如果参数大小大于 8192，为什么 numpy.sin 会返回不同的结果? [英] Why does numpy.sin return a different result if the argument size is greater than 8192?

问题描述

我发现当参数大小为 <= 8192 和 > 8192 时，numpy.sin 的行为不同.不同之处在于性能和返回的值.有人能解释一下这种效果吗?

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?

例如，让我们计算 sin(pi/4):

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

超过 8192 个元素限制后，计算速度提高了 3 倍以上，并给出了不同的结果:最后一位数字变为 5 而不是 6.

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.

当我尝试以其他方式计算相同的值时:

When I tried to calculate the same value in other ways I obtained:

• C++ std::sin(Visual Studio 2017，Win32 平台)给出 0.7071067811865475；
• C++ std::sin(Visual Studio 2017，x64 平台)给出 0.70710678118654756；
• math.sin 给出 0.7071067811865476，这是合乎逻辑的，因为我使用的是 64 位 Python.

• C++ std::sin (Visual Studio 2017, Win32 platform) gives 0.7071067811865475;
• C++ std::sin (Visual Studio 2017, x64 platform) gives 0.70710678118654756;
• math.sin gives 0.7071067811865476, which is logical because I used 64-bit Python.

我在 NumPy 文档及其代码中都找不到任何解释.

I couldn't find any explanation in the NumPy documentation, nor in its code.

更新 #2:很难相信，但是将 sin 替换为 sqrt 给出了这样的结果:

Update #2: It is hard to believe, but replacing sin by sqrt gives this:

44.2 µs ± 751 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
8191 0.8862269254527579
44.1 µs ± 543 ns per loop (mean ± std. dev. of 7 runs, 10000 loops each)
8192 0.8862269254527579
10.3 µs ± 105 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
8193 0.886226925452758
10.4 µs ± 4.41 ns per loop (mean ± std. dev. of 7 runs, 100000 loops each)
8194 0.886226925452758

更新:np.show_config() 输出:

mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/GNU/Anaconda3\Library\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\include', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\lib', 'C:/GNU/Anaconda3\Library\include']
blas_mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/GNU/Anaconda3\Library\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\include', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\lib', 'C:/GNU/Anaconda3\Library\include']
blas_opt_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/GNU/Anaconda3\Library\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\include', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\lib', 'C:/GNU/Anaconda3\Library\include']
lapack_mkl_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/GNU/Anaconda3\Library\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\include', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\lib', 'C:/GNU/Anaconda3\Library\include']
lapack_opt_info:
    libraries = ['mkl_rt']
    library_dirs = ['C:/GNU/Anaconda3\Library\lib']
    define_macros = [('SCIPY_MKL_H', None), ('HAVE_CBLAS', None)]
    include_dirs = ['C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\include', 'C:\Program Files (x86)\IntelSWTools\compilers_and_libraries_2019.0.117\windows\mkl\lib', 'C:/GNU/Anaconda3\Library\include']

推荐答案

正如@WarrenWeckesser 所写，这几乎可以肯定是 Anaconda 和 Intel MKL 的问题；参见 https://github.com/numpy/numpy/issues/11448 和 https://github.com/ContinuumIO/anaconda-issues/issues/9129".

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".

不幸的是，在 Windows 下解决此问题的唯一方法是卸载 Anaconda 并使用另一个具有 MKL-free numpy 的发行版.我使用了 https://www.python.org/ 中的 python-3.6.6-amd64 并安装了所有东西否则通过 pip，包括 numpy 1.14.5.我什至设法让 Spyder 工作(不得不将 PyQt5 降级到 5.11.3，它拒绝在 >= 5.12 上启动).

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).

现在 np.sin(xx) 始终为 0.7071067811865476(n = 8192 时为 67.1 µs)和 np.sqrt(xx) 0.8862269254527579(16.4 微秒).有点慢，但完全可以重现.

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.

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