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).
The real-world value ฯ 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'
Likewise, ฯ 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'
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.
- Support math operations for fixed-point types using the applicable context
Chainfix can be installed in developer mode after cloning the repository:
$ pip install -e .
To run all tests:
$ pytest