From f05f579ac866e96ffd5e069dcec70f211b1f21ab Mon Sep 17 00:00:00 2001
From: Demetrios Agourakis <demetrios@agourakis.med.br>
Date: Thu, 29 Oct 2026 23:05:27 -0300
Subject: [PATCH] Select the principal branch of complex acosh in both
 half-planes

---
 .../xsimd/arch/common/xsimd_common_trigo.hpp  |  3 +-
 test/test_complex_hyperbolic.cpp              | 37 +++++++++++++++++++
 2 files changed, 38 insertions(+), 2 deletions(-)

diff --git a/include/xsimd/arch/common/xsimd_common_trigo.hpp b/include/xsimd/arch/common/xsimd_common_trigo.hpp
index 00ad75076..598c81906 100644
--- a/include/xsimd/arch/common/xsimd_common_trigo.hpp
+++ b/include/xsimd/arch/common/xsimd_common_trigo.hpp
@@ -80,8 +80,7 @@ namespace xsimd
         {
             using batch_type = batch<std::complex<T>, A>;
             batch_type w = acos(z);
-            w = batch_type(-w.imag(), w.real());
-            return w;
+            return batch_type(abs(w.imag()), copysign(w.real(), z.imag()));
         }
 
         // asin
diff --git a/test/test_complex_hyperbolic.cpp b/test/test_complex_hyperbolic.cpp
index 40e97ca7c..e13d936fc 100644
--- a/test/test_complex_hyperbolic.cpp
+++ b/test/test_complex_hyperbolic.cpp
@@ -172,4 +172,41 @@ TEST_CASE_TEMPLATE("[complex hyperbolic]", B, BATCH_COMPLEX_TYPES)
         Test.test_atanh();
     }
 }
+TEST_CASE_TEMPLATE("[complex acosh principal branch]", B, BATCH_COMPLEX_TYPES)
+{
+    using value_type = typename B::value_type;
+    using real_type = typename value_type::value_type;
+    const std::array<value_type, 16> samples = {
+        value_type(-4, 1), value_type(-4, -1),
+        value_type(-2, 1), value_type(-2, -1),
+        value_type(-1, 1), value_type(-1, -1),
+        value_type(real_type(-0.5), 1), value_type(real_type(-0.5), -1),
+        value_type(real_type(0.5), 1), value_type(real_type(0.5), -1),
+        value_type(1, 1), value_type(1, -1),
+        value_type(2, 1), value_type(2, -1),
+        value_type(4, 1), value_type(4, -1)
+    };
+    std::array<value_type, B::size> inputs;
+    std::array<value_type, B::size> results;
+    const auto tolerance = real_type(64) * std::numeric_limits<real_type>::epsilon();
+    for (size_t start = 0; start < samples.size(); ++start)
+    {
+        for (size_t lane = 0; lane < B::size; ++lane)
+        {
+            inputs[lane] = samples[(start + lane) % samples.size()];
+        }
+        xsimd::acosh(B::load_unaligned(inputs.data())).store_unaligned(results.data());
+        for (size_t lane = 0; lane < B::size; ++lane)
+        {
+            const auto expected = std::acosh(inputs[lane]);
+            CHECK_EQ(results[lane].real(), doctest::Approx(expected.real()).epsilon(tolerance).scale(1));
+            CHECK_EQ(results[lane].imag(), doctest::Approx(expected.imag()).epsilon(tolerance).scale(1));
+            CHECK_GE(results[lane].real(), real_type(0));
+            CHECK_EQ(std::signbit(results[lane].imag()), std::signbit(inputs[lane].imag()));
+            const auto recovered = std::cosh(results[lane]);
+            CHECK_EQ(recovered.real(), doctest::Approx(inputs[lane].real()).epsilon(tolerance).scale(1));
+            CHECK_EQ(recovered.imag(), doctest::Approx(inputs[lane].imag()).epsilon(tolerance).scale(1));
+        }
+    }
+}
 #endif