10. Subnormal / Denormal numbers - Audio Number Formats
In this video, we learn about the elusive, and often confusing topic of subnormal or denormal numbers in the floating point range. We'll learn that the floating point format is a real oddity, it’s full of interesting nuances. A large portion of the numbers, normalized numbers are logarithmically spaced out, with floating point representation and precision, and then a small subset of numbers, denormalized numbers are linearly spaced out, with fixed point representation.
Watch the full playlist here:
• Audio Number Formats
Content:
0:00 Logarithmic scale
2:33 The island of zero
3:50 Coding 1
7:06 Subnormal representation
9:42 Coding 2
13:18 Conclusion
References:
https://en.wikipedia.org/wiki/Subnorm...
Floating Point Calculator - https://www.h-schmidt.net/FloatConver...
The story behind the IEEE 754 format, it's a great read! - https://bit.ly/3sLGSLf
Intel SSE Flush to Zero flag - https://intel.ly/32KkbMJ
This series describes the 2 fundamental formats for expressing numbers and audio data in the digital domain - fixed point format and floating point format. They both have their advantages, their areas of usage where they absolutely shine, and they both fall short or completely fail in other aspects. There is no one over the other. As audio and DSP enthusiasts, you'd need to know what where a particular format is preferred and under what circumstances they fall short. Why do digital playback hardware prefer fixed point number format. Why do DAW softwares prefer to work with floating point numbers? What even is a double precision number? And what number format do you use when implementing a DSP algorithm. The series will address these questions and a lot more.
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