From 3dafc076e83a80747d5009067d58ef4ffa279862 Mon Sep 17 00:00:00 2001
From: jzmaddock <john@johnmaddock.co.uk>
Date: Fri, 3 May 2024 18:07:06 +0100
Subject: [PATCH] Correct ellint_1 logic for types with no infinity. Fixes
 multiprecision failures.

---
 include/boost/math/special_functions/ellint_1.hpp | 13 +++++++++----
 1 file changed, 9 insertions(+), 4 deletions(-)

diff --git a/include/boost/math/special_functions/ellint_1.hpp b/include/boost/math/special_functions/ellint_1.hpp
index 6eeb4761c7..dfc1815f7f 100644
--- a/include/boost/math/special_functions/ellint_1.hpp
+++ b/include/boost/math/special_functions/ellint_1.hpp
@@ -123,12 +123,17 @@ T ellint_f_imp(T phi, T k, const Policy& pol, T one_minus_k2)
           //
           T c = 1 / sinp;
           T c_minus_one = cosp / sinp;
-          T cross = fabs(c / (k * k));
           T arg2;
-          if ((cross > 0.9f) && (cross < 1.1f))
-             arg2 = c_minus_one + one_minus_k2;
+          if (k != 0)
+          {
+             T cross = fabs(c / (k * k));
+             if ((cross > 0.9f) && (cross < 1.1f))
+                arg2 = c_minus_one + one_minus_k2;
+             else
+                arg2 = c - k * k;
+          }
           else
-             arg2 = c - k * k;
+             arg2 = c;
           result = static_cast<T>(s * ellint_rf_imp(c_minus_one, arg2, c, pol));
        }
        else