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I've opened this issue to track efforts to improve the quality of the Python/dtoa.c file, which provides Python's string-to-float and float-to-string conversions.
Particular issues in mind (non-exhaustive):
 - do a thorough review and test of _Py_dg_dtoa; this has already
 been done for _Py_dg_strtod (issue 7632, issue 7743), and uncovered
 several problems, including a memory leak, some asserts that were
 triggered in debug mode, and many cases of wrong output. 
 - break out the parsing code from _Py_dg_strtod into a separate
 function, for clarity and maintainability (and possible re-use
 of the parsing code itself)
 - improve _Py_dg_strtod tests, by using contined-fractions to generate
 and test particularly difficult cases.
 - _Py_dg_strtod silently gives wrong results for huge inputs; while
 not particular serious, this is easily avoidable.
 - improve API to rely on errno less.
 - some pieces of code are currently unused; improve code coverage
 and tests to identify thoses pieces and remove them.
 - the current code is convoluted in places and hard to explain;
 at least some extra comments should be added.
 - try to make Python/dtoa.c as Python-agnostic as possible, so that
 the code can be reused in other projects where desired.