1. First steps in Reaktor Core - Native Instruments

A typical situation in which denormal numbers appear for prolonged
periods of time is in calculating exponentially decaying values, as in
filters, some envelopes, and feedback structures. In such structures,
after the input signal reaches zero level, the output signal asymptotically
decays to zero. Asymptotically means that the signal gets closer and
closer to zero without ever reaching it. In that situation, denormal numbers
can appear and stay in the structure for relatively long time (until
their absolute value falls below 10 -45 ), and that can cause a significant
increase in CPU load.
Another situation in which denormal numbers may occur is when you
change the precision of a floating point value from a higher precision (64
bit) to a lower precision (32 bit), because a value 10 -41 is not a denormal
in a 64 bit precision float but it is a denormal in a 32 bit precision float
(changing the precision of floats is discussed later).
Let’s consider modeling an analog 1-pole lowpass filter with its cutoff set to
20 Hz. Our digital signal values will correspond to analog voltages (measured
in volts). Let’s imagine that the input signal level was equal to 1V (volt) over a
long enough period of time. Then the voltage at the filter output is also equal
to 1V. Now we abruptly change the input voltage to zero. The output voltage
will decay according to the law:
V
out
� V e
98 – REAKTOR CORE
0
�2�
f t
c
where f c is the filter cutoff in Hz, t is time in seconds and 0 1V
� V (initial
voltage).
Then the output voltage will change as follows:
after 0.5 sec V ≈10 out -29 volt
after 0.6 sec V ≈10 out -33 volt
after 0.7 sec V ≈10 out -38 volt
after 0.8 sec V ≈10 out -44 volt
Oops, the numbers between 10 -38 and 10 -45 are in the denormal range. So in
the time period from approximately 0.7 to 0.8 seconds, our voltage is represented
by a denormal value. And it’s not only inside the filter. The filter output
is probably further processed by the downstream structure, causing at least
the few following modules also to deal with denormal values.
At a sampling rate of 44.1 kHz, the time interval of 0.1 second corresponds to
4,410 samples. Assuming that the typical ASIO buffer size is a few hundred