Fixed-Point Arithmetic in Python

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What is Fixed-Point Arithmetic?

Fixed-point arithmetic is a way of representing real numbers using a fixed number of integer bits for the whole part and a fixed number of integer bits for the fractional part․ Unlike floating-point arithmetic, the position of the decimal point is fixed․ This makes it particularly useful in environments where floating-point operations are expensive or unavailable, such as embedded systems and Digital Signal Processing (DSP)․

Why Use Fixed-Point Arithmetic in Python?

While Python natively supports floating-point numbers, there are scenarios where fixed-point arithmetic offers advantages:

  • Determinism: Fixed-point arithmetic avoids the rounding errors inherent in floating-point calculations, leading to more predictable and deterministic results․
  • Performance: In certain applications, especially those running on resource-constrained devices, fixed-point operations can be significantly faster than floating-point operations․
  • Precision Control: You have explicit control over the precision of your numbers․
  • Portability: Fixed-point representations can be more easily ported across different platforms and languages․

Python Libraries for Fixed-Point Arithmetic

Several Python libraries facilitate working with fixed-point numbers:

The fixedpoint Package

The fixedpoint package is a dedicated library for fixed-point arithmetic in Python․ It provides a comprehensive set of features:

  • Number Generation: Create fixed-point numbers from strings, integers, or floating-point numbers․
  • Bit Width and Signedness Control: Specify the number of bits and whether the number is signed․
  • Rounding Methods: Choose from various rounding methods (e․g․, round to nearest, round up, round down)․
  • Overflow Handling: Configure how overflows are handled (e․g․, saturation, wrapping)․
  • Bitwise Operations: Supports bitwise operations (AND, OR, XOR, inversion)․

Installation: pip install fixedpoint

apytypes (and fxpmath)

The apytypes library (installable from source) offers a more comprehensive approach to type handling, including fixed-point numbers․ Within apytypes, fxpmath is often considered the most complete library for fixed-point arithmetic at the moment․ It provides exact representation, which is useful for reliable data exchange and platform independence․

bigfloat Package

While primarily focused on arbitrary-precision floating-point arithmetic, the bigfloat package (a Cython wrapper around GNU MPFR) can be relevant when high precision is required, even if not strictly fixed-point․

The decimal Module

Python’s built-in decimal module provides arbitrary-precision decimal arithmetic․ While not strictly fixed-point, it allows you to control the number of decimal places, effectively simulating fixed-point behavior․ The CPython and PyPy3 implementations integrate the libmpdec library for high-speed decimal calculations․

Converting Float to Fixed-Point Decimal (2 Decimal Places)

Let’s say you have a function foo that returns a float with two decimal places, and you need to pass it to a function bar that expects a Decimal with fixed-point precision for two decimal places․ Here’s how you can convert:


from decimal import Decimal

def foo:
 return 3․14159

def bar(decimal_value):
 # Do something with the Decimal value
 print(f"Received Decimal: {decimal_value}")

float_value = foo
decimal_value = Decimal(str(float_value))․quantize(Decimal("0․00"))

bar(decimal_value)

Explanation:

  1. Decimal(str(float_value)): First, convert the float to a string․ This avoids potential floating-point representation issues when directly creating a Decimal from a float․
  2. ․quantize(Decimal("0․00")): This is the key step․ The quantize method rounds the Decimal to the specified precision (in this case, two decimal places)․

Formatting Floating-Point Numbers for Fixed-Width Output

If you need to format a floating-point number to a fixed width with leading zeros, you can use Python’s string formatting capabilities:


number = 12․34
formatted_number = "{:08․2f}"․format(number) #  total, 2 decimal places, leading zeros
print(formatted_number) # Output: 00012․34

Explanation:

  • {:08․2f}: This is the format specifier․
  • 0: Indicates that leading zeros should be used for padding․
  • 8: Specifies the total width of the formatted string (including the decimal point)․
  • ․2f: Specifies that the number should be formatted as a floating-point number with two decimal places․

Fixed-point arithmetic can be a valuable tool in specific Python applications, offering benefits in terms of determinism, performance, and precision control․ By leveraging libraries like fixedpoint, apytypes, and the decimal module, you can effectively implement fixed-point calculations in your Python projects․

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