Why does numpy.sin return a different result if the argument size is greater than 8192?

Question

I discovered that `numpy.sin` behaves differently when the argument size is <= 8192 and when it is > 8192. The difference is in both performance and values returned. Can someone explain this effect? For example, let's calculate sin(pi/4): ``` x = np.pi*0.25 for n in range(8191, 8195): xx = np.repeat(x, n) %timeit np.sin(xx) print(n, np.sin(xx)[0]) ``` ``` 64.7 µs ± 194 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each) 8191 0.7071067811865476 64.6 µs ± 166 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each) 8192 0.7071067811865476 20.1 µs ± 189 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each) 8193 0.7071067811865475 21.8 µs ± 13.4 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each) 8194 0.7071067811865475 ``` After crossing the 8192 elements limit the calculations become more than 3 times faster and give a different result: the last digit becomes 5 instead of 6. When I tried to calculate the same value in other ways I obtained: - C++ `std::sin` (Visual…

Accepted Answer

As @WarrenWeckesser wrote, "it's almost certainly an Anaconda & Intel MKL issue; cf. https://github.com/numpy/numpy/issues/11448 and https://github.com/ContinuumIO/anaconda-issues/issues/9129".

And unfortunately, the only way to solve the issue under Windows is to uninstall Anaconda and use another distribution with MKL-free `numpy`. I used python-3.6.6-amd64 from https://www.python.org/ and installed everything else via `pip`, including numpy 1.14.5. I even managed to make Spyder work (had to downgrade PyQt5 to 5.11.3, it refused to launch on >= 5.12).

Now `np.sin(xx)` is consistently 0.7071067811865476 (67.1 µs at `n = 8192`) and `np.sqrt(xx)` 0.8862269254527579 (16.4 µs). A bit slower, but perfectly reproducible.

Why does numpy.sin return a different result if the argument size is greater than 8192?

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