From d7819f425e9d58ef7104046bbdfadd8e81b37a26 Mon Sep 17 00:00:00 2001
From: Demetrios Chiuratto Agourakis <demetrios@agourakis.med.br>
Date: Tue, 10 Nov 2026 23:28:35 +0000
Subject: [PATCH] Select the principal branch of complex acosh in both
 half-planes

Take the nonnegative imaginary magnitude of acos and the sign of imag(z). Keep the signed real-axis asin branch so the cut matches std::acosh.
---
 .../xsimd/arch/common/xsimd_common_trigo.hpp  |  8 ++---
 test/test_complex_hyperbolic.cpp              | 31 +++++++++++++++++++
 2 files changed, 35 insertions(+), 4 deletions(-)

diff --git a/include/xsimd/arch/common/xsimd_common_trigo.hpp b/include/xsimd/arch/common/xsimd_common_trigo.hpp
index 00ad75076..0ad5bc2a8 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
@@ -141,8 +140,9 @@ namespace xsimd
 
             return select(y == real_batch(0.),
                           select(fabs(x) > real_batch(1.),
-                                 batch_type(constants::pio2<real_batch>(), real_batch(0.)),
-                                 batch_type(asin(x), real_batch(0.))),
+                                 batch_type(copysign(constants::pio2<real_batch>(), x),
+                                            copysign(acosh(max(fabs(x), real_batch(1.))), y)),
+                                 batch_type(asin(x), y)),
                           resg);
         }
 
diff --git a/test/test_complex_hyperbolic.cpp b/test/test_complex_hyperbolic.cpp
index 40e97ca7c..780749af8 100644
--- a/test/test_complex_hyperbolic.cpp
+++ b/test/test_complex_hyperbolic.cpp
@@ -121,6 +121,37 @@ struct complex_hyperbolic_test
             detail::load_batch(ref, expected, i);
             CHECK_BATCH_EQ(ref, out);
         }
+
+        using R = real_value_type;
+        const R zero(0);
+        const R re[] = { -R(4), -R(2), -R(1), -R(0.5), R(0.5), R(1), R(2), R(4) };
+        const R im[] = { -R(2), -R(1), -R(0.5), -zero, zero, R(0.5), R(1), R(2) };
+        vector_type inputs;
+        inputs.reserve(64 + size);
+        for (R real : re)
+        {
+            for (R imag : im)
+            {
+                inputs.push_back(value_type(real, imag));
+            }
+        }
+        while (inputs.size() % size != 0)
+        {
+            inputs.push_back(inputs.front());
+        }
+        for (size_t i = 0; i < inputs.size(); i += size)
+        {
+            batch_type in, out, ref;
+            detail::load_batch(in, inputs, i);
+            out = acosh(in);
+            vector_type scalar(size);
+            for (size_t lane = 0; lane < size; ++lane)
+            {
+                scalar[lane] = std::acosh(inputs[i + lane]);
+            }
+            detail::load_batch(ref, scalar, 0);
+            CHECK_BATCH_EQ(ref, out);
+        }
     }
 
     void test_atanh()