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author | Raghuveer Devulapalli <raghuveer.devulapalli@intel.com> | 2019-03-20 15:12:50 -0700 |
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committer | Raghuveer Devulapalli <raghuveer.devulapalli@intel.com> | 2019-08-03 10:48:43 -0700 |
commit | bd2c82bf141852b4737da297c081e5f621604317 (patch) | |
tree | db9b0bf70cabe5fb3199f5fa3b9693de841c0b8c /numpy/lib/recfunctions.py | |
parent | 71c8a1030d5a32342edc2e2311cb71dc38a7374e (diff) | |
download | numpy-bd2c82bf141852b4737da297c081e5f621604317.tar.gz |
ENH: Use AVX for float32 implementation of np.sin & np.cos
This commit implements vectorized single precision sine and cosine using
AVX2 and AVX512. Both sine and cosine are computed using a
polynomial approximation which are accurate for values between
[-PI/4,PI/4]. The original input is reduced to this range using a 3-step
Cody-Waite's range reduction method. This method is only accurate for
values between [-71476.0625f, 71476.0625f] for cosine and [-117435.992f,
117435.992f] for sine. The algorithm identifies elements outside this
range and calls glibc in a scalar loop to compute their output.
The algorithm is a vectorized version of the methods presented
here: https://stackoverflow.com/questions/30463616/payne-hanek-algorithm-implementation-in-c/30465751#30465751
Accuracy: maximum ULP error = 1.49
Performance: The speed-up this implementation provides is dependent on
the values of the input array. It performs best when all the input
values are within the range specified above. Details of the performance
boost are provided below. Its worst performance is when all the array
elements are outside the range leading to about 1-2% reduction in
performance.
Three different benchmarking data are provided, each of which was benchmarked
using timeit package in python. Each function is executed 1000 times and
this is repeated 100 times. The standard deviation for all the runs was
less than 2% of their mean value and hence not included in the data.
(1) Micro-bencharking:
Array size = 10000, Command = "%timeit np.cos([myarr])"
|---------------+------------+--------+---------+----------+----------|
| Function Name | NumPy 1.16 | AVX2 | AVX512 | AVX2 | AVX512 |
| | | | | speed up | speed up |
|---------------+------------+--------+---------+----------+----------|
| np.cos | 1.5174 | 0.1553 | 0.06634 | 9.77 | 22.87 |
| np.sin | 1.4738 | 0.1517 | 0.06406 | 9.71 | 23.00 |
|---------------+------------+--------+---------+----------+----------|
(2) Package ai.cs provides an API to transform spherical coordinates to
cartesean system:
Array size = 10000, Command = "%timeit ai.cs.sp2cart(r,theta,phi)"
|---------------+------------+--------+--------+----------+----------|
| Function Name | NumPy 1.16 | AVX2 | AVX512 | AVX2 | AVX512 |
| | | | | speed up | speed up |
|---------------+------------+--------+--------+----------+----------|
| ai.cs.sp2cart | 0.6371 | 0.1066 | 0.0605 | 5.97 | 10.53 |
|---------------+------------+--------+--------+----------+----------|
(3) Package photutils provides an API to find the best fit of first and
second harmonic functions to a set of (angle, intensity) pairs:
Array size = 1000, Command = "%timeit fit_first_and_second_harmonics(E, data)"
|--------------------------------+------------+--------+--------+----------+----------|
| Function Name | NumPy 1.16 | AVX2 | AVX512 | AVX2 | AVX512 |
| | | | | speed up | speed up |
|--------------------------------+------------+--------+--------+----------+----------|
| fit_first_and_second_harmonics | 1.598 | 0.8709 | 0.7761 | 1.83 | 2.05 |
|--------------------------------+------------+--------+--------+----------+----------|
Diffstat (limited to 'numpy/lib/recfunctions.py')
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