ", cutoff = " << phi_cutoff
           << " grad_phi at cutoff - 1e-8: " << gradients_before[1]
-          << ", grad_phi at cutoff + 1e-8: " << gradients_after[1];      
+          << ", grad_phi at cutoff + 1e-8: " << gradients_after[1];
     }
   }
 }

From eb7f7fc7d38600f0551fc99791efaf109a82dd25 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 14:26:10 +0100
Subject: [PATCH 19/82] Updated Mathematica code+reference

---
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index d6f75e40d40..9036b3b14b4 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -21,14 +21,17 @@ struct TestValue {
         grad_phi(_grad_phi) {}
 };
 
-// Test data generated in Mathematica (Wolfram Cloud) via
+// Test data generated in Mathematica (Wolfram Cloud). The code can be re-ran
+// at https://www.wolframcloud.com/env/martin.modrak/NegBinomial2_Tests.nb
+// but is also presented below for conveniece:
+//
 // nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi ]+
 //   n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
 // nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
 // nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
 // out = OpenWrite["nb_test.txt"]
-// mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
-//  phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
+// mus= {256*10^-7,314*10^-3,15*10^-1,8,180,  1123,10586};
+// phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324,150000};
 // ns = {0,6,14,1525,10233};
 //  WriteString[out, "std::array<TestValue, ",
 //      Length[mus]*Length[phis]*Length[ns], "> testValues = {"];

From d54bedd827dde61d8e6889f6e31d17877586c6e1 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Wed, 11 Dec 2019 14:29:36 +0100
Subject: [PATCH 20/82] Removing old code

---
 stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp | 7 -------
 1 file changed, 7 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index c2fa67dcbd3..fb2bccb3560 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -98,13 +98,6 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
         logp += multiply_log(n_vec[i], mu__[i]) - mu__[i];
       }
 
-      // if (include_summand<propto, T_location, T_precision>::value) {
-      //   logp += (mu__[i] * (mu__[i] - 2 * n_vec[i]) +
-      //     n_vec[i] * (n_vec[i] - 1)) / ( 2 * phi__[i] );
-      //   // logp += (mu__[i] * mu__[i] - n_vec[i] -
-      //   //   2 * mu__[i] * n_vec[i] + n_vec[i] * n_vec[i])/phi
-      // }
-
       if (!is_constant_all<T_location>::value) {
         // This is the Taylor series of the full derivative for phi -> Inf
         // Obtained in Mathematica via

From c306f5abd101e75bccf05878a38213206df17e9e Mon Sep 17 00:00:00 2001
From: martinmodrak <modrak.mar@gmail.com>
Date: Wed, 18 Dec 2019 16:39:34 +0100
Subject: [PATCH 21/82] Test with complex_step WIP

---
 .../math/rev/scal/prob/neg_binomial_2_test.cpp    | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 9036b3b14b4..3de6d5fd530 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -1,4 +1,5 @@
 #include <stan/math/rev/scal.hpp>
+#include <boost/math/tools/numerical_differentiation.hpp>
 #include <gtest/gtest.h>
 #include <vector>
 #include <algorithm>
@@ -512,7 +513,16 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   }
 }
 
-TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
+namespace test_internal {
+  template<typename T_mu, typename T_phi>
+  double //TDO
+  nb2_log_for_test(int n, const T_mu& mu, const T_phi& phi) {
+        return  binomial_coefficient_log(n + phi - 1, n) + phi__ * (log(phi) - log(mu + phi)) 
+                - n * log(mu + phi) + multiply_log(n, mu);
+  }
+}
+
+TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
@@ -521,6 +531,9 @@ TEST(ProbDistributionsNegBinomial, derivativesFiniteDiffs) {
   std::array<double, 2> mu_to_test = {8, 24};
   // std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835};
   // std::array<double, 6> mu_to_test = {0.8, 8, 24, 271};
+
+
+
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
        ++mu_iter) {

From 2745243254b56bffe74c02ed7f832c7cd00215c4 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Thu, 19 Dec 2019 10:58:49 +0000
Subject: [PATCH 22/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp  |  2 +-
 .../math/rev/scal/prob/neg_binomial_2_test.cpp    | 15 +++++++--------
 2 files changed, 8 insertions(+), 9 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 942edf30938..b6b6b9fc779 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -124,7 +124,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       }
 
       logp += phi__[i] * (log_phi[i] - log_mu_plus_phi[i])
-                - (n_vec[i]) * log_mu_plus_phi[i];
+              - (n_vec[i]) * log_mu_plus_phi[i];
 
       if (include_summand<propto, T_location>::value) {
         logp += multiply_log(n_vec[i], mu__[i]);
diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 3de6d5fd530..384133969c9 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -514,13 +514,14 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
 }
 
 namespace test_internal {
-  template<typename T_mu, typename T_phi>
-  double //TDO
-  nb2_log_for_test(int n, const T_mu& mu, const T_phi& phi) {
-        return  binomial_coefficient_log(n + phi - 1, n) + phi__ * (log(phi) - log(mu + phi)) 
-                - n * log(mu + phi) + multiply_log(n, mu);
-  }
+template <typename T_mu, typename T_phi>
+double  // TDO
+nb2_log_for_test(int n, const T_mu& mu, const T_phi& phi) {
+  return binomial_coefficient_log(n + phi - 1, n)
+         + phi__ * (log(phi) - log(mu + phi)) - n * log(mu + phi)
+         + multiply_log(n, mu);
 }
+}  // namespace test_internal
 
 TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   using stan::math::is_nan;
@@ -532,8 +533,6 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   // std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835};
   // std::array<double, 6> mu_to_test = {0.8, 8, 24, 271};
 
-
-
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
        ++mu_iter) {

From 06f926a18993cf0cfea5c9df6fe45298c0c3e490 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 19 Dec 2019 12:45:48 +0100
Subject: [PATCH 23/82] Changing finite diffs to complex step

---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 70 ++++++++++---------
 1 file changed, 38 insertions(+), 32 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 3de6d5fd530..359e47a8bb3 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -1,5 +1,6 @@
 #include <stan/math/rev/scal.hpp>
 #include <boost/math/tools/numerical_differentiation.hpp>
+#include <boost/math/special_functions/digamma.hpp>
 #include <gtest/gtest.h>
 #include <vector>
 #include <algorithm>
@@ -513,25 +514,29 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   }
 }
 
-namespace test_internal {
-  template<typename T_mu, typename T_phi>
-  double //TDO
-  nb2_log_for_test(int n, const T_mu& mu, const T_phi& phi) {
-        return  binomial_coefficient_log(n + phi - 1, n) + phi__ * (log(phi) - log(mu + phi)) 
-                - n * log(mu + phi) + multiply_log(n, mu);
-  }
-}
-
 TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
+  using boost::math::tools::complex_step_derivative;
+
+  std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835, 14238};
+  std::array<double, 6> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
 
-  std::array<unsigned int, 3> n_to_test = {7, 100, 835};
-  std::array<double, 2> mu_to_test = {8, 24};
-  // std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835};
-  // std::array<double, 6> mu_to_test = {0.8, 8, 24, 271};
+  auto nb2_log_for_test = [](
+      int n, const std::complex<double>& mu, const std::complex<double>& phi) {
+    //Encoding the explicit derivative (digamma) so that it is compatible with
+    //Complex-step differentiation...
+    auto lgamma_c_approx = [](const std::complex<double>& x) {
+      return std::complex<double>(
+        lgamma(x.real()), x.imag() * boost::math::digamma(x.real()));
+    };
 
+   
+    const double n_(n);
+    return  lgamma_c_approx(n_ + phi) - lgamma(n + 1) - lgamma_c_approx(phi) + 
+     phi * (log(phi) - log(mu + phi)) - n_ * log(mu + phi) + n_ * log(mu);
+  };
 
 
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
@@ -545,7 +550,7 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
       for (int k = 0; k < 20; ++k) {
         var mu(mu_dbl);
         var phi(phi_dbl);
-        var val = neg_binomial_2_log(n, mu, phi);
+        var val = neg_binomial_2_lpmf(n, mu, phi);
 
         std::vector<var> x;
         x.push_back(mu);
@@ -561,26 +566,27 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
           EXPECT_FALSE(is_nan(gradients[i]));
         }
 
-        std::vector<double> finite_diffs;
-        double eps = 1e-10;
-        double inv2e = 0.5 / eps;
-        double dmu = neg_binomial_2_log(n, mu_dbl + eps, phi_dbl)
-                     - neg_binomial_2_log(n, mu_dbl - eps, phi_dbl);
-        double dphi = neg_binomial_2_log(n, mu_dbl, phi_dbl + eps)
-                      - neg_binomial_2_log(n, mu_dbl, phi_dbl - eps);
-        finite_diffs.push_back(dmu * inv2e);
-        finite_diffs.push_back(dphi * inv2e);
-
-        EXPECT_NEAR(gradients[0], finite_diffs[0],
-                    std::max(1.0, gradients[0] * 1e-4))
+        auto nb2_log_mu= [n, phi_dbl, nb2_log_for_test](
+            const std::complex<double>& mu) {
+          return nb2_log_for_test(n, mu, phi_dbl);
+        };
+        auto nb2_log_phi = [n, mu_dbl, nb2_log_for_test](
+            const std::complex<double>& phi) {
+          return nb2_log_for_test(n, mu_dbl, phi);
+        };
+        double complex_step_dmu = 
+          complex_step_derivative(nb2_log_mu, mu_dbl);
+        double complex_step_dphi = 
+          complex_step_derivative(nb2_log_phi, phi_dbl);
+
+        EXPECT_NEAR(gradients[0], complex_step_dmu,
+                    std::max(1e-10, fabs(gradients[0]) * 1e-5))
             << "grad_mu, n = " << n << ", mu = " << mu_dbl
-            << "  +/- epsilon, phi = " << phi_dbl
-            << " +/- epsilon, dmu = " << dmu;
-        EXPECT_NEAR(gradients[1], finite_diffs[1],
-                    std::max(1.0, gradients[1] * 1e-4))
+            << ", phi = " << phi_dbl;
+        EXPECT_NEAR(gradients[1], complex_step_dphi,
+                    std::max(1e-10, fabs(gradients[1]) * 1e-5))
             << "grad_phi, n = " << n << ", mu = " << mu_dbl
-            << "  +/- epsilon, phi = " << phi_dbl
-            << " +/- epsilon, dphi = " << dphi;
+            << ", phi = " << phi_dbl;
 
         phi_dbl *= 10;
       }

From 69083c7c158a36aa08d08652e59db76d7afc0b61 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Thu, 19 Dec 2019 11:48:18 +0000
Subject: [PATCH 24/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 .../rev/scal/prob/neg_binomial_2_test.cpp     | 44 +++++++++----------
 1 file changed, 21 insertions(+), 23 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 359e47a8bb3..e13b66a58a8 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -515,30 +515,29 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
 }
 
 TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
+  using boost::math::tools::complex_step_derivative;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
-  using boost::math::tools::complex_step_derivative;
 
   std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835, 14238};
   std::array<double, 6> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
 
-  auto nb2_log_for_test = [](
-      int n, const std::complex<double>& mu, const std::complex<double>& phi) {
-    //Encoding the explicit derivative (digamma) so that it is compatible with
-    //Complex-step differentiation...
+  auto nb2_log_for_test = [](int n, const std::complex<double>& mu,
+                             const std::complex<double>& phi) {
+    // Encoding the explicit derivative (digamma) so that it is compatible with
+    // Complex-step differentiation...
     auto lgamma_c_approx = [](const std::complex<double>& x) {
-      return std::complex<double>(
-        lgamma(x.real()), x.imag() * boost::math::digamma(x.real()));
+      return std::complex<double>(lgamma(x.real()),
+                                  x.imag() * boost::math::digamma(x.real()));
     };
 
-   
     const double n_(n);
-    return  lgamma_c_approx(n_ + phi) - lgamma(n + 1) - lgamma_c_approx(phi) + 
-     phi * (log(phi) - log(mu + phi)) - n_ * log(mu + phi) + n_ * log(mu);
+    return lgamma_c_approx(n_ + phi) - lgamma(n + 1) - lgamma_c_approx(phi)
+           + phi * (log(phi) - log(mu + phi)) - n_ * log(mu + phi)
+           + n_ * log(mu);
   };
 
-
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
        ++mu_iter) {
@@ -566,18 +565,17 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
           EXPECT_FALSE(is_nan(gradients[i]));
         }
 
-        auto nb2_log_mu= [n, phi_dbl, nb2_log_for_test](
-            const std::complex<double>& mu) {
-          return nb2_log_for_test(n, mu, phi_dbl);
-        };
-        auto nb2_log_phi = [n, mu_dbl, nb2_log_for_test](
-            const std::complex<double>& phi) {
-          return nb2_log_for_test(n, mu_dbl, phi);
-        };
-        double complex_step_dmu = 
-          complex_step_derivative(nb2_log_mu, mu_dbl);
-        double complex_step_dphi = 
-          complex_step_derivative(nb2_log_phi, phi_dbl);
+        auto nb2_log_mu
+            = [n, phi_dbl, nb2_log_for_test](const std::complex<double>& mu) {
+                return nb2_log_for_test(n, mu, phi_dbl);
+              };
+        auto nb2_log_phi
+            = [n, mu_dbl, nb2_log_for_test](const std::complex<double>& phi) {
+                return nb2_log_for_test(n, mu_dbl, phi);
+              };
+        double complex_step_dmu = complex_step_derivative(nb2_log_mu, mu_dbl);
+        double complex_step_dphi
+            = complex_step_derivative(nb2_log_phi, phi_dbl);
 
         EXPECT_NEAR(gradients[0], complex_step_dmu,
                     std::max(1e-10, fabs(gradients[0]) * 1e-5))

From 6f5a9d2f54116f20b178f3115802d52a08c93a45 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 19 Dec 2019 13:54:38 +0100
Subject: [PATCH 25/82] Moved test values to separate namespace

---
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index e13b66a58a8..2eea9276132 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -5,6 +5,7 @@
 #include <vector>
 #include <algorithm>
 
+namespace neg_binomial_2_test_internal {
 struct TestValue {
   unsigned int n;
   double mu;
@@ -479,11 +480,15 @@ std::array<TestValue, 210> testValues = {
               -2.2067081495436014e-6),
 };
 
+} // namespace neg_binomial_2_test_internal 
+
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
   using stan::math::var;
+  using neg_binomial_2_test_internal::TestValue;
+  using neg_binomial_2_test_internal::testValues;
 
   for (auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
     TestValue t = *iter;

From 9dd904f56a6940860fe5a9b77fb21ebbab919293 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Thu, 19 Dec 2019 12:55:14 +0000
Subject: [PATCH 26/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index 2eea9276132..a4dd4f22b55 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -480,15 +480,15 @@ std::array<TestValue, 210> testValues = {
               -2.2067081495436014e-6),
 };
 
-} // namespace neg_binomial_2_test_internal 
+}  // namespace neg_binomial_2_test_internal
 
 TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
+  using neg_binomial_2_test_internal::TestValue;
+  using neg_binomial_2_test_internal::testValues;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
   using stan::math::var;
-  using neg_binomial_2_test_internal::TestValue;
-  using neg_binomial_2_test_internal::testValues;
 
   for (auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
     TestValue t = *iter;

From dae4a78dd0a699e3c477a47c0c4d31442d22705b Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 19 Dec 2019 14:15:36 +0100
Subject: [PATCH 27/82] Updated comments

---
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index a4dd4f22b55..d7c9d1be6b3 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -26,7 +26,7 @@ struct TestValue {
 
 // Test data generated in Mathematica (Wolfram Cloud). The code can be re-ran
 // at https://www.wolframcloud.com/env/martin.modrak/NegBinomial2_Tests.nb
-// but is also presented below for conveniece:
+// but is also presented below for convenience:
 //
 // nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi ]+
 //   n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
@@ -530,8 +530,9 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
 
   auto nb2_log_for_test = [](int n, const std::complex<double>& mu,
                              const std::complex<double>& phi) {
-    // Encoding the explicit derivative (digamma) so that it is compatible with
-    // Complex-step differentiation...
+    // Using first-order Taylor expansion of lgamma(a + b*i) around b = 0
+    // Which happens to work nice in this case, as b is always 0 or the very 
+    // small complex step
     auto lgamma_c_approx = [](const std::complex<double>& x) {
       return std::complex<double>(lgamma(x.real()),
                                   x.imag() * boost::math::digamma(x.real()));

From fe8a133558a4c02524d5eff52cd9097213151897 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Thu, 19 Dec 2019 13:16:11 +0000
Subject: [PATCH 28/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
index d7c9d1be6b3..7a6dc504982 100644
--- a/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/scal/prob/neg_binomial_2_test.cpp
@@ -531,7 +531,7 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   auto nb2_log_for_test = [](int n, const std::complex<double>& mu,
                              const std::complex<double>& phi) {
     // Using first-order Taylor expansion of lgamma(a + b*i) around b = 0
-    // Which happens to work nice in this case, as b is always 0 or the very 
+    // Which happens to work nice in this case, as b is always 0 or the very
     // small complex step
     auto lgamma_c_approx = [](const std::complex<double>& x) {
       return std::complex<double>(lgamma(x.real()),

From 6cd8b9d851fae3b388a4590a190e274b18012472 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 2 Jan 2020 11:21:08 +0100
Subject: [PATCH 29/82] Fixed #1531 for neg_binomial_2_lpmf

---
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    | 19 +++++++++----------
 1 file changed, 9 insertions(+), 10 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index b6b6b9fc779..030b8aba283 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -53,25 +53,24 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   scalar_seq_view<T_n> n_vec(n);
   scalar_seq_view<T_location> mu_vec(mu);
   scalar_seq_view<T_precision> phi_vec(phi);
-  size_t size = max_size(n, mu, phi);
+  size_t size_max = max_size(n, mu, phi);
 
   operands_and_partials<T_location, T_precision> ops_partials(mu, phi);
 
   size_t len_ep = max_size(mu, phi);
   size_t len_np = max_size(n, phi);
 
-  VectorBuilder<true, T_partials_return, T_location> mu__(length(mu));
-  for (size_t i = 0, size = length(mu); i < size; ++i) {
+  size_t len_mu = length(mu);
+  VectorBuilder<true, T_partials_return, T_location> mu__(len_mu);
+  for (size_t i = 0; i < len_mu; ++i) {
     mu__[i] = value_of(mu_vec[i]);
   }
 
-  VectorBuilder<true, T_partials_return, T_precision> phi__(length(phi));
-  for (size_t i = 0, size = length(phi); i < size; ++i) {
+  size_t len_phi = length(phi);
+  VectorBuilder<true, T_partials_return, T_precision> phi__(len_phi);
+  VectorBuilder<true, T_partials_return, T_precision> log_phi(len_phi);
+  for (size_t i = 0; i < len_phi; ++i) {
     phi__[i] = value_of(phi_vec[i]);
-  }
-
-  VectorBuilder<true, T_partials_return, T_precision> log_phi(length(phi));
-  for (size_t i = 0, size = length(phi); i < size; ++i) {
     log_phi[i] = log(phi__[i]);
   }
 
@@ -86,7 +85,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     n_plus_phi[i] = n_vec[i] + phi__[i];
   }
 
-  for (size_t i = 0; i < size; i++) {
+  for (size_t i = 0; i < size_max; i++) {
     if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
       // Phi is large, deferring to Poisson.
       // Copying the code here as just calling

From fdab10cb0592cb437576a73090461c5a2dc50e6d Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 2 Jan 2020 11:54:18 +0100
Subject: [PATCH 30/82] Moved tests touched by the flattening

---
 .../math/prim/prob/neg_binomial_2_test.cpp    | 70 +++++++++++++++++--
 1 file changed, 63 insertions(+), 7 deletions(-)

diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index 2414d2026db..fed29c8eb2c 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -239,16 +239,72 @@ TEST(ProbDistributionsNegBinomial, chiSquareGoodnessFitTest4) {
 }
 
 TEST(ProbDistributionsNegBinomial, extreme_values) {
-  int N = 100;
-  double mu = 8;
-  double phi = 1e12;
-  for (int n = 0; n < 10; ++n) {
-    phi *= 10;
-    double logp = stan::math::neg_binomial_2_log<false>(N, mu, phi);
-    EXPECT_LT(logp, 0);
+  std::array<unsigned int, 5> n_to_test = {1, 5, 100, 12985, 1968422};
+  std::array<double, 6> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
+  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
+       ++mu_iter) {
+    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
+      double mu = *mu_iter;
+      unsigned int n = *n_iter;
+      // Test just before cutoff
+      double logp
+          = stan::math::neg_binomial_2_log<false>(n, mu, phi_cutoff - 1e-8);
+      EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << mu
+                         << ", phi = " << (phi_cutoff - 1e-8);
+
+      // Test across a range of phi
+      double phi = 1e12;
+      for (int i = 0; i < 10; ++i) {
+        phi *= 10;
+        double logp = stan::math::neg_binomial_2_log<false>(n, mu, phi);
+        EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << mu
+                           << ", phi = " << phi;
+      }
+    }
   }
 }
 
+TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
+  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  std::array<double, 7> mu_to_test
+      = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
+  std::array<unsigned int, 8> n_to_test
+      = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
+  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
+       ++mu_iter) {
+    double mu = *mu_iter;
+    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
+      unsigned int n = *n_iter;
+
+      double before_cutoff
+          = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff - 1e-8);
+      double after_cutoff
+          = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff + 1e-8);
+      double relative_error_at_cutoff = log(before_cutoff / after_cutoff);
+      EXPECT_NEAR(relative_error_at_cutoff, 0, 1e-8)
+          << "neg_binomial_2_lpmf changes too much around phi cutoff for n = "
+          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
+          << " value at cutoff - 1e-8: " << before_cutoff
+          << ", value at cutoff + 1e-8: " << after_cutoff;
+    }
+  }
+}
+
+TEST(ProbDistributionsNegativeBinomial2, vectorAroundCutoff) {
+  int y = 10;
+  double mu = 9.36;
+  std::vector<double> phi;
+  phi.push_back(1);
+  phi.push_back(stan::math::internal::neg_binomial_2_phi_cutoff + 1);
+  double vector_value = stan::math::neg_binomial_2_lpmf(y, mu, phi);
+  double scalar_value = stan::math::neg_binomial_2_lpmf(y, mu, phi[0])
+                        + stan::math::neg_binomial_2_lpmf(y, mu, phi[1]);
+
+  EXPECT_FLOAT_EQ(vector_value, scalar_value);
+}
+
+
 TEST(ProbDistributionsNegativeBinomial2Log, distributionCheck) {
   check_counts_real_real(NegativeBinomial2LogTestRig());
 }

From 8c8283d562a5e02eb1eb66bd6a24a480538be832 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Thu, 2 Jan 2020 10:54:52 +0000
Subject: [PATCH 31/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 test/unit/math/prim/prob/neg_binomial_2_test.cpp | 1 -
 1 file changed, 1 deletion(-)

diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index fed29c8eb2c..edd30b227d4 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -304,7 +304,6 @@ TEST(ProbDistributionsNegativeBinomial2, vectorAroundCutoff) {
   EXPECT_FLOAT_EQ(vector_value, scalar_value);
 }
 
-
 TEST(ProbDistributionsNegativeBinomial2Log, distributionCheck) {
   check_counts_real_real(NegativeBinomial2LogTestRig());
 }

From d19a2a4fd9016de5f155532c860a36619a28bdfc Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 2 Jan 2020 12:05:17 +0100
Subject: [PATCH 32/82] Fixed missing length reference

---
 stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index b3c9b66afed..975e7d37933 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -58,13 +58,13 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   size_t len_ep = max_size(mu, phi);
   size_t len_np = max_size(n, phi);
 
-  size_t len_mu = length(mu);
+  size_t len_mu = size(mu);
   VectorBuilder<true, T_partials_return, T_location> mu__(len_mu);
   for (size_t i = 0; i < len_mu; ++i) {
     mu__[i] = value_of(mu_vec[i]);
   }
 
-  size_t len_phi = length(phi);
+  size_t len_phi = size(phi);
   VectorBuilder<true, T_partials_return, T_precision> phi__(len_phi);
   VectorBuilder<true, T_partials_return, T_precision> log_phi(len_phi);
   for (size_t i = 0; i < len_phi; ++i) {
@@ -83,7 +83,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     n_plus_phi[i] = n_vec[i] + phi__[i];
   }
 
-  for (size_t i = 0; i < size_max; i++) {
+  for (size_t i = 0; i < max_size_seq_view; i++) {
     if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
       // Phi is large, deferring to Poisson.
       // Copying the code here as just calling

From 3493b1476336bc640957180751331c5ee76fe2bf Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 2 Jan 2020 14:19:35 +0100
Subject: [PATCH 33/82] Using for range-based for loops

---
 .../unit/math/prim/prob/neg_binomial_2_test.cpp | 15 ++++-----------
 test/unit/math/rev/prob/neg_binomial_2_test.cpp | 17 +++++------------
 2 files changed, 9 insertions(+), 23 deletions(-)

diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index edd30b227d4..76863aff375 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -242,11 +242,8 @@ TEST(ProbDistributionsNegBinomial, extreme_values) {
   std::array<unsigned int, 5> n_to_test = {1, 5, 100, 12985, 1968422};
   std::array<double, 6> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
-       ++mu_iter) {
-    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
-      double mu = *mu_iter;
-      unsigned int n = *n_iter;
+  for (double mu : mu_to_test) {
+    for (unsigned int n : n_to_test) {
       // Test just before cutoff
       double logp
           = stan::math::neg_binomial_2_log<false>(n, mu, phi_cutoff - 1e-8);
@@ -271,12 +268,8 @@ TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
       = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
   std::array<unsigned int, 8> n_to_test
       = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
-  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
-       ++mu_iter) {
-    double mu = *mu_iter;
-    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
-      unsigned int n = *n_iter;
-
+  for (double mu : mu_to_test) {
+    for (unsigned int n : n_to_test) {
       double before_cutoff
           = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff - 1e-8);
       double after_cutoff
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 7a6dc504982..772b5e3e40e 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -490,8 +490,7 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::value_of;
   using stan::math::var;
 
-  for (auto iter = testValues.begin(); iter != testValues.end(); ++iter) {
-    TestValue t = *iter;
+  for (TestValue t: testValues) {
     unsigned int n = t.n;
     var mu(t.mu);
     var phi(t.phi);
@@ -545,11 +544,8 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   };
 
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
-       ++mu_iter) {
-    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
-      double mu_dbl = *mu_iter;
-      unsigned int n = *n_iter;
+  for (double mu_dbl : mu_to_test) {
+    for (unsigned int n : n_to_test) {
       double phi_dbl = 1.5;
 
       for (int k = 0; k < 20; ++k) {
@@ -622,11 +618,8 @@ TEST(ProbDistributionsNegBinomial, derivativesAtCutoff) {
       = {9.3e-6, 0.0028252, 4, 11, 8522, 984256, 5036842};
   std::array<unsigned int, 8> n_to_test
       = {0, 1, 5, 48, 1158, 224582, 48235842, 20314458};
-  for (auto mu_iter = mu_to_test.begin(); mu_iter != mu_to_test.end();
-       ++mu_iter) {
-    double mu = *mu_iter;
-    for (auto n_iter = n_to_test.begin(); n_iter != n_to_test.end(); ++n_iter) {
-      unsigned int n = *n_iter;
+  for (double mu : mu_to_test) {
+    for (unsigned int n : n_to_test) {
       var mu_before(mu);
       var phi_before(phi_cutoff - 1e-8);
       var value_before = neg_binomial_2_lpmf(n, mu_before, phi_before);

From 699ca2525e1718a1c5851970dcbfbc357c61ff38 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Thu, 2 Jan 2020 08:20:28 -0500
Subject: [PATCH 34/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 test/unit/math/rev/prob/neg_binomial_2_test.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 772b5e3e40e..fa14bde0406 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -490,7 +490,7 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   using stan::math::value_of;
   using stan::math::var;
 
-  for (TestValue t: testValues) {
+  for (TestValue t : testValues) {
     unsigned int n = t.n;
     var mu(t.mu);
     var phi(t.phi);

From f5bee192932b54a22ec8fa7d49c3439300634a4d Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Fri, 3 Jan 2020 09:02:37 +0100
Subject: [PATCH 35/82] Addressing review

---
 .../prim/scal/prob/neg_binomial_2_lpmf.hpp    | 34 +++++++++----------
 .../math/prim/prob/neg_binomial_2_test.cpp    | 12 +++----
 .../math/rev/prob/neg_binomial_2_test.cpp     | 19 ++++-------
 3 files changed, 29 insertions(+), 36 deletions(-)

diff --git a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
index 975e7d37933..99f28accde8 100644
--- a/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/scal/prob/neg_binomial_2_lpmf.hpp
@@ -87,7 +87,21 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
       // Phi is large, deferring to Poisson.
       // Copying the code here as just calling
-      // poisson_lpmf does not preserve propto logic correctly
+      // poisson_lpmf does not preserve propto logic correctly.
+      // Note that Poisson can be seen as first term of Taylor series for 
+      // phi -> Inf. Similarly, the derivativew wrt. mu and phi can be obtained
+      // via the Same Taylor expansions:
+      // 
+      // For mu, the expansions can be obtained in Mathematica via
+      // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
+      // Currently ignoring the 2nd order term (mu__[i] - n_vec[i]) / phi__[i]
+      //
+      // The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2),
+      // But the quadratic term is big enough to warrant inclusion here
+      // (can be around 1e-6 at cutoff).
+      // Expansion obtained in Mathematica via
+      // Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] -
+      //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 2}]
       if (include_summand<propto>::value) {
         logp -= lgamma(n_vec[i] + 1.0);
       }
@@ -96,36 +110,22 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       }
 
       if (!is_constant_all<T_location>::value) {
-        // This is the Taylor series of the full derivative for phi -> Inf
-        // Obtained in Mathematica via
-        // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
-        // Currently ignoring the term (mu__[i] - n_vec[i]) / phi__[i]
         ops_partials.edge1_.partials_[i] += n_vec[i] / mu__[i] - 1;
       }
-
-      // The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2),
-      // But the quadratic term is big enough to warrant inclusion here
-      // (can be around 1e-6 at cutoff).
-      // Expansion obtained in Mathematica via
-      // Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] -
-      //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 2}]
       if (!is_constant_all<T_precision>::value) {
         ops_partials.edge2_.partials_[i]
             += (mu__[i] * (-mu__[i] + 2 * n_vec[i]) + n_vec[i] * (1 - n_vec[i]))
                / (2 * square(phi__[i]));
       }
-
     } else {
       if (include_summand<propto, T_precision>::value) {
         logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
       }
-
-      logp += phi__[i] * (log_phi[i] - log_mu_plus_phi[i])
-              - (n_vec[i]) * log_mu_plus_phi[i];
-
       if (include_summand<propto, T_location>::value) {
         logp += multiply_log(n_vec[i], mu__[i]);
       }
+      logp += phi__[i] * (log_phi[i] - log_mu_plus_phi[i])
+              - n_vec[i] * log_mu_plus_phi[i];
 
       if (!is_constant_all<T_location>::value) {
         ops_partials.edge1_.partials_[i]
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index 76863aff375..b30ca51d33a 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -239,8 +239,8 @@ TEST(ProbDistributionsNegBinomial, chiSquareGoodnessFitTest4) {
 }
 
 TEST(ProbDistributionsNegBinomial, extreme_values) {
-  std::array<unsigned int, 5> n_to_test = {1, 5, 100, 12985, 1968422};
-  std::array<double, 6> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
+  std::vector<unsigned int> n_to_test = {1, 5, 100, 12985, 1968422};
+  std::vector<double> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (double mu : mu_to_test) {
     for (unsigned int n : n_to_test) {
@@ -251,9 +251,7 @@ TEST(ProbDistributionsNegBinomial, extreme_values) {
                          << ", phi = " << (phi_cutoff - 1e-8);
 
       // Test across a range of phi
-      double phi = 1e12;
-      for (int i = 0; i < 10; ++i) {
-        phi *= 10;
+      for (double phi = 1e12; phi < 1e22; phi *= 10) {
         double logp = stan::math::neg_binomial_2_log<false>(n, mu, phi);
         EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << mu
                            << ", phi = " << phi;
@@ -264,9 +262,9 @@ TEST(ProbDistributionsNegBinomial, extreme_values) {
 
 TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  std::array<double, 7> mu_to_test
+  std::vector<double> mu_to_test
       = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
-  std::array<unsigned int, 8> n_to_test
+  std::vector<unsigned int> n_to_test
       = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
   for (double mu : mu_to_test) {
     for (unsigned int n : n_to_test) {
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index fa14bde0406..b8bf3d69966 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -36,8 +36,7 @@ struct TestValue {
 // mus= {256*10^-7,314*10^-3,15*10^-1,8,180,  1123,10586};
 // phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324,150000};
 // ns = {0,6,14,1525,10233};
-//  WriteString[out, "std::array<TestValue, ",
-//      Length[mus]*Length[phis]*Length[ns], "> testValues = {"];
+//  WriteString[out, "std::vector<TestValue> testValues = {"];
 //    Block[{$MaxPrecision = 80, $MinPrecision = 40}, {
 //      For[i = 1, i <= Length[mus], i++, {
 //        For[j = 1, j <= Length[phis], j++, {
@@ -57,7 +56,7 @@ struct TestValue {
 //  WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::array<TestValue, 210> testValues = {
+std::vector<TestValue> testValues = {
     TestValue(0, 0.0000256, 0.0004, -0.000024814156367780882,
               -0.9398496240601504, -0.0018850149796021398),
     TestValue(0, 0.0000256, 0.065, -0.000025594960092480967,
@@ -524,8 +523,8 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
 
-  std::array<unsigned int, 5> n_to_test = {0, 7, 100, 835, 14238};
-  std::array<double, 6> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
+  std::vector<unsigned int> n_to_test = {0, 7, 100, 835, 14238};
+  std::vector<double> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
 
   auto nb2_log_for_test = [](int n, const std::complex<double>& mu,
                              const std::complex<double>& phi) {
@@ -546,9 +545,7 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (double mu_dbl : mu_to_test) {
     for (unsigned int n : n_to_test) {
-      double phi_dbl = 1.5;
-
-      for (int k = 0; k < 20; ++k) {
+      for (double phi_dbl = 1.5; phi_dbl < 1e22; phi_dbl *= 10) {
         var mu(mu_dbl);
         var phi(phi_dbl);
         var val = neg_binomial_2_lpmf(n, mu, phi);
@@ -587,8 +584,6 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
                     std::max(1e-10, fabs(gradients[1]) * 1e-5))
             << "grad_phi, n = " << n << ", mu = " << mu_dbl
             << ", phi = " << phi_dbl;
-
-        phi_dbl *= 10;
       }
     }
   }
@@ -614,9 +609,9 @@ TEST(ProbDistributionsNegBinomial, derivativesAtCutoff) {
   using stan::math::is_nan;
   using stan::math::var;
 
-  std::array<double, 7> mu_to_test
+  std::vector<double> mu_to_test
       = {9.3e-6, 0.0028252, 4, 11, 8522, 984256, 5036842};
-  std::array<unsigned int, 8> n_to_test
+  std::vector<unsigned int> n_to_test
       = {0, 1, 5, 48, 1158, 224582, 48235842, 20314458};
   for (double mu : mu_to_test) {
     for (unsigned int n : n_to_test) {

From b5f40b18a05a876c0f122210aef9d16e78fe5120 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Fri, 3 Jan 2020 03:13:49 -0500
Subject: [PATCH 36/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index dbde4e66d97..2189a1897ce 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -88,10 +88,10 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       // Phi is large, deferring to Poisson.
       // Copying the code here as just calling
       // poisson_lpmf does not preserve propto logic correctly.
-      // Note that Poisson can be seen as first term of Taylor series for 
+      // Note that Poisson can be seen as first term of Taylor series for
       // phi -> Inf. Similarly, the derivativew wrt. mu and phi can be obtained
       // via the Same Taylor expansions:
-      // 
+      //
       // For mu, the expansions can be obtained in Mathematica via
       // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
       // Currently ignoring the 2nd order term (mu__[i] - n_vec[i]) / phi__[i]

From 00f612abf7f94f18db9ed7ca5860933aeff20fcf Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Fri, 3 Jan 2020 11:50:04 +0100
Subject: [PATCH 37/82] Test large n in derivativesComplexStep, correctly name
 tests

---
 .../math/prim/prob/neg_binomial_2_test.cpp    | 12 +++----
 .../math/rev/prob/neg_binomial_2_test.cpp     | 31 ++++++++++++-------
 2 files changed, 26 insertions(+), 17 deletions(-)

diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index b30ca51d33a..ec75f6c215b 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -30,11 +30,11 @@ class NegativeBinomial2TestRig : public VectorIntRNGTestRig {
   }
 };
 
-TEST(ProbDistributionsNegativeBinomial2, errorCheck) {
+TEST(ProbDistributionsNegBinomial2, errorCheck) {
   check_dist_throws_all_types(NegativeBinomial2TestRig());
 }
 
-TEST(ProbDistributionsNegativeBinomial2, distributionCheck) {
+TEST(ProbDistributionsNegBinomial2, distributionCheck) {
   check_counts_real_real(NegativeBinomial2TestRig());
 }
 
@@ -201,7 +201,7 @@ TEST(ProbDistributionsNegBinomial2, chiSquareGoodnessFitTest3) {
   EXPECT_TRUE(chi < quantile(complement(mydist, 1e-6)));
 }
 
-TEST(ProbDistributionsNegBinomial, chiSquareGoodnessFitTest4) {
+TEST(ProbDistributionsNegBinomial2, chiSquareGoodnessFitTest4) {
   boost::random::mt19937 rng;
   int N = 1000;
   int K = stan::math::round(2 * std::pow(N, 0.4));
@@ -238,7 +238,7 @@ TEST(ProbDistributionsNegBinomial, chiSquareGoodnessFitTest4) {
   EXPECT_TRUE(chi < quantile(complement(mydist, 1e-6)));
 }
 
-TEST(ProbDistributionsNegBinomial, extreme_values) {
+TEST(ProbDistributionsNegBinomial2, extreme_values) {
   std::vector<unsigned int> n_to_test = {1, 5, 100, 12985, 1968422};
   std::vector<double> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
@@ -260,7 +260,7 @@ TEST(ProbDistributionsNegBinomial, extreme_values) {
   }
 }
 
-TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
+TEST(ProbDistributionsNegBinomial2, poissonCutoff) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   std::vector<double> mu_to_test
       = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
@@ -282,7 +282,7 @@ TEST(ProbDistributionsNegativeBinomial2, poissonCutoff) {
   }
 }
 
-TEST(ProbDistributionsNegativeBinomial2, vectorAroundCutoff) {
+TEST(ProbDistributionsNegBinomial2, vectorAroundCutoff) {
   int y = 10;
   double mu = 9.36;
   std::vector<double> phi;
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index b8bf3d69966..72a10d7d4e4 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -481,7 +481,7 @@ std::vector<TestValue> testValues = {
 
 }  // namespace neg_binomial_2_test_internal
 
-TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
+TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
   using neg_binomial_2_test_internal::TestValue;
   using neg_binomial_2_test_internal::testValues;
   using stan::math::is_nan;
@@ -517,13 +517,14 @@ TEST(ProbDistributionsNegBinomial, derivativesPrecomputed) {
   }
 }
 
-TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
+TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
   using boost::math::tools::complex_step_derivative;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
 
-  std::vector<unsigned int> n_to_test = {0, 7, 100, 835, 14238};
+  std::vector<unsigned int> n_to_test = 
+    {0, 7, 100, 835, 14238, 385000, 1000000};
   std::vector<double> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
 
   auto nb2_log_for_test = [](int n, const std::complex<double>& mu,
@@ -576,20 +577,28 @@ TEST(ProbDistributionsNegBinomial, derivativesComplexStep) {
         double complex_step_dphi
             = complex_step_derivative(nb2_log_phi, phi_dbl);
 
+        std::ostringstream message;
+        message << ", n = " << n << ", mu = " << mu_dbl 
+          << ", phi = " << phi_dbl;
+
         EXPECT_NEAR(gradients[0], complex_step_dmu,
                     std::max(1e-10, fabs(gradients[0]) * 1e-5))
-            << "grad_mu, n = " << n << ", mu = " << mu_dbl
-            << ", phi = " << phi_dbl;
-        EXPECT_NEAR(gradients[1], complex_step_dphi,
-                    std::max(1e-10, fabs(gradients[1]) * 1e-5))
-            << "grad_phi, n = " << n << ", mu = " << mu_dbl
-            << ", phi = " << phi_dbl;
+            << "grad_mu" << message.str();
+
+        double tolerance_phi;
+        if(phi < phi_cutoff || n < 100000) {
+          tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-5);
+        } else {
+          tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
+        }
+        EXPECT_NEAR(gradients[1], complex_step_dphi, tolerance_phi)                    
+            << "grad_phi" << message.str();
       }
     }
   }
 }
 
-TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
+TEST(ProbDistributionsNegBinomial2, proptoAtPoissonCutoff) {
   using stan::math::internal::neg_binomial_2_phi_cutoff;
   using stan::math::neg_binomial_2_lpmf;
   using stan::math::var;
@@ -604,7 +613,7 @@ TEST(ProbDistributionsNegativeBinomial2, proptoAtPoissonCutoff) {
   EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
 }
 
-TEST(ProbDistributionsNegBinomial, derivativesAtCutoff) {
+TEST(ProbDistributionsNegBinomial2, derivativesAtCutoff) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   using stan::math::is_nan;
   using stan::math::var;

From 5fcc1d4b55b46942daf1e643271b6f8279c8c3ed Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Fri, 3 Jan 2020 10:50:53 +0000
Subject: [PATCH 38/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 test/unit/math/rev/prob/neg_binomial_2_test.cpp | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 72a10d7d4e4..b3b7bc0bc10 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -523,8 +523,8 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
 
-  std::vector<unsigned int> n_to_test = 
-    {0, 7, 100, 835, 14238, 385000, 1000000};
+  std::vector<unsigned int> n_to_test
+      = {0, 7, 100, 835, 14238, 385000, 1000000};
   std::vector<double> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
 
   auto nb2_log_for_test = [](int n, const std::complex<double>& mu,
@@ -578,20 +578,20 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
             = complex_step_derivative(nb2_log_phi, phi_dbl);
 
         std::ostringstream message;
-        message << ", n = " << n << ", mu = " << mu_dbl 
-          << ", phi = " << phi_dbl;
+        message << ", n = " << n << ", mu = " << mu_dbl
+                << ", phi = " << phi_dbl;
 
         EXPECT_NEAR(gradients[0], complex_step_dmu,
                     std::max(1e-10, fabs(gradients[0]) * 1e-5))
             << "grad_mu" << message.str();
 
         double tolerance_phi;
-        if(phi < phi_cutoff || n < 100000) {
+        if (phi < phi_cutoff || n < 100000) {
           tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-5);
         } else {
           tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
         }
-        EXPECT_NEAR(gradients[1], complex_step_dphi, tolerance_phi)                    
+        EXPECT_NEAR(gradients[1], complex_step_dphi, tolerance_phi)
             << "grad_phi" << message.str();
       }
     }

From faaf5800c59fe1870e710620c8c85580d30fb75f Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 6 Jan 2020 12:20:02 +0100
Subject: [PATCH 39/82] Addressing review, boost upgrade

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   | 44 +++++++++----------
 .../math/rev/prob/neg_binomial_2_test.cpp     |  4 +-
 2 files changed, 24 insertions(+), 24 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 2189a1897ce..5edb5af97f2 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -59,44 +59,44 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   size_t len_np = max_size(n, phi);
 
   size_t len_mu = size(mu);
-  VectorBuilder<true, T_partials_return, T_location> mu__(len_mu);
+  VectorBuilder<true, T_partials_return, T_location> mu_val(len_mu);
   for (size_t i = 0; i < len_mu; ++i) {
-    mu__[i] = value_of(mu_vec[i]);
+    mu_val[i] = value_of(mu_vec[i]);
   }
 
   size_t len_phi = size(phi);
-  VectorBuilder<true, T_partials_return, T_precision> phi__(len_phi);
+  VectorBuilder<true, T_partials_return, T_precision> phi_val(len_phi);
   VectorBuilder<true, T_partials_return, T_precision> log_phi(len_phi);
   for (size_t i = 0; i < len_phi; ++i) {
-    phi__[i] = value_of(phi_vec[i]);
-    log_phi[i] = log(phi__[i]);
+    phi_val[i] = value_of(phi_vec[i]);
+    log_phi[i] = log(phi_val[i]);
   }
 
   VectorBuilder<true, T_partials_return, T_location, T_precision>
       log_mu_plus_phi(len_ep);
   for (size_t i = 0; i < len_ep; ++i) {
-    log_mu_plus_phi[i] = log(mu__[i] + phi__[i]);
+    log_mu_plus_phi[i] = log(mu_val[i] + phi_val[i]);
   }
 
   VectorBuilder<true, T_partials_return, T_n, T_precision> n_plus_phi(len_np);
   for (size_t i = 0; i < len_np; ++i) {
-    n_plus_phi[i] = n_vec[i] + phi__[i];
+    n_plus_phi[i] = n_vec[i] + phi_val[i];
   }
 
   for (size_t i = 0; i < max_size_seq_view; i++) {
-    if (phi__[i] > internal::neg_binomial_2_phi_cutoff) {
-      // Phi is large, deferring to Poisson.
+    if (phi_val[i] > internal::neg_binomial_2_phi_cutoff) {
+      // Phi is large, delegate to Poisson.
       // Copying the code here as just calling
       // poisson_lpmf does not preserve propto logic correctly.
       // Note that Poisson can be seen as first term of Taylor series for
-      // phi -> Inf. Similarly, the derivativew wrt. mu and phi can be obtained
+      // phi -> Inf. Similarly, the derivative wrt mu and phi can be obtained
       // via the Same Taylor expansions:
       //
       // For mu, the expansions can be obtained in Mathematica via
       // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
-      // Currently ignoring the 2nd order term (mu__[i] - n_vec[i]) / phi__[i]
+      // Currently ignoring the 2nd order term (mu_val[i] - n_vec[i]) / phi_val[i]
       //
-      // The derivative wrt. phi = 0 + O(1/neg_binomial_2_phi_cutoff^2),
+      // The derivative wrt phi = 0 + O(1/phi^2),
       // But the quadratic term is big enough to warrant inclusion here
       // (can be around 1e-6 at cutoff).
       // Expansion obtained in Mathematica via
@@ -106,36 +106,36 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
         logp -= lgamma(n_vec[i] + 1.0);
       }
       if (include_summand<propto, T_location>::value) {
-        logp += multiply_log(n_vec[i], mu__[i]) - mu__[i];
+        logp += multiply_log(n_vec[i], mu_val[i]) - mu_val[i];
       }
 
       if (!is_constant_all<T_location>::value) {
-        ops_partials.edge1_.partials_[i] += n_vec[i] / mu__[i] - 1;
+        ops_partials.edge1_.partials_[i] += n_vec[i] / mu_val[i] - 1;
       }
       if (!is_constant_all<T_precision>::value) {
         ops_partials.edge2_.partials_[i]
-            += (mu__[i] * (-mu__[i] + 2 * n_vec[i]) + n_vec[i] * (1 - n_vec[i]))
-               / (2 * square(phi__[i]));
+            += (mu_val[i] * (-mu_val[i] + 2 * n_vec[i]) + n_vec[i] * (1 - n_vec[i]))
+               / (2 * square(phi_val[i]));
       }
     } else {
       if (include_summand<propto, T_precision>::value) {
         logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
       }
       if (include_summand<propto, T_location>::value) {
-        logp += multiply_log(n_vec[i], mu__[i]);
+        logp += multiply_log(n_vec[i], mu_val[i]);
       }
-      logp += phi__[i] * (log_phi[i] - log_mu_plus_phi[i])
+      logp += phi_val[i] * (log_phi[i] - log_mu_plus_phi[i])
               - n_vec[i] * log_mu_plus_phi[i];
 
       if (!is_constant_all<T_location>::value) {
         ops_partials.edge1_.partials_[i]
-            += n_vec[i] / mu__[i]
-               - (n_vec[i] + phi__[i]) / (mu__[i] + phi__[i]);
+            += n_vec[i] / mu_val[i]
+               - (n_vec[i] + phi_val[i]) / (mu_val[i] + phi_val[i]);
       }
       if (!is_constant_all<T_precision>::value) {
         ops_partials.edge2_.partials_[i]
-            += 1.0 - n_plus_phi[i] / (mu__[i] + phi__[i]) + log_phi[i]
-               - log_mu_plus_phi[i] - digamma(phi__[i])
+            += 1.0 - n_plus_phi[i] / (mu_val[i] + phi_val[i]) + log_phi[i]
+               - log_mu_plus_phi[i] - digamma(phi_val[i])
                + digamma(n_plus_phi[i]);
       }
     }
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index b3b7bc0bc10..ba6a9213fa5 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -1,5 +1,5 @@
 #include <stan/math/rev/scal.hpp>
-#include <boost/math/tools/numerical_differentiation.hpp>
+#include <boost/math/differentiaton/finite_difference.hpp>
 #include <boost/math/special_functions/digamma.hpp>
 #include <gtest/gtest.h>
 #include <vector>
@@ -518,7 +518,7 @@ TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
 }
 
 TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
-  using boost::math::tools::complex_step_derivative;
+  using boost::math::differentiation::complex_step_derivative;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;

From 90add5d5cee373702f07c8d6fb18bf85530a4b32 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 6 Jan 2020 11:20:52 +0000
Subject: [PATCH 40/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 5edb5af97f2..8d3b5ebb115 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -94,7 +94,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       //
       // For mu, the expansions can be obtained in Mathematica via
       // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
-      // Currently ignoring the 2nd order term (mu_val[i] - n_vec[i]) / phi_val[i]
+      // Currently ignoring the 2nd order term (mu_val[i] - n_vec[i]) /
+      // phi_val[i]
       //
       // The derivative wrt phi = 0 + O(1/phi^2),
       // But the quadratic term is big enough to warrant inclusion here
@@ -114,7 +115,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       }
       if (!is_constant_all<T_precision>::value) {
         ops_partials.edge2_.partials_[i]
-            += (mu_val[i] * (-mu_val[i] + 2 * n_vec[i]) + n_vec[i] * (1 - n_vec[i]))
+            += (mu_val[i] * (-mu_val[i] + 2 * n_vec[i])
+                + n_vec[i] * (1 - n_vec[i]))
                / (2 * square(phi_val[i]));
       }
     } else {

From f186b88e986982a744722cddeba1c4bc7f19f73d Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 6 Jan 2020 12:30:28 +0100
Subject: [PATCH 41/82] Fixed include typo

---
 test/unit/math/rev/prob/neg_binomial_2_test.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index ba6a9213fa5..62b9dd93a05 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -1,5 +1,5 @@
 #include <stan/math/rev/scal.hpp>
-#include <boost/math/differentiaton/finite_difference.hpp>
+#include <boost/math/differentiation/finite_difference.hpp>
 #include <boost/math/special_functions/digamma.hpp>
 #include <gtest/gtest.h>
 #include <vector>

From d051928c6da4a6d6618a9b43f98fa12cb10f3870 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 6 Jan 2020 12:51:35 +0100
Subject: [PATCH 42/82] Removed use of unsigned int

---
 stan/math/prim/scal/fun/lgamma.hpp               | 11 -----------
 test/unit/math/prim/prob/neg_binomial_2_test.cpp |  8 ++++----
 test/unit/math/rev/prob/neg_binomial_2_test.cpp  | 14 +++++++-------
 3 files changed, 11 insertions(+), 22 deletions(-)

diff --git a/stan/math/prim/scal/fun/lgamma.hpp b/stan/math/prim/scal/fun/lgamma.hpp
index 6b5794855a5..43d74f1b684 100644
--- a/stan/math/prim/scal/fun/lgamma.hpp
+++ b/stan/math/prim/scal/fun/lgamma.hpp
@@ -89,17 +89,6 @@ inline double lgamma(int x) {
 #endif
 }
 
-inline double lgamma(unsigned int x) {
-#if !__MINGW32__
-  int sign = 1;
-  return ::lgamma_r(x, &sign);
-#else
-  if (unlikely(x == 0.0))
-    return std::numeric_limits<double>::infinity();
-  return boost::math::lgamma(x, boost_policy_t());
-#endif
-}
-
 }  // namespace math
 }  // namespace stan
 #endif
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index ec75f6c215b..6aabc0b4cdf 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -239,11 +239,11 @@ TEST(ProbDistributionsNegBinomial2, chiSquareGoodnessFitTest4) {
 }
 
 TEST(ProbDistributionsNegBinomial2, extreme_values) {
-  std::vector<unsigned int> n_to_test = {1, 5, 100, 12985, 1968422};
+  std::vector<int> n_to_test = {1, 5, 100, 12985, 1968422};
   std::vector<double> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (double mu : mu_to_test) {
-    for (unsigned int n : n_to_test) {
+    for (int n : n_to_test) {
       // Test just before cutoff
       double logp
           = stan::math::neg_binomial_2_log<false>(n, mu, phi_cutoff - 1e-8);
@@ -264,10 +264,10 @@ TEST(ProbDistributionsNegBinomial2, poissonCutoff) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   std::vector<double> mu_to_test
       = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
-  std::vector<unsigned int> n_to_test
+  std::vector<int> n_to_test
       = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
   for (double mu : mu_to_test) {
-    for (unsigned int n : n_to_test) {
+    for (int n : n_to_test) {
       double before_cutoff
           = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff - 1e-8);
       double after_cutoff
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 62b9dd93a05..ac3e02d64dd 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -7,14 +7,14 @@
 
 namespace neg_binomial_2_test_internal {
 struct TestValue {
-  unsigned int n;
+  int n;
   double mu;
   double phi;
   double value;
   double grad_mu;
   double grad_phi;
 
-  TestValue(unsigned int _n, double _mu, double _phi, double _value,
+  TestValue(int _n, double _mu, double _phi, double _value,
             double _grad_mu, double _grad_phi)
       : n(_n),
         mu(_mu),
@@ -490,7 +490,7 @@ TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
   using stan::math::var;
 
   for (TestValue t : testValues) {
-    unsigned int n = t.n;
+    int n = t.n;
     var mu(t.mu);
     var phi(t.phi);
     var val = neg_binomial_2_log(n, mu, phi);
@@ -523,7 +523,7 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
 
-  std::vector<unsigned int> n_to_test
+  std::vector<int> n_to_test
       = {0, 7, 100, 835, 14238, 385000, 1000000};
   std::vector<double> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
 
@@ -545,7 +545,7 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
 
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (double mu_dbl : mu_to_test) {
-    for (unsigned int n : n_to_test) {
+    for (int n : n_to_test) {
       for (double phi_dbl = 1.5; phi_dbl < 1e22; phi_dbl *= 10) {
         var mu(mu_dbl);
         var phi(phi_dbl);
@@ -620,10 +620,10 @@ TEST(ProbDistributionsNegBinomial2, derivativesAtCutoff) {
 
   std::vector<double> mu_to_test
       = {9.3e-6, 0.0028252, 4, 11, 8522, 984256, 5036842};
-  std::vector<unsigned int> n_to_test
+  std::vector<int> n_to_test
       = {0, 1, 5, 48, 1158, 224582, 48235842, 20314458};
   for (double mu : mu_to_test) {
-    for (unsigned int n : n_to_test) {
+    for (int n : n_to_test) {
       var mu_before(mu);
       var phi_before(phi_cutoff - 1e-8);
       var value_before = neg_binomial_2_lpmf(n, mu_before, phi_before);

From ab8827c06e5d56ec4308ef7300fcd7a667b1c643 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 6 Jan 2020 11:52:11 +0000
Subject: [PATCH 43/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 test/unit/math/prim/prob/neg_binomial_2_test.cpp |  3 +--
 test/unit/math/rev/prob/neg_binomial_2_test.cpp  | 10 ++++------
 2 files changed, 5 insertions(+), 8 deletions(-)

diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index 6aabc0b4cdf..b71056a2aa4 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -264,8 +264,7 @@ TEST(ProbDistributionsNegBinomial2, poissonCutoff) {
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   std::vector<double> mu_to_test
       = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
-  std::vector<int> n_to_test
-      = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
+  std::vector<int> n_to_test = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
   for (double mu : mu_to_test) {
     for (int n : n_to_test) {
       double before_cutoff
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index ac3e02d64dd..46c385816cf 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -14,8 +14,8 @@ struct TestValue {
   double grad_mu;
   double grad_phi;
 
-  TestValue(int _n, double _mu, double _phi, double _value,
-            double _grad_mu, double _grad_phi)
+  TestValue(int _n, double _mu, double _phi, double _value, double _grad_mu,
+            double _grad_phi)
       : n(_n),
         mu(_mu),
         phi(_phi),
@@ -523,8 +523,7 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
 
-  std::vector<int> n_to_test
-      = {0, 7, 100, 835, 14238, 385000, 1000000};
+  std::vector<int> n_to_test = {0, 7, 100, 835, 14238, 385000, 1000000};
   std::vector<double> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
 
   auto nb2_log_for_test = [](int n, const std::complex<double>& mu,
@@ -620,8 +619,7 @@ TEST(ProbDistributionsNegBinomial2, derivativesAtCutoff) {
 
   std::vector<double> mu_to_test
       = {9.3e-6, 0.0028252, 4, 11, 8522, 984256, 5036842};
-  std::vector<int> n_to_test
-      = {0, 1, 5, 48, 1158, 224582, 48235842, 20314458};
+  std::vector<int> n_to_test = {0, 1, 5, 48, 1158, 224582, 48235842, 20314458};
   for (double mu : mu_to_test) {
     for (int n : n_to_test) {
       var mu_before(mu);

From f15e7e0a5323258b5e24233db8e0fa7dda1ecc3f Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 6 Jan 2020 13:24:38 +0100
Subject: [PATCH 44/82] Tightened test acuraccy

---
 .../unit/math/rev/prob/neg_binomial_2_test.cpp | 18 +++++++++++++-----
 1 file changed, 13 insertions(+), 5 deletions(-)

diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 46c385816cf..d70b7c6b31b 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -580,16 +580,24 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
         message << ", n = " << n << ", mu = " << mu_dbl
                 << ", phi = " << phi_dbl;
 
-        EXPECT_NEAR(gradients[0], complex_step_dmu,
-                    std::max(1e-10, fabs(gradients[0]) * 1e-5))
-            << "grad_mu" << message.str();
-
         double tolerance_phi;
+        double tolerance_mu;
         if (phi < phi_cutoff || n < 100000) {
-          tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-5);
+          tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-8);
         } else {
           tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
         }
+
+        if (phi < phi_cutoff) {
+          tolerance_mu = std::max(1e-10, fabs(gradients[0]) * 1e-8);
+        } else {
+          tolerance_mu = std::max(1e-8, fabs(gradients[0]) * 1e-5);
+        }
+
+
+        EXPECT_NEAR(gradients[0], complex_step_dmu, tolerance_mu)
+            << "grad_mu" << message.str();
+
         EXPECT_NEAR(gradients[1], complex_step_dphi, tolerance_phi)
             << "grad_phi" << message.str();
       }

From cbd023409f18068173119d320595b00ff8f5ef2c Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 6 Jan 2020 12:25:14 +0000
Subject: [PATCH 45/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 test/unit/math/rev/prob/neg_binomial_2_test.cpp | 1 -
 1 file changed, 1 deletion(-)

diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index d70b7c6b31b..70a4f51c381 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -594,7 +594,6 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
           tolerance_mu = std::max(1e-8, fabs(gradients[0]) * 1e-5);
         }
 
-
         EXPECT_NEAR(gradients[0], complex_step_dmu, tolerance_mu)
             << "grad_mu" << message.str();
 

From 315d9b161a00a1a561e7f904b124d02f0b103bfd Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Tue, 7 Jan 2020 16:38:03 +0100
Subject: [PATCH 46/82] Precomputed (failing) test for binomial_coefficient_log

---
 .../fun/binomial_coefficient_log_test.cpp     | 26 +++++++++++++++++++
 1 file changed, 26 insertions(+)

diff --git a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
index d2a40da0887..1e3063f992e 100644
--- a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
@@ -1,3 +1,4 @@
+#include <test/unit/math/expect_near_rel.hpp>
 #include <stan/math/prim/scal.hpp>
 #include <gtest/gtest.h>
 #include <cmath>
@@ -41,3 +42,28 @@ TEST(MathFunctions, binomial_coefficient_log_nan) {
   EXPECT_TRUE(std::isnan(stan::math::binomial_coefficient_log(nan, 2.0)));
   EXPECT_TRUE(std::isnan(stan::math::binomial_coefficient_log(nan, nan)));
 }
+
+namespace binomial_coefficient_test_internal {
+  struct TestValue {
+    double n;
+    double k;
+    double val;
+  };  
+
+std::vector<TestValue> testValues = {  {0.00003,3.e-20,1.4804082055036736261e-24},  {0.00003,3.e-15,1.4804082053556342859e-19},  {0.00003,3.e-10,1.4803934014216156867e-14},  {0.00003,3.e-7,1.4656041234443424231e-11},  {0.00003,6.e-6,2.3686531286936713477e-10},  {0.00003,0.000015,3.7010205134852404454e-10},  {0.00003,0.0000291,4.3079878779785775469e-11},  {0.00003,0.0000299999982,8.8824487000750964998e-17},  {0.00003,0.00003,1.4804082055036751063e-28},  {0.002,2.e-18,6.5701370962226547789e-21},  {0.002,2.e-13,6.5701370955656467768e-16},  {0.002,2.e-8,6.5700713947654458316e-11},  {0.002,0.00002,6.5044356407218957555e-8},  {0.002,0.0004,1.0512217145828735086e-6},  {0.002,0.001,1.6425337349621531325e-6},  {0.002,0.00194,1.9119098219591897636e-7},  {0.002,0.00199999988,3.9420820212083508274e-13},  {0.002,0.002,6.5701370962226613484e-25},  {1,1.e-15,9.999999999999988551e-16},  {1,1.e-10,9.999999998855065933e-11},  {1,0.00001,9.9998855069266455991e-6},  {1,0.01,0.0098858370348613105263},  {1,0.2,0.15645796291768801671},  {1,0.5,0.24156447527049044469},  {1,0.97,0.028978328236256312961},  {1,0.99999994,5.9999995878237431346e-8},  {1,1.,9.999999999999999999e-20},  {8,8.e-15,2.1742857142857086459e-14},  {8,8.e-10,2.1742857137217315398e-9},  {8,0.00008,0.00021742293180507342042},  {8,0.08,0.21198226737825583898},  {8,1.6,2.9067860629113428343},  {8,4,4.2484952420493589891},  {8,7.76,0.60627458624545365112},  {8,7.99999952,1.3045712255376840361e-6},  {8,8.,2.1742857142857142852e-18},  {1325,1.325e-12,1.0290957946506935679e-11},  {1325,1.325e-7,1.0290957802047796044e-6},  {1325,0.01325,0.10276604269137043037},  {1325,13.25,71.989832127409062998},  {1325,265,659.43564932902941932},  {1325,662.5,914.5994503408452751},  {1325,1285.25,175.78626065119186267},  {1325,1324.9999205,0.00061745227641045219017},  {1325,1325.,1.029095794650838014e-15},  {845000,8.45e-10,1.2019540397111151912e-8},  {845000,0.0000845,0.0012019481673871213658},  {845000,8.45,103.7383038277367436},  {845000,8450,47315.861645757620061},  {845000,169000,422833.22169549650655},  {845000,422500,585702.31823555211409},  {845000,819650,113851.15813267856212},  {845000,844999.9493,0.7191087768194817628},  {845000,845000.,1.2019540397698355631e-12},  {3000000000000000.0,3,105.12040658150832885},  {3000000000000000.0,100,3199.999492802314355},  {3000000000000000.0,12895,350387.52436058836877},  {100000000000000000000.0,3,136.36334611041468604},  {100000000000000000000.0,100,4241.4308104325278778},  {100000000000000000000.0,12895,484680.0927690319003},};
+
+}
+
+TEST(MathFunctions, binomial_coefficient_log_precomputed) {
+  using binomial_coefficient_test_internal::TestValue;
+  using binomial_coefficient_test_internal::testValues;
+  using stan::test::expect_near_rel;
+
+  for (TestValue t : testValues) {
+    double val = stan::math::binomial_coefficient_log(t.n, t.k);
+
+    std::ostringstream msg;
+    msg << "n = " << t.n << ", k = " << t.k;
+    expect_near_rel(msg.str(), val, t.val);
+  }
+}

From c070cc6e9ccdf1e1bc8dcd3d73f9905320789005 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Tue, 7 Jan 2020 17:03:46 +0100
Subject: [PATCH 47/82] More tests, avoiding Poisson

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   |  48 +-
 .../math/prim/prob/neg_binomial_2_test.cpp    |  60 ++-
 .../prim/prob/neg_binomial_2_test_tools.hpp   |  17 +
 .../math/rev/prob/neg_binomial_2_test.cpp     | 505 +++---------------
 4 files changed, 159 insertions(+), 471 deletions(-)
 create mode 100644 test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 8d3b5ebb115..740620f463c 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -17,10 +17,10 @@ namespace stan {
 namespace math {
 
 namespace internal {
-// Exposing to let me us this in tests
+// When to switch to approximations for neg. binom for large phi
 // The current tests fail when the cutoff is 1e8 and pass with 1e9,
 // setting 1e10 to be safe
-constexpr double neg_binomial_2_phi_cutoff = 1e10;
+constexpr double neg_binomial_2_phi_cutoff = 1e15;
 }  // namespace internal
 
 // NegBinomial(n|mu, phi)  [mu >= 0; phi > 0;  n >= 0]
@@ -84,12 +84,13 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   }
 
   for (size_t i = 0; i < max_size_seq_view; i++) {
-    if (phi_val[i] > internal::neg_binomial_2_phi_cutoff) {
+    if(false) {
+    //if (phi_val[i] > internal::neg_binomial_2_phi_cutoff) {
       // Phi is large, delegate to Poisson.
       // Copying the code here as just calling
       // poisson_lpmf does not preserve propto logic correctly.
       // Note that Poisson can be seen as first term of Taylor series for
-      // phi -> Inf. Similarly, the derivative wrt mu and phi can be obtained
+      // phi -> Inf. Similarly, the derivative w.r.t. mu and phi can be obtained
       // via the Same Taylor expansions:
       //
       // For mu, the expansions can be obtained in Mathematica via
@@ -97,27 +98,31 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       // Currently ignoring the 2nd order term (mu_val[i] - n_vec[i]) /
       // phi_val[i]
       //
-      // The derivative wrt phi = 0 + O(1/phi^2),
+      // The derivative w.r.t. phi = 0 + O(1/phi^2),
       // But the quadratic term is big enough to warrant inclusion here
       // (can be around 1e-6 at cutoff).
       // Expansion obtained in Mathematica via
       // Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] -
       //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 2}]
-      if (include_summand<propto>::value) {
-        logp -= lgamma(n_vec[i] + 1.0);
-      }
-      if (include_summand<propto, T_location>::value) {
-        logp += multiply_log(n_vec[i], mu_val[i]) - mu_val[i];
-      }
-
-      if (!is_constant_all<T_location>::value) {
-        ops_partials.edge1_.partials_[i] += n_vec[i] / mu_val[i] - 1;
-      }
-      if (!is_constant_all<T_precision>::value) {
-        ops_partials.edge2_.partials_[i]
-            += (mu_val[i] * (-mu_val[i] + 2 * n_vec[i])
-                + n_vec[i] * (1 - n_vec[i]))
-               / (2 * square(phi_val[i]));
+      if(n_vec[i] == 0) {
+        logp += phi_val[i] * (-log1p(mu_val[i] / phi_val[i]));
+      } else {
+        if (include_summand<propto>::value) {
+          logp -= lgamma(n_vec[i] + 1.0);
+        }
+        if (include_summand<propto, T_location>::value) {
+          logp += multiply_log(n_vec[i], mu_val[i]) - mu_val[i];
+        }
+
+        if (!is_constant_all<T_location>::value) {
+          ops_partials.edge1_.partials_[i] += n_vec[i] / mu_val[i] - 1;
+        }
+        if (!is_constant_all<T_precision>::value) {
+          ops_partials.edge2_.partials_[i]
+              += (mu_val[i] * (-mu_val[i] + 2 * n_vec[i])
+                  + n_vec[i] * (1 - n_vec[i]))
+                / (2 * square(phi_val[i]));
+        }
       }
     } else {
       if (include_summand<propto, T_precision>::value) {
@@ -126,7 +131,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       if (include_summand<propto, T_location>::value) {
         logp += multiply_log(n_vec[i], mu_val[i]);
       }
-      logp += phi_val[i] * (log_phi[i] - log_mu_plus_phi[i])
+      // logp += phi_val[i] * (log_phi[i] - log_mu_plus_phi[i])
+      logp += - phi_val[i] * (log1p(mu_val[i] / phi_val[i]))
               - n_vec[i] * log_mu_plus_phi[i];
 
       if (!is_constant_all<T_location>::value) {
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index b71056a2aa4..1091a946652 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -3,6 +3,8 @@
 #include <test/unit/math/prim/prob/vector_rng_test_helper.hpp>
 #include <test/unit/math/prim/prob/NegativeBinomial2LogTestRig.hpp>
 #include <test/unit/math/prim/prob/VectorIntRNGTestRig.hpp>
+#include <test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp>
+#include <test/unit/math/expect_near_rel.hpp>
 #include <gtest/gtest.h>
 #include <boost/random/mersenne_twister.hpp>
 #include <boost/math/distributions.hpp>
@@ -239,7 +241,7 @@ TEST(ProbDistributionsNegBinomial2, chiSquareGoodnessFitTest4) {
 }
 
 TEST(ProbDistributionsNegBinomial2, extreme_values) {
-  std::vector<int> n_to_test = {1, 5, 100, 12985, 1968422};
+  std::vector<int> n_to_test = {0, 1, 5, 100, 12985, 1968422};
   std::vector<double> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
   double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (double mu : mu_to_test) {
@@ -261,26 +263,60 @@ TEST(ProbDistributionsNegBinomial2, extreme_values) {
 }
 
 TEST(ProbDistributionsNegBinomial2, poissonCutoff) {
-  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  using stan::test::expect_near_rel;
+  using namespace stan::test::neg_binomial_2_test_internal;
+
+  // std::vector<double> mu_to_test
+  //     = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345, 
+  //       static_cast<double>(std::numeric_limits<int>::max()) };
+  // std::vector<int> n_to_test = {0, 1, 3, 16, 24, 181, 2132, 121358, 865422242};
   std::vector<double> mu_to_test
-      = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345};
-  std::vector<int> n_to_test = {0, 3, 16, 24, 181, 2132, 121358, 865422242};
+      = {10};
+  std::vector<int> n_to_test = {16};
   for (double mu : mu_to_test) {
     for (int n : n_to_test) {
       double before_cutoff
-          = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff - 1e-8);
+          = stan::math::neg_binomial_2_lpmf(n, mu, just_below_phi_cutoff);
       double after_cutoff
-          = stan::math::neg_binomial_2_lpmf(n, mu, phi_cutoff + 1e-8);
-      double relative_error_at_cutoff = log(before_cutoff / after_cutoff);
-      EXPECT_NEAR(relative_error_at_cutoff, 0, 1e-8)
-          << "neg_binomial_2_lpmf changes too much around phi cutoff for n = "
-          << n << ", mu = " << mu << ", cutoff = " << phi_cutoff
-          << " value at cutoff - 1e-8: " << before_cutoff
-          << ", value at cutoff + 1e-8: " << after_cutoff;
+          = stan::math::neg_binomial_2_lpmf(n, mu, just_above_phi_cutoff);
+      std::ostringstream msg;
+      msg << "neg_binomial_2_lpmf changes too much around phi cutoff for n = "
+          << std::setprecision(17) << n << ", mu = " << mu 
+          << ", below cutoff = "  << just_below_phi_cutoff 
+          << ", above cutoff = " << just_above_phi_cutoff;
+      expect_near_rel(msg.str(), before_cutoff, after_cutoff);
+          
     }
   }
 }
 
+TEST(ProbDistributionsNegBinomial2, zeroOne) { 
+  using stan::test::expect_near_rel;
+  using namespace stan::test::neg_binomial_2_test_internal;
+
+  std::vector<double> mu_to_test
+      = {2.345e-5, 0.2, 13, 150, 1621, 18432, phi_cutoff };
+  double phi_start = 1e-8;
+  double phi_max = just_above_phi_cutoff * 1e10;
+  for (double mu : mu_to_test) {
+    for(double phi = phi_start; phi < phi_max; 
+        phi *= stan::math::pi()) {
+
+      std::ostringstream msg;
+      msg << ", mu = " << mu << ", phi = " << phi;
+
+      double expected_value_0 = phi * (-log1p(mu / phi)); 
+      double value_0 = stan::math::neg_binomial_2_lpmf(0, mu, phi);
+      expect_near_rel("n = 0 " + msg.str(), value_0, expected_value_0);
+
+      double expected_value_1 = (phi + 1) * (-log1p(mu / phi)) + log(mu);
+      double value_1 = stan::math::neg_binomial_2_lpmf(1, mu, phi);
+      expect_near_rel("n = 1 " + msg.str(), value_1, expected_value_1);
+    }
+  }
+
+}
+
 TEST(ProbDistributionsNegBinomial2, vectorAroundCutoff) {
   int y = 10;
   double mu = 9.36;
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp b/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp
new file mode 100644
index 00000000000..97eb4bb33fc
--- /dev/null
+++ b/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp
@@ -0,0 +1,17 @@
+#ifndef STAN_TEST_UNIT_PRIM_PROB_NEG_BINOMIAL_2_TEST_TOOLS_HPP
+#define STAN_TEST_UNIT_PRIM_PROB_NEG_BINOMIAL_2_TEST_TOOLS_HPP
+
+#include<limits>
+#include<cmath>
+#include<stan/math/prim/prob/neg_binomial_2_lpmf.hpp>
+
+namespace stan { namespace test { 
+namespace neg_binomial_2_test_internal {
+  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+  double just_below_phi_cutoff = std::nextafter(phi_cutoff, 0);
+  double just_above_phi_cutoff = 
+    std::nextafter(phi_cutoff, std::numeric_limits<double>::infinity());
+}
+}}
+
+#endif
\ No newline at end of file
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 70a4f51c381..424380f0b1a 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -1,6 +1,7 @@
 #include <stan/math/rev/scal.hpp>
 #include <boost/math/differentiation/finite_difference.hpp>
 #include <boost/math/special_functions/digamma.hpp>
+#include <test/unit/math/expect_near_rel.hpp>
 #include <gtest/gtest.h>
 #include <vector>
 #include <algorithm>
@@ -28,462 +29,39 @@ struct TestValue {
 // at https://www.wolframcloud.com/env/martin.modrak/NegBinomial2_Tests.nb
 // but is also presented below for convenience:
 //
-// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi ]+
-//   n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] + 
+//    n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
 // nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
 // nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
-// out = OpenWrite["nb_test.txt"]
-// mus= {256*10^-7,314*10^-3,15*10^-1,8,180,  1123,10586};
-// phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324,150000};
+// out = OpenWrite["nb_test.txt"] 
+// mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
+// phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
 // ns = {0,6,14,1525,10233};
 //  WriteString[out, "std::vector<TestValue> testValues = {"];
-//    Block[{$MaxPrecision = 80, $MinPrecision = 40}, {
-//      For[i = 1, i <= Length[mus], i++, {
+//      For[k = 1, k <= Length[ns], k++, {
+//   For[i = 1, i <= Length[mus], i++, {
 //        For[j = 1, j <= Length[phis], j++, {
-//        For[k = 1, k <= Length[ns], k++, {
 //          cmu = mus[[i]];
 //          cphi = phis[[j]];
 //     cn=ns[[k]];
-//          val = N[nb2[cn,cmu,cphi]];
-//     ddmu= N[nb2dmu[cn,cmu,cphi]];
-//     ddphi= N[nb2dphi[cn,cmu,cphi]];
-//          WriteString[out,"  TestValue(",CForm[cn],",",CForm[cmu],",",
-//            CForm[cphi],",", CForm[val],","CForm[ddmu],",",CForm[ddphi],"),"]
+//          val = N[nb2[cn,cmu,cphi], 20];
+//     ddmu= N[nb2dmu[cn,cmu,cphi], 20];
+//     ddphi= N[nb2dphi[cn,cmu,cphi], 20];
+//         WriteString[out,"  TestValue(",CForm[cn],",",CForm[cmu],",",
+//            CForm[cphi],",", CForm[val],",",CForm[ddmu],",",CForm[ddphi],"),"]
 //        }]
 //      }]
 //   }]
-//    }];
-//  WriteString[out,"};"];
+// WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::vector<TestValue> testValues = {
-    TestValue(0, 0.0000256, 0.0004, -0.000024814156367780882,
-              -0.9398496240601504, -0.0018850149796021398),
-    TestValue(0, 0.0000256, 0.065, -0.000025594960092480967,
-              -0.9996063088998794, -7.751668684718993e-8),
-    TestValue(0, 0.0000256, 4.42, -0.000025599925864390194, -0.9999942081783417,
-              -1.677258332222209e-11),
-    TestValue(0, 0.0000256, 800, -0.00002559999998652529, -0.999999968000001,
-              -8.881784197001252e-16),
-    TestValue(0, 0.0000256, 15324, -0.000025599996959613236,
-              -0.9999999983294179, 0.),
-    TestValue(0, 0.0000256, 150000, -0.00002560005540885868,
-              -0.9999999998293333, 0.),
-    TestValue(0, 0.314, 0.0004, -0.002666782716971683, -0.001272264631043257,
-              -5.66822905706025),
-    TestValue(0, 0.314, 0.065, -0.11460468078714132, -0.17150395778364116,
-              -0.9346528929704305),
-    TestValue(0, 0.314, 4.42, -0.30334820230965986, -0.9336713138994508,
-              -0.00230212890163628),
-    TestValue(0, 0.314, 800, -0.31393839362010567, -0.9996076539958066,
-              -7.698783210940974e-8),
-    TestValue(0, 0.314, 15324, -0.31399678298770084, -0.9999795096863716,
-              -2.099280749234822e-10),
-    TestValue(0, 0.314, 150000, -0.3139996713308335, -0.9999979066710487,
-              -2.190247982980509e-12),
-    TestValue(0, 1.5, 0.0004, -0.003291911100032755, -0.00026659557451346307,
-              -7.230044345656401),
-    TestValue(0, 1.5, 0.065, -0.2067814991501101, -0.04153354632587859,
-              -2.2227873794044952),
-    TestValue(0, 1.5, 4.42, -1.2915096474038796, -0.7466216216216216,
-              -0.03881837442792935),
-    TestValue(0, 1.5, 800, -1.4985955053447242, -0.9981285090455396,
-              -1.7534272203079126e-6),
-    TestValue(0, 1.5, 15324, -1.499926590534038, -0.9999021239111285,
-              -4.790177143831897e-9),
-    TestValue(0, 1.5, 150000, -1.4999925000758196, -0.999990000099999,
-              -4.999911595859885e-11),
-    TestValue(0, 8, 0.0004, -0.003961415020514468, -0.00004999750012499375,
-              -8.903587548786295),
-    TestValue(0, 8, 0.065, -0.3133586118431387, -0.008059516429014259,
-              -3.8289612370926864),
-    TestValue(0, 8, 4.42, -4.566604241437509, -0.355877616747182,
-              -0.3890459971629081),
-    TestValue(0, 8, 800, -7.9602646825343015, -0.9900990099009901,
-              -0.000049340754157967126),
-    TestValue(0, 8, 15324, -7.99791249886043, -0.9994782154969998,
-              -1.361769044194716e-7),
-    TestValue(0, 8, 150000, -7.999786674428577, -0.9999466695109595,
-              -1.4221228639144101e-9),
-    TestValue(0, 180, 0.0004, -0.0052068020335865025, -2.2222172839615914e-6,
-              -12.01700730618354),
-    TestValue(0, 180, 0.065, -0.5152345838836883, -0.00036098075694887956,
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-    TestValue(10233, 10586, 150000, -11.132452601363184, -0.031147729489111892,
-              -2.2067081495436014e-6),
-};
-
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TestValue(14,3,15324,-12.807159398994470731,3.6659489789260781627,-2.2763181750167069646e-7),  TestValue(14,180,0.0004,-10.467069325725552339,-2.049378161875689659e-6,2491.0847206783138),  TestValue(14,180,0.065,-5.6892191980516647312,-0.00033290447585285560461,11.462631774529800832),  TestValue(14,180,4.42,-9.6533765795967992717,-0.02210292930388364723,-1.3136829976451384132),  TestValue(14,180,800,-117.57055678993798607,-0.7528344671201814059,-0.016193696733894170103),  TestValue(14,180,15324,-131.59841923497641062,-0.9115153078775369797,-0.000057701678183561534688),  TestValue(14,1123,0.0004,-10.467775521386168611,-3.5174818911841171522e-7,2489.3192333086024842),  TestValue(14,1123,0.065,-5.8039572920094235935,-0.000057155792875192843316,9.6977197567649025541),  TestValue(14,1123,4.42,-17.371029398463366472,-0.0038715807735588641672,-3.0406118289506228066),  TestValue(14,1123,800,-640.64791491033069867,-0.41083032457540509991,-0.28296755763737220502),  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TestValue(1525,1.5,800,-8088.5487996808837997,1013.7658556872530672,-0.8354105724129184353),  TestValue(1525,1.5,15324,-8967.3316408400039725,1015.5672571857361913,-0.0046333275254863264045),  TestValue(1525,3,0.0004,-15.357522072066896545,0.067635426387592765409,1991.7174903993567368),  TestValue(1525,3,0.065,-42.491829475398155315,10.75910821098423056,-477.23846708705704922),  TestValue(1525,3,4.42,-1360.5497881858611964,302.21203953279424978,-199.67578957112613322),  TestValue(1525,3,800,-7035.8464992378503203,505.43794105437941054,-0.83186161385039575293),  TestValue(1525,3,15324,-7911.9312240083236782,507.23403144777190579,-0.0046236034557581425194),  TestValue(1525,180,0.0004,-15.159228863591761992,0.000016604901371824111996,2487.4167692289850077),  TestValue(1525,180,0.065,-10.618383986015501881,0.0026973284338680167964,7.7929628140754776749),  TestValue(1525,180,4.42,-30.75693264206759737,0.17908698743206931039,-5.0606677133089086733),  TestValue(1525,180,800,-1255.1060610431618143,6.0997732426303854875,-0.50811617220616562857),  TestValue(1525,180,15324,-1861.5172673616192307,7.3854704162366701066,-0.0035556000115225182714),  TestValue(1525,1123,0.0004,-15.157115486356269288,1.2750475385536655502e-7,2492.7002050120397202),  TestValue(1525,1123,0.065,-10.275036857130705184,0.000020718330690556828686,13.074039765317043251),  TestValue(1525,1123,4.42,-7.754816867258728553,0.0014034043922188128,0.065429851608050629578),  TestValue(1525,1123,800,-30.390182048283734404,0.1489213620192180795,-0.018804728472968400557),  TestValue(1525,1123,15324,-64.393847149111855643,0.33352757644959136666,-0.00029097614079605979039),  TestValue(1525,10586,0.0004,-15.157527333190073382,-3.2342406105998390275e-8,2491.6705880068073821),  TestValue(1525,10586,0.065,-10.341961135413218919,-5.2556089204012518156e-6,12.04444836642472918),  TestValue(1525,10586,4.42,-12.301855613945737855,-0.00035723444395259380558,-0.96243723577972978183),  TestValue(1525,10586,800,-744.01691670628731344,-0.060139948001942982935,-0.79245256852502796007),  TestValue(1525,10586,15324,-4300.6455934139147727,-0.50623127346524902759,-0.080624196979174112178),  TestValue(10233,0.0000256,0.0004,-28781.070852895156444,3.7568285855263157895e8,-2.4041193199521680582e7),  TestValue(10233,0.0000256,0.065,-80237.47905503410844,3.9956919271025565316e8,-157343.69709836101487),  TestValue(10233,0.0000256,4.42,-123371.16336416773985,3.9972424635504373549e8,-2307.2799792939510176),  TestValue(10233,0.0000256,800,-173733.65594636811604,3.9972654870875044132e8,-10.166635446653598855),  TestValue(10233,0.0000256,15324,-189611.39394380092393,3.997265608322239652e8,-0.1562719469099034673),  TestValue(10233,0.314,0.0004,-30.083534640956912654,41.460778593539812969,-30043.568270589792096),  TestValue(10233,0.314,0.065,-1936.7165917584869886,5589.0004705645093525,-26975.841613138526635),  TestValue(10233,0.314,4.42,-27734.555886932752049,30426.6413450334886,-2153.7342775414124626),  TestValue(10233,0.314,800,-77398.834534311059049,32575.386135464123325,-10.161617337135278412),  TestValue(10233,0.314,15324,-93272.766915544350705,32587.504232657958969,-0.15625826529496379204),  TestValue(10233,1.5,0.0004,-19.785223133324616937,1.8184484137563316449,-4317.6014472049352643),  TestValue(10233,1.5,0.065,-445.63039240802026812,283.30031948881789137,-6515.7878945898169301),  TestValue(10233,1.5,4.42,-14020.648493631530079,5092.7060810810810811,-1720.7211329093311099),  TestValue(10233,1.5,800,-61412.526640407231264,6808.2345601996257018,-10.142698900729563784),  TestValue(10233,1.5,15324,-77272.098984563728691,6820.3323871978075756,-0.15620659350885388317),  TestValue(10233,3,0.0004,-18.421373162288964031,0.45460605252632982269,-908.65830344005301507),  TestValue(10233,3,0.065,-230.93012488941404482,72.316476345840130506,-3316.4438994781907491),  TestValue(10233,3,4.42,-9239.7190298539962311,2031.293800539083558,-1371.3592560596120078),  TestValue(10233,3,800,-54340.180404088611315,3397.2602739726027397,-10.118854869649679896),  TestValue(10233,3,15324,-70181.625182690519906,3409.3325504012526913,-0.15614126136305778491),  TestValue(10233,180,0.0004,-17.081441774321808558,0.00012411083530925486832,2440.9430011582593451),  TestValue(10233,180,0.065,-15.542242814932986052,0.020160775275594924055,-38.663485376183506373),  TestValue(10233,180,4.42,-235.49737914944659778,1.3385587246502548531,-50.377534581977016966),  TestValue(10233,180,800,-14640.502463070959489,45.591836734693877551,-7.8364899652763980015),  TestValue(10233,180,15324,-28577.644697168082129,55.201586687306501548,-0.14858705144088737228),  TestValue(10233,1123,0.0004,-17.063078998820718915,2.8894734020457445678e-6,2486.8498802333634116),  TestValue(10233,1123,0.065,-12.558918107945625621,0.00046951241938052912769,7.2241249583196655846),  TestValue(10233,1123,4.42,-35.455061578657784001,0.031803517445555683105,-5.7569606052102630188),  TestValue(10233,1123,800,-3343.1303902972739556,3.3748099701370067269,-2.9898053694742608731),  TestValue(10233,1123,15324,-11352.060718035326883,7.5582990583477048515,-0.11311918072723555384),  TestValue(10233,10586,0.0004,-17.060718192656536162,-1.2600010324928188685e-9,2492.7518943576552348),  TestValue(10233,10586,0.065,-12.175300607237463447,-2.0474891832045490463e-7,13.125723676609068062),  TestValue(10233,10586,4.42,-9.4307920456266217014,-0.000013917201050134158853,0.11674937200192659959),  TestValue(10233,10586,800,-7.2703661972122617808,-0.0023429424616141566026,0.00008904830662418682316),  TestValue(10233,10586,15324,-9.3278240351663417157,-0.019721845219427536336,-0.00008059480750115928323),};
 }  // namespace neg_binomial_2_test_internal
 
 TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
   using neg_binomial_2_test_internal::TestValue;
   using neg_binomial_2_test_internal::testValues;
+  using stan::test::internal::expect_near_rel_finite;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
@@ -518,6 +96,7 @@ TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
 }
 
 TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
+  using stan::test::internal::expect_near_rel_finite;
   using boost::math::differentiation::complex_step_derivative;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
@@ -604,6 +183,56 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
   }
 }
 
+TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) { 
+  using stan::test::expect_near_rel;
+  using stan::math::var;
+
+  std::vector<double> mu_to_test
+      = {2.345e-5, 0.2, 13, 150, 1621, 18432, 1e10 };
+  double phi_start = 1e-8;
+  double phi_max = 1e20;
+  for (double mu_dbl : mu_to_test) {
+    for(double phi_dbl = phi_start; phi_dbl < phi_max; 
+        phi_dbl *= stan::math::pi()) {
+
+      std::ostringstream msg;
+      msg << ", mu = " << mu_dbl << ", phi = " << phi_dbl;
+
+      var mu0(mu_dbl);
+      var phi0(phi_dbl);
+      var val0 = neg_binomial_2_lpmf(0, mu0, phi0);
+
+      std::vector<var> x0;
+      x0.push_back(mu0);
+      x0.push_back(phi0);
+
+      std::vector<double> gradients0;
+      val0.grad(x0, gradients0);
+
+      var mu1(mu_dbl);
+      var phi1(phi_dbl);
+      var val1 = neg_binomial_2_lpmf(1, mu1, phi1);
+
+      std::vector<var> x1;
+      x1.push_back(mu1);
+      x1.push_back(phi1);
+
+      std::vector<double> gradients1;
+      val1.grad(x1, gradients1);
+
+      double expected_dmu_0 = - phi_dbl / (mu_dbl + phi_dbl); 
+      double expected_dphi_0 = mu_dbl / (mu_dbl + phi_dbl) 
+        - log1p(mu_dbl / phi_dbl);
+      expect_near_rel("dmu, n = 0 " + msg.str(), gradients0[0], expected_dmu_0);
+      expect_near_rel("dphi, n = 0 " + msg.str(), gradients0[1], expected_dphi_0);
+
+      double expected_dmu_1 = (phi_dbl * (1 - mu_dbl)) / (mu_dbl * (mu_dbl + phi_dbl));
+      expect_near_rel("dmu, n = 1 " + msg.str(), gradients1[0], expected_dmu_1);
+    }
+  }
+
+}
+
 TEST(ProbDistributionsNegBinomial2, proptoAtPoissonCutoff) {
   using stan::math::internal::neg_binomial_2_phi_cutoff;
   using stan::math::neg_binomial_2_lpmf;

From 7c4a8195cfcb7f1110577d98de1291e1a5e90f5a Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Tue, 7 Jan 2020 11:04:42 -0500
Subject: [PATCH 48/82] [Jenkins] auto-formatting by clang-format version
 5.0.2-svn328729-1~exp1~20180509124008.99 (branches/release_50)

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   |  10 +-
 .../math/prim/prob/neg_binomial_2_test.cpp    |  24 +-
 .../prim/prob/neg_binomial_2_test_tools.hpp   |  22 +-
 .../fun/binomial_coefficient_log_test.cpp     |  75 +++-
 .../math/rev/prob/neg_binomial_2_test.cpp     | 386 +++++++++++++++++-
 5 files changed, 463 insertions(+), 54 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 740620f463c..f9e867d23a9 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -84,8 +84,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   }
 
   for (size_t i = 0; i < max_size_seq_view; i++) {
-    if(false) {
-    //if (phi_val[i] > internal::neg_binomial_2_phi_cutoff) {
+    if (false) {
+      // if (phi_val[i] > internal::neg_binomial_2_phi_cutoff) {
       // Phi is large, delegate to Poisson.
       // Copying the code here as just calling
       // poisson_lpmf does not preserve propto logic correctly.
@@ -104,7 +104,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       // Expansion obtained in Mathematica via
       // Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] -
       //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 2}]
-      if(n_vec[i] == 0) {
+      if (n_vec[i] == 0) {
         logp += phi_val[i] * (-log1p(mu_val[i] / phi_val[i]));
       } else {
         if (include_summand<propto>::value) {
@@ -121,7 +121,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
           ops_partials.edge2_.partials_[i]
               += (mu_val[i] * (-mu_val[i] + 2 * n_vec[i])
                   + n_vec[i] * (1 - n_vec[i]))
-                / (2 * square(phi_val[i]));
+                 / (2 * square(phi_val[i]));
         }
       }
     } else {
@@ -132,7 +132,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
         logp += multiply_log(n_vec[i], mu_val[i]);
       }
       // logp += phi_val[i] * (log_phi[i] - log_mu_plus_phi[i])
-      logp += - phi_val[i] * (log1p(mu_val[i] / phi_val[i]))
+      logp += -phi_val[i] * (log1p(mu_val[i] / phi_val[i]))
               - n_vec[i] * log_mu_plus_phi[i];
 
       if (!is_constant_all<T_location>::value) {
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index 1091a946652..cacabc9ff2b 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -267,11 +267,11 @@ TEST(ProbDistributionsNegBinomial2, poissonCutoff) {
   using namespace stan::test::neg_binomial_2_test_internal;
 
   // std::vector<double> mu_to_test
-  //     = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345, 
+  //     = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345,
   //       static_cast<double>(std::numeric_limits<int>::max()) };
-  // std::vector<int> n_to_test = {0, 1, 3, 16, 24, 181, 2132, 121358, 865422242};
-  std::vector<double> mu_to_test
-      = {10};
+  // std::vector<int> n_to_test = {0, 1, 3, 16, 24, 181, 2132, 121358,
+  // 865422242};
+  std::vector<double> mu_to_test = {10};
   std::vector<int> n_to_test = {16};
   for (double mu : mu_to_test) {
     for (int n : n_to_test) {
@@ -281,31 +281,28 @@ TEST(ProbDistributionsNegBinomial2, poissonCutoff) {
           = stan::math::neg_binomial_2_lpmf(n, mu, just_above_phi_cutoff);
       std::ostringstream msg;
       msg << "neg_binomial_2_lpmf changes too much around phi cutoff for n = "
-          << std::setprecision(17) << n << ", mu = " << mu 
-          << ", below cutoff = "  << just_below_phi_cutoff 
+          << std::setprecision(17) << n << ", mu = " << mu
+          << ", below cutoff = " << just_below_phi_cutoff
           << ", above cutoff = " << just_above_phi_cutoff;
       expect_near_rel(msg.str(), before_cutoff, after_cutoff);
-          
     }
   }
 }
 
-TEST(ProbDistributionsNegBinomial2, zeroOne) { 
+TEST(ProbDistributionsNegBinomial2, zeroOne) {
   using stan::test::expect_near_rel;
   using namespace stan::test::neg_binomial_2_test_internal;
 
   std::vector<double> mu_to_test
-      = {2.345e-5, 0.2, 13, 150, 1621, 18432, phi_cutoff };
+      = {2.345e-5, 0.2, 13, 150, 1621, 18432, phi_cutoff};
   double phi_start = 1e-8;
   double phi_max = just_above_phi_cutoff * 1e10;
   for (double mu : mu_to_test) {
-    for(double phi = phi_start; phi < phi_max; 
-        phi *= stan::math::pi()) {
-
+    for (double phi = phi_start; phi < phi_max; phi *= stan::math::pi()) {
       std::ostringstream msg;
       msg << ", mu = " << mu << ", phi = " << phi;
 
-      double expected_value_0 = phi * (-log1p(mu / phi)); 
+      double expected_value_0 = phi * (-log1p(mu / phi));
       double value_0 = stan::math::neg_binomial_2_lpmf(0, mu, phi);
       expect_near_rel("n = 0 " + msg.str(), value_0, expected_value_0);
 
@@ -314,7 +311,6 @@ TEST(ProbDistributionsNegBinomial2, zeroOne) {
       expect_near_rel("n = 1 " + msg.str(), value_1, expected_value_1);
     }
   }
-
 }
 
 TEST(ProbDistributionsNegBinomial2, vectorAroundCutoff) {
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp b/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp
index 97eb4bb33fc..36d82734bae 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp
@@ -1,17 +1,19 @@
 #ifndef STAN_TEST_UNIT_PRIM_PROB_NEG_BINOMIAL_2_TEST_TOOLS_HPP
 #define STAN_TEST_UNIT_PRIM_PROB_NEG_BINOMIAL_2_TEST_TOOLS_HPP
 
-#include<limits>
-#include<cmath>
-#include<stan/math/prim/prob/neg_binomial_2_lpmf.hpp>
+#include <limits>
+#include <cmath>
+#include <stan/math/prim/prob/neg_binomial_2_lpmf.hpp>
 
-namespace stan { namespace test { 
+namespace stan {
+namespace test {
 namespace neg_binomial_2_test_internal {
-  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  double just_below_phi_cutoff = std::nextafter(phi_cutoff, 0);
-  double just_above_phi_cutoff = 
-    std::nextafter(phi_cutoff, std::numeric_limits<double>::infinity());
-}
-}}
+double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
+double just_below_phi_cutoff = std::nextafter(phi_cutoff, 0);
+double just_above_phi_cutoff
+    = std::nextafter(phi_cutoff, std::numeric_limits<double>::infinity());
+}  // namespace neg_binomial_2_test_internal
+}  // namespace test
+}  // namespace stan
 
 #endif
\ No newline at end of file
diff --git a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
index 1e3063f992e..a8e59a736b7 100644
--- a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
@@ -44,15 +44,76 @@ TEST(MathFunctions, binomial_coefficient_log_nan) {
 }
 
 namespace binomial_coefficient_test_internal {
-  struct TestValue {
-    double n;
-    double k;
-    double val;
-  };  
+struct TestValue {
+  double n;
+  double k;
+  double val;
+};
 
-std::vector<TestValue> testValues = {  {0.00003,3.e-20,1.4804082055036736261e-24},  {0.00003,3.e-15,1.4804082053556342859e-19},  {0.00003,3.e-10,1.4803934014216156867e-14},  {0.00003,3.e-7,1.4656041234443424231e-11},  {0.00003,6.e-6,2.3686531286936713477e-10},  {0.00003,0.000015,3.7010205134852404454e-10},  {0.00003,0.0000291,4.3079878779785775469e-11},  {0.00003,0.0000299999982,8.8824487000750964998e-17},  {0.00003,0.00003,1.4804082055036751063e-28},  {0.002,2.e-18,6.5701370962226547789e-21},  {0.002,2.e-13,6.5701370955656467768e-16},  {0.002,2.e-8,6.5700713947654458316e-11},  {0.002,0.00002,6.5044356407218957555e-8},  {0.002,0.0004,1.0512217145828735086e-6},  {0.002,0.001,1.6425337349621531325e-6},  {0.002,0.00194,1.9119098219591897636e-7},  {0.002,0.00199999988,3.9420820212083508274e-13},  {0.002,0.002,6.5701370962226613484e-25},  {1,1.e-15,9.999999999999988551e-16},  {1,1.e-10,9.999999998855065933e-11},  {1,0.00001,9.9998855069266455991e-6},  {1,0.01,0.0098858370348613105263},  {1,0.2,0.15645796291768801671},  {1,0.5,0.24156447527049044469},  {1,0.97,0.028978328236256312961},  {1,0.99999994,5.9999995878237431346e-8},  {1,1.,9.999999999999999999e-20},  {8,8.e-15,2.1742857142857086459e-14},  {8,8.e-10,2.1742857137217315398e-9},  {8,0.00008,0.00021742293180507342042},  {8,0.08,0.21198226737825583898},  {8,1.6,2.9067860629113428343},  {8,4,4.2484952420493589891},  {8,7.76,0.60627458624545365112},  {8,7.99999952,1.3045712255376840361e-6},  {8,8.,2.1742857142857142852e-18},  {1325,1.325e-12,1.0290957946506935679e-11},  {1325,1.325e-7,1.0290957802047796044e-6},  {1325,0.01325,0.10276604269137043037},  {1325,13.25,71.989832127409062998},  {1325,265,659.43564932902941932},  {1325,662.5,914.5994503408452751},  {1325,1285.25,175.78626065119186267},  {1325,1324.9999205,0.00061745227641045219017},  {1325,1325.,1.029095794650838014e-15},  {845000,8.45e-10,1.2019540397111151912e-8},  {845000,0.0000845,0.0012019481673871213658},  {845000,8.45,103.7383038277367436},  {845000,8450,47315.861645757620061},  {845000,169000,422833.22169549650655},  {845000,422500,585702.31823555211409},  {845000,819650,113851.15813267856212},  {845000,844999.9493,0.7191087768194817628},  {845000,845000.,1.2019540397698355631e-12},  {3000000000000000.0,3,105.12040658150832885},  {3000000000000000.0,100,3199.999492802314355},  {3000000000000000.0,12895,350387.52436058836877},  {100000000000000000000.0,3,136.36334611041468604},  {100000000000000000000.0,100,4241.4308104325278778},  {100000000000000000000.0,12895,484680.0927690319003},};
+std::vector<TestValue> testValues = {
+    {0.00003, 3.e-20, 1.4804082055036736261e-24},
+    {0.00003, 3.e-15, 1.4804082053556342859e-19},
+    {0.00003, 3.e-10, 1.4803934014216156867e-14},
+    {0.00003, 3.e-7, 1.4656041234443424231e-11},
+    {0.00003, 6.e-6, 2.3686531286936713477e-10},
+    {0.00003, 0.000015, 3.7010205134852404454e-10},
+    {0.00003, 0.0000291, 4.3079878779785775469e-11},
+    {0.00003, 0.0000299999982, 8.8824487000750964998e-17},
+    {0.00003, 0.00003, 1.4804082055036751063e-28},
+    {0.002, 2.e-18, 6.5701370962226547789e-21},
+    {0.002, 2.e-13, 6.5701370955656467768e-16},
+    {0.002, 2.e-8, 6.5700713947654458316e-11},
+    {0.002, 0.00002, 6.5044356407218957555e-8},
+    {0.002, 0.0004, 1.0512217145828735086e-6},
+    {0.002, 0.001, 1.6425337349621531325e-6},
+    {0.002, 0.00194, 1.9119098219591897636e-7},
+    {0.002, 0.00199999988, 3.9420820212083508274e-13},
+    {0.002, 0.002, 6.5701370962226613484e-25},
+    {1, 1.e-15, 9.999999999999988551e-16},
+    {1, 1.e-10, 9.999999998855065933e-11},
+    {1, 0.00001, 9.9998855069266455991e-6},
+    {1, 0.01, 0.0098858370348613105263},
+    {1, 0.2, 0.15645796291768801671},
+    {1, 0.5, 0.24156447527049044469},
+    {1, 0.97, 0.028978328236256312961},
+    {1, 0.99999994, 5.9999995878237431346e-8},
+    {1, 1., 9.999999999999999999e-20},
+    {8, 8.e-15, 2.1742857142857086459e-14},
+    {8, 8.e-10, 2.1742857137217315398e-9},
+    {8, 0.00008, 0.00021742293180507342042},
+    {8, 0.08, 0.21198226737825583898},
+    {8, 1.6, 2.9067860629113428343},
+    {8, 4, 4.2484952420493589891},
+    {8, 7.76, 0.60627458624545365112},
+    {8, 7.99999952, 1.3045712255376840361e-6},
+    {8, 8., 2.1742857142857142852e-18},
+    {1325, 1.325e-12, 1.0290957946506935679e-11},
+    {1325, 1.325e-7, 1.0290957802047796044e-6},
+    {1325, 0.01325, 0.10276604269137043037},
+    {1325, 13.25, 71.989832127409062998},
+    {1325, 265, 659.43564932902941932},
+    {1325, 662.5, 914.5994503408452751},
+    {1325, 1285.25, 175.78626065119186267},
+    {1325, 1324.9999205, 0.00061745227641045219017},
+    {1325, 1325., 1.029095794650838014e-15},
+    {845000, 8.45e-10, 1.2019540397111151912e-8},
+    {845000, 0.0000845, 0.0012019481673871213658},
+    {845000, 8.45, 103.7383038277367436},
+    {845000, 8450, 47315.861645757620061},
+    {845000, 169000, 422833.22169549650655},
+    {845000, 422500, 585702.31823555211409},
+    {845000, 819650, 113851.15813267856212},
+    {845000, 844999.9493, 0.7191087768194817628},
+    {845000, 845000., 1.2019540397698355631e-12},
+    {3000000000000000.0, 3, 105.12040658150832885},
+    {3000000000000000.0, 100, 3199.999492802314355},
+    {3000000000000000.0, 12895, 350387.52436058836877},
+    {100000000000000000000.0, 3, 136.36334611041468604},
+    {100000000000000000000.0, 100, 4241.4308104325278778},
+    {100000000000000000000.0, 12895, 484680.0927690319003},
+};
 
-}
+}  // namespace binomial_coefficient_test_internal
 
 TEST(MathFunctions, binomial_coefficient_log_precomputed) {
   using binomial_coefficient_test_internal::TestValue;
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 424380f0b1a..77c28956c4a 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -29,11 +29,11 @@ struct TestValue {
 // at https://www.wolframcloud.com/env/martin.modrak/NegBinomial2_Tests.nb
 // but is also presented below for convenience:
 //
-// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] + 
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] +
 //    n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
 // nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
 // nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
-// out = OpenWrite["nb_test.txt"] 
+// out = OpenWrite["nb_test.txt"]
 // mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
 // phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
 // ns = {0,6,14,1525,10233};
@@ -55,17 +55,368 @@ struct TestValue {
 // WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::vector<TestValue> testValues = {  TestValue(0,0.0000256,0.0004,-0.000024814156367781056525,-0.93984962406015037594,-0.001885014979603017252),  TestValue(0,0.0000256,0.065,-0.000025594960092486140389,-0.9996063088998794321,-7.7516686911183493794e-8),  TestValue(0,0.0000256,4.42,-0.000025599925864539648095,-0.9999942081783417725,-1.6772663823239562834e-11),  TestValue(0,0.0000256,800,-0.000025599999590400008738,-0.999999968000001024,-5.119999781546674531e-16),  TestValue(0,0.0000256,15324,-0.000025599999978616549228,-0.99999999832941790934,-1.3954222623666383236e-18),  TestValue(0,0.314,0.0004,-0.002666782716971682618,-0.0012722646310432569975,-5.668229057060249802),  TestValue(0,0.314,0.065,-0.11460468078714130042,-0.17150395778364116095,-0.93465289297043039811),  TestValue(0,0.314,4.42,-0.30334820230965961631,-0.93367131389945078158,-0.0023021289016362151355),  TestValue(0,0.314,800,-0.313938393619808991,-0.99960765399580664589,-7.6987831407130236997e-8),  TestValue(0,0.314,15324,-0.3139967829987878124,-0.99997950968637160528,-2.0992934397861783072e-10),  TestValue(0,1.5,0.0004,-0.0032919111000327549336,-0.00026659557451346307651,-7.2300443456564007971),  TestValue(0,1.5,0.065,-0.20678149915011007124,-0.041533546325878594249,-2.2227873794044950749),  TestValue(0,1.5,4.42,-1.2915096474038793989,-0.74662162162162162162,-0.038818374427929177938),  TestValue(0,1.5,800,-1.4985955053442782733,-0.99812850904553961323,-1.7534272199610668797e-6),  TestValue(0,1.5,15324,-1.4999265905382969801,-0.9999021239111285113,-4.7901769514626171505e-9),  TestValue(0,3,0.0004,-0.003569116649587854519,-0.00013331555792560991868,-7.9229249395275619074),  TestValue(0,3,0.065,-0.25047201260085385312,-0.021207177814029363785,-2.8746227562887040272),  TestValue(0,3,4.42,-2.2897339760163958674,-0.59568733153638814016,-0.11372669262607046311),  TestValue(0,3,800,-2.9943890230675014931,-0.99626400996264009963,-6.9962414744764927742e-6),  TestValue(0,3,15324,-2.9997063813121767354,-0.99980426697983949892,-1.9158207560574170962e-8),  TestValue(0,180,0.0004,-0.0052068020335865022334,-2.2222172839615911965e-6,-12.017007306183539545),  TestValue(0,180,0.065,-0.51523458388368826209,-0.00036098075694887957127,-6.9270468866598452194),  TestValue(0,180,4.42,-16.491356225074536835,-0.023967031775295521093,-2.7550431007966839452),  TestValue(0,180,800,-162.35267519735224589,-0.81632653061224489796,-0.019267374608935205317),  TestValue(0,180,15324,-178.95104102256056893,-0.98839009287925696594,-0.000067921189264833924309),  TestValue(0,1123,0.0004,-0.0059391221287133807664,-3.5618865318302647087e-7,-13.847805677972105099),  TestValue(0,1123,0.065,-0.63421701478373420435,-0.000057877326779839101032,-8.7572427201534599061),  TestValue(0,1123,4.42,-24.493639593452325812,-0.0039204555533873800358,-4.5454678748864927673),  TestValue(0,1123,800,-701.62401433668194795,-0.41601664066562662507,-0.29304665858647906001),  TestValue(0,1123,15324,-1083.7571513972578336,-0.93172007052957986259,-0.0024429334503092957394),  TestValue(0,10586,0.0004,-0.0068365334804239916148,-3.7785753342688330146e-8,-16.09133373884573238),  TestValue(0,10586,0.065,-0.78004301710859758932,-6.1401474485561915594e-6,-11.0006679418181807),  TestValue(0,10586,4.42,-34.39451907585020003,-0.00041735832950912239552,-6.7819827601055724777),  TestValue(0,10586,800,-2124.4224654744799162,-0.070261724925346917267,-1.7257898067684468125),  TestValue(0,10586,15324,-8048.2991567805804192,-0.59143187958317252026,-0.11664064731878857477),  TestValue(6,0.0000256,0.0004,-26.480362597222490265,220276.31578947368421,-11595.463497838709543),  TestValue(6,0.0000256,0.065,-51.419388136448102673,234281.72904210034202,-74.693807545973030394),  TestValue(6,0.0000256,4.42,-67.52038137511190777,234372.64254759067459,-0.43125592475849002503),  TestValue(6,0.0000256,800,-69.998079065742703551,234373.99250003224,-0.000023330384471037817491),  TestValue(6,0.0000256,15324,-70.015807321298395432,234373.99960845899308,-6.3861427657507748849e-8),  TestValue(6,0.314,0.0004,-9.6251974944123758225,0.023038524497171844865,2477.5305495558165941),  TestValue(6,0.314,0.065,-5.6231627412658002701,3.1056417323496294304,0.81175666468752807101),  TestValue(6,0.314,4.42,-11.748118636048988335,16.907181817937188357,-0.34352697543671422216),  TestValue(6,0.314,800,-13.827010724885832016,18.101175543376294868,-0.000020465017270475111936),  TestValue(6,0.314,15324,-13.842565956985816742,18.107909210435378814,-5.6049178830042368725e-8),  TestValue(6,1.5,0.0004,-9.6197839616192332262,0.00079978672354038922954,2491.0537701151673519),  TestValue(6,1.5,0.065,-4.8410045398874440986,0.12460063897763578275,11.520890928200777244),  TestValue(6,1.5,4.42,-4.6947113008756524511,2.2398648648648648649,-0.12612961153608977325),  TestValue(6,1.5,800,-5.6375883578559464151,2.9943855271366188397,-0.000011047869532026303582),  TestValue(6,1.5,15324,-5.6459956995659817151,2.9997063717333855339,-3.0329592747982916341e-8),  TestValue(6,3,0.0004,-9.6192613271356102502,0.00013331555792560991868,2492.3600897701139881),  TestValue(6,3,0.065,-4.7587824423548651205,0.021207177814029363785,12.745335721641112642),  TestValue(6,3,4.42,-2.8891081958287456629,0.59568733153638814016,0.0038502468520587354154),  TestValue(6,3,800,-2.9857172436024219525,0.99626400996264009963,-2.3069406647953774853e-6),  TestValue(6,3,15324,-2.9874796347761073428,0.99980426697983949892,-6.3824584044662864326e-9),  TestValue(6,180,0.0004,-9.620112399166720505,-2.1481433744962048232e-6,2490.2324075130827354),  TestValue(6,180,0.065,-4.897099604874425479,-0.00034894806505058358556,10.617175935000477685),  TestValue(6,180,4.42,-11.802883319144519128,-0.023168130716119003723,-1.861375256665487843),  TestValue(6,180,800,-138.97312319086169782,-0.78911564625850340136,-0.01791315421299756019),  TestValue(6,180,15324,-154.44163935948173426,-0.95544375644994840041,-0.000063439277219443465219),  TestValue(6,1123,0.0004,-9.6208335230756285524,-3.5428559715533443274e-7,2488.4295995707558483),  TestValue(6,1123,0.065,-5.0142630342277769584,-0.000057568097963562133439,8.8149588796763128876),  TestValue(6,1123,4.42,-19.683182166303213058,-0.0038995092191751589493,-3.6245874838477290528),  TestValue(6,1123,800,-671.30418475064697583,-0.4137939337698174,-0.28869011401594177783),  TestValue(6,1123,15324,-1048.6172073187539315,-0.92674204700048148398,-0.0024162628059421836267),  TestValue(6,10586,0.0004,-9.6217290240095637933,-3.7764336894543976284e-8,2486.1908475533798261),  TestValue(6,10586,0.065,-5.1597786035400147054,-6.1366672969700081899e-6,6.576309397642172055),  TestValue(6,10586,4.42,-29.562997357281896989,-0.00041712177651676884042,-5.856347033468783979),  TestValue(6,10586,800,-2091.3124520859014907,-0.07022190154073024605,-1.7188401003298574325),  TestValue(6,10586,15324,-8002.4249559448888988,-0.59109666408369216554,-0.11648073932479483488),  TestValue(14,0.0000256,0.0004,-49.814562438358640072,513979.32330827067669,-30391.559221530806766),  TestValue(14,0.0000256,0.065,-114.92817109028837255,546658.70057331266455,-196.8323920932659291),  TestValue(14,0.0000256,4.42,-161.64931287705226916,546870.83260332247849,-1.6501286909020252132),  TestValue(14,0.0000256,800,-173.09898662779720676,546873.98250003256,-0.00014060727924520899117),  TestValue(14,0.0000256,15324,-173.2061650426294071,546873.99908640208975,-3.8729368917100577369e-7),  TestValue(14,0.314,0.0004,-10.482321240387567839,0.055452910001458647348,2452.9820144458617505),  TestValue(14,0.314,0.065,-7.9175397204269351928,7.475169319193990219,-19.406538514452968028),  TestValue(14,0.314,4.42,-31.109603016060397045,40.694985993719373875,-1.442358303971396938),  TestValue(14,0.314,800,-41.614610107637548392,43.568886473205763553,-0.00013381877200270250453),  TestValue(14,0.314,15324,-41.716640281901644559,43.585094170597712707,-3.6878520278347562598e-7),  TestValue(14,1.5,0.0004,-10.468856159359487018,0.0022216297876121923043,2486.6186161358083867),  TestValue(14,1.5,0.065,-5.9696014927268124315,0.34611288604898828541,7.2989540823233662764),  TestValue(14,1.5,4.42,-13.334103973863653606,6.2218468468468468468,-0.88640946083488260684),  TestValue(14,1.5,800,-20.926415102268522946,8.3177375753794967769,-0.00010961017476158336951),  TestValue(14,1.5,15324,-21.010069937869350607,8.3325176992594042609,-3.0266583844869157132e-7),  TestValue(14,3,0.0004,-10.467267071498293274,0.00048882371239390303515,2490.5905361225120861),  TestValue(14,3,0.065,-5.7194959138831364402,0.077759651984774333877,11.025105769529760809),  TestValue(14,3,4.42,-7.7900642906041824751,2.1841868823000898473,-0.48324536699834770639),  TestValue(14,3,800,-12.744324478712668241,3.6529680365296803653,-0.000082224255065357307428),  TestValue(14,3,15324,-12.807159398994470731,3.6659489789260781627,-2.2763181750167069646e-7),  TestValue(14,180,0.0004,-10.467069325725552339,-2.049378161875689659e-6,2491.0847206783138),  TestValue(14,180,0.065,-5.6892191980516647312,-0.00033290447585285560461,11.462631774529800832),  TestValue(14,180,4.42,-9.6533765795967992717,-0.02210292930388364723,-1.3136829976451384132),  TestValue(14,180,800,-117.57055678993798607,-0.7528344671201814059,-0.016193696733894170103),  TestValue(14,180,15324,-131.59841923497641062,-0.9115153078775369797,-0.000057701678183561534688),  TestValue(14,1123,0.0004,-10.467775521386168611,-3.5174818911841171522e-7,2489.3192333086024842),  TestValue(14,1123,0.065,-5.8039572920094235935,-0.000057155792875192843316,9.6977197567649025541),  TestValue(14,1123,4.42,-17.371029398463366472,-0.0038715807735588641672,-3.0406118289506228066),  TestValue(14,1123,800,-640.64791491033069867,-0.41083032457540509991,-0.28296755763737220502),  TestValue(14,1123,15324,-1011.5999306403485179,-0.92010468229501697917,-0.0023809402304773394913),  TestValue(14,10586,0.0004,-10.468668475096403359,-3.7735781630351504468e-8,2487.0868493492232687),  TestValue(14,10586,0.065,-5.9490589506381604899,-6.1320270948550970306e-6,7.4654379275715350026),  TestValue(14,10586,4.42,-27.222758867549796685,-0.00041680637252696410027,-5.2660309311076446873),  TestValue(14,10586,800,-2056.9359371755272758,-0.070168803694574684427,-1.7096599947938850626),  TestValue(14,10586,15324,-7951.0953369235666607,-0.5906497100843850259,-0.11626776694982782037),  TestValue(1525,0.0000256,0.0004,-4301.7847274670157821,5.5987134868421052632e7,-3.5806687876344080158e6),  TestValue(1525,0.0000256,0.065,-11965.467128123482119,5.9546859198531040083e7,-23429.112689114767404),  TestValue(1525,0.0000256,4.42,-18367.342891800584413,5.9569966479379666941e7,-339.05708253439450269),  TestValue(1525,0.0000256,800,-24826.228135638531385,5.9570309593750093e7,-0.83897628761764105052),  TestValue(1525,0.0000256,15324,-25707.717028801610058,5.9570311400482904473e7,-0.0046430629133236893109),  TestValue(1525,0.314,0.0004,-17.094738795518807033,6.1777199721236284663,-2348.2711549792054389),  TestValue(1525,0.314,0.065,-296.5855682860990671,832.76969228442263415,-4001.4921811261694014),  TestValue(1525,0.314,4.42,-4115.1016067852616032,4533.6164996945796636,-316.17648561909186371),  TestValue(1525,0.314,800,-10469.942676752557863,4853.7827883447466615,-0.83822851603497641238),  TestValue(1525,0.314,15324,-11350.864477542964446,4855.5884035212585267,-0.0046410241529681445478),  TestValue(1525,1.5,0.0004,-15.560537541616769004,0.27077223851417399804,1484.2803077520377337),  TestValue(1525,1.5,0.065,-74.450927586875279684,42.184238551650692226,-953.4745083343278627),  TestValue(1525,1.5,4.42,-2072.1910365790187577,758.31869369369369369,-251.67662613527664787),  TestValue(1525,1.5,800,-8088.5487996808837997,1013.7658556872530672,-0.8354105724129184353),  TestValue(1525,1.5,15324,-8967.3316408400039725,1015.5672571857361913,-0.0046333275254863264045),  TestValue(1525,3,0.0004,-15.357522072066896545,0.067635426387592765409,1991.7174903993567368),  TestValue(1525,3,0.065,-42.491829475398155315,10.75910821098423056,-477.23846708705704922),  TestValue(1525,3,4.42,-1360.5497881858611964,302.21203953279424978,-199.67578957112613322),  TestValue(1525,3,800,-7035.8464992378503203,505.43794105437941054,-0.83186161385039575293),  TestValue(1525,3,15324,-7911.9312240083236782,507.23403144777190579,-0.0046236034557581425194),  TestValue(1525,180,0.0004,-15.159228863591761992,0.000016604901371824111996,2487.4167692289850077),  TestValue(1525,180,0.065,-10.618383986015501881,0.0026973284338680167964,7.7929628140754776749),  TestValue(1525,180,4.42,-30.75693264206759737,0.17908698743206931039,-5.0606677133089086733),  TestValue(1525,180,800,-1255.1060610431618143,6.0997732426303854875,-0.50811617220616562857),  TestValue(1525,180,15324,-1861.5172673616192307,7.3854704162366701066,-0.0035556000115225182714),  TestValue(1525,1123,0.0004,-15.157115486356269288,1.2750475385536655502e-7,2492.7002050120397202),  TestValue(1525,1123,0.065,-10.275036857130705184,0.000020718330690556828686,13.074039765317043251),  TestValue(1525,1123,4.42,-7.754816867258728553,0.0014034043922188128,0.065429851608050629578),  TestValue(1525,1123,800,-30.390182048283734404,0.1489213620192180795,-0.018804728472968400557),  TestValue(1525,1123,15324,-64.393847149111855643,0.33352757644959136666,-0.00029097614079605979039),  TestValue(1525,10586,0.0004,-15.157527333190073382,-3.2342406105998390275e-8,2491.6705880068073821),  TestValue(1525,10586,0.065,-10.341961135413218919,-5.2556089204012518156e-6,12.04444836642472918),  TestValue(1525,10586,4.42,-12.301855613945737855,-0.00035723444395259380558,-0.96243723577972978183),  TestValue(1525,10586,800,-744.01691670628731344,-0.060139948001942982935,-0.79245256852502796007),  TestValue(1525,10586,15324,-4300.6455934139147727,-0.50623127346524902759,-0.080624196979174112178),  TestValue(10233,0.0000256,0.0004,-28781.070852895156444,3.7568285855263157895e8,-2.4041193199521680582e7),  TestValue(10233,0.0000256,0.065,-80237.47905503410844,3.9956919271025565316e8,-157343.69709836101487),  TestValue(10233,0.0000256,4.42,-123371.16336416773985,3.9972424635504373549e8,-2307.2799792939510176),  TestValue(10233,0.0000256,800,-173733.65594636811604,3.9972654870875044132e8,-10.166635446653598855),  TestValue(10233,0.0000256,15324,-189611.39394380092393,3.997265608322239652e8,-0.1562719469099034673),  TestValue(10233,0.314,0.0004,-30.083534640956912654,41.460778593539812969,-30043.568270589792096),  TestValue(10233,0.314,0.065,-1936.7165917584869886,5589.0004705645093525,-26975.841613138526635),  TestValue(10233,0.314,4.42,-27734.555886932752049,30426.6413450334886,-2153.7342775414124626),  TestValue(10233,0.314,800,-77398.834534311059049,32575.386135464123325,-10.161617337135278412),  TestValue(10233,0.314,15324,-93272.766915544350705,32587.504232657958969,-0.15625826529496379204),  TestValue(10233,1.5,0.0004,-19.785223133324616937,1.8184484137563316449,-4317.6014472049352643),  TestValue(10233,1.5,0.065,-445.63039240802026812,283.30031948881789137,-6515.7878945898169301),  TestValue(10233,1.5,4.42,-14020.648493631530079,5092.7060810810810811,-1720.7211329093311099),  TestValue(10233,1.5,800,-61412.526640407231264,6808.2345601996257018,-10.142698900729563784),  TestValue(10233,1.5,15324,-77272.098984563728691,6820.3323871978075756,-0.15620659350885388317),  TestValue(10233,3,0.0004,-18.421373162288964031,0.45460605252632982269,-908.65830344005301507),  TestValue(10233,3,0.065,-230.93012488941404482,72.316476345840130506,-3316.4438994781907491),  TestValue(10233,3,4.42,-9239.7190298539962311,2031.293800539083558,-1371.3592560596120078),  TestValue(10233,3,800,-54340.180404088611315,3397.2602739726027397,-10.118854869649679896),  TestValue(10233,3,15324,-70181.625182690519906,3409.3325504012526913,-0.15614126136305778491),  TestValue(10233,180,0.0004,-17.081441774321808558,0.00012411083530925486832,2440.9430011582593451),  TestValue(10233,180,0.065,-15.542242814932986052,0.020160775275594924055,-38.663485376183506373),  TestValue(10233,180,4.42,-235.49737914944659778,1.3385587246502548531,-50.377534581977016966),  TestValue(10233,180,800,-14640.502463070959489,45.591836734693877551,-7.8364899652763980015),  TestValue(10233,180,15324,-28577.644697168082129,55.201586687306501548,-0.14858705144088737228),  TestValue(10233,1123,0.0004,-17.063078998820718915,2.8894734020457445678e-6,2486.8498802333634116),  TestValue(10233,1123,0.065,-12.558918107945625621,0.00046951241938052912769,7.2241249583196655846),  TestValue(10233,1123,4.42,-35.455061578657784001,0.031803517445555683105,-5.7569606052102630188),  TestValue(10233,1123,800,-3343.1303902972739556,3.3748099701370067269,-2.9898053694742608731),  TestValue(10233,1123,15324,-11352.060718035326883,7.5582990583477048515,-0.11311918072723555384),  TestValue(10233,10586,0.0004,-17.060718192656536162,-1.2600010324928188685e-9,2492.7518943576552348),  TestValue(10233,10586,0.065,-12.175300607237463447,-2.0474891832045490463e-7,13.125723676609068062),  TestValue(10233,10586,4.42,-9.4307920456266217014,-0.000013917201050134158853,0.11674937200192659959),  TestValue(10233,10586,800,-7.2703661972122617808,-0.0023429424616141566026,0.00008904830662418682316),  TestValue(10233,10586,15324,-9.3278240351663417157,-0.019721845219427536336,-0.00008059480750115928323),};
+std::vector<TestValue> testValues = {
+    TestValue(0, 0.0000256, 0.0004, -0.000024814156367781056525,
+              -0.93984962406015037594, -0.001885014979603017252),
+    TestValue(0, 0.0000256, 0.065, -0.000025594960092486140389,
+              -0.9996063088998794321, -7.7516686911183493794e-8),
+    TestValue(0, 0.0000256, 4.42, -0.000025599925864539648095,
+              -0.9999942081783417725, -1.6772663823239562834e-11),
+    TestValue(0, 0.0000256, 800, -0.000025599999590400008738,
+              -0.999999968000001024, -5.119999781546674531e-16),
+    TestValue(0, 0.0000256, 15324, -0.000025599999978616549228,
+              -0.99999999832941790934, -1.3954222623666383236e-18),
+    TestValue(0, 0.314, 0.0004, -0.002666782716971682618,
+              -0.0012722646310432569975, -5.668229057060249802),
+    TestValue(0, 0.314, 0.065, -0.11460468078714130042, -0.17150395778364116095,
+              -0.93465289297043039811),
+    TestValue(0, 0.314, 4.42, -0.30334820230965961631, -0.93367131389945078158,
+              -0.0023021289016362151355),
+    TestValue(0, 0.314, 800, -0.313938393619808991, -0.99960765399580664589,
+              -7.6987831407130236997e-8),
+    TestValue(0, 0.314, 15324, -0.3139967829987878124, -0.99997950968637160528,
+              -2.0992934397861783072e-10),
+    TestValue(0, 1.5, 0.0004, -0.0032919111000327549336,
+              -0.00026659557451346307651, -7.2300443456564007971),
+    TestValue(0, 1.5, 0.065, -0.20678149915011007124, -0.041533546325878594249,
+              -2.2227873794044950749),
+    TestValue(0, 1.5, 4.42, -1.2915096474038793989, -0.74662162162162162162,
+              -0.038818374427929177938),
+    TestValue(0, 1.5, 800, -1.4985955053442782733, -0.99812850904553961323,
+              -1.7534272199610668797e-6),
+    TestValue(0, 1.5, 15324, -1.4999265905382969801, -0.9999021239111285113,
+              -4.7901769514626171505e-9),
+    TestValue(0, 3, 0.0004, -0.003569116649587854519,
+              -0.00013331555792560991868, -7.9229249395275619074),
+    TestValue(0, 3, 0.065, -0.25047201260085385312, -0.021207177814029363785,
+              -2.8746227562887040272),
+    TestValue(0, 3, 4.42, -2.2897339760163958674, -0.59568733153638814016,
+              -0.11372669262607046311),
+    TestValue(0, 3, 800, -2.9943890230675014931, -0.99626400996264009963,
+              -6.9962414744764927742e-6),
+    TestValue(0, 3, 15324, -2.9997063813121767354, -0.99980426697983949892,
+              -1.9158207560574170962e-8),
+    TestValue(0, 180, 0.0004, -0.0052068020335865022334,
+              -2.2222172839615911965e-6, -12.017007306183539545),
+    TestValue(0, 180, 0.065, -0.51523458388368826209,
+              -0.00036098075694887957127, -6.9270468866598452194),
+    TestValue(0, 180, 4.42, -16.491356225074536835, -0.023967031775295521093,
+              -2.7550431007966839452),
+    TestValue(0, 180, 800, -162.35267519735224589, -0.81632653061224489796,
+              -0.019267374608935205317),
+    TestValue(0, 180, 15324, -178.95104102256056893, -0.98839009287925696594,
+              -0.000067921189264833924309),
+    TestValue(0, 1123, 0.0004, -0.0059391221287133807664,
+              -3.5618865318302647087e-7, -13.847805677972105099),
+    TestValue(0, 1123, 0.065, -0.63421701478373420435,
+              -0.000057877326779839101032, -8.7572427201534599061),
+    TestValue(0, 1123, 4.42, -24.493639593452325812, -0.0039204555533873800358,
+              -4.5454678748864927673),
+    TestValue(0, 1123, 800, -701.62401433668194795, -0.41601664066562662507,
+              -0.29304665858647906001),
+    TestValue(0, 1123, 15324, -1083.7571513972578336, -0.93172007052957986259,
+              -0.0024429334503092957394),
+    TestValue(0, 10586, 0.0004, -0.0068365334804239916148,
+              -3.7785753342688330146e-8, -16.09133373884573238),
+    TestValue(0, 10586, 0.065, -0.78004301710859758932,
+              -6.1401474485561915594e-6, -11.0006679418181807),
+    TestValue(0, 10586, 4.42, -34.39451907585020003, -0.00041735832950912239552,
+              -6.7819827601055724777),
+    TestValue(0, 10586, 800, -2124.4224654744799162, -0.070261724925346917267,
+              -1.7257898067684468125),
+    TestValue(0, 10586, 15324, -8048.2991567805804192, -0.59143187958317252026,
+              -0.11664064731878857477),
+    TestValue(6, 0.0000256, 0.0004, -26.480362597222490265,
+              220276.31578947368421, -11595.463497838709543),
+    TestValue(6, 0.0000256, 0.065, -51.419388136448102673,
+              234281.72904210034202, -74.693807545973030394),
+    TestValue(6, 0.0000256, 4.42, -67.52038137511190777, 234372.64254759067459,
+              -0.43125592475849002503),
+    TestValue(6, 0.0000256, 800, -69.998079065742703551, 234373.99250003224,
+              -0.000023330384471037817491),
+    TestValue(6, 0.0000256, 15324, -70.015807321298395432,
+              234373.99960845899308, -6.3861427657507748849e-8),
+    TestValue(6, 0.314, 0.0004, -9.6251974944123758225, 0.023038524497171844865,
+              2477.5305495558165941),
+    TestValue(6, 0.314, 0.065, -5.6231627412658002701, 3.1056417323496294304,
+              0.81175666468752807101),
+    TestValue(6, 0.314, 4.42, -11.748118636048988335, 16.907181817937188357,
+              -0.34352697543671422216),
+    TestValue(6, 0.314, 800, -13.827010724885832016, 18.101175543376294868,
+              -0.000020465017270475111936),
+    TestValue(6, 0.314, 15324, -13.842565956985816742, 18.107909210435378814,
+              -5.6049178830042368725e-8),
+    TestValue(6, 1.5, 0.0004, -9.6197839616192332262, 0.00079978672354038922954,
+              2491.0537701151673519),
+    TestValue(6, 1.5, 0.065, -4.8410045398874440986, 0.12460063897763578275,
+              11.520890928200777244),
+    TestValue(6, 1.5, 4.42, -4.6947113008756524511, 2.2398648648648648649,
+              -0.12612961153608977325),
+    TestValue(6, 1.5, 800, -5.6375883578559464151, 2.9943855271366188397,
+              -0.000011047869532026303582),
+    TestValue(6, 1.5, 15324, -5.6459956995659817151, 2.9997063717333855339,
+              -3.0329592747982916341e-8),
+    TestValue(6, 3, 0.0004, -9.6192613271356102502, 0.00013331555792560991868,
+              2492.3600897701139881),
+    TestValue(6, 3, 0.065, -4.7587824423548651205, 0.021207177814029363785,
+              12.745335721641112642),
+    TestValue(6, 3, 4.42, -2.8891081958287456629, 0.59568733153638814016,
+              0.0038502468520587354154),
+    TestValue(6, 3, 800, -2.9857172436024219525, 0.99626400996264009963,
+              -2.3069406647953774853e-6),
+    TestValue(6, 3, 15324, -2.9874796347761073428, 0.99980426697983949892,
+              -6.3824584044662864326e-9),
+    TestValue(6, 180, 0.0004, -9.620112399166720505, -2.1481433744962048232e-6,
+              2490.2324075130827354),
+    TestValue(6, 180, 0.065, -4.897099604874425479, -0.00034894806505058358556,
+              10.617175935000477685),
+    TestValue(6, 180, 4.42, -11.802883319144519128, -0.023168130716119003723,
+              -1.861375256665487843),
+    TestValue(6, 180, 800, -138.97312319086169782, -0.78911564625850340136,
+              -0.01791315421299756019),
+    TestValue(6, 180, 15324, -154.44163935948173426, -0.95544375644994840041,
+              -0.000063439277219443465219),
+    TestValue(6, 1123, 0.0004, -9.6208335230756285524,
+              -3.5428559715533443274e-7, 2488.4295995707558483),
+    TestValue(6, 1123, 0.065, -5.0142630342277769584,
+              -0.000057568097963562133439, 8.8149588796763128876),
+    TestValue(6, 1123, 4.42, -19.683182166303213058, -0.0038995092191751589493,
+              -3.6245874838477290528),
+    TestValue(6, 1123, 800, -671.30418475064697583, -0.4137939337698174,
+              -0.28869011401594177783),
+    TestValue(6, 1123, 15324, -1048.6172073187539315, -0.92674204700048148398,
+              -0.0024162628059421836267),
+    TestValue(6, 10586, 0.0004, -9.6217290240095637933,
+              -3.7764336894543976284e-8, 2486.1908475533798261),
+    TestValue(6, 10586, 0.065, -5.1597786035400147054,
+              -6.1366672969700081899e-6, 6.576309397642172055),
+    TestValue(6, 10586, 4.42, -29.562997357281896989,
+              -0.00041712177651676884042, -5.856347033468783979),
+    TestValue(6, 10586, 800, -2091.3124520859014907, -0.07022190154073024605,
+              -1.7188401003298574325),
+    TestValue(6, 10586, 15324, -8002.4249559448888988, -0.59109666408369216554,
+              -0.11648073932479483488),
+    TestValue(14, 0.0000256, 0.0004, -49.814562438358640072,
+              513979.32330827067669, -30391.559221530806766),
+    TestValue(14, 0.0000256, 0.065, -114.92817109028837255,
+              546658.70057331266455, -196.8323920932659291),
+    TestValue(14, 0.0000256, 4.42, -161.64931287705226916,
+              546870.83260332247849, -1.6501286909020252132),
+    TestValue(14, 0.0000256, 800, -173.09898662779720676, 546873.98250003256,
+              -0.00014060727924520899117),
+    TestValue(14, 0.0000256, 15324, -173.2061650426294071,
+              546873.99908640208975, -3.8729368917100577369e-7),
+    TestValue(14, 0.314, 0.0004, -10.482321240387567839,
+              0.055452910001458647348, 2452.9820144458617505),
+    TestValue(14, 0.314, 0.065, -7.9175397204269351928, 7.475169319193990219,
+              -19.406538514452968028),
+    TestValue(14, 0.314, 4.42, -31.109603016060397045, 40.694985993719373875,
+              -1.442358303971396938),
+    TestValue(14, 0.314, 800, -41.614610107637548392, 43.568886473205763553,
+              -0.00013381877200270250453),
+    TestValue(14, 0.314, 15324, -41.716640281901644559, 43.585094170597712707,
+              -3.6878520278347562598e-7),
+    TestValue(14, 1.5, 0.0004, -10.468856159359487018, 0.0022216297876121923043,
+              2486.6186161358083867),
+    TestValue(14, 1.5, 0.065, -5.9696014927268124315, 0.34611288604898828541,
+              7.2989540823233662764),
+    TestValue(14, 1.5, 4.42, -13.334103973863653606, 6.2218468468468468468,
+              -0.88640946083488260684),
+    TestValue(14, 1.5, 800, -20.926415102268522946, 8.3177375753794967769,
+              -0.00010961017476158336951),
+    TestValue(14, 1.5, 15324, -21.010069937869350607, 8.3325176992594042609,
+              -3.0266583844869157132e-7),
+    TestValue(14, 3, 0.0004, -10.467267071498293274, 0.00048882371239390303515,
+              2490.5905361225120861),
+    TestValue(14, 3, 0.065, -5.7194959138831364402, 0.077759651984774333877,
+              11.025105769529760809),
+    TestValue(14, 3, 4.42, -7.7900642906041824751, 2.1841868823000898473,
+              -0.48324536699834770639),
+    TestValue(14, 3, 800, -12.744324478712668241, 3.6529680365296803653,
+              -0.000082224255065357307428),
+    TestValue(14, 3, 15324, -12.807159398994470731, 3.6659489789260781627,
+              -2.2763181750167069646e-7),
+    TestValue(14, 180, 0.0004, -10.467069325725552339, -2.049378161875689659e-6,
+              2491.0847206783138),
+    TestValue(14, 180, 0.065, -5.6892191980516647312,
+              -0.00033290447585285560461, 11.462631774529800832),
+    TestValue(14, 180, 4.42, -9.6533765795967992717, -0.02210292930388364723,
+              -1.3136829976451384132),
+    TestValue(14, 180, 800, -117.57055678993798607, -0.7528344671201814059,
+              -0.016193696733894170103),
+    TestValue(14, 180, 15324, -131.59841923497641062, -0.9115153078775369797,
+              -0.000057701678183561534688),
+    TestValue(14, 1123, 0.0004, -10.467775521386168611,
+              -3.5174818911841171522e-7, 2489.3192333086024842),
+    TestValue(14, 1123, 0.065, -5.8039572920094235935,
+              -0.000057155792875192843316, 9.6977197567649025541),
+    TestValue(14, 1123, 4.42, -17.371029398463366472, -0.0038715807735588641672,
+              -3.0406118289506228066),
+    TestValue(14, 1123, 800, -640.64791491033069867, -0.41083032457540509991,
+              -0.28296755763737220502),
+    TestValue(14, 1123, 15324, -1011.5999306403485179, -0.92010468229501697917,
+              -0.0023809402304773394913),
+    TestValue(14, 10586, 0.0004, -10.468668475096403359,
+              -3.7735781630351504468e-8, 2487.0868493492232687),
+    TestValue(14, 10586, 0.065, -5.9490589506381604899,
+              -6.1320270948550970306e-6, 7.4654379275715350026),
+    TestValue(14, 10586, 4.42, -27.222758867549796685,
+              -0.00041680637252696410027, -5.2660309311076446873),
+    TestValue(14, 10586, 800, -2056.9359371755272758, -0.070168803694574684427,
+              -1.7096599947938850626),
+    TestValue(14, 10586, 15324, -7951.0953369235666607, -0.5906497100843850259,
+              -0.11626776694982782037),
+    TestValue(1525, 0.0000256, 0.0004, -4301.7847274670157821,
+              5.5987134868421052632e7, -3.5806687876344080158e6),
+    TestValue(1525, 0.0000256, 0.065, -11965.467128123482119,
+              5.9546859198531040083e7, -23429.112689114767404),
+    TestValue(1525, 0.0000256, 4.42, -18367.342891800584413,
+              5.9569966479379666941e7, -339.05708253439450269),
+    TestValue(1525, 0.0000256, 800, -24826.228135638531385,
+              5.9570309593750093e7, -0.83897628761764105052),
+    TestValue(1525, 0.0000256, 15324, -25707.717028801610058,
+              5.9570311400482904473e7, -0.0046430629133236893109),
+    TestValue(1525, 0.314, 0.0004, -17.094738795518807033,
+              6.1777199721236284663, -2348.2711549792054389),
+    TestValue(1525, 0.314, 0.065, -296.5855682860990671, 832.76969228442263415,
+              -4001.4921811261694014),
+    TestValue(1525, 0.314, 4.42, -4115.1016067852616032, 4533.6164996945796636,
+              -316.17648561909186371),
+    TestValue(1525, 0.314, 800, -10469.942676752557863, 4853.7827883447466615,
+              -0.83822851603497641238),
+    TestValue(1525, 0.314, 15324, -11350.864477542964446, 4855.5884035212585267,
+              -0.0046410241529681445478),
+    TestValue(1525, 1.5, 0.0004, -15.560537541616769004, 0.27077223851417399804,
+              1484.2803077520377337),
+    TestValue(1525, 1.5, 0.065, -74.450927586875279684, 42.184238551650692226,
+              -953.4745083343278627),
+    TestValue(1525, 1.5, 4.42, -2072.1910365790187577, 758.31869369369369369,
+              -251.67662613527664787),
+    TestValue(1525, 1.5, 800, -8088.5487996808837997, 1013.7658556872530672,
+              -0.8354105724129184353),
+    TestValue(1525, 1.5, 15324, -8967.3316408400039725, 1015.5672571857361913,
+              -0.0046333275254863264045),
+    TestValue(1525, 3, 0.0004, -15.357522072066896545, 0.067635426387592765409,
+              1991.7174903993567368),
+    TestValue(1525, 3, 0.065, -42.491829475398155315, 10.75910821098423056,
+              -477.23846708705704922),
+    TestValue(1525, 3, 4.42, -1360.5497881858611964, 302.21203953279424978,
+              -199.67578957112613322),
+    TestValue(1525, 3, 800, -7035.8464992378503203, 505.43794105437941054,
+              -0.83186161385039575293),
+    TestValue(1525, 3, 15324, -7911.9312240083236782, 507.23403144777190579,
+              -0.0046236034557581425194),
+    TestValue(1525, 180, 0.0004, -15.159228863591761992,
+              0.000016604901371824111996, 2487.4167692289850077),
+    TestValue(1525, 180, 0.065, -10.618383986015501881,
+              0.0026973284338680167964, 7.7929628140754776749),
+    TestValue(1525, 180, 4.42, -30.75693264206759737, 0.17908698743206931039,
+              -5.0606677133089086733),
+    TestValue(1525, 180, 800, -1255.1060610431618143, 6.0997732426303854875,
+              -0.50811617220616562857),
+    TestValue(1525, 180, 15324, -1861.5172673616192307, 7.3854704162366701066,
+              -0.0035556000115225182714),
+    TestValue(1525, 1123, 0.0004, -15.157115486356269288,
+              1.2750475385536655502e-7, 2492.7002050120397202),
+    TestValue(1525, 1123, 0.065, -10.275036857130705184,
+              0.000020718330690556828686, 13.074039765317043251),
+    TestValue(1525, 1123, 4.42, -7.754816867258728553, 0.0014034043922188128,
+              0.065429851608050629578),
+    TestValue(1525, 1123, 800, -30.390182048283734404, 0.1489213620192180795,
+              -0.018804728472968400557),
+    TestValue(1525, 1123, 15324, -64.393847149111855643, 0.33352757644959136666,
+              -0.00029097614079605979039),
+    TestValue(1525, 10586, 0.0004, -15.157527333190073382,
+              -3.2342406105998390275e-8, 2491.6705880068073821),
+    TestValue(1525, 10586, 0.065, -10.341961135413218919,
+              -5.2556089204012518156e-6, 12.04444836642472918),
+    TestValue(1525, 10586, 4.42, -12.301855613945737855,
+              -0.00035723444395259380558, -0.96243723577972978183),
+    TestValue(1525, 10586, 800, -744.01691670628731344,
+              -0.060139948001942982935, -0.79245256852502796007),
+    TestValue(1525, 10586, 15324, -4300.6455934139147727,
+              -0.50623127346524902759, -0.080624196979174112178),
+    TestValue(10233, 0.0000256, 0.0004, -28781.070852895156444,
+              3.7568285855263157895e8, -2.4041193199521680582e7),
+    TestValue(10233, 0.0000256, 0.065, -80237.47905503410844,
+              3.9956919271025565316e8, -157343.69709836101487),
+    TestValue(10233, 0.0000256, 4.42, -123371.16336416773985,
+              3.9972424635504373549e8, -2307.2799792939510176),
+    TestValue(10233, 0.0000256, 800, -173733.65594636811604,
+              3.9972654870875044132e8, -10.166635446653598855),
+    TestValue(10233, 0.0000256, 15324, -189611.39394380092393,
+              3.997265608322239652e8, -0.1562719469099034673),
+    TestValue(10233, 0.314, 0.0004, -30.083534640956912654,
+              41.460778593539812969, -30043.568270589792096),
+    TestValue(10233, 0.314, 0.065, -1936.7165917584869886,
+              5589.0004705645093525, -26975.841613138526635),
+    TestValue(10233, 0.314, 4.42, -27734.555886932752049, 30426.6413450334886,
+              -2153.7342775414124626),
+    TestValue(10233, 0.314, 800, -77398.834534311059049, 32575.386135464123325,
+              -10.161617337135278412),
+    TestValue(10233, 0.314, 15324, -93272.766915544350705,
+              32587.504232657958969, -0.15625826529496379204),
+    TestValue(10233, 1.5, 0.0004, -19.785223133324616937, 1.8184484137563316449,
+              -4317.6014472049352643),
+    TestValue(10233, 1.5, 0.065, -445.63039240802026812, 283.30031948881789137,
+              -6515.7878945898169301),
+    TestValue(10233, 1.5, 4.42, -14020.648493631530079, 5092.7060810810810811,
+              -1720.7211329093311099),
+    TestValue(10233, 1.5, 800, -61412.526640407231264, 6808.2345601996257018,
+              -10.142698900729563784),
+    TestValue(10233, 1.5, 15324, -77272.098984563728691, 6820.3323871978075756,
+              -0.15620659350885388317),
+    TestValue(10233, 3, 0.0004, -18.421373162288964031, 0.45460605252632982269,
+              -908.65830344005301507),
+    TestValue(10233, 3, 0.065, -230.93012488941404482, 72.316476345840130506,
+              -3316.4438994781907491),
+    TestValue(10233, 3, 4.42, -9239.7190298539962311, 2031.293800539083558,
+              -1371.3592560596120078),
+    TestValue(10233, 3, 800, -54340.180404088611315, 3397.2602739726027397,
+              -10.118854869649679896),
+    TestValue(10233, 3, 15324, -70181.625182690519906, 3409.3325504012526913,
+              -0.15614126136305778491),
+    TestValue(10233, 180, 0.0004, -17.081441774321808558,
+              0.00012411083530925486832, 2440.9430011582593451),
+    TestValue(10233, 180, 0.065, -15.542242814932986052,
+              0.020160775275594924055, -38.663485376183506373),
+    TestValue(10233, 180, 4.42, -235.49737914944659778, 1.3385587246502548531,
+              -50.377534581977016966),
+    TestValue(10233, 180, 800, -14640.502463070959489, 45.591836734693877551,
+              -7.8364899652763980015),
+    TestValue(10233, 180, 15324, -28577.644697168082129, 55.201586687306501548,
+              -0.14858705144088737228),
+    TestValue(10233, 1123, 0.0004, -17.063078998820718915,
+              2.8894734020457445678e-6, 2486.8498802333634116),
+    TestValue(10233, 1123, 0.065, -12.558918107945625621,
+              0.00046951241938052912769, 7.2241249583196655846),
+    TestValue(10233, 1123, 4.42, -35.455061578657784001,
+              0.031803517445555683105, -5.7569606052102630188),
+    TestValue(10233, 1123, 800, -3343.1303902972739556, 3.3748099701370067269,
+              -2.9898053694742608731),
+    TestValue(10233, 1123, 15324, -11352.060718035326883, 7.5582990583477048515,
+              -0.11311918072723555384),
+    TestValue(10233, 10586, 0.0004, -17.060718192656536162,
+              -1.2600010324928188685e-9, 2492.7518943576552348),
+    TestValue(10233, 10586, 0.065, -12.175300607237463447,
+              -2.0474891832045490463e-7, 13.125723676609068062),
+    TestValue(10233, 10586, 4.42, -9.4307920456266217014,
+              -0.000013917201050134158853, 0.11674937200192659959),
+    TestValue(10233, 10586, 800, -7.2703661972122617808,
+              -0.0023429424616141566026, 0.00008904830662418682316),
+    TestValue(10233, 10586, 15324, -9.3278240351663417157,
+              -0.019721845219427536336, -0.00008059480750115928323),
+};
 }  // namespace neg_binomial_2_test_internal
 
 TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
   using neg_binomial_2_test_internal::TestValue;
   using neg_binomial_2_test_internal::testValues;
-  using stan::test::internal::expect_near_rel_finite;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
   using stan::math::var;
+  using stan::test::internal::expect_near_rel_finite;
 
   for (TestValue t : testValues) {
     int n = t.n;
@@ -96,11 +447,11 @@ TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
 }
 
 TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
-  using stan::test::internal::expect_near_rel_finite;
   using boost::math::differentiation::complex_step_derivative;
   using stan::math::is_nan;
   using stan::math::neg_binomial_2_log;
   using stan::math::var;
+  using stan::test::internal::expect_near_rel_finite;
 
   std::vector<int> n_to_test = {0, 7, 100, 835, 14238, 385000, 1000000};
   std::vector<double> mu_to_test = {0.8, 8, 24, 271, 2586, 33294};
@@ -183,18 +534,16 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
   }
 }
 
-TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) { 
-  using stan::test::expect_near_rel;
+TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
   using stan::math::var;
+  using stan::test::expect_near_rel;
 
-  std::vector<double> mu_to_test
-      = {2.345e-5, 0.2, 13, 150, 1621, 18432, 1e10 };
+  std::vector<double> mu_to_test = {2.345e-5, 0.2, 13, 150, 1621, 18432, 1e10};
   double phi_start = 1e-8;
   double phi_max = 1e20;
   for (double mu_dbl : mu_to_test) {
-    for(double phi_dbl = phi_start; phi_dbl < phi_max; 
-        phi_dbl *= stan::math::pi()) {
-
+    for (double phi_dbl = phi_start; phi_dbl < phi_max;
+         phi_dbl *= stan::math::pi()) {
       std::ostringstream msg;
       msg << ", mu = " << mu_dbl << ", phi = " << phi_dbl;
 
@@ -220,17 +569,18 @@ TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
       std::vector<double> gradients1;
       val1.grad(x1, gradients1);
 
-      double expected_dmu_0 = - phi_dbl / (mu_dbl + phi_dbl); 
-      double expected_dphi_0 = mu_dbl / (mu_dbl + phi_dbl) 
-        - log1p(mu_dbl / phi_dbl);
+      double expected_dmu_0 = -phi_dbl / (mu_dbl + phi_dbl);
+      double expected_dphi_0
+          = mu_dbl / (mu_dbl + phi_dbl) - log1p(mu_dbl / phi_dbl);
       expect_near_rel("dmu, n = 0 " + msg.str(), gradients0[0], expected_dmu_0);
-      expect_near_rel("dphi, n = 0 " + msg.str(), gradients0[1], expected_dphi_0);
+      expect_near_rel("dphi, n = 0 " + msg.str(), gradients0[1],
+                      expected_dphi_0);
 
-      double expected_dmu_1 = (phi_dbl * (1 - mu_dbl)) / (mu_dbl * (mu_dbl + phi_dbl));
+      double expected_dmu_1
+          = (phi_dbl * (1 - mu_dbl)) / (mu_dbl * (mu_dbl + phi_dbl));
       expect_near_rel("dmu, n = 1 " + msg.str(), gradients1[0], expected_dmu_1);
     }
   }
-
 }
 
 TEST(ProbDistributionsNegBinomial2, proptoAtPoissonCutoff) {

From 70fedb4243a35b020a13b7f0b8830c77bc6a4538 Mon Sep 17 00:00:00 2001
From: martinmodrak <modrak.mar@gmail.com>
Date: Wed, 8 Jan 2020 15:11:29 +0100
Subject: [PATCH 49/82] Dummy and failing test for lgamma_stirling_diff

---
 .../prim/scal/fun/lgamma_stirling_diff.hpp    | 15 ++++++++++
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 28 +++++++++++++++++++
 2 files changed, 43 insertions(+)
 create mode 100644 stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
 create mode 100644 test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp

diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
new file mode 100644
index 00000000000..eb593dc17fc
--- /dev/null
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -0,0 +1,15 @@
+#ifndef STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_DIFF_HPP
+#define STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_DIFF_HPP
+
+#include <cmath>
+
+namespace stan {
+namespace math {
+
+double lgamma_stirling_diff(const double x) {
+    return std::log1p(1 / (12 * x));
+}
+
+}} //namespace
+
+#endif
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
new file mode 100644
index 00000000000..5bed2348434
--- /dev/null
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -0,0 +1,28 @@
+#include <stan/math/prim/scal.hpp>
+#include <stan/math/prim/scal/fun/lgamma_stirling_diff.hpp>
+#include <gtest/gtest.h>
+#include <cmath>
+#include <limits>
+#include <test/unit/math/expect_near_rel.hpp>
+
+TEST(MathFunctions, lgamma_stirling_diff_errors) {
+    //TODO[martinmodrak] nan, negative values, ...
+}
+
+TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
+  using stan::math::lgamma_stirling_diff;
+  using stan::test::expect_near_rel;
+
+  double start = std::nextafter(10, 11);
+  for(double x = start; x < 1e150; x *= 1.5) {
+      double stirling = x * (log(x) - 1) + log(x) 
+        + 0.5 * (stan::math::LOG_SQRT_PI + stan::math::LOG_TWO - log(x));
+      double lgamma_res = stan::math::lgamma(x);
+      double diff = lgamma_stirling_diff(x);
+
+      std::ostringstream msg;
+      msg << "x = " << x;
+      expect_near_rel(msg.str(), stirling + diff, lgamma_res);
+  }
+}
+

From 08e4203e8422e8b206a85a95de8bfc2c3a318ca3 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Wed, 8 Jan 2020 10:50:49 -0500
Subject: [PATCH 50/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 .../prim/scal/fun/lgamma_stirling_diff.hpp    |  7 +++----
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 20 +++++++++----------
 2 files changed, 13 insertions(+), 14 deletions(-)

diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
index eb593dc17fc..8e217aedaec 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -6,10 +6,9 @@
 namespace stan {
 namespace math {
 
-double lgamma_stirling_diff(const double x) {
-    return std::log1p(1 / (12 * x));
-}
+double lgamma_stirling_diff(const double x) { return std::log1p(1 / (12 * x)); }
 
-}} //namespace
+}  // namespace math
+}  // namespace stan
 
 #endif
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
index 5bed2348434..8d8f6c1fb48 100644
--- a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -6,7 +6,7 @@
 #include <test/unit/math/expect_near_rel.hpp>
 
 TEST(MathFunctions, lgamma_stirling_diff_errors) {
-    //TODO[martinmodrak] nan, negative values, ...
+  // TODO[martinmodrak] nan, negative values, ...
 }
 
 TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
@@ -14,15 +14,15 @@ TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
   using stan::test::expect_near_rel;
 
   double start = std::nextafter(10, 11);
-  for(double x = start; x < 1e150; x *= 1.5) {
-      double stirling = x * (log(x) - 1) + log(x) 
-        + 0.5 * (stan::math::LOG_SQRT_PI + stan::math::LOG_TWO - log(x));
-      double lgamma_res = stan::math::lgamma(x);
-      double diff = lgamma_stirling_diff(x);
+  for (double x = start; x < 1e150; x *= 1.5) {
+    double stirling
+        = x * (log(x) - 1) + log(x)
+          + 0.5 * (stan::math::LOG_SQRT_PI + stan::math::LOG_TWO - log(x));
+    double lgamma_res = stan::math::lgamma(x);
+    double diff = lgamma_stirling_diff(x);
 
-      std::ostringstream msg;
-      msg << "x = " << x;
-      expect_near_rel(msg.str(), stirling + diff, lgamma_res);
+    std::ostringstream msg;
+    msg << "x = " << x;
+    expect_near_rel(msg.str(), stirling + diff, lgamma_res);
   }
 }
-

From 45d9f992ad635d7aa9ce15abdff33c6cff1d0c2e Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Thu, 9 Jan 2020 18:52:42 +0100
Subject: [PATCH 51/82] Some progress towards better binomial_coefficient_log
 (messy)

---
 .../scal/fun/binomial_coefficient_log.hpp     | 55 +++++++++++++++++--
 stan/math/prim/scal/fun/lgamma_stirling.hpp   | 20 +++++++
 .../prim/scal/fun/lgamma_stirling_diff.hpp    | 39 ++++++++++++-
 .../fun/binomial_coefficient_log_test.cpp     |  2 +-
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 13 +++--
 5 files changed, 117 insertions(+), 12 deletions(-)
 create mode 100644 stan/math/prim/scal/fun/lgamma_stirling.hpp

diff --git a/stan/math/prim/scal/fun/binomial_coefficient_log.hpp b/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
index b7d2900ac1b..06a625d2473 100644
--- a/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
@@ -4,10 +4,15 @@
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/scal/fun/inv.hpp>
 #include <stan/math/prim/scal/fun/lgamma.hpp>
+#include <stan/math/prim/scal/fun/constants.hpp>
+#include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
+#include <stan/math/prim/scal/fun/log_sum_exp.hpp>
+#include <stan/math/prim/scal/fun/lgamma_stirling_diff.hpp>
 #include <stan/math/prim/scal/fun/multiply_log.hpp>
 
 namespace stan {
 namespace math {
+
 /**
  * Return the log of the binomial coefficient for the specified
  * arguments.
@@ -58,18 +63,56 @@ namespace math {
  * @param n number of objects chosen.
  * @return log (N choose n).
  */
+
+namespace internal {
+  constexpr double lbeta_stirling_bound = 10;
+}
+
+inline double lbeta(const double a, const double b) {
+  double x; //x is the smaller of the two
+  double y;
+  if( a < b ) {
+    x = a;
+    y = b;
+  } else {
+    x = b;
+    y = a;
+  }
+
+  if(y < internal::lbeta_stirling_bound) {
+    //both small
+    return lgamma(x) + lgamma(y) - lgamma(x + y);
+  } else if (x < internal::lbeta_stirling_bound) {
+    //y large, x small    
+    double stirling_diff = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
+    double log_x_y = log(x + y);//log_sum_exp(log(x), log(y));
+    double stirling = (y - 0.5) * log1p(-x/(x+y)) + x * (1 - log_x_y);
+    // std::cout << std::setprecision(18) << x << " " << y << std::endl;
+    // std::cout << std::setprecision(18) << lgamma_stirling_diff(y) << " " << lgamma(y) << " " << lgamma_stirling_diff(x + y) << " " << lgamma(x + y) << std::endl;
+    return stirling + lgamma(x) + stirling_diff;
+  } else {
+    //both large
+    double stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
+    double stirling = (x - 0.5) *log(x/(x+y)) + y * log1p(- x /(x+y)) + 0.5*( log(2 * stan::math::pi())  -log(y));
+    return stirling + stirling_diff;
+  }
+}
+
 template <typename T_N, typename T_n>
 inline return_type_t<T_N, T_n> binomial_coefficient_log(const T_N N,
                                                         const T_n n) {
   const double CUTOFF = 1000;
-  if (N - n < CUTOFF) {
-    const T_N N_plus_1 = N + 1;
+  const T_N N_plus_1 = N + 1;
+  if(n == 0) {
+    return 0;
+  } else if (N - n < CUTOFF) {
     return lgamma(N_plus_1) - lgamma(n + 1) - lgamma(N_plus_1 - n);
   } else {
-    return_type_t<T_N, T_n> N_minus_n = N - n;
-    const double one_twelfth = inv(12);
-    return multiply_log(n, N_minus_n) + multiply_log((N + 0.5), N / N_minus_n)
-           + one_twelfth / N - n - one_twelfth / N_minus_n - lgamma(n + 1);
+    return -lbeta(N - n + 1, n + 1) - log(N_plus_1);
+    // return_type_t<T_N, T_n> N_minus_n = N - n;
+    // const double one_twelfth = inv(12);
+    // return multiply_log(n, N_minus_n) + multiply_log((N + 0.5), N / N_minus_n)
+    //        + one_twelfth / N - n - one_twelfth / N_minus_n - lgamma(n + 1);
   }
 }
 
diff --git a/stan/math/prim/scal/fun/lgamma_stirling.hpp b/stan/math/prim/scal/fun/lgamma_stirling.hpp
new file mode 100644
index 00000000000..32d8a82de0d
--- /dev/null
+++ b/stan/math/prim/scal/fun/lgamma_stirling.hpp
@@ -0,0 +1,20 @@
+#ifndef STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_HPP
+#define STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_HPP
+
+#include <cmath>
+#include <stan/math/prim/scal/fun/constants.hpp>
+#include <stan/math/prim/scal/fun/lgamma.hpp>
+
+
+namespace stan {
+namespace math {
+
+template <typename T>
+T lgamma_stirling(const T x) {     
+    return 0.5 * log(2*stan::math::pi()) + (x - 0.5)*log(x) -x;
+}
+
+}  // namespace math
+}  // namespace stan
+
+#endif
diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
index 8e217aedaec..c33f3e0dd46 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -2,11 +2,48 @@
 #define STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_DIFF_HPP
 
 #include <cmath>
+//#include <boost/math/special_functions/chebyshev_transform.hpp>
+#include <stan/math/prim/scal/fun/constants.hpp>
+#include <stan/math/prim/scal/fun/lgamma.hpp>
+#include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
+
 
 namespace stan {
 namespace math {
 
-double lgamma_stirling_diff(const double x) { return std::log1p(1 / (12 * x)); }
+// namespace internal {
+//     boost::math::chebyshev_transform<double> build_lgamma_stirling_diff_chebyshev() {
+//         auto f = [](double t) {
+//             double x = 10 * sqrt(2 / (t + 1));
+//             double stirling = 0.5 * log(2*stan::math::pi()) + (x - 0.5)*log(x) -x;
+//             return (lgamma(x) - stirling);
+//         };
+//         auto transform = boost::math::chebyshev_transform<double>(f, -1, 1, 1e-10);
+//         std::cout << "Coeffs: " << transform.coefficients().size() << std::endl;
+//         //std::cout << transform.coefficients()[0];
+//         for(const double c : transform.coefficients()) {
+//             std::cout << c << " ";
+//         }
+//         return transform;
+//     }
+
+//     boost::math::chebyshev_transform<double> lgamma_stirling_diff_chebyshev = build_lgamma_stirling_diff_chebyshev();
+// }
+
+namespace internal {
+    constexpr double lgamma_stirling_diff_big = 1e5;
+}
+
+double lgamma_stirling_diff(const double x) {     
+    if(x < internal::lgamma_stirling_diff_big) {
+        return lgamma(x) - lgamma_stirling(x);
+    } else {
+        return 1.0 / (12.0 * x) + 1.0 / (288 * x * x);
+    }
+    // double ten_over_x = 10.0 / x;
+    // double t = ten_over_x * ten_over_x * 2 - 1;
+    // return internal::lgamma_stirling_diff_chebyshev(t); 
+}
 
 }  // namespace math
 }  // namespace stan
diff --git a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
index a8e59a736b7..da1d49bf60f 100644
--- a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
@@ -8,7 +8,7 @@ template <typename T_N, typename T_n>
 void test_binom_coefficient(const T_N& N, const T_n& n) {
   using stan::math::binomial_coefficient_log;
   EXPECT_FLOAT_EQ(lgamma(N + 1) - lgamma(n + 1) - lgamma(N - n + 1),
-                  binomial_coefficient_log(N, n));
+                  binomial_coefficient_log(N, n)) << "N = " << N << ", n = " << n;
 }
 
 TEST(MathFunctions, binomial_coefficient_log) {
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
index 8d8f6c1fb48..3b54d98ecad 100644
--- a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -12,17 +12,22 @@ TEST(MathFunctions, lgamma_stirling_diff_errors) {
 TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
   using stan::math::lgamma_stirling_diff;
   using stan::test::expect_near_rel;
+  using stan::math::internal::lgamma_stirling_diff_big;
 
   double start = std::nextafter(10, 11);
-  for (double x = start; x < 1e150; x *= 1.5) {
+//  for (double x = start; x < 1e150; x *= 1.5) {
+  for (double x = start; x < 100; x *= 1.5) {
     double stirling
-        = x * (log(x) - 1) + log(x)
-          + 0.5 * (stan::math::LOG_SQRT_PI + stan::math::LOG_TWO - log(x));
+        = 0.5 * log(2*stan::math::pi()) + (x - 0.5)*log(x) -x;
     double lgamma_res = stan::math::lgamma(x);
     double diff = lgamma_stirling_diff(x);
 
     std::ostringstream msg;
-    msg << "x = " << x;
+    msg << "x = " << x << "; diff = " << diff << "; diff_actual = " << (lgamma_res - stirling);
     expect_near_rel(msg.str(), stirling + diff, lgamma_res);
   }
+
+  double before_big = std::nextafter(lgamma_stirling_diff_big, 0);
+  double after_big = std::nextafter(lgamma_stirling_diff_big, stan::math::positive_infinity());
+  expect_near_rel("big cutoff", lgamma_stirling_diff(before_big), lgamma_stirling_diff(after_big));
 }

From fb8718bf014d2cf2a0b68ab8a1ca3a9f9daa7c86 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Thu, 9 Jan 2020 17:55:58 +0000
Subject: [PATCH 52/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 .../scal/fun/binomial_coefficient_log.hpp     | 36 +++++++++++--------
 stan/math/prim/scal/fun/lgamma_stirling.hpp   |  5 ++-
 .../prim/scal/fun/lgamma_stirling_diff.hpp    | 36 ++++++++++---------
 .../fun/binomial_coefficient_log_test.cpp     |  3 +-
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 16 +++++----
 5 files changed, 53 insertions(+), 43 deletions(-)

diff --git a/stan/math/prim/scal/fun/binomial_coefficient_log.hpp b/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
index 06a625d2473..04a8b561046 100644
--- a/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
@@ -65,13 +65,13 @@ namespace math {
  */
 
 namespace internal {
-  constexpr double lbeta_stirling_bound = 10;
+constexpr double lbeta_stirling_bound = 10;
 }
 
 inline double lbeta(const double a, const double b) {
-  double x; //x is the smaller of the two
+  double x;  // x is the smaller of the two
   double y;
-  if( a < b ) {
+  if (a < b) {
     x = a;
     y = b;
   } else {
@@ -79,21 +79,26 @@ inline double lbeta(const double a, const double b) {
     y = a;
   }
 
-  if(y < internal::lbeta_stirling_bound) {
-    //both small
+  if (y < internal::lbeta_stirling_bound) {
+    // both small
     return lgamma(x) + lgamma(y) - lgamma(x + y);
   } else if (x < internal::lbeta_stirling_bound) {
-    //y large, x small    
-    double stirling_diff = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
-    double log_x_y = log(x + y);//log_sum_exp(log(x), log(y));
-    double stirling = (y - 0.5) * log1p(-x/(x+y)) + x * (1 - log_x_y);
+    // y large, x small
+    double stirling_diff
+        = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
+    double log_x_y = log(x + y);  // log_sum_exp(log(x), log(y));
+    double stirling = (y - 0.5) * log1p(-x / (x + y)) + x * (1 - log_x_y);
     // std::cout << std::setprecision(18) << x << " " << y << std::endl;
-    // std::cout << std::setprecision(18) << lgamma_stirling_diff(y) << " " << lgamma(y) << " " << lgamma_stirling_diff(x + y) << " " << lgamma(x + y) << std::endl;
+    // std::cout << std::setprecision(18) << lgamma_stirling_diff(y) << " " <<
+    // lgamma(y) << " " << lgamma_stirling_diff(x + y) << " " << lgamma(x + y)
+    // << std::endl;
     return stirling + lgamma(x) + stirling_diff;
   } else {
-    //both large
-    double stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
-    double stirling = (x - 0.5) *log(x/(x+y)) + y * log1p(- x /(x+y)) + 0.5*( log(2 * stan::math::pi())  -log(y));
+    // both large
+    double stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y)
+                           - lgamma_stirling_diff(x + y);
+    double stirling = (x - 0.5) * log(x / (x + y)) + y * log1p(-x / (x + y))
+                      + 0.5 * (log(2 * stan::math::pi()) - log(y));
     return stirling + stirling_diff;
   }
 }
@@ -103,7 +108,7 @@ inline return_type_t<T_N, T_n> binomial_coefficient_log(const T_N N,
                                                         const T_n n) {
   const double CUTOFF = 1000;
   const T_N N_plus_1 = N + 1;
-  if(n == 0) {
+  if (n == 0) {
     return 0;
   } else if (N - n < CUTOFF) {
     return lgamma(N_plus_1) - lgamma(n + 1) - lgamma(N_plus_1 - n);
@@ -111,7 +116,8 @@ inline return_type_t<T_N, T_n> binomial_coefficient_log(const T_N N,
     return -lbeta(N - n + 1, n + 1) - log(N_plus_1);
     // return_type_t<T_N, T_n> N_minus_n = N - n;
     // const double one_twelfth = inv(12);
-    // return multiply_log(n, N_minus_n) + multiply_log((N + 0.5), N / N_minus_n)
+    // return multiply_log(n, N_minus_n) + multiply_log((N + 0.5), N /
+    // N_minus_n)
     //        + one_twelfth / N - n - one_twelfth / N_minus_n - lgamma(n + 1);
   }
 }
diff --git a/stan/math/prim/scal/fun/lgamma_stirling.hpp b/stan/math/prim/scal/fun/lgamma_stirling.hpp
index 32d8a82de0d..66810bc5cf3 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling.hpp
@@ -5,13 +5,12 @@
 #include <stan/math/prim/scal/fun/constants.hpp>
 #include <stan/math/prim/scal/fun/lgamma.hpp>
 
-
 namespace stan {
 namespace math {
 
 template <typename T>
-T lgamma_stirling(const T x) {     
-    return 0.5 * log(2*stan::math::pi()) + (x - 0.5)*log(x) -x;
+T lgamma_stirling(const T x) {
+  return 0.5 * log(2 * stan::math::pi()) + (x - 0.5) * log(x) - x;
 }
 
 }  // namespace math
diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
index c33f3e0dd46..89c26590b4a 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -7,19 +7,20 @@
 #include <stan/math/prim/scal/fun/lgamma.hpp>
 #include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
 
-
 namespace stan {
 namespace math {
 
 // namespace internal {
-//     boost::math::chebyshev_transform<double> build_lgamma_stirling_diff_chebyshev() {
+//     boost::math::chebyshev_transform<double>
+//     build_lgamma_stirling_diff_chebyshev() {
 //         auto f = [](double t) {
 //             double x = 10 * sqrt(2 / (t + 1));
-//             double stirling = 0.5 * log(2*stan::math::pi()) + (x - 0.5)*log(x) -x;
-//             return (lgamma(x) - stirling);
+//             double stirling = 0.5 * log(2*stan::math::pi()) + (x -
+//             0.5)*log(x) -x; return (lgamma(x) - stirling);
 //         };
-//         auto transform = boost::math::chebyshev_transform<double>(f, -1, 1, 1e-10);
-//         std::cout << "Coeffs: " << transform.coefficients().size() << std::endl;
+//         auto transform = boost::math::chebyshev_transform<double>(f, -1, 1,
+//         1e-10); std::cout << "Coeffs: " << transform.coefficients().size() <<
+//         std::endl;
 //         //std::cout << transform.coefficients()[0];
 //         for(const double c : transform.coefficients()) {
 //             std::cout << c << " ";
@@ -27,22 +28,23 @@ namespace math {
 //         return transform;
 //     }
 
-//     boost::math::chebyshev_transform<double> lgamma_stirling_diff_chebyshev = build_lgamma_stirling_diff_chebyshev();
+//     boost::math::chebyshev_transform<double> lgamma_stirling_diff_chebyshev =
+//     build_lgamma_stirling_diff_chebyshev();
 // }
 
 namespace internal {
-    constexpr double lgamma_stirling_diff_big = 1e5;
+constexpr double lgamma_stirling_diff_big = 1e5;
 }
 
-double lgamma_stirling_diff(const double x) {     
-    if(x < internal::lgamma_stirling_diff_big) {
-        return lgamma(x) - lgamma_stirling(x);
-    } else {
-        return 1.0 / (12.0 * x) + 1.0 / (288 * x * x);
-    }
-    // double ten_over_x = 10.0 / x;
-    // double t = ten_over_x * ten_over_x * 2 - 1;
-    // return internal::lgamma_stirling_diff_chebyshev(t); 
+double lgamma_stirling_diff(const double x) {
+  if (x < internal::lgamma_stirling_diff_big) {
+    return lgamma(x) - lgamma_stirling(x);
+  } else {
+    return 1.0 / (12.0 * x) + 1.0 / (288 * x * x);
+  }
+  // double ten_over_x = 10.0 / x;
+  // double t = ten_over_x * ten_over_x * 2 - 1;
+  // return internal::lgamma_stirling_diff_chebyshev(t);
 }
 
 }  // namespace math
diff --git a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
index da1d49bf60f..dc89b20f0a1 100644
--- a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
@@ -8,7 +8,8 @@ template <typename T_N, typename T_n>
 void test_binom_coefficient(const T_N& N, const T_n& n) {
   using stan::math::binomial_coefficient_log;
   EXPECT_FLOAT_EQ(lgamma(N + 1) - lgamma(n + 1) - lgamma(N - n + 1),
-                  binomial_coefficient_log(N, n)) << "N = " << N << ", n = " << n;
+                  binomial_coefficient_log(N, n))
+      << "N = " << N << ", n = " << n;
 }
 
 TEST(MathFunctions, binomial_coefficient_log) {
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
index 3b54d98ecad..886aab54901 100644
--- a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -10,24 +10,26 @@ TEST(MathFunctions, lgamma_stirling_diff_errors) {
 }
 
 TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
+  using stan::math::internal::lgamma_stirling_diff_big;
   using stan::math::lgamma_stirling_diff;
   using stan::test::expect_near_rel;
-  using stan::math::internal::lgamma_stirling_diff_big;
 
   double start = std::nextafter(10, 11);
-//  for (double x = start; x < 1e150; x *= 1.5) {
+  //  for (double x = start; x < 1e150; x *= 1.5) {
   for (double x = start; x < 100; x *= 1.5) {
-    double stirling
-        = 0.5 * log(2*stan::math::pi()) + (x - 0.5)*log(x) -x;
+    double stirling = 0.5 * log(2 * stan::math::pi()) + (x - 0.5) * log(x) - x;
     double lgamma_res = stan::math::lgamma(x);
     double diff = lgamma_stirling_diff(x);
 
     std::ostringstream msg;
-    msg << "x = " << x << "; diff = " << diff << "; diff_actual = " << (lgamma_res - stirling);
+    msg << "x = " << x << "; diff = " << diff
+        << "; diff_actual = " << (lgamma_res - stirling);
     expect_near_rel(msg.str(), stirling + diff, lgamma_res);
   }
 
   double before_big = std::nextafter(lgamma_stirling_diff_big, 0);
-  double after_big = std::nextafter(lgamma_stirling_diff_big, stan::math::positive_infinity());
-  expect_near_rel("big cutoff", lgamma_stirling_diff(before_big), lgamma_stirling_diff(after_big));
+  double after_big = std::nextafter(lgamma_stirling_diff_big,
+                                    stan::math::positive_infinity());
+  expect_near_rel("big cutoff", lgamma_stirling_diff(before_big),
+                  lgamma_stirling_diff(after_big));
 }

From 8e461ad017a74ecb5c6a85fb04f92405acd7a49f Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Fri, 10 Jan 2020 13:39:19 +0100
Subject: [PATCH 53/82] Some more tweaks to stirling_diff

---
 .../prim/scal/fun/lgamma_stirling_diff.hpp    | 64 +++++++++++--------
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 20 +++---
 2 files changed, 51 insertions(+), 33 deletions(-)

diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
index 89c26590b4a..2dd15b6c8d1 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -7,44 +7,58 @@
 #include <stan/math/prim/scal/fun/lgamma.hpp>
 #include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
 
+
 namespace stan {
 namespace math {
 
-// namespace internal {
-//     boost::math::chebyshev_transform<double>
+namespace internal {
+    constexpr double lgamma_stirling_diff_big = 1e10;
+}
+
+
+// namespace lgamma_stirling_diff_internal { 
+//     typedef long double Real;
+
+//     boost::math::chebyshev_transform<Real> 
 //     build_lgamma_stirling_diff_chebyshev() {
-//         auto f = [](double t) {
-//             double x = 10 * sqrt(2 / (t + 1));
-//             double stirling = 0.5 * log(2*stan::math::pi()) + (x -
-//             0.5)*log(x) -x; return (lgamma(x) - stirling);
+//         std::cout << "Size: " << sizeof(Real) << std::endl;
+//         auto f = [](Real t) {
+//             Real x = 10 * std::sqrt(2 / (t + 1));
+//             if(x > internal::lgamma_stirling_diff_big) {
+//                 return 1.0 / (12.0 * x);
+//             } else {
+//                 Real stirling = 0.5 
+//                     * std::log(2* static_cast<Real>(stan::math::pi())) 
+//                     + (x - 0.5)*std::log(x) -x;
+//                 return (std::lgamma(x) - stirling);
+//             }
 //         };
-//         auto transform = boost::math::chebyshev_transform<double>(f, -1, 1,
-//         1e-10); std::cout << "Coeffs: " << transform.coefficients().size() <<
-//         std::endl;
+//         auto transform = boost::math::chebyshev_transform<Real>(f, -1, 1, 1e-8);
+//         std::cout << "Coeffs: " << transform.coefficients().size() << std::endl;
 //         //std::cout << transform.coefficients()[0];
-//         for(const double c : transform.coefficients()) {
-//             std::cout << c << " ";
+//         size_t coeffs_to_print = 
+//             std::min(size_t(20), transform.coefficients().size());
+//         for(size_t i = 0; i < coeffs_to_print ; i ++) {
+//             std::cout << std::setprecision(17) << transform.coefficients()[i] 
+//                 << std::endl;
 //         }
 //         return transform;
 //     }
 
-//     boost::math::chebyshev_transform<double> lgamma_stirling_diff_chebyshev =
-//     build_lgamma_stirling_diff_chebyshev();
+//     boost::math::chebyshev_transform<Real> lgamma_stirling_diff_chebyshev = 
+//         build_lgamma_stirling_diff_chebyshev();
 // }
 
-namespace internal {
-constexpr double lgamma_stirling_diff_big = 1e5;
-}
 
-double lgamma_stirling_diff(const double x) {
-  if (x < internal::lgamma_stirling_diff_big) {
-    return lgamma(x) - lgamma_stirling(x);
-  } else {
-    return 1.0 / (12.0 * x) + 1.0 / (288 * x * x);
-  }
-  // double ten_over_x = 10.0 / x;
-  // double t = ten_over_x * ten_over_x * 2 - 1;
-  // return internal::lgamma_stirling_diff_chebyshev(t);
+double lgamma_stirling_diff(const double x) {     
+    if (x < internal::lgamma_stirling_diff_big) {
+        return std::lgamma(x) - lgamma_stirling(x);
+        // double ten_over_x = 10.0 / x;
+        // double t = ten_over_x * ten_over_x * 2 - 1;
+        // return internal::lgamma_stirling_diff_chebyshev(t); 
+    } else {
+        return 1.0 / (12.0 * x);
+    }
 }
 
 }  // namespace math
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
index 886aab54901..947d0e996a1 100644
--- a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -14,17 +14,21 @@ TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
   using stan::math::lgamma_stirling_diff;
   using stan::test::expect_near_rel;
 
-  double start = std::nextafter(10, 11);
-  //  for (double x = start; x < 1e150; x *= 1.5) {
-  for (double x = start; x < 100; x *= 1.5) {
-    double stirling = 0.5 * log(2 * stan::math::pi()) + (x - 0.5) * log(x) - x;
-    double lgamma_res = stan::math::lgamma(x);
+  long double start = std::nextafter(10, 11);
+  for (long double x = start; x < lgamma_stirling_diff_big; x *= 1.5) {
+  //for (long double x = start; x < 1e150; x *= 1.5) {
+  //for (double x = start; x < 100; x *= 1.5) {
+    long double stirling = 0.5 
+      * std::log(2 * static_cast<long double>(stan::math::pi())) 
+      + (x - 0.5) * std::log(x) - x;
+    long double lgamma_res = std::lgamma(x);
+    double diff_actual = static_cast<double>(lgamma_res - stirling);
     double diff = lgamma_stirling_diff(x);
 
     std::ostringstream msg;
-    msg << "x = " << x << "; diff = " << diff
-        << "; diff_actual = " << (lgamma_res - stirling);
-    expect_near_rel(msg.str(), stirling + diff, lgamma_res);
+    msg << "x = " << x << "; lgamma = " << lgamma_res
+        << "; stirling = " << stirling;
+    expect_near_rel(msg.str(), diff, diff_actual, 1e-4);
   }
 
   double before_big = std::nextafter(lgamma_stirling_diff_big, 0);

From 1d38cf32431e32c84851a7f22b99813766fea735 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Fri, 10 Jan 2020 15:35:34 +0100
Subject: [PATCH 54/82] More (still failing) work on lgamma_stirling_diff

---
 stan/math/prim/scal/fun/lgamma_stirling.hpp   |  1 +
 .../prim/scal/fun/lgamma_stirling_diff.hpp    |  3 ++-
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 25 ++++++++++++++++---
 3 files changed, 25 insertions(+), 4 deletions(-)

diff --git a/stan/math/prim/scal/fun/lgamma_stirling.hpp b/stan/math/prim/scal/fun/lgamma_stirling.hpp
index 66810bc5cf3..209de3cb24c 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling.hpp
@@ -10,6 +10,7 @@ namespace math {
 
 template <typename T>
 T lgamma_stirling(const T x) {
+  using std::log;
   return 0.5 * log(2 * stan::math::pi()) + (x - 0.5) * log(x) - x;
 }
 
diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
index 2dd15b6c8d1..ec2e89f5778 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -52,7 +52,8 @@ namespace internal {
 
 double lgamma_stirling_diff(const double x) {     
     if (x < internal::lgamma_stirling_diff_big) {
-        return std::lgamma(x) - lgamma_stirling(x);
+        return std::lgamma(static_cast<long double>(x)) - lgamma_stirling(static_cast<long double>(x));
+
         // double ten_over_x = 10.0 / x;
         // double t = ten_over_x * ten_over_x * 2 - 1;
         // return internal::lgamma_stirling_diff_chebyshev(t); 
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
index 947d0e996a1..f271f5d6453 100644
--- a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -15,9 +15,7 @@ TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
   using stan::test::expect_near_rel;
 
   long double start = std::nextafter(10, 11);
-  for (long double x = start; x < lgamma_stirling_diff_big; x *= 1.5) {
-  //for (long double x = start; x < 1e150; x *= 1.5) {
-  //for (double x = start; x < 100; x *= 1.5) {
+  for (long double x = start; x < 2 * lgamma_stirling_diff_big; x *= 1.5) {
     long double stirling = 0.5 
       * std::log(2 * static_cast<long double>(stan::math::pi())) 
       + (x - 0.5) * std::log(x) - x;
@@ -37,3 +35,24 @@ TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
   expect_near_rel("big cutoff", lgamma_stirling_diff(before_big),
                   lgamma_stirling_diff(after_big));
 }
+
+namespace lgamma_stirling_diff_test_internal {
+  struct TestValue {
+    double x;
+    double val;
+  };
+
+  std::vector<TestValue> testValues = {  {10.049787068367863943,0.0082893206359322200849},  {10.135335283236612692,0.0082193992370778811855},  {10.367879441171442322,0.0080351590240775284273},  {11.,0.007573675487951840795},  {12.718281828459045235,0.0065508998676477812047},  {17.389056098930650227,0.0047917583976502091168},  {30.085536923187667741,0.0027697782366142911547},  {64.598150033144239078,0.0012900163188678122747},  {158.41315910257660342,0.00052604987562270910548},  {413.42879349273512261,0.0002015663117649479817},  {1106.6331584284585993,0.000075303482848309432847},  {2990.9579870417282747,0.000027861753118520084151},  {8113.0839275753840077,0.000010271474329002342817},  {22036.465794806716517,3.7816106313768371052e-6},  {59884.141715197818455,1.3915759823173656792e-6},  {162764.79141900392081,5.1198623858832122975e-7},  {442423.39200892050333,1.8835652643709875774e-7},  {1.2026142841647767777e6,6.9293483730078043652e-8},  {3.2690273724721106393e6,2.5491782061865871668e-8},  {8.8861205205078726368e6,9.3779206731455076929e-9},  {2.4154962753575298215e7,3.4499466707312036902e-9},  {6.5659979137330511139e7,1.2691647854325126115e-9},  {1.7848231096318726084e8,4.6689967696866715977e-10},  {4.8516520540979027797e8,1.717627983295846792e-10},  {1.3188157444832146972e9,6.318800308680570434e-11},  {3.5849128561315915617e9,2.3245567375731604902e-11},  {9.7448034562489026e9,8.5515663509760607976e-12},  {2.6489122139843472294e10,3.1459454523782780579e-12},  {7.2004899347385872524e10,1.1573286552529392289e-12},};
+}
+
+TEST(MathFunctions, lgamma_stirling_diff_precomputed) {
+  using stan::math::lgamma_stirling_diff;
+  using stan::test::expect_near_rel;
+  using namespace lgamma_stirling_diff_test_internal;
+
+  for(TestValue t : testValues) {
+    std::ostringstream msg;
+    msg << "x = " << t.x;
+    expect_near_rel(msg.str(), lgamma_stirling_diff(t.x), t.val);
+  }
+}
\ No newline at end of file

From 3f129062a8515326503b19f9912c688adac3b593 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Fri, 10 Jan 2020 14:36:15 +0000
Subject: [PATCH 55/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 .../prim/scal/fun/lgamma_stirling_diff.hpp    | 43 ++++++++--------
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 50 +++++++++++++++----
 2 files changed, 61 insertions(+), 32 deletions(-)

diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
index ec2e89f5778..645444d4212 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -7,19 +7,17 @@
 #include <stan/math/prim/scal/fun/lgamma.hpp>
 #include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
 
-
 namespace stan {
 namespace math {
 
 namespace internal {
-    constexpr double lgamma_stirling_diff_big = 1e10;
+constexpr double lgamma_stirling_diff_big = 1e10;
 }
 
-
-// namespace lgamma_stirling_diff_internal { 
+// namespace lgamma_stirling_diff_internal {
 //     typedef long double Real;
 
-//     boost::math::chebyshev_transform<Real> 
+//     boost::math::chebyshev_transform<Real>
 //     build_lgamma_stirling_diff_chebyshev() {
 //         std::cout << "Size: " << sizeof(Real) << std::endl;
 //         auto f = [](Real t) {
@@ -27,39 +25,40 @@ namespace internal {
 //             if(x > internal::lgamma_stirling_diff_big) {
 //                 return 1.0 / (12.0 * x);
 //             } else {
-//                 Real stirling = 0.5 
-//                     * std::log(2* static_cast<Real>(stan::math::pi())) 
+//                 Real stirling = 0.5
+//                     * std::log(2* static_cast<Real>(stan::math::pi()))
 //                     + (x - 0.5)*std::log(x) -x;
 //                 return (std::lgamma(x) - stirling);
 //             }
 //         };
-//         auto transform = boost::math::chebyshev_transform<Real>(f, -1, 1, 1e-8);
-//         std::cout << "Coeffs: " << transform.coefficients().size() << std::endl;
+//         auto transform = boost::math::chebyshev_transform<Real>(f, -1, 1,
+//         1e-8); std::cout << "Coeffs: " << transform.coefficients().size() <<
+//         std::endl;
 //         //std::cout << transform.coefficients()[0];
-//         size_t coeffs_to_print = 
+//         size_t coeffs_to_print =
 //             std::min(size_t(20), transform.coefficients().size());
 //         for(size_t i = 0; i < coeffs_to_print ; i ++) {
-//             std::cout << std::setprecision(17) << transform.coefficients()[i] 
+//             std::cout << std::setprecision(17) << transform.coefficients()[i]
 //                 << std::endl;
 //         }
 //         return transform;
 //     }
 
-//     boost::math::chebyshev_transform<Real> lgamma_stirling_diff_chebyshev = 
+//     boost::math::chebyshev_transform<Real> lgamma_stirling_diff_chebyshev =
 //         build_lgamma_stirling_diff_chebyshev();
 // }
 
+double lgamma_stirling_diff(const double x) {
+  if (x < internal::lgamma_stirling_diff_big) {
+    return std::lgamma(static_cast<long double>(x))
+           - lgamma_stirling(static_cast<long double>(x));
 
-double lgamma_stirling_diff(const double x) {     
-    if (x < internal::lgamma_stirling_diff_big) {
-        return std::lgamma(static_cast<long double>(x)) - lgamma_stirling(static_cast<long double>(x));
-
-        // double ten_over_x = 10.0 / x;
-        // double t = ten_over_x * ten_over_x * 2 - 1;
-        // return internal::lgamma_stirling_diff_chebyshev(t); 
-    } else {
-        return 1.0 / (12.0 * x);
-    }
+    // double ten_over_x = 10.0 / x;
+    // double t = ten_over_x * ten_over_x * 2 - 1;
+    // return internal::lgamma_stirling_diff_chebyshev(t);
+  } else {
+    return 1.0 / (12.0 * x);
+  }
 }
 
 }  // namespace math
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
index f271f5d6453..e7c96deeeb0 100644
--- a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -16,9 +16,9 @@ TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
 
   long double start = std::nextafter(10, 11);
   for (long double x = start; x < 2 * lgamma_stirling_diff_big; x *= 1.5) {
-    long double stirling = 0.5 
-      * std::log(2 * static_cast<long double>(stan::math::pi())) 
-      + (x - 0.5) * std::log(x) - x;
+    long double stirling
+        = 0.5 * std::log(2 * static_cast<long double>(stan::math::pi()))
+          + (x - 0.5) * std::log(x) - x;
     long double lgamma_res = std::lgamma(x);
     double diff_actual = static_cast<double>(lgamma_res - stirling);
     double diff = lgamma_stirling_diff(x);
@@ -37,20 +37,50 @@ TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
 }
 
 namespace lgamma_stirling_diff_test_internal {
-  struct TestValue {
-    double x;
-    double val;
-  };
+struct TestValue {
+  double x;
+  double val;
+};
 
-  std::vector<TestValue> testValues = {  {10.049787068367863943,0.0082893206359322200849},  {10.135335283236612692,0.0082193992370778811855},  {10.367879441171442322,0.0080351590240775284273},  {11.,0.007573675487951840795},  {12.718281828459045235,0.0065508998676477812047},  {17.389056098930650227,0.0047917583976502091168},  {30.085536923187667741,0.0027697782366142911547},  {64.598150033144239078,0.0012900163188678122747},  {158.41315910257660342,0.00052604987562270910548},  {413.42879349273512261,0.0002015663117649479817},  {1106.6331584284585993,0.000075303482848309432847},  {2990.9579870417282747,0.000027861753118520084151},  {8113.0839275753840077,0.000010271474329002342817},  {22036.465794806716517,3.7816106313768371052e-6},  {59884.141715197818455,1.3915759823173656792e-6},  {162764.79141900392081,5.1198623858832122975e-7},  {442423.39200892050333,1.8835652643709875774e-7},  {1.2026142841647767777e6,6.9293483730078043652e-8},  {3.2690273724721106393e6,2.5491782061865871668e-8},  {8.8861205205078726368e6,9.3779206731455076929e-9},  {2.4154962753575298215e7,3.4499466707312036902e-9},  {6.5659979137330511139e7,1.2691647854325126115e-9},  {1.7848231096318726084e8,4.6689967696866715977e-10},  {4.8516520540979027797e8,1.717627983295846792e-10},  {1.3188157444832146972e9,6.318800308680570434e-11},  {3.5849128561315915617e9,2.3245567375731604902e-11},  {9.7448034562489026e9,8.5515663509760607976e-12},  {2.6489122139843472294e10,3.1459454523782780579e-12},  {7.2004899347385872524e10,1.1573286552529392289e-12},};
-}
+std::vector<TestValue> testValues = {
+    {10.049787068367863943, 0.0082893206359322200849},
+    {10.135335283236612692, 0.0082193992370778811855},
+    {10.367879441171442322, 0.0080351590240775284273},
+    {11., 0.007573675487951840795},
+    {12.718281828459045235, 0.0065508998676477812047},
+    {17.389056098930650227, 0.0047917583976502091168},
+    {30.085536923187667741, 0.0027697782366142911547},
+    {64.598150033144239078, 0.0012900163188678122747},
+    {158.41315910257660342, 0.00052604987562270910548},
+    {413.42879349273512261, 0.0002015663117649479817},
+    {1106.6331584284585993, 0.000075303482848309432847},
+    {2990.9579870417282747, 0.000027861753118520084151},
+    {8113.0839275753840077, 0.000010271474329002342817},
+    {22036.465794806716517, 3.7816106313768371052e-6},
+    {59884.141715197818455, 1.3915759823173656792e-6},
+    {162764.79141900392081, 5.1198623858832122975e-7},
+    {442423.39200892050333, 1.8835652643709875774e-7},
+    {1.2026142841647767777e6, 6.9293483730078043652e-8},
+    {3.2690273724721106393e6, 2.5491782061865871668e-8},
+    {8.8861205205078726368e6, 9.3779206731455076929e-9},
+    {2.4154962753575298215e7, 3.4499466707312036902e-9},
+    {6.5659979137330511139e7, 1.2691647854325126115e-9},
+    {1.7848231096318726084e8, 4.6689967696866715977e-10},
+    {4.8516520540979027797e8, 1.717627983295846792e-10},
+    {1.3188157444832146972e9, 6.318800308680570434e-11},
+    {3.5849128561315915617e9, 2.3245567375731604902e-11},
+    {9.7448034562489026e9, 8.5515663509760607976e-12},
+    {2.6489122139843472294e10, 3.1459454523782780579e-12},
+    {7.2004899347385872524e10, 1.1573286552529392289e-12},
+};
+}  // namespace lgamma_stirling_diff_test_internal
 
 TEST(MathFunctions, lgamma_stirling_diff_precomputed) {
   using stan::math::lgamma_stirling_diff;
   using stan::test::expect_near_rel;
   using namespace lgamma_stirling_diff_test_internal;
 
-  for(TestValue t : testValues) {
+  for (TestValue t : testValues) {
     std::ostringstream msg;
     msg << "x = " << t.x;
     expect_near_rel(msg.str(), lgamma_stirling_diff(t.x), t.val);

From a85623aa21ae11d37c472c42e915d84baf1d8f33 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 19:13:48 +0100
Subject: [PATCH 56/82] Failing test for lbeta (#1611)

---
 test/unit/math/prim/scal/fun/lbeta_test.cpp | 28 +++++++++++++++++++++
 1 file changed, 28 insertions(+)

diff --git a/test/unit/math/prim/scal/fun/lbeta_test.cpp b/test/unit/math/prim/scal/fun/lbeta_test.cpp
index 7c7bc3825f7..512a103bd44 100644
--- a/test/unit/math/prim/scal/fun/lbeta_test.cpp
+++ b/test/unit/math/prim/scal/fun/lbeta_test.cpp
@@ -1,7 +1,10 @@
+#include <test/unit/math/expect_near_rel.hpp>
 #include <stan/math/prim/scal.hpp>
 #include <gtest/gtest.h>
 #include <cmath>
 #include <limits>
+#include <vector>
+
 
 TEST(MathFunctions, lbeta) {
   using stan::math::lbeta;
@@ -21,3 +24,28 @@ TEST(MathFunctions, lbeta_nan) {
 
   EXPECT_TRUE(std::isnan(stan::math::lbeta(nan, nan)));
 }
+
+namespace lbeta_test_internal {
+  struct TestValue {
+    double x;
+    double y;
+    double val;
+  };
+
+std::vector<TestValue> testValues = {  {8.e-8,7.e-11,23.3834004912898500586445},  {8.e-8,0.00002,16.3452312235394351410033},  {8.e-8,1.000000000001,16.3412392022725295437606},  {8.e-8,0.5,16.3412393131760679059067},  {8.e-8,2,16.3412391222725327438921},  {8.e-8,1624,16.3412385647081130254943},  {0.004,7.e-11,23.3825258913787298259023},  {0.004,0.00002,10.8247656947117878792194},  {0.004,1.000000000001,5.52146091786223987264715},  {0.004,0.5,5.52697992926150653113797},  {0.004,2,5.51746889659270898022044},  {0.004,1624,5.48959582574332555214719},  {1,7.e-11,23.3825258738791892190926},  {1,0.00002,10.8197782844102831106727},  {1,1.000000000001,-9.999999999995e-13},  {1,0.5,0.693147180559945309417232},  {1,2,-0.693147180559945309417232},  {1,1624,-7.39264752072162326054032},  {1.00000001,7.e-11,23.3825258738791892179411},  {1.00000001,0.00002,10.8197782844099541286699},  {1.00000001,1.000000000001,-1.00009999500064491739816e-8},  {1.00000001,0.5,0.693147174422888956122731},  {1.00000001,2,-0.693147195559945246917232},  {1.00000001,1624,-7.39264760042333353631934},  {5,7.e-11,23.3825258737333558857627},  {5,0.00002,10.8197366180283355258393},  {5,1.000000000001,-1.60943791243638370793409},  {5,0.5,-0.207395194346070587158746},  {5,2,-3.40119738166215537541324},  {5,1624,-33.7913357290267948074624},  {23,7.e-11,23.3825258736208322915813},  {23,0.00002,10.819704468465374949026},  {23,1.000000000001,-3.13549421593288398231784},  {23,0.5,-0.989947810259228199543883},  {23,2,-6.31354804627709531045369},  {23,1624,-121.714785277510463870251},  {19845,7.e-11,23.3825258731460863706715},  {19845,0.00002,10.8195688267825637640878},  {19845,1.000000000001,-9.89570736522763869861762},  {19845,0.5,-4.37548244086806082919414},  {19845,2,-19.7914651196913525680177},  {19845,1624,-5756.4146766727238501215},  {3000000000000000.0,3,-106.219018870176440545578},  {3000000000000000.0,100,-3204.60466298830574639047},  {3000000000000000.0,12895,-350396.988955562106921852},  {100000000000000000000.0,3,-137.461958399082795731692},  {100000000000000000000.0,100,-4246.03598061851596930944},  {100000000000000000000.0,12895,-484689.557363950217404711},};
+}
+
+TEST(MathFunctions, lbeta_precomputed) {
+  using lbeta_test_internal::TestValue;
+  using lbeta_test_internal::testValues;
+  using stan::test::expect_near_rel;
+
+  for (TestValue t : testValues) {
+
+    std::ostringstream msg;
+    msg << std::setprecision(22) << "x = " << t.x << ", y = " << t.y;
+
+    double val = stan::math::lbeta(t.x, t.y);
+    expect_near_rel(msg.str(), val, t.val);
+  }
+}

From d2f955a77621d4f5c2d9ca188a5d66bd79281a72 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 19:33:35 +0100
Subject: [PATCH 57/82] More strict criteria in expect_near_rel

---
 test/unit/math/expect_near_rel.hpp | 38 +++++++++++++++++++++---------
 1 file changed, 27 insertions(+), 11 deletions(-)

diff --git a/test/unit/math/expect_near_rel.hpp b/test/unit/math/expect_near_rel.hpp
index 37d12c266cb..4093aba00fe 100644
--- a/test/unit/math/expect_near_rel.hpp
+++ b/test/unit/math/expect_near_rel.hpp
@@ -5,6 +5,7 @@
 #include <gtest/gtest.h>
 #include <string>
 #include <vector>
+#include <limits>
 
 namespace stan {
 namespace test {
@@ -32,23 +33,37 @@ namespace internal {
  */
 template <typename T1, typename T2, require_all_stan_scalar_t<T1, T2>...>
 void expect_near_rel_finite(const std::string& msg, const T1& x1, const T2& x2,
-                            double tol = 1e-8) {
+                            double tol_rel = 1e-8, 
+                            double tol_min = std::numeric_limits<double>::quiet_NaN()) {
   using stan::math::fabs;
   // if either arg near zero, must use absolute tolerance as rel tol -> 2
-  if (fabs(x1) < tol || fabs(x2) < tol) {
-    EXPECT_NEAR(x1, x2, tol) << "expect_near_rel_finite(" << x1 << ", " << x2
-                             << ", absolute tolerance = " << tol << ")"
-                             << "; absolute diff = " << fabs(x1 - x2)
-                             << "    in: " << msg << std::endl;
-    return;
+  // if (fabs(x1) < tol || fabs(x2) < tol) {
+  //   EXPECT_NEAR(x1, x2, tol) << "expect_near_rel_finite(" << x1 << ", " << x2
+  //                            << ", absolute tolerance = " << tol << ")"
+  //                            << "; absolute diff = " << fabs(x1 - x2)
+  //                            << "    in: " << msg << std::endl;
+  //   return;
+  // }
+  // auto avg = 0.5 * (fabs(x1) + fabs(x2));
+  // auto relative_diff = (x1 - x2) / avg;
+  // EXPECT_NEAR(0, relative_diff, tol)
+  //     << "expect_near_rel_finite(" << x1 << ", " << x2
+  //     << ", relative tolerance = " << tol << ")"
+  //     << "; relative diff = " << relative_diff << std::endl
+  //     << "    in: " << msg << std::endl;
+  if(stan::math::is_nan(tol_min)) {
+    tol_min = tol_rel * tol_rel;
   }
   auto avg = 0.5 * (fabs(x1) + fabs(x2));
+  auto tol = std::max(avg * tol_rel, tol_min);
   auto relative_diff = (x1 - x2) / avg;
-  EXPECT_NEAR(0, relative_diff, tol)
+  EXPECT_NEAR(x1, x2, tol)
       << "expect_near_rel_finite(" << x1 << ", " << x2
-      << ", relative tolerance = " << tol << ")"
+      << ", relative tolerance = " << tol_rel << ")"
+      << ", minimum tolerance = " << tol_min << ")"
       << "; relative diff = " << relative_diff << std::endl
       << "    in: " << msg << std::endl;
+
 }
 
 template <typename EigMat1, typename EigMat2,
@@ -89,7 +104,8 @@ void expect_near_rel_finite(const std::string& msg, const std::vector<T1>& x1,
  */
 template <typename T1, typename T2, require_all_stan_scalar_t<T1, T2>...>
 void expect_near_rel(const std::string& msg, const T1& x1, const T2& x2,
-                     double tol = 1e-8) {
+                     double tol_rel = 1e-8, 
+                     double tol_min = std::numeric_limits<double>::quiet_NaN()) {
   if (stan::math::is_nan(x1) || stan::math::is_nan(x2))
     EXPECT_TRUE(stan::math::is_nan(x1) && stan::math::is_nan(x2))
         << "expect_near_rel(" << x1 << ", " << x2 << ")" << std::endl
@@ -99,7 +115,7 @@ void expect_near_rel(const std::string& msg, const T1& x1, const T2& x2,
                       << std::endl
                       << msg << std::endl;
   else
-    internal::expect_near_rel_finite(msg, x1, x2, tol);
+    internal::expect_near_rel_finite(msg, x1, x2, tol_rel, tol_min);
 }
 
 /**

From 9e708aff848165dac06c2108da96c4cc9cd46dcb Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 19:50:03 +0100
Subject: [PATCH 58/82] Fixing lbeta and binomial_coefficient_log (#1611,
 #1592)

---
 .../scal/fun/binomial_coefficient_log.hpp     | 82 ++++++----------
 stan/math/prim/scal/fun/lbeta.hpp             | 52 +++++++++-
 stan/math/prim/scal/fun/lgamma_stirling.hpp   | 14 +++
 .../prim/scal/fun/lgamma_stirling_diff.hpp    | 96 ++++++++++---------
 .../fun/binomial_coefficient_log_test.cpp     | 93 ++++++------------
 test/unit/math/prim/scal/fun/lbeta_test.cpp   | 33 +++++++
 .../scal/fun/lgamma_stirling_diff_test.cpp    | 50 +++-------
 7 files changed, 214 insertions(+), 206 deletions(-)

diff --git a/stan/math/prim/scal/fun/binomial_coefficient_log.hpp b/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
index 04a8b561046..7c17f4d996e 100644
--- a/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/scal/fun/binomial_coefficient_log.hpp
@@ -2,13 +2,11 @@
 #define STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
 
 #include <stan/math/prim/meta.hpp>
-#include <stan/math/prim/scal/fun/inv.hpp>
 #include <stan/math/prim/scal/fun/lgamma.hpp>
+#include <stan/math/prim/scal/fun/lbeta.hpp>
 #include <stan/math/prim/scal/fun/constants.hpp>
-#include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
-#include <stan/math/prim/scal/fun/log_sum_exp.hpp>
-#include <stan/math/prim/scal/fun/lgamma_stirling_diff.hpp>
-#include <stan/math/prim/scal/fun/multiply_log.hpp>
+#include <stan/math/prim/err/check_nonnegative.hpp>
+#include <stan/math/prim/err/check_greater_or_equal.hpp>
 
 namespace stan {
 namespace math {
@@ -27,12 +25,15 @@ namespace math {
  *
  * \f$ \log {N \choose n}
  * = \log \ \Gamma(N+1) - \log \Gamma(n+1) - \log \Gamma(N-n+1)\f$.
+ * 
  *
+ * TODO[martinmodrak] figure out the cases for x < 0 and for partials
    \f[
    \mbox{binomial\_coefficient\_log}(x, y) =
    \begin{cases}
-     \textrm{error} & \mbox{if } y > x \textrm{ or } y < 0\\
-     \ln\Gamma(x+1) & \mbox{if } 0\leq y \leq x \\
+     \textrm{error} & \mbox{if } y > x + 1 \textrm{ or } y < -1 \textrm{ or } x < 0\\
+     \textrm{-\infty} & \mbox{if } y = x + 1 \textrm{ or } y = -1\\
+     \ln\Gamma(x+1) & \mbox{if } -1 < y < x + 1 \\
      \quad -\ln\Gamma(y+1)& \\
      \quad -\ln\Gamma(x-y+1)& \\[6pt]
      \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN}
@@ -59,66 +60,39 @@ namespace math {
    \end{cases}
    \f]
  *
+ *  This function is numerically more stable than naive evaluation via lgamma
+ *
  * @param N total number of objects.
  * @param n number of objects chosen.
  * @return log (N choose n).
  */
 
-namespace internal {
-constexpr double lbeta_stirling_bound = 10;
-}
-
-inline double lbeta(const double a, const double b) {
-  double x;  // x is the smaller of the two
-  double y;
-  if (a < b) {
-    x = a;
-    y = b;
-  } else {
-    x = b;
-    y = a;
-  }
-
-  if (y < internal::lbeta_stirling_bound) {
-    // both small
-    return lgamma(x) + lgamma(y) - lgamma(x + y);
-  } else if (x < internal::lbeta_stirling_bound) {
-    // y large, x small
-    double stirling_diff
-        = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
-    double log_x_y = log(x + y);  // log_sum_exp(log(x), log(y));
-    double stirling = (y - 0.5) * log1p(-x / (x + y)) + x * (1 - log_x_y);
-    // std::cout << std::setprecision(18) << x << " " << y << std::endl;
-    // std::cout << std::setprecision(18) << lgamma_stirling_diff(y) << " " <<
-    // lgamma(y) << " " << lgamma_stirling_diff(x + y) << " " << lgamma(x + y)
-    // << std::endl;
-    return stirling + lgamma(x) + stirling_diff;
-  } else {
-    // both large
-    double stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y)
-                           - lgamma_stirling_diff(x + y);
-    double stirling = (x - 0.5) * log(x / (x + y)) + y * log1p(-x / (x + y))
-                      + 0.5 * (log(2 * stan::math::pi()) - log(y));
-    return stirling + stirling_diff;
-  }
-}
-
 template <typename T_N, typename T_n>
 inline return_type_t<T_N, T_n> binomial_coefficient_log(const T_N N,
                                                         const T_n n) {
-  const double CUTOFF = 1000;
-  const T_N N_plus_1 = N + 1;
+  if(is_nan(value_of_rec(N)) || is_nan(value_of_rec(n))) {
+    return std::numeric_limits<double>::quiet_NaN();
+  } 
+  
+  // For some uses it is important this works even when N < 0 and therefore
+  // it is before checks
   if (n == 0) {
     return 0;
-  } else if (N - n < CUTOFF) {
+  }                                                  
+  const T_N N_plus_1 = N + 1;
+
+  static const char* function = "binomial_coefficient_log";
+  check_nonnegative(function, "first argument", N);
+  check_greater_or_equal(function, "second argument", n, -1);
+  check_greater_or_equal(function, "(first argument - second argument + 1)", 
+    N - n + 1, 0.0);
+
+  if (N / 2 < n) {
+    return binomial_coefficient_log(N, N - n);
+  } else if (N_plus_1 < lgamma_stirling_diff_useful) {
     return lgamma(N_plus_1) - lgamma(n + 1) - lgamma(N_plus_1 - n);
   } else {
     return -lbeta(N - n + 1, n + 1) - log(N_plus_1);
-    // return_type_t<T_N, T_n> N_minus_n = N - n;
-    // const double one_twelfth = inv(12);
-    // return multiply_log(n, N_minus_n) + multiply_log((N + 0.5), N /
-    // N_minus_n)
-    //        + one_twelfth / N - n - one_twelfth / N_minus_n - lgamma(n + 1);
   }
 }
 
diff --git a/stan/math/prim/scal/fun/lbeta.hpp b/stan/math/prim/scal/fun/lbeta.hpp
index 8b5af38646e..fca51ac0081 100644
--- a/stan/math/prim/scal/fun/lbeta.hpp
+++ b/stan/math/prim/scal/fun/lbeta.hpp
@@ -3,6 +3,12 @@
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/scal/fun/lgamma.hpp>
+#include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
+#include <stan/math/prim/scal/fun/log_sum_exp.hpp>
+#include <stan/math/prim/scal/fun/lgamma_stirling_diff.hpp>
+#include <stan/math/prim/scal/fun/multiply_log.hpp>
+#include <stan/math/prim/err/check_nonnegative.hpp>
+#include <stan/math/prim/scal/fun/inv.hpp>
 
 namespace stan {
 namespace math {
@@ -22,7 +28,7 @@ namespace math {
  *
  * See stan::math::lgamma() for the double-based and stan::math for the
  * variable-based log Gamma function.
- *
+ * This function is numerically more stable than naive evaluation via lgamma
  *
    \f[
    \mbox{lbeta}(\alpha, \beta) =
@@ -55,7 +61,49 @@ namespace math {
  */
 template <typename T1, typename T2>
 inline return_type_t<T1, T2> lbeta(const T1 a, const T2 b) {
-  return lgamma(a) + lgamma(b) - lgamma(a + b);
+  typedef return_type_t<T1, T2> T_ret;
+
+  if(is_nan(value_of_rec(a)) || is_nan(value_of_rec(b))) {
+    return std::numeric_limits<double>::quiet_NaN();
+  } 
+
+  static const char* function = "lbeta";
+  check_nonnegative(function, "first argument", a);
+  check_nonnegative(function, "second argument", b);
+  T_ret x;  // x is the smaller of the two
+  T_ret y;
+  if (a < b) {
+    x = a;
+    y = b;
+  } else {
+    x = b;
+    y = a;
+  }
+
+  // For large x or y, separate the lgamma values into Stirling approximations
+  // and appropriate corrections. The Stirling approximations allow for
+  // analytic simplifaction and the corrections are added later.
+  //
+  // The overall approach is inspired by the code in R, where the algorithm is
+  // credited to W. Fullerton of Los Alamos Scientific Laboratory
+  if (y < lgamma_stirling_diff_useful) {
+    // both small
+    return lgamma(x) + lgamma(y) - lgamma(x + y);
+  } else if (x < lgamma_stirling_diff_useful) {
+    // y large, x small
+    T_ret stirling_diff
+        = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
+    T_ret log_x_y = log(x + y); 
+    T_ret stirling = (y - 0.5) * log1p(-x / (x + y)) + x * (1 - log_x_y);
+    return stirling + lgamma(x) + stirling_diff;
+  } else {
+    // both large
+    T_ret stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y)
+                           - lgamma_stirling_diff(x + y);
+    T_ret stirling = (x - 0.5) * log(x / (x + y)) + y * log1p(-x / (x + y))
+                      + 0.5 * (log(2 * stan::math::pi()) - log(y));
+    return stirling + stirling_diff;
+  }
 }
 
 }  // namespace math
diff --git a/stan/math/prim/scal/fun/lgamma_stirling.hpp b/stan/math/prim/scal/fun/lgamma_stirling.hpp
index 209de3cb24c..ced1fd6584f 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling.hpp
@@ -8,6 +8,20 @@
 namespace stan {
 namespace math {
 
+/**
+ * Return the Stirling approximation to the gamma function.
+ *
+
+   \f[
+   \mbox{lgamma_stirling}(x) =
+    \frac{1}{2} \log(2\pi) + (x-\frac{1}{2})*\log(x) - x
+   \f]
+
+ *
+ * @param x value
+ * @return Stirling's approximation to lgamma(x).
+ * @tparam T Type of  value.
+ */
 template <typename T>
 T lgamma_stirling(const T x) {
   using std::log;
diff --git a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
index 645444d4212..2c24f45cbaf 100644
--- a/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/scal/fun/lgamma_stirling_diff.hpp
@@ -2,63 +2,67 @@
 #define STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_DIFF_HPP
 
 #include <cmath>
-//#include <boost/math/special_functions/chebyshev_transform.hpp>
+#include <stan/math/prim/scal/fun/value_of.hpp>
 #include <stan/math/prim/scal/fun/constants.hpp>
 #include <stan/math/prim/scal/fun/lgamma.hpp>
+#include <stan/math/prim/scal/fun/inv.hpp>
+#include <stan/math/prim/scal/fun/square.hpp>
 #include <stan/math/prim/scal/fun/lgamma_stirling.hpp>
+#include <stan/math/prim/err/check_nonnegative.hpp>
+
 
 namespace stan {
 namespace math {
 
-namespace internal {
-constexpr double lgamma_stirling_diff_big = 1e10;
-}
-
-// namespace lgamma_stirling_diff_internal {
-//     typedef long double Real;
+constexpr double lgamma_stirling_diff_useful = 10;
 
-//     boost::math::chebyshev_transform<Real>
-//     build_lgamma_stirling_diff_chebyshev() {
-//         std::cout << "Size: " << sizeof(Real) << std::endl;
-//         auto f = [](Real t) {
-//             Real x = 10 * std::sqrt(2 / (t + 1));
-//             if(x > internal::lgamma_stirling_diff_big) {
-//                 return 1.0 / (12.0 * x);
-//             } else {
-//                 Real stirling = 0.5
-//                     * std::log(2* static_cast<Real>(stan::math::pi()))
-//                     + (x - 0.5)*std::log(x) -x;
-//                 return (std::lgamma(x) - stirling);
-//             }
-//         };
-//         auto transform = boost::math::chebyshev_transform<Real>(f, -1, 1,
-//         1e-8); std::cout << "Coeffs: " << transform.coefficients().size() <<
-//         std::endl;
-//         //std::cout << transform.coefficients()[0];
-//         size_t coeffs_to_print =
-//             std::min(size_t(20), transform.coefficients().size());
-//         for(size_t i = 0; i < coeffs_to_print ; i ++) {
-//             std::cout << std::setprecision(17) << transform.coefficients()[i]
-//                 << std::endl;
-//         }
-//         return transform;
-//     }
+/**
+ * Return the difference between log of the gamma function and it's Stirling 
+ * approximation.
+ * This is useful to stably compute log of ratios of gamma functions with large
+ * arguments where the Stirling approximation allows for analytic solution 
+ * and the (small) differences can be added afterwards. 
+ * This is for example used in the implementation of lbeta.
+ * 
+ * The function will return correct value for all arguments, but the can add
+ * precision only when x >= lgamma_stirling_diff_useful.
+ *
+   \f[
+   \mbox{lgamma_stirling_diff}(x) =
+    \log(\Gamma(x)) - \frac{1}{2} \log(2\pi) + 
+    (x-\frac{1}{2})*\log(x) - x
+   \f]
 
-//     boost::math::chebyshev_transform<Real> lgamma_stirling_diff_chebyshev =
-//         build_lgamma_stirling_diff_chebyshev();
-// }
+ *
+ * @param x value
+ * @return Difference between lgamma(x) and it's Stirling approximation.
+ * @tparam T Type of  value.
+ */
 
-double lgamma_stirling_diff(const double x) {
-  if (x < internal::lgamma_stirling_diff_big) {
-    return std::lgamma(static_cast<long double>(x))
-           - lgamma_stirling(static_cast<long double>(x));
+template <typename T>
+T lgamma_stirling_diff(const T x) {  
+    static const char* function = "lgamma_stirling_diff";
+    check_nonnegative(function, "argument", x);
 
-    // double ten_over_x = 10.0 / x;
-    // double t = ten_over_x * ten_over_x * 2 - 1;
-    // return internal::lgamma_stirling_diff_chebyshev(t);
-  } else {
-    return 1.0 / (12.0 * x);
-  }
+    if (value_of(x) < lgamma_stirling_diff_useful) {
+        return lgamma(x) - lgamma_stirling(x);
+    } else {
+        // Using the Stirling series as expressed in formula 5.11.1. at
+        // https://dlmf.nist.gov/5.11
+        constexpr double stirling_series[] = {
+            0.0833333333333333333333333,  -0.00277777777777777777777778,
+            0.000793650793650793650793651,-0.000595238095238095238095238,
+            };
+        constexpr int n_stirling_terms = 3;
+        T result(0.0);
+        T multiplier = inv(x);
+        T inv_x_squared = inv(square(x));
+        for(int n = 0; n < n_stirling_terms; 
+                n++, multiplier *= inv_x_squared) {
+            result += stirling_series[n] * multiplier;
+        }
+        return result;
+    }
 }
 
 }  // namespace math
diff --git a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
index dc89b20f0a1..5a86fd89bf1 100644
--- a/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/scal/fun/binomial_coefficient_log_test.cpp
@@ -21,9 +21,13 @@ TEST(MathFunctions, binomial_coefficient_log) {
 
   EXPECT_FLOAT_EQ(29979.16, binomial_coefficient_log(100000, 91116));
 
+  EXPECT_EQ(binomial_coefficient_log(-1, 0), 0); // Needed for neg_binomial_2
   EXPECT_EQ(binomial_coefficient_log(50, 0), 0);
   EXPECT_EQ(binomial_coefficient_log(10000, 0), 0);
 
+  EXPECT_EQ(binomial_coefficient_log(10, 11), -std::numeric_limits<double>::infinity()); 
+  EXPECT_EQ(binomial_coefficient_log(10, -1), -std::numeric_limits<double>::infinity()); 
+
   for (int n = 0; n < 1010; ++n) {
     test_binom_coefficient(1010, n);
     test_binom_coefficient(1010.0, n);
@@ -44,6 +48,15 @@ TEST(MathFunctions, binomial_coefficient_log_nan) {
   EXPECT_TRUE(std::isnan(stan::math::binomial_coefficient_log(nan, nan)));
 }
 
+TEST(MathFunctions, binomial_coefficient_log_errors) {
+  using stan::math::binomial_coefficient_log;
+  EXPECT_NO_THROW(binomial_coefficient_log(10, 11));
+  EXPECT_THROW(binomial_coefficient_log(10, 11.01), std::domain_error);
+  EXPECT_THROW(binomial_coefficient_log(-1, 0.3), std::domain_error);
+  EXPECT_THROW(binomial_coefficient_log(10, -1.1), std::domain_error);
+  EXPECT_NO_THROW(binomial_coefficient_log(10, -0.9));
+}
+
 namespace binomial_coefficient_test_internal {
 struct TestValue {
   double n;
@@ -51,69 +64,7 @@ struct TestValue {
   double val;
 };
 
-std::vector<TestValue> testValues = {
-    {0.00003, 3.e-20, 1.4804082055036736261e-24},
-    {0.00003, 3.e-15, 1.4804082053556342859e-19},
-    {0.00003, 3.e-10, 1.4803934014216156867e-14},
-    {0.00003, 3.e-7, 1.4656041234443424231e-11},
-    {0.00003, 6.e-6, 2.3686531286936713477e-10},
-    {0.00003, 0.000015, 3.7010205134852404454e-10},
-    {0.00003, 0.0000291, 4.3079878779785775469e-11},
-    {0.00003, 0.0000299999982, 8.8824487000750964998e-17},
-    {0.00003, 0.00003, 1.4804082055036751063e-28},
-    {0.002, 2.e-18, 6.5701370962226547789e-21},
-    {0.002, 2.e-13, 6.5701370955656467768e-16},
-    {0.002, 2.e-8, 6.5700713947654458316e-11},
-    {0.002, 0.00002, 6.5044356407218957555e-8},
-    {0.002, 0.0004, 1.0512217145828735086e-6},
-    {0.002, 0.001, 1.6425337349621531325e-6},
-    {0.002, 0.00194, 1.9119098219591897636e-7},
-    {0.002, 0.00199999988, 3.9420820212083508274e-13},
-    {0.002, 0.002, 6.5701370962226613484e-25},
-    {1, 1.e-15, 9.999999999999988551e-16},
-    {1, 1.e-10, 9.999999998855065933e-11},
-    {1, 0.00001, 9.9998855069266455991e-6},
-    {1, 0.01, 0.0098858370348613105263},
-    {1, 0.2, 0.15645796291768801671},
-    {1, 0.5, 0.24156447527049044469},
-    {1, 0.97, 0.028978328236256312961},
-    {1, 0.99999994, 5.9999995878237431346e-8},
-    {1, 1., 9.999999999999999999e-20},
-    {8, 8.e-15, 2.1742857142857086459e-14},
-    {8, 8.e-10, 2.1742857137217315398e-9},
-    {8, 0.00008, 0.00021742293180507342042},
-    {8, 0.08, 0.21198226737825583898},
-    {8, 1.6, 2.9067860629113428343},
-    {8, 4, 4.2484952420493589891},
-    {8, 7.76, 0.60627458624545365112},
-    {8, 7.99999952, 1.3045712255376840361e-6},
-    {8, 8., 2.1742857142857142852e-18},
-    {1325, 1.325e-12, 1.0290957946506935679e-11},
-    {1325, 1.325e-7, 1.0290957802047796044e-6},
-    {1325, 0.01325, 0.10276604269137043037},
-    {1325, 13.25, 71.989832127409062998},
-    {1325, 265, 659.43564932902941932},
-    {1325, 662.5, 914.5994503408452751},
-    {1325, 1285.25, 175.78626065119186267},
-    {1325, 1324.9999205, 0.00061745227641045219017},
-    {1325, 1325., 1.029095794650838014e-15},
-    {845000, 8.45e-10, 1.2019540397111151912e-8},
-    {845000, 0.0000845, 0.0012019481673871213658},
-    {845000, 8.45, 103.7383038277367436},
-    {845000, 8450, 47315.861645757620061},
-    {845000, 169000, 422833.22169549650655},
-    {845000, 422500, 585702.31823555211409},
-    {845000, 819650, 113851.15813267856212},
-    {845000, 844999.9493, 0.7191087768194817628},
-    {845000, 845000., 1.2019540397698355631e-12},
-    {3000000000000000.0, 3, 105.12040658150832885},
-    {3000000000000000.0, 100, 3199.999492802314355},
-    {3000000000000000.0, 12895, 350387.52436058836877},
-    {100000000000000000000.0, 3, 136.36334611041468604},
-    {100000000000000000000.0, 100, 4241.4308104325278778},
-    {100000000000000000000.0, 12895, 484680.0927690319003},
-};
-
+std::vector<TestValue> testValues = {  {0.00003,-0.9,-2.21375637737528044964112},  {0.00003,3.e-15,1.48040820535563428588846e-19},  {0.00003,3.e-10,1.48039340142161568666212e-14},  {0.00003,3.e-7,1.46560412344434242311062e-11},  {0.00003,6.e-6,2.36865312869367134774661e-10},  {0.00003,0.000015,3.70102051348524044535716e-10},  {0.00003,0.0000291,4.30798787797857754693695e-11},  {0.00003,0.0000299999982,8.88244870007509649977929e-17},  {0.00003,0.00002999999991,4.44122460318735146597007e-18},  {0.00003,0.90003,-2.21375637737528044964112},  {0.002,-0.9,-2.21559326412971099686943},  {0.002,2.e-13,6.57013709556564677684856e-16},  {0.002,2.e-8,6.57007139476544583161173e-11},  {0.002,0.00002,6.50443564072189575550994e-8},  {0.002,0.0004,1.05122171458287350859763e-6},  {0.002,0.001,1.64253373496215313253469e-6},  {0.002,0.00194,1.91190982195918976356429e-7},  {0.002,0.00199999988,3.94208202120835082737684e-13},  {0.002,0.001999999994,1.97104112295366725515452e-14},  {0.002,0.902,-2.21559326412971099686943},  {1,-0.9,-2.85558226198351740582195},  {1,1.e-10,9.9999999988550659331851e-11},  {1,0.00001,9.99988550692664559909352e-6},  {1,0.01,0.00988583703486131052627978},  {1,0.2,0.156457962917688016707705},  {1,0.5,0.241564475270490444691037},  {1,0.97,0.028978328236256312960776},  {1,0.99999994,5.99999958782374313463811e-8},  {1,0.999999997,2.99999998969559340736596e-9},  {1,1.9,-2.85558226198351740582195},  {8,-0.9,-4.22528965320883461943031},  {8,8.e-10,2.17428571372173153982474e-9},  {8,0.00008,0.000217422931805073420417006},  {8,0.08,0.211982267378255838975509},  {8,1.6,2.90678606291134283426263},  {8,4,4.24849524204935898912334},  {8,7.76,0.606274586245453651115361},  {8,7.99999952,1.30457122553768403613331e-6},  {8,7.999999976,6.52285709209869625945566e-8},  {8,8.9,-4.22528965320883461943031},  {1325,-0.9,-8.72360867216657209762532},  {1325,1.325e-7,1.02909578020477960435539e-6},  {1325,0.01325,0.102766042691370430370992},  {1325,13.25,71.9898321274090629975055},  {1325,265,659.435649329029419323398},  {1325,662.5,914.599450340845275100724},  {1325,1285.25,175.786260651191862665015},  {1325,1324.9999205,0.000617452276410452190170437},  {1325,1324.999996025,0.0000308728608380968862741097},  {1325,1325.9,-8.72360867216657209762532},  {845000,-0.9,-14.5350963792733464918229},  {845000,0.0000845,0.00120194816738712136581358},  {845000,8.45,103.738303827736743600251},  {845000,8450,47315.8616457576200611209},  {845000,169000,422833.221695496506553128},  {845000,422500,585702.318235552114086514},  {845000,819650,113851.158132678562120685},  {845000,844999.9493,0.719108776819481762797449},  {845000,844999.997465,0.036053342347290003917417},  {845000,845000.9,-14.5350963792733464918229},  {3000000000000000.0,3,105.120406581508328854183},  {3000000000000000.0,100,3199.99949280231435502243},  {3000000000000000.0,12895,350387.5243605883687667},  {100000000000000000000.0,3,136.363346110414686040237},  {100000000000000000000.0,100,4241.4308104325278778424},  {100000000000000000000.0,12895,484680.092769031900296878},};
 }  // namespace binomial_coefficient_test_internal
 
 TEST(MathFunctions, binomial_coefficient_log_precomputed) {
@@ -122,10 +73,22 @@ TEST(MathFunctions, binomial_coefficient_log_precomputed) {
   using stan::test::expect_near_rel;
 
   for (TestValue t : testValues) {
-    double val = stan::math::binomial_coefficient_log(t.n, t.k);
 
     std::ostringstream msg;
-    msg << "n = " << t.n << ", k = " << t.k;
+    msg << std::setprecision(22) << "n = " << t.n << ", k = " << t.k;
+
+    double val = stan::math::binomial_coefficient_log(t.n, t.k);
     expect_near_rel(msg.str(), val, t.val);
+
+    if(t.k > t.n / 10) {
+      // Testing the mirrored binomial coefficient is not performed for
+      // small k, as we may loose so much precision computing k2
+      // that the test becomes invalid
+      std::ostringstream msg2;
+      double k2 = t.n - t.k;
+      msg2 << std::setprecision(22) << "n = " << t.n << ", k = " << k2;
+      double val2 = stan::math::binomial_coefficient_log(t.n, k2);
+      expect_near_rel(msg2.str(), val2, t.val);
+    }
   }
 }
diff --git a/test/unit/math/prim/scal/fun/lbeta_test.cpp b/test/unit/math/prim/scal/fun/lbeta_test.cpp
index 512a103bd44..d924680f1ce 100644
--- a/test/unit/math/prim/scal/fun/lbeta_test.cpp
+++ b/test/unit/math/prim/scal/fun/lbeta_test.cpp
@@ -32,6 +32,39 @@ namespace lbeta_test_internal {
     double val;
   };
 
+// Test values generated in Mathematice, reproducible notebook at
+// https://www.wolframcloud.com/obj/martin.modrak/Published/lbeta.nb
+// Mathematica Code reproduced below for convenience:
+//
+// lbeta[x_,y_]:= LogGamma[x] + LogGamma[y] - LogGamma[x + y]
+// out = OpenWrite["lbeta_test.txt"]
+// xs= {8*10^-8,4*10^-3,1,1+10^-8,5,23, 19845};
+// ys =  {7*10^-11,2*10^-5,1+10^-12,1/2,2,1624};
+//  WriteString[out, "std::vector<TestValue> testValues = {"];
+//  For[i = 1, i <= Length[xs], i++, {
+//        For[j = 1, j <= Length[ys], j++, {
+//      cx = xs[[i]];
+//      cy = ys[[j]];
+            
+//     val = N[lbeta[cx,cy],24];
+//          WriteString[out,"  {",CForm[cx],",",CForm[cy],",",
+//            CForm[val],"},"]
+// }]
+// }]
+// extremeXs = {3*10^15,10^20};
+// lowYs = {3, 100, 12895};
+//      For[i = 1, i <= Length[extremeXs], i++, {
+//        For[j = 1, j <= Length[lowYs], j++, {
+//      cx = extremeXs[[i]];
+//          cy = lowYs[[j]];
+//     val = N[lbeta[cx,cy],24];
+//          WriteString[out,"  {",CForm[cx],".0,",CForm[cy],",",
+//            CForm[val],"},"]
+//      }]
+//   }]
+// WriteString[out,"};"];
+//  Close[out];
+//  FilePrint[%]
 std::vector<TestValue> testValues = {  {8.e-8,7.e-11,23.3834004912898500586445},  {8.e-8,0.00002,16.3452312235394351410033},  {8.e-8,1.000000000001,16.3412392022725295437606},  {8.e-8,0.5,16.3412393131760679059067},  {8.e-8,2,16.3412391222725327438921},  {8.e-8,1624,16.3412385647081130254943},  {0.004,7.e-11,23.3825258913787298259023},  {0.004,0.00002,10.8247656947117878792194},  {0.004,1.000000000001,5.52146091786223987264715},  {0.004,0.5,5.52697992926150653113797},  {0.004,2,5.51746889659270898022044},  {0.004,1624,5.48959582574332555214719},  {1,7.e-11,23.3825258738791892190926},  {1,0.00002,10.8197782844102831106727},  {1,1.000000000001,-9.999999999995e-13},  {1,0.5,0.693147180559945309417232},  {1,2,-0.693147180559945309417232},  {1,1624,-7.39264752072162326054032},  {1.00000001,7.e-11,23.3825258738791892179411},  {1.00000001,0.00002,10.8197782844099541286699},  {1.00000001,1.000000000001,-1.00009999500064491739816e-8},  {1.00000001,0.5,0.693147174422888956122731},  {1.00000001,2,-0.693147195559945246917232},  {1.00000001,1624,-7.39264760042333353631934},  {5,7.e-11,23.3825258737333558857627},  {5,0.00002,10.8197366180283355258393},  {5,1.000000000001,-1.60943791243638370793409},  {5,0.5,-0.207395194346070587158746},  {5,2,-3.40119738166215537541324},  {5,1624,-33.7913357290267948074624},  {23,7.e-11,23.3825258736208322915813},  {23,0.00002,10.819704468465374949026},  {23,1.000000000001,-3.13549421593288398231784},  {23,0.5,-0.989947810259228199543883},  {23,2,-6.31354804627709531045369},  {23,1624,-121.714785277510463870251},  {19845,7.e-11,23.3825258731460863706715},  {19845,0.00002,10.8195688267825637640878},  {19845,1.000000000001,-9.89570736522763869861762},  {19845,0.5,-4.37548244086806082919414},  {19845,2,-19.7914651196913525680177},  {19845,1624,-5756.4146766727238501215},  {3000000000000000.0,3,-106.219018870176440545578},  {3000000000000000.0,100,-3204.60466298830574639047},  {3000000000000000.0,12895,-350396.988955562106921852},  {100000000000000000000.0,3,-137.461958399082795731692},  {100000000000000000000.0,100,-4246.03598061851596930944},  {100000000000000000000.0,12895,-484689.557363950217404711},};
 }
 
diff --git a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
index e7c96deeeb0..35c4c08f048 100644
--- a/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/scal/fun/lgamma_stirling_diff_test.cpp
@@ -10,16 +10,17 @@ TEST(MathFunctions, lgamma_stirling_diff_errors) {
 }
 
 TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
-  using stan::math::internal::lgamma_stirling_diff_big;
+  using stan::math::lgamma_stirling_diff_useful;
   using stan::math::lgamma_stirling_diff;
   using stan::test::expect_near_rel;
 
-  long double start = std::nextafter(10, 11);
-  for (long double x = start; x < 2 * lgamma_stirling_diff_big; x *= 1.5) {
+  double start = std::nextafter(10, 11);
+  for (double x = start; x < 1e8; x *= 1.5) {
+    long double x_l = static_cast<long double>(x);
     long double stirling
         = 0.5 * std::log(2 * static_cast<long double>(stan::math::pi()))
-          + (x - 0.5) * std::log(x) - x;
-    long double lgamma_res = std::lgamma(x);
+          + (x_l - 0.5) * std::log(x_l) - x_l;
+    long double lgamma_res = std::lgamma(x_l);
     double diff_actual = static_cast<double>(lgamma_res - stirling);
     double diff = lgamma_stirling_diff(x);
 
@@ -29,8 +30,8 @@ TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
     expect_near_rel(msg.str(), diff, diff_actual, 1e-4);
   }
 
-  double before_big = std::nextafter(lgamma_stirling_diff_big, 0);
-  double after_big = std::nextafter(lgamma_stirling_diff_big,
+  double before_big = std::nextafter(lgamma_stirling_diff_useful, 0);
+  double after_big = std::nextafter(lgamma_stirling_diff_useful,
                                     stan::math::positive_infinity());
   expect_near_rel("big cutoff", lgamma_stirling_diff(before_big),
                   lgamma_stirling_diff(after_big));
@@ -42,37 +43,8 @@ struct TestValue {
   double val;
 };
 
-std::vector<TestValue> testValues = {
-    {10.049787068367863943, 0.0082893206359322200849},
-    {10.135335283236612692, 0.0082193992370778811855},
-    {10.367879441171442322, 0.0080351590240775284273},
-    {11., 0.007573675487951840795},
-    {12.718281828459045235, 0.0065508998676477812047},
-    {17.389056098930650227, 0.0047917583976502091168},
-    {30.085536923187667741, 0.0027697782366142911547},
-    {64.598150033144239078, 0.0012900163188678122747},
-    {158.41315910257660342, 0.00052604987562270910548},
-    {413.42879349273512261, 0.0002015663117649479817},
-    {1106.6331584284585993, 0.000075303482848309432847},
-    {2990.9579870417282747, 0.000027861753118520084151},
-    {8113.0839275753840077, 0.000010271474329002342817},
-    {22036.465794806716517, 3.7816106313768371052e-6},
-    {59884.141715197818455, 1.3915759823173656792e-6},
-    {162764.79141900392081, 5.1198623858832122975e-7},
-    {442423.39200892050333, 1.8835652643709875774e-7},
-    {1.2026142841647767777e6, 6.9293483730078043652e-8},
-    {3.2690273724721106393e6, 2.5491782061865871668e-8},
-    {8.8861205205078726368e6, 9.3779206731455076929e-9},
-    {2.4154962753575298215e7, 3.4499466707312036902e-9},
-    {6.5659979137330511139e7, 1.2691647854325126115e-9},
-    {1.7848231096318726084e8, 4.6689967696866715977e-10},
-    {4.8516520540979027797e8, 1.717627983295846792e-10},
-    {1.3188157444832146972e9, 6.318800308680570434e-11},
-    {3.5849128561315915617e9, 2.3245567375731604902e-11},
-    {9.7448034562489026e9, 8.5515663509760607976e-12},
-    {2.6489122139843472294e10, 3.1459454523782780579e-12},
-    {7.2004899347385872524e10, 1.1573286552529392289e-12},
-};
+std::vector<TestValue> testValues = {  {1.049787068367863943,0.077388806767834476832},  {1.1353352832366126919,0.071790358566585005482},  {1.3678794411714423216,0.059960812482712981438},  {2.,0.041340695955409294094},  {3.7182818284590452354,0.022358812123082674471},  {8.3890560989306502272,0.0099288907523535997267},  {21.085536923187667741,0.0039518599801395734578},  {55.598150033144239078,0.0014988346688724404687},  {149.41315910257660342,0.0005577367442531155476},  {404.42879349273512261,0.00020605188772717995062},  {1097.6331584284585993,0.000075920930766205666598},  {2981.9579870417282747,0.00002794584410078046085},  {8104.0839275753840077,0.000010282881326966996581},  {22027.465794806716517,3.7831557249429676373e-6},  {59875.141715197818455,1.3917851539949910276e-6},  {162755.79141900392081,5.1201455018391551878e-7},  {442414.39200892050333,1.8836035815859912686e-7},  {1.2026052841647767777e6,6.9294002305342748064e-8},  {3.2690183724721106393e6,2.5491852243801980915e-8},  {8.8861115205078726368e6,9.3779301712579119232e-9},  {2.4154953753575298215e7,3.4499479561619419703e-9},  {6.5659970137330511139e7,1.2691649593966957356e-9},  {1.7848230196318726084e8,4.6689970051216164913e-10},  {4.8516519640979027797e8,1.7176280151585029843e-10},  {1.3188157354832146972e9,6.3188003518019870566e-11},  {3.5849128471315915617e9,2.3245567434090096532e-11},  {9.7448034472489026e9,8.5515663588740238069e-12},  {2.6489122130843472294e10,3.1459454534471511195e-12},  {7.2004899338385872524e10,1.1573286553975954675e-12},  {1.9572960942983876427e11,4.2575741900310182743e-13},  {5.3204824060279861668e11,1.5662740137796255552e-13},  {1.4462570642924751737e12,5.7620000891128517638e-14},};
+
 }  // namespace lgamma_stirling_diff_test_internal
 
 TEST(MathFunctions, lgamma_stirling_diff_precomputed) {
@@ -83,6 +55,6 @@ TEST(MathFunctions, lgamma_stirling_diff_precomputed) {
   for (TestValue t : testValues) {
     std::ostringstream msg;
     msg << "x = " << t.x;
-    expect_near_rel(msg.str(), lgamma_stirling_diff(t.x), t.val);
+    expect_near_rel(msg.str(), lgamma_stirling_diff(t.x), t.val, 1e-10);
   }
 }
\ No newline at end of file

From a791f8ffd08737c63705079a665ea1b5a94ef70a Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 19:50:41 +0100
Subject: [PATCH 59/82] Fixing derivative w.r.t. phi for large difference
 between mu and phi

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   |  12 +-
 .../math/rev/prob/neg_binomial_2_test.cpp     | 570 ++++++------------
 2 files changed, 189 insertions(+), 393 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index f9e867d23a9..e07abc03d6e 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -141,10 +141,16 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
                - (n_vec[i] + phi_val[i]) / (mu_val[i] + phi_val[i]);
       }
       if (!is_constant_all<T_precision>::value) {
+        T_partials_return log_term;
+        if(mu_val[i] < phi_val[i]) {
+          log_term = log1p(-mu_val[i]/(mu_val[i] + phi_val[i]));
+        } else {
+          log_term = log_phi[i] - log_mu_plus_phi[i];
+        }
         ops_partials.edge2_.partials_[i]
-            += 1.0 - n_plus_phi[i] / (mu_val[i] + phi_val[i]) + log_phi[i]
-               - log_mu_plus_phi[i] - digamma(phi_val[i])
-               + digamma(n_plus_phi[i]);
+            += (mu_val[i] - n_vec[i]) / (mu_val[i] + phi_val[i])
+               + log_term
+               - (digamma(phi_val[i]) - digamma(n_plus_phi[i]));
       }
     }
   }
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 10aad48bb84..4ca9374cd6d 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -13,401 +13,190 @@ struct TestValue {
   double phi;
   double value;
   double grad_mu;
-  double grad_phi;
-
-  TestValue(int _n, double _mu, double _phi, double _value, double _grad_mu,
-            double _grad_phi)
-      : n(_n),
-        mu(_mu),
-        phi(_phi),
-        value(_value),
-        grad_mu(_grad_mu),
-        grad_phi(_grad_phi) {}
+  double grad_phi;  
 };
 
 // Test data generated in Mathematica (Wolfram Cloud). The code can be re-ran
 // at https://www.wolframcloud.com/env/martin.modrak/NegBinomial2_Tests.nb
 // but is also presented below for convenience:
 //
-// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] +
-//    n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
-// nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
-// nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
-// out = OpenWrite["nb_test.txt"]
-// mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
-// phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
-// ns = {0,6,14,1525,10233};
-//  WriteString[out, "std::vector<TestValue> testValues = {"];
-//      For[k = 1, k <= Length[ns], k++, {
-//   For[i = 1, i <= Length[mus], i++, {
-//        For[j = 1, j <= Length[phis], j++, {
-//          cmu = mus[[i]];
-//          cphi = phis[[j]];
-//     cn=ns[[k]];
-//          val = N[nb2[cn,cmu,cphi], 20];
-//     ddmu= N[nb2dmu[cn,cmu,cphi], 20];
-//     ddphi= N[nb2dphi[cn,cmu,cphi], 20];
-//         WriteString[out,"  TestValue(",CForm[cn],",",CForm[cmu],",",
-//            CForm[cphi],",", CForm[val],",",CForm[ddmu],",",CForm[ddphi],"),"]
-//        }]
-//      }]
-//   }]
-// WriteString[out,"};"];
-//  Close[out];
-//  FilePrint[%]
-std::vector<TestValue> testValues = {
-    TestValue(0, 0.0000256, 0.0004, -0.000024814156367781056525,
-              -0.93984962406015037594, -0.001885014979603017252),
-    TestValue(0, 0.0000256, 0.065, -0.000025594960092486140389,
-              -0.9996063088998794321, -7.7516686911183493794e-8),
-    TestValue(0, 0.0000256, 4.42, -0.000025599925864539648095,
-              -0.9999942081783417725, -1.6772663823239562834e-11),
-    TestValue(0, 0.0000256, 800, -0.000025599999590400008738,
-              -0.999999968000001024, -5.119999781546674531e-16),
-    TestValue(0, 0.0000256, 15324, -0.000025599999978616549228,
-              -0.99999999832941790934, -1.3954222623666383236e-18),
-    TestValue(0, 0.314, 0.0004, -0.002666782716971682618,
-              -0.0012722646310432569975, -5.668229057060249802),
-    TestValue(0, 0.314, 0.065, -0.11460468078714130042, -0.17150395778364116095,
-              -0.93465289297043039811),
-    TestValue(0, 0.314, 4.42, -0.30334820230965961631, -0.93367131389945078158,
-              -0.0023021289016362151355),
-    TestValue(0, 0.314, 800, -0.313938393619808991, -0.99960765399580664589,
-              -7.6987831407130236997e-8),
-    TestValue(0, 0.314, 15324, -0.3139967829987878124, -0.99997950968637160528,
-              -2.0992934397861783072e-10),
-    TestValue(0, 1.5, 0.0004, -0.0032919111000327549336,
-              -0.00026659557451346307651, -7.2300443456564007971),
-    TestValue(0, 1.5, 0.065, -0.20678149915011007124, -0.041533546325878594249,
-              -2.2227873794044950749),
-    TestValue(0, 1.5, 4.42, -1.2915096474038793989, -0.74662162162162162162,
-              -0.038818374427929177938),
-    TestValue(0, 1.5, 800, -1.4985955053442782733, -0.99812850904553961323,
-              -1.7534272199610668797e-6),
-    TestValue(0, 1.5, 15324, -1.4999265905382969801, -0.9999021239111285113,
-              -4.7901769514626171505e-9),
-    TestValue(0, 3, 0.0004, -0.003569116649587854519,
-              -0.00013331555792560991868, -7.9229249395275619074),
-    TestValue(0, 3, 0.065, -0.25047201260085385312, -0.021207177814029363785,
-              -2.8746227562887040272),
-    TestValue(0, 3, 4.42, -2.2897339760163958674, -0.59568733153638814016,
-              -0.11372669262607046311),
-    TestValue(0, 3, 800, -2.9943890230675014931, -0.99626400996264009963,
-              -6.9962414744764927742e-6),
-    TestValue(0, 3, 15324, -2.9997063813121767354, -0.99980426697983949892,
-              -1.9158207560574170962e-8),
-    TestValue(0, 180, 0.0004, -0.0052068020335865022334,
-              -2.2222172839615911965e-6, -12.017007306183539545),
-    TestValue(0, 180, 0.065, -0.51523458388368826209,
-              -0.00036098075694887957127, -6.9270468866598452194),
-    TestValue(0, 180, 4.42, -16.491356225074536835, -0.023967031775295521093,
-              -2.7550431007966839452),
-    TestValue(0, 180, 800, -162.35267519735224589, -0.81632653061224489796,
-              -0.019267374608935205317),
-    TestValue(0, 180, 15324, -178.95104102256056893, -0.98839009287925696594,
-              -0.000067921189264833924309),
-    TestValue(0, 1123, 0.0004, -0.0059391221287133807664,
-              -3.5618865318302647087e-7, -13.847805677972105099),
-    TestValue(0, 1123, 0.065, -0.63421701478373420435,
-              -0.000057877326779839101032, -8.7572427201534599061),
-    TestValue(0, 1123, 4.42, -24.493639593452325812, -0.0039204555533873800358,
-              -4.5454678748864927673),
-    TestValue(0, 1123, 800, -701.62401433668194795, -0.41601664066562662507,
-              -0.29304665858647906001),
-    TestValue(0, 1123, 15324, -1083.7571513972578336, -0.93172007052957986259,
-              -0.0024429334503092957394),
-    TestValue(0, 10586, 0.0004, -0.0068365334804239916148,
-              -3.7785753342688330146e-8, -16.09133373884573238),
-    TestValue(0, 10586, 0.065, -0.78004301710859758932,
-              -6.1401474485561915594e-6, -11.0006679418181807),
-    TestValue(0, 10586, 4.42, -34.39451907585020003, -0.00041735832950912239552,
-              -6.7819827601055724777),
-    TestValue(0, 10586, 800, -2124.4224654744799162, -0.070261724925346917267,
-              -1.7257898067684468125),
-    TestValue(0, 10586, 15324, -8048.2991567805804192, -0.59143187958317252026,
-              -0.11664064731878857477),
-    TestValue(6, 0.0000256, 0.0004, -26.480362597222490265,
-              220276.31578947368421, -11595.463497838709543),
-    TestValue(6, 0.0000256, 0.065, -51.419388136448102673,
-              234281.72904210034202, -74.693807545973030394),
-    TestValue(6, 0.0000256, 4.42, -67.52038137511190777, 234372.64254759067459,
-              -0.43125592475849002503),
-    TestValue(6, 0.0000256, 800, -69.998079065742703551, 234373.99250003224,
-              -0.000023330384471037817491),
-    TestValue(6, 0.0000256, 15324, -70.015807321298395432,
-              234373.99960845899308, -6.3861427657507748849e-8),
-    TestValue(6, 0.314, 0.0004, -9.6251974944123758225, 0.023038524497171844865,
-              2477.5305495558165941),
-    TestValue(6, 0.314, 0.065, -5.6231627412658002701, 3.1056417323496294304,
-              0.81175666468752807101),
-    TestValue(6, 0.314, 4.42, -11.748118636048988335, 16.907181817937188357,
-              -0.34352697543671422216),
-    TestValue(6, 0.314, 800, -13.827010724885832016, 18.101175543376294868,
-              -0.000020465017270475111936),
-    TestValue(6, 0.314, 15324, -13.842565956985816742, 18.107909210435378814,
-              -5.6049178830042368725e-8),
-    TestValue(6, 1.5, 0.0004, -9.6197839616192332262, 0.00079978672354038922954,
-              2491.0537701151673519),
-    TestValue(6, 1.5, 0.065, -4.8410045398874440986, 0.12460063897763578275,
-              11.520890928200777244),
-    TestValue(6, 1.5, 4.42, -4.6947113008756524511, 2.2398648648648648649,
-              -0.12612961153608977325),
-    TestValue(6, 1.5, 800, -5.6375883578559464151, 2.9943855271366188397,
-              -0.000011047869532026303582),
-    TestValue(6, 1.5, 15324, -5.6459956995659817151, 2.9997063717333855339,
-              -3.0329592747982916341e-8),
-    TestValue(6, 3, 0.0004, -9.6192613271356102502, 0.00013331555792560991868,
-              2492.3600897701139881),
-    TestValue(6, 3, 0.065, -4.7587824423548651205, 0.021207177814029363785,
-              12.745335721641112642),
-    TestValue(6, 3, 4.42, -2.8891081958287456629, 0.59568733153638814016,
-              0.0038502468520587354154),
-    TestValue(6, 3, 800, -2.9857172436024219525, 0.99626400996264009963,
-              -2.3069406647953774853e-6),
-    TestValue(6, 3, 15324, -2.9874796347761073428, 0.99980426697983949892,
-              -6.3824584044662864326e-9),
-    TestValue(6, 180, 0.0004, -9.620112399166720505, -2.1481433744962048232e-6,
-              2490.2324075130827354),
-    TestValue(6, 180, 0.065, -4.897099604874425479, -0.00034894806505058358556,
-              10.617175935000477685),
-    TestValue(6, 180, 4.42, -11.802883319144519128, -0.023168130716119003723,
-              -1.861375256665487843),
-    TestValue(6, 180, 800, -138.97312319086169782, -0.78911564625850340136,
-              -0.01791315421299756019),
-    TestValue(6, 180, 15324, -154.44163935948173426, -0.95544375644994840041,
-              -0.000063439277219443465219),
-    TestValue(6, 1123, 0.0004, -9.6208335230756285524,
-              -3.5428559715533443274e-7, 2488.4295995707558483),
-    TestValue(6, 1123, 0.065, -5.0142630342277769584,
-              -0.000057568097963562133439, 8.8149588796763128876),
-    TestValue(6, 1123, 4.42, -19.683182166303213058, -0.0038995092191751589493,
-              -3.6245874838477290528),
-    TestValue(6, 1123, 800, -671.30418475064697583, -0.4137939337698174,
-              -0.28869011401594177783),
-    TestValue(6, 1123, 15324, -1048.6172073187539315, -0.92674204700048148398,
-              -0.0024162628059421836267),
-    TestValue(6, 10586, 0.0004, -9.6217290240095637933,
-              -3.7764336894543976284e-8, 2486.1908475533798261),
-    TestValue(6, 10586, 0.065, -5.1597786035400147054,
-              -6.1366672969700081899e-6, 6.576309397642172055),
-    TestValue(6, 10586, 4.42, -29.562997357281896989,
-              -0.00041712177651676884042, -5.856347033468783979),
-    TestValue(6, 10586, 800, -2091.3124520859014907, -0.07022190154073024605,
-              -1.7188401003298574325),
-    TestValue(6, 10586, 15324, -8002.4249559448888988, -0.59109666408369216554,
-              -0.11648073932479483488),
-    TestValue(14, 0.0000256, 0.0004, -49.814562438358640072,
-              513979.32330827067669, -30391.559221530806766),
-    TestValue(14, 0.0000256, 0.065, -114.92817109028837255,
-              546658.70057331266455, -196.8323920932659291),
-    TestValue(14, 0.0000256, 4.42, -161.64931287705226916,
-              546870.83260332247849, -1.6501286909020252132),
-    TestValue(14, 0.0000256, 800, -173.09898662779720676, 546873.98250003256,
-              -0.00014060727924520899117),
-    TestValue(14, 0.0000256, 15324, -173.2061650426294071,
-              546873.99908640208975, -3.8729368917100577369e-7),
-    TestValue(14, 0.314, 0.0004, -10.482321240387567839,
-              0.055452910001458647348, 2452.9820144458617505),
-    TestValue(14, 0.314, 0.065, -7.9175397204269351928, 7.475169319193990219,
-              -19.406538514452968028),
-    TestValue(14, 0.314, 4.42, -31.109603016060397045, 40.694985993719373875,
-              -1.442358303971396938),
-    TestValue(14, 0.314, 800, -41.614610107637548392, 43.568886473205763553,
-              -0.00013381877200270250453),
-    TestValue(14, 0.314, 15324, -41.716640281901644559, 43.585094170597712707,
-              -3.6878520278347562598e-7),
-    TestValue(14, 1.5, 0.0004, -10.468856159359487018, 0.0022216297876121923043,
-              2486.6186161358083867),
-    TestValue(14, 1.5, 0.065, -5.9696014927268124315, 0.34611288604898828541,
-              7.2989540823233662764),
-    TestValue(14, 1.5, 4.42, -13.334103973863653606, 6.2218468468468468468,
-              -0.88640946083488260684),
-    TestValue(14, 1.5, 800, -20.926415102268522946, 8.3177375753794967769,
-              -0.00010961017476158336951),
-    TestValue(14, 1.5, 15324, -21.010069937869350607, 8.3325176992594042609,
-              -3.0266583844869157132e-7),
-    TestValue(14, 3, 0.0004, -10.467267071498293274, 0.00048882371239390303515,
-              2490.5905361225120861),
-    TestValue(14, 3, 0.065, -5.7194959138831364402, 0.077759651984774333877,
-              11.025105769529760809),
-    TestValue(14, 3, 4.42, -7.7900642906041824751, 2.1841868823000898473,
-              -0.48324536699834770639),
-    TestValue(14, 3, 800, -12.744324478712668241, 3.6529680365296803653,
-              -0.000082224255065357307428),
-    TestValue(14, 3, 15324, -12.807159398994470731, 3.6659489789260781627,
-              -2.2763181750167069646e-7),
-    TestValue(14, 180, 0.0004, -10.467069325725552339, -2.049378161875689659e-6,
-              2491.0847206783138),
-    TestValue(14, 180, 0.065, -5.6892191980516647312,
-              -0.00033290447585285560461, 11.462631774529800832),
-    TestValue(14, 180, 4.42, -9.6533765795967992717, -0.02210292930388364723,
-              -1.3136829976451384132),
-    TestValue(14, 180, 800, -117.57055678993798607, -0.7528344671201814059,
-              -0.016193696733894170103),
-    TestValue(14, 180, 15324, -131.59841923497641062, -0.9115153078775369797,
-              -0.000057701678183561534688),
-    TestValue(14, 1123, 0.0004, -10.467775521386168611,
-              -3.5174818911841171522e-7, 2489.3192333086024842),
-    TestValue(14, 1123, 0.065, -5.8039572920094235935,
-              -0.000057155792875192843316, 9.6977197567649025541),
-    TestValue(14, 1123, 4.42, -17.371029398463366472, -0.0038715807735588641672,
-              -3.0406118289506228066),
-    TestValue(14, 1123, 800, -640.64791491033069867, -0.41083032457540509991,
-              -0.28296755763737220502),
-    TestValue(14, 1123, 15324, -1011.5999306403485179, -0.92010468229501697917,
-              -0.0023809402304773394913),
-    TestValue(14, 10586, 0.0004, -10.468668475096403359,
-              -3.7735781630351504468e-8, 2487.0868493492232687),
-    TestValue(14, 10586, 0.065, -5.9490589506381604899,
-              -6.1320270948550970306e-6, 7.4654379275715350026),
-    TestValue(14, 10586, 4.42, -27.222758867549796685,
-              -0.00041680637252696410027, -5.2660309311076446873),
-    TestValue(14, 10586, 800, -2056.9359371755272758, -0.070168803694574684427,
-              -1.7096599947938850626),
-    TestValue(14, 10586, 15324, -7951.0953369235666607, -0.5906497100843850259,
-              -0.11626776694982782037),
-    TestValue(1525, 0.0000256, 0.0004, -4301.7847274670157821,
-              5.5987134868421052632e7, -3.5806687876344080158e6),
-    TestValue(1525, 0.0000256, 0.065, -11965.467128123482119,
-              5.9546859198531040083e7, -23429.112689114767404),
-    TestValue(1525, 0.0000256, 4.42, -18367.342891800584413,
-              5.9569966479379666941e7, -339.05708253439450269),
-    TestValue(1525, 0.0000256, 800, -24826.228135638531385,
-              5.9570309593750093e7, -0.83897628761764105052),
-    TestValue(1525, 0.0000256, 15324, -25707.717028801610058,
-              5.9570311400482904473e7, -0.0046430629133236893109),
-    TestValue(1525, 0.314, 0.0004, -17.094738795518807033,
-              6.1777199721236284663, -2348.2711549792054389),
-    TestValue(1525, 0.314, 0.065, -296.5855682860990671, 832.76969228442263415,
-              -4001.4921811261694014),
-    TestValue(1525, 0.314, 4.42, -4115.1016067852616032, 4533.6164996945796636,
-              -316.17648561909186371),
-    TestValue(1525, 0.314, 800, -10469.942676752557863, 4853.7827883447466615,
-              -0.83822851603497641238),
-    TestValue(1525, 0.314, 15324, -11350.864477542964446, 4855.5884035212585267,
-              -0.0046410241529681445478),
-    TestValue(1525, 1.5, 0.0004, -15.560537541616769004, 0.27077223851417399804,
-              1484.2803077520377337),
-    TestValue(1525, 1.5, 0.065, -74.450927586875279684, 42.184238551650692226,
-              -953.4745083343278627),
-    TestValue(1525, 1.5, 4.42, -2072.1910365790187577, 758.31869369369369369,
-              -251.67662613527664787),
-    TestValue(1525, 1.5, 800, -8088.5487996808837997, 1013.7658556872530672,
-              -0.8354105724129184353),
-    TestValue(1525, 1.5, 15324, -8967.3316408400039725, 1015.5672571857361913,
-              -0.0046333275254863264045),
-    TestValue(1525, 3, 0.0004, -15.357522072066896545, 0.067635426387592765409,
-              1991.7174903993567368),
-    TestValue(1525, 3, 0.065, -42.491829475398155315, 10.75910821098423056,
-              -477.23846708705704922),
-    TestValue(1525, 3, 4.42, -1360.5497881858611964, 302.21203953279424978,
-              -199.67578957112613322),
-    TestValue(1525, 3, 800, -7035.8464992378503203, 505.43794105437941054,
-              -0.83186161385039575293),
-    TestValue(1525, 3, 15324, -7911.9312240083236782, 507.23403144777190579,
-              -0.0046236034557581425194),
-    TestValue(1525, 180, 0.0004, -15.159228863591761992,
-              0.000016604901371824111996, 2487.4167692289850077),
-    TestValue(1525, 180, 0.065, -10.618383986015501881,
-              0.0026973284338680167964, 7.7929628140754776749),
-    TestValue(1525, 180, 4.42, -30.75693264206759737, 0.17908698743206931039,
-              -5.0606677133089086733),
-    TestValue(1525, 180, 800, -1255.1060610431618143, 6.0997732426303854875,
-              -0.50811617220616562857),
-    TestValue(1525, 180, 15324, -1861.5172673616192307, 7.3854704162366701066,
-              -0.0035556000115225182714),
-    TestValue(1525, 1123, 0.0004, -15.157115486356269288,
-              1.2750475385536655502e-7, 2492.7002050120397202),
-    TestValue(1525, 1123, 0.065, -10.275036857130705184,
-              0.000020718330690556828686, 13.074039765317043251),
-    TestValue(1525, 1123, 4.42, -7.754816867258728553, 0.0014034043922188128,
-              0.065429851608050629578),
-    TestValue(1525, 1123, 800, -30.390182048283734404, 0.1489213620192180795,
-              -0.018804728472968400557),
-    TestValue(1525, 1123, 15324, -64.393847149111855643, 0.33352757644959136666,
-              -0.00029097614079605979039),
-    TestValue(1525, 10586, 0.0004, -15.157527333190073382,
-              -3.2342406105998390275e-8, 2491.6705880068073821),
-    TestValue(1525, 10586, 0.065, -10.341961135413218919,
-              -5.2556089204012518156e-6, 12.04444836642472918),
-    TestValue(1525, 10586, 4.42, -12.301855613945737855,
-              -0.00035723444395259380558, -0.96243723577972978183),
-    TestValue(1525, 10586, 800, -744.01691670628731344,
-              -0.060139948001942982935, -0.79245256852502796007),
-    TestValue(1525, 10586, 15324, -4300.6455934139147727,
-              -0.50623127346524902759, -0.080624196979174112178),
-    TestValue(10233, 0.0000256, 0.0004, -28781.070852895156444,
-              3.7568285855263157895e8, -2.4041193199521680582e7),
-    TestValue(10233, 0.0000256, 0.065, -80237.47905503410844,
-              3.9956919271025565316e8, -157343.69709836101487),
-    TestValue(10233, 0.0000256, 4.42, -123371.16336416773985,
-              3.9972424635504373549e8, -2307.2799792939510176),
-    TestValue(10233, 0.0000256, 800, -173733.65594636811604,
-              3.9972654870875044132e8, -10.166635446653598855),
-    TestValue(10233, 0.0000256, 15324, -189611.39394380092393,
-              3.997265608322239652e8, -0.1562719469099034673),
-    TestValue(10233, 0.314, 0.0004, -30.083534640956912654,
-              41.460778593539812969, -30043.568270589792096),
-    TestValue(10233, 0.314, 0.065, -1936.7165917584869886,
-              5589.0004705645093525, -26975.841613138526635),
-    TestValue(10233, 0.314, 4.42, -27734.555886932752049, 30426.6413450334886,
-              -2153.7342775414124626),
-    TestValue(10233, 0.314, 800, -77398.834534311059049, 32575.386135464123325,
-              -10.161617337135278412),
-    TestValue(10233, 0.314, 15324, -93272.766915544350705,
-              32587.504232657958969, -0.15625826529496379204),
-    TestValue(10233, 1.5, 0.0004, -19.785223133324616937, 1.8184484137563316449,
-              -4317.6014472049352643),
-    TestValue(10233, 1.5, 0.065, -445.63039240802026812, 283.30031948881789137,
-              -6515.7878945898169301),
-    TestValue(10233, 1.5, 4.42, -14020.648493631530079, 5092.7060810810810811,
-              -1720.7211329093311099),
-    TestValue(10233, 1.5, 800, -61412.526640407231264, 6808.2345601996257018,
-              -10.142698900729563784),
-    TestValue(10233, 1.5, 15324, -77272.098984563728691, 6820.3323871978075756,
-              -0.15620659350885388317),
-    TestValue(10233, 3, 0.0004, -18.421373162288964031, 0.45460605252632982269,
-              -908.65830344005301507),
-    TestValue(10233, 3, 0.065, -230.93012488941404482, 72.316476345840130506,
-              -3316.4438994781907491),
-    TestValue(10233, 3, 4.42, -9239.7190298539962311, 2031.293800539083558,
-              -1371.3592560596120078),
-    TestValue(10233, 3, 800, -54340.180404088611315, 3397.2602739726027397,
-              -10.118854869649679896),
-    TestValue(10233, 3, 15324, -70181.625182690519906, 3409.3325504012526913,
-              -0.15614126136305778491),
-    TestValue(10233, 180, 0.0004, -17.081441774321808558,
-              0.00012411083530925486832, 2440.9430011582593451),
-    TestValue(10233, 180, 0.065, -15.542242814932986052,
-              0.020160775275594924055, -38.663485376183506373),
-    TestValue(10233, 180, 4.42, -235.49737914944659778, 1.3385587246502548531,
-              -50.377534581977016966),
-    TestValue(10233, 180, 800, -14640.502463070959489, 45.591836734693877551,
-              -7.8364899652763980015),
-    TestValue(10233, 180, 15324, -28577.644697168082129, 55.201586687306501548,
-              -0.14858705144088737228),
-    TestValue(10233, 1123, 0.0004, -17.063078998820718915,
-              2.8894734020457445678e-6, 2486.8498802333634116),
-    TestValue(10233, 1123, 0.065, -12.558918107945625621,
-              0.00046951241938052912769, 7.2241249583196655846),
-    TestValue(10233, 1123, 4.42, -35.455061578657784001,
-              0.031803517445555683105, -5.7569606052102630188),
-    TestValue(10233, 1123, 800, -3343.1303902972739556, 3.3748099701370067269,
-              -2.9898053694742608731),
-    TestValue(10233, 1123, 15324, -11352.060718035326883, 7.5582990583477048515,
-              -0.11311918072723555384),
-    TestValue(10233, 10586, 0.0004, -17.060718192656536162,
-              -1.2600010324928188685e-9, 2492.7518943576552348),
-    TestValue(10233, 10586, 0.065, -12.175300607237463447,
-              -2.0474891832045490463e-7, 13.125723676609068062),
-    TestValue(10233, 10586, 4.42, -9.4307920456266217014,
-              -0.000013917201050134158853, 0.11674937200192659959),
-    TestValue(10233, 10586, 800, -7.2703661972122617808,
-              -0.0023429424616141566026, 0.00008904830662418682316),
-    TestValue(10233, 10586, 15324, -9.3278240351663417157,
-              -0.019721845219427536336, -0.00008059480750115928323),
-};
-}  // namespace neg_binomial_2_test_internal
+//TODO[martinmodrak] add updated code here
+std::vector<TestValue> testValues = { {0,0.0000256,0.0004,-0.0000248141563677810565248409,-0.93984962406015037593985,-0.0018850149796030172519518},
+ {0,0.0000256,0.065,-0.0000255949600924861403888716,-0.999606308899879432100588,-7.75166869111834937935475e-8},
+ {0,0.0000256,4.42,-0.0000255999258645396480948713,-0.999994208178341772500141,-1.67726638232395628338958e-11},
+ {0,0.0000256,800,-0.0000255999995904000087381331,-0.999999968000001023999967,-5.1199997815466745309864e-16},
+ {0,0.0000256,15324,-0.0000255999999786165492276784,-0.999999998329417909342659,-1.39542226236663832355842e-18},
+ {0,0.314,0.0004,-0.00266678271697168261798476,-0.00127226463104325699745547,-5.66822905706024980195936},
+ {0,0.314,0.065,-0.114604680787141300415594,-0.171503957783641160949868,-0.934652892970430398112858},
+ {0,0.314,4.42,-0.303348202309659616314882,-0.933671313899450781580059,-0.00230212890163621513546237},
+ {0,0.314,800,-0.313938393619808990999524,-0.999607653995806645891488,-7.69878314071302369967267e-8},
+ {0,0.314,15324,-0.313996782998787812397665,-0.999979509686371605280341,-2.09929343978617830724328e-10},
+ {0,1.5,0.0004,-0.00329191110003275493362122,-0.00026659557451346307651293,-7.23004434565640079712956},
+ {0,1.5,0.065,-0.206781499150110071240643,-0.0415335463258785942492013,-2.22278737940449507487448},
+ {0,1.5,4.42,-1.29150964740387939892012,-0.746621621621621621621622,-0.0388183744279291779383916},
+ {0,1.5,800,-1.49859550534427827334156,-0.998128509045539613225203,-1.75342721996106687969703e-6},
+ {0,1.5,15324,-1.49992659053829698010225,-0.999902123911128511304688,-4.79017695146261715054393e-9},
+ {0,3,0.0004,-0.00356911664958785451901203,-0.00013331555792560991867751,-7.92292493952756190744874},
+ {0,3,0.065,-0.250472012600853853120106,-0.0212071778140293637846656,-2.87462275628870402717091},
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+ {10233,10586,4.42,-9.43079204562662170137108,-0.0000139172010501341588531831,0.116749372001926599593782},
+ {10233,10586,800,-7.27036619721226178082317,-0.002342942461614156602606,0.0000890483066241868231597611},
+ {10233,10586,15324,-9.3278240351663417156768,-0.0197218452194275363359762,-0.0000805948075011592832299515},
+};}  // namespace neg_binomial_2_test_internal
 
 TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
   using neg_binomial_2_test_internal::TestValue;
@@ -545,7 +334,8 @@ TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
     for (double phi_dbl = phi_start; phi_dbl < phi_max;
          phi_dbl *= stan::math::pi()) {
       std::ostringstream msg;
-      msg << ", mu = " << mu_dbl << ", phi = " << phi_dbl;
+      msg << std::setprecision(20) << ", mu = " << mu_dbl 
+        << ", phi = " << phi_dbl;
 
       var mu0(mu_dbl);
       var phi0(phi_dbl);

From 70430fb3c9d23ae0aa6a9ff8f67c5996b6968fee Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 20:10:34 +0100
Subject: [PATCH 60/82] Fixes after merge

---
 .../prim/fun/binomial_coefficient_log.hpp     | 49 +++++++++++----
 stan/math/prim/fun/lbeta.hpp                  | 56 +++++++++++++++--
 .../fun/binomial_coefficient_log_test.cpp     | 56 ++++++++++++++++-
 test/unit/math/prim/fun/lbeta_test.cpp        | 61 +++++++++++++++++++
 4 files changed, 204 insertions(+), 18 deletions(-)

diff --git a/stan/math/prim/fun/binomial_coefficient_log.hpp b/stan/math/prim/fun/binomial_coefficient_log.hpp
index 89600a35c55..e81a97e8b55 100644
--- a/stan/math/prim/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/fun/binomial_coefficient_log.hpp
@@ -1,13 +1,16 @@
-#ifndef STAN_MATH_PRIM_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
-#define STAN_MATH_PRIM_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
+#ifndef STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
+#define STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
 
 #include <stan/math/prim/meta.hpp>
-#include <stan/math/prim/fun/inv.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
-#include <stan/math/prim/fun/multiply_log.hpp>
+#include <stan/math/prim/fun/lbeta.hpp>
+#include <stan/math/prim/fun/constants.hpp>
+#include <stan/math/prim/err/check_nonnegative.hpp>
+#include <stan/math/prim/err/check_greater_or_equal.hpp>
 
 namespace stan {
 namespace math {
+
 /**
  * Return the log of the binomial coefficient for the specified
  * arguments.
@@ -22,12 +25,15 @@ namespace math {
  *
  * \f$ \log {N \choose n}
  * = \log \ \Gamma(N+1) - \log \Gamma(n+1) - \log \Gamma(N-n+1)\f$.
+ * 
  *
+ * TODO[martinmodrak] figure out the cases for x < 0 and for partials
    \f[
    \mbox{binomial\_coefficient\_log}(x, y) =
    \begin{cases}
-     \textrm{error} & \mbox{if } y > x \textrm{ or } y < 0\\
-     \ln\Gamma(x+1) & \mbox{if } 0\leq y \leq x \\
+     \textrm{error} & \mbox{if } y > x + 1 \textrm{ or } y < -1 \textrm{ or } x < 0\\
+     \textrm{-\infty} & \mbox{if } y = x + 1 \textrm{ or } y = -1\\
+     \ln\Gamma(x+1) & \mbox{if } -1 < y < x + 1 \\
      \quad -\ln\Gamma(y+1)& \\
      \quad -\ln\Gamma(x-y+1)& \\[6pt]
      \textrm{NaN} & \mbox{if } x = \textrm{NaN or } y = \textrm{NaN}
@@ -54,22 +60,39 @@ namespace math {
    \end{cases}
    \f]
  *
+ *  This function is numerically more stable than naive evaluation via lgamma
+ *
  * @param N total number of objects.
  * @param n number of objects chosen.
  * @return log (N choose n).
  */
+
 template <typename T_N, typename T_n>
 inline return_type_t<T_N, T_n> binomial_coefficient_log(const T_N N,
                                                         const T_n n) {
-  const double CUTOFF = 1000;
-  if (N - n < CUTOFF) {
-    const T_N N_plus_1 = N + 1;
+  if(is_nan(value_of_rec(N)) || is_nan(value_of_rec(n))) {
+    return std::numeric_limits<double>::quiet_NaN();
+  } 
+  
+  // For some uses it is important this works even when N < 0 and therefore
+  // it is before checks
+  if (n == 0) {
+    return 0;
+  }                                                  
+  const T_N N_plus_1 = N + 1;
+
+  static const char* function = "binomial_coefficient_log";
+  check_nonnegative(function, "first argument", N);
+  check_greater_or_equal(function, "second argument", n, -1);
+  check_greater_or_equal(function, "(first argument - second argument + 1)", 
+    N - n + 1, 0.0);
+
+  if (N / 2 < n) {
+    return binomial_coefficient_log(N, N - n);
+  } else if (N_plus_1 < lgamma_stirling_diff_useful) {
     return lgamma(N_plus_1) - lgamma(n + 1) - lgamma(N_plus_1 - n);
   } else {
-    return_type_t<T_N, T_n> N_minus_n = N - n;
-    const double one_twelfth = inv(12);
-    return multiply_log(n, N_minus_n) + multiply_log((N + 0.5), N / N_minus_n)
-           + one_twelfth / N - n - one_twelfth / N_minus_n - lgamma(n + 1);
+    return -lbeta(N - n + 1, n + 1) - log(N_plus_1);
   }
 }
 
diff --git a/stan/math/prim/fun/lbeta.hpp b/stan/math/prim/fun/lbeta.hpp
index 23a9ba9e5fb..ab4fbcb3050 100644
--- a/stan/math/prim/fun/lbeta.hpp
+++ b/stan/math/prim/fun/lbeta.hpp
@@ -1,8 +1,14 @@
-#ifndef STAN_MATH_PRIM_FUN_LBETA_HPP
-#define STAN_MATH_PRIM_FUN_LBETA_HPP
+#ifndef STAN_MATH_PRIM_SCAL_FUN_LBETA_HPP
+#define STAN_MATH_PRIM_SCAL_FUN_LBETA_HPP
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
+#include <stan/math/prim/fun/lgamma_stirling.hpp>
+#include <stan/math/prim/fun/log_sum_exp.hpp>
+#include <stan/math/prim/fun/lgamma_stirling_diff.hpp>
+#include <stan/math/prim/fun/multiply_log.hpp>
+#include <stan/math/prim/fun/inv.hpp>
+#include <stan/math/prim/err/check_nonnegative.hpp>
 
 namespace stan {
 namespace math {
@@ -22,7 +28,7 @@ namespace math {
  *
  * See stan::math::lgamma() for the double-based and stan::math for the
  * variable-based log Gamma function.
- *
+ * This function is numerically more stable than naive evaluation via lgamma
  *
    \f[
    \mbox{lbeta}(\alpha, \beta) =
@@ -55,7 +61,49 @@ namespace math {
  */
 template <typename T1, typename T2>
 inline return_type_t<T1, T2> lbeta(const T1 a, const T2 b) {
-  return lgamma(a) + lgamma(b) - lgamma(a + b);
+  typedef return_type_t<T1, T2> T_ret;
+
+  if(is_nan(value_of_rec(a)) || is_nan(value_of_rec(b))) {
+    return std::numeric_limits<double>::quiet_NaN();
+  } 
+
+  static const char* function = "lbeta";
+  check_nonnegative(function, "first argument", a);
+  check_nonnegative(function, "second argument", b);
+  T_ret x;  // x is the smaller of the two
+  T_ret y;
+  if (a < b) {
+    x = a;
+    y = b;
+  } else {
+    x = b;
+    y = a;
+  }
+
+  // For large x or y, separate the lgamma values into Stirling approximations
+  // and appropriate corrections. The Stirling approximations allow for
+  // analytic simplifaction and the corrections are added later.
+  //
+  // The overall approach is inspired by the code in R, where the algorithm is
+  // credited to W. Fullerton of Los Alamos Scientific Laboratory
+  if (y < lgamma_stirling_diff_useful) {
+    // both small
+    return lgamma(x) + lgamma(y) - lgamma(x + y);
+  } else if (x < lgamma_stirling_diff_useful) {
+    // y large, x small
+    T_ret stirling_diff
+        = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
+    T_ret log_x_y = log(x + y); 
+    T_ret stirling = (y - 0.5) * log1p(-x / (x + y)) + x * (1 - log_x_y);
+    return stirling + lgamma(x) + stirling_diff;
+  } else {
+    // both large
+    T_ret stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y)
+                           - lgamma_stirling_diff(x + y);
+    T_ret stirling = (x - 0.5) * log(x / (x + y)) + y * log1p(-x / (x + y))
+                      + 0.5 * (log(2 * stan::math::pi()) - log(y));
+    return stirling + stirling_diff;
+  }
 }
 
 }  // namespace math
diff --git a/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
index 23cea698637..6b85505fd37 100644
--- a/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
@@ -1,3 +1,4 @@
+#include <test/unit/math/expect_near_rel.hpp>
 #include <stan/math/prim.hpp>
 #include <gtest/gtest.h>
 #include <cmath>
@@ -7,7 +8,8 @@ template <typename T_N, typename T_n>
 void test_binom_coefficient(const T_N& N, const T_n& n) {
   using stan::math::binomial_coefficient_log;
   EXPECT_FLOAT_EQ(lgamma(N + 1) - lgamma(n + 1) - lgamma(N - n + 1),
-                  binomial_coefficient_log(N, n));
+                  binomial_coefficient_log(N, n))
+      << "N = " << N << ", n = " << n;
 }
 
 TEST(MathFunctions, binomial_coefficient_log) {
@@ -19,6 +21,13 @@ TEST(MathFunctions, binomial_coefficient_log) {
 
   EXPECT_FLOAT_EQ(29979.16, binomial_coefficient_log(100000, 91116));
 
+  EXPECT_EQ(binomial_coefficient_log(-1, 0), 0); // Needed for neg_binomial_2
+  EXPECT_EQ(binomial_coefficient_log(50, 0), 0);
+  EXPECT_EQ(binomial_coefficient_log(10000, 0), 0);
+
+  EXPECT_EQ(binomial_coefficient_log(10, 11), -std::numeric_limits<double>::infinity()); 
+  EXPECT_EQ(binomial_coefficient_log(10, -1), -std::numeric_limits<double>::infinity()); 
+
   for (int n = 0; n < 1010; ++n) {
     test_binom_coefficient(1010, n);
     test_binom_coefficient(1010.0, n);
@@ -38,3 +47,48 @@ TEST(MathFunctions, binomial_coefficient_log_nan) {
   EXPECT_TRUE(std::isnan(stan::math::binomial_coefficient_log(nan, 2.0)));
   EXPECT_TRUE(std::isnan(stan::math::binomial_coefficient_log(nan, nan)));
 }
+
+TEST(MathFunctions, binomial_coefficient_log_errors) {
+  using stan::math::binomial_coefficient_log;
+  EXPECT_NO_THROW(binomial_coefficient_log(10, 11));
+  EXPECT_THROW(binomial_coefficient_log(10, 11.01), std::domain_error);
+  EXPECT_THROW(binomial_coefficient_log(-1, 0.3), std::domain_error);
+  EXPECT_THROW(binomial_coefficient_log(10, -1.1), std::domain_error);
+  EXPECT_NO_THROW(binomial_coefficient_log(10, -0.9));
+}
+
+namespace binomial_coefficient_test_internal {
+struct TestValue {
+  double n;
+  double k;
+  double val;
+};
+
+std::vector<TestValue> testValues = {  {0.00003,-0.9,-2.21375637737528044964112},  {0.00003,3.e-15,1.48040820535563428588846e-19},  {0.00003,3.e-10,1.48039340142161568666212e-14},  {0.00003,3.e-7,1.46560412344434242311062e-11},  {0.00003,6.e-6,2.36865312869367134774661e-10},  {0.00003,0.000015,3.70102051348524044535716e-10},  {0.00003,0.0000291,4.30798787797857754693695e-11},  {0.00003,0.0000299999982,8.88244870007509649977929e-17},  {0.00003,0.00002999999991,4.44122460318735146597007e-18},  {0.00003,0.90003,-2.21375637737528044964112},  {0.002,-0.9,-2.21559326412971099686943},  {0.002,2.e-13,6.57013709556564677684856e-16},  {0.002,2.e-8,6.57007139476544583161173e-11},  {0.002,0.00002,6.50443564072189575550994e-8},  {0.002,0.0004,1.05122171458287350859763e-6},  {0.002,0.001,1.64253373496215313253469e-6},  {0.002,0.00194,1.91190982195918976356429e-7},  {0.002,0.00199999988,3.94208202120835082737684e-13},  {0.002,0.001999999994,1.97104112295366725515452e-14},  {0.002,0.902,-2.21559326412971099686943},  {1,-0.9,-2.85558226198351740582195},  {1,1.e-10,9.9999999988550659331851e-11},  {1,0.00001,9.99988550692664559909352e-6},  {1,0.01,0.00988583703486131052627978},  {1,0.2,0.156457962917688016707705},  {1,0.5,0.241564475270490444691037},  {1,0.97,0.028978328236256312960776},  {1,0.99999994,5.99999958782374313463811e-8},  {1,0.999999997,2.99999998969559340736596e-9},  {1,1.9,-2.85558226198351740582195},  {8,-0.9,-4.22528965320883461943031},  {8,8.e-10,2.17428571372173153982474e-9},  {8,0.00008,0.000217422931805073420417006},  {8,0.08,0.211982267378255838975509},  {8,1.6,2.90678606291134283426263},  {8,4,4.24849524204935898912334},  {8,7.76,0.606274586245453651115361},  {8,7.99999952,1.30457122553768403613331e-6},  {8,7.999999976,6.52285709209869625945566e-8},  {8,8.9,-4.22528965320883461943031},  {1325,-0.9,-8.72360867216657209762532},  {1325,1.325e-7,1.02909578020477960435539e-6},  {1325,0.01325,0.102766042691370430370992},  {1325,13.25,71.9898321274090629975055},  {1325,265,659.435649329029419323398},  {1325,662.5,914.599450340845275100724},  {1325,1285.25,175.786260651191862665015},  {1325,1324.9999205,0.000617452276410452190170437},  {1325,1324.999996025,0.0000308728608380968862741097},  {1325,1325.9,-8.72360867216657209762532},  {845000,-0.9,-14.5350963792733464918229},  {845000,0.0000845,0.00120194816738712136581358},  {845000,8.45,103.738303827736743600251},  {845000,8450,47315.8616457576200611209},  {845000,169000,422833.221695496506553128},  {845000,422500,585702.318235552114086514},  {845000,819650,113851.158132678562120685},  {845000,844999.9493,0.719108776819481762797449},  {845000,844999.997465,0.036053342347290003917417},  {845000,845000.9,-14.5350963792733464918229},  {3000000000000000.0,3,105.120406581508328854183},  {3000000000000000.0,100,3199.99949280231435502243},  {3000000000000000.0,12895,350387.5243605883687667},  {100000000000000000000.0,3,136.363346110414686040237},  {100000000000000000000.0,100,4241.4308104325278778424},  {100000000000000000000.0,12895,484680.092769031900296878},};
+}  // namespace binomial_coefficient_test_internal
+
+TEST(MathFunctions, binomial_coefficient_log_precomputed) {
+  using binomial_coefficient_test_internal::TestValue;
+  using binomial_coefficient_test_internal::testValues;
+  using stan::test::expect_near_rel;
+
+  for (TestValue t : testValues) {
+
+    std::ostringstream msg;
+    msg << std::setprecision(22) << "n = " << t.n << ", k = " << t.k;
+
+    double val = stan::math::binomial_coefficient_log(t.n, t.k);
+    expect_near_rel(msg.str(), val, t.val);
+
+    if(t.k > t.n / 10) {
+      // Testing the mirrored binomial coefficient is not performed for
+      // small k, as we may loose so much precision computing k2
+      // that the test becomes invalid
+      std::ostringstream msg2;
+      double k2 = t.n - t.k;
+      msg2 << std::setprecision(22) << "n = " << t.n << ", k = " << k2;
+      double val2 = stan::math::binomial_coefficient_log(t.n, k2);
+      expect_near_rel(msg2.str(), val2, t.val);
+    }
+  }
+}
diff --git a/test/unit/math/prim/fun/lbeta_test.cpp b/test/unit/math/prim/fun/lbeta_test.cpp
index 6bb2f73621c..528359dd3f4 100644
--- a/test/unit/math/prim/fun/lbeta_test.cpp
+++ b/test/unit/math/prim/fun/lbeta_test.cpp
@@ -1,7 +1,10 @@
+#include <test/unit/math/expect_near_rel.hpp>
 #include <stan/math/prim.hpp>
 #include <gtest/gtest.h>
 #include <cmath>
 #include <limits>
+#include <vector>
+
 
 TEST(MathFunctions, lbeta) {
   using stan::math::lbeta;
@@ -21,3 +24,61 @@ TEST(MathFunctions, lbeta_nan) {
 
   EXPECT_TRUE(std::isnan(stan::math::lbeta(nan, nan)));
 }
+
+namespace lbeta_test_internal {
+  struct TestValue {
+    double x;
+    double y;
+    double val;
+  };
+
+// Test values generated in Mathematice, reproducible notebook at
+// https://www.wolframcloud.com/obj/martin.modrak/Published/lbeta.nb
+// Mathematica Code reproduced below for convenience:
+//
+// lbeta[x_,y_]:= LogGamma[x] + LogGamma[y] - LogGamma[x + y]
+// out = OpenWrite["lbeta_test.txt"]
+// xs= {8*10^-8,4*10^-3,1,1+10^-8,5,23, 19845};
+// ys =  {7*10^-11,2*10^-5,1+10^-12,1/2,2,1624};
+//  WriteString[out, "std::vector<TestValue> testValues = {"];
+//  For[i = 1, i <= Length[xs], i++, {
+//        For[j = 1, j <= Length[ys], j++, {
+//      cx = xs[[i]];
+//      cy = ys[[j]];
+            
+//     val = N[lbeta[cx,cy],24];
+//          WriteString[out,"  {",CForm[cx],",",CForm[cy],",",
+//            CForm[val],"},"]
+// }]
+// }]
+// extremeXs = {3*10^15,10^20};
+// lowYs = {3, 100, 12895};
+//      For[i = 1, i <= Length[extremeXs], i++, {
+//        For[j = 1, j <= Length[lowYs], j++, {
+//      cx = extremeXs[[i]];
+//          cy = lowYs[[j]];
+//     val = N[lbeta[cx,cy],24];
+//          WriteString[out,"  {",CForm[cx],".0,",CForm[cy],",",
+//            CForm[val],"},"]
+//      }]
+//   }]
+// WriteString[out,"};"];
+//  Close[out];
+//  FilePrint[%]
+std::vector<TestValue> testValues = {  {8.e-8,7.e-11,23.3834004912898500586445},  {8.e-8,0.00002,16.3452312235394351410033},  {8.e-8,1.000000000001,16.3412392022725295437606},  {8.e-8,0.5,16.3412393131760679059067},  {8.e-8,2,16.3412391222725327438921},  {8.e-8,1624,16.3412385647081130254943},  {0.004,7.e-11,23.3825258913787298259023},  {0.004,0.00002,10.8247656947117878792194},  {0.004,1.000000000001,5.52146091786223987264715},  {0.004,0.5,5.52697992926150653113797},  {0.004,2,5.51746889659270898022044},  {0.004,1624,5.48959582574332555214719},  {1,7.e-11,23.3825258738791892190926},  {1,0.00002,10.8197782844102831106727},  {1,1.000000000001,-9.999999999995e-13},  {1,0.5,0.693147180559945309417232},  {1,2,-0.693147180559945309417232},  {1,1624,-7.39264752072162326054032},  {1.00000001,7.e-11,23.3825258738791892179411},  {1.00000001,0.00002,10.8197782844099541286699},  {1.00000001,1.000000000001,-1.00009999500064491739816e-8},  {1.00000001,0.5,0.693147174422888956122731},  {1.00000001,2,-0.693147195559945246917232},  {1.00000001,1624,-7.39264760042333353631934},  {5,7.e-11,23.3825258737333558857627},  {5,0.00002,10.8197366180283355258393},  {5,1.000000000001,-1.60943791243638370793409},  {5,0.5,-0.207395194346070587158746},  {5,2,-3.40119738166215537541324},  {5,1624,-33.7913357290267948074624},  {23,7.e-11,23.3825258736208322915813},  {23,0.00002,10.819704468465374949026},  {23,1.000000000001,-3.13549421593288398231784},  {23,0.5,-0.989947810259228199543883},  {23,2,-6.31354804627709531045369},  {23,1624,-121.714785277510463870251},  {19845,7.e-11,23.3825258731460863706715},  {19845,0.00002,10.8195688267825637640878},  {19845,1.000000000001,-9.89570736522763869861762},  {19845,0.5,-4.37548244086806082919414},  {19845,2,-19.7914651196913525680177},  {19845,1624,-5756.4146766727238501215},  {3000000000000000.0,3,-106.219018870176440545578},  {3000000000000000.0,100,-3204.60466298830574639047},  {3000000000000000.0,12895,-350396.988955562106921852},  {100000000000000000000.0,3,-137.461958399082795731692},  {100000000000000000000.0,100,-4246.03598061851596930944},  {100000000000000000000.0,12895,-484689.557363950217404711},};
+}
+
+TEST(MathFunctions, lbeta_precomputed) {
+  using lbeta_test_internal::TestValue;
+  using lbeta_test_internal::testValues;
+  using stan::test::expect_near_rel;
+
+  for (TestValue t : testValues) {
+
+    std::ostringstream msg;
+    msg << std::setprecision(22) << "x = " << t.x << ", y = " << t.y;
+
+    double val = stan::math::lbeta(t.x, t.y);
+    expect_near_rel(msg.str(), val, t.val);
+  }
+}

From 36f24d70bb6334e8abdb5fa52477cda942c047e3 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 13 Jan 2020 19:10:57 +0000
Subject: [PATCH 61/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 stan/math/prim/fun/lgamma_stirling_diff.hpp   |  54 +-
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   |   7 +-
 test/unit/math/expect_near_rel.hpp            |  24 +-
 .../prim/fun/lgamma_stirling_diff_test.cpp    |  37 +-
 .../math/rev/prob/neg_binomial_2_test.cpp     | 537 ++++++++++++------
 5 files changed, 434 insertions(+), 225 deletions(-)

diff --git a/stan/math/prim/fun/lgamma_stirling_diff.hpp b/stan/math/prim/fun/lgamma_stirling_diff.hpp
index 45c9f26c1fe..bbe3f721383 100644
--- a/stan/math/prim/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/fun/lgamma_stirling_diff.hpp
@@ -10,26 +10,25 @@
 #include <stan/math/prim/fun/lgamma_stirling.hpp>
 #include <stan/math/prim/err/check_nonnegative.hpp>
 
-
 namespace stan {
 namespace math {
 
 constexpr double lgamma_stirling_diff_useful = 10;
 
 /**
- * Return the difference between log of the gamma function and it's Stirling 
+ * Return the difference between log of the gamma function and it's Stirling
  * approximation.
  * This is useful to stably compute log of ratios of gamma functions with large
- * arguments where the Stirling approximation allows for analytic solution 
- * and the (small) differences can be added afterwards. 
+ * arguments where the Stirling approximation allows for analytic solution
+ * and the (small) differences can be added afterwards.
  * This is for example used in the implementation of lbeta.
- * 
+ *
  * The function will return correct value for all arguments, but the can add
  * precision only when x >= lgamma_stirling_diff_useful.
  *
    \f[
    \mbox{lgamma_stirling_diff}(x) =
-    \log(\Gamma(x)) - \frac{1}{2} \log(2\pi) + 
+    \log(\Gamma(x)) - \frac{1}{2} \log(2\pi) +
     (x-\frac{1}{2})*\log(x) - x
    \f]
 
@@ -40,29 +39,30 @@ constexpr double lgamma_stirling_diff_useful = 10;
  */
 
 template <typename T>
-T lgamma_stirling_diff(const T x) {  
-    static const char* function = "lgamma_stirling_diff";
-    check_nonnegative(function, "argument", x);
+T lgamma_stirling_diff(const T x) {
+  static const char* function = "lgamma_stirling_diff";
+  check_nonnegative(function, "argument", x);
 
-    if (value_of(x) < lgamma_stirling_diff_useful) {
-        return lgamma(x) - lgamma_stirling(x);
-    } else {
-        // Using the Stirling series as expressed in formula 5.11.1. at
-        // https://dlmf.nist.gov/5.11
-        constexpr double stirling_series[] = {
-            0.0833333333333333333333333,  -0.00277777777777777777777778,
-            0.000793650793650793650793651,-0.000595238095238095238095238,
-            };
-        constexpr int n_stirling_terms = 3;
-        T result(0.0);
-        T multiplier = inv(x);
-        T inv_x_squared = inv(square(x));
-        for(int n = 0; n < n_stirling_terms; 
-                n++, multiplier *= inv_x_squared) {
-            result += stirling_series[n] * multiplier;
-        }
-        return result;
+  if (value_of(x) < lgamma_stirling_diff_useful) {
+    return lgamma(x) - lgamma_stirling(x);
+  } else {
+    // Using the Stirling series as expressed in formula 5.11.1. at
+    // https://dlmf.nist.gov/5.11
+    constexpr double stirling_series[] = {
+        0.0833333333333333333333333,
+        -0.00277777777777777777777778,
+        0.000793650793650793650793651,
+        -0.000595238095238095238095238,
+    };
+    constexpr int n_stirling_terms = 3;
+    T result(0.0);
+    T multiplier = inv(x);
+    T inv_x_squared = inv(square(x));
+    for (int n = 0; n < n_stirling_terms; n++, multiplier *= inv_x_squared) {
+      result += stirling_series[n] * multiplier;
     }
+    return result;
+  }
 }
 
 }  // namespace math
diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 73e1d0365cf..d3a0fa04e61 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -142,14 +142,13 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       }
       if (!is_constant_all<T_precision>::value) {
         T_partials_return log_term;
-        if(mu_val[i] < phi_val[i]) {
-          log_term = log1p(-mu_val[i]/(mu_val[i] + phi_val[i]));
+        if (mu_val[i] < phi_val[i]) {
+          log_term = log1p(-mu_val[i] / (mu_val[i] + phi_val[i]));
         } else {
           log_term = log_phi[i] - log_mu_plus_phi[i];
         }
         ops_partials.edge2_.partials_[i]
-            += (mu_val[i] - n_vec[i]) / (mu_val[i] + phi_val[i])
-               + log_term
+            += (mu_val[i] - n_vec[i]) / (mu_val[i] + phi_val[i]) + log_term
                - (digamma(phi_val[i]) - digamma(n_plus_phi[i]));
       }
     }
diff --git a/test/unit/math/expect_near_rel.hpp b/test/unit/math/expect_near_rel.hpp
index 4093aba00fe..0fd0a004b2a 100644
--- a/test/unit/math/expect_near_rel.hpp
+++ b/test/unit/math/expect_near_rel.hpp
@@ -33,8 +33,9 @@ namespace internal {
  */
 template <typename T1, typename T2, require_all_stan_scalar_t<T1, T2>...>
 void expect_near_rel_finite(const std::string& msg, const T1& x1, const T2& x2,
-                            double tol_rel = 1e-8, 
-                            double tol_min = std::numeric_limits<double>::quiet_NaN()) {
+                            double tol_rel = 1e-8,
+                            double tol_min
+                            = std::numeric_limits<double>::quiet_NaN()) {
   using stan::math::fabs;
   // if either arg near zero, must use absolute tolerance as rel tol -> 2
   // if (fabs(x1) < tol || fabs(x2) < tol) {
@@ -51,19 +52,17 @@ void expect_near_rel_finite(const std::string& msg, const T1& x1, const T2& x2,
   //     << ", relative tolerance = " << tol << ")"
   //     << "; relative diff = " << relative_diff << std::endl
   //     << "    in: " << msg << std::endl;
-  if(stan::math::is_nan(tol_min)) {
+  if (stan::math::is_nan(tol_min)) {
     tol_min = tol_rel * tol_rel;
   }
   auto avg = 0.5 * (fabs(x1) + fabs(x2));
   auto tol = std::max(avg * tol_rel, tol_min);
   auto relative_diff = (x1 - x2) / avg;
-  EXPECT_NEAR(x1, x2, tol)
-      << "expect_near_rel_finite(" << x1 << ", " << x2
-      << ", relative tolerance = " << tol_rel << ")"
-      << ", minimum tolerance = " << tol_min << ")"
-      << "; relative diff = " << relative_diff << std::endl
-      << "    in: " << msg << std::endl;
-
+  EXPECT_NEAR(x1, x2, tol) << "expect_near_rel_finite(" << x1 << ", " << x2
+                           << ", relative tolerance = " << tol_rel << ")"
+                           << ", minimum tolerance = " << tol_min << ")"
+                           << "; relative diff = " << relative_diff << std::endl
+                           << "    in: " << msg << std::endl;
 }
 
 template <typename EigMat1, typename EigMat2,
@@ -104,8 +103,9 @@ void expect_near_rel_finite(const std::string& msg, const std::vector<T1>& x1,
  */
 template <typename T1, typename T2, require_all_stan_scalar_t<T1, T2>...>
 void expect_near_rel(const std::string& msg, const T1& x1, const T2& x2,
-                     double tol_rel = 1e-8, 
-                     double tol_min = std::numeric_limits<double>::quiet_NaN()) {
+                     double tol_rel = 1e-8,
+                     double tol_min
+                     = std::numeric_limits<double>::quiet_NaN()) {
   if (stan::math::is_nan(x1) || stan::math::is_nan(x2))
     EXPECT_TRUE(stan::math::is_nan(x1) && stan::math::is_nan(x2))
         << "expect_near_rel(" << x1 << ", " << x2 << ")" << std::endl
diff --git a/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
index 8160d374172..56e97501374 100644
--- a/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
@@ -10,8 +10,8 @@ TEST(MathFunctions, lgamma_stirling_diff_errors) {
 }
 
 TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
-  using stan::math::lgamma_stirling_diff_useful;
   using stan::math::lgamma_stirling_diff;
+  using stan::math::lgamma_stirling_diff_useful;
   using stan::test::expect_near_rel;
 
   double start = std::nextafter(10, 11);
@@ -43,7 +43,40 @@ struct TestValue {
   double val;
 };
 
-std::vector<TestValue> testValues = {  {1.049787068367863943,0.077388806767834476832},  {1.1353352832366126919,0.071790358566585005482},  {1.3678794411714423216,0.059960812482712981438},  {2.,0.041340695955409294094},  {3.7182818284590452354,0.022358812123082674471},  {8.3890560989306502272,0.0099288907523535997267},  {21.085536923187667741,0.0039518599801395734578},  {55.598150033144239078,0.0014988346688724404687},  {149.41315910257660342,0.0005577367442531155476},  {404.42879349273512261,0.00020605188772717995062},  {1097.6331584284585993,0.000075920930766205666598},  {2981.9579870417282747,0.00002794584410078046085},  {8104.0839275753840077,0.000010282881326966996581},  {22027.465794806716517,3.7831557249429676373e-6},  {59875.141715197818455,1.3917851539949910276e-6},  {162755.79141900392081,5.1201455018391551878e-7},  {442414.39200892050333,1.8836035815859912686e-7},  {1.2026052841647767777e6,6.9294002305342748064e-8},  {3.2690183724721106393e6,2.5491852243801980915e-8},  {8.8861115205078726368e6,9.3779301712579119232e-9},  {2.4154953753575298215e7,3.4499479561619419703e-9},  {6.5659970137330511139e7,1.2691649593966957356e-9},  {1.7848230196318726084e8,4.6689970051216164913e-10},  {4.8516519640979027797e8,1.7176280151585029843e-10},  {1.3188157354832146972e9,6.3188003518019870566e-11},  {3.5849128471315915617e9,2.3245567434090096532e-11},  {9.7448034472489026e9,8.5515663588740238069e-12},  {2.6489122130843472294e10,3.1459454534471511195e-12},  {7.2004899338385872524e10,1.1573286553975954675e-12},  {1.9572960942983876427e11,4.2575741900310182743e-13},  {5.3204824060279861668e11,1.5662740137796255552e-13},  {1.4462570642924751737e12,5.7620000891128517638e-14},};
+std::vector<TestValue> testValues = {
+    {1.049787068367863943, 0.077388806767834476832},
+    {1.1353352832366126919, 0.071790358566585005482},
+    {1.3678794411714423216, 0.059960812482712981438},
+    {2., 0.041340695955409294094},
+    {3.7182818284590452354, 0.022358812123082674471},
+    {8.3890560989306502272, 0.0099288907523535997267},
+    {21.085536923187667741, 0.0039518599801395734578},
+    {55.598150033144239078, 0.0014988346688724404687},
+    {149.41315910257660342, 0.0005577367442531155476},
+    {404.42879349273512261, 0.00020605188772717995062},
+    {1097.6331584284585993, 0.000075920930766205666598},
+    {2981.9579870417282747, 0.00002794584410078046085},
+    {8104.0839275753840077, 0.000010282881326966996581},
+    {22027.465794806716517, 3.7831557249429676373e-6},
+    {59875.141715197818455, 1.3917851539949910276e-6},
+    {162755.79141900392081, 5.1201455018391551878e-7},
+    {442414.39200892050333, 1.8836035815859912686e-7},
+    {1.2026052841647767777e6, 6.9294002305342748064e-8},
+    {3.2690183724721106393e6, 2.5491852243801980915e-8},
+    {8.8861115205078726368e6, 9.3779301712579119232e-9},
+    {2.4154953753575298215e7, 3.4499479561619419703e-9},
+    {6.5659970137330511139e7, 1.2691649593966957356e-9},
+    {1.7848230196318726084e8, 4.6689970051216164913e-10},
+    {4.8516519640979027797e8, 1.7176280151585029843e-10},
+    {1.3188157354832146972e9, 6.3188003518019870566e-11},
+    {3.5849128471315915617e9, 2.3245567434090096532e-11},
+    {9.7448034472489026e9, 8.5515663588740238069e-12},
+    {2.6489122130843472294e10, 3.1459454534471511195e-12},
+    {7.2004899338385872524e10, 1.1573286553975954675e-12},
+    {1.9572960942983876427e11, 4.2575741900310182743e-13},
+    {5.3204824060279861668e11, 1.5662740137796255552e-13},
+    {1.4462570642924751737e12, 5.7620000891128517638e-14},
+};
 
 }  // namespace lgamma_stirling_diff_test_internal
 
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 4ca9374cd6d..c8844be55b6 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -13,190 +13,367 @@ struct TestValue {
   double phi;
   double value;
   double grad_mu;
-  double grad_phi;  
+  double grad_phi;
 };
 
 // Test data generated in Mathematica (Wolfram Cloud). The code can be re-ran
 // at https://www.wolframcloud.com/env/martin.modrak/NegBinomial2_Tests.nb
 // but is also presented below for convenience:
 //
-//TODO[martinmodrak] add updated code here
-std::vector<TestValue> testValues = { {0,0.0000256,0.0004,-0.0000248141563677810565248409,-0.93984962406015037593985,-0.0018850149796030172519518},
- {0,0.0000256,0.065,-0.0000255949600924861403888716,-0.999606308899879432100588,-7.75166869111834937935475e-8},
- {0,0.0000256,4.42,-0.0000255999258645396480948713,-0.999994208178341772500141,-1.67726638232395628338958e-11},
- {0,0.0000256,800,-0.0000255999995904000087381331,-0.999999968000001023999967,-5.1199997815466745309864e-16},
- {0,0.0000256,15324,-0.0000255999999786165492276784,-0.999999998329417909342659,-1.39542226236663832355842e-18},
- {0,0.314,0.0004,-0.00266678271697168261798476,-0.00127226463104325699745547,-5.66822905706024980195936},
- {0,0.314,0.065,-0.114604680787141300415594,-0.171503957783641160949868,-0.934652892970430398112858},
- {0,0.314,4.42,-0.303348202309659616314882,-0.933671313899450781580059,-0.00230212890163621513546237},
- {0,0.314,800,-0.313938393619808990999524,-0.999607653995806645891488,-7.69878314071302369967267e-8},
- {0,0.314,15324,-0.313996782998787812397665,-0.999979509686371605280341,-2.09929343978617830724328e-10},
- {0,1.5,0.0004,-0.00329191110003275493362122,-0.00026659557451346307651293,-7.23004434565640079712956},
- {0,1.5,0.065,-0.206781499150110071240643,-0.0415335463258785942492013,-2.22278737940449507487448},
- {0,1.5,4.42,-1.29150964740387939892012,-0.746621621621621621621622,-0.0388183744279291779383916},
- {0,1.5,800,-1.49859550534427827334156,-0.998128509045539613225203,-1.75342721996106687969703e-6},
- {0,1.5,15324,-1.49992659053829698010225,-0.999902123911128511304688,-4.79017695146261715054393e-9},
- {0,3,0.0004,-0.00356911664958785451901203,-0.00013331555792560991867751,-7.92292493952756190744874},
- {0,3,0.065,-0.250472012600853853120106,-0.0212071778140293637846656,-2.87462275628870402717091},
- {0,3,4.42,-2.28973397601639586742486,-0.595687331536388140161725,-0.113726692626070463108525},
- {0,3,800,-2.99438902306750149309853,-0.996264009962640099626401,-6.99624147447649277415792e-6},
- {0,3,15324,-2.99970638131217673536622,-0.999804266979839498923468,-1.91582075605741709616675e-8},
- {0,180,0.0004,-0.00520680203358650223341638,-2.22221728396159119646401e-6,-12.0170073061835395451321},
- {0,180,0.065,-0.515234583883688262086666,-0.000360980756948879571265932,-6.92704688665984521936613},
- {0,180,4.42,-16.4913562250745368347413,-0.0239670317752955210931569,-2.75504310079668394524277},
- {0,180,800,-162.3526751973522458866,-0.816326530612244897959184,-0.0192673746089352053174335},
- {0,180,15324,-178.951041022560568926078,-0.988390092879256965944272,-0.0000679211892648339243088643},
- {0,1123,0.0004,-0.00593912212871338076639709,-3.56188653183026470872139e-7,-13.8478056779721050990192},
- {0,1123,0.065,-0.634217014783734204352692,-0.000057877326779839101031552,-8.75724272015345990606553},
- {0,1123,4.42,-24.4936395934523258117904,-0.00392045555338738003583403,-4.54546787488649276731873},
- {0,1123,800,-701.624014336681947952778,-0.416016640665626625065003,-0.293046658586479060005975},
- {0,1123,15324,-1083.75715139725783359741,-0.931720070529579862588922,-0.00244293345030929573936621},
- {0,10586,0.0004,-0.00683653348042399161482707,-3.77857533426883301459161e-8,-16.091333738845732379756},
- {0,10586,0.065,-0.780043017108597589318463,-6.14014744855619155937546e-6,-11.0006679418181806995525},
- {0,10586,4.42,-34.3945190758502000304634,-0.000417358329509122395523501,-6.78198276010557247770399},
- {0,10586,800,-2124.42246547447991619038,-0.0702617249253469172668189,-1.72578980676844681250479},
- {0,10586,15324,-8048.29915678058041924358,-0.591431879583172520262447,-0.116640647318788574768032},
- {6,0.0000256,0.0004,-26.4803625972224902645113,220276.315789473684210526,-11595.4634978387095432955},
- {6,0.0000256,0.065,-51.4193881364481026728232,234281.729042100342019143,-74.6938075459730303944346},
- {6,0.0000256,4.42,-67.5203813751119077704357,234372.642547590674587948,-0.431255924758490025034736},
- {6,0.0000256,800,-69.998079065742703551293,234373.992500032239998968,-0.0000233303844710378174909984},
- {6,0.0000256,15324,-70.0158073212983954315096,234373.999608458993084276,-6.38614276575077488493398e-8},
- {6,0.314,0.0004,-9.62519749441237582251687,0.023038524497171844864751,2477.5305495558165940557},
- {6,0.314,0.065,-5.62316274126580027012417,3.10564173234962943044888,0.811756664687528071010215},
- {6,0.314,4.42,-11.7481186360489883350416,16.9071818179371883568924,-0.343526975436714222156802},
- {6,0.314,800,-13.8270107248858320162615,18.1011755433762948679586,-0.0000204650172704751119362432},
- {6,0.314,15324,-13.8425659569858167417764,18.1079092104353788140892,-5.6049178830042368725488e-8},
- {6,1.5,0.0004,-9.61978396161923322623754,0.00079978672354038922953879,2491.05377011516735187466},
- {6,1.5,0.065,-4.84100453988744409858109,0.124600638977635782747604,11.5208909282007772435409},
- {6,1.5,4.42,-4.69471130087565245107321,2.23986486486486486486486,-0.126129611536089773251445},
- {6,1.5,800,-5.6375883578559464150792,2.99438552713661883967561,-0.0000110478695320263035818071},
- {6,1.5,15324,-5.64599569956598171509704,2.99970637173338553391406,-3.03295927479829163411156e-8},
- {6,3,0.0004,-9.61926132713561025018161,0.00013331555792560991867751,2492.36008977011398813188},
- {6,3,0.065,-4.75878244235486512052296,0.0212071778140293637846656,12.745335721641112641817},
- {6,3,4.42,-2.88910819582874566285473,0.595687331536388140161725,0.00385024685205873541538553},
- {6,3,800,-2.98571724360242195248096,0.996264009962640099626401,-2.3069406647953774852549e-6},
- {6,3,15324,-2.98747963477610734281426,0.999804266979839498923468,-6.38245840446628643263247e-9},
- {6,180,0.0004,-9.62011239916672050497847,-2.14814337449620482324854e-6,2490.23240751308273540641},
- {6,180,0.065,-4.89709960487442547895843,-0.000348948065050583585557067,10.6171759350004776847048},
- {6,180,4.42,-11.8028833191445191284052,-0.023168130716119003723385,-1.86137525666548784300587},
- {6,180,800,-138.973123190861697819951,-0.789115646258503401360544,-0.0179131542129975601896404},
- {6,180,15324,-154.441639359481734262519,-0.955443756449948400412797,-0.0000634392772194434652186986},
- {6,1123,0.0004,-9.62083352307562855236427,-3.5428559715533443273747e-7,2488.4295995707558483234},
- {6,1123,0.065,-5.0142630342277769583843,-0.0000575680979635621334392196,8.81495887967631288756553},
- {6,1123,4.42,-19.6831821663032130583962,-0.00389950921917515894926679,-3.62458748384772905278683},
- {6,1123,800,-671.304184750646975825767,-0.41379393376981739999787,-0.288690114015941777831476},
- {6,1123,15324,-1048.61720731875393149901,-0.926742047000481483982035,-0.00241626280594218362665218},
- {6,10586,0.0004,-9.62172902400956379331308,-3.77643368945439762841293e-8,2486.19084755337982611478},
- {6,10586,0.065,-5.15977860354001470537965,-6.13666729697000818989159e-6,6.57630939764217205495288},
- {6,10586,4.42,-29.5629973572818969888733,-0.000417121776516768840415515,-5.85634703346878397904497},
- {6,10586,800,-2091.3124520859014907288,-0.0702219015407302460497774,-1.71884010032985743252181},
- {6,10586,15324,-8002.42495594488889877697,-0.59109666408369216553719,-0.116480739324794834878369},
- {14,0.0000256,0.0004,-49.8145624383586400724923,513979.323308270676691729,-30391.5592215308067657195},
- {14,0.0000256,0.065,-114.928171090288372551513,546658.700573312664550577,-196.832392093265929097095},
- {14,0.0000256,4.42,-161.649312877052269163198,546870.832603322478494242,-1.65012869090202521315342},
- {14,0.0000256,800,-173.098986627797206761932,546873.982500032559998958,-0.00014060727924520899116967},
- {14,0.0000256,15324,-173.206165042629407096483,546873.999086402089753857,-3.87293689171005773693536e-7},
- {14,0.314,0.0004,-10.48232124038756783909,0.0554529100014586473476929,2452.9820144458617504796},
- {14,0.314,0.065,-7.91753972042693519284807,7.47516931919399021898056,-19.4065385144529680284843},
- {14,0.314,4.42,-31.1096030160603970450565,40.6949859937193738748557,-1.44235830397139693802194},
- {14,0.314,800,-41.6146101076375483922037,43.568886473205763553092,-0.000133818772002702504530118},
- {14,0.314,15324,-41.7166402819016445593073,43.585094170597712706582,-3.68785202783475625980072e-7},
- {14,1.5,0.0004,-10.4688561593594870180174,0.00222162978761219230427442,2486.61861613580838671742},
- {14,1.5,0.065,-5.96960149272681243148081,0.346112886048988285410011,7.29895408232336627643618},
- {14,1.5,4.42,-13.3341039738636536056565,6.22184684684684684684685,-0.886409460834882606838869},
- {14,1.5,800,-20.9264151022685229463224,8.31773757537949677687669,-0.000109610174761583369512834},
- {14,1.5,15324,-21.0100699378693506067827,8.3325176992594042608724,-3.02665838448691571323444e-7},
- {14,3,0.0004,-10.4672670714982932744397,0.000488823712393903035150869,2490.59053612251208613134},
- {14,3,0.065,-5.71949591388313644017256,0.0777596519847743338771071,11.025105769529760808809},
- {14,3,4.42,-7.79006429060418247514041,2.18418688230008984725966,-0.483245366998347706389421},
- {14,3,800,-12.7443244787126682405839,3.6529680365296803652968,-0.0000822242550653573074282639},
- {14,3,15324,-12.8071593989944707311042,3.66594897892607816271938,-2.27631817501670696455485e-7},
- {14,180,0.0004,-10.4670693257255523386798,-2.04937816187568965896125e-6,2491.08472067831379995549},
- {14,180,0.065,-5.68921919805166473123324,-0.000332904475852855604611915,11.4626317745298008318075},
- {14,180,4.42,-9.65337657959679927166961,-0.0221029293038836472303558,-1.31368299764513841319336},
- {14,180,800,-117.570556789937986073345,-0.752834467120181405895692,-0.0161936967338941701029113},
- {14,180,15324,-131.5984192349764106228,-0.911515307877536979704162,-0.0000577016781835615346878727},
- {14,1123,0.0004,-10.4677755213861686112027,-3.51748189118411715224579e-7,2489.319233308602484167},
- {14,1123,0.065,-5.8039572920094235935389,-0.0000571557928751928433161097,9.69771975676490255408168},
- {14,1123,4.42,-17.3710293984633664722496,-0.00387158077355886416717715,-3.04061182895062280658097},
- {14,1123,800,-640.647914910330698665346,-0.41083032457540509990836,-0.282967557637372205015805},
- {14,1123,15324,-1011.59993064034851794618,-0.920104682295016979172854,-0.00238094023047733949128954},
- {14,10586,0.0004,-10.468668475096403358952,-3.77357816303515044684135e-8,2487.08684934922326872119},
- {14,10586,0.065,-5.94905895063816048990702,-6.13202709485509703057976e-6,7.46543792757153500263484},
- {14,10586,4.42,-27.2227588675497966851323,-0.000416806372526964100271534,-5.26603093110764468733629},
- {14,10586,800,-2056.93593717552727578896,-0.0701688036945746844270555,-1.70965999479388506262815},
- {14,10586,15324,-7951.09533692356666073317,-0.590649710084385025903513,-0.116267766949827820373742},
- {1525,0.0000256,0.0004,-4301.78472746701578211824,5.59871348684210526315789e7,-3.58066878763440801575999e6},
- {1525,0.0000256,0.065,-11965.4671281234821192651,5.95468591985310400826751e7,-23429.1126891147674041279},
- {1525,0.0000256,4.42,-18367.3428918005844132604,5.95699664793796669412955e7,-339.057082534394502685042},
- {1525,0.0000256,800,-24826.2281356385313850842,5.9570309593750092999997e7,-0.838976287617641050521018},
- {1525,0.0000256,15324,-25707.7170288016100578067,5.95703114004829044732209e7,-0.00464306291332368931093164},
- {1525,0.314,0.0004,-17.0947387955188070326685,6.17771997212362846631335,-2348.2711549792054388957},
- {1525,0.314,0.065,-296.585568286099067098382,832.7696922844226341529,-4001.49218112616940138645},
- {1525,0.314,4.42,-4115.10160678526160318827,4533.61649969457966358017,-316.176485619091863713022},
- {1525,0.314,800,-10469.9426767525578633112,4853.78278834474666145767,-0.838228516034976412381988},
- {1525,0.314,15324,-11350.8644775429644460839,4855.58840352125852665115,-0.00464102415296814454780544},
- {1525,1.5,0.0004,-15.5605375416167690037651,0.270772238514173998044966,1484.28030775203773370257},
- {1525,1.5,0.065,-74.4509275868752796839738,42.1842385516506922257721,-953.474508334327862701411},
- {1525,1.5,4.42,-2072.19103657901875771673,758.318693693693693693694,-251.676626135276647866636},
- {1525,1.5,800,-8088.5487996808837996978,1013.76585568725306716573,-0.835410572412918435298525},
- {1525,1.5,15324,-8967.33164084000397251235,1015.56725718573619131513,-0.00463332752548632640449661},
- {1525,3,0.0004,-15.3575220720668965445137,0.0676354263875927654090566,1991.71749039935673683979},
- {1525,3,0.065,-42.4918294753981553150494,10.759108210984230560087,-477.238467087057049216524},
- {1525,3,4.42,-1360.54978818586119643475,302.212039532794249775382,-199.675789571126133218244},
- {1525,3,800,-7035.84649923785032031894,505.437941054379410543794,-0.831861613850395752926704},
- {1525,3,15324,-7911.93122400832367818281,507.234031447771905787173,-0.00462360345575814251935502},
- {1525,180,0.0004,-15.1592288635917619923534,0.0000166049013718241119958005,2487.41676922898500772359},
- {1525,180,0.065,-10.6183839860155018806964,0.00269732843386801679640377,7.79296281407547767488829},
- {1525,180,4.42,-30.7569326420675973698907,0.179086987432069310390534,-5.06066771330890867332748},
- {1525,180,800,-1255.10606104316181434609,6.09977324263038548752834,-0.50811617220616562857323},
- {1525,180,15324,-1861.51726736161923065929,7.38547041623667010663915,-0.00355560001152251827139362},
- {1525,1123,0.0004,-15.1571154863562692876443,1.27504753855366555022796e-7,2492.70020501203972018602},
- {1525,1123,0.065,-10.2750368571307051844228,0.0000207183306905568286862724,13.0740397653170432513801},
- {1525,1123,4.42,-7.7548168672587285529831,0.0014034043922188128000047,0.0654298516080506295778705},
- {1525,1123,800,-30.3901820482837344036952,0.148921362019218079497891,-0.0188047284729684005572389},
- {1525,1123,15324,-64.3938471491118556432688,0.333527576449591366661395,-0.000290976140796059790385352},
- {1525,10586,0.0004,-15.1575273331900733823398,-3.23424061059983902750941e-8,2491.6705880068073820668},
- {1525,10586,0.065,-10.341961135413218918573,-5.25560892040125181555838e-6,12.0444483664247291801249},
- {1525,10586,4.42,-12.3018556139457378552047,-0.000357234443952593805577031,-0.96243723577972978183147},
- {1525,10586,800,-744.016916706287313438782,-0.0601399480019429829354474,-0.792452568525027960065769},
- {1525,10586,15324,-4300.64559341391477270059,-0.506231273465249027592861,-0.080624196979174112177973},
- {10233,0.0000256,0.0004,-28781.0708528951564436868,3.75682858552631578947368e8,-2.40411931995216805817928e7},
- {10233,0.0000256,0.065,-80237.4790550341084402889,3.99569192710255653158141e8,-157343.697098361014871643},
- {10233,0.0000256,4.42,-123371.163364167739853751,3.99724246355043735493297e8,-2307.2799792939510175957},
- {10233,0.0000256,800,-173733.655946368116040227,3.99726548708750441319986e8,-10.1666354466535988554224},
- {10233,0.0000256,15324,-189611.393943800923934812,3.9972656083222396519806e8,-0.156271946909903467303064},
- {10233,0.314,0.0004,-30.0835346409569126537712,41.4607785935398129689956,-30043.5682705897920957967},
- {10233,0.314,0.065,-1936.71659175848698855364,5589.00047056450935246962,-26975.8416131385266353558},
- {10233,0.314,4.42,-27734.5558869327520485077,30426.6413450334885998832,-2153.7342775414124625757},
- {10233,0.314,800,-77398.8345343110590488869,32575.3861354641233252254,-10.1616173371352784115726},
- {10233,0.314,15324,-93272.7669155443507051479,32587.5042326579589686295,-0.156258265294963792040417},
- {10233,1.5,0.0004,-19.7852231333246169373824,1.81844841375633164489469,-4317.60144720493526427937},
- {10233,1.5,0.065,-445.630392408020268115618,283.300319488817891373802,-6515.78789458981693006454},
- {10233,1.5,4.42,-14020.6484936315300789489,5092.70608108108108108108,-1720.72113290933110987002},
- {10233,1.5,800,-61412.5266404072312643186,6808.23456019962570180911,-10.1426989007295637839166},
- {10233,1.5,15324,-77272.0989845637286907938,6820.33238719780757560928,-0.156206593508853883167535},
- {10233,3,0.0004,-18.4213731622889640306878,0.454606052526329822690308,-908.658303440053015065049},
- {10233,3,0.065,-230.930124889414044823939,72.3164763458401305057096,-3316.44389947819074911539},
- {10233,3,4.42,-9239.71902985399623107597,2031.29380053908355795148,-1371.35925605961200776625},
- {10233,3,800,-54340.1804040886113152815,3397.26027397260273972603,-10.1188548696496798960218},
- {10233,3,15324,-70181.625182690519906018,3409.33255040125269132903,-0.156141261363057784911755},
- {10233,180,0.0004,-17.081441774321808557538,0.000124110835309254868322515,2440.94300115825934508112},
- {10233,180,0.065,-15.5422428149329860521265,0.0201607752755949240552023,-38.663485376183506373452},
- {10233,180,4.42,-235.497379149446597781456,1.33855872465025485305281,-50.3775345819770169658823},
- {10233,180,800,-14640.5024630709594885282,45.5918367346938775510204,-7.83648996527639800152069},
- {10233,180,15324,-28577.6446971680821285066,55.2015866873065015479876,-0.148587051440887372280679},
- {10233,1123,0.0004,-17.0630789988207189145522,2.88947340204574456780515e-6,2486.84988023336341161969},
- {10233,1123,0.065,-12.5589181079456256205069,0.000469512419380529127691397,7.22412495831966558459338},
- {10233,1123,4.42,-35.4550615786577840007616,0.0318035174455556831045841,-5.75696060521026301882133},
- {10233,1123,800,-3343.1303902972739556477,3.37480997013700672692981,-2.98980536947426087305154},
- {10233,1123,15324,-11352.0607180353268830661,7.55829905834770485145599,-0.113119180727235553840235},
- {10233,10586,0.0004,-17.0607181926565361616021,-1.26000103249281886845913e-9,2492.75189435765523482408},
- {10233,10586,0.065,-12.175300607237463446918,-2.04748918320454904634379e-7,13.1257236766090680623184},
- {10233,10586,4.42,-9.43079204562662170137108,-0.0000139172010501341588531831,0.116749372001926599593782},
- {10233,10586,800,-7.27036619721226178082317,-0.002342942461614156602606,0.0000890483066241868231597611},
- {10233,10586,15324,-9.3278240351663417156768,-0.0197218452194275363359762,-0.0000805948075011592832299515},
-};}  // namespace neg_binomial_2_test_internal
+// TODO[martinmodrak] add updated code here
+std::vector<TestValue> testValues = {
+    {0, 0.0000256, 0.0004, -0.0000248141563677810565248409,
+     -0.93984962406015037593985, -0.0018850149796030172519518},
+    {0, 0.0000256, 0.065, -0.0000255949600924861403888716,
+     -0.999606308899879432100588, -7.75166869111834937935475e-8},
+    {0, 0.0000256, 4.42, -0.0000255999258645396480948713,
+     -0.999994208178341772500141, -1.67726638232395628338958e-11},
+    {0, 0.0000256, 800, -0.0000255999995904000087381331,
+     -0.999999968000001023999967, -5.1199997815466745309864e-16},
+    {0, 0.0000256, 15324, -0.0000255999999786165492276784,
+     -0.999999998329417909342659, -1.39542226236663832355842e-18},
+    {0, 0.314, 0.0004, -0.00266678271697168261798476,
+     -0.00127226463104325699745547, -5.66822905706024980195936},
+    {0, 0.314, 0.065, -0.114604680787141300415594, -0.171503957783641160949868,
+     -0.934652892970430398112858},
+    {0, 0.314, 4.42, -0.303348202309659616314882, -0.933671313899450781580059,
+     -0.00230212890163621513546237},
+    {0, 0.314, 800, -0.313938393619808990999524, -0.999607653995806645891488,
+     -7.69878314071302369967267e-8},
+    {0, 0.314, 15324, -0.313996782998787812397665, -0.999979509686371605280341,
+     -2.09929343978617830724328e-10},
+    {0, 1.5, 0.0004, -0.00329191110003275493362122,
+     -0.00026659557451346307651293, -7.23004434565640079712956},
+    {0, 1.5, 0.065, -0.206781499150110071240643, -0.0415335463258785942492013,
+     -2.22278737940449507487448},
+    {0, 1.5, 4.42, -1.29150964740387939892012, -0.746621621621621621621622,
+     -0.0388183744279291779383916},
+    {0, 1.5, 800, -1.49859550534427827334156, -0.998128509045539613225203,
+     -1.75342721996106687969703e-6},
+    {0, 1.5, 15324, -1.49992659053829698010225, -0.999902123911128511304688,
+     -4.79017695146261715054393e-9},
+    {0, 3, 0.0004, -0.00356911664958785451901203, -0.00013331555792560991867751,
+     -7.92292493952756190744874},
+    {0, 3, 0.065, -0.250472012600853853120106, -0.0212071778140293637846656,
+     -2.87462275628870402717091},
+    {0, 3, 4.42, -2.28973397601639586742486, -0.595687331536388140161725,
+     -0.113726692626070463108525},
+    {0, 3, 800, -2.99438902306750149309853, -0.996264009962640099626401,
+     -6.99624147447649277415792e-6},
+    {0, 3, 15324, -2.99970638131217673536622, -0.999804266979839498923468,
+     -1.91582075605741709616675e-8},
+    {0, 180, 0.0004, -0.00520680203358650223341638,
+     -2.22221728396159119646401e-6, -12.0170073061835395451321},
+    {0, 180, 0.065, -0.515234583883688262086666, -0.000360980756948879571265932,
+     -6.92704688665984521936613},
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+     -0.156141261363057784911755},
+    {10233, 180, 0.0004, -17.081441774321808557538,
+     0.000124110835309254868322515, 2440.94300115825934508112},
+    {10233, 180, 0.065, -15.5422428149329860521265, 0.0201607752755949240552023,
+     -38.663485376183506373452},
+    {10233, 180, 4.42, -235.497379149446597781456, 1.33855872465025485305281,
+     -50.3775345819770169658823},
+    {10233, 180, 800, -14640.5024630709594885282, 45.5918367346938775510204,
+     -7.83648996527639800152069},
+    {10233, 180, 15324, -28577.6446971680821285066, 55.2015866873065015479876,
+     -0.148587051440887372280679},
+    {10233, 1123, 0.0004, -17.0630789988207189145522,
+     2.88947340204574456780515e-6, 2486.84988023336341161969},
+    {10233, 1123, 0.065, -12.5589181079456256205069,
+     0.000469512419380529127691397, 7.22412495831966558459338},
+    {10233, 1123, 4.42, -35.4550615786577840007616, 0.0318035174455556831045841,
+     -5.75696060521026301882133},
+    {10233, 1123, 800, -3343.1303902972739556477, 3.37480997013700672692981,
+     -2.98980536947426087305154},
+    {10233, 1123, 15324, -11352.0607180353268830661, 7.55829905834770485145599,
+     -0.113119180727235553840235},
+    {10233, 10586, 0.0004, -17.0607181926565361616021,
+     -1.26000103249281886845913e-9, 2492.75189435765523482408},
+    {10233, 10586, 0.065, -12.175300607237463446918,
+     -2.04748918320454904634379e-7, 13.1257236766090680623184},
+    {10233, 10586, 4.42, -9.43079204562662170137108,
+     -0.0000139172010501341588531831, 0.116749372001926599593782},
+    {10233, 10586, 800, -7.27036619721226178082317, -0.002342942461614156602606,
+     0.0000890483066241868231597611},
+    {10233, 10586, 15324, -9.3278240351663417156768,
+     -0.0197218452194275363359762, -0.0000805948075011592832299515},
+};
+}  // namespace neg_binomial_2_test_internal
 
 TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
   using neg_binomial_2_test_internal::TestValue;
@@ -334,8 +511,8 @@ TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
     for (double phi_dbl = phi_start; phi_dbl < phi_max;
          phi_dbl *= stan::math::pi()) {
       std::ostringstream msg;
-      msg << std::setprecision(20) << ", mu = " << mu_dbl 
-        << ", phi = " << phi_dbl;
+      msg << std::setprecision(20) << ", mu = " << mu_dbl
+          << ", phi = " << phi_dbl;
 
       var mu0(mu_dbl);
       var phi0(phi_dbl);

From 4c48fc67a66ca83f81f76cc68356d41f70ab9da4 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 20:11:43 +0100
Subject: [PATCH 62/82] More fixes after merge

---
 stan/math/prim/fun/lgamma_stirling.hpp      | 4 ++--
 stan/math/prim/fun/lgamma_stirling_diff.hpp | 4 ++--
 2 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/stan/math/prim/fun/lgamma_stirling.hpp b/stan/math/prim/fun/lgamma_stirling.hpp
index 9aaa627447d..cf63a1f0656 100644
--- a/stan/math/prim/fun/lgamma_stirling.hpp
+++ b/stan/math/prim/fun/lgamma_stirling.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_HPP
-#define STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_HPP
+#ifndef STAN_MATH_PRIM_FUN_LGAMMA_STIRLING_HPP
+#define STAN_MATH_PRIM_FUN_LGAMMA_STIRLING_HPP
 
 #include <cmath>
 #include <stan/math/prim/fun/constants.hpp>
diff --git a/stan/math/prim/fun/lgamma_stirling_diff.hpp b/stan/math/prim/fun/lgamma_stirling_diff.hpp
index 45c9f26c1fe..5432ad6e044 100644
--- a/stan/math/prim/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/fun/lgamma_stirling_diff.hpp
@@ -1,5 +1,5 @@
-#ifndef STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_DIFF_HPP
-#define STAN_MATH_PRIM_SCAL_FUN_LGAMMA_STIRLING_DIFF_HPP
+#ifndef STAN_MATH_PRIM_FUN_LGAMMA_STIRLING_DIFF_HPP
+#define STAN_MATH_PRIM_FUN_LGAMMA_STIRLING_DIFF_HPP
 
 #include <cmath>
 #include <stan/math/prim/fun/value_of.hpp>

From 584d5056d8c46fb94627c165795459a47c96871b Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 13 Jan 2020 19:16:18 +0000
Subject: [PATCH 63/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 .../prim/fun/binomial_coefficient_log.hpp     | 17 ++--
 stan/math/prim/fun/lbeta.hpp                  | 13 ++-
 .../fun/binomial_coefficient_log_test.cpp     | 80 +++++++++++++++++--
 test/unit/math/prim/fun/lbeta_test.cpp        | 67 +++++++++++++---
 4 files changed, 146 insertions(+), 31 deletions(-)

diff --git a/stan/math/prim/fun/binomial_coefficient_log.hpp b/stan/math/prim/fun/binomial_coefficient_log.hpp
index e81a97e8b55..5355a625a8d 100644
--- a/stan/math/prim/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/fun/binomial_coefficient_log.hpp
@@ -25,13 +25,14 @@ namespace math {
  *
  * \f$ \log {N \choose n}
  * = \log \ \Gamma(N+1) - \log \Gamma(n+1) - \log \Gamma(N-n+1)\f$.
- * 
+ *
  *
  * TODO[martinmodrak] figure out the cases for x < 0 and for partials
    \f[
    \mbox{binomial\_coefficient\_log}(x, y) =
    \begin{cases}
-     \textrm{error} & \mbox{if } y > x + 1 \textrm{ or } y < -1 \textrm{ or } x < 0\\
+     \textrm{error} & \mbox{if } y > x + 1 \textrm{ or } y < -1 \textrm{ or } x
+ < 0\\
      \textrm{-\infty} & \mbox{if } y = x + 1 \textrm{ or } y = -1\\
      \ln\Gamma(x+1) & \mbox{if } -1 < y < x + 1 \\
      \quad -\ln\Gamma(y+1)& \\
@@ -70,22 +71,22 @@ namespace math {
 template <typename T_N, typename T_n>
 inline return_type_t<T_N, T_n> binomial_coefficient_log(const T_N N,
                                                         const T_n n) {
-  if(is_nan(value_of_rec(N)) || is_nan(value_of_rec(n))) {
+  if (is_nan(value_of_rec(N)) || is_nan(value_of_rec(n))) {
     return std::numeric_limits<double>::quiet_NaN();
-  } 
-  
+  }
+
   // For some uses it is important this works even when N < 0 and therefore
   // it is before checks
   if (n == 0) {
     return 0;
-  }                                                  
+  }
   const T_N N_plus_1 = N + 1;
 
   static const char* function = "binomial_coefficient_log";
   check_nonnegative(function, "first argument", N);
   check_greater_or_equal(function, "second argument", n, -1);
-  check_greater_or_equal(function, "(first argument - second argument + 1)", 
-    N - n + 1, 0.0);
+  check_greater_or_equal(function, "(first argument - second argument + 1)",
+                         N - n + 1, 0.0);
 
   if (N / 2 < n) {
     return binomial_coefficient_log(N, N - n);
diff --git a/stan/math/prim/fun/lbeta.hpp b/stan/math/prim/fun/lbeta.hpp
index ab4fbcb3050..644fc82bf28 100644
--- a/stan/math/prim/fun/lbeta.hpp
+++ b/stan/math/prim/fun/lbeta.hpp
@@ -63,9 +63,9 @@ template <typename T1, typename T2>
 inline return_type_t<T1, T2> lbeta(const T1 a, const T2 b) {
   typedef return_type_t<T1, T2> T_ret;
 
-  if(is_nan(value_of_rec(a)) || is_nan(value_of_rec(b))) {
+  if (is_nan(value_of_rec(a)) || is_nan(value_of_rec(b))) {
     return std::numeric_limits<double>::quiet_NaN();
-  } 
+  }
 
   static const char* function = "lbeta";
   check_nonnegative(function, "first argument", a);
@@ -91,17 +91,16 @@ inline return_type_t<T1, T2> lbeta(const T1 a, const T2 b) {
     return lgamma(x) + lgamma(y) - lgamma(x + y);
   } else if (x < lgamma_stirling_diff_useful) {
     // y large, x small
-    T_ret stirling_diff
-        = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
-    T_ret log_x_y = log(x + y); 
+    T_ret stirling_diff = lgamma_stirling_diff(y) - lgamma_stirling_diff(x + y);
+    T_ret log_x_y = log(x + y);
     T_ret stirling = (y - 0.5) * log1p(-x / (x + y)) + x * (1 - log_x_y);
     return stirling + lgamma(x) + stirling_diff;
   } else {
     // both large
     T_ret stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y)
-                           - lgamma_stirling_diff(x + y);
+                          - lgamma_stirling_diff(x + y);
     T_ret stirling = (x - 0.5) * log(x / (x + y)) + y * log1p(-x / (x + y))
-                      + 0.5 * (log(2 * stan::math::pi()) - log(y));
+                     + 0.5 * (log(2 * stan::math::pi()) - log(y));
     return stirling + stirling_diff;
   }
 }
diff --git a/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
index 6b85505fd37..91b5c3afaa8 100644
--- a/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
@@ -21,12 +21,14 @@ TEST(MathFunctions, binomial_coefficient_log) {
 
   EXPECT_FLOAT_EQ(29979.16, binomial_coefficient_log(100000, 91116));
 
-  EXPECT_EQ(binomial_coefficient_log(-1, 0), 0); // Needed for neg_binomial_2
+  EXPECT_EQ(binomial_coefficient_log(-1, 0), 0);  // Needed for neg_binomial_2
   EXPECT_EQ(binomial_coefficient_log(50, 0), 0);
   EXPECT_EQ(binomial_coefficient_log(10000, 0), 0);
 
-  EXPECT_EQ(binomial_coefficient_log(10, 11), -std::numeric_limits<double>::infinity()); 
-  EXPECT_EQ(binomial_coefficient_log(10, -1), -std::numeric_limits<double>::infinity()); 
+  EXPECT_EQ(binomial_coefficient_log(10, 11),
+            -std::numeric_limits<double>::infinity());
+  EXPECT_EQ(binomial_coefficient_log(10, -1),
+            -std::numeric_limits<double>::infinity());
 
   for (int n = 0; n < 1010; ++n) {
     test_binom_coefficient(1010, n);
@@ -64,7 +66,74 @@ struct TestValue {
   double val;
 };
 
-std::vector<TestValue> testValues = {  {0.00003,-0.9,-2.21375637737528044964112},  {0.00003,3.e-15,1.48040820535563428588846e-19},  {0.00003,3.e-10,1.48039340142161568666212e-14},  {0.00003,3.e-7,1.46560412344434242311062e-11},  {0.00003,6.e-6,2.36865312869367134774661e-10},  {0.00003,0.000015,3.70102051348524044535716e-10},  {0.00003,0.0000291,4.30798787797857754693695e-11},  {0.00003,0.0000299999982,8.88244870007509649977929e-17},  {0.00003,0.00002999999991,4.44122460318735146597007e-18},  {0.00003,0.90003,-2.21375637737528044964112},  {0.002,-0.9,-2.21559326412971099686943},  {0.002,2.e-13,6.57013709556564677684856e-16},  {0.002,2.e-8,6.57007139476544583161173e-11},  {0.002,0.00002,6.50443564072189575550994e-8},  {0.002,0.0004,1.05122171458287350859763e-6},  {0.002,0.001,1.64253373496215313253469e-6},  {0.002,0.00194,1.91190982195918976356429e-7},  {0.002,0.00199999988,3.94208202120835082737684e-13},  {0.002,0.001999999994,1.97104112295366725515452e-14},  {0.002,0.902,-2.21559326412971099686943},  {1,-0.9,-2.85558226198351740582195},  {1,1.e-10,9.9999999988550659331851e-11},  {1,0.00001,9.99988550692664559909352e-6},  {1,0.01,0.00988583703486131052627978},  {1,0.2,0.156457962917688016707705},  {1,0.5,0.241564475270490444691037},  {1,0.97,0.028978328236256312960776},  {1,0.99999994,5.99999958782374313463811e-8},  {1,0.999999997,2.99999998969559340736596e-9},  {1,1.9,-2.85558226198351740582195},  {8,-0.9,-4.22528965320883461943031},  {8,8.e-10,2.17428571372173153982474e-9},  {8,0.00008,0.000217422931805073420417006},  {8,0.08,0.211982267378255838975509},  {8,1.6,2.90678606291134283426263},  {8,4,4.24849524204935898912334},  {8,7.76,0.606274586245453651115361},  {8,7.99999952,1.30457122553768403613331e-6},  {8,7.999999976,6.52285709209869625945566e-8},  {8,8.9,-4.22528965320883461943031},  {1325,-0.9,-8.72360867216657209762532},  {1325,1.325e-7,1.02909578020477960435539e-6},  {1325,0.01325,0.102766042691370430370992},  {1325,13.25,71.9898321274090629975055},  {1325,265,659.435649329029419323398},  {1325,662.5,914.599450340845275100724},  {1325,1285.25,175.786260651191862665015},  {1325,1324.9999205,0.000617452276410452190170437},  {1325,1324.999996025,0.0000308728608380968862741097},  {1325,1325.9,-8.72360867216657209762532},  {845000,-0.9,-14.5350963792733464918229},  {845000,0.0000845,0.00120194816738712136581358},  {845000,8.45,103.738303827736743600251},  {845000,8450,47315.8616457576200611209},  {845000,169000,422833.221695496506553128},  {845000,422500,585702.318235552114086514},  {845000,819650,113851.158132678562120685},  {845000,844999.9493,0.719108776819481762797449},  {845000,844999.997465,0.036053342347290003917417},  {845000,845000.9,-14.5350963792733464918229},  {3000000000000000.0,3,105.120406581508328854183},  {3000000000000000.0,100,3199.99949280231435502243},  {3000000000000000.0,12895,350387.5243605883687667},  {100000000000000000000.0,3,136.363346110414686040237},  {100000000000000000000.0,100,4241.4308104325278778424},  {100000000000000000000.0,12895,484680.092769031900296878},};
+std::vector<TestValue> testValues = {
+    {0.00003, -0.9, -2.21375637737528044964112},
+    {0.00003, 3.e-15, 1.48040820535563428588846e-19},
+    {0.00003, 3.e-10, 1.48039340142161568666212e-14},
+    {0.00003, 3.e-7, 1.46560412344434242311062e-11},
+    {0.00003, 6.e-6, 2.36865312869367134774661e-10},
+    {0.00003, 0.000015, 3.70102051348524044535716e-10},
+    {0.00003, 0.0000291, 4.30798787797857754693695e-11},
+    {0.00003, 0.0000299999982, 8.88244870007509649977929e-17},
+    {0.00003, 0.00002999999991, 4.44122460318735146597007e-18},
+    {0.00003, 0.90003, -2.21375637737528044964112},
+    {0.002, -0.9, -2.21559326412971099686943},
+    {0.002, 2.e-13, 6.57013709556564677684856e-16},
+    {0.002, 2.e-8, 6.57007139476544583161173e-11},
+    {0.002, 0.00002, 6.50443564072189575550994e-8},
+    {0.002, 0.0004, 1.05122171458287350859763e-6},
+    {0.002, 0.001, 1.64253373496215313253469e-6},
+    {0.002, 0.00194, 1.91190982195918976356429e-7},
+    {0.002, 0.00199999988, 3.94208202120835082737684e-13},
+    {0.002, 0.001999999994, 1.97104112295366725515452e-14},
+    {0.002, 0.902, -2.21559326412971099686943},
+    {1, -0.9, -2.85558226198351740582195},
+    {1, 1.e-10, 9.9999999988550659331851e-11},
+    {1, 0.00001, 9.99988550692664559909352e-6},
+    {1, 0.01, 0.00988583703486131052627978},
+    {1, 0.2, 0.156457962917688016707705},
+    {1, 0.5, 0.241564475270490444691037},
+    {1, 0.97, 0.028978328236256312960776},
+    {1, 0.99999994, 5.99999958782374313463811e-8},
+    {1, 0.999999997, 2.99999998969559340736596e-9},
+    {1, 1.9, -2.85558226198351740582195},
+    {8, -0.9, -4.22528965320883461943031},
+    {8, 8.e-10, 2.17428571372173153982474e-9},
+    {8, 0.00008, 0.000217422931805073420417006},
+    {8, 0.08, 0.211982267378255838975509},
+    {8, 1.6, 2.90678606291134283426263},
+    {8, 4, 4.24849524204935898912334},
+    {8, 7.76, 0.606274586245453651115361},
+    {8, 7.99999952, 1.30457122553768403613331e-6},
+    {8, 7.999999976, 6.52285709209869625945566e-8},
+    {8, 8.9, -4.22528965320883461943031},
+    {1325, -0.9, -8.72360867216657209762532},
+    {1325, 1.325e-7, 1.02909578020477960435539e-6},
+    {1325, 0.01325, 0.102766042691370430370992},
+    {1325, 13.25, 71.9898321274090629975055},
+    {1325, 265, 659.435649329029419323398},
+    {1325, 662.5, 914.599450340845275100724},
+    {1325, 1285.25, 175.786260651191862665015},
+    {1325, 1324.9999205, 0.000617452276410452190170437},
+    {1325, 1324.999996025, 0.0000308728608380968862741097},
+    {1325, 1325.9, -8.72360867216657209762532},
+    {845000, -0.9, -14.5350963792733464918229},
+    {845000, 0.0000845, 0.00120194816738712136581358},
+    {845000, 8.45, 103.738303827736743600251},
+    {845000, 8450, 47315.8616457576200611209},
+    {845000, 169000, 422833.221695496506553128},
+    {845000, 422500, 585702.318235552114086514},
+    {845000, 819650, 113851.158132678562120685},
+    {845000, 844999.9493, 0.719108776819481762797449},
+    {845000, 844999.997465, 0.036053342347290003917417},
+    {845000, 845000.9, -14.5350963792733464918229},
+    {3000000000000000.0, 3, 105.120406581508328854183},
+    {3000000000000000.0, 100, 3199.99949280231435502243},
+    {3000000000000000.0, 12895, 350387.5243605883687667},
+    {100000000000000000000.0, 3, 136.363346110414686040237},
+    {100000000000000000000.0, 100, 4241.4308104325278778424},
+    {100000000000000000000.0, 12895, 484680.092769031900296878},
+};
 }  // namespace binomial_coefficient_test_internal
 
 TEST(MathFunctions, binomial_coefficient_log_precomputed) {
@@ -73,14 +142,13 @@ TEST(MathFunctions, binomial_coefficient_log_precomputed) {
   using stan::test::expect_near_rel;
 
   for (TestValue t : testValues) {
-
     std::ostringstream msg;
     msg << std::setprecision(22) << "n = " << t.n << ", k = " << t.k;
 
     double val = stan::math::binomial_coefficient_log(t.n, t.k);
     expect_near_rel(msg.str(), val, t.val);
 
-    if(t.k > t.n / 10) {
+    if (t.k > t.n / 10) {
       // Testing the mirrored binomial coefficient is not performed for
       // small k, as we may loose so much precision computing k2
       // that the test becomes invalid
diff --git a/test/unit/math/prim/fun/lbeta_test.cpp b/test/unit/math/prim/fun/lbeta_test.cpp
index 528359dd3f4..b0a368a20f8 100644
--- a/test/unit/math/prim/fun/lbeta_test.cpp
+++ b/test/unit/math/prim/fun/lbeta_test.cpp
@@ -5,7 +5,6 @@
 #include <limits>
 #include <vector>
 
-
 TEST(MathFunctions, lbeta) {
   using stan::math::lbeta;
 
@@ -26,11 +25,11 @@ TEST(MathFunctions, lbeta_nan) {
 }
 
 namespace lbeta_test_internal {
-  struct TestValue {
-    double x;
-    double y;
-    double val;
-  };
+struct TestValue {
+  double x;
+  double y;
+  double val;
+};
 
 // Test values generated in Mathematice, reproducible notebook at
 // https://www.wolframcloud.com/obj/martin.modrak/Published/lbeta.nb
@@ -45,7 +44,7 @@ namespace lbeta_test_internal {
 //        For[j = 1, j <= Length[ys], j++, {
 //      cx = xs[[i]];
 //      cy = ys[[j]];
-            
+
 //     val = N[lbeta[cx,cy],24];
 //          WriteString[out,"  {",CForm[cx],",",CForm[cy],",",
 //            CForm[val],"},"]
@@ -65,8 +64,57 @@ namespace lbeta_test_internal {
 // WriteString[out,"};"];
 //  Close[out];
 //  FilePrint[%]
-std::vector<TestValue> testValues = {  {8.e-8,7.e-11,23.3834004912898500586445},  {8.e-8,0.00002,16.3452312235394351410033},  {8.e-8,1.000000000001,16.3412392022725295437606},  {8.e-8,0.5,16.3412393131760679059067},  {8.e-8,2,16.3412391222725327438921},  {8.e-8,1624,16.3412385647081130254943},  {0.004,7.e-11,23.3825258913787298259023},  {0.004,0.00002,10.8247656947117878792194},  {0.004,1.000000000001,5.52146091786223987264715},  {0.004,0.5,5.52697992926150653113797},  {0.004,2,5.51746889659270898022044},  {0.004,1624,5.48959582574332555214719},  {1,7.e-11,23.3825258738791892190926},  {1,0.00002,10.8197782844102831106727},  {1,1.000000000001,-9.999999999995e-13},  {1,0.5,0.693147180559945309417232},  {1,2,-0.693147180559945309417232},  {1,1624,-7.39264752072162326054032},  {1.00000001,7.e-11,23.3825258738791892179411},  {1.00000001,0.00002,10.8197782844099541286699},  {1.00000001,1.000000000001,-1.00009999500064491739816e-8},  {1.00000001,0.5,0.693147174422888956122731},  {1.00000001,2,-0.693147195559945246917232},  {1.00000001,1624,-7.39264760042333353631934},  {5,7.e-11,23.3825258737333558857627},  {5,0.00002,10.8197366180283355258393},  {5,1.000000000001,-1.60943791243638370793409},  {5,0.5,-0.207395194346070587158746},  {5,2,-3.40119738166215537541324},  {5,1624,-33.7913357290267948074624},  {23,7.e-11,23.3825258736208322915813},  {23,0.00002,10.819704468465374949026},  {23,1.000000000001,-3.13549421593288398231784},  {23,0.5,-0.989947810259228199543883},  {23,2,-6.31354804627709531045369},  {23,1624,-121.714785277510463870251},  {19845,7.e-11,23.3825258731460863706715},  {19845,0.00002,10.8195688267825637640878},  {19845,1.000000000001,-9.89570736522763869861762},  {19845,0.5,-4.37548244086806082919414},  {19845,2,-19.7914651196913525680177},  {19845,1624,-5756.4146766727238501215},  {3000000000000000.0,3,-106.219018870176440545578},  {3000000000000000.0,100,-3204.60466298830574639047},  {3000000000000000.0,12895,-350396.988955562106921852},  {100000000000000000000.0,3,-137.461958399082795731692},  {100000000000000000000.0,100,-4246.03598061851596930944},  {100000000000000000000.0,12895,-484689.557363950217404711},};
-}
+std::vector<TestValue> testValues = {
+    {8.e-8, 7.e-11, 23.3834004912898500586445},
+    {8.e-8, 0.00002, 16.3452312235394351410033},
+    {8.e-8, 1.000000000001, 16.3412392022725295437606},
+    {8.e-8, 0.5, 16.3412393131760679059067},
+    {8.e-8, 2, 16.3412391222725327438921},
+    {8.e-8, 1624, 16.3412385647081130254943},
+    {0.004, 7.e-11, 23.3825258913787298259023},
+    {0.004, 0.00002, 10.8247656947117878792194},
+    {0.004, 1.000000000001, 5.52146091786223987264715},
+    {0.004, 0.5, 5.52697992926150653113797},
+    {0.004, 2, 5.51746889659270898022044},
+    {0.004, 1624, 5.48959582574332555214719},
+    {1, 7.e-11, 23.3825258738791892190926},
+    {1, 0.00002, 10.8197782844102831106727},
+    {1, 1.000000000001, -9.999999999995e-13},
+    {1, 0.5, 0.693147180559945309417232},
+    {1, 2, -0.693147180559945309417232},
+    {1, 1624, -7.39264752072162326054032},
+    {1.00000001, 7.e-11, 23.3825258738791892179411},
+    {1.00000001, 0.00002, 10.8197782844099541286699},
+    {1.00000001, 1.000000000001, -1.00009999500064491739816e-8},
+    {1.00000001, 0.5, 0.693147174422888956122731},
+    {1.00000001, 2, -0.693147195559945246917232},
+    {1.00000001, 1624, -7.39264760042333353631934},
+    {5, 7.e-11, 23.3825258737333558857627},
+    {5, 0.00002, 10.8197366180283355258393},
+    {5, 1.000000000001, -1.60943791243638370793409},
+    {5, 0.5, -0.207395194346070587158746},
+    {5, 2, -3.40119738166215537541324},
+    {5, 1624, -33.7913357290267948074624},
+    {23, 7.e-11, 23.3825258736208322915813},
+    {23, 0.00002, 10.819704468465374949026},
+    {23, 1.000000000001, -3.13549421593288398231784},
+    {23, 0.5, -0.989947810259228199543883},
+    {23, 2, -6.31354804627709531045369},
+    {23, 1624, -121.714785277510463870251},
+    {19845, 7.e-11, 23.3825258731460863706715},
+    {19845, 0.00002, 10.8195688267825637640878},
+    {19845, 1.000000000001, -9.89570736522763869861762},
+    {19845, 0.5, -4.37548244086806082919414},
+    {19845, 2, -19.7914651196913525680177},
+    {19845, 1624, -5756.4146766727238501215},
+    {3000000000000000.0, 3, -106.219018870176440545578},
+    {3000000000000000.0, 100, -3204.60466298830574639047},
+    {3000000000000000.0, 12895, -350396.988955562106921852},
+    {100000000000000000000.0, 3, -137.461958399082795731692},
+    {100000000000000000000.0, 100, -4246.03598061851596930944},
+    {100000000000000000000.0, 12895, -484689.557363950217404711},
+};
+}  // namespace lbeta_test_internal
 
 TEST(MathFunctions, lbeta_precomputed) {
   using lbeta_test_internal::TestValue;
@@ -74,7 +122,6 @@ TEST(MathFunctions, lbeta_precomputed) {
   using stan::test::expect_near_rel;
 
   for (TestValue t : testValues) {
-
     std::ostringstream msg;
     msg << std::setprecision(22) << "x = " << t.x << ", y = " << t.y;
 

From a85d4497b432ca81e8c4d26bd572594b7ded1a27 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 20:20:41 +0100
Subject: [PATCH 64/82] LOG_TWO_PI

---
 stan/math/prim/fun/lbeta.hpp           | 2 +-
 stan/math/prim/fun/lgamma_stirling.hpp | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/stan/math/prim/fun/lbeta.hpp b/stan/math/prim/fun/lbeta.hpp
index 644fc82bf28..cb53799ea04 100644
--- a/stan/math/prim/fun/lbeta.hpp
+++ b/stan/math/prim/fun/lbeta.hpp
@@ -100,7 +100,7 @@ inline return_type_t<T1, T2> lbeta(const T1 a, const T2 b) {
     T_ret stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y)
                           - lgamma_stirling_diff(x + y);
     T_ret stirling = (x - 0.5) * log(x / (x + y)) + y * log1p(-x / (x + y))
-                     + 0.5 * (log(2 * stan::math::pi()) - log(y));
+                      + 0.5 * (LOG_TWO_PI - log(y));
     return stirling + stirling_diff;
   }
 }
diff --git a/stan/math/prim/fun/lgamma_stirling.hpp b/stan/math/prim/fun/lgamma_stirling.hpp
index cf63a1f0656..be99bd5585e 100644
--- a/stan/math/prim/fun/lgamma_stirling.hpp
+++ b/stan/math/prim/fun/lgamma_stirling.hpp
@@ -25,7 +25,7 @@ namespace math {
 template <typename T>
 T lgamma_stirling(const T x) {
   using std::log;
-  return 0.5 * log(2 * stan::math::pi()) + (x - 0.5) * log(x) - x;
+  return 0.5 * LOG_TWO_PI + (x - 0.5) * log(x) - x;
 }
 
 }  // namespace math

From 6e5026955c58a057588ea765f1fa620bc8e00aaa Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 13 Jan 2020 19:21:17 +0000
Subject: [PATCH 65/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 stan/math/prim/fun/lbeta.hpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/stan/math/prim/fun/lbeta.hpp b/stan/math/prim/fun/lbeta.hpp
index cb53799ea04..f5d1aabe540 100644
--- a/stan/math/prim/fun/lbeta.hpp
+++ b/stan/math/prim/fun/lbeta.hpp
@@ -100,7 +100,7 @@ inline return_type_t<T1, T2> lbeta(const T1 a, const T2 b) {
     T_ret stirling_diff = lgamma_stirling_diff(x) + lgamma_stirling_diff(y)
                           - lgamma_stirling_diff(x + y);
     T_ret stirling = (x - 0.5) * log(x / (x + y)) + y * log1p(-x / (x + y))
-                      + 0.5 * (LOG_TWO_PI - log(y));
+                     + 0.5 * (LOG_TWO_PI - log(y));
     return stirling + stirling_diff;
   }
 }

From 446f04269fc07397f0eba91f60bdaf2a62b74aee Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Mon, 13 Jan 2020 20:28:50 +0100
Subject: [PATCH 66/82] Minor optimization in lgamma_stirling_dff

---
 stan/math/prim/fun/lgamma_stirling_diff.hpp | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/stan/math/prim/fun/lgamma_stirling_diff.hpp b/stan/math/prim/fun/lgamma_stirling_diff.hpp
index 1a5510825a8..cd260320caf 100644
--- a/stan/math/prim/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/fun/lgamma_stirling_diff.hpp
@@ -55,13 +55,13 @@ T lgamma_stirling_diff(const T x) {
         -0.000595238095238095238095238,
     };
     constexpr int n_stirling_terms = 3;
-    T result(0.0);
-    T multiplier = inv(x);
-    T inv_x_squared = inv(square(x));
-    for (int n = 0; n < n_stirling_terms; n++, multiplier *= inv_x_squared) {
-      result += stirling_series[n] * multiplier;
-    }
-    return result;
+    T inv_x = inv(x);
+    T inv_x_squared = square(inv_x);
+    T inv_x_cubed = inv_x * inv_x_squared;
+    T inv_x_fifth = inv_x_cubed * inv_x_squared;
+    return stirling_series[0] * inv_x 
+      + stirling_series[1] * inv_x_cubed
+      + stirling_series[2] * inv_x_fifth;
   }
 }
 

From 52dce3c78c5803242c761c532403e3ea9e77d77f Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 13 Jan 2020 19:29:32 +0000
Subject: [PATCH 67/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 stan/math/prim/fun/lgamma_stirling_diff.hpp | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/stan/math/prim/fun/lgamma_stirling_diff.hpp b/stan/math/prim/fun/lgamma_stirling_diff.hpp
index cd260320caf..dca3c687bb7 100644
--- a/stan/math/prim/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/fun/lgamma_stirling_diff.hpp
@@ -59,9 +59,8 @@ T lgamma_stirling_diff(const T x) {
     T inv_x_squared = square(inv_x);
     T inv_x_cubed = inv_x * inv_x_squared;
     T inv_x_fifth = inv_x_cubed * inv_x_squared;
-    return stirling_series[0] * inv_x 
-      + stirling_series[1] * inv_x_cubed
-      + stirling_series[2] * inv_x_fifth;
+    return stirling_series[0] * inv_x + stirling_series[1] * inv_x_cubed
+           + stirling_series[2] * inv_x_fifth;
   }
 }
 

From e505f53993e46db39d0b8782e4011d04189c7bb6 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Tue, 14 Jan 2020 08:23:08 +0100
Subject: [PATCH 68/82] Fixing lint, cleanup

---
 .../prim/fun/binomial_coefficient_log.hpp     |   1 +
 stan/math/prim/fun/lbeta.hpp                  |   1 +
 stan/math/prim/fun/lgamma_stirling.hpp        |   4 +-
 stan/math/prim/fun/lgamma_stirling_diff.hpp   |  20 ++-
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   |  95 ++++----------
 test/unit/math/expect_near_rel.hpp            |   1 +
 test/unit/math/expect_near_rel_test.cpp       |  22 ++--
 .../prim/fun/lgamma_stirling_diff_test.cpp    |  25 +++-
 .../math/prim/prob/neg_binomial_2_test.cpp    |  53 +-------
 .../prim/prob/neg_binomial_2_test_tools.hpp   |  19 ---
 .../math/rev/prob/neg_binomial_2_test.cpp     | 124 ++++++------------
 11 files changed, 111 insertions(+), 254 deletions(-)
 delete mode 100644 test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp

diff --git a/stan/math/prim/fun/binomial_coefficient_log.hpp b/stan/math/prim/fun/binomial_coefficient_log.hpp
index 5355a625a8d..c9c0e35e0fd 100644
--- a/stan/math/prim/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/fun/binomial_coefficient_log.hpp
@@ -1,6 +1,7 @@
 #ifndef STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
 #define STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
 
+#include <limits>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
 #include <stan/math/prim/fun/lbeta.hpp>
diff --git a/stan/math/prim/fun/lbeta.hpp b/stan/math/prim/fun/lbeta.hpp
index f5d1aabe540..a4e52bd44eb 100644
--- a/stan/math/prim/fun/lbeta.hpp
+++ b/stan/math/prim/fun/lbeta.hpp
@@ -1,6 +1,7 @@
 #ifndef STAN_MATH_PRIM_SCAL_FUN_LBETA_HPP
 #define STAN_MATH_PRIM_SCAL_FUN_LBETA_HPP
 
+#include <limits>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
 #include <stan/math/prim/fun/lgamma_stirling.hpp>
diff --git a/stan/math/prim/fun/lgamma_stirling.hpp b/stan/math/prim/fun/lgamma_stirling.hpp
index be99bd5585e..76a93d2260e 100644
--- a/stan/math/prim/fun/lgamma_stirling.hpp
+++ b/stan/math/prim/fun/lgamma_stirling.hpp
@@ -4,6 +4,7 @@
 #include <cmath>
 #include <stan/math/prim/fun/constants.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
+#include <stan/math/prim/meta/return_type.hpp>
 
 namespace stan {
 namespace math {
@@ -23,8 +24,7 @@ namespace math {
  * @tparam T Type of  value.
  */
 template <typename T>
-T lgamma_stirling(const T x) {
-  using std::log;
+return_type_t<T> lgamma_stirling(const T x) {
   return 0.5 * LOG_TWO_PI + (x - 0.5) * log(x) - x;
 }
 
diff --git a/stan/math/prim/fun/lgamma_stirling_diff.hpp b/stan/math/prim/fun/lgamma_stirling_diff.hpp
index dca3c687bb7..190acc22fdf 100644
--- a/stan/math/prim/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/fun/lgamma_stirling_diff.hpp
@@ -9,6 +9,7 @@
 #include <stan/math/prim/fun/square.hpp>
 #include <stan/math/prim/fun/lgamma_stirling.hpp>
 #include <stan/math/prim/err/check_nonnegative.hpp>
+#include <stan/math/prim/meta/return_type.hpp>
 
 namespace stan {
 namespace math {
@@ -39,11 +40,18 @@ constexpr double lgamma_stirling_diff_useful = 10;
  */
 
 template <typename T>
-T lgamma_stirling_diff(const T x) {
+return_type_t<T> lgamma_stirling_diff(const T x) {
+  if (is_nan(value_of_rec(x))) {
+    return std::numeric_limits<double>::quiet_NaN();
+  }
+  typedef return_type_t<T> T_Ret;
+
   static const char* function = "lgamma_stirling_diff";
   check_nonnegative(function, "argument", x);
 
-  if (value_of(x) < lgamma_stirling_diff_useful) {
+  if(x == 0) {
+    return std::numeric_limits<double>::infinity();
+  } else if (value_of(x) < lgamma_stirling_diff_useful) {
     return lgamma(x) - lgamma_stirling(x);
   } else {
     // Using the Stirling series as expressed in formula 5.11.1. at
@@ -55,10 +63,10 @@ T lgamma_stirling_diff(const T x) {
         -0.000595238095238095238095238,
     };
     constexpr int n_stirling_terms = 3;
-    T inv_x = inv(x);
-    T inv_x_squared = square(inv_x);
-    T inv_x_cubed = inv_x * inv_x_squared;
-    T inv_x_fifth = inv_x_cubed * inv_x_squared;
+    T_Ret inv_x = inv(x);
+    T_Ret inv_x_squared = square(inv_x);
+    T_Ret inv_x_cubed = inv_x * inv_x_squared;
+    T_Ret inv_x_fifth = inv_x_cubed * inv_x_squared;
     return stirling_series[0] * inv_x + stirling_series[1] * inv_x_cubed
            + stirling_series[2] * inv_x_fifth;
   }
diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index d3a0fa04e61..f4609a89da6 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -16,13 +16,6 @@
 namespace stan {
 namespace math {
 
-namespace internal {
-// When to switch to approximations for neg. binom for large phi
-// The current tests fail when the cutoff is 1e8 and pass with 1e9,
-// setting 1e10 to be safe
-constexpr double neg_binomial_2_phi_cutoff = 1e15;
-}  // namespace internal
-
 // NegBinomial(n|mu, phi)  [mu >= 0; phi > 0;  n >= 0]
 template <bool propto, typename T_n, typename T_location, typename T_precision>
 return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
@@ -84,73 +77,31 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   }
 
   for (size_t i = 0; i < max_size_seq_view; i++) {
-    if (false) {
-      // if (phi_val[i] > internal::neg_binomial_2_phi_cutoff) {
-      // Phi is large, delegate to Poisson.
-      // Copying the code here as just calling
-      // poisson_lpmf does not preserve propto logic correctly.
-      // Note that Poisson can be seen as first term of Taylor series for
-      // phi -> Inf. Similarly, the derivative w.r.t. mu and phi can be obtained
-      // via the Same Taylor expansions:
-      //
-      // For mu, the expansions can be obtained in Mathematica via
-      // Series[n/mu - (n + phi)/(mu+phi),{phi,Infinity, 1}]
-      // Currently ignoring the 2nd order term (mu_val[i] - n_vec[i]) /
-      // phi_val[i]
-      //
-      // The derivative w.r.t. phi = 0 + O(1/phi^2),
-      // But the quadratic term is big enough to warrant inclusion here
-      // (can be around 1e-6 at cutoff).
-      // Expansion obtained in Mathematica via
-      // Series[1 - (n + phi) / (mu + phi) + Log[phi] - Log[mu + phi] -
-      //  PolyGamma[phi] + PolyGamma[n + phi],{phi,Infinity, 2}]
-      if (n_vec[i] == 0) {
-        logp += phi_val[i] * (-log1p(mu_val[i] / phi_val[i]));
+    if (include_summand<propto, T_precision>::value) {
+      logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
+    }
+    if (include_summand<propto, T_location>::value) {
+      logp += multiply_log(n_vec[i], mu_val[i]);
+    }
+    // logp += phi_val[i] * (log_phi[i] - log_mu_plus_phi[i])
+    logp += -phi_val[i] * (log1p(mu_val[i] / phi_val[i]))
+            - n_vec[i] * log_mu_plus_phi[i];
+
+    if (!is_constant_all<T_location>::value) {
+      ops_partials.edge1_.partials_[i]
+          += n_vec[i] / mu_val[i]
+              - (n_vec[i] + phi_val[i]) / (mu_val[i] + phi_val[i]);
+    }
+    if (!is_constant_all<T_precision>::value) {
+      T_partials_return log_term;
+      if (mu_val[i] < phi_val[i]) {
+        log_term = log1p(-mu_val[i] / (mu_val[i] + phi_val[i]));
       } else {
-        if (include_summand<propto>::value) {
-          logp -= lgamma(n_vec[i] + 1.0);
-        }
-        if (include_summand<propto, T_location>::value) {
-          logp += multiply_log(n_vec[i], mu_val[i]) - mu_val[i];
-        }
-
-        if (!is_constant_all<T_location>::value) {
-          ops_partials.edge1_.partials_[i] += n_vec[i] / mu_val[i] - 1;
-        }
-        if (!is_constant_all<T_precision>::value) {
-          ops_partials.edge2_.partials_[i]
-              += (mu_val[i] * (-mu_val[i] + 2 * n_vec[i])
-                  + n_vec[i] * (1 - n_vec[i]))
-                 / (2 * square(phi_val[i]));
-        }
-      }
-    } else {
-      if (include_summand<propto, T_precision>::value) {
-        logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
-      }
-      if (include_summand<propto, T_location>::value) {
-        logp += multiply_log(n_vec[i], mu_val[i]);
-      }
-      // logp += phi_val[i] * (log_phi[i] - log_mu_plus_phi[i])
-      logp += -phi_val[i] * (log1p(mu_val[i] / phi_val[i]))
-              - n_vec[i] * log_mu_plus_phi[i];
-
-      if (!is_constant_all<T_location>::value) {
-        ops_partials.edge1_.partials_[i]
-            += n_vec[i] / mu_val[i]
-               - (n_vec[i] + phi_val[i]) / (mu_val[i] + phi_val[i]);
-      }
-      if (!is_constant_all<T_precision>::value) {
-        T_partials_return log_term;
-        if (mu_val[i] < phi_val[i]) {
-          log_term = log1p(-mu_val[i] / (mu_val[i] + phi_val[i]));
-        } else {
-          log_term = log_phi[i] - log_mu_plus_phi[i];
-        }
-        ops_partials.edge2_.partials_[i]
-            += (mu_val[i] - n_vec[i]) / (mu_val[i] + phi_val[i]) + log_term
-               - (digamma(phi_val[i]) - digamma(n_plus_phi[i]));
+        log_term = log_phi[i] - log_mu_plus_phi[i];
       }
+      ops_partials.edge2_.partials_[i]
+          += (mu_val[i] - n_vec[i]) / (mu_val[i] + phi_val[i]) + log_term
+              - (digamma(phi_val[i]) - digamma(n_plus_phi[i]));
     }
   }
   return ops_partials.build(logp);
diff --git a/test/unit/math/expect_near_rel.hpp b/test/unit/math/expect_near_rel.hpp
index 0fd0a004b2a..8c62c008e36 100644
--- a/test/unit/math/expect_near_rel.hpp
+++ b/test/unit/math/expect_near_rel.hpp
@@ -6,6 +6,7 @@
 #include <string>
 #include <vector>
 #include <limits>
+#include <algorithm>
 
 namespace stan {
 namespace test {
diff --git a/test/unit/math/expect_near_rel_test.cpp b/test/unit/math/expect_near_rel_test.cpp
index a07f5195f68..62b189ff139 100644
--- a/test/unit/math/expect_near_rel_test.cpp
+++ b/test/unit/math/expect_near_rel_test.cpp
@@ -9,10 +9,10 @@ TEST(testUnitMath, ExpectNearRelScalar) {
   expect_near_rel("test A1", 0, 0, 1e-16);
   expect_near_rel("test A2", 0, 0.0, 1e-16);
   expect_near_rel("test A3", 0.0, 0, 1e-16);
-  expect_near_rel("test B1", 0, 1e-8, 1e-5);
-  expect_near_rel("test B2", 0.0, 1e-8, 1e-5);
-  expect_near_rel("test C1", 1e-8, 0, 1e-5);
-  expect_near_rel("test C2", 1e-8, 0.0, 1e-5);
+  expect_near_rel("test B1", 0, 1e-10, 1e-5);
+  expect_near_rel("test B2", 0.0, 1e-10, 1e-5);
+  expect_near_rel("test C1", 1e-10, 0, 1e-5);
+  expect_near_rel("test C2", 1e-10, 0.0, 1e-5);
 
   // non-zero examples
   expect_near_rel("test D1", 1, 1, 1e-16);
@@ -55,8 +55,8 @@ TEST(testUnitMath, ExpectNearRelMatrix) {
 
   m_t d1(2, 3);
   m_t d2(2, 3);
-  d1 << 1, 2, 3, 0, 0, 0 - 1e-8;
-  d2 << 1 + 1e-8, 2 - 1e-8, 3, 0, 0 + 1e-8, 0;
+  d1 << 1, 2, 3, 0, 0, 0 - 1e-12;
+  d2 << 1 + 1e-8, 2 - 1e-8, 3, 0, 0 + 1e-12, 0;
   expect_near_rel("test D", d1, d2, 1e-6);
 
   // these will fail
@@ -82,7 +82,7 @@ TEST(testUnitMath, ExpectNearRelVector) {
 
   expect_near_rel("test C", v_t{1, 1, 1}, v_t{1 + 1e-8, 1 - 1e-9, 1}, 1e-6);
 
-  expect_near_rel("test D", v_t{0, 0, 0}, v_t{0, 0 + 1e-6, 0 - 1e-6}, 1e-4);
+  expect_near_rel("test D", v_t{0, 0, 0}, v_t{0, 0 + 1e-8, 0 - 1e-8}, 1e-4);
 
   // ones after here fail
   // expect_near_rel("test E", v_t{1}, v_t{1, 2}, 1e-6);
@@ -102,19 +102,19 @@ TEST(testUnitMath, ExpectNearRelVectorNesting) {
   expect_near_rel("test A", vv_t{}, vv_t{}, 1e-10);
 
   expect_near_rel("test B", vv_t{v_t{1, 2, 3}, v_t{0, 0, 0}},
-                  vv_t{v_t{1, 2, 3}, v_t{0, 0 + 1e-6, 0 - 1e-6}}, 1e-5);
+                  vv_t{v_t{1, 2, 3}, v_t{0, 0 + 1e-10, 0 - 1e-10}}, 1e-5);
 
   expect_near_rel(
       "test C",
       vvv_t{vv_t{v_t{1, 2, 3}, v_t{0, 0, 0}}, vv_t{v_t{1, 2, 3}, v_t{0, 0, 0}}},
-      vvv_t{vv_t{v_t{1, 2, 3}, v_t{0, 0 + 1e-6, 0 - 1e-6}},
-            vv_t{v_t{1, 2, 3}, v_t{0, 0 + 1e-6, 0 - 1e-6}}},
+      vvv_t{vv_t{v_t{1, 2, 3}, v_t{0, 0 + 1e-10, 0 - 1e-10}},
+            vv_t{v_t{1, 2, 3}, v_t{0, 0 + 1e-10, 0 - 1e-10}}},
       1e-5);
 
   ev_t d1(3);
   ev_t d2(3);
   d1 << 1, 0, 0;
-  d2 << 1 + 1e-8, 0 + 1e-8, 0;
+  d2 << 1 + 1e-12, 0 + 1e-12, 0;
   vev_t e1{d1, d2};
   vev_t e2{d2, d1};
   expect_near_rel("test E", e1, e2, 1e-6);
diff --git a/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
index 56e97501374..1c53d797f1c 100644
--- a/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
@@ -1,12 +1,22 @@
-#include <stan/math/prim.hpp>
-#include <stan/math/prim/fun/lgamma_stirling_diff.hpp>
-#include <gtest/gtest.h>
 #include <cmath>
 #include <limits>
+#include <vector>
+#include <gtest/gtest.h>
 #include <test/unit/math/expect_near_rel.hpp>
+#include <stan/math/prim.hpp>
+#include <stan/math/prim/fun/lgamma_stirling_diff.hpp>
+
+TEST(MathFunctions, lgamma_stirling_diff_errors_special_cases) {
+  using stan::math::lgamma_stirling_diff;
+  
+  double nan = std::numeric_limits<double>::quiet_NaN();
+  double inf = std::numeric_limits<double>::infinity();
 
-TEST(MathFunctions, lgamma_stirling_diff_errors) {
-  // TODO[martinmodrak] nan, negative values, ...
+  EXPECT_TRUE(std::isnan(lgamma_stirling_diff(nan)));
+  EXPECT_FLOAT_EQ(lgamma_stirling_diff(inf), 0);
+  EXPECT_THROW(std::isnan(lgamma_stirling_diff(-1.0)), std::domain_error);
+  EXPECT_TRUE(std::isinf(lgamma_stirling_diff(0.0)));
+  EXPECT_TRUE(lgamma_stirling_diff(0) > 0);
 }
 
 TEST(MathFunctions, lgamma_stirling_diff_accuracy) {
@@ -83,11 +93,12 @@ std::vector<TestValue> testValues = {
 TEST(MathFunctions, lgamma_stirling_diff_precomputed) {
   using stan::math::lgamma_stirling_diff;
   using stan::test::expect_near_rel;
-  using namespace lgamma_stirling_diff_test_internal;
+  using lgamma_stirling_diff_test_internal::TestValue;
+  using lgamma_stirling_diff_test_internal::testValues;
 
   for (TestValue t : testValues) {
     std::ostringstream msg;
     msg << "x = " << t.x;
     expect_near_rel(msg.str(), lgamma_stirling_diff(t.x), t.val, 1e-10);
   }
-}
\ No newline at end of file
+}
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index d0b77093947..648c068ba59 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -2,7 +2,6 @@
 #include <test/unit/math/prim/prob/vector_rng_test_helper.hpp>
 #include <test/unit/math/prim/prob/NegativeBinomial2LogTestRig.hpp>
 #include <test/unit/math/prim/prob/VectorIntRNGTestRig.hpp>
-#include <test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp>
 #include <test/unit/math/expect_near_rel.hpp>
 #include <gtest/gtest.h>
 #include <boost/random/mersenne_twister.hpp>
@@ -242,15 +241,8 @@ TEST(ProbDistributionsNegBinomial2, chiSquareGoodnessFitTest4) {
 TEST(ProbDistributionsNegBinomial2, extreme_values) {
   std::vector<int> n_to_test = {0, 1, 5, 100, 12985, 1968422};
   std::vector<double> mu_to_test = {1e-5, 0.1, 8, 713, 28311, 19850054};
-  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (double mu : mu_to_test) {
     for (int n : n_to_test) {
-      // Test just before cutoff
-      double logp
-          = stan::math::neg_binomial_2_log<false>(n, mu, phi_cutoff - 1e-8);
-      EXPECT_LT(logp, 0) << "n = " << n << ", mu = " << mu
-                         << ", phi = " << (phi_cutoff - 1e-8);
-
       // Test across a range of phi
       for (double phi = 1e12; phi < 1e22; phi *= 10) {
         double logp = stan::math::neg_binomial_2_log<false>(n, mu, phi);
@@ -261,41 +253,13 @@ TEST(ProbDistributionsNegBinomial2, extreme_values) {
   }
 }
 
-TEST(ProbDistributionsNegBinomial2, poissonCutoff) {
-  using stan::test::expect_near_rel;
-  using namespace stan::test::neg_binomial_2_test_internal;
-
-  // std::vector<double> mu_to_test
-  //     = {2.345e-5, 0.2, 13, 150, 1621, 18432, 73582345,
-  //       static_cast<double>(std::numeric_limits<int>::max()) };
-  // std::vector<int> n_to_test = {0, 1, 3, 16, 24, 181, 2132, 121358,
-  // 865422242};
-  std::vector<double> mu_to_test = {10};
-  std::vector<int> n_to_test = {16};
-  for (double mu : mu_to_test) {
-    for (int n : n_to_test) {
-      double before_cutoff
-          = stan::math::neg_binomial_2_lpmf(n, mu, just_below_phi_cutoff);
-      double after_cutoff
-          = stan::math::neg_binomial_2_lpmf(n, mu, just_above_phi_cutoff);
-      std::ostringstream msg;
-      msg << "neg_binomial_2_lpmf changes too much around phi cutoff for n = "
-          << std::setprecision(17) << n << ", mu = " << mu
-          << ", below cutoff = " << just_below_phi_cutoff
-          << ", above cutoff = " << just_above_phi_cutoff;
-      expect_near_rel(msg.str(), before_cutoff, after_cutoff);
-    }
-  }
-}
-
 TEST(ProbDistributionsNegBinomial2, zeroOne) {
   using stan::test::expect_near_rel;
-  using namespace stan::test::neg_binomial_2_test_internal;
 
   std::vector<double> mu_to_test
-      = {2.345e-5, 0.2, 13, 150, 1621, 18432, phi_cutoff};
+      = {2.345e-5, 0.2, 13, 150, 1621, 18432, 1e10};
   double phi_start = 1e-8;
-  double phi_max = just_above_phi_cutoff * 1e10;
+  double phi_max = 1e22;
   for (double mu : mu_to_test) {
     for (double phi = phi_start; phi < phi_max; phi *= stan::math::pi()) {
       std::ostringstream msg;
@@ -312,19 +276,6 @@ TEST(ProbDistributionsNegBinomial2, zeroOne) {
   }
 }
 
-TEST(ProbDistributionsNegBinomial2, vectorAroundCutoff) {
-  int y = 10;
-  double mu = 9.36;
-  std::vector<double> phi;
-  phi.push_back(1);
-  phi.push_back(stan::math::internal::neg_binomial_2_phi_cutoff + 1);
-  double vector_value = stan::math::neg_binomial_2_lpmf(y, mu, phi);
-  double scalar_value = stan::math::neg_binomial_2_lpmf(y, mu, phi[0])
-                        + stan::math::neg_binomial_2_lpmf(y, mu, phi[1]);
-
-  EXPECT_FLOAT_EQ(vector_value, scalar_value);
-}
-
 TEST(ProbDistributionsNegativeBinomial2Log, distributionCheck) {
   check_counts_real_real(NegativeBinomial2LogTestRig());
 }
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp b/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp
deleted file mode 100644
index 36d82734bae..00000000000
--- a/test/unit/math/prim/prob/neg_binomial_2_test_tools.hpp
+++ /dev/null
@@ -1,19 +0,0 @@
-#ifndef STAN_TEST_UNIT_PRIM_PROB_NEG_BINOMIAL_2_TEST_TOOLS_HPP
-#define STAN_TEST_UNIT_PRIM_PROB_NEG_BINOMIAL_2_TEST_TOOLS_HPP
-
-#include <limits>
-#include <cmath>
-#include <stan/math/prim/prob/neg_binomial_2_lpmf.hpp>
-
-namespace stan {
-namespace test {
-namespace neg_binomial_2_test_internal {
-double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-double just_below_phi_cutoff = std::nextafter(phi_cutoff, 0);
-double just_above_phi_cutoff
-    = std::nextafter(phi_cutoff, std::numeric_limits<double>::infinity());
-}  // namespace neg_binomial_2_test_internal
-}  // namespace test
-}  // namespace stan
-
-#endif
\ No newline at end of file
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index c8844be55b6..d8e92e404b7 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -16,11 +16,37 @@ struct TestValue {
   double grad_phi;
 };
 
-// Test data generated in Mathematica (Wolfram Cloud). The code can be re-ran
-// at https://www.wolframcloud.com/env/martin.modrak/NegBinomial2_Tests.nb
+// Test data generated in Mathematica (Wolfram Cloud). The code can be re-ran at
+// https://www.wolframcloud.com/obj/martin.modrak/Published/neg_binomial_2_lpmf.nb
 // but is also presented below for convenience:
-//
-// TODO[martinmodrak] add updated code here
+// 
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] + 
+//    n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
+// nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
+// nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
+// out = OpenWrite["nb_test.txt"] 
+// mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
+// phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
+// ns = {0,6,14,1525,10233};
+// WriteString[out, "std::vector<TestValue> testValues = {"];
+//   For[k = 1, k <= Length[ns], k++, {
+//     For[i = 1, i <= Length[mus], i++, {
+//       For[j = 1, j <= Length[phis], j++, {
+//         cmu = mus[[i]];
+//         cphi = phis[[j]];
+//         cn=ns[[k]];
+//         val = N[nb2[cn,cmu,cphi], 24];
+//         ddmu= N[nb2dmu[cn,cmu,cphi], 24];
+//         ddphi= N[nb2dphi[cn,cmu,cphi], 24];
+//         WriteString[out," {",CForm[cn],",",CForm[cmu],",",
+//           CForm[cphi],",", CForm[val],",",CForm[ddmu],",",CForm[ddphi],"},"]
+//       }]
+//     }]
+//   }]
+// WriteString[out,"};"];
+// Close[out];
+// FilePrint[%]
+// 
 std::vector<TestValue> testValues = {
     {0, 0.0000256, 0.0004, -0.0000248141563677810565248409,
      -0.93984962406015037593985, -0.0018850149796030172519518},
@@ -438,7 +464,6 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
            + n_ * log(mu);
   };
 
-  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
   for (double mu_dbl : mu_to_test) {
     for (int n : n_to_test) {
       for (double phi_dbl = 1.5; phi_dbl < 1e22; phi_dbl *= 10) {
@@ -478,17 +503,17 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
 
         double tolerance_phi;
         double tolerance_mu;
-        if (phi < phi_cutoff || n < 100000) {
-          tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-8);
-        } else {
+        // if (phi < phi_cutoff || n < 100000) {
+        //   tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-8);
+        // } else {
           tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
-        }
+        // }
 
-        if (phi < phi_cutoff) {
+        // if (phi < phi_cutoff) {
           tolerance_mu = std::max(1e-10, fabs(gradients[0]) * 1e-8);
-        } else {
-          tolerance_mu = std::max(1e-8, fabs(gradients[0]) * 1e-5);
-        }
+        // } else {
+        //   tolerance_mu = std::max(1e-8, fabs(gradients[0]) * 1e-5);
+        // }
 
         EXPECT_NEAR(gradients[0], complex_step_dmu, tolerance_mu)
             << "grad_mu" << message.str();
@@ -549,76 +574,3 @@ TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
     }
   }
 }
-
-TEST(ProbDistributionsNegBinomial2, proptoAtPoissonCutoff) {
-  using stan::math::internal::neg_binomial_2_phi_cutoff;
-  using stan::math::neg_binomial_2_lpmf;
-  using stan::math::var;
-
-  var mu_var(10);
-  int y = 11;
-  var value_before_cutoff = neg_binomial_2_lpmf<true, int, var, double>(
-      y, mu_var, neg_binomial_2_phi_cutoff - 1e-8);
-  var value_after_cutoff = neg_binomial_2_lpmf<true, int, var, double>(
-      y, mu_var, neg_binomial_2_phi_cutoff + 1e-8);
-
-  EXPECT_NEAR(value_of(value_before_cutoff), value_of(value_after_cutoff), 1);
-}
-
-TEST(ProbDistributionsNegBinomial2, derivativesAtCutoff) {
-  double phi_cutoff = stan::math::internal::neg_binomial_2_phi_cutoff;
-  using stan::math::is_nan;
-  using stan::math::var;
-
-  std::vector<double> mu_to_test
-      = {9.3e-6, 0.0028252, 4, 11, 8522, 984256, 5036842};
-  std::vector<int> n_to_test = {0, 1, 5, 48, 1158, 224582, 48235842, 20314458};
-  for (double mu : mu_to_test) {
-    for (int n : n_to_test) {
-      var mu_before(mu);
-      var phi_before(phi_cutoff - 1e-8);
-      var value_before = neg_binomial_2_lpmf(n, mu_before, phi_before);
-      std::vector<var> x_before;
-      x_before.push_back(mu_before);
-      x_before.push_back(phi_before);
-
-      std::vector<double> gradients_before;
-      value_before.grad(x_before, gradients_before);
-
-      var mu_after(mu);
-      var phi_after(phi_cutoff + 1e-8);
-      var value_after = neg_binomial_2_lpmf(n, mu_after, phi_after);
-      std::vector<var> x_after;
-      x_after.push_back(mu_after);
-      x_after.push_back(phi_after);
-
-      std::vector<double> gradients_after;
-      value_after.grad(x_after, gradients_after);
-
-      for (int i = 0; i < 2; ++i) {
-        EXPECT_FALSE(is_nan(gradients_before[i]));
-        EXPECT_FALSE(is_nan(gradients_after[i]));
-      }
-
-      EXPECT_NEAR(value_of(value_before), value_of(value_after),
-                  1e-8 * fabs(value_of(value_after)))
-          << "value changes too much around phi cutoff for n = " << n
-          << ", mu = " << mu << ", cutoff = " << phi_cutoff
-          << " value at cutoff - 1e-8: " << value_of(value_before)
-          << ", value at cutoff + 1e-8: " << value_of(value_after);
-      EXPECT_NEAR(gradients_before[0], gradients_after[0],
-                  1e-8 * fabs(gradients_before[0]))
-          << "grad_mu changes too much around phi cutoff for n = " << n
-          << ", mu = " << mu << ", cutoff = " << phi_cutoff
-          << " grad_mu at cutoff - 1e-8: " << gradients_before[0]
-          << ", grad_mu at cutoff + 1e-8: " << gradients_after[0];
-
-      EXPECT_NEAR(gradients_before[1], gradients_after[1],
-                  1e-8 * fabs(gradients_before[1]))
-          << "grad_phi changes too much around phi cutoff for n = " << n
-          << ", mu = " << mu << ", cutoff = " << phi_cutoff
-          << " grad_phi at cutoff - 1e-8: " << gradients_before[1]
-          << ", grad_phi at cutoff + 1e-8: " << gradients_after[1];
-    }
-  }
-}

From ec5e5ed6bf17c00a565af769d2dafd38f1dc22c9 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Tue, 14 Jan 2020 07:25:01 +0000
Subject: [PATCH 69/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 stan/math/prim/fun/lgamma_stirling_diff.hpp          |  2 +-
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp          |  4 ++--
 .../unit/math/prim/fun/lgamma_stirling_diff_test.cpp |  6 +++---
 test/unit/math/prim/prob/neg_binomial_2_test.cpp     |  3 +--
 test/unit/math/rev/prob/neg_binomial_2_test.cpp      | 12 ++++++------
 5 files changed, 13 insertions(+), 14 deletions(-)

diff --git a/stan/math/prim/fun/lgamma_stirling_diff.hpp b/stan/math/prim/fun/lgamma_stirling_diff.hpp
index 190acc22fdf..9ff77a296de 100644
--- a/stan/math/prim/fun/lgamma_stirling_diff.hpp
+++ b/stan/math/prim/fun/lgamma_stirling_diff.hpp
@@ -49,7 +49,7 @@ return_type_t<T> lgamma_stirling_diff(const T x) {
   static const char* function = "lgamma_stirling_diff";
   check_nonnegative(function, "argument", x);
 
-  if(x == 0) {
+  if (x == 0) {
     return std::numeric_limits<double>::infinity();
   } else if (value_of(x) < lgamma_stirling_diff_useful) {
     return lgamma(x) - lgamma_stirling(x);
diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index f4609a89da6..25c2f9c6a13 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -90,7 +90,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     if (!is_constant_all<T_location>::value) {
       ops_partials.edge1_.partials_[i]
           += n_vec[i] / mu_val[i]
-              - (n_vec[i] + phi_val[i]) / (mu_val[i] + phi_val[i]);
+             - (n_vec[i] + phi_val[i]) / (mu_val[i] + phi_val[i]);
     }
     if (!is_constant_all<T_precision>::value) {
       T_partials_return log_term;
@@ -101,7 +101,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
       }
       ops_partials.edge2_.partials_[i]
           += (mu_val[i] - n_vec[i]) / (mu_val[i] + phi_val[i]) + log_term
-              - (digamma(phi_val[i]) - digamma(n_plus_phi[i]));
+             - (digamma(phi_val[i]) - digamma(n_plus_phi[i]));
     }
   }
   return ops_partials.build(logp);
diff --git a/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp b/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
index 1c53d797f1c..a1d0533bfbd 100644
--- a/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
+++ b/test/unit/math/prim/fun/lgamma_stirling_diff_test.cpp
@@ -8,7 +8,7 @@
 
 TEST(MathFunctions, lgamma_stirling_diff_errors_special_cases) {
   using stan::math::lgamma_stirling_diff;
-  
+
   double nan = std::numeric_limits<double>::quiet_NaN();
   double inf = std::numeric_limits<double>::infinity();
 
@@ -91,10 +91,10 @@ std::vector<TestValue> testValues = {
 }  // namespace lgamma_stirling_diff_test_internal
 
 TEST(MathFunctions, lgamma_stirling_diff_precomputed) {
-  using stan::math::lgamma_stirling_diff;
-  using stan::test::expect_near_rel;
   using lgamma_stirling_diff_test_internal::TestValue;
   using lgamma_stirling_diff_test_internal::testValues;
+  using stan::math::lgamma_stirling_diff;
+  using stan::test::expect_near_rel;
 
   for (TestValue t : testValues) {
     std::ostringstream msg;
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index 648c068ba59..0affe135bbd 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -256,8 +256,7 @@ TEST(ProbDistributionsNegBinomial2, extreme_values) {
 TEST(ProbDistributionsNegBinomial2, zeroOne) {
   using stan::test::expect_near_rel;
 
-  std::vector<double> mu_to_test
-      = {2.345e-5, 0.2, 13, 150, 1621, 18432, 1e10};
+  std::vector<double> mu_to_test = {2.345e-5, 0.2, 13, 150, 1621, 18432, 1e10};
   double phi_start = 1e-8;
   double phi_max = 1e22;
   for (double mu : mu_to_test) {
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index d8e92e404b7..285255db70a 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -19,12 +19,12 @@ struct TestValue {
 // Test data generated in Mathematica (Wolfram Cloud). The code can be re-ran at
 // https://www.wolframcloud.com/obj/martin.modrak/Published/neg_binomial_2_lpmf.nb
 // but is also presented below for convenience:
-// 
-// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] + 
+//
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] +
 //    n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
 // nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
 // nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
-// out = OpenWrite["nb_test.txt"] 
+// out = OpenWrite["nb_test.txt"]
 // mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
 // phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
 // ns = {0,6,14,1525,10233};
@@ -46,7 +46,7 @@ struct TestValue {
 // WriteString[out,"};"];
 // Close[out];
 // FilePrint[%]
-// 
+//
 std::vector<TestValue> testValues = {
     {0, 0.0000256, 0.0004, -0.0000248141563677810565248409,
      -0.93984962406015037593985, -0.0018850149796030172519518},
@@ -506,11 +506,11 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
         // if (phi < phi_cutoff || n < 100000) {
         //   tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-8);
         // } else {
-          tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
+        tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
         // }
 
         // if (phi < phi_cutoff) {
-          tolerance_mu = std::max(1e-10, fabs(gradients[0]) * 1e-8);
+        tolerance_mu = std::max(1e-10, fabs(gradients[0]) * 1e-8);
         // } else {
         //   tolerance_mu = std::max(1e-8, fabs(gradients[0]) * 1e-5);
         // }

From 10fdef947c35375b248d6145b49ba310a691d087 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Tue, 14 Jan 2020 14:46:30 +0100
Subject: [PATCH 70/82] Fixing incomplete merge

---
 stan/math/prim/fun/binomial_coefficient_log.hpp | 1 -
 stan/math/prim/fun/lbeta.hpp                    | 5 ++---
 test/unit/math/prim/fun/lbeta_test.cpp          | 1 -
 3 files changed, 2 insertions(+), 5 deletions(-)

diff --git a/stan/math/prim/fun/binomial_coefficient_log.hpp b/stan/math/prim/fun/binomial_coefficient_log.hpp
index 6af05d08703..260d2ce25bb 100644
--- a/stan/math/prim/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/fun/binomial_coefficient_log.hpp
@@ -1,7 +1,6 @@
 #ifndef STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
 #define STAN_MATH_PRIM_SCAL_FUN_BINOMIAL_COEFFICIENT_LOG_HPP
 
-#include <limits>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
 #include <stan/math/prim/fun/lbeta.hpp>
diff --git a/stan/math/prim/fun/lbeta.hpp b/stan/math/prim/fun/lbeta.hpp
index 6eba8c98728..fd88cbcd3a6 100644
--- a/stan/math/prim/fun/lbeta.hpp
+++ b/stan/math/prim/fun/lbeta.hpp
@@ -1,7 +1,6 @@
-#ifndef STAN_MATH_PRIM_SCAL_FUN_LBETA_HPP
-#define STAN_MATH_PRIM_SCAL_FUN_LBETA_HPP
+#ifndef STAN_MATH_PRIM_FUN_LBETA_HPP
+#define STAN_MATH_PRIM_FUN_LBETA_HPP
 
-#include <limits>
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
 #include <stan/math/prim/fun/lgamma_stirling.hpp>
diff --git a/test/unit/math/prim/fun/lbeta_test.cpp b/test/unit/math/prim/fun/lbeta_test.cpp
index 3cc919d4190..66661f41e23 100644
--- a/test/unit/math/prim/fun/lbeta_test.cpp
+++ b/test/unit/math/prim/fun/lbeta_test.cpp
@@ -1,4 +1,3 @@
-#include <test/unit/math/expect_near_rel.hpp>
 #include <stan/math/prim.hpp>
 #include <test/unit/math/expect_near_rel.hpp>
 #include <gtest/gtest.h>

From e420333a9528263ec2f0ad0e23543642ab304ef6 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Tue, 14 Jan 2020 16:21:59 +0100
Subject: [PATCH 71/82] Improved code style

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   | 19 ++++++++-------
 .../math/prim/prob/neg_binomial_2_test.cpp    |  2 +-
 .../math/rev/prob/neg_binomial_2_test.cpp     | 24 +++++--------------
 3 files changed, 18 insertions(+), 27 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 25c2f9c6a13..6b0c363e735 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -3,12 +3,12 @@
 
 #include <stan/math/prim/meta.hpp>
 #include <stan/math/prim/err.hpp>
-#include <stan/math/prim/fun/size_zero.hpp>
-#include <stan/math/prim/fun/multiply_log.hpp>
+#include <stan/math/prim/fun/binomial_coefficient_log.hpp>
 #include <stan/math/prim/fun/digamma.hpp>
-#include <stan/math/prim/fun/square.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
-#include <stan/math/prim/fun/binomial_coefficient_log.hpp>
+#include <stan/math/prim/fun/multiply_log.hpp>
+#include <stan/math/prim/fun/size_zero.hpp>
+#include <stan/math/prim/fun/square.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
 #include <stan/math/prim/prob/poisson_lpmf.hpp>
 #include <cmath>
@@ -65,10 +65,13 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     log_phi[i] = log(phi_val[i]);
   }
 
+  VectorBuilder<true, T_partials_return, T_location, T_precision>
+      mu_plus_phi(len_ep);
   VectorBuilder<true, T_partials_return, T_location, T_precision>
       log_mu_plus_phi(len_ep);
   for (size_t i = 0; i < len_ep; ++i) {
-    log_mu_plus_phi[i] = log(mu_val[i] + phi_val[i]);
+    mu_plus_phi[i] = mu_val[i] + phi_val[i];
+    log_mu_plus_phi[i] = log(mu_plus_phi[i]);
   }
 
   VectorBuilder<true, T_partials_return, T_n, T_precision> n_plus_phi(len_np);
@@ -90,17 +93,17 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     if (!is_constant_all<T_location>::value) {
       ops_partials.edge1_.partials_[i]
           += n_vec[i] / mu_val[i]
-             - (n_vec[i] + phi_val[i]) / (mu_val[i] + phi_val[i]);
+             - (n_vec[i] + phi_val[i]) / (mu_plus_phi[i]);
     }
     if (!is_constant_all<T_precision>::value) {
       T_partials_return log_term;
       if (mu_val[i] < phi_val[i]) {
-        log_term = log1p(-mu_val[i] / (mu_val[i] + phi_val[i]));
+        log_term = log1p(-mu_val[i] / (mu_plus_phi[i]));
       } else {
         log_term = log_phi[i] - log_mu_plus_phi[i];
       }
       ops_partials.edge2_.partials_[i]
-          += (mu_val[i] - n_vec[i]) / (mu_val[i] + phi_val[i]) + log_term
+          += (mu_val[i] - n_vec[i]) / (mu_plus_phi[i]) + log_term
              - (digamma(phi_val[i]) - digamma(n_plus_phi[i]));
     }
   }
diff --git a/test/unit/math/prim/prob/neg_binomial_2_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
index 0affe135bbd..47853d4e0b8 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_test.cpp
@@ -261,7 +261,7 @@ TEST(ProbDistributionsNegBinomial2, zeroOne) {
   double phi_max = 1e22;
   for (double mu : mu_to_test) {
     for (double phi = phi_start; phi < phi_max; phi *= stan::math::pi()) {
-      std::ostringstream msg;
+      std::stringstream msg;
       msg << ", mu = " << mu << ", phi = " << phi;
 
       double expected_value_0 = phi * (-log1p(mu / phi));
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 285255db70a..2fc5178f374 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -1,8 +1,8 @@
 #include <stan/math/rev.hpp>
-#include <boost/math/differentiation/finite_difference.hpp>
-#include <boost/math/special_functions/digamma.hpp>
 #include <test/unit/math/expect_near_rel.hpp>
 #include <gtest/gtest.h>
+#include <boost/math/differentiation/finite_difference.hpp>
+#include <boost/math/special_functions/digamma.hpp>
 #include <vector>
 #include <algorithm>
 
@@ -408,7 +408,6 @@ TEST(ProbDistributionsNegativeBinomial2, derivativesPrecomputed) {
   using stan::math::neg_binomial_2_log;
   using stan::math::value_of;
   using stan::math::var;
-  using stan::test::internal::expect_near_rel_finite;
 
   for (TestValue t : testValues) {
     int n = t.n;
@@ -497,23 +496,12 @@ TEST(ProbDistributionsNegBinomial2, derivativesComplexStep) {
         double complex_step_dphi
             = complex_step_derivative(nb2_log_phi, phi_dbl);
 
-        std::ostringstream message;
+        std::stringstream message;
         message << ", n = " << n << ", mu = " << mu_dbl
                 << ", phi = " << phi_dbl;
 
-        double tolerance_phi;
-        double tolerance_mu;
-        // if (phi < phi_cutoff || n < 100000) {
-        //   tolerance_phi = std::max(1e-10, fabs(gradients[1]) * 1e-8);
-        // } else {
-        tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
-        // }
-
-        // if (phi < phi_cutoff) {
-        tolerance_mu = std::max(1e-10, fabs(gradients[0]) * 1e-8);
-        // } else {
-        //   tolerance_mu = std::max(1e-8, fabs(gradients[0]) * 1e-5);
-        // }
+        double tolerance_phi = std::max(1e-8, fabs(gradients[1]) * 1e-5);
+        double tolerance_mu = std::max(1e-10, fabs(gradients[0]) * 1e-8);
 
         EXPECT_NEAR(gradients[0], complex_step_dmu, tolerance_mu)
             << "grad_mu" << message.str();
@@ -535,7 +523,7 @@ TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
   for (double mu_dbl : mu_to_test) {
     for (double phi_dbl = phi_start; phi_dbl < phi_max;
          phi_dbl *= stan::math::pi()) {
-      std::ostringstream msg;
+      std::stringstream msg;
       msg << std::setprecision(20) << ", mu = " << mu_dbl
           << ", phi = " << phi_dbl;
 

From fbe958d633c0701b91edc51405626bc253371866 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Tue, 14 Jan 2020 15:24:53 +0000
Subject: [PATCH 72/82] [Jenkins] auto-formatting by clang-format version
 5.0.0-3~16.04.1 (tags/RELEASE_500/final)

---
 stan/math/prim/fun/binomial_coefficient_log.hpp           | 4 ++--
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp               | 7 +++----
 test/unit/math/prim/fun/binomial_coefficient_log_test.cpp | 2 +-
 3 files changed, 6 insertions(+), 7 deletions(-)

diff --git a/stan/math/prim/fun/binomial_coefficient_log.hpp b/stan/math/prim/fun/binomial_coefficient_log.hpp
index cd39e80b0fe..7365f9aab55 100644
--- a/stan/math/prim/fun/binomial_coefficient_log.hpp
+++ b/stan/math/prim/fun/binomial_coefficient_log.hpp
@@ -90,10 +90,10 @@ inline return_type_t<T_N, T_n> binomial_coefficient_log(const T_N N,
   }
   if (N / 2 < n) {
     return binomial_coefficient_log(N, N - n);
-  } 
+  }
   if (N_plus_1 < lgamma_stirling_diff_useful) {
     return lgamma(N_plus_1) - lgamma(n + 1) - lgamma(N_plus_1 - n);
-  } 
+  }
   return -lbeta(N - n + 1, n + 1) - log(N_plus_1);
 }
 
diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 6b0c363e735..0312ce10824 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -65,8 +65,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     log_phi[i] = log(phi_val[i]);
   }
 
-  VectorBuilder<true, T_partials_return, T_location, T_precision>
-      mu_plus_phi(len_ep);
+  VectorBuilder<true, T_partials_return, T_location, T_precision> mu_plus_phi(
+      len_ep);
   VectorBuilder<true, T_partials_return, T_location, T_precision>
       log_mu_plus_phi(len_ep);
   for (size_t i = 0; i < len_ep; ++i) {
@@ -92,8 +92,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
 
     if (!is_constant_all<T_location>::value) {
       ops_partials.edge1_.partials_[i]
-          += n_vec[i] / mu_val[i]
-             - (n_vec[i] + phi_val[i]) / (mu_plus_phi[i]);
+          += n_vec[i] / mu_val[i] - (n_vec[i] + phi_val[i]) / (mu_plus_phi[i]);
     }
     if (!is_constant_all<T_precision>::value) {
       T_partials_return log_term;
diff --git a/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp b/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
index e372b6815d9..ef379939828 100644
--- a/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
+++ b/test/unit/math/prim/fun/binomial_coefficient_log_test.cpp
@@ -50,8 +50,8 @@ TEST(MathFunctions, binomial_coefficient_log_nan) {
 }
 
 TEST(MathFunctions, binomial_coefficient_log_errors_edge_cases) {
-  using stan::math::binomial_coefficient_log;
   using stan::math::INFTY;
+  using stan::math::binomial_coefficient_log;
 
   EXPECT_NO_THROW(binomial_coefficient_log(10, 11));
   EXPECT_THROW(binomial_coefficient_log(10, 11.01), std::domain_error);

From e560179cd3ebbe9b6ae47668e27a6329ce498f43 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Fri, 13 Mar 2020 15:52:04 +0100
Subject: [PATCH 73/82] Fixed merge

---
 test/unit/math/expect_near_rel.hpp | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/test/unit/math/expect_near_rel.hpp b/test/unit/math/expect_near_rel.hpp
index 3bbab6d2ff1..9f7f7ae0696 100644
--- a/test/unit/math/expect_near_rel.hpp
+++ b/test/unit/math/expect_near_rel.hpp
@@ -6,8 +6,6 @@
 #include <test/unit/math/relative_tolerance.hpp>
 #include <string>
 #include <vector>
-#include <limits>
-#include <algorithm>
 
 namespace stan {
 namespace test {
@@ -84,7 +82,7 @@ void expect_near_rel(const std::string& msg, const T1& x1, const T2& x2,
                       << std::endl
                       << msg << std::endl;
   else
-    internal::expect_near_rel_finite(msg, x1, x2, tol_rel, tol_min);
+    internal::expect_near_rel_finite(msg, x1, x2, tol);
 }
 
 /**

From 815f0a9b6bb77b43e9f7b83e2e9303978e8ffbc6 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Fri, 13 Mar 2020 16:58:09 +0100
Subject: [PATCH 74/82] Fixes #1496

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   |   4 +-
 .../math/rev/prob/neg_binomial_2_test.cpp     | 565 ++++++------------
 2 files changed, 196 insertions(+), 373 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 77e1d72b8f9..b69387ae5e5 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -48,11 +48,9 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   size_t size_n_phi = max_size(n, phi);
   size_t max_size_seq_view = max_size(n, mu, phi);
 
-  operands_and_partials<T_location, T_precision> ops_partials(mu, phi);
-
   size_t len_ep = max_size(mu, phi);
   size_t len_np = max_size(n, phi);
-
+  
   size_t len_mu = size(mu);
   VectorBuilder<true, T_partials_return, T_location> mu_val(len_mu);
   for (size_t i = 0; i < len_mu; ++i) {
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 6322ad564d3..cc28fc42fb8 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -20,384 +20,209 @@ struct TestValue {
 // https://www.wolframcloud.com/obj/martin.modrak/Published/neg_binomial_2_lpmf.nb
 // but is also presented below for convenience:
 //
-// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] +
+// toCString[x_] := ToString[CForm[N[x, 24]]];
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] + 
 //    n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
 // nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
 // nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
-// out = OpenWrite["nb_test.txt"]
-// mus= {256*10^-7,314*10^-3,15*10^-1,3,180,  1123,10586};
-// phis=  {4*10^-4,65*10^-3,442*10^-2,800, 15324};
+// mus= SetPrecision[{0.0000256,0.314,1.5,3.0,180.0,1123.0,10586.0}, Infinity];
+// phis=  SetPrecision[{0.0004,0.065,4.42,800.0, 15324.0}, Infinity];
 // ns = {0,6,14,1525,10233};
-// WriteString[out, "std::vector<TestValue> testValues = {"];
-//   For[k = 1, k <= Length[ns], k++, {
-//     For[i = 1, i <= Length[mus], i++, {
-//       For[j = 1, j <= Length[phis], j++, {
-//         cmu = mus[[i]];
-//         cphi = phis[[j]];
-//         cn=ns[[k]];
-//         val = N[nb2[cn,cmu,cphi], 24];
-//         ddmu= N[nb2dmu[cn,cmu,cphi], 24];
-//         ddphi= N[nb2dphi[cn,cmu,cphi], 24];
-//         WriteString[out," {",CForm[cn],",",CForm[cmu],",",
-//           CForm[cphi],",", CForm[val],",",CForm[ddmu],",",CForm[ddphi],"},"]
-//       }]
+// out = "std::vector<TestValue> testValues = {\n";
+// For[k = 1, k <= Length[ns], k++, {
+//   For[i = 1, i <= Length[mus], i++, {
+//     For[j = 1, j <= Length[phis], j++, {
+//       cmu = mus[[i]];
+//       cphi = phis[[j]];
+//       cn=ns[[k]];
+//       val = nb2[cn,cmu,cphi];
+//       ddmu= nb2dmu[cn,cmu,cphi];
+//       ddphi= nb2dphi[cn,cmu,cphi];
+//       out = StringJoin[out,"  {",ToString[cn],",",toCString[cmu],",",
+//         toCString[cphi],",", toCString[val],",",toCString[ddmu],",",
+//         toCString[ddphi],"},\n"];
 //     }]
 //   }]
-// WriteString[out,"};"];
-// Close[out];
-// FilePrint[%]
+// }]
+// out = StringJoin[out,"};\n"];
+// out
 //
 std::vector<TestValue> testValues = {
-    {0, 0.0000256, 0.0004, -0.0000248141563677810565248409,
-     -0.93984962406015037593985, -0.0018850149796030172519518},
-    {0, 0.0000256, 0.065, -0.0000255949600924861403888716,
-     -0.999606308899879432100588, -7.75166869111834937935475e-8},
-    {0, 0.0000256, 4.42, -0.0000255999258645396480948713,
-     -0.999994208178341772500141, -1.67726638232395628338958e-11},
-    {0, 0.0000256, 800, -0.0000255999995904000087381331,
-     -0.999999968000001023999967, -5.1199997815466745309864e-16},
-    {0, 0.0000256, 15324, -0.0000255999999786165492276784,
-     -0.999999998329417909342659, -1.39542226236663832355842e-18},
-    {0, 0.314, 0.0004, -0.00266678271697168261798476,
-     -0.00127226463104325699745547, -5.66822905706024980195936},
-    {0, 0.314, 0.065, -0.114604680787141300415594, -0.171503957783641160949868,
-     -0.934652892970430398112858},
-    {0, 0.314, 4.42, -0.303348202309659616314882, -0.933671313899450781580059,
-     -0.00230212890163621513546237},
-    {0, 0.314, 800, -0.313938393619808990999524, -0.999607653995806645891488,
-     -7.69878314071302369967267e-8},
-    {0, 0.314, 15324, -0.313996782998787812397665, -0.999979509686371605280341,
-     -2.09929343978617830724328e-10},
-    {0, 1.5, 0.0004, -0.00329191110003275493362122,
-     -0.00026659557451346307651293, -7.23004434565640079712956},
-    {0, 1.5, 0.065, -0.206781499150110071240643, -0.0415335463258785942492013,
-     -2.22278737940449507487448},
-    {0, 1.5, 4.42, -1.29150964740387939892012, -0.746621621621621621621622,
-     -0.0388183744279291779383916},
-    {0, 1.5, 800, -1.49859550534427827334156, -0.998128509045539613225203,
-     -1.75342721996106687969703e-6},
-    {0, 1.5, 15324, -1.49992659053829698010225, -0.999902123911128511304688,
-     -4.79017695146261715054393e-9},
-    {0, 3, 0.0004, -0.00356911664958785451901203, -0.00013331555792560991867751,
-     -7.92292493952756190744874},
-    {0, 3, 0.065, -0.250472012600853853120106, -0.0212071778140293637846656,
-     -2.87462275628870402717091},
-    {0, 3, 4.42, -2.28973397601639586742486, -0.595687331536388140161725,
-     -0.113726692626070463108525},
-    {0, 3, 800, -2.99438902306750149309853, -0.996264009962640099626401,
-     -6.99624147447649277415792e-6},
-    {0, 3, 15324, -2.99970638131217673536622, -0.999804266979839498923468,
-     -1.91582075605741709616675e-8},
-    {0, 180, 0.0004, -0.00520680203358650223341638,
-     -2.22221728396159119646401e-6, -12.0170073061835395451321},
-    {0, 180, 0.065, -0.515234583883688262086666, -0.000360980756948879571265932,
-     -6.92704688665984521936613},
-    {0, 180, 4.42, -16.4913562250745368347413, -0.0239670317752955210931569,
-     -2.75504310079668394524277},
-    {0, 180, 800, -162.3526751973522458866, -0.816326530612244897959184,
-     -0.0192673746089352053174335},
-    {0, 180, 15324, -178.951041022560568926078, -0.988390092879256965944272,
-     -0.0000679211892648339243088643},
-    {0, 1123, 0.0004, -0.00593912212871338076639709,
-     -3.56188653183026470872139e-7, -13.8478056779721050990192},
-    {0, 1123, 0.065, -0.634217014783734204352692,
-     -0.000057877326779839101031552, -8.75724272015345990606553},
-    {0, 1123, 4.42, -24.4936395934523258117904, -0.00392045555338738003583403,
-     -4.54546787488649276731873},
-    {0, 1123, 800, -701.624014336681947952778, -0.416016640665626625065003,
-     -0.293046658586479060005975},
-    {0, 1123, 15324, -1083.75715139725783359741, -0.931720070529579862588922,
-     -0.00244293345030929573936621},
-    {0, 10586, 0.0004, -0.00683653348042399161482707,
-     -3.77857533426883301459161e-8, -16.091333738845732379756},
-    {0, 10586, 0.065, -0.780043017108597589318463,
-     -6.14014744855619155937546e-6, -11.0006679418181806995525},
-    {0, 10586, 4.42, -34.3945190758502000304634, -0.000417358329509122395523501,
-     -6.78198276010557247770399},
-    {0, 10586, 800, -2124.42246547447991619038, -0.0702617249253469172668189,
-     -1.72578980676844681250479},
-    {0, 10586, 15324, -8048.29915678058041924358, -0.591431879583172520262447,
-     -0.116640647318788574768032},
-    {6, 0.0000256, 0.0004, -26.4803625972224902645113,
-     220276.315789473684210526, -11595.4634978387095432955},
-    {6, 0.0000256, 0.065, -51.4193881364481026728232, 234281.729042100342019143,
-     -74.6938075459730303944346},
-    {6, 0.0000256, 4.42, -67.5203813751119077704357, 234372.642547590674587948,
-     -0.431255924758490025034736},
-    {6, 0.0000256, 800, -69.998079065742703551293, 234373.992500032239998968,
-     -0.0000233303844710378174909984},
-    {6, 0.0000256, 15324, -70.0158073212983954315096, 234373.999608458993084276,
-     -6.38614276575077488493398e-8},
-    {6, 0.314, 0.0004, -9.62519749441237582251687, 0.023038524497171844864751,
-     2477.5305495558165940557},
-    {6, 0.314, 0.065, -5.62316274126580027012417, 3.10564173234962943044888,
-     0.811756664687528071010215},
-    {6, 0.314, 4.42, -11.7481186360489883350416, 16.9071818179371883568924,
-     -0.343526975436714222156802},
-    {6, 0.314, 800, -13.8270107248858320162615, 18.1011755433762948679586,
-     -0.0000204650172704751119362432},
-    {6, 0.314, 15324, -13.8425659569858167417764, 18.1079092104353788140892,
-     -5.6049178830042368725488e-8},
-    {6, 1.5, 0.0004, -9.61978396161923322623754, 0.00079978672354038922953879,
-     2491.05377011516735187466},
-    {6, 1.5, 0.065, -4.84100453988744409858109, 0.124600638977635782747604,
-     11.5208909282007772435409},
-    {6, 1.5, 4.42, -4.69471130087565245107321, 2.23986486486486486486486,
-     -0.126129611536089773251445},
-    {6, 1.5, 800, -5.6375883578559464150792, 2.99438552713661883967561,
-     -0.0000110478695320263035818071},
-    {6, 1.5, 15324, -5.64599569956598171509704, 2.99970637173338553391406,
-     -3.03295927479829163411156e-8},
-    {6, 3, 0.0004, -9.61926132713561025018161, 0.00013331555792560991867751,
-     2492.36008977011398813188},
-    {6, 3, 0.065, -4.75878244235486512052296, 0.0212071778140293637846656,
-     12.745335721641112641817},
-    {6, 3, 4.42, -2.88910819582874566285473, 0.595687331536388140161725,
-     0.00385024685205873541538553},
-    {6, 3, 800, -2.98571724360242195248096, 0.996264009962640099626401,
-     -2.3069406647953774852549e-6},
-    {6, 3, 15324, -2.98747963477610734281426, 0.999804266979839498923468,
-     -6.38245840446628643263247e-9},
-    {6, 180, 0.0004, -9.62011239916672050497847, -2.14814337449620482324854e-6,
-     2490.23240751308273540641},
-    {6, 180, 0.065, -4.89709960487442547895843, -0.000348948065050583585557067,
-     10.6171759350004776847048},
-    {6, 180, 4.42, -11.8028833191445191284052, -0.023168130716119003723385,
-     -1.86137525666548784300587},
-    {6, 180, 800, -138.973123190861697819951, -0.789115646258503401360544,
-     -0.0179131542129975601896404},
-    {6, 180, 15324, -154.441639359481734262519, -0.955443756449948400412797,
-     -0.0000634392772194434652186986},
-    {6, 1123, 0.0004, -9.62083352307562855236427, -3.5428559715533443273747e-7,
-     2488.4295995707558483234},
-    {6, 1123, 0.065, -5.0142630342277769583843, -0.0000575680979635621334392196,
-     8.81495887967631288756553},
-    {6, 1123, 4.42, -19.6831821663032130583962, -0.00389950921917515894926679,
-     -3.62458748384772905278683},
-    {6, 1123, 800, -671.304184750646975825767, -0.41379393376981739999787,
-     -0.288690114015941777831476},
-    {6, 1123, 15324, -1048.61720731875393149901, -0.926742047000481483982035,
-     -0.00241626280594218362665218},
-    {6, 10586, 0.0004, -9.62172902400956379331308,
-     -3.77643368945439762841293e-8, 2486.19084755337982611478},
-    {6, 10586, 0.065, -5.15977860354001470537965, -6.13666729697000818989159e-6,
-     6.57630939764217205495288},
-    {6, 10586, 4.42, -29.5629973572818969888733, -0.000417121776516768840415515,
-     -5.85634703346878397904497},
-    {6, 10586, 800, -2091.3124520859014907288, -0.0702219015407302460497774,
-     -1.71884010032985743252181},
-    {6, 10586, 15324, -8002.42495594488889877697, -0.59109666408369216553719,
-     -0.116480739324794834878369},
-    {14, 0.0000256, 0.0004, -49.8145624383586400724923,
-     513979.323308270676691729, -30391.5592215308067657195},
-    {14, 0.0000256, 0.065, -114.928171090288372551513,
-     546658.700573312664550577, -196.832392093265929097095},
-    {14, 0.0000256, 4.42, -161.649312877052269163198, 546870.832603322478494242,
-     -1.65012869090202521315342},
-    {14, 0.0000256, 800, -173.098986627797206761932, 546873.982500032559998958,
-     -0.00014060727924520899116967},
-    {14, 0.0000256, 15324, -173.206165042629407096483,
-     546873.999086402089753857, -3.87293689171005773693536e-7},
-    {14, 0.314, 0.0004, -10.48232124038756783909, 0.0554529100014586473476929,
-     2452.9820144458617504796},
-    {14, 0.314, 0.065, -7.91753972042693519284807, 7.47516931919399021898056,
-     -19.4065385144529680284843},
-    {14, 0.314, 4.42, -31.1096030160603970450565, 40.6949859937193738748557,
-     -1.44235830397139693802194},
-    {14, 0.314, 800, -41.6146101076375483922037, 43.568886473205763553092,
-     -0.000133818772002702504530118},
-    {14, 0.314, 15324, -41.7166402819016445593073, 43.585094170597712706582,
-     -3.68785202783475625980072e-7},
-    {14, 1.5, 0.0004, -10.4688561593594870180174, 0.00222162978761219230427442,
-     2486.61861613580838671742},
-    {14, 1.5, 0.065, -5.96960149272681243148081, 0.346112886048988285410011,
-     7.29895408232336627643618},
-    {14, 1.5, 4.42, -13.3341039738636536056565, 6.22184684684684684684685,
-     -0.886409460834882606838869},
-    {14, 1.5, 800, -20.9264151022685229463224, 8.31773757537949677687669,
-     -0.000109610174761583369512834},
-    {14, 1.5, 15324, -21.0100699378693506067827, 8.3325176992594042608724,
-     -3.02665838448691571323444e-7},
-    {14, 3, 0.0004, -10.4672670714982932744397, 0.000488823712393903035150869,
-     2490.59053612251208613134},
-    {14, 3, 0.065, -5.71949591388313644017256, 0.0777596519847743338771071,
-     11.025105769529760808809},
-    {14, 3, 4.42, -7.79006429060418247514041, 2.18418688230008984725966,
-     -0.483245366998347706389421},
-    {14, 3, 800, -12.7443244787126682405839, 3.6529680365296803652968,
-     -0.0000822242550653573074282639},
-    {14, 3, 15324, -12.8071593989944707311042, 3.66594897892607816271938,
-     -2.27631817501670696455485e-7},
-    {14, 180, 0.0004, -10.4670693257255523386798, -2.04937816187568965896125e-6,
-     2491.08472067831379995549},
-    {14, 180, 0.065, -5.68921919805166473123324, -0.000332904475852855604611915,
-     11.4626317745298008318075},
-    {14, 180, 4.42, -9.65337657959679927166961, -0.0221029293038836472303558,
-     -1.31368299764513841319336},
-    {14, 180, 800, -117.570556789937986073345, -0.752834467120181405895692,
-     -0.0161936967338941701029113},
-    {14, 180, 15324, -131.5984192349764106228, -0.911515307877536979704162,
-     -0.0000577016781835615346878727},
-    {14, 1123, 0.0004, -10.4677755213861686112027,
-     -3.51748189118411715224579e-7, 2489.319233308602484167},
-    {14, 1123, 0.065, -5.8039572920094235935389,
-     -0.0000571557928751928433161097, 9.69771975676490255408168},
-    {14, 1123, 4.42, -17.3710293984633664722496, -0.00387158077355886416717715,
-     -3.04061182895062280658097},
-    {14, 1123, 800, -640.647914910330698665346, -0.41083032457540509990836,
-     -0.282967557637372205015805},
-    {14, 1123, 15324, -1011.59993064034851794618, -0.920104682295016979172854,
-     -0.00238094023047733949128954},
-    {14, 10586, 0.0004, -10.468668475096403358952,
-     -3.77357816303515044684135e-8, 2487.08684934922326872119},
-    {14, 10586, 0.065, -5.94905895063816048990702,
-     -6.13202709485509703057976e-6, 7.46543792757153500263484},
-    {14, 10586, 4.42, -27.2227588675497966851323,
-     -0.000416806372526964100271534, -5.26603093110764468733629},
-    {14, 10586, 800, -2056.93593717552727578896, -0.0701688036945746844270555,
-     -1.70965999479388506262815},
-    {14, 10586, 15324, -7951.09533692356666073317, -0.590649710084385025903513,
-     -0.116267766949827820373742},
-    {1525, 0.0000256, 0.0004, -4301.78472746701578211824,
-     5.59871348684210526315789e7, -3.58066878763440801575999e6},
-    {1525, 0.0000256, 0.065, -11965.4671281234821192651,
-     5.95468591985310400826751e7, -23429.1126891147674041279},
-    {1525, 0.0000256, 4.42, -18367.3428918005844132604,
-     5.95699664793796669412955e7, -339.057082534394502685042},
-    {1525, 0.0000256, 800, -24826.2281356385313850842,
-     5.9570309593750092999997e7, -0.838976287617641050521018},
-    {1525, 0.0000256, 15324, -25707.7170288016100578067,
-     5.95703114004829044732209e7, -0.00464306291332368931093164},
-    {1525, 0.314, 0.0004, -17.0947387955188070326685, 6.17771997212362846631335,
-     -2348.2711549792054388957},
-    {1525, 0.314, 0.065, -296.585568286099067098382, 832.7696922844226341529,
-     -4001.49218112616940138645},
-    {1525, 0.314, 4.42, -4115.10160678526160318827, 4533.61649969457966358017,
-     -316.176485619091863713022},
-    {1525, 0.314, 800, -10469.9426767525578633112, 4853.78278834474666145767,
-     -0.838228516034976412381988},
-    {1525, 0.314, 15324, -11350.8644775429644460839, 4855.58840352125852665115,
-     -0.00464102415296814454780544},
-    {1525, 1.5, 0.0004, -15.5605375416167690037651, 0.270772238514173998044966,
-     1484.28030775203773370257},
-    {1525, 1.5, 0.065, -74.4509275868752796839738, 42.1842385516506922257721,
-     -953.474508334327862701411},
-    {1525, 1.5, 4.42, -2072.19103657901875771673, 758.318693693693693693694,
-     -251.676626135276647866636},
-    {1525, 1.5, 800, -8088.5487996808837996978, 1013.76585568725306716573,
-     -0.835410572412918435298525},
-    {1525, 1.5, 15324, -8967.33164084000397251235, 1015.56725718573619131513,
-     -0.00463332752548632640449661},
-    {1525, 3, 0.0004, -15.3575220720668965445137, 0.0676354263875927654090566,
-     1991.71749039935673683979},
-    {1525, 3, 0.065, -42.4918294753981553150494, 10.759108210984230560087,
-     -477.238467087057049216524},
-    {1525, 3, 4.42, -1360.54978818586119643475, 302.212039532794249775382,
-     -199.675789571126133218244},
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+  {14,3.,4.41999999999999992894573,-7.79006429060418244080376,2.18418688230008983306336,-0.483245366998347713019428},
+  {14,3.,800.,-12.7443244787126682405839,3.6529680365296803652968,-0.0000822242550653573074282639},
+  {14,3.,15324.,-12.8071593989944707311042,3.66594897892607816271938,-2.27631817501670696455485e-7},
+  {14,180.,0.000400000000000000019168694,-10.467069325725552290929,-2.04937816187568975717079e-6,2491.08472067831368019905},
+  {14,180.,0.065000000000000002220446,-5.68921919805166470578108,-0.000332904475852855615980062,11.4626317745298003372252},
+  {14,180.,4.41999999999999992894573,-9.65337657959679917832682,-0.0221029293038836468835533,-1.31368299764513841447103},
+  {14,180.,800.,-117.570556789937986073345,-0.752834467120181405895692,-0.0161936967338941701029113},
+  {14,180.,15324.,-131.5984192349764106228,-0.911515307877536979704162,-0.0000577016781835615346878727},
+  {14,1123.,0.000400000000000000019168694,-10.4677755213861685634857,-3.51748189118411732080956e-7,2489.31923330860236441056},
+  {14,1123.,0.065000000000000002220446,-5.80395729200942357200564,-0.0000571557928751928452684791,9.6977197567649020595191},
+  {14,1123.,4.41999999999999992894573,-17.3710293984633662562012,-0.00387158077355886410518306,-3.04061182895062280846571},
+  {14,1123.,800.,-640.647914910330698665346,-0.41083032457540509990836,-0.282967557637372205015805},
+  {14,1123.,15324.,-1011.59993064034851794618,-0.920104682295016979172854,-0.00238094023047733949128954},
+  {14,10586.,0.000400000000000000019168694,-10.4686684750964033112778,-3.77357816303515062767776e-8,2487.08684934922314896474},
+  {14,10586.,0.065000000000000002220446,-5.94905895063816047333042,-6.13202709485509724005287e-6,7.46543792757153450807576},
+  {14,10586.,4.41999999999999992894573,-27.2227588675497963109583,-0.000416806372526964093573906,-5.26603093110764468933264},
+  {14,10586.,800.,-2056.93593717552727578896,-0.0701688036945746844270555,-1.70965999479388506262815},
+  {14,10586.,15324.,-7951.09533692356666073317,-0.590649710084385025903513,-0.116267766949827820373742},
+  {1525,0.0000255999999999999988415517,0.000400000000000000019168694,-4301.78472746701591561319,5.59871348684210554788785e7,-3.5806687876344078642494e6},
+  {1525,0.0000255999999999999988415517,0.065000000000000002220446,-11965.4671281234822402701,5.95468591985310427791447e7,-23429.1126891147666042428},
+  {1525,0.0000255999999999999988415517,4.41999999999999992894573,-18367.3428918005844581777,5.95699664793796696369591e7,-339.05708253439450821354},
+  {1525,0.0000255999999999999988415517,800.,-24826.2281356385314540934,5.95703095937500956956661e7,-0.838976287617641050521021},
+  {1525,0.0000255999999999999988415517,15324.,-25707.7170288016101268158,5.95703114004829071688901e7,-0.00464306291332368931093165},
+  {1525,0.314000000000000001332268,0.000400000000000000019168694,-17.0947387955188070694514,6.17771997212362870958894,-2348.27115497920553780678},
+  {1525,0.314000000000000001332268,0.065000000000000002220446,-296.585568286099074874008,832.769692284422651260512,-4001.49218112616936417653},
+  {1525,0.314000000000000001332268,4.41999999999999992894573,-4115.10160678526157468258,4533.61649969457963823061,-316.176485619091868439549},
+  {1525,0.314000000000000001332268,800.,-10469.9426767525578568447,4853.78278834474664085128,-0.838228516034976412378816},
+  {1525,0.314000000000000001332268,15324.,-11350.864477542964439615,4855.58840352125850604476,-0.00464102415296814454779679},
+  {1525,1.5,0.000400000000000000019168694,-15.5605375416167689753134,0.270772238514174011017382,1484.28030775203761395908},
+  {1525,1.5,0.065000000000000002220446,-74.4509275868752818011125,42.1842385516506936069639,-953.474508334327861816359},
+  {1525,1.5,4.41999999999999992894573,-2072.19103657901873983403,758.318693693693690604898,-251.676626135276650941522},
+  {1525,1.5,800.,-8088.5487996808837996978,1013.76585568725306716573,-0.835410572412918435298525},
+  {1525,1.5,15324.,-8967.33164084000397251235,1015.56725718573619131513,-0.00463332752548632640449661},
+  {1525,3.,0.000400000000000000019168694,-15.3575220720668965063351,0.0676354263875927686498315,1991.71749039935661708657},
+  {1525,3.,0.065000000000000002220446,-42.4918294753981563747316,10.7591082109842309198313,-477.238467087057049352225},
+  {1525,3.,4.41999999999999992894573,-1360.54978818586118224694,302.212039532794247811131,-199.675789571126135171012},
+  {1525,3.,800.,-7035.84649923785032031894,505.437941054379410543794,-0.831861613850395752926704},
+  {1525,3.,15324.,-7911.93122400832367818281,507.234031447771905787173,-0.00462360345575814251935502},
+  {1525,180.,0.000400000000000000019168694,-15.1592288635917619446729,0.0000166049013718241127915344,2487.41676922898488796714},
+  {1525,180.,0.065000000000000002220446,-10.6183839860155018633925,0.00269732843386801688851316,7.79296281407547718024725},
+  {1525,180.,4.41999999999999992894573,-30.7569326420675970103087,0.179086987432069307580598,-5.06066771330890867384431},
+  {1525,180.,800.,-1255.10606104316181434609,6.09977324263038548752834,-0.50811617220616562857323},
+  {1525,180.,15324.,-1861.51726736161923065929,7.38547041623667010663915,-0.00355560001152251827139362},
+  {1525,1123.,0.000400000000000000019168694,-15.1571154863562692398625,1.27504753855366561133043e-7,2492.70020501203960042957},
+  {1525,1123.,0.065000000000000002220446,-10.2750368571307051553926,0.0000207183306905568293939843,13.074039765317042756658},
+  {1525,1123.,4.41999999999999992894573,-7.75481686725872855763217,0.00140340439221881277753254,0.0654298516080506315262451},
+  {1525,1123.,800.,-30.3901820482837344036952,0.148921362019218079497891,-0.0188047284729684005572389},
+  {1525,1123.,15324.,-64.3938471491118556432688,0.333527576449591366661395,-0.000290976140796059790385352},
+  {1525,10586.,0.000400000000000000019168694,-15.1575273331900733345777,-3.23424061059983918249983e-8,2491.67058800680726231035},
+  {1525,10586.,0.065000000000000002220446,-10.341961135413218891829,-5.25560892040125199509261e-6,12.0444483664247286854037},
+  {1525,10586.,4.41999999999999992894573,-12.3018556139457377868195,-0.00035723444395259379983666,-0.962437235779729779911197},
+  {1525,10586.,800.,-744.016916706287313438782,-0.0601399480019429829354474,-0.792452568525027960065769},
+  {1525,10586.,15324.,-4300.64559341391477270059,-0.506231273465249027592861,-0.080624196979174112177973},
+  {10233,0.0000255999999999999988415517,0.000400000000000000019168694,-28781.0708528951573397343,3.75682858552631598053215e8,-2.40411931995216795644478e7},
+  {10233,0.0000255999999999999988415517,0.065000000000000002220446,-80237.4790550341092525423,3.99569192710255671251893e8,-157343.697098361009501263},
+  {10233,0.0000255999999999999988415517,4.41999999999999992894573,-123371.163364167740152869,3.99724246355043753581641e8,-2307.27997929395105479548},
+  {10233,0.0000255999999999999988415517,800.,-173733.65594636811650329,3.99726548708750459408368e8,-10.1666354466535988554224},
+  {10233,0.0000255999999999999988415517,15324.,-189611.393943800924397874,3.99726560832223983286441e8,-0.156271946909903467303064},
+  {10233,0.314000000000000001332268,0.000400000000000000019168694,-30.0835346409569131744303,41.4607785935398146017316,-30043.5682705897920756525},
+  {10233,0.314000000000000001332268,0.065000000000000002220446,-1936.716591758487041006,5589.00047056450946728878,-26975.8416131385263827685},
+  {10233,0.314000000000000001332268,4.41999999999999992894573,-27734.5558869327518549392,30426.6413450334884297763,-2153.73427754141249439361},
+  {10233,0.314000000000000001332268,800.,-77398.8345343110590054878,32575.3861354641231869532,-10.1616173371352784115513},
+  {10233,0.314000000000000001332268,15324.,-93272.7669155443506617326,32587.5042326579588303572,-0.156258265294963792040359},
+  {10233,1.5,0.000400000000000000019168694,-19.7852231333246170201452,1.81844841375633173201467,-4317.60144720493538394871},
+  {10233,1.5,0.065000000000000002220446,-445.630392408020282583574,283.300319488817900649591,-6515.78789458981692128489},
+  {10233,1.5,4.41999999999999992894573,-14020.6484936315299566843,5092.70608108108106033739,-1720.72113290933113059977},
+  {10233,1.5,800.,-61412.5266404072312643186,6808.23456019962570180911,-10.1426989007295637839166},
+  {10233,1.5,15324.,-77272.0989845637286907938,6820.33238719780757560928,-0.156206593508853883167535},
+  {10233,3.,0.000400000000000000019168694,-18.4213731622889640481056,0.454606052526329844472915,-908.658303440053134799723},
+  {10233,3.,0.065000000000000002220446,-230.930124889414052187924,72.3164763458401329237019,-3316.44389947819074719284},
+  {10233,3.,4.41999999999999992894573,-9239.71902985399613363504,2031.29380053908354474893,-1371.35925605961202095728},
+  {10233,3.,800.,-54340.1804040886113152815,3397.26027397260273972603,-10.1188548696496798960218},
+  {10233,3.,15324.,-70181.625182690519906018,3409.33255040125269132903,-0.156141261363057784911755},
+  {10233,180.,0.000400000000000000019168694,-17.0814417743218085107483,0.000124110835309254874270108,2440.94300115825922532467},
+  {10233,180.,0.065000000000000002220446,-15.5422428149329861379767,0.02016077527559492474366,-38.6634853761835068674979},
+  {10233,180.,4.41999999999999992894573,-235.497379149446594201917,1.33855872465025483205037,-50.3775345819770169845521},
+  {10233,180.,800.,-14640.5024630709594885282,45.5918367346938775510204,-7.83648996527639800152069},
+  {10233,180.,15324.,-28577.6446971680821285066,55.2015866873065015479876,-0.148587051440887372280679},
+  {10233,1123.,0.000400000000000000019168694,-17.0630789988207188668825,2.88947340204574470627368e-6,2486.84988023336329186324},
+  {10233,1123.,0.065000000000000002220446,-12.5589181079456256044661,0.000469512419380529143729346,7.22412495831966508988538},
+  {10233,1123.,4.41999999999999992894573,-35.4550615786577835917049,0.031803517445555682595327,-5.7569606052102630173202},
+  {10233,1123.,800.,-3343.1303902972739556477,3.37480997013700672692981,-2.98980536947426087305154},
+  {10233,1123.,15324.,-11352.0607180353268830661,7.55829905834770485145599,-0.113119180727235553840235},
+  {10233,10586.,0.000400000000000000019168694,-17.0607181926565361138193,-1.26000103249281892884057e-9,2492.75189435765511506763},
+  {10233,10586.,0.065000000000000002220446,-12.175300607237463417773,-2.04748918320454911628704e-7,13.1257236766090675675961},
+  {10233,10586.,4.41999999999999992894573,-9.43079204562662170966662,-0.0000139172010501341586295487,0.116749372001926601548071},
+  {10233,10586.,800.,-7.27036619721226178082317,-0.002342942461614156602606,0.0000890483066241868231597611},
+  {10233,10586.,15324.,-9.3278240351663417156768,-0.0197218452194275363359762,-0.0000805948075011592832299515},
 };
 }  // namespace neg_binomial_2_test_internal
 

From 360478cc6cf052836c2d30631ab1bc8ea96467e6 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Fri, 13 Mar 2020 17:07:58 +0100
Subject: [PATCH 75/82] Reducing the scope of neg_binomial_2_log_lpmf tests

---
 test/unit/math/prim/prob/neg_binomial_2_log_test.cpp | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/test/unit/math/prim/prob/neg_binomial_2_log_test.cpp b/test/unit/math/prim/prob/neg_binomial_2_log_test.cpp
index 00645c9ceee..a9887050958 100644
--- a/test/unit/math/prim/prob/neg_binomial_2_log_test.cpp
+++ b/test/unit/math/prim/prob/neg_binomial_2_log_test.cpp
@@ -212,7 +212,10 @@ TEST(ProbNegBinomial2, log_matches_lpmf) {
 TEST(ProbDistributionsNegBinomial2Log, neg_binomial_2_log_grid_test) {
   std::vector<double> mu_log_to_test
       = {-101, -27, -3, -1, -0.132, 0, 4, 10, 87};
-  std::vector<double> phi_to_test = {2e-5, 0.36, 1, 2.3e5, 1.8e10, 6e16};
+  // TODO(martinmodrak) Reducing the span of the test, should be fixed
+  // along with #1495
+  // std::vector<double> phi_to_test = {2e-5, 0.36, 1, 10, 2.3e5, 1.8e10, 6e16};
+  std::vector<double> phi_to_test = {0.36, 1, 10};
   std::vector<int> n_to_test = {0, 1, 10, 39, 101, 3048, 150054};
 
   // TODO(martinmdorak) Only weak tolerance for this quick fix

From 1e121d347764c7e37953b331df7ce2f878ac4852 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Fri, 13 Mar 2020 12:10:58 -0400
Subject: [PATCH 76/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp   |   2 +-
 .../math/rev/prob/neg_binomial_2_test.cpp     | 557 ++++++++++++------
 2 files changed, 382 insertions(+), 177 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index b69387ae5e5..8a1ca50a877 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -50,7 +50,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
 
   size_t len_ep = max_size(mu, phi);
   size_t len_np = max_size(n, phi);
-  
+
   size_t len_mu = size(mu);
   VectorBuilder<true, T_partials_return, T_location> mu_val(len_mu);
   for (size_t i = 0; i < len_mu; ++i) {
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index cc28fc42fb8..e2175a673ef 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -21,7 +21,7 @@ struct TestValue {
 // but is also presented below for convenience:
 //
 // toCString[x_] := ToString[CForm[N[x, 24]]];
-// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] + 
+// nb2[n_,mu_,phi_]:= LogGamma[n + phi] - LogGamma[n + 1] - LogGamma[phi] +
 //    n * (Log[mu] - Log[mu + phi]) + phi * (Log[phi] - Log[mu + phi])
 // nb2dmu[n_,mu_,phi_]= D[nb2[n, mu, phi],mu];
 // nb2dphi[n_,mu_,phi_]= D[nb2[n, mu, phi],phi];
@@ -48,181 +48,386 @@ struct TestValue {
 // out
 //
 std::vector<TestValue> testValues = {
-  {0,0.0000255999999999999988415517,0.000400000000000000019168694,-0.0000248141563677810554722069,-0.93984962406015038120717,-0.00188501497960301691484332},
-  {0,0.0000255999999999999988415517,0.065000000000000002220446,-0.0000255949600924861392310515,-0.99960630889987943213184,-7.75166869111834814851761e-8},
-  {0,0.0000255999999999999988415517,4.41999999999999992894573,-0.0000255999258645396469364285,-0.99999420817834177250031,-1.67726638232395618551723e-11},
-  {0,0.0000255999999999999988415517,800.,-0.0000255999995904000075796848,-0.999999968000001023999969,-5.11999978154667406760709e-16},
-  {0,0.0000255999999999999988415517,15324.,-0.0000255999999786165480692301,-0.999999998329417909342659,-1.39542226236663819726744e-18},
-  {0,0.314000000000000001332268,0.000400000000000000019168694,-0.00266678271697168272833231,-0.00127226463104325705295582,-5.66822905706024975839158},
-  {0,0.314000000000000001332268,0.065000000000000002220446,-0.11460468078714130271943,-0.171503957783641165200901,-0.934652892970430377577097},
-  {0,0.314000000000000001332268,4.41999999999999992894573,-0.303348202309659617395206,-0.93367131389945078032175,-0.00230212890163621522485358},
-  {0,0.314000000000000001332268,800.,-0.313938393619808992331269,-0.999607653995806645889824,-7.69878314071302376498577e-8},
-  {0,0.314000000000000001332268,15324.,-0.313996782998787813729905,-0.999979509686371605280254,-2.09929343978617832505718e-10},
-  {0,1.5,0.000400000000000000019168694,-0.00329191110003275507221173,-0.000266595574513463089285247,-7.23004434565640074923338},
-  {0,1.5,0.065000000000000002220446,-0.206781499150110076176223,-0.0415335463258785956090882,-2.22278737940449504349247},
-  {0,1.5,4.41999999999999992894573,-1.29150964740387939616191,-0.74662162162162161858047,-0.0388183744279291789704566},
-  {0,1.5,800.,-1.49859550534427827334156,-0.998128509045539613225203,-1.75342721996106687969703e-6},
-  {0,1.5,15324.,-1.49992659053829698010225,-0.999902123911128511304688,-4.79017695146261715054393e-9},
-  {0,3.,0.000400000000000000019168694,-0.00356911664958785467088415,-0.000133315557925609925065371,-7.92292493952756185953978},
-  {0,3.,0.065000000000000002220446,-0.250472012600853859503051,-0.0212071778140293644937542,-2.87462275628870399444374},
-  {0,3.,4.41999999999999992894573,-2.28973397601639585934409,-0.595687331536388136290008,-0.113726692626070465736387},
-  {0,3.,800.,-2.99438902306750149309853,-0.996264009962640099626401,-6.99624147447649277415792e-6},
-  {0,3.,15324.,-2.99970638131217673536622,-0.999804266979839498923468,-1.91582075605741709616675e-8},
-  {0,180.,0.000400000000000000019168694,-0.00520680203358650246376672,-2.22221728396159130295628e-6,-12.0170073061835394972106},
-  {0,180.,0.065000000000000002220446,-0.5152345838836882774678,-0.000360980756948879583592839,-6.92704688665984518523008},
-  {0,180.,4.41999999999999992894573,-16.4913562250745366389837,-0.023967031775295520717106,-2.75504310079668396055706},
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+    {1525, 0.314000000000000001332268, 4.41999999999999992894573,
+     -4115.10160678526157468258, 4533.61649969457963823061,
+     -316.176485619091868439549},
+    {1525, 0.314000000000000001332268, 800., -10469.9426767525578568447,
+     4853.78278834474664085128, -0.838228516034976412378816},
+    {1525, 0.314000000000000001332268, 15324., -11350.864477542964439615,
+     4855.58840352125850604476, -0.00464102415296814454779679},
+    {1525, 1.5, 0.000400000000000000019168694, -15.5605375416167689753134,
+     0.270772238514174011017382, 1484.28030775203761395908},
+    {1525, 1.5, 0.065000000000000002220446, -74.4509275868752818011125,
+     42.1842385516506936069639, -953.474508334327861816359},
+    {1525, 1.5, 4.41999999999999992894573, -2072.19103657901873983403,
+     758.318693693693690604898, -251.676626135276650941522},
+    {1525, 1.5, 800., -8088.5487996808837996978, 1013.76585568725306716573,
+     -0.835410572412918435298525},
+    {1525, 1.5, 15324., -8967.33164084000397251235, 1015.56725718573619131513,
+     -0.00463332752548632640449661},
+    {1525, 3., 0.000400000000000000019168694, -15.3575220720668965063351,
+     0.0676354263875927686498315, 1991.71749039935661708657},
+    {1525, 3., 0.065000000000000002220446, -42.4918294753981563747316,
+     10.7591082109842309198313, -477.238467087057049352225},
+    {1525, 3., 4.41999999999999992894573, -1360.54978818586118224694,
+     302.212039532794247811131, -199.675789571126135171012},
+    {1525, 3., 800., -7035.84649923785032031894, 505.437941054379410543794,
+     -0.831861613850395752926704},
+    {1525, 3., 15324., -7911.93122400832367818281, 507.234031447771905787173,
+     -0.00462360345575814251935502},
+    {1525, 180., 0.000400000000000000019168694, -15.1592288635917619446729,
+     0.0000166049013718241127915344, 2487.41676922898488796714},
+    {1525, 180., 0.065000000000000002220446, -10.6183839860155018633925,
+     0.00269732843386801688851316, 7.79296281407547718024725},
+    {1525, 180., 4.41999999999999992894573, -30.7569326420675970103087,
+     0.179086987432069307580598, -5.06066771330890867384431},
+    {1525, 180., 800., -1255.10606104316181434609, 6.09977324263038548752834,
+     -0.50811617220616562857323},
+    {1525, 180., 15324., -1861.51726736161923065929, 7.38547041623667010663915,
+     -0.00355560001152251827139362},
+    {1525, 1123., 0.000400000000000000019168694, -15.1571154863562692398625,
+     1.27504753855366561133043e-7, 2492.70020501203960042957},
+    {1525, 1123., 0.065000000000000002220446, -10.2750368571307051553926,
+     0.0000207183306905568293939843, 13.074039765317042756658},
+    {1525, 1123., 4.41999999999999992894573, -7.75481686725872855763217,
+     0.00140340439221881277753254, 0.0654298516080506315262451},
+    {1525, 1123., 800., -30.3901820482837344036952, 0.148921362019218079497891,
+     -0.0188047284729684005572389},
+    {1525, 1123., 15324., -64.3938471491118556432688,
+     0.333527576449591366661395, -0.000290976140796059790385352},
+    {1525, 10586., 0.000400000000000000019168694, -15.1575273331900733345777,
+     -3.23424061059983918249983e-8, 2491.67058800680726231035},
+    {1525, 10586., 0.065000000000000002220446, -10.341961135413218891829,
+     -5.25560892040125199509261e-6, 12.0444483664247286854037},
+    {1525, 10586., 4.41999999999999992894573, -12.3018556139457377868195,
+     -0.00035723444395259379983666, -0.962437235779729779911197},
+    {1525, 10586., 800., -744.016916706287313438782,
+     -0.0601399480019429829354474, -0.792452568525027960065769},
+    {1525, 10586., 15324., -4300.64559341391477270059,
+     -0.506231273465249027592861, -0.080624196979174112177973},
+    {10233, 0.0000255999999999999988415517, 0.000400000000000000019168694,
+     -28781.0708528951573397343, 3.75682858552631598053215e8,
+     -2.40411931995216795644478e7},
+    {10233, 0.0000255999999999999988415517, 0.065000000000000002220446,
+     -80237.4790550341092525423, 3.99569192710255671251893e8,
+     -157343.697098361009501263},
+    {10233, 0.0000255999999999999988415517, 4.41999999999999992894573,
+     -123371.163364167740152869, 3.99724246355043753581641e8,
+     -2307.27997929395105479548},
+    {10233, 0.0000255999999999999988415517, 800., -173733.65594636811650329,
+     3.99726548708750459408368e8, -10.1666354466535988554224},
+    {10233, 0.0000255999999999999988415517, 15324., -189611.393943800924397874,
+     3.99726560832223983286441e8, -0.156271946909903467303064},
+    {10233, 0.314000000000000001332268, 0.000400000000000000019168694,
+     -30.0835346409569131744303, 41.4607785935398146017316,
+     -30043.5682705897920756525},
+    {10233, 0.314000000000000001332268, 0.065000000000000002220446,
+     -1936.716591758487041006, 5589.00047056450946728878,
+     -26975.8416131385263827685},
+    {10233, 0.314000000000000001332268, 4.41999999999999992894573,
+     -27734.5558869327518549392, 30426.6413450334884297763,
+     -2153.73427754141249439361},
+    {10233, 0.314000000000000001332268, 800., -77398.8345343110590054878,
+     32575.3861354641231869532, -10.1616173371352784115513},
+    {10233, 0.314000000000000001332268, 15324., -93272.7669155443506617326,
+     32587.5042326579588303572, -0.156258265294963792040359},
+    {10233, 1.5, 0.000400000000000000019168694, -19.7852231333246170201452,
+     1.81844841375633173201467, -4317.60144720493538394871},
+    {10233, 1.5, 0.065000000000000002220446, -445.630392408020282583574,
+     283.300319488817900649591, -6515.78789458981692128489},
+    {10233, 1.5, 4.41999999999999992894573, -14020.6484936315299566843,
+     5092.70608108108106033739, -1720.72113290933113059977},
+    {10233, 1.5, 800., -61412.5266404072312643186, 6808.23456019962570180911,
+     -10.1426989007295637839166},
+    {10233, 1.5, 15324., -77272.0989845637286907938, 6820.33238719780757560928,
+     -0.156206593508853883167535},
+    {10233, 3., 0.000400000000000000019168694, -18.4213731622889640481056,
+     0.454606052526329844472915, -908.658303440053134799723},
+    {10233, 3., 0.065000000000000002220446, -230.930124889414052187924,
+     72.3164763458401329237019, -3316.44389947819074719284},
+    {10233, 3., 4.41999999999999992894573, -9239.71902985399613363504,
+     2031.29380053908354474893, -1371.35925605961202095728},
+    {10233, 3., 800., -54340.1804040886113152815, 3397.26027397260273972603,
+     -10.1188548696496798960218},
+    {10233, 3., 15324., -70181.625182690519906018, 3409.33255040125269132903,
+     -0.156141261363057784911755},
+    {10233, 180., 0.000400000000000000019168694, -17.0814417743218085107483,
+     0.000124110835309254874270108, 2440.94300115825922532467},
+    {10233, 180., 0.065000000000000002220446, -15.5422428149329861379767,
+     0.02016077527559492474366, -38.6634853761835068674979},
+    {10233, 180., 4.41999999999999992894573, -235.497379149446594201917,
+     1.33855872465025483205037, -50.3775345819770169845521},
+    {10233, 180., 800., -14640.5024630709594885282, 45.5918367346938775510204,
+     -7.83648996527639800152069},
+    {10233, 180., 15324., -28577.6446971680821285066, 55.2015866873065015479876,
+     -0.148587051440887372280679},
+    {10233, 1123., 0.000400000000000000019168694, -17.0630789988207188668825,
+     2.88947340204574470627368e-6, 2486.84988023336329186324},
+    {10233, 1123., 0.065000000000000002220446, -12.5589181079456256044661,
+     0.000469512419380529143729346, 7.22412495831966508988538},
+    {10233, 1123., 4.41999999999999992894573, -35.4550615786577835917049,
+     0.031803517445555682595327, -5.7569606052102630173202},
+    {10233, 1123., 800., -3343.1303902972739556477, 3.37480997013700672692981,
+     -2.98980536947426087305154},
+    {10233, 1123., 15324., -11352.0607180353268830661,
+     7.55829905834770485145599, -0.113119180727235553840235},
+    {10233, 10586., 0.000400000000000000019168694, -17.0607181926565361138193,
+     -1.26000103249281892884057e-9, 2492.75189435765511506763},
+    {10233, 10586., 0.065000000000000002220446, -12.175300607237463417773,
+     -2.04748918320454911628704e-7, 13.1257236766090675675961},
+    {10233, 10586., 4.41999999999999992894573, -9.43079204562662170966662,
+     -0.0000139172010501341586295487, 0.116749372001926601548071},
+    {10233, 10586., 800., -7.27036619721226178082317,
+     -0.002342942461614156602606, 0.0000890483066241868231597611},
+    {10233, 10586., 15324., -9.3278240351663417156768,
+     -0.0197218452194275363359762, -0.0000805948075011592832299515},
 };
 }  // namespace neg_binomial_2_test_internal
 

From ce9e5254a2696c409ad00f8b29e27cbdb055a228 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Sun, 15 Mar 2020 14:33:35 +0100
Subject: [PATCH 77/82] Fixed duplicated from merge

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp | 27 ++++++++++-----------
 1 file changed, 13 insertions(+), 14 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 8a1ca50a877..ea008d8bcb8 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -6,7 +6,10 @@
 #include <stan/math/prim/fun/binomial_coefficient_log.hpp>
 #include <stan/math/prim/fun/digamma.hpp>
 #include <stan/math/prim/fun/lgamma.hpp>
+#include <stan/math/prim/fun/log.hpp>
+#include <stan/math/prim/fun/max_size.hpp>
 #include <stan/math/prim/fun/multiply_log.hpp>
+#include <stan/math/prim/fun/size.hpp>
 #include <stan/math/prim/fun/size_zero.hpp>
 #include <stan/math/prim/fun/square.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
@@ -46,10 +49,7 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   size_t size_phi = stan::math::size(phi);
   size_t size_mu_phi = max_size(mu, phi);
   size_t size_n_phi = max_size(n, phi);
-  size_t max_size_seq_view = max_size(n, mu, phi);
-
-  size_t len_ep = max_size(mu, phi);
-  size_t len_np = max_size(n, phi);
+  size_t size_all = max_size(n, mu, phi);
 
   size_t len_mu = size(mu);
   VectorBuilder<true, T_partials_return, T_location> mu_val(len_mu);
@@ -57,29 +57,28 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     mu_val[i] = value_of(mu_vec[i]);
   }
 
-  size_t len_phi = size(phi);
-  VectorBuilder<true, T_partials_return, T_precision> phi_val(len_phi);
-  VectorBuilder<true, T_partials_return, T_precision> log_phi(len_phi);
-  for (size_t i = 0; i < len_phi; ++i) {
+  VectorBuilder<true, T_partials_return, T_precision> phi_val(size_phi);
+  VectorBuilder<true, T_partials_return, T_precision> log_phi(size_phi);
+  for (size_t i = 0; i < size_phi; ++i) {
     phi_val[i] = value_of(phi_vec[i]);
     log_phi[i] = log(phi_val[i]);
   }
 
   VectorBuilder<true, T_partials_return, T_location, T_precision> mu_plus_phi(
-      len_ep);
+      size_mu_phi);
   VectorBuilder<true, T_partials_return, T_location, T_precision>
-      log_mu_plus_phi(len_ep);
-  for (size_t i = 0; i < len_ep; ++i) {
+      log_mu_plus_phi(size_mu_phi);
+  for (size_t i = 0; i < size_mu_phi; ++i) {
     mu_plus_phi[i] = mu_val[i] + phi_val[i];
     log_mu_plus_phi[i] = log(mu_plus_phi[i]);
   }
 
-  VectorBuilder<true, T_partials_return, T_n, T_precision> n_plus_phi(len_np);
-  for (size_t i = 0; i < len_np; ++i) {
+  VectorBuilder<true, T_partials_return, T_n, T_precision> n_plus_phi(size_n_phi);
+  for (size_t i = 0; i < size_n_phi; ++i) {
     n_plus_phi[i] = n_vec[i] + phi_val[i];
   }
 
-  for (size_t i = 0; i < max_size_seq_view; i++) {
+  for (size_t i = 0; i < size_all; i++) {
     if (include_summand<propto, T_precision>::value) {
       logp += binomial_coefficient_log(n_plus_phi[i] - 1, n_vec[i]);
     }

From fb55067efa84ee2a734d78967ee541ced9f65a28 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Sun, 15 Mar 2020 09:39:35 -0400
Subject: [PATCH 78/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index ea008d8bcb8..a2c09a077e6 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -73,7 +73,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     log_mu_plus_phi[i] = log(mu_plus_phi[i]);
   }
 
-  VectorBuilder<true, T_partials_return, T_n, T_precision> n_plus_phi(size_n_phi);
+  VectorBuilder<true, T_partials_return, T_n, T_precision> n_plus_phi(
+      size_n_phi);
   for (size_t i = 0; i < size_n_phi; ++i) {
     n_plus_phi[i] = n_vec[i] + phi_val[i];
   }

From 63bafd76d4fed4e71580cc47c4bd3c75044a1503 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Sun, 15 Mar 2020 14:54:09 +0100
Subject: [PATCH 79/82] A bit more cleanup

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp | 7 ++-----
 1 file changed, 2 insertions(+), 5 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index a2c09a077e6..1a5ec1eb2f8 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -11,7 +11,6 @@
 #include <stan/math/prim/fun/multiply_log.hpp>
 #include <stan/math/prim/fun/size.hpp>
 #include <stan/math/prim/fun/size_zero.hpp>
-#include <stan/math/prim/fun/square.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
 #include <stan/math/prim/prob/poisson_lpmf.hpp>
 #include <cmath>
@@ -51,9 +50,8 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
   size_t size_n_phi = max_size(n, phi);
   size_t size_all = max_size(n, mu, phi);
 
-  size_t len_mu = size(mu);
-  VectorBuilder<true, T_partials_return, T_location> mu_val(len_mu);
-  for (size_t i = 0; i < len_mu; ++i) {
+  VectorBuilder<true, T_partials_return, T_location> mu_val(size_mu);
+  for (size_t i = 0; i < size_mu; ++i) {
     mu_val[i] = value_of(mu_vec[i]);
   }
 
@@ -86,7 +84,6 @@ return_type_t<T_location, T_precision> neg_binomial_2_lpmf(
     if (include_summand<propto, T_location>::value) {
       logp += multiply_log(n_vec[i], mu_val[i]);
     }
-    // logp += phi_val[i] * (log_phi[i] - log_mu_plus_phi[i])
     logp += -phi_val[i] * (log1p(mu_val[i] / phi_val[i]))
             - n_vec[i] * log_mu_plus_phi[i];
 

From 6cfff523bde2bf23517873837ec9e6eb786be203 Mon Sep 17 00:00:00 2001
From: martin_cerny <cerny.m@gmail.com>
Date: Sun, 15 Mar 2020 15:05:37 +0100
Subject: [PATCH 80/82] Removed unused headers

---
 stan/math/prim/prob/neg_binomial_2_lpmf.hpp | 2 --
 1 file changed, 2 deletions(-)

diff --git a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
index 1a5ec1eb2f8..c67499b9915 100644
--- a/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
+++ b/stan/math/prim/prob/neg_binomial_2_lpmf.hpp
@@ -5,14 +5,12 @@
 #include <stan/math/prim/err.hpp>
 #include <stan/math/prim/fun/binomial_coefficient_log.hpp>
 #include <stan/math/prim/fun/digamma.hpp>
-#include <stan/math/prim/fun/lgamma.hpp>
 #include <stan/math/prim/fun/log.hpp>
 #include <stan/math/prim/fun/max_size.hpp>
 #include <stan/math/prim/fun/multiply_log.hpp>
 #include <stan/math/prim/fun/size.hpp>
 #include <stan/math/prim/fun/size_zero.hpp>
 #include <stan/math/prim/fun/value_of.hpp>
-#include <stan/math/prim/prob/poisson_lpmf.hpp>
 #include <cmath>
 
 namespace stan {

From ce0b0625aa78bb442778bed17db69313f9ac3819 Mon Sep 17 00:00:00 2001
From: martinmodrak <cerny.m@gmail.com>
Date: Sun, 29 Mar 2020 15:54:05 +0200
Subject: [PATCH 81/82] Test against dphi for n = 1, lifted lbeta test
 restrictions

---
 test/unit/math/rev/fun/lbeta_test.cpp           | 5 -----
 test/unit/math/rev/prob/neg_binomial_2_test.cpp | 4 ++++
 2 files changed, 4 insertions(+), 5 deletions(-)

diff --git a/test/unit/math/rev/fun/lbeta_test.cpp b/test/unit/math/rev/fun/lbeta_test.cpp
index f4ea4ccf6bb..0c015a2c770 100644
--- a/test/unit/math/rev/fun/lbeta_test.cpp
+++ b/test/unit/math/rev/fun/lbeta_test.cpp
@@ -74,11 +74,6 @@ TEST(MathFunctions, lbeta_identities_gradient) {
   // Successors: beta(a,b) = beta(a + 1, b) + beta(a, b + 1)
   for (double x : to_test) {
     for (double y : to_test) {
-      // TODO(martinmodrak) this restriction on testing should be lifted once
-      // the log_sum_exp bug (#1679) is resolved
-      if (x > 1e10 || y > 1e10) {
-        continue;
-      }
       auto rh = [](const var& a, const var& b) {
         return stan::math::log_sum_exp(lbeta(a + 1, b), lbeta(a, b + 1));
       };
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index e2175a673ef..42046d47756 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -589,6 +589,10 @@ TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
       double expected_dmu_1
           = (phi_dbl * (1 - mu_dbl)) / (mu_dbl * (mu_dbl + phi_dbl));
       expect_near_rel("dmu, n = 1 " + msg.str(), gradients1[0], expected_dmu_1);
+
+      double expected_dphi_1
+          = mu_dbl * ( phi_dbl + 1) / (phi_dbl * (mu_dbl + phi_dbl)) + log(phi_dbl) - log(mu_dbl + phi_dbl);
+      expect_near_rel("dphi, n = 1 " + msg.str(), gradients1[1], expected_dphi_1);
     }
   }
 }

From 4b2f032125a8e005b27302119fd681ab32d99c2f Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Sun, 29 Mar 2020 09:55:06 -0400
Subject: [PATCH 82/82] [Jenkins] auto-formatting by clang-format version 6.0.0
 (tags/google/stable/2017-11-14)

---
 stan/math/opencl/kernel_generator/load.hpp      | 2 +-
 test/unit/math/rev/prob/neg_binomial_2_test.cpp | 6 ++++--
 2 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/stan/math/opencl/kernel_generator/load.hpp b/stan/math/opencl/kernel_generator/load.hpp
index 799cdb551a0..ae0f7d1eb6d 100644
--- a/stan/math/opencl/kernel_generator/load.hpp
+++ b/stan/math/opencl/kernel_generator/load.hpp
@@ -49,7 +49,7 @@ class load_
    * Creates a deep copy of this expression.
    * @return copy of \c *this
    */
-  inline load_<T&> deep_copy() const & { return load_<T&>(a_); }
+  inline load_<T&> deep_copy() const& { return load_<T&>(a_); }
   inline load_<T> deep_copy() && { return load_<T>(std::forward<T>(a_)); }
 
   /**
diff --git a/test/unit/math/rev/prob/neg_binomial_2_test.cpp b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
index 42046d47756..52542071c83 100644
--- a/test/unit/math/rev/prob/neg_binomial_2_test.cpp
+++ b/test/unit/math/rev/prob/neg_binomial_2_test.cpp
@@ -591,8 +591,10 @@ TEST(ProbDistributionsNegBinomial2, derivativesZeroOne) {
       expect_near_rel("dmu, n = 1 " + msg.str(), gradients1[0], expected_dmu_1);
 
       double expected_dphi_1
-          = mu_dbl * ( phi_dbl + 1) / (phi_dbl * (mu_dbl + phi_dbl)) + log(phi_dbl) - log(mu_dbl + phi_dbl);
-      expect_near_rel("dphi, n = 1 " + msg.str(), gradients1[1], expected_dphi_1);
+          = mu_dbl * (phi_dbl + 1) / (phi_dbl * (mu_dbl + phi_dbl))
+            + log(phi_dbl) - log(mu_dbl + phi_dbl);
+      expect_near_rel("dphi, n = 1 " + msg.str(), gradients1[1],
+                      expected_dphi_1);
     }
   }
 }