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      "title": "remove import-time 'exec' calls from polynomial (Trac #2181)",
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      "body": "_Original ticket http://projects.scipy.org/numpy/ticket/2181 on 2012-07-06 by trac user dalke, assigned to @charris._\n\nnumpy/polynomial/*.py contains 5 files which do an 'exec' of a ~25K template, generated at import-time. The extra overhead of parsing and byte-compiling takes roughly 25% of the entire 'import numpy' overhead.\n\nI changed the code so it's the responsibility of the person who edits the template to rerun the 'polytemplate.py' file as a command-line program. This then goes through the correct files to find the special markers which indicate where the template should be inserted, get the file-specific parameters, apply those to the template, and replacing the old code which was between the two markers with the newly evaluated template output.\n\nIn more details, currently there are 5 places under numpy/polynomial which do something like:\n\n  exec polytemplate.substitute(name='Hermite', nick='herm', domain='[-1,1]')\n\nI have changed those so there are start/end markers, like\n# REPLACE POLYTEMPLATE name='Hermite', nick='herm', domain='[-1,1]'\n\n  ...\n# END REPLACE\n\nI have edited  polytemplate.py so that it implements a **main** which finds those block markers and replaces the content with the appropriate \"polytemplate\" substitution.\n\nThe performance of \n\n```\npython -c 'import time; t1=time.time(); import numpy; print time.time()-t1'\n```\n\ngoes from 0.079 seconds to 0.057 seconds (best of 10), for an import speedup of ~25%. \n",
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      "body": "_Original ticket http://projects.scipy.org/numpy/ticket/2208 on 2012-08-28 by trac user smeared ink, assigned to @charris._\n\nI am very new to evaluating Chebyshev polynomials, but shouldn't chebval subtract off 0.5*(first coefficient), as in Numerical Recipes, or here?: http://mathworld.wolfram.com/ChebyshevApproximationFormula.html (which cites Numerical Recipes, actually).\n\nI was finding unexpected differences in how numpy evaluated Chebyshev polynomials from some code I was trying to replicate, and I traced it back to this little thing.\n",
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      "body": "In most of the functions in polynomial.polynomial you can read this line:\n\n```\n>>> from numpy import polynomial as P\n```\n\nand then:\n\n```\n>>> P.polyline(1,-1)\n>>> sum = P.polyadd(c1,c2); sum\n>>> P.polysub(c1,c2)\n>>> P.polyder(c) # (d/dx)(c) = 2 + 6x + 12x**2\n[...]\n```\n\nhttps://g<response clipped><NOTE>Due to the max output limit, only part of the full response has been shown to you.</NOTE>p.array([1.59255172, 1.552, 1.49986207, 1.45186207, 1.39972414, 1.35337931, 1.30124138, 1.28717241, 1.25241379, 1.20855172, 1.20027586, 1.15227586, 1.10013793, 1.05213793, 1.03806897, 1.0, 0.952, 0.90565517])\r\n\r\ndegree = 3\r\nf = Polynomial.fit(x, y, degree)\r\ng = Polynomial(np.polyfit(x, y, degree)[::-1])\r\n\r\nprint(f\"f(x) = {f}\")\r\nprint(f\"g(x) = {g}\")\r\n\r\nplt.plot(x, y, 'o')\r\nxx, yy = f.linspace()\r\nplt.plot(xx, yy, lw=2, label='f(x)')\r\nxxx, yyy = g.linspace()\r\nplt.plot(xxx, yyy, lw=2, label='g(x)')\r\nplt.legend()\r\nplt.show()\n```\n\n\n### Error message:\n\n_No response_\n\n### Runtime information:\n\n>>> import sys, numpy; print(numpy.__version__); print(sys.version)\r\n1.25.2\r\n3.11.4 (tags/v3.11.4:d2340ef, Jun  7 2023, 05:45:37) [MSC v.1934 64 bit (AMD64)]\r\n>>> print(numpy.show_runtime())\r\n[{'numpy_version': '1.25.2',\r\n  'python': '3.11.4 (tags/v3.11.4:d2340ef, Jun  7 2023, 05:45:37) [MSC v.1934 '\r\n            '64 bit (AMD64)]',\r\n  'uname': uname_result(system='Windows', node='KPC22026425', release='10', version='10.0.19045', machine='AMD64')},\r\n {'simd_extensions': {'baseline': ['SSE', 'SSE2', 'SSE3'],\r\n                      'found': ['SSSE3',\r\n                                'SSE41',\r\n                                'POPCNT',\r\n                                'SSE42',\r\n                                'AVX',\r\n                                'F16C',\r\n                                'FMA3',\r\n                                'AVX2'],\r\n                      'not_found': ['AVX512F',\r\n                                    'AVX512CD',\r\n                                    'AVX512_SKX',\r\n                                    'AVX512_CLX',\r\n                                    'AVX512_CNL',\r\n                                    'AVX512_ICL']}},\r\n {'architecture': 'Haswell',\r\n  'filepath': 'C:\\\\Users\\\\olejeh\\\\testing\\\\ultra_battery_tuning\\\\venv\\\\Lib\\\\site-packages\\\\numpy\\\\.libs\\\\libopenblas64__v0.3.23-246-g3d31191b-gcc_10_3_0.dll',\r\n  'internal_api': 'openblas',\r\n  'num_threads': 12,\r\n  'prefix': 'libopenblas',\r\n  'threading_layer': 'pthreads',\r\n  'user_api': 'blas',\r\n  'version': '0.3.23.dev'}]\r\nNone\n\n### Context for the issue:\n\n_No response_",
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      "body": "### Describe the issue:\n\nHi,\n\nFor a research paper, we carried out a large-scale benchmark of [Pynguin](https://www.pynguin.eu/), an Automatic Unit Test Generation Tool for Python, to test its new feature that can find Python interpreter crashes. In this benchmark, we found a potential bug in numpy, and we are reporting this issue.\n\nThe example was run with the command `python -X faulthandler <test>` to dump the traceback.\n\n### Reproduce the code example:\n\n```python\nimport numpy.polynomial.legendre as legendre\n\nlegendre.legder((\"0\", \"0\"), scl=20)\n```\n\n### Error message:\n\n```shell\nFatal Python error: Segmentation fault\n\nCurrent thread 0x00007f3e28300bc0 [python] (most recent call first):\n  Garbage-collecting\n  <no Python frame>\n\nCurrent thread's C stack trace (most recent call first):\n  Binary file \"/lib64/libpython3.14.so.1.0\", at _Py_DumpStack+0x4c [0x7f3e27d213fa]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at +0x121e7e [0x7f3e27d21e7e]\n  Binary file \"/lib64/libc.so.6\", at +0x1a2c0 [0x7f3e27a262c0]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at +0x1facd8 [0x7f3e27dfacd8]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at +0x183bf9 [0x7f3e27d83bf9]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at +0x1fab68 [0x7f3e27dfab68]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at +0x1fa12a [0x7f3e27dfa12a]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at +0x25ed69 [0x7f3e27e5ed69]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at +0x27fcd1 [0x7f3e27e7fcd1]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at Py_RunMain+0x231 [0x7f3e27e52401]\n  Binary file \"/lib64/libpython3.14.so.1.0\", at Py_BytesMain+0x3b [0x7f3e27e4c75b]\n  Binary file \"/lib64/libc.so.6\", at +0x35b5 [0x7f3e27a0f5b5]\n  Binary file \"/lib64/libc.so.6\", at __libc_start_main+0x88 [0x7f3e27a0f668]\n  Binary file \"python\", at _start+0x25 [0x55c7863453d5]\n\nExtension modules: numpy._core._multiarray_umath, numpy.linalg._umath_linalg (total: 2)\nSegmentation fault         (core dumped)\n```\n\n### Python and NumPy Versions:\n\n2.4.0\n3.14.0 (main, Oct 17 2025, 00:00:00) [GCC 15.2.1 20251022 (Red Hat 15.2.1-3)]\n\n### Runtime Environment:\n\n[{'numpy_version': '2.4.0',\n  'python': '3.14.0 (main, Oct 17 2025, 00:00:00) [GCC 15.2.1 20251022 (Red '\n            'Hat 15.2.1-3)]',\n  'uname': uname_result(system='Linux', node='lucas-hp', release='6.17.10-300.fc43.x86_64', version='#1 SMP PREEMPT_DYNAMIC Mon Dec  1 14:59:36 UTC 2025', machine='x86_64')},\n {'simd_extensions': {'baseline': ['X86_V2'],\n                      'found': ['X86_V3'],\n                      'not_found': ['X86_V4', 'AVX512_ICL', 'AVX512_SPR']}},\n {'ignore_floating_point_errors_in_matmul': False},\n {'architecture': 'Haswell',\n  'filepath': '/home/lucas/Documents/crashes/.venv/lib/python3.14/site-packages/numpy.libs/libscipy_openblas64_-fdde5778.so',\n  'internal_api': 'openblas',\n  'num_threads': 12,\n  'prefix': 'libscipy_openblas',\n  'threading_layer': 'pthreads',\n  'user_api': 'blas',\n  'version': '0.3.30'}]\n\n### How does this issue affect you or how did you find it:\n\nIt's not a serious problem, but we thought it was important to at least warn you that this behaviour exists, so that you can take the action that suits you best.",
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      "body": "### Proposed new feature or change:\n\nI have a need for a function `polyvalnd` which is just like `polyval`, `polyval2d`, or `polyval3d`, but that handles arbitrary dimensions. Surprisingly this function does not already exist in Numpy. It is trivial to implement with existing non-public utilities in Numpy, i.e.,\n\n```python\nfrom numpy.polynomial import polyutils as pu\nfrom numpy.polynomial.polynomial import polyval\n\n\ndef polyvalnd(x, c):\n    \"\"\"Evaluate an arbitrary multivariate polynomial.\"\"\"\n    return pu._valnd(polyval, c, *x)\n```\n\nOf course there is a decision to make about the signature, because with `polyval2d` and `polyval3d` the arguments are passed like this:\n\n```python\npolyval2d(x, y, c)\npolyval3d(x, y, c)\n```\n\nSo we would have to decide which of these we prefer:\n\n```python\npolyvalnd(p, q, ..., x, y, z, c)  # ordinates first\npolyvalnd(c, p, q, ..., x, y, z)  # ordinates last\npolyvalnd([p, q, ..., x, y, z], c)  # ordinates first, in an list\n```\n\nThis has been suggested before in #6071, but my needs are much narrower: I don't need N-D Chebyshev polynomials, etc.\n\nMy application is that I need some multivariate polynomial test data for a multivariate interpolation scheme that I am working on with a student.",
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