clamdad / chainfix

Fixed-point data types for signal processing and blockchain applications

Welcome to Chainfix

Chainfix provides a way to represent numbers and perform simple math operations using fixed-point data types.

Chainfix supports binary fixed-point (base-2), decimal fixed-point (base-10) or even arbitrary (base-N) fixed-point types.

Fixed-point data types are used in a wide range of computing applications. Binary-fixed point types are commonly used in the design of specialized hardware, FPGAs, ASICS, and signal processing applications.

Decimal-fixed point types are commonly found in financial applications, blockchain, decentralized finance, and smart contracts (e.g. the solidity programming language).

Decimal fixed-point representations

The real-world value π can be represented with limited precision using two bytes in decimal fixed point format

>>> from chainfix import * 
>>> from math import pi
>>> pid = Fixd(pi, wordlength=16, precision=4)
Fixd(3.1416, 16, 4)

The .int property returns the stored integer value:

>>> pid.int
31416

The resolution of the decimal fixed-point data type is 10 ** -precision, which is also the value of one least significant bit:

>>> pid.lsb
0.0001

The range of numbers that can be represented with this precision using 16 bits is:

>>> (pid.lower_bound, pid.upper_bound)
(-3.2768, 3.2767)

The real-world value can also be displayed as an exact ratio of integers

>>> pid.as_integer_ratio()
(3927, 1250)

The .hex property returns the two's complement representation of the stored integer

>>> pid.hex
'0x7ab8'

When Fixd stores a negative number, the MSB of the stored integer is always 1:

>>> Fixd(-pi, 16, 4).hex
'0x8548'

Binary fixed-point representations

Likewise, π can also be represented with limited precision using two bytes in binary fixed point format

>>> pib = Fixb(pi, 16, 12)
Fixb(3.1416015625, 16, 12)

The .int property returns the stored integer value:

>>> pib.int
12868

The resolution of the decimal fixed-point data type is 2 ** -precision, which is also the value of one least significant bit:

>>> pib.lsb
0.000244140625

The range of numbers that can be represented with this precision using 16 bits is:

>>> (pib.lower_bound, pib.upper_bound)
(-8.0, 7.999755859375)

The .hex property returns the two's complement representation of the stored integer

>>> pib.hex
'0x3244'

When Fixb is used to store a negative number, the MSB of the stored integer is always 1:

>>> Fixb(-pi, 16, 4).hex
'0xffce'

Contexts

Chainfix provides a fixed-point context to control the default behavior for new fixed-point objects.

The current context can be retrieved using

>>> ctx = get_decimal_context()
>>> ctx.wordlength
256
>>> ctx.precision
18

for Fixd and Ufixd values or

>>> ctx = get_binary_context()
>>> ctx.wordlength
32
>>> ctx.precision
16

for Fixb and Ufixb values.

The context can be modified to change the behavior of newly constructed values:

>>> get_decimal_context().wordlength = 20
>>> get_decimal_context().precision = 5
>>> Fixd(pi)
Fixd(3.14159, 20, 5)

When passed through the constructor, the values for wordlength and precision always take precedence over the context.

>>> Fixd(pi, precision=10)
Fixd(3.1415926536, 256, 10)

Note that resulting data type has insufficinet range to represent the value pi.

Future Work

• Support math operations for fixed-point types using the applicable context

Contributing

Chainfix can be installed in developer mode after cloning the repository:

$ pip install -e .

To run all tests:

$ pytest