Assessing Trends in Performance per Watt for Signal Processing Applications

Now that my latest paper has been accepted, Assessing Trends in Performance per Watt for Signal Processing Applications, I can actually talk about the what was important about it. This paper is about power, so here are the important parts:

• Processing GMAC/W calculations are approaching a Powerwall
• Memory Power halves every 29 years, which creates a fixed power requirement
• Non-data flow: Cache is king

The summary is that data-flow processing will have stagnant power improvements from scaling, memory transfers are of fixed power, and cache is really not helping as much as you think when it comes to relative performance per Watt.

The GMAC, everybody does it.

The Multiply ACcumulate (MAC) is a mathematical calculation that computers spend a good deal of their time doing. It's used heavily in natural signal processing, such as audio, and video cards have GPUs that designed to quickly do these calculations. There are two players in the marketing of the semiconductor space who have "Law's" that are not actual laws, but more of trends that have been noticed: Moore and Koomey[1]. Moore said that more transistors will fit on a die, and Koomey did a survey that showed that power consumption is still scaling. The assumption is that as transistors have scaled, their relative behavior has scaled, which is not true. Another item that comes into to play on the marketing side is how you measure power. Most processors offload some power requirements to RAM that has sense amps just burning current to have an effective input capacitance, which makes the CPU power lower at the cost of increased RAM power. If you really want to get a good feel for the power requirements of a system the Giga-MAC per Watt (GMAC/W) is a great calculation.

The the graph above, I present Koomey's system trend and then the trend specific to the GMAC/W . Koomey included systems until 2006, but did not focus on specifically on data flow applications. If you are trying to do things like audio, video games, watching the sky, processing speech, RADAR, and just about any natural system, you are burdened by how much data you can move through the system, and how to get the heat out and data and power in. I am confident that for digital approaches there exists a Powerwall at between 10 to 30 GMAC/W. ie: the end of useful scaling for power constrained systems.

When I first started looking at this with Dr. Marr, it was because of a program called DARPA ACT. The question was if the specs were actually achievable with classical digital approaches, and I happen to play in the space of non-classical digital and analog processing. The idea of ACT is to build a phased array system where the amount of bandwidth and number of beams that can be formed scales per unit Watt. This would allow powerful phased array technology to proliferate in many types of devices, not just expensive military radars. Also, the cloud computing revolution, in part, depends on Koomey's law continuing; if we are to cloud compute with mobile devices, we must be able to transmit, receive, and process wireless data for ever smaller energy levels assuming fixed or slowly growing energy density in batteries, which so far has been the case.

Conclusion: DARPA ACT will not hit their power target with classical digital approaches.
I have not yet seen the final reports, but I hope the teams prove me wrong. I doubt it.

Memory Power is stagnant?

Memory transfer power halves every 29 years, which makes memory power a fixed commodity calculation for data-flow systems. If you have data that is constantly changing, you are burdened by the speed and power of the data bus.

When it comes to memory, it really depends on architecture. As far as improvements, it's life in the slow lane.

What about measured performance in a non-dataflow system?

In a non-dataflow system, cache is king. If you cannot get data in faster, you need to keep it local and handy. I looked into what SPECInt2006 had to say about this using the Stanford CPUDB. If data transfer power is constrained by IO, you need have a lot of cache to minimize non-data instructions coming into the system, but what about power? Using the data in the CPUDB, I plotted SPECInt2006 basemean score per Watt, and then normalized it for processor cache.

I believe that these improvements in SPECint96 score are based upon increases in processor cache because the graph shows almost no trend when the cache is normalized across the processors. As data flow applications are not affected by substantial increase in cache sizes, I believe that there is little improvement between years due to scaling regarding score per Watt.
However, it does make a good argument for simpler code. When you consider that how large programs have gotten relative to cache, the Computer Science community should consider trimming the fat a bit.

Appendix

Of course, the data for the first figure, and the references.

year	node(nm)	processor	GMAC/W	ref
1980	3000	IBM PC-XT	0.000001	[19]
1980	3000	IBM PC	0.000002	[19]
1982	3000	commodore 64	0.000000	[20]
1984	3500	MACINTOSH 128K	0.000005	[21, 22]
1985	1500	IBM PC-AT	0.000002	[23]
1988	2000	MC68030	0.000017	[24]
1991	1000	INTEL 486	0.000065	[25]
1991	1000	IBM PS/2E	0.000086	[25]
1995	500	Pentium Pro 200	0.000182	[26, 27]
1992	750	DEC Alpha 21064 EV4	0.002632	[28]
1996	350	DEC Alpha 21264 EV6	0.001989	[28, 29]
1997	200	Early PowerPC	0.024056	[30]
1998	250	Pentium III 600B	0.003043	[31]
2001	180	PPC 7410	0.014720	[32]
2003	130	PPC 7447	0.017355	[33]
2003	130	Pentium 4 ee HT 3.2	0.006080	[34]
2003	130	TMS-320C6412-500	0.235215	[35, 36]
2003	90	TMS-320C6455-1000	0.210843	[37]
2004	90	POWER5	0.133000	[38, 39]
2006	65	Athlon X2 BE2300	0.029556	[40]
2006	65	Core 2 Extreme X6800	0.027375	[41]
2006	65	Core 2 QX6700	0.028711	[42]
2007	65	Pentium Dual-Core E2140	0.017231	[43]
2007	90	Monarch	0.746592	[44, 45]
2007	65	IBM Cell	0.248889	[46]
2007	90	PPC 8641D	0.027364	[47]
2007	90	TMS-320C6424-700	0.341988	[48]
2007	65	POWER6	0.063000	[39, 49]
2008	45	Core 2 T9400	0.050660	[50, 51]
2008	45	Atom 230	0.140000	[52]
2008	65	TMS-320C6474-850	0.153879	[53]
2008	65	TMS-320C6474-1000	0.166667	[53]
2008	65	TMS-320C6474-1200	0.193846	[53]
2008	40	Tesla C2050	0.757647	[54, 55]
2008	40	Tesla C2075	0.838698	[54]
2008	40	Tesla M2050	0.801422	[54]
2008	40	Tesla M2070	0.801422	[54]
2008	40	Tesla M2090	1.035378	[54, 56]
2008	45	Core i7-965 ee	0.034462	[57]
2009	65	TMS-320C6748	1.360703	[58]
2008	45	Atom N270	0.224000	[59]
2009	90	Tile64	0.712727	[60]
2009	40	ARM Cortex-A	1.085000	[61]
2010	NA	Qualcomm Snapdragon	0.234500	[62]
2010	NA	Tegra 3	0.101500	[62]
2010	45	POWER7	0.112000	[39, 63]
2010	40	Virtex 6	4.736630	[64]
2010	32	Core i7 980 ee	0.107682	[65]
2010	40	Fermi GTX480	0.941472	[54]
2011	40	Fermi GTX580	0.566977	[54, 66]
2011	40	SPARC T4	0.069953	[67]
2012	40	Virtex 7	7.269231	[64]
2012	28	Fermi GTX680	2.773465	[54, 68]
2012	32	Atom D2550	0.130200	[69]
2013	22	POWER8	0.168000	[39, 70]
2013	22	SPARC T5	0.168000	[71]
2013	22	Core i7-4960X	0.116308	[72]
2013	40	TMS320C6678-1250	0.823529	[73]
2013	28	R9 290x	3.942400	[74]
2013	28	Fermi GTX780	3.528000	[75]
2013	40	TILE-Gx72	0.806400	[76]
2014	28	Titan Black	3.584448	[77]
2014	22	E3-1284LV3	0.190638	[4]
2015	14	Kintex Ultrascale	4.806519	[64]

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Reimporting SVN exports.

As a followup to my post regarding SVN exports, I now have an importer. This script re-imports whatever I had exported. You do need to set 3 variables:
SVN_TARGET_REPO, the target repository.
SVN_LOCAL_REPO, this is the new location of your files
SVN_BACKUP, this is the svn export directory

#!/bin/sh
SVN_TARGET_REPO="svn+ssh://LOGIN@SERVER/var/svn/nextretro"
SVN_LOCAL_REPO="/Users/degs/personal/projects.svn/nextretro.new"
SVN_BACKUP="/Users/degs/personal/projects.svn/nextretro/svnbackup"

#create the directory for the target, and checkout revision 0, if no .svn
if [[ ! -e $SVN_LOCAL_REPO/.svn ]]; then
 echo "creating SVN repo"
 mkdir -p $SVN_LOCAL_REPO
 svn co $SVN_TARGET_REPO $SVN_LOCAL_REPO/.
else
 echo "skipping export: $SVN_LOCAL_REPO/.svn" 
fi
#now reimport everything
cd $SVN_BACKUP
for f in $(ls -d * |sort -n); do
    if [[ -d $f ]]; then
     echo "importing rev: $f"
        rsync -r --exclude=.svn --exclude=commit.log $SVN_BACKUP/$f/* $SVN_LOCAL_REPO
        svn add $SVN_LOCAL_REPO/* --force
        COMMITLOG=`cat $SVN_BACKUP/$f/commit.log`
        svn commit $SVN_LOCAL_REPO -m "$COMMITLOG"
        
    fi
done

Switching devices off of different supplies, flyback, and realities of the electron

The microcontroller can only drive about 5mA per pin; however, most non-digital circuits take much more power. Let's say you have a controller that runs off of 3 volts and you want to switch something that requires 5V or 12V. How is this done? The easiest way in a shared GND system is to use a NPN transistor so that when the input line goes "high", the NPN pulls hard to low.
Consider the following schematic:

For this example, let us assume that the power supply is 12v, and you have a BJT that you know very little about except that it's a NPN. The first order of business is to protect the MCU. You want to be sure to not zap your MCU. So we will assign our first value:
R0 1kOhm

R0 will limit the current drawn by the BJT to MCU Vdd/R. If you decrease R, the driving strength of the BJT increases (until saturation); however, you risk over driving your MCU output pin. If you need more driving strength use a Darlington Transistor or a motor driver IC.

R1 and LED0 exist purely to signal that your circuit works. You do not need these in reality. A good value for R1 would also be 1kOhm, and be sure that your LED is connected in the right direction

R2, LED1 and IND0 are where things get interesting. Firstly, let's talk about IND0, the inductor. A relay and a motor are basically inductors, and inductors resist a change in current, ie: they store current in their field. This means that if you change the state of an inductor, there will be a change in voltage based upon the internal resistance of the coil. This is where R2 and LED1 come in. R2 should be about 10ohms, only to increase the resistance for this experiment. R2 should be 0ohms otherwise. LED2 responds as something called a "flyback" diode, so that when the inductor changes state from on to off, it does not cause a voltage spike back into VDD. You dissipate this voltage into LED2 and you can see it flash for an instant. The larger the inductor, the larger this flyback voltage that is produced when the inductor is switched off. This flyback current is the number one cause of stress in college lab classes because it will cause something called "latchup" if the spike makes it back to the MCU.

Exporting SVN to a file hierarchy

Google code is shutting down, and I wanted not migrate the code to GIT on bitbucket because my scripts are all dependent on a version number and not a hash. Furthermore, I have found that GIT does not do well with binary.

The script will make a directory called svnbackup/REVISION so that I can easily import them later.

I pulled my nextretro project, and now I just have to decide where to put it.

#!/bin/bash
#this script exports any SVN repo to a possibly huge directory export
BACKUP_LOCATION='svnbackup'
#get the current repo
REMOTE_URL=$(svn info| grep -vi "Relative" | grep URL)
CURRENT_URL="${REMOTE_URL#*:}"
#get this repo version
REMOTE_VERSION=$(svn info | grep Revision)
CURRENT_VERSION="${REMOTE_VERSION#*:}" # strip out the version number
#create the directory
mkdir -p $BACKUP_LOCATION
svn info > $BACKUP_LOCATION/repo.info
echo "backing up current svn: $REMOTE_URL"
echo "current version: $CURRENT_VERSION"
COUNTER=1
while [  $COUNTER -ne $CURRENT_VERSION ]; do
     echo Exporting revision: $COUNTER
     mkdir -p $BACKUP_LOCATION/$COUNTER
     svn co -r$COUNTER $CURRENT_URL $BACKUP_LOCATION/$COUNTER/.
     svn log --revision $COUNTER > $BACKUP_LOCATION/$COUNTER/commit.log
     let COUNTER=COUNTER+1 
done

Would a Tesla battery system be worth it?

Telsa motors loves good press; however, when it came to the press about their battery technology, I had to scratch my head a bit. I spend most of my time counting electrons, and I have a pretty good feel for battery capability and battery chemistry. For starters, here's the original article: This new Tesla battery will power your home, and maybe the electric grid too.

The premise is a super efficient battery and inverter. You still charge up the batteries from a power source, but you can get power off-peak at a discount rate and save it, or use solar and save it. This is a nobel cause, but you still need to fill the batteries from a source. Batteries have loss, and if you look at the proposal from a purely power perspective, you have a loss due to the cost of conversion; however, you could have a net-gain monetarily if you can purchase power cheaper and reuse it.

The kicker is that I find power to be inexpensive in the USA, when compared to what I paid in Japan (unless you are in Hawai'i). The questions I see are:

1) At what point does it make sense to purchase an expensive battery pack?
2) How large does it have to be to be useful?

To start, here's a summary of energy density in Mega-Joules per Kilogram.

and then you can assume Telsa is using what they know: 20130187591, 20130181511.

In my figure, one needs to remember that energy storage is not conversion! This means that there are losses to different degrees depending on the power source. In the Telsa patents, you have a fast and a slow responding battery and a controller that makes the battery usage general purpose because you use different batteries for sustained load or instantaneous load, which makes sense for both a car or a house. In the case of batteries, you store energy that is saved/recovered as DC power, and then you take a 15% conversion loss to AC for houses.

How much power does the average American home use? 10000kWh per year. To make the math easy, let's day that it's 900kWh per month, so 30kWh per day. Let's say that you only want to save a single hour of power, that's 1kWh.

Ignoring losses of the conversion, the 12v truck battery gives you about 1kWh. If you wanted to save a day's work of power, you'd need 30 of these. So, what Telsa is actually offering is an attempt to scale down power for space. Lithium-Ion batteries being 7x better than lead acid for energy density, that would still be the displacement of about 4 lead acid batteries. The question is if Tesla can get the cost down for the batteries, and the conversion efficiency up. In 30 battery case, that would be $3k in batteries. Tesla would have to hit price point much lower than that; however, would it still be worth it. The cost of power varies greatly; however, let's say that you save 5cents per kWh by charging off peak, and store 5kWh per day at a discount. This results in 25 cents of savings per day. That's $USD 91.25 per year in savings, if your new found cheap power doesn't make you use more of it. (Higher efficiency cars seem to make us use more gas, for example [Knittel, Christopher R. 2011. "Automobiles on Steroids: Product Attribute Trade-Offs and Technological Progress in the Automobile Sector." American Economic Review, 101(7): 3368-99.])

Bottom line, assuming that the lifecycle of the batteries do not exist, and converters are 100% efficient, and you save five cents per kilowatt hour, you'll need the device to come to market at $91.25 if you want to recoup the device cost in a year.