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Select the principal branch of complex acosh in both half-planes #1436

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Select the principal branch of complex acosh in both half-planes #1436

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3 changes: 1 addition & 2 deletions include/xsimd/arch/common/xsimd_common_trigo.hpp
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Expand Up @@ -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
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37 changes: 37 additions & 0 deletions test/test_complex_hyperbolic.cpp
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Expand Up @@ -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