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 currently
implemented as a Python extension module (generated using Cython) around the
MPFR library (http://www.mpfr.org).

## Features

- correct rounding on all operations; 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 Python’s ‘with’ statement.

## A quick tour

The `bigfloat` module is small and simple to use. Here’s a quick
tour of some of its features. See the full tutorial and reference
documentation for more
details.

For demonstration purposes, start with:

>>> from bigfloat import *

Note that this import clobbers some builtin Python functions, namely
`abs`, `max`, `min` and `pow`. 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='RoundTiesToEven')

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` module 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)

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