Introduction

fpbinary is a binary fixed point package for Python. It is written as an extension module for the CPython implementation of Python.

fpbinary was created with fast simulation of math-intensive systems destined for digital hardware (e.g. signal processing) in mind. While Python has great support for signal processing functions, there is no offical fixed point package. Implementaions written completely in Python tend to be frustratingly slow, so fpbinary is an attempt to make fixed point simulation of large, complex hardware systems in Python viable.

Features

  • Arbitrary precision representation of real numbers (including a str_ex() method for string display of high precision numbers)
  • Complex number object
  • Definable integer and fractional bit formats
  • Fixed point basic math operations
  • Bitwise/index/slice operations
  • Gracefully plays with int and float Python types
  • Switch between fixed and floating point math without changing code
  • Tracking of min/max values for prototyping
  • Follows the VHDL fixed point library conventions (relatively) closely
  • Objects are picklable (only pickle protocols >= 2 are supported)
  • The fpbinary objects ARE NOT subclassable at present

Installation

The easiest way is to install using the pip utility. If you don’t already have pip installed, first follow the instructions at pip Installation . Then follow the instructions for your operating system below.

Linux

pip will install fpbinary on Linux using a source distribution. This does require a C99 compliant compiler on your system, which your distribution is likely to already have. If not, install something like gcc. Then, to install fpbinary:

pip install fpbinary

If you come across a missing Python.h error, you may need to install the python3-dev package:

sudo apt-get update
sudo apt-get install python3-dev

Windows

fpbinary is tested on Windows 10 and binaries are produced on PyPi. Only python versions >= 3.5 are supported for Windows. Install via:

pip install fpbinary

macOS

fpbinary is currently tested on macOS 10.14 (Mojave) but binaries are produced on PyPi that should install on macOS 10.9 and newer. Install via:

pip install fpbinary

These binaries only support 64 bit systems. If you are running 32 bit or an older OS, the above command will still probably work as long as you have a C99 compliant compiler installed.

Going Bush

If you want to test the very latest source code or for some other reason you want to install directly from the repository, you can install via:

pip install git+https://github.com/smlgit/fpbinary.git

or:

git clone https://github.com/smlgit/fpbinary.git

cd fpbinary
python setup install

Use

fpbinary provides three main objects - FpBinary, FpBinaryComplex and FpBinarySwitchable. The best way to learn how they work is to read the help documentation:

from fpbinary import FpBinary, FpBinarySwitchable
help(FpBinary)
help(FpBinaryComplex)
help(FpBinarySwitchable)

This documentation is also avaliable at Read the Docs. There are also some useful demos.

Below is a very brief introduction to the objects.

Objects

FpBinary

This object represents a real number with a specified number of integer and fractional bits.

Some basic usage:

>>> fp_num = FpBinary(int_bits=4, frac_bits=4, signed=True, value=2.5)
>>> fp_num
2.5
>>> fp_num.format
(4, 4)
>>> fp_num * 2.0
5.0
>>> fp_num.resize((1,4))
0.5

FpBinarySwitchable

This object is intended to be used in simulation code where the user wants to switch between fixed and floating point math operation. It allows a simulation to be coded with fixed point method calls (like resize()) but to be run in floating point mode at the flick of a constructor switch:

def dsp_sim(fp_mode):
    num1 = FpBinarySwitchable(fp_mode=fp_mode, fp_value=FpBinary(8, 8, value=6.7), float_value=6.7)
    num2 = FpBinary(16, 16, value=0.005)

    num3 = (num1 * num2).resize((8, 8), overflow_mode=OverflowEnum.wrap,
                                        rounding_mode=RoundingEnum.direct_neg_inf)

    # Do other stuff...

    return num3

FpBinarySwitchable also provides the value property. This can be set to fixed or floating point objects (depending on the mode) and the min and max values over the lifetime of the object are tracked. This gives the designer an indication of the required fixed point format of the various data points in their design:

inp = FpBinarySwitchable(fp_mode=fp_mode, fp_value=FpBinary(8, 8, value=0.0), float_value=0.0)
scaled = FpBinarySwitchable(fp_mode=fp_mode, fp_value=FpBinary(16, 16, value=0.0), float_value=0.0)

def some_dsp_next_sample(sample):
    inp.value = sample.resize(format_inst=inp)
    scaled.value = inp * scale_factor

    # ....
    return val

def run(fp_mode):
    # call some_dsp_next_sample a whole heap

    return inp.min_value, inp.max_value, scaled.min_value, scaled.max_value

Development

fpbinary was designed from the point of view of a frustrated FPGA designer. Speed and useability for FPGA/hardware engineers drove the implementation decisions.

Architecture

The main objects are FpBinary, FpBinaryComplex and FpBinarySwitchable.

FpBinary

Is a wrapper that is composed of an instance of one of two “base” types:

  • _FpBinarySmall: this object uses native c types for the underlying value representation. This makes operations as fast as possible. However, use of this object is limited by the machine bit width.
  • _FpBinaryLarge: this object uses Python integer objects (PyLong) for the value representation. This allows arbitrary length data at the expense of slower operation (and messier c code…).

The purpose of FpBinary is to work out whether the faster object can be used for a representation or operation result and select between the two base types accordingly. It also must make sure the operands of binary/ternary operations are cast to the base type before forwarding them on.

This architecture does make the code and maintenance more complicated and it is questionable whether it is worth having the small object at all. Basic profiling does suggest that FpBinary is faster than _FpBinaryLarge on its own (for numbers < 64 bits), but the difference isn’t that big (and is mostly in the creation of objects rather than the math ops).

FpBinaryComplex

This object holds two FpBinary objects, one for the real part and one for the imaginary part of a fixed point complex number.

Only signed numbers are supported.

FpBinarySwitchable

The point of this object is to allow a designer to write their simulation code assuming fixed point operation (i.e. with fixed point operations like the resize()) method, but to be able to force floating point math with the flick of a switch. Not only is the normal workflow to try out a design using floating point math first, it is also incredibly handy to be able to switch back and forth through the entire project lifecycle.

FpBinarySwitchable is composed of a FpBinary instance and a native c double variable. Which variable is actually used when an operation is invoked on the instance is dictated by the fp_mode, which is defined at constructor time. The FpBinarySwitchable code is essentially tasked with casting the other operand to the right type (fixed or float) and then forwarding on the underlying operation to the right object.

FpBinarySwitchable also implements a value property that can be used to set the composition instances. This makes it easy for the designer to write simulation code with apparently mutable data points. The advantage of this is that minimum and maximum values can be tracked during the lifetime of the object - Matlab implements a similar feature for its fixed point variables and it allows the user to get an idea for the required format of each data point. FpBinarySwitchable implements this functionality with simple logic in the property setter method. Note that this is only done when in floating point mode.

FpBinarySwitchable is designed to “look” like an FpBinary object, at least when it makes sense to flick the operation to float mode. So I have implemented resize() operations (no change in float mode) and shifting operations (mult/div by powers of 2) as well as the math operations. But index/slice and bitwise operations have not been implemented.

Coding Notes

  • Direct calls to object methods (like the tp_as_number methods) was favoured over the c api PyNumber abstract methods where possible. This was done for speed.
  • Similarly, a private interface was created for _FpBinarySmall and _FpBinaryLarge to implement so FpBinary could access them without going through the abstract call functions (that use string methods for lookup). This provided some type of polymorphism via the fpbinary_base_t type placed at the top of the base’s object definitions.

Enhancements

  • [ ] Possibly jettison the base class architecure and use _FpBinaryLarge as the main object.
  • [ ] Add global contexts that allows the user to define “hardware” specifications so inputs and outputs to math operations can be resized automatically (i.e. without the need for explicit resizing code).
  • [ ] Add more advanced operations like log, exp, sin/cos/tan. I have stopped short of doing these thus far because a user may rather simulate the actual hardware implementation (e.g. a lookup table would likely be used for sin). Having said that, a convienient fpbinary method should give the same result.
  • [ ] Allow FpBinary and FpBinarySwitchable to be subclassable. Would require some basic changes to (mostly) FpBinarySwitchable to use the abstract methods from the Python Numeric/Sequence interfaces rather than direct accessing via the type memory. Might reduce speed slightly.