[lang] [refactor] deprecate @boardcast_if_scalar, all use @binary and @unary

[archibate]

Related issue = #937 (comment)

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[archibate]

========================================= FAILURES ==========================================
_____________________________________ test_mat_inverse ______________________________________
[gw2] linux -- Python 3.8.2 /usr/bin/python3

    def test_mat_inverse():
        for n in range(1, 5):
>           _test_mat_inverse_size(n)

tests/python/test_linalg.py:129: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
python/taichi/lang/__init__.py:351: in wrapped
    test(*test_args, **test_kwargs)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

n = 2

    @ti.all_archs
    def _test_mat_inverse_size(n):
        m = ti.Matrix(n, n, dt=ti.f32, shape=())
        M = np.empty(shape=(n, n), dtype=np.float32)
        for i in range(n):
            for j in range(n):
                M[i, j] = i * j + i * 3 + j + 1 + int(i == j) * 4
        assert np.linalg.det(M) != 0
    
        m.from_numpy(M)
    
        @ti.kernel
        def invert():
            m[None] = ti.inversed(m[None])
    
        invert()
    
        m_np = m.to_numpy()
>       np.testing.assert_almost_equal(m_np, np.linalg.inv(M))
E       AssertionError: 
E       Arrays are not almost equal to 7 decimals
E       
E       Mismatched elements: 1 / 4 (25%)
E       Max absolute difference: 0.11337869
E       Max relative difference: 0.95238096
E        x: array([[ 0.2380952, -0.047619 ],
E              [-0.0952381,  0.0056689]], dtype=float32)
E        y: array([[ 0.2380952, -0.047619 ],
E              [-0.0952381,  0.1190476]], dtype=float32)

tests/python/test_linalg.py:124: AssertionError
========================= 1 failed, 355 passed in 90.75s (0:01:30) ==========================

Why fail?

[archibate]

I found why: cannot self assign. If I change to y[None] = ti.inversed(m[None] the problem gone.

[archibate]

Have to sleep to prevent a class drop, I believe CI will pass and you will like these changes, cutmr.
Update: opengl failed on pow:

========================================= FAILURES ==========================================
_______________________________________ test_pow_i32 ________________________________________
[gw2] linux -- Python 3.8.2 /usr/bin/python3

    @ti.all_archs
    def test_pow_i32():
>       _test_pow_i(ti.i32)

tests/python/test_pow.py:43: 
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

dt = DataType.int32

    def _test_pow_i(dt):
        z = ti.var(dt, shape=())
    
        @ti.kernel
        def func(x: dt, y: ti.template()):
            z[None] = x**y
    
        for x in range(-5, 5):
            for y in range(0, 4):
                func(x, y)
>               assert z[None] == x**y
E               assert 124 == -125
E                 -124
E                 +-125

tests/python/test_pow.py:27: AssertionError
=============================== 1 failed, 3 passed in 10.05s ================================

Will fix tmr.

[yuanming-hu]

Looks good in general! Just some minor issues.

[yuanming-hu]

Not sure what this means...sorry.

[archibate]

Because GLSL doesn't provide pow(int, int), it only provide pow(float, float), so:

pow(4.999, 3) = 124
pow(5.001, 3) = 125

And due to binary floating-point problems, 5 becames 4.99, therefore:

pow(5, 4) = 124

[yuanming-hu]

Sounds good. (Btw should the comment be something like "prevent integer operands in pow in GLSL")?

[archibate]

Because it's the same case with floordiv... let's say prevent integer operands in pow and floordiv in GLSL then.

[archibate]

@k-ye I'm merging this now to prevent further conflict. Please try this out when you are free.

[k-ye]

I can confirm that sdf_renderer.py is running fast again, thanks!