Avoid NaN real components in complex tanh after overflow

include/xsimd/arch/common/xsimd_common_trigo.hpp

@@ -986,7 +986,11 @@ namespace xsimd
             auto y = z.imag();
             real_batch two(2);
             auto d = cosh(two * x) + cos(two * y);
-            return { sinh(two * x) / d, sin(two * y) / d };
+            auto real_part = sinh(two * x) / d;
+#ifndef __FAST_MATH__
+            real_part = select(isinf(d), copysign(real_batch(1), x), real_part);
+#endif
+            return { real_part, sin(two * y) / d };
         }
 
     }

test/test_complex_hyperbolic.cpp

@@ -91,6 +91,41 @@ struct complex_hyperbolic_test
             detail::load_batch(ref, expected, i);
             CHECK_BATCH_EQ(ref, out);
         }
+
+#ifndef __FAST_MATH__
+        // Fast-math drops overflow recovery and does not match std::tanh.
+        using R = real_value_type;
+        const R zero(0);
+        const R huge = std::is_same_v<R, float> ? R(45) : R(356);
+        const R re[] = { -huge, -R(20), -R(1), -zero, zero, R(1), R(20), huge };
+        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 = tanh(in);
+            vector_type scalar(size);
+            for (size_t lane = 0; lane < size; ++lane)
+            {
+                scalar[lane] = std::tanh(inputs[i + lane]);
+            }
+            detail::load_batch(ref, scalar, 0);
+            CHECK_BATCH_EQ(ref, out);
+        }
+#endif
     }
 
     void test_asinh()