Faster tan and arctan possible? about pandora HOT 7 CLOSED

CORDIC-like method is ~5x slower (cached table, 60 entries). Accuracy would be sufficient.

Pre-calculate table (takes negligible time):

cordic_table_size = 60
l1 = np.empty(cordic_table_size)
l2 = l1.copy()
for idx in range(cordic_table_size):
    exp = np.exp2(-idx)
    l1[idx] = exp
    l2[idx] = np.arctan(exp)

Call function (too slow):

@jit(cache=False, nopython=True, fastmath=True)
def arctan_cordic(y, l1, l2, x=1.0):
    r = 0.0
    for idx in range(len(l1)):
        if y < 0:
            r, x, y = r - l2[idx], x - l1[idx]*y, y + l1[idx]*x
        else:
            r, x, y = r + l2[idx], x + l1[idx]*y, y - l1[idx]*x
    return r

from pandora.

20x faster with new numpy
numpy/numpy#19478

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New numpy with AVX512 not released yet
Will make only Intel CPUs faster (and future AMD if they get AVX512?), and currently only on Linux
Installed numpy dev from source
have to modify "setup.py" with version numbers (lines 60ff)
then pip install .
Own test for 1m linspace values artcan: 1s vs 0.2s (~5x)
In new env: numba installs (old) numpy --> install all else first, then new numpy version
Problem: numba requires version >1.17 <1.20
Can change, but is linked to github version (hard to change)(
not sure if it would break numba
easier to extract arctan source?

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Will be released with Numpy 1.22 https://numpy.org/devdocs/release/1.22.0-notes.html

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Can switch off numba warning in__init__.py
for ellipse_pos_iter: is hardly faster (9.18 vs 8.96)
for ellipse_pos: (10.92 8.01) vs (7.82 7.91)

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Try CUDA https://numba.discourse.group/t/cant-use-basic-numpy-functions-with-cuda-like-zeros-or-empty/628/3

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It takes ~0.1ms to transfer data from CPU to GPU and back, i.e. <10k models/sec even at zero model calc time
==> not worth using GPU (or only in vectorized case which is hard to implement)

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