# 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.