Fibonacci Sequence Generator

This section describes the usage of the more complex CBD.lib.std.DelayBlock. It will always output the previous value whenever it receives a new one, unless (obviously), there is no previous value (e.g. at the beginning of the simulation). In that case, its output is the value it obtains from the IC.

We will create a generator that outputs the Fibonacci numbers, starting from 1, 1, 2, 3, 5…; or more mathematically:

\[\begin{split}y(i) &= y(i - 1) + y(i - 2)\\ y(0) &= y(1) = 1\end{split}\]

For this we need the CBD.lib.std.AdderBlock and obviously the CBD.lib.std.DelayBlock. Additionally, the CBD.lib.std.ConstantBlock will need to be used, as will be discussed later on.

from CBD.Core import CBD
from CBD.lib.std import ConstantBlock, AdderBlock, DelayBlock

By linking two delay blocks after one another and sending both outputs through the adder, we can implement the first equation. This yields:

class FibonacciGen(CBD):
    def __init__(self, block_name):
        CBD.__init__(self, block_name, input_ports=[], output_ports=['OUT1'])

        # Create the Blocks
        self.addBlock(DelayBlock("delay1"))
        self.addBlock(DelayBlock("delay2"))
        self.addBlock(AdderBlock("sum"))

        # Create the Connections
        self.addConnection("delay1", "delay2")
        self.addConnection("delay1", "sum")
        self.addConnection("delay2", "sum")
        self.addConnection("sum", "delay1", input_port_name='IN1')
        self.addConnection("sum", "OUT1")

Now, at time 0 and at time 1, we would like to output 1. We know:

\[\begin{split}y(0) &= delay1.IC + delay2.IC &= 1 \\ y(1) &= delay1(1) + delay2(1) &= y(0) + delay1.IC\\ & \Leftrightarrow \\ delay1.IC &= 0\\ delay2.IC &= 1\end{split}\]

Do, let’s add this to our model:

self.addBlock(ConstantBlock("zero", value=0))
self.addBlock(ConstantBlock("one", value=1))

self.addConnection("zero", "delay1", input_port_name='IC')
self.addConnection("one", "delay2", input_port_name='IC')

The complete generator is therefore as follows:

from CBD.Core import CBD
from CBD.lib.std import ConstantBlock, AdderBlock, DelayBlock

class FibonacciGen(CBD):
    def __init__(self, block_name):
        CBD.__init__(self, block_name, input_ports=[], output_ports=['OUT1'])

        # Create the Blocks
        self.addBlock(DelayBlock("delay1"))
        self.addBlock(DelayBlock("delay2"))
        self.addBlock(AdderBlock("sum"))
        self.addBlock(ConstantBlock("zero", value=0))
        self.addBlock(ConstantBlock("one", value=1))

        # Create the Connections
        self.addConnection("delay1", "delay2")
        self.addConnection("delay1", "sum")
        self.addConnection("delay2", "sum")
        self.addConnection("sum", "delay1", input_port_name='IN1')
        self.addConnection("sum", "OUT1")
        self.addConnection("zero", "delay1", input_port_name='IC')
        self.addConnection("one", "delay2", input_port_name='IC')

When running the simulation for 10 time-units, we obtain the first 10 values:

from CBD.simulator import Simulator

cbd = FibonacciGen("FibonacciGen")
sim = Simulator(cbd)
sim.run(10)
data = cbd.getSignalHistory('OUT1')
t, v = [t for t, _ in data], [v for _, v in data]

print(v)  # prints [1, 1, 2, 3, 5, 8, 13, 21, 34, 55]