Floating a new idea

Gene Frantz
TI Principal Fellow and Business Development Manager, DSP

We recently announced a new floating-point core that allows our designers to do fixed- and floating-point instructions on the same DSP opening up many new applications that need this type of precision for fixed-point prices.  If you are interested in that, you can see it here: www.ti.com/c674xgfblog. This announcement got me thinking about floating-point again…to be honest, it had been a long time.   

Floating point has been around for a very long time.  I can remember the day we introduced the TMS320C30 to the industry.  There had been a long debate on whether the DSP community would embrace floating point.  What we found, to our surprise, was immediate acceptance.  But, this raised a question in my mind of whether the TMS320C30 was accepted because it was floating point, 32-bits or C friendly?  And, unfortunately, when I asked our system design customers, their answer to the question was “yes.” 

Several years later, I spent about a half a year visiting many companies using floating-point processors.  My hope was to determine why many of our customers were still using the TMS320C30 when we had told them not to.  At the same time the TMS320C67x (a VLIW based floating-point device) was not being accepted even though we recommended it for design.  And then there was a third question rolling around in my mind of “why were we considering the design of a yet third floating-point device without knowing the answer to the first two questions?” 

Well, I did find the answer to all three questions – none of which were very satisfying.  I’ll leave the answers to another blog.  What I want to cover in this blog is something I learned from the study, which had nothing to do with the three questions I had hoped to answer.

What I learned was that floating point, as we defined it, had only one significant market – professional audio.  Professional audio first went digital when the Motorola 56K was introduced.  That processor gave 24-bits of data accuracy and 56-bits of internal accuracy.  This was enough to drive the market until ADI introduced its 21060, which was an extended precision floating-point device (8-bit exponent and 32-bit mantissa).  We, at TI, were beginning to enter this market with our TMS320C67x generation, which did not have extended precision floating point, but could do a pretty good job of double precision floating point (11 bit exponent and 53 bit mantissa).  What I realized was that every application had three accuracy requirements:

• Data.  The accuracy of the data coming in and going out.  For pro audio this is 24-bits.
• Internal.  The accuracy needed to guarantee that the output data was a true representation of the input data.  For pro audio, this is greater than 32-bits (the reason the TMS320C30 was unacceptable for pro audio).
• Coefficient.  Surprisingly this became the most important.  The reason for its importance has to do with the accuracy needed for the biquad coefficients and the least accurate point in a floating point representation being at 1 (i.e., the unit circle).  For pro audio at 48 KHz, 32 was adequate but 53 was noticeably better.  As an aside, this accuracy requirement increases one bit for every doubling of the sample rate. 

It turned out that the key to audio was the coefficient accuracy.  And, as we move from 48 KHz sampling to 96 to 192 to 384 KHz, the accuracy requirement only increases. 

But, let’s get back to the point of this blog.  That is, when we speak of floating point we are always speaking of a 32-bit version (or a 64-bit double precision version).  What this means is that floating point is always lower in raw performance compared to a fixed-point processor.  But this is actually more determined by the fact that the fixed-point processor is 16-bits and the floating-point processor is 32-bits. 

So, what if we decided to do a floating-point processor of a different size?  Let’s take a simple example of a 16-bit floating-point processor.  For now let’s call it “half precision.” For simplicity let’s also assume its format is 5-bits exponent and 11-bits mantissa.  We now have an interesting set of new questions to answer:

• What application(s) could use this new format?
• How would this impact performance?
• Is this the only other floating point option available? 

Let me give quick answers to the first and third question, and then spend a bit of time on the second.  There are several applications that could use this “half precision” floating-point format.  And, there are other formats that might also be interesting. 

With those two answered, albeit not satisfactorily, let’s focus on performance.  In simple terms because the multiplier would be an 11 X 11 rather than a 24 X 24 (single precision), the raw performance could be easily four times that of a 32-bit floating-point device.  That is the 24 X 24 bit multiplier found in a single precision could be split into four 12 X 12 bit multipliers giving four times the multiplies each instruction cycle,  It could also be 30% faster than a 16-bit multiply in a fixed point system.  That means the 16-bit floating-point machine could be 4X a present day floating-point machine and perhaps 30% faster than its 16-bit fixed-point equivalent. 

With this in mind, I asked two professor friends of mine to help me push this a bit further.  Dr. Armand Tanguay at USC is looking at a possible application area that 16-bit floating point could be used, and Dr. David Anderson at Georgia Tech University is thinking about the 16-bit floating-point math system.

To sum it up, I’m floating a new idea surrounding floating point.  As usual, it asks more questions than it answers.  But, then, that is the fun of it all. 

What are your thoughts on this?