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Preserve real-axis branches in complex asin and acos #1437

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Preserve real-axis branches in complex asin and acos #1437

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5 changes: 3 additions & 2 deletions include/xsimd/arch/common/xsimd_common_trigo.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -141,8 +141,9 @@ 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);
}

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44 changes: 44 additions & 0 deletions test/test_complex_trigonometric.cpp
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Original file line number Diff line number Diff line change
Expand Up @@ -124,6 +124,10 @@ struct complex_trigonometric_test
detail::load_batch(ref, expected, i);
CHECK_BATCH_EQ(ref, out);
}
check_real_axis([](const batch_type& z)
{ return asin(z); },
[](const value_type& v)
{ return std::asin(v); });
}

void test_acos()
Expand All @@ -139,6 +143,10 @@ struct complex_trigonometric_test
detail::load_batch(ref, expected, i);
CHECK_BATCH_EQ(ref, out);
}
check_real_axis([](const batch_type& z)
{ return acos(z); },
[](const value_type& v)
{ return std::acos(v); });
}

void test_atan()
Expand All @@ -157,6 +165,42 @@ struct complex_trigonometric_test
}

private:
template <class BatchFn, class ScalarFn>

@DiamonDinoia DiamonDinoia Nov 11, 2026

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I would do this:

template <class BatchFn, class ScalarFn>
void check_real_axis(BatchFn batch_fn, ScalarFn scalar_fn)
{
    using R = real_value_type;
    const R outside = std::nextafter(R(1), R(2));
    const std::array<R, 8> re = { -R(4), -outside, -R(1), -R(0), R(0), R(1), outside, R(4) };
    const std::array<R, 8> im = { -R(2), -R(1), -R(0.5), -R(0), R(0), R(0.5), R(1), R(2) };
    const std::size_t n = re.size() * im.size();

    // Round up to a multiple of `size`. The tail stays value_type(0, 0),
    // which is already in the grid.
    vector_type inputs((n + size - 1) / size * size);
    auto it = inputs.begin();
    for (R real : re)
    {
        for (R imag : im)
        {
            *it++ = value_type(real, imag);
        }
    }

    vector_type expected(inputs.size());
    std::transform(inputs.cbegin(), inputs.cend(), expected.begin(), scalar_fn);

    for (std::size_t i = 0; i < inputs.size(); i += size)
    {
        batch_type in, ref;
        detail::load_batch(in, inputs, i);
        detail::load_batch(ref, expected, i);
        CHECK_BATCH_EQ(ref, batch_fn(in));
    }
}

void check_real_axis(BatchFn batch_fn, ScalarFn scalar_fn)
{
using R = real_value_type;
const R zero(0);
const R outside = std::nextafter(R(1), R(2));
const R re[] = { -R(4), -outside, -R(1), -zero, zero, R(1), outside, 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 = batch_fn(in);
vector_type scalar(size);
for (size_t lane = 0; lane < size; ++lane)
{
scalar[lane] = scalar_fn(inputs[i + lane]);
}
detail::load_batch(ref, scalar, 0);
CHECK_BATCH_EQ(ref, out);
}
}

void test_tan_impl()
{
std::transform(input.cbegin(), input.cend(), expected.begin(),
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