Add gamma function, error functions and other C99 math.h functions to math module

[terryjreedy]

BPO	3366
Nosy	@tim-one, @rhettinger, @terryjreedy, @mdickinson, @ned-deily, @stevendaprano
Files	math_private.h: header for erf, erfc, lgamma and tgamma pymath.c.diff mathmodule.c.diff pymath.h.diff test_math.py.diff math.rst.diff mathmodule.diff: patch for erf, erfc, lgamma and gamma pymath.c.diff: erf and gamma patches without math_private.h gamma.patch gamma3.patch: Implementation of math.gamma gamma4.patch gamma5.patch lgamma1.patch gamma-failures.txt pymath.h.diff: Euler constant mathmodule.c.diff: expm1 erf.py: error function mathmodule.c.diff erf.patch erf_c.patch: Add erf and erfc functions to math module. expm1.patch

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields: ```python assignee = 'https://github.com/mdickinson' closed_at = created_at = labels = ['type-feature', 'library'] title = 'Add gamma function, error functions and other C99 math.h functions to math module' updated_at = user = 'https://github.com/terryjreedy' ``` bugs.python.org fields: ```python activity = actor = 'mark.dickinson' assignee = 'mark.dickinson' closed = True closed_date = closer = 'mark.dickinson' components = ['Library (Lib)'] creation = creator = 'terry.reedy' dependencies = [] files = ['10955', '10973', '10974', '10975', '10976', '10977', '10982', '11005', '14844', '14927', '14940', '14943', '15008', '15152', '15488', '15489', '15490', '15491', '15539', '15540', '15574'] hgrepos = [] issue_num = 3366 keywords = ['patch', 'needs review'] message_count = 54.0 messages = ['69698', '70106', '70108', '70120', '70125', '70128', '70131', '70232', '70233', '70241', '70262', '70266', '70267', '70270', '70361', '70412', '77075', '92294', '92844', '92928', '92935', '92936', '92939', '92944', '92948', '93228', '93370', '93373', '94165', '94166', '94168', '94169', '94170', '94171', '94172', '94175', '94224', '96108', '96109', '96110', '96111', '96266', '96267', '96268', '96332', '96333', '96485', '96497', '96599', '96600', '97127', '97131', '97133', '97160'] nosy_count = 8.0 nosy_names = ['tim.peters', 'rhettinger', 'terry.reedy', 'mark.dickinson', 'ned.deily', 'stutzbach', 'nirinA', 'steven.daprano'] pr_nums = [] priority = 'normal' resolution = None stage = 'commit review' status = 'closed' superseder = None type = 'enhancement' url = 'https://bugs.python.org/issue3366' versions = ['Python 2.7', 'Python 3.2'] ```

[mdickinson]

The last two functions to consider adding are exp2 and log2. Does anyone care about these?

[cfc9f3e0-e33f-4ecd-9ddd-4123842d6c1e]

Any time I've ever needed log2(x), log(x)/log(2) was sufficient.

In Python, exp2(x) can be spelled 2.0**x. What would exp2(x) gain us?

[mdickinson]

In Python, exp2(x) can be spelled 2.0**x. What would exp2(x) gain us?

Not much, I suspect. :)

I'd expect (but am mostly guessing) exp2(x) to have better accuracy than pow(2.0, x) for some math libraries; I'd further guess that it's somewhat more likely to give exact results for (small) integral x.

Similarly for log2: log2(n) should be a touch more accurate than log(n)/log(2), and the time you're most likely to notice the difference is when n is an exact power of 2.

But we've already got the 'bit_length' method for integers, which fills some of the potential uses for log2. So unless there's a feeling that these functions are needed, I'd rather leave them out.

[mdickinson]

Will close this unless there's an outcry of support for exp2 and log2. nirinA, if you're still interested in adding the euler constant, please open another issue.