Expanded math ops

[ShrutheeshIR]

I want more math ops for fancier math. Main changes

1. Add asin, acos and atan inverse trigonometric functions in avx.hh. -- Use cephes implementations from here. Note that I have used _mm256_sqrt_ps ops here instead of the custom defined sqrt(), b/c the precision is pretty poor and acos has differences in the 3rd FP itself.
2. Add them to the interface as well
3. Expanded math.hh to include these ops and other operations that are useful in general

TODO --

• Add them to neon
• Add wasm

Tested it using

    size_t total_tests_failed = 0;
    std::cout << "Check atan2 implementation" << std::endl;
    for (auto i = -10; i <= 10; ++i)
    {
        for (auto j = -10; j <= 10; ++j)
        {
            if (i == 0 && j == 0)
            {
                continue;
            }
            float angle = std::atan2(static_cast<float>(i), static_cast<float>(j));

            // now convert it to a FloatVector<rake> and call atan
            vamp::FloatVector<rake> i_vec;
            i_vec[0] = static_cast<float>(i);
            vamp::FloatVector<rake> j_vec;
            j_vec[0] = static_cast<float>(j);
            auto angle_vec = atan2(i_vec, j_vec);

            if (std::abs(angle - angle_vec[{0, 0}]) > 1e-6)
            {
                std::cout << "Mismatch for (" << i << ", " << j << "): "
                          << "std::atan2 = " << angle << ", "
                          << "FloatVector<rake>::atan2 = " << angle_vec[{0, 0}] << std::endl;
                total_tests_failed++;
            }
        }
    }

    // check acos and asin   
    std::cout << "Check acos and asin implementation" << std::endl;
    for (auto i = -10; i <= 10; ++i)
    {
        float value = static_cast<float>(i) / 10.0f;  // values from -1.0 to 1.0
        if (value < -1.0f || value > 1.0f)
        {
            continue;  // skip out-of-range values
        }
        float angle = std::acos(value);
        float asin_angle = std::asin(value);

        vamp::FloatVector<rake> value_vec;
        value_vec[0] = value;
        auto angle_vec = acos(value_vec);
        auto asin_angle_vec = asin(value_vec);

        if (std::abs(angle - angle_vec[{0, 0}]) > 1e-6)
        {
            std::cout << "Mismatch for " << value << ": "
                      << "std::acos = " << angle << ", "
                      << "FloatVector<rake>::acos = " << angle_vec[{0, 0}] << std::endl;
            total_tests_failed++;
        }
        if (std::abs(asin_angle - asin_angle_vec[{0, 0}]) > 1e-6)
        {
            std::cout << "Mismatch for " << value << ": "
                      << "std::asin = " << asin_angle << ", "
                      << "FloatVector<rake>::asin = " << asin_angle_vec[{0, 0}] << std::endl;
            total_tests_failed++;
        }

    }
    std::cout << "Total tests failed : " << total_tests_failed << std::endl;

PS: The custom implementation of sqrt honestly is pretty bad for most use cases, I think the default behavior should be _mm256_sqrt_ps, and we can expose a sqrt_low_precision for other use cases (eg cc). This is the 2nd time I've wasted a couple of hours tracking down precision issues from my implementation only to realize sqrt is the culprit :(

[ShrutheeshIR]

Codegen can generate blend() ops, good to use it right

[zkingston]

Overall good, please add the NEON and WASM equivalents.

[zkingston]

What's this extra blend instruction?

[ShrutheeshIR]

Just a unified expr for scalar and a vectorized conditional expr
cppad sometimes spits out a
v[14] = blend(v[14], -0.9999, (v[14]) - (-0.9999)); I want to be able to handle that, so I'll just pin it to the datatype of the first arg

[zkingston]

Can you verify the formatting is correct and that all builds pass? Otherwise LGTM.