From 7b05d7a1a0cef4167e466dee591d683379b043ea Mon Sep 17 00:00:00 2001
From: Rose <83477269+AtariDreams@users.noreply.github.com>
Date: Thu, 29 Dec 2022 13:49:13 -0500
Subject: [PATCH 1/3] Update Boost to 1.81

I will be the first to say it; I did in fact contribute to this release of Boost. However, it fixes a platitude of issues as this is a bugfix release.

Therefore, I think updating to 1.81 is worth it.
---
 boost-math                                              | 2 +-
 docs/cgmanifest.json                                    | 2 +-
 tests/std/tests/LWG3234_math_special_overloads/test.cpp | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/boost-math b/boost-math
index db2a7cbb44a..f395de082ec 160000
--- a/boost-math
+++ b/boost-math
@@ -1 +1 @@
-Subproject commit db2a7cbb44a84c4c9cba62232c07f18b22bd965d
+Subproject commit f395de082eca6ee993a15f2bdb90277eda518295
diff --git a/docs/cgmanifest.json b/docs/cgmanifest.json
index 81d35d6dd53..a7d932b2729 100644
--- a/docs/cgmanifest.json
+++ b/docs/cgmanifest.json
@@ -6,7 +6,7 @@
                 "type": "git",
                 "git": {
                     "repositoryUrl": "https://github.com/boostorg/math",
-                    "commitHash": "db2a7cbb44a84c4c9cba62232c07f18b22bd965d"
+                    "commitHash": "f395de082eca6ee993a15f2bdb90277eda518295"
                 }
             }
         },
diff --git a/tests/std/tests/LWG3234_math_special_overloads/test.cpp b/tests/std/tests/LWG3234_math_special_overloads/test.cpp
index 8975a1e2a2f..1654c10bc6d 100644
--- a/tests/std/tests/LWG3234_math_special_overloads/test.cpp
+++ b/tests/std/tests/LWG3234_math_special_overloads/test.cpp
@@ -197,7 +197,7 @@ void test_comp_ellint_2() {
     static_assert(is_same_v<decltype(comp_ellint_2f(0)), float>);
     static_assert(is_same_v<decltype(comp_ellint_2l(0)), long double>);
     static_assert(is_same_v<decltype(comp_ellint_2(Ambiguous{})), Ambiguous>);
-    assert(comp_ellint_2(0) == acos(-1.0) / 2);
+    assert(expect_epsilons(comp_ellint_2(0), acos(-1.0) / 2, 2));
 }
 
 void test_comp_ellint_3() {

From 981619b40363ddde89e13258ef9498d65e7c2b89 Mon Sep 17 00:00:00 2001
From: Nicole Mazzuca <mazzucan@outlook.com>
Date: Thu, 5 Jan 2023 15:07:31 -0800
Subject: [PATCH 2/3] switch to isclose

---
 .../LWG3234_math_special_overloads/test.cpp   | 30 ++++++++++++++-----
 1 file changed, 23 insertions(+), 7 deletions(-)

diff --git a/tests/std/tests/LWG3234_math_special_overloads/test.cpp b/tests/std/tests/LWG3234_math_special_overloads/test.cpp
index 1654c10bc6d..0f1e5b1c2a8 100644
--- a/tests/std/tests/LWG3234_math_special_overloads/test.cpp
+++ b/tests/std/tests/LWG3234_math_special_overloads/test.cpp
@@ -102,8 +102,24 @@ Ambiguous sph_neumann(unsigned int, Ambiguous) {
     return Ambiguous{};
 }
 
-bool expect_epsilons(double expected, double calculated, unsigned int multiple) {
-    return abs((calculated - expected) / expected) <= multiple * numeric_limits<double>::epsilon();
+template <class Float>
+bool isclose(Float f, Float g, const int ulps = 1) {
+    if (f == g) {
+        return true;
+    }
+
+    if (f > g) {
+        swap(f, g);
+    }
+    // f < g
+    for (int i = 0; i < ulps; ++i) {
+        f = nextafter(f, numeric_limits<Float>::infinity());
+        if (f == g) {
+            return true;
+        }
+    }
+
+    return false;
 }
 
 void test_assoc_laguerre() {
@@ -197,7 +213,7 @@ void test_comp_ellint_2() {
     static_assert(is_same_v<decltype(comp_ellint_2f(0)), float>);
     static_assert(is_same_v<decltype(comp_ellint_2l(0)), long double>);
     static_assert(is_same_v<decltype(comp_ellint_2(Ambiguous{})), Ambiguous>);
-    assert(expect_epsilons(comp_ellint_2(0), acos(-1.0) / 2, 2));
+    assert(isclose(comp_ellint_2(0), acos(-1.0) / 2));
 }
 
 void test_comp_ellint_3() {
@@ -285,7 +301,7 @@ void test_cyl_bessel_k() {
     static_assert(is_same_v<decltype(cyl_bessel_kl(0, 0)), long double>);
     static_assert(is_same_v<decltype(cyl_bessel_k(0, 0)), double>);
     static_assert(is_same_v<decltype(cyl_bessel_k(Ambiguous{}, Ambiguous{})), Ambiguous>);
-    assert(expect_epsilons(cyl_bessel_k(0.5, 1), acos(-1.0) / 2 * (cyl_bessel_i(-0.5, 1) - cyl_bessel_i(0.5, 1)), 10));
+    assert(isclose(cyl_bessel_k(0.5, 1), acos(-1.0) / 2 * (cyl_bessel_i(-0.5, 1) - cyl_bessel_i(0.5, 1)), 15));
 }
 
 void test_cyl_neumann() {
@@ -507,7 +523,7 @@ void test_sph_bessel() {
     static_assert(is_same_v<decltype(sph_besself(0u, 0)), float>);
     static_assert(is_same_v<decltype(sph_bessell(0u, 0)), long double>);
     static_assert(is_same_v<decltype(sph_bessel(0u, Ambiguous{})), Ambiguous>);
-    assert(expect_epsilons(sph_bessel(1, 2), sin(2) / (static_cast<double>(2) * 2) - cos(2) / 2, 2));
+    assert(isclose(sph_bessel(1, 2), sin(2) / (2.0 * 2) - cos(2) / 2, 2));
 }
 
 void test_sph_legendre() {
@@ -527,7 +543,7 @@ void test_sph_legendre() {
     static_assert(is_same_v<decltype(sph_legendre(0u, 0u, Ambiguous{})), Ambiguous>);
 
     const double pi = acos(-1.0);
-    assert(expect_epsilons(sph_legendre(3, 0, 1), 0.25 * sqrt(7 / pi) * (5 * pow(cos(1), 3) - 3 * cos(1)), 2));
+    assert(isclose(sph_legendre(3, 0, 1), 0.25 * sqrt(7 / pi) * (5 * pow(cos(1), 3) - 3 * cos(1))));
 }
 
 void test_sph_neumann() {
@@ -545,7 +561,7 @@ void test_sph_neumann() {
     static_assert(is_same_v<decltype(sph_neumannf(0u, 0)), float>);
     static_assert(is_same_v<decltype(sph_neumannl(0u, 0)), long double>);
     static_assert(is_same_v<decltype(sph_neumann(0u, Ambiguous{})), Ambiguous>);
-    assert(expect_epsilons(sph_neumann(1, 1), -cos(1) - sin(1), 2));
+    assert(isclose(sph_neumann(1, 1), -cos(1) - sin(1), 2));
 }
 
 int main() {

From fbc08d5741e3a1ffb968508e22cf53a3fd3aa767 Mon Sep 17 00:00:00 2001
From: Nicole Mazzuca <mazzucan@outlook.com>
Date: Fri, 6 Jan 2023 10:47:08 -0800
Subject: [PATCH 3/3] include utility for swap

---
 tests/std/tests/LWG3234_math_special_overloads/test.cpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/tests/std/tests/LWG3234_math_special_overloads/test.cpp b/tests/std/tests/LWG3234_math_special_overloads/test.cpp
index 0f1e5b1c2a8..8594c3cf11e 100644
--- a/tests/std/tests/LWG3234_math_special_overloads/test.cpp
+++ b/tests/std/tests/LWG3234_math_special_overloads/test.cpp
@@ -5,6 +5,7 @@
 #include <cmath>
 #include <limits>
 #include <type_traits>
+#include <utility>
 
 using namespace std;