omelancon

> Maybe I misunderstand, but isn't that a similar idea to what I just described? Adding an offset to "rotate" the ranges of the exponent by a segment...

Yes it is similar. It seems to me that there really isn't that many useful operations that can be applied to the exponent beside adding an offset. But that's only a suspicion, do not take my word for it.

> I suspect that ensuring NaN and Infinity are in there will be crucial to avoid performance cliffs...

This is a reasonable assumption. There are in fact ways to rotate and add an offset such that the exponent can overflows/underflows to capture exponents 0 and 0x7ff (for inf and nan) with a single well-positioned tag. Making it work in practice is not as simple, but we are working on it.

Hi, I'm one of the authors of the paper. Thanks for your questions and comments!

There are many reasons why 3-bit tags work well in practice. Importantly, it allows aligning heap objects on 64-bit machine words. Dereferencing a tagged pointer can then be done in a single machine instruction, a MOV offset by the tag.

One of our goals is to make self-tagging as straightforward to implement in existing systems as possible. Thus requiring to move away from the ubiquitous 3-bit tag scheme is definitely a no-go.

Another goal is performance, obviously. It turns out that if the transformation from self-tagged float to IEEE754 float requires more than a few (2-3) machine instructions, it is no longer as advantageous. Thus the choice of tags 000, 011 and 100, which encoding/decoding is a single bitwise rotation.

Also keep in mind that assigning more tags to self-tagging to capture floats that are never used in practice just adds a strain on other objects. That's why we include a usage analysis of floats to guide tag selection in our paper.

In fact, we are currently working on an improved version that uses a single tag to capture all "useful" values. Capturing 3/8 of floats seems unnecessary, especially since one of the tag is only meant to capture +-0.0. The trick is to rotate the tag to bits 2-3-4 of the exponent instead of 1-2-3 and add an offset to the exponent to "shift" the range of captured values.

But in the end, it feels like we are barely scratching the surface and that a lot of fine-tuning can still be done by toying with tag placement and transformation. But I think the next step is a quality over quantity improvement: capture less floats but capture the right ones.