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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 3
  • 0.69314718055994530941723212145 79
  • 1.414213562373095048801688724209 1

The struck-through digits show where the values computed at 100-bit precision differ from the true values 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 2006-2020 RW Penney.