From f1c5e6c7d852dd295527bd5d34879ce8da328123 Mon Sep 17 00:00:00 2001
From: Andrew Johnson <andrew.johnson@arjohnsonau.com>
Date: Mon, 16 Jun 2025 15:35:42 +0800
Subject: [PATCH 1/2] Improve numerical stability of fwd gradients for
 std_normal_log_qf

---
 stan/math/fwd/prob/std_normal_log_qf.hpp           |  8 +-------
 test/unit/math/mix/prob/std_normal_log_qf_test.cpp | 12 ++++++++++++
 2 files changed, 13 insertions(+), 7 deletions(-)

diff --git a/stan/math/fwd/prob/std_normal_log_qf.hpp b/stan/math/fwd/prob/std_normal_log_qf.hpp
index 2dc0a855cf7..18ffd5ce74a 100644
--- a/stan/math/fwd/prob/std_normal_log_qf.hpp
+++ b/stan/math/fwd/prob/std_normal_log_qf.hpp
@@ -16,15 +16,9 @@ namespace math {
 template <typename T>
 inline fvar<T> std_normal_log_qf(const fvar<T>& p) {
   const T xv = std_normal_log_qf(p.val_);
-  int p_sign = 1;
-  auto p_d = p.d_;
-  if (p.d_ < 0) {
-    p_sign = -1;
-    p_d *= -1;
-  }
   return fvar<T>(
       xv,
-      p_sign * exp(p.val_ + log(p_d) - NEG_LOG_SQRT_TWO_PI + 0.5 * square(xv)));
+      p.d_ * exp(p.val_ - std_normal_lpdf(xv)));
 }
 }  // namespace math
 }  // namespace stan
diff --git a/test/unit/math/mix/prob/std_normal_log_qf_test.cpp b/test/unit/math/mix/prob/std_normal_log_qf_test.cpp
index 1ae44dd9c27..f26d386ee66 100644
--- a/test/unit/math/mix/prob/std_normal_log_qf_test.cpp
+++ b/test/unit/math/mix/prob/std_normal_log_qf_test.cpp
@@ -4,6 +4,7 @@
 #include <test/unit/math/test_ad.hpp>
 #include <stan/math/fwd/prob/std_normal_log_qf.hpp>
 
+
 TEST_F(AgradRev, mathMixLogFun_stdNormalLogQf) {
   auto f = [](const auto& x1) { return stan::math::std_normal_log_qf(x1); };
   stan::test::expect_ad(f, -100.25);
@@ -46,3 +47,14 @@ TEST_F(AgradRev, mathMixMatFunLog_stdNormalLogQfVarmat) {
   }
   expect_ad_vector_matvar(f, A);
 }
+
+TEST_F(AgradRev, GradientStabilityStdNormalLogQf) {
+  auto f = [](const auto& y) {
+    return stan::math::sum(stan::math::std_normal_log_qf(y));
+  };
+
+  Eigen::VectorXd y1(2);
+  y1 << -10, -2;
+
+  stan::test::expect_ad(f, y1);
+}

From 597fd7e41b8a2c532c0eb640b513d2fbe0ba9993 Mon Sep 17 00:00:00 2001
From: Stan Jenkins <mc.stanislaw@gmail.com>
Date: Mon, 16 Jun 2025 03:40:26 -0400
Subject: [PATCH 2/2] [Jenkins] auto-formatting by clang-format version
 10.0.0-4ubuntu1

---
 stan/math/fwd/prob/std_normal_log_qf.hpp           | 4 +---
 test/unit/math/mix/prob/std_normal_log_qf_test.cpp | 1 -
 2 files changed, 1 insertion(+), 4 deletions(-)

diff --git a/stan/math/fwd/prob/std_normal_log_qf.hpp b/stan/math/fwd/prob/std_normal_log_qf.hpp
index 18ffd5ce74a..52f53dc107f 100644
--- a/stan/math/fwd/prob/std_normal_log_qf.hpp
+++ b/stan/math/fwd/prob/std_normal_log_qf.hpp
@@ -16,9 +16,7 @@ namespace math {
 template <typename T>
 inline fvar<T> std_normal_log_qf(const fvar<T>& p) {
   const T xv = std_normal_log_qf(p.val_);
-  return fvar<T>(
-      xv,
-      p.d_ * exp(p.val_ - std_normal_lpdf(xv)));
+  return fvar<T>(xv, p.d_ * exp(p.val_ - std_normal_lpdf(xv)));
 }
 }  // namespace math
 }  // namespace stan
diff --git a/test/unit/math/mix/prob/std_normal_log_qf_test.cpp b/test/unit/math/mix/prob/std_normal_log_qf_test.cpp
index f26d386ee66..8a2908da869 100644
--- a/test/unit/math/mix/prob/std_normal_log_qf_test.cpp
+++ b/test/unit/math/mix/prob/std_normal_log_qf_test.cpp
@@ -4,7 +4,6 @@
 #include <test/unit/math/test_ad.hpp>
 #include <stan/math/fwd/prob/std_normal_log_qf.hpp>
 
-
 TEST_F(AgradRev, mathMixLogFun_stdNormalLogQf) {
   auto f = [](const auto& x1) { return stan::math::std_normal_log_qf(x1); };
   stan::test::expect_ad(f, -100.25);