On Sun, 2 Aug 2015, Jeffrey Sarnoff wrote:
Quiet NaNs (QNaNs) were introduced into the Floating Point Standard as a tool for applied numerical work. That's why there are so many of them (Float64s have nearly 2^52 of them, Float32s have nearly 2^23 and Float16s have nearly 2^10 QNaNs). AFAIK Julia and most other languages use one or two of each in most circumstances. Half of the QNaNs are in some sense positive and the other half negative (their sign bits can be queried, even though they are not magnitudes). While QNaNs are unordered by definition, they each have an embedded *payload:* an embedded integer value that exists to be set with information of reflective value. And then to carry it, propagating through the rest of the numerical work so it becomes available for use by the designer or investigator.
A logical application for the many different quiet NaNs is to encode different types of meta-numeric value. Of course, there is the basic NaN, for example 0/0 => NaN. However using a different payload in the NaN might be used to signal NA (i.e. missing). One can think of many other fault states which arise in numerical computing with real data, such as "value out of bounds", "invalid value", etc. All these different states might be encoded using NaNs of different payloads. The devil is in the details, however. For example, the missing value NA propagates differently from the standard NaN. Consider: mean([1 2 NA 4 5]) => 3 mean([1 2 NaN 4 5]) => NaN. Therefore, the function "mean()" needs to know how to treat the NaN differently from the NA. Moreover, I believe that to make use of the different NaN payloads, hardware makers would need to build knowledge of the different NaN types (and propagation rules) into their floating point ALUs. Is this right? One can implement this scheme in software, but the problem is that one needs to match the NaN payload in software, which degrades floating point performance in a big way. Therefore, standardization and hardware support are important. My question: Have any hardware makers ever looked into utilizing the different NaN payloads for the above scheme? How about standardization bodies? Stuart
