The future is 24bit

preda · 2020-09-18, 21:46

In light of Nvidia's new GPU launch, it appears we need to find a way of doing big convolutions using SP FP (FP32). This has been an elusive task in the past.

That new GPU has 2x FP32 vs. INT32, and 64x FP32 vs. FP64.

preda · 2020-09-18, 22:48

AKA "The Holy Grail" :)

storm5510 · 2020-09-18, 23:44

Quote:

Originally Posted by preda

In light of Nvidia's new GPU launch, it appears we need to find a way of doing big convolutions using SP FP (FP32). This has been an elusive task in the past.

That new GPU has 2x FP32 vs. INT32, and 64x FP32 vs. FP64.

Sorry, I cannot make a connection to 24-bit. FP32 seems to represent 32-bit. FP64 is 64-bit. 2x FP32 suggests 64-bit as wall. Would you care to elaborate a little?

kriesel · 2020-09-19, 00:26

Quote:

Originally Posted by storm5510

Sorry, I cannot make a connection to 24-bit.

https://en.wikipedia.org/wiki/IEEE_754

Mark Rose · 2020-09-19, 00:26

Quote:

Originally Posted by storm5510

Sorry, I cannot make a connection to 24-bit. FP32 seems to represent 32-bit. FP64 is 64-bit. 2x FP32 suggests 64-bit as wall. Would you care to elaborate a little?

Normal FP32 has 23 bits for the fraction component, 8 for the exponent, and 1 for the sign (+/-). The exponent bits effectively give one more bit of precision, either being all zero or not, meaning FP32 can do INT24 math.

preda · 2020-09-19, 03:14

Some previous discussion:
https://www.mersenneforum.org/showthread.php?t=23926

henryzz · 2020-09-19, 05:31

It sounds like the additional memory usage(and hence memory bandwidth) may be an issue. Would 64x be enough that arithmetic using double-floats would be useful?

Prime95 · 2020-09-19, 05:35

Years ago I toyed with using two or three 32-bit ints to create a 64 or 96-bit float (no exponent bits -- all mantissa).

I did enough work to prove to myself it was feasible and, at the time, would be about a fast as a double-precision FFT. As nVidia has lowered and lowered the DP-to-SP ratio, it would be a substantial winner now.

An awful lot of code to write though.

M344587487 · 2020-09-19, 08:48

This post ( https://mersenneforum.org/showpost.p...4&postcount=85 ) suggests that the doubling of fp32 is because they upgraded the int32 units to also do fp32. If int32 and fp32 operations can be freely mixed or if the workload can be split into int32-only and fp32-only operations then there's more bits up for grabs. A split solution should also work on the 20 series as that can do fp32 and int32 concurrently but that is highly memory limited so there may not be a benefit.

preda · 2020-09-19, 09:11

Quote:

Originally Posted by M344587487

This post ( https://mersenneforum.org/showpost.p...4&postcount=85 ) suggests that the doubling of fp32 is because they upgraded the int32 units to also do fp32. If int32 and fp32 operations can be freely mixed or if the workload can be split into int32-only and fp32-only operations then there's more bits up for grabs. A split solution should also work on the 20 series as that can do fp32 and int32 concurrently but that is highly memory limited so there may not be a benefit.

Yes. But a number of INT32 is used anyway to do pointer arithmetic, conditional expression, etc; so it's not like when doing a "pure SP" FFT the INT32 is idle.

storm5510 · 2020-09-19, 16:11

I got to thinking about color palettes. A 24-bit palette is capable of 16,777,215 unique values. This has been in use a long time. Before was 16-bit capable of only 65,536 colors. Whether this is any way relative to the discussion here, I don't know.

2020-09-18, 21:46	#1
preda "Mihai Preda" Apr 2015 2·23·29 Posts	The future is 24bit In light of Nvidia's new GPU launch, it appears we need to find a way of doing big convolutions using SP FP (FP32). This has been an elusive task in the past. That new GPU has 2x FP32 vs. INT32, and 64x FP32 vs. FP64.

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2020-09-18, 22:48	#2
preda "Mihai Preda" Apr 2015 2×23×29 Posts	AKA "The Holy Grail" :)

2020-09-19, 03:14	#6
preda "Mihai Preda" Apr 2015 1334₁₀ Posts	Some previous discussion: https://www.mersenneforum.org/showthread.php?t=23926

2020-09-19, 05:31	#7
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 5794₁₀ Posts	It sounds like the additional memory usage(and hence memory bandwidth) may be an issue. Would 64x be enough that arithmetic using double-floats would be useful?

2020-09-19, 05:35	#8
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 2×41×89 Posts	Years ago I toyed with using two or three 32-bit ints to create a 64 or 96-bit float (no exponent bits -- all mantissa). I did enough work to prove to myself it was feasible and, at the time, would be about a fast as a double-precision FFT. As nVidia has lowered and lowered the DP-to-SP ratio, it would be a substantial winner now. An awful lot of code to write though.

2020-09-19, 08:48	#9
M344587487 "Composite as Heck" Oct 2017 3×5×7² Posts	This post ( https://mersenneforum.org/showpost.p...4&postcount=85 ) suggests that the doubling of fp32 is because they upgraded the int32 units to also do fp32. If int32 and fp32 operations can be freely mixed or if the workload can be split into int32-only and fp32-only operations then there's more bits up for grabs. A split solution should also work on the 20 series as that can do fp32 and int32 concurrently but that is highly memory limited so there may not be a benefit.

2020-09-19, 16:11	#11
storm5510 Random Account Aug 2009 U.S.A. 3²×199 Posts	I got to thinking about color palettes. A 24-bit palette is capable of 16,777,215 unique values. This has been in use a long time. Before was 16-bit capable of only 65,536 colors. Whether this is any way relative to the discussion here, I don't know.