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