Arbitrary-precision correctly-rounded floating-point arithmetic, via MPFR.

## Project description

The bigfloat package is a Python package providing arbitrary-precision correctly-rounded binary floating-point arithmetic. It is implemented as a Cython wrapper around the GNU MPFR library. A couple of lines of Python code should give the idea:

>>> from bigfloat import * >>> with precision(200) + RoundTowardZero: ... print(sqrt(2)) ... 1.4142135623730950488016887242096980785696718753769480731766796 >>> with quadruple_precision: ... const_pi() ... BigFloat.exact('3.14159265358979323846264338327950280', precision=113)

## Features

Supports Python 2 (version 2.7) and Python 3 (version 3.5 or later).

Exactly reproducible correctly-rounded results across platforms; precisely-defined semantics compatible with the IEEE 754-2008 standard.

Support for mixed-type operations with Python integers and floats.

Support for emulating IEEE 754 arithmetic in any of the IEEE binary interchange formats described in IEEE 754-2008. Infinities, NaNs, signed zeros, and subnormals are all supported.

Easy control of rounding modes and precisions via Context objects and Python’s with statement.

## Documentation

Full package documentation is hosted at Read the Docs. Read on for a quick tour.

## A quick tour

The bigfloat package is small and simple to use. Here’s a quick tour of some of its features.

For demonstration purposes, start with:

>>> from bigfloat import *

Note that this import shadows some builtin Python functions, namely abs, max, min, pow, round and (on Python 2 only) cmp. In normal usage you’ll probably only want to import the classes and functions that you actually need.

The main class is the BigFloat class:

>>> BigFloat(1) # can be constructed from an integer, float or string BigFloat.exact('1.0000000000000000', precision=53) >>> BigFloat('3.14159') ** 2 / 6.0 # can combine with ints and floats BigFloat.exact('1.6449312880166664', precision=53) >>> BigFloat('0.1', precision(200)) # high-precision value from string BigFloat.exact('0.1000000000000000000000000000000000000000000000000000 0000000002', precision=200)

Newly-created BigFloat instances refer to the current *context* to
determine what precision and rounding modes to use. This current
context is represented by a Context instance, and can be retrieved
by calling getcontext:

>>> getcontext() Context(precision=53, emax=1073741823, emin=-1073741823, subnormalize=False, rounding=ROUND_TIES_TO_EVEN)

The precision(200) argument passed to the BigFloat constructor above is also an example of a Context:

>>> precision(200) Context(precision=200)

The context used for a calculation can be set using the setcontext function, but a better way to make a temporary change to the context is to use Python’s with statement:

>>> with precision(1000): ... print sqrt(2) ... 1.41421356237309504880168872420969807856967187537694807317667973 7990732478462107038850387534327641572735013846230912297024924836 0558507372126441214970999358314132226659275055927557999505011527 8206057147010955997160597027453459686201472851741864088919860955 232923048430871432145083976260362799525140798964

Here, sqrt is one of a number of mathematical functions that the bigfloat package exports. As you can see, these functions operate on integers and floats as well as BigFloat instances, but always return a BigFloat instance.

Rounding modes can be controlled similarly. Here are upper and lower bounds for π, accurate to 53 significant bits:

>>> with RoundTowardPositive: ... const_pi() ... BigFloat.exact('3.1415926535897936', precision=53) >>> with RoundTowardNegative: ... const_pi() ... BigFloat.exact('3.1415926535897931', precision=53)

And as you’d expect, with statements like those above can be nested. Context objects can also be combined using addition:

>>> with RoundTowardPositive + precision(24): ... BigFloat(1) / 3 ... BigFloat.exact('0.333333343', precision=24)

Various Context objects corresponding to IEEE 754 interchange formats are predefined:

>>> quadruple_precision Context(precision=113, emax=16384, emin=-16493, subnormalize=True) >>> half_precision Context(precision=11, emax=16, emin=-23, subnormalize=True) >>> with half_precision: log(2) ... BigFloat.exact('0.69336', precision=11)

## Installation

The bigfloat package is available on the Python package index, and can be installed in the usual way using easy_install or pip. Alternatively, the development sources may be downloaded from the project’s homepage on GitHub.

For more comprehensive installation instructions, please see the full documentation.

## Feedback

Feedback is welcome! Please use the GitHub issue tracker to report issues. Alternatively, you can contact Mark Dickinson directly at dickinsm@gmail.com with suggestions, complaints, bug reports, etc.

## License

The bigfloat package is copyright (C) 2009–2019 Mark Dickinson

The bigfloat package is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

The bigfloat package is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with the bigfloat package. If not, see <http://www.gnu.org/licenses/>.

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