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4-bit floating point FP4

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Re: 4-bit floating point FP4

#11

Post by indolering »

convolvatron wrote: post #10
ant6n wrote: post #4

> In ancient times, floating point numbers were stored in 32 bits. I thought in ancient times, floating point numbers used to be 80 bit. They lived in a funky mini stack on the coprocessor (x87). Then one day, somebody came along and standardized those 32 and 64 bit floats we still have today.

I was going to reply that just because intel did something funny doesn't mean that it was the beginning of the story. but it turns out that the release of the 8087 predates the ratification of IEEE floats by 2 years. in addition, the primary numeric designer for the 8087 was apparently Kahan, which means that they were both part of the same design process. of course there were other formats predating both of these

The floating point "standard" was basically codifying multiple different vendor implementations of the same idea. Hence the mess that floating point is not consistent across implementations.

Re: 4-bit floating point FP4

#12

Post by karmakaze »

There's an "Update:" note for a next post on NF4 format. As far as I can tell this is neither NVFP4 nor MXFP4 which are commonly used with LLM model files. The thing with these formats is that common information is separated in batches so not a singular format but a format for groups of values. I'd like to know more about these (but not enough to go research them myself).

Re: 4-bit floating point FP4

#14

Post by jcranmer »

indolering wrote: post #11
convolvatron wrote: post #10

Earlier quoted context omitted.

I was going to reply that just because intel did something funny doesn't mean that it was the beginning of the story. but it turns out that the release of the 8087 predates the ratification of IEEE floats by 2 years. in addition, the primary numeric designer for the 8087 was apparently Kahan, which means that they were both part of the same design process. of course there were other formats predating both of these

The floating point "standard" was basically codifying multiple different vendor implementations of the same idea. Hence the mess that floating point is not consistent across implementations.

IEEE 754 basically had three major proposals that were considered for standardization. There was the "KCS draft" (Kahan, Coonen, Stone), which was the draft implemented for the x87 coprocessor. There was DEC's counter proposal (aka the PS draft, for Payne and Strecker), and HP's counter proposal (aka, the FW draft for Fraley and Walther). Ultimately, it was the KCS draft that won out and become what we now know as IEEE 754.

One of the striking things, though, is just how radically different KCS was. By the time IEEE 754 forms, there is a basic commonality of how floating-point numbers work. Most systems have a single-precision and double-precision form, and many have an additional extended-precision form. These formats are usually radix-2, with a sign bit, a biased exponent, and an integer mantissa, and several implementations had hit on the implicit integer bit representation. (See http://www.quadibloc.com/comp/cp0201.htm for a tour of several pre-IEEE 754 floating-point formats). What KCS did that was really new was add denormals, and this was very controversial. I also think that support for infinities was introduced with KCS, although there were more precedents for the existence of NaN-like values. I'm also pretty sure that sticky bits as opposed to trapping for exceptions was considered innovative. (See, e.g., https://ethw-images.s3.us-east-va.perf.cloud.ovh.us/ieee/f/f... for a discussion of the differences between the early drafts.)

Now, once IEEE 754 came out, pretty much every subsequent implementation of floating-point has started from the IEEE 754 standard. But it was definitely not a codification of existing behavior when it came out, given the number of innovations that it had!

Re: 4-bit floating point FP4

#16

Post by Sharlin »

ant6n wrote: post #4

> In ancient times, floating point numbers were stored in 32 bits. I thought in ancient times, floating point numbers used to be 80 bit. They lived in a funky mini stack on the coprocessor (x87). Then one day, somebody came along and standardized those 32 and 64 bit floats we still have today.

x87 always had a choice of 32/64/80-bit user-facing floats. It just operated internally on 80 bits.

Re: 4-bit floating point FP4

#17

Post by Sharlin »

chrisjj wrote: post #2

> Programmers were grateful for the move from 32-bit floats to 64-bit floats. It doesn’t hurt to have more precision Someome didn't try it on GPU...

Yeah, and even on CPU using doubles is almost unheard of in many fields.

Re: 4-bit floating point FP4

#18

Post by sc0ttyd »

mysterydip wrote: post #15
sc0ttyd wrote: post #13

9 years ago, I shared this as an April Fools joke here on HN. It seems that life is imitating art. https://github.com/sdd/ieee754-rrp

I especially like your HQQ precision

I think it is only a matter of time before HQQ / 1FP takes over. It's the logical conclusion. I hope to be using my 96-blade razor by then too

Re: 4-bit floating point FP4

#19

Post by kimixa »

pixelesque wrote: post #9
kimixa wrote: post #3

Earlier quoted context omitted.

Even the latest CPUs have a 2:1 fp64:fp32 performance ratio - plus the effects of 2x the data size in cache and bandwidth use mean you can often get greater than a 2x difference. If you're in a numeric heavy use case that's a massive difference. It's not some outdated "Ancient Lore" that causes languages that care about performance to default to fp32 :P

> Even the latest CPUs have a 2:1 fp64:fp32 performance ratio Not completely - for basic operations (and ignoring byte size for things like cache hit ratios and memory bandwidth) if you look at (say Agner Fog's optimisation PDFs of instruction latency) the basic SSE/AVX latency for basic add/sub/mult/div (yes, even divides these days), the latency between float and double is almost always the same on the most recent…

> ... if you look at (say Agner Fog's optimisation PDFs of instruction latency) ...

That.... doesn't seem true? At least for most architectures I looked at?

While true the latency for ADDPS and ADDPD are the same latency, using the zen4 example at least, the double variant only calculates 4 fp64 values compared to the single-precision's 8 fp32. Which was my point? If each double precision instruction processes a smaller number of inputs, it needs to be lower latency to keep the same operation rate.

And DIV also has a significntly lower throughput for fp32 vs fp64 on zen4, 5clk/op vs 3, while also processing half the values?

Sure, if you're doing scalar fp32/fp64 instructions it's not much of a difference (though DIV still has a lower throughput) - but then you're already leaving significant peak flops on the table I'm not sure it's a particularly useful comparison. It's just the truism of "if you're not performance limited you don't need to think about performance" - which has always been the case.

So yes, they do at least have a 2:1 difference in throughput on zen4 - even higher for DIV.

Re: 4-bit floating point FP4

#20

Post by kimixa »

adgjlsfhk1 wrote: post #5
kimixa wrote: post #3

Earlier quoted context omitted.

Even the latest CPUs have a 2:1 fp64:fp32 performance ratio - plus the effects of 2x the data size in cache and bandwidth use mean you can often get greater than a 2x difference. If you're in a numeric heavy use case that's a massive difference. It's not some outdated "Ancient Lore" that causes languages that care about performance to default to fp32 :P

> languages that care about performance to default to fp32 What do you mean by this? In C 1.0 is a double.

But the "float" typename is generally fp32 - if we assume the "most generically named type" is the "default". Though this is a bit of an inconsistency with C - the type name "double" surely implies it's double the expected baseline while, as you mentioned, constants and much of libm default to 'double'.
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