https://github.com/python/cpython/commit/a025d4ca99fb4c652465368e0b4eb03cf4b... commit: a025d4ca99fb4c652465368e0b4eb03cf4b316b9 branch: master author: Stefan Krah <skrah@bytereef.org> committer: GitHub <noreply@github.com> date: 2020-02-21T21:27:37+01:00 summary: bpo-39576: docs: set context for decimal arbitrary precision arithmetic (#18594) files: M Doc/library/decimal.rst diff --git a/Doc/library/decimal.rst b/Doc/library/decimal.rst index bcae55eb82178..2a51429bdff5c 100644 --- a/Doc/library/decimal.rst +++ b/Doc/library/decimal.rst @@ -2121,17 +2121,67 @@ Q. Is the CPython implementation fast for large numbers? A. Yes. In the CPython and PyPy3 implementations, the C/CFFI versions of the decimal module integrate the high speed `libmpdec <https://www.bytereef.org/mpdecimal/doc/libmpdec/index.html>`_ library for -arbitrary precision correctly-rounded decimal floating point arithmetic. +arbitrary precision correctly-rounded decimal floating point arithmetic [#]_. ``libmpdec`` uses `Karatsuba multiplication <https://en.wikipedia.org/wiki/Karatsuba_algorithm>`_ for medium-sized numbers and the `Number Theoretic Transform <https://en.wikipedia.org/wiki/Discrete_Fourier_transform_(general)#Number-theoretic_transform>`_ -for very large numbers. However, to realize this performance gain, the -context needs to be set for unrounded calculations. +for very large numbers. - >>> c = getcontext() - >>> c.prec = MAX_PREC - >>> c.Emax = MAX_EMAX - >>> c.Emin = MIN_EMIN +The context must be adapted for exact arbitrary precision arithmetic. :attr:`Emin` +and :attr:`Emax` should always be set to the maximum values, :attr:`clamp` +should always be 0 (the default). Setting :attr:`prec` requires some care. -.. versionadded:: 3.3 \ No newline at end of file +The easiest approach for trying out bignum arithmetic is to use the maximum +value for :attr:`prec` as well [#]_:: + + >>> setcontext(Context(prec=MAX_PREC, Emax=MAX_EMAX, Emin=MIN_EMIN)) + >>> x = Decimal(2) ** 256 + >>> x / 128 + Decimal('904625697166532776746648320380374280103671755200316906558262375061821325312') + + +For inexact results, :attr:`MAX_PREC` is far too large on 64-bit platforms and +the available memory will be insufficient:: + + >>> Decimal(1) / 3 + Traceback (most recent call last): + File "<stdin>", line 1, in <module> + MemoryError + +On systems with overallocation (e.g. Linux), a more sophisticated approach is to +adjust :attr:`prec` to the amount of available RAM. Suppose that you have 8GB of +RAM and expect 10 simultaneous operands using a maximum of 500MB each:: + + >>> import sys + >>> + >>> # Maximum number of digits for a single operand using 500MB in 8 byte words + >>> # with 19 (9 for the 32-bit version) digits per word: + >>> maxdigits = 19 * ((500 * 1024**2) // 8) + >>> + >>> # Check that this works: + >>> c = Context(prec=maxdigits, Emax=MAX_EMAX, Emin=MIN_EMIN) + >>> c.traps[Inexact] = True + >>> setcontext(c) + >>> + >>> # Fill the available precision with nines: + >>> x = Decimal(0).logical_invert() * 9 + >>> sys.getsizeof(x) + 524288112 + >>> x + 2 + Traceback (most recent call last): + File "<stdin>", line 1, in <module> + decimal.Inexact: [<class 'decimal.Inexact'>] + +In general (and especially on systems without overallocation), it is recommended +to estimate even tighter bounds and set the :attr:`Inexact` trap if all calculations +are expected to be exact. + + +.. [#] + .. versionadded:: 3.3 + +.. [#] + .. versionchanged:: 3.9 + This approach now works for all exact results except for non-integer powers. + Also backported to 3.7 and 3.8.