# The bigfloat package — high precision floating-point arithmetic¶

Release v0.3.0.

The `bigfloat`

package is a Python wrapper for the GNU MPFR library for arbitrary-precision floating-point reliable
arithmetic. The MPFR library is a well-known portable C library for
arbitrary-precision arithmetic on floating-point numbers. It provides precise
control over precisions and rounding modes and gives correctly-rounded
reproducible platform-independent results.

The `bigfloat`

package aims to provide a convenient and friendly
Python interface to the operations and functions provided by the MPFR
library. The main class, `BigFloat`

, gives an immutable
multiple-precision floating-point type that can be freely mixed with
Python integers and floats. The `Context`

class, when used in
conjunction with Python’s `with`

statement, gives a simple way of
controlling precisions and rounding modes. Additional module-level
functions provide various standard mathematical operations. There is
full support for IEEE 754 signed zeros, nans, infinities and
subnormals.

## Features¶

- Supports Python 2 (version 2.6 or later) and Python 3 (version 3.2 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.

## Introduction¶

Here’s a quick tour:

```
>>> from bigfloat import *
>>> sqrt(2, precision(100)) # compute sqrt(2) with 100 bits of precision
BigFloat.exact('1.4142135623730950488016887242092', precision=100)
>>> with precision(100): # another way to get the same result
... sqrt(2)
...
BigFloat.exact('1.4142135623730950488016887242092', precision=100)
>>> my_context = precision(100) + RoundTowardPositive
>>> my_context
Context(precision=100, rounding='RoundTowardPositive')
>>> sqrt(2, my_context) # and another, this time rounding up
BigFloat.exact('1.4142135623730950488016887242108', precision=100)
>>> with RoundTowardNegative: # a lower bound for zeta(2)
... sum(1/sqr(n) for n in range(1, 10000))
...
BigFloat.exact('1.6448340618469506', precision=53)
>>> zeta(2) # actual value, for comparison
BigFloat.exact('1.6449340668482264', precision=53)
>>> const_pi()**2/6.0 # double check value
BigFloat.exact('1.6449340668482264', precision=53)
>>> quadruple_precision # context implementing IEEE 754 binary128 format
Context(precision=113, emax=16384, emin=-16493, subnormalize=True)
>>> next_up(0, quadruple_precision) # smallest subnormal for binary128
BigFloat.exact('6.47517511943802511092443895822764655e-4966', precision=113)
>>> log2(_)
BigFloat.exact('-16494.000000000000', precision=53)
```

## Installation¶

### Where to get it¶

The latest released version of the `bigfloat`

package can be
downloaded from its place at the Python Package Index. Development sources can be
checked out from the project’s GitHub page.

### Prerequisites¶

In order to use the `bigfloat`

package you will need to have both the GMP
and MPFR libraries already installed on your system, along with the include
files for those libraries. See the MPFR homepage and
the GMP homepage for more information about these
libraries. Currently, MPFR version 2.3.0 or later is required.

The `bigfloat`

package works with Python 2 (version 2.6 or later) or
Python 3 (version 3.2 or later), using a single codebase for both Python
dialects.

### Installation¶

Like most third party Python libraries, the `bigfloat`

package is
installed by means of the `setup.py`

script included in the
distribution. On many systems, installation should be as simple as
doing:

```
python setup.py install
```

in the top-level directory of the unpacked distribution. You may need superuser privileges to install the library, for example with:

```
sudo python setup.py install
```

The MPFR and GMP libraries will need to be installed on your system prior to
installation of `bigfloat`

, along with any necessary development header
files. On Linux, look for a package called something like `libmpfr-dev`

or
`mpfr-devel`

, along with correspondingly named packages for GMP. If the
libraries and/or include files are installed in an unusual place, it may be
necessary to specify their location using environment variables on the command
line. As an example, on my OS X 10.9 system, with MPFR and GMP installed in
/opt/local/, I need to do:

```
LIBRARY_PATH=/opt/local/lib CPATH=/opt/local/include python setup.py install
```

Similarly, if installing from the Python package index using `easy_install`

or `pip`

, you may also need to add the necessary environment variables first.