Refactor math module to use C99+ special functions (erf, erfc, etc)

[skirpichev]

The PEP 7 documents, that we must use C11 (without optional features) since CPython 3.11. erf, erfc, lgamma and tgamma (math.gamma) are part of the C99 (and mandatory for C11 too).

Probably, it's not a bad idea to get rid of custom implementations of such functions or document why it's present (e.g. for some exotic platform, broken libc implementation, speed optimization, etc). Keep in mind, that this code isn't tested by CI if we optionally include using standard implementations (as for erf with #ifdef HAVE_ERF).

Linked PRs

• gh-101678: refactor the math module to use special functions from c11 #101679
• gh-101678: Merge math_1_to_whatever() and math_1() #101730

[skirpichev]

(@arhadthedev, I think it's more related to the stdlib.)

[arhadthedev]

Should work because:

• starting with 3.11 Building Python now requires [...] Support for IEEE 754 floating point numbers. (Contributed by Victor Stinner in bpo-46917.)

• Wikipedia description of the C11-optional Annex F doesn't mention erf or erfc so it should be supported on all platforms.

[arhadthedev]

I think it's more related to the stdlib.

Tags are about affected directories, not user-visible effect. From descriptions of the labels:

• extension-modules - C modules in the Modules dir
• interpreter-core - Objects, Python, Grammar, and Parser dirs
• stdlib Python modules in the Lib dir

[arhadthedev]

cc @vstinner

[mdickinson]

We've tried this before. The key issue is not availability, but quality. Both when I originally implemented these functions, and when we last tried using the libm versions, the libm versions turned out to be of unacceptably poor quality (cases where the computed results were many millions of ulps out from the correct results).

If you do this, please augment the tests to do very thorough testing of the relevant functions, and then run on all the buildbots. But really, I'd strongly recommend leaving this alone - there's no issue being fixed here. We're only increasing the uncertainty over the quality of the functions.

[mdickinson]

See #70309 for the previous attempt.

[mdickinson]

Probably, it's not a bad idea [...]

The rationale for making changes to stable, working code needs to be a lot stronger than this.

[skirpichev]

the libm versions turned out to be of unacceptably poor quality

Isn't that the case where fixes should be submitted to upstream? Or libm implementations will be of poor quality forever...

there's no issue being fixed here

At least, there is no regular testing.

[arhadthedev]

For history, here is an example from the failed macOS run:

======================================================================
FAIL: test_mtestfile (test.test_math.MathTests.test_mtestfile)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "/Users/runner/work/cpython/cpython/Lib/test/test_math.py", line 2053, in test_mtestfile
    self.fail('Failures in test_mtestfile:\n  ' +
AssertionError: Failures in test_mtestfile:
  lgam0080: lgamma(-0.9999999999999999): expected 36.7368005696771, got 36.25168935623487 (error = 0.485 (6[827](https://github.com/python/cpython/actions/runs/4121854833/jobs/7117957687#step:7:828)3333752865 ulps); permitted error = 1e-15 or 5 ulps)
  lgam0082: lgamma(-1.9999999999999998): expected 35.35050620855721, got 34.9797722396[830](https://github.com/python/cpython/actions/runs/4121854833/jobs/7117957687#step:7:831)3 (error = 0.371 (52176167627355 ulps); permitted error = 1e-15 or 5 ulps)
  lgam0085: lgamma(-99.99999999999999): expected -331.85460524980596, got -331.86198661322277 (error = 0.00738 (129854318490 ulps); permitted error = 1e-15 or 5 ulps)
  lgam0106: lgamma(2.5599[833](https://github.com/python/cpython/actions/runs/4121854833/jobs/7117957687#step:7:834)2785163e+305): expected 1.79769313486231e+308, got inf (not equal)
  lgam0107: lgamma(2.55998332785164e+305): expected 'OverflowError', got inf (not equal)
  lgam0108: lgamma(1.7e+308): expected 'OverflowError', got inf (not equal)
  gam0048: gamma(5.5e-309): expected 'OverflowError', got inf (not equal)
  gam0049: gamma(1e-309): expected 'OverflowError', got inf (not equal)
  gam0050: gamma(1e-323): expected 'OverflowError', got inf (not equal)
  gam0051: gamma(5e-324): expected 'OverflowError', got inf (not equal)
  gam0068: gamma(-5.5e-309): expected 'OverflowError', got -inf (not equal)
  gam0069: gamma(-1e-309): expected 'OverflowError', got -inf (not equal)
  gam0070: gamma(-1e-323): expected 'OverflowError', got -inf (not equal)
  gam0071: gamma(-5e-324): expected 'OverflowError', got -inf (not equal)
  gam0103: gamma(171.625): expected 'OverflowError', got inf (not equal)
  gam0104: gamma(172.0): expected 'OverflowError', got inf (not equal)
  gam0105: gamma(2000.0): expected 'OverflowError', got inf (not equal)
  gam0106: gamma(1.7e+308): expected 'OverflowError', got inf (not equal)
  gam0122: gamma(-170.5): expected -3.3127395215386074e-308, got -3.312739521538751e-308 (error = 1.44e-321 (291 ulps); permitted error = 0 or 20 ulps)

[arhadthedev]

For Windows (x64):

======================================================================
FAIL: test_mtestfile (test.test_math.MathTests.test_mtestfile)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "D:\a\cpython\cpython\Lib\test\test_math.py", line 2053, in test_mtestfile
    self.fail('Failures in test_mtestfile:\n  ' +
AssertionError: Failures in test_mtestfile:
  lgam0085: lgamma(-99.99999999999999): expected -331.85460524980596, got -331.8619866132228 (error = 0.00738 (129854318491 ulps); permitted error = 1e-15 or 5 ulps)
  gam0085: gamma(-99.99999999999999): expected 7.540083334884096e-145, got 7.484632144060727e-145 (error = 5.55e-147 (38979707393610 ulps); permitted error = 0 or 20 ulps)
  gam0124: gamma(-176.5): expected -1.196e-321, got 0.0 (error = 1.2e-321 (243 ulps); permitted error = 0 or 20 ulps)

For Windows (x86):

======================================================================
FAIL: test_mtestfile (test.test_math.MathTests.test_mtestfile)
----------------------------------------------------------------------
Traceback (most recent call last):
  File "D:\a\cpython\cpython\Lib\test\test_math.py", line 2053, in test_mtestfile
    self.fail('Failures in test_mtestfile:\n  ' +
AssertionError: Failures in test_mtestfile:
  lgam0085: lgamma(-99.99999999999999): expected -331.85460524980596, got -331.8619866132228 (error = 0.00738 (129854318491 ulps); permitted error = 1e-15 or 5 ulps)
  gam0085: gamma(-99.99999999999999): expected 7.540083334884096e-145, got 7.484632144060727e-145 (error = 5.55e-147 (389797073[936](https://github.com/python/cpython/actions/runs/4121854833/jobs/7117957822#step:5:936)10 ulps); permitted error = 0 or 20 ulps)
  gam0124: gamma(-176.5): expected -1.196e-321, got 0.0 (error = 1.2e-321 (243 ulps); permitted error = 0 or 20 ulps)
----------------------------------------------------------------------

[skirpichev]

Yes, that's from that 5+ old PR, right? But not for erf/erfc.

[arhadthedev]

Unfortunately, that's from your PR: https://github.com/python/cpython/actions/runs/4121854833. It seems that C standard library implementations didn't get better.

However, erf really has no flaws here.

[skirpichev]

Indeed. Could we test the first commit only too?

[mdickinson]

Isn't that the case where fixes should be submitted to upstream?

Good luck with that. Upstream often isn't open source. I've certainly made bug reports on these topics upstream in the past, with typically zero response.

[mdickinson]

At least, there is no regular testing.

True - for erf and erfc, we're never not going to be using the libm versions on current platforms, and it seems that using the libm versions hasn't caused error reports in recent years. It does seem reasonable to drop the custom implementations there.

For gamma and lgamma, let's add a note to the source (possibly referencing the relevant GitHub issues / PRs) that explains why we're using a custom implementation.

[skirpichev]

True - for erf and erfc

It seems, also for log2.

[mdickinson]

It seems, also for log2.

Yes, agreed; we should be able to assume that HAVE_LOG2 is always defined at this point.

[mdickinson]

Closed by #101678 #101679.

[mdickinson]

@erlend-aasland Gah. Thanks! I'll edit the message.