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Simple Python Fixed-Point Module (SPFPM)
spfpm is a pure-Python toolkit for performing binary fixed-point arithmetic, including trigonometric and exponential functions.
The package provides:
- Representations of values with a fixed number of fractional bits
- Optional constraints on the number of whole-number bits
- Interconversion between native Python types and fixed-point objects
- Arithmetic operations (addition, subtraction, multiplication, division) of fixed-point numbers
- Methods for computing powers, logarithms and exponents
- Methods for computing trigonometric functions and their inverses
- Computation of various mathematical constants, such as pi and log(2), to maximal precision for the chosen fixed-point resolution
- Printing fixed-point numbers as decimal numbers, or as binary/octal/hexadecimal representations.
- Support for numbers with thousands of bits of resolution
On a modern desktop PC, spfpm is typically capable of hundreds of thousands of arithmetic operations per second, i.e. over 100 kilo-FLOPS, even for a few hundred bits of resolution. As a pure-Python library SPFPM offers portability and interactivity, but will never compete with the performance of lower-level libraries such as mpmath, Boost multiprecision or GMP for heavyweight calculations.
Development currently targets Python versions 3.3 and later, although the library may also be usable with python-2.7. The latest version of spfpm can be found on GitHub.
Examples
After installation there are two main classes that you need from the FixedPoint module:
from FixedPoint import FXfamily, FXnum
you can create fixed-point numbers with the default (64-bit) resolution as follows:
x = FXnum(22) / FXnum(7)
y = FXnum(3.1415)
print(x - y)
Creating numbers with a specific precision requires use
of the FXfamily
class:
fam100 = FXfamily(100)
z = FXnum(1, fam100)
z2 = fam100(2)
One can then apply various computations such as:
print(z.atan() * 4)
print(z2.sqrt())
The FXfamily
class also provides access to pre-computed constants
which should be accurate to about 1/2 of the least significant bit (LSB):
print('pi = ', fam100.pi)
print('log2 = ', fam100.log2)
print('sqrt2 = ', fam100.sqrt2)
This produces the following printed values of those constants:
- 3.141592653589793238462643383279
- 0.69314718055994530941723212145
7 - 1.414213562373095048801688724209
The struck-through digits show where the values computed at 100-bit precision differ from the true digits in the decimal representations of these constants. Alternatively, one could print these values in base-16:
print(FXfamily(400).pi.toBinaryString(logBase=4))
giving a hexadecimal value of Pi as:
- 3.243f6a8885a308d313198a2e03707344a4093822299f31d0082efa98ec4e6c89452821e638d01377be5466cf34e90c6cc0ac
which agrees exactly with the accepted result.
Licensing
All files are released under the Python PSF License and are Copyright 2006-2024 RW Penney.