Weird Differences Between 32 and 64 bit Conversions

Question

Windows Users:
Ever convert exactly the same raw file using exactly the same parameters into 16 bits/channel images with Photoshop CS6 32 bit and 64 bit, overlay them, set the top layer to "Differences", then add a couple of extreme curves adjustment layers over the top?
Amazingly, there's a difference between the two conversions.
Even more amazingly, while there's a slight correllation to the image content, there are patterns in the differences that don't really match much of anything in the image, yet they differ from raw file to raw file.
Try it some time.  If you can't reproduce it, I'll be happy to share my raw file.
Here are two small images, the converted raw file, and the enhanced differences between a 32 and 64 bit conversion of that same raw file.
Enhanced/blurred differences betwen the 32 and 64 bit conversions.
Artificial intelligence trying to express itself?  Cosmic rays?  Kirlean messages from Beyond? 
I happened to be using the 32 bit Photoshop today to access some plug-ins I only can get in 32 bits, converted the same image in both, and just wondered whether there might be differences.  You never know what you'll find until you look!
Oh, and sorry Mac folks - I know you only have a 64 bit converter to play with.
I'm reminded of the old adage:  A man with one watch knows what time it is.  A man with two watches is never sure.
-Noel

Answer 1

Thanks for your response, Eric.
I understand what you're saying, but a several bit difference in a 15 bit result is actually quite a lot to be attributed to math inaccuracy due to floating point operations.  Even single precision 32 bit floating point operations should give you 24 bits of precision.  A few bits at the end shouldn't add up to a visible difference, unless decisions are being made in the code based on results (e.g., if noise > threshold, do something).
Perhaps you don't use the Strict Floating Point Model, because if you did that should give you consistent results.
I've been through the decision of which floating point model to use in my own software, initially thinking that the Fast model would be better for speed (obviously), but as it turns out the repeatability of results with the Strict model is well worth the tiny bit of extra time it takes for the results to be predictable.  You might want to reconsider using Strict, as I have, especially if these are not just round-off errors but decisions being made in the code based on floating point results.  Looking around on the web, I see more folks than just I have made that specific choice.
Food for thought.
-Noel