ECM Takes far longer than estimated time

Rhyled · 2010-10-18, 03:02

I set one of my cores to ECM work, just to see what it would do, and have noticed a repeatable discrpency. The thing that grabbed by attention was several exponents with -2 and -1 days remaining in my assignment list.

I have ECM work automatically assigned by Prime 95, which sets an estimated 2:50 (h:mm) time between completions. Actual completion time is about 5:05 between trials (3 curves of 5M candidates). Other type work is much more accurately predicted (as long as I'm not playing Starcraft 2).

I've checked everything I can think of to explain this significant slowdown. I have 3 GB assigned to memory. I've let the machine run solely Prime 95 for 2 days, just to get clean data.

The time discrepancy exists both on v. 25.11 and 26.3b3 (both the estimated time and actual completion time are about 10% lower under 26.3, but the relative ratio is roughly constant).

System:
i7-920 @ 3.71 GHz 6 GB RAM @ 1062 MHz Win 7 64-bit home premium

I double checked my older Athlon 64 x2 4200+ system. Estimated times are separated by 9:30, actual completion times are 13:30 apart. (Stock speed, only 4 GB @ PC3200 on this system ) Windows XP 32-bit, Prime 95 v26.2

Is this something I've done or configured, or are ECM completion estimates consistently 40% lower than actual times for most people?

Prime95 · 2010-10-18, 04:54

I'd like to hear if other users see the same thing.

I'm inclined to believe this is just an error in my attempt at estimating ECM costs. I've a lot more experience with LL timings.

One question: How much time are you spending in stage 1 and stage 2? My only concern is thrashing during stage 2 due to lack of RAM.

petrw1 · 2010-10-18, 05:39

I reported this about a couple years ago and at the time the suggestion was that ECM was lower credits because it is less significant in the search for primes....I'll see if I can find that thread.

Found one: http://www.mersenneforum.org/showpos...03&postcount=9

...in the meantime.

I had several different PCs doing ECM in the fall / winter of 2008. I did NOT have immediate access to all of them but the few I did the results were quite consistent:
- The actual completion time was close to double the original estimate
- The GhzDays per day for each PC was about half of what they produced with TF of LL/DC.

Again as we speak I have a PIV 3.4 Ghz doing ECM also in the 5M range.
The estimates were about 5.5 hours while the actual times were about 13 hours. Unlike P-1, Stage 2 ECM is actually a little faster than Stage 1.

This PC will output 2 GhzDays per day in any other work type but drops to about 1 per day with ECM (Fermat too).

If there is some good news: when I upgraded to 26.2 the actual times dropped to 11 hours ... about 15% faster.

P.S. On this same machine also after the upgrade P-1 was only about 5% faster even though I would have though it was the same basic code.

sdbardwick · 2010-10-18, 05:49

Prime95 26.2 estimates about 55 minutes, while completion is about 1:55. No disk thrashing (W7x64 reports >400MB available during stage 2).

Code:

1808977	NF-ECM	2010-10-18 05:33	0.3	3 curves, B1=50000, B2=5000000	 0.154
1808969	NF-ECM	2010-10-18 03:39	0.2	3 curves, B1=50000, B2=5000000	 0.1546

Prime95 · 2010-10-18, 20:34

Do you find the estimate to be off by a factor of 2 for exponents below 1 million? For B1 = 250000 too?

sdbardwick · 2010-10-18, 21:31

Lets find out:
M823051 B1=50000 gives an ETA of around 16.75 hrs (150 curves).
M1809209 B1=250000 gives ETA of around 3.25 hrs (3 curves).

ECM is not my thing ( I haven't examined the relationships between the bounds, exponent size and number of curves), so if you wanted the <1MM exponent with B1=250000, let me know.

Rhyled · 2010-10-19, 00:30

I looked over the last sets of ECM data in my worker window and found a consistent pattern. Stage 1 takes 60 minutes, Stage 2 takes 34 minutes.

This is on ECMs in the 5M range.

If I were going solely for maximum GHz-day credits, I'd stick with LL under 26.x, which brings in roughly 4.6 GHz-day/day. (it used to be < 4 under 25.11). My second choice being TF which nets me about 4.3 GHz-day credits per core compared to ECM's 2.7. I think ECM-F comes in even lower, but I don't have enough data to accurately estimate that.

My personal goal is to see if I can reach the 90% mark in all categories and get all sorts of colors in my status pie chart. I needed some excuse to OC my i7, after all.

Code:

[Oct 18 08:08] ECM on M5346227: curve #2 with s=3959854856274645, B1=50000, B2=5000000
[Oct 18 08:19] M5346227 curve 2 stage 1 at prime 9241 [18.48%]. Time: 668957.08 ms.
[Oct 18 08:31] M5346227 curve 2 stage 1 at prime 18587 [37.17%]. Time: 686872.08 ms.
[Oct 18 08:42] M5346227 curve 2 stage 1 at prime 27997 [55.99%]. Time: 667264.33 ms.
[Oct 18 08:53] M5346227 curve 2 stage 1 at prime 37313 [74.62%]. Time: 667994.29 ms.
[Oct 18 09:04] M5346227 curve 2 stage 1 at prime 46687 [93.37%]. Time: 665848.92 ms.
[Oct 18 09:08] Stage 1 complete. 1286025 transforms, 1 modular inverses. Time: 237661.41 ms.
[Oct 18 09:08] Using 1435MB of memory in stage 2.
[Oct 18 09:08] Stage 2 init complete. 7129 transforms, 1 modular inverses. Time: 26272.08 ms.
[Oct 18 09:21] M5346227 curve 2 stage 2 at prime 1810213 [35.55%]. Time: 730060.37 ms.
[Oct 18 09:33] M5346227 curve 2 stage 2 at prime 3678377 [73.30%]. Time: 735423.91 ms.
[Oct 18 09:41] Stage 2 complete. 641525 transforms, 14 modular inverses. Time: 487886.31 ms.
[Oct 18 09:41] Stage 2 GCD complete. Time: 4047.01 ms.
[Oct 18 09:41] ECM on M5346227: curve #3 with s=4630087126100238, B1=50000, B2=5000000
[Oct 18 09:52] M5346227 curve 3 stage 1 at prime 9241 [18.48%]. Time: 668169.93 ms.
[Oct 18 10:03] M5346227 curve 3 stage 1 at prime 18587 [37.17%]. Time: 668837.56 ms.
[Oct 18 10:14] M5346227 curve 3 stage 1 at prime 27997 [55.99%]. Time: 666613.52 ms.
[Oct 18 10:26] M5346227 curve 3 stage 1 at prime 37313 [74.62%]. Time: 668173.77 ms.
[Oct 18 10:37] M5346227 curve 3 stage 1 at prime 46687 [93.37%]. Time: 675533.52 ms.
[Oct 18 10:41] Stage 1 complete. 1286025 transforms, 1 modular inverses. Time: 237770.38 ms.
[Oct 18 10:41] Using 1435MB of memory in stage 2.
[Oct 18 10:41] Stage 2 init complete. 7129 transforms, 1 modular inverses. Time: 26124.28 ms.
[Oct 18 10:53] M5346227 curve 3 stage 2 at prime 1810213 [35.55%]. Time: 734652.72 ms.
[Oct 18 11:06] M5346227 curve 3 stage 2 at prime 3678377 [73.30%]. Time: 740824.76 ms.
[Oct 18 11:14] Stage 2 complete. 641525 transforms, 14 modular inverses. Time: 498160.99 ms.
[Oct 18 11:14] Stage 2 GCD complete. Time: 4235.70 ms.
[Oct 18 11:14] M5346227 completed 3 ECM curves, B1=50000, B2=5000000, We4: 8A28C044
[Oct 18 11:14] Using Core2 type-3 FFT length 288K, Pass1=384, Pass2=768
[Oct 18 11:14] ECM on M5346307: curve #1 with s=6577352004968829, B1=50000, B2=5000000
[Oct 18 11:25] M5346307 curve 1 stage 1 at prime 9257 [18.51%]. Time: 676291.25 ms.
[Oct 18 11:37] M5346307 curve 1 stage 1 at prime 18593 [37.18%]. Time: 679936.53 ms.
[Oct 18 11:48] M5346307 curve 1 stage 1 at prime 28001 [56.00%]. Time: 666833.96 ms.
[Oct 18 11:59] M5346307 curve 1 stage 1 at prime 37321 [74.64%]. Time: 668202.71 ms.
[Oct 18 12:10] M5346307 curve 1 stage 1 at prime 46691 [93.38%]. Time: 666216.70 ms.
[Oct 18 12:14] Stage 1 complete. 1286025 transforms, 1 modular inverses. Time: 237611.44 ms.
[Oct 18 12:14] Using 1435MB of memory in stage 2.
[Oct 18 12:15] Stage 2 init complete. 7129 transforms, 1 modular inverses. Time: 25614.31 ms.
[Oct 18 12:27] M5346307 curve 1 stage 2 at prime 1810213 [35.55%]. Time: 730033.41 ms.
[Oct 18 12:39] M5346307 curve 1 stage 2 at prime 3678377 [73.30%]. Time: 741758.74 ms.
[Oct 18 12:47] Stage 2 complete. 641525 transforms, 14 modular inverses. Time: 487752.87 ms.
[Oct 18 12:47] Stage 2 GCD complete. Time: 4041.83 ms.
[Oct 18 12:47] ECM on M5346307: curve #2 with s=8744690854802613, B1=50000, B2=5000000
[Oct 18 12:58] M5346307 curve 2 stage 1 at prime 9241 [18.48%]. Time: 669026.74 ms.
[Oct 18 13:10] M5346307 curve 2 stage 1 at prime 18587 [37.17%]. Time: 667459.10 ms.
[Oct 18 13:21] M5346307 curve 2 stage 1 at prime 27997 [55.99%]. Time: 666842.28 ms.
[Oct 18 13:32] M5346307 curve 2 stage 1 at prime 37313 [74.62%]. Time: 667675.53 ms.
[Oct 18 13:43] M5346307 curve 2 stage 1 at prime 46687 [93.37%]. Time: 665764.93 ms.
[Oct 18 13:47] Stage 1 complete. 1286025 transforms, 1 modular inverses. Time: 238434.54 ms.
[Oct 18 13:47] Using 1435MB of memory in stage 2.
[Oct 18 13:47] Stage 2 init complete. 7129 transforms, 1 modular inverses. Time: 26260.59 ms.
[Oct 18 14:00] M5346307 curve 2 stage 2 at prime 1810213 [35.55%]. Time: 732289.21 ms.
[Oct 18 14:12] M5346307 curve 2 stage 2 at prime 3678377 [73.30%]. Time: 737348.08 ms.
[Oct 18 14:20] Stage 2 complete. 641525 transforms, 14 modular inverses. Time: 491219.40 ms.
[Oct 18 14:20] Stage 2 GCD complete. Time: 4235.47 ms.
[Oct 18 14:20] ECM on M5346307: curve #3 with s=6305224986021923, B1=50000, B2=5000000
[Oct 18 14:31] M5346307 curve 3 stage 1 at prime 9241 [18.48%]. Time: 667893.83 ms.
[Oct 18 14:42] M5346307 curve 3 stage 1 at prime 18587 [37.17%]. Time: 675206.04 ms.
[Oct 18 14:54] M5346307 curve 3 stage 1 at prime 27997 [55.99%]. Time: 667115.13 ms.
[Oct 18 15:05] M5346307 curve 3 stage 1 at prime 37313 [74.62%]. Time: 667153.30 ms.
[Oct 18 15:16] M5346307 curve 3 stage 1 at prime 46687 [93.37%]. Time: 666043.84 ms.
[Oct 18 15:20] Stage 1 complete. 1286025 transforms, 1 modular inverses. Time: 237737.22 ms.
[Oct 18 15:20] Using 1435MB of memory in stage 2.
[Oct 18 15:20] Stage 2 init complete. 7129 transforms, 1 modular inverses. Time: 26175.70 ms.
[Oct 18 15:32] M5346307 curve 3 stage 2 at prime 1810213 [35.55%]. Time: 732643.81 ms.
[Oct 18 15:45] M5346307 curve 3 stage 2 at prime 3678377 [73.30%]. Time: 737581.26 ms.
[Oct 18 15:53] Stage 2 complete. 641525 transforms, 14 modular inverses. Time: 489887.84 ms.
[Oct 18 15:53] Stage 2 GCD complete. Time: 4241.84 ms.
[Oct 18 15:53] M5346307 completed 3 ECM curves, B1=50000, B2=5000000, We4: 8A15C040
[Oct 18 15:53] Using Core2 type-3 FFT length 288K, Pass1=384, Pass2=768
[Oct 18 15:53] ECM on M5346317: curve #1 with s=6536885047291095, B1=50000, B2=5000000
[Oct 18 16:04] M5346317 curve 1 stage 1 at prime 9257 [18.51%]. Time: 670165.62 ms.
[Oct 18 16:15] M5346317 curve 1 stage 1 at prime 18593 [37.18%]. Time: 667559.79 ms.
[Oct 18 16:26] M5346317 curve 1 stage 1 at prime 28001 [56.00%]. Time: 666960.05 ms.
[Oct 18 16:38] M5346317 curve 1 stage 1 at prime 37321 [74.64%]. Time: 667745.78 ms.
[Oct 18 16:49] M5346317 curve 1 stage 1 at prime 46691 [93.38%]. Time: 674392.78 ms.
[Oct 18 16:53] Stage 1 complete. 1286025 transforms, 1 modular inverses. Time: 237330.25 ms.
[Oct 18 16:53] Using 1435MB of memory in stage 2.
[Oct 18 16:53] Stage 2 init complete. 7129 transforms, 1 modular inverses. Time: 26211.91 ms.
[Oct 18 17:05] M5346317 curve 1 stage 2 at prime 1810213 [35.55%]. Time: 733536.68 ms.
[Oct 18 17:18] M5346317 curve 1 stage 2 at prime 3678377 [73.30%]. Time: 736486.30 ms.
[Oct 18 17:26] Stage 2 complete. 641527 transforms, 14 modular inverses. Time: 490900.45 ms.
[Oct 18 17:26] Stage 2 GCD complete. Time: 4247.59 ms.
[Oct 18 17:26] ECM on M5346317: curve #2 with s=2306703053935178, B1=50000, B2=5000000
[Oct 18 17:37] M5346317 curve 2 stage 1 at prime 9241 [18.48%]. Time: 669569.10 ms.
[Oct 18 17:48] M5346317 curve 2 stage 1 at prime 18587 [37.17%]. Time: 669012.09 ms.
[Oct 18 17:59] M5346317 curve 2 stage 1 at prime 27997 [55.99%]. Time: 667672.69 ms.
[Oct 18 18:11] M5346317 curve 2 stage 1 at prime 37313 [74.62%]. Time: 668901.21 ms.
[Oct 18 18:22] M5346317 curve 2 stage 1 at prime 46687 [93.37%]. Time: 666734.86 ms.
[Oct 18 18:26] Stage 1 complete. 1286025 transforms, 1 modular inverses. Time: 238727.96 ms.
[Oct 18 18:26] Using 1435MB of memory in stage 2.
[Oct 18 18:26] Stage 2 init complete. 7129 transforms, 1 modular inverses. Time: 26065.16 ms.
[Oct 18 18:38] M5346317 curve 2 stage 2 at prime 1810213 [35.55%]. Time: 732045.98 ms.
[Oct 18 18:51] M5346317 curve 2 stage 2 at prime 3678377 [73.30%]. Time: 747303.87 ms.
[Oct 18 18:59] Stage 2 complete. 641525 transforms, 14 modular inverses. Time: 490230.41 ms.
[Oct 18 18:59] Stage 2 GCD complete. Time: 4248.69 ms.
[Oct 18 18:59] ECM on M5346317: curve #3 with s=1762390611020433, B1=50000, B2=5000000
[Oct 18 19:10] M5346317 curve 3 stage 1 at prime 9241 [18.48%]. Time: 667292.30 ms.
[Oct 18 19:21] M5346317 curve 3 stage 1 at prime 18587 [37.17%]. Time: 635002.78 ms.
[Oct 18 19:31] M5346317 curve 3 stage 1 at prime 27997 [55.99%]. Time: 635107.50 ms.

sdbardwick · 2010-10-19, 05:16

Quote:

Originally Posted by sdbardwick

Lets find out:
M823051 B1=50000 gives an ETA of around 16.75 hrs (150 curves).
M1809209 B1=250000 gives ETA of around 3.25 hrs (3 curves).

M1809209 B1=250000 actual time to completion was just under 7 hours, so the ETA x2 holds true. M823051 just started, so I'll give an estimated actual completion time when some data is available.

sdbardwick · 2010-10-20, 20:28

Quote:

Originally Posted by sdbardwick

Lets find out:
M823051 B1=50000 gives an ETA of around 16.75 hrs (150 curves).
M1809209 B1=250000 gives ETA of around 3.25 hrs (3 curves).

Quote:

Originally Posted by sdbardwick

M1809209 B1=250000 actual time to completion was just under 7 hours, so the ETA x2 holds true. M823051 just started, so I'll give an estimated actual completion time when some data is available.

M823051 completed 150 curves in 37 hours, so again more than 2x the estimated time.

Both were tested with 26.2B1, W7x64, Phenom2 940@stock (3.06 GHz) with DDR2-800, 640MB/640MB day/night memory setting.

Prime95 · 2010-10-26, 00:53

Question for y'all:

Is "hours per day" set at 24?
What is your rolling average?
Do you get better estimates if you reset your rolling average back to 1000?
@sdbardwick: Do you think you are getting shortchanged on PrimeNet credit?

On my Mac running Windows Vista 32-bit, I am getting good estimates for M510331, B1 = 50000.

My one curve on a 2.5GHz machine took 585 sec. 585/86400*2.5 = 0.0169 GHzD expected credit. Actual credit was 0.0139 GHzD. Not wildly off.

sdbardwick · 2010-10-26, 02:40

Hours per day = 24
Rolling Average = 1032

8.93hrs to complete 3 curves (stage 1 and stage 2) of M5356357 with 1524MB/1524MB RAM setting.

(8.93*60*60)/(24*60*60)*3.2=
32556/86400 * 3.2 = 1.19467 GHz-days anticipated

Code:

Sending result to server: UID: xxxxxxx/PH2x6-1090T, M5356357 completed 3 ECM curves, B1=50000, B2=5000000, We4: 8ADFC1A7, AID: AF7578AE94B8222E53CDAEE5D73022C9

PrimeNet success code with additional info:
CPU credit is 0.5051 GHz-days.

Random thought: Is it possible that only one stage is being credited and/or being used to calculate ETA?
Estimated time is 4:20; actual time is still about double.

2010-10-18, 05:49	#4
sdbardwick Aug 2002 North San Diego County 5·137 Posts	Prime95 26.2 estimates about 55 minutes, while completion is about 1:55. No disk thrashing (W7x64 reports >400MB available during stage 2). Code: 1808977 NF-ECM 2010-10-18 05:33 0.3 3 curves, B1=50000, B2=5000000 0.154 1808969 NF-ECM 2010-10-18 03:39 0.2 3 curves, B1=50000, B2=5000000 0.1546 Last fiddled with by sdbardwick on 2010-10-18 at 05:50

2010-10-26, 00:53	#10
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 7,537 Posts	Question for y'all: Is "hours per day" set at 24? What is your rolling average? Do you get better estimates if you reset your rolling average back to 1000? @sdbardwick: Do you think you are getting shortchanged on PrimeNet credit? On my Mac running Windows Vista 32-bit, I am getting good estimates for M510331, B1 = 50000. My one curve on a 2.5GHz machine took 585 sec. 585/864002.5 = 0.0169 GHzD expected credit. Actual credit was 0.0139 GHzD. Not wildly off. Last fiddled with by Prime95 on 2010-10-26 at 01:22*

2010-10-26, 02:40	#11
sdbardwick Aug 2002 North San Diego County 5×137 Posts	Hours per day = 24 Rolling Average = 1032 8.93hrs to complete 3 curves (stage 1 and stage 2) of M5356357 with 1524MB/1524MB RAM setting. (8.936060)/(246060)3.2= 32556/86400 3.2 = 1.19467 GHz-days anticipated Code: Sending result to server: UID: xxxxxxx/PH2x6-1090T, M5356357 completed 3 ECM curves, B1=50000, B2=5000000, We4: 8ADFC1A7, AID: AF7578AE94B8222E53CDAEE5D73022C9 PrimeNet success code with additional info: CPU credit is 0.5051 GHz-days. Random thought: Is it possible that only one stage is being credited and/or being used to calculate ETA? Estimated time is 4:20; actual time is still about double. Last fiddled with by sdbardwick on 2010-10-26 at 02:48 Reason: Random thought added.

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Estimated relations Factmsieve	cimpresovec	Msieve	21	2016-01-17 15:58
Question about Estimated Days to Complete	Mark Rose	GPU to 72	5	2013-10-04 06:12
Estimated completion dates	Yura	Software	3	2012-11-13 19:45
Time it takes to select polynomials for 154 digits	John5788	Factoring	23	2008-08-27 07:54
Prime95 takes over machine???!!!	kwstone	Software	4	2003-08-10 22:46

2010-10-18, 03:02	#1
Rhyled May 2010 77₈ Posts	ECM Takes far longer than estimated time I set one of my cores to ECM work, just to see what it would do, and have noticed a repeatable discrpency. The thing that grabbed by attention was several exponents with -2 and -1 days remaining in my assignment list. I have ECM work automatically assigned by Prime 95, which sets an estimated 2:50 (h:mm) time between completions. Actual completion time is about 5:05 between trials (3 curves of 5M candidates). Other type work is much more accurately predicted (as long as I'm not playing Starcraft 2). I've checked everything I can think of to explain this significant slowdown. I have 3 GB assigned to memory. I've let the machine run solely Prime 95 for 2 days, just to get clean data. The time discrepancy exists both on v. 25.11 and 26.3b3 (both the estimated time and actual completion time are about 10% lower under 26.3, but the relative ratio is roughly constant). System: i7-920 @ 3.71 GHz 6 GB RAM @ 1062 MHz Win 7 64-bit home premium I double checked my older Athlon 64 x2 4200+ system. Estimated times are separated by 9:30, actual completion times are 13:30 apart. (Stock speed, only 4 GB @ PC3200 on this system ) Windows XP 32-bit, Prime 95 v26.2 Is this something I've done or configured, or are ECM completion estimates consistently 40% lower than actual times for most people? Last fiddled with by Rhyled on 2010-10-18 at 03:04

2010-10-18, 04:54	#2
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 1110101110001₂ Posts	I'd like to hear if other users see the same thing. I'm inclined to believe this is just an error in my attempt at estimating ECM costs. I've a lot more experience with LL timings. One question: How much time are you spending in stage 1 and stage 2? My only concern is thrashing during stage 2 due to lack of RAM.

2010-10-18, 05:39	#3
petrw1 1976 Toyota Corona years forever! "Wayne" Nov 2006 Saskatchewan, Canada 2²·3·17·23 Posts	Same here..... I reported this about a couple years ago and at the time the suggestion was that ECM was lower credits because it is less significant in the search for primes....I'll see if I can find that thread. Found one: http://www.mersenneforum.org/showpos...03&postcount=9 ...in the meantime. I had several different PCs doing ECM in the fall / winter of 2008. I did NOT have immediate access to all of them but the few I did the results were quite consistent: - The actual completion time was close to double the original estimate - The GhzDays per day for each PC was about half of what they produced with TF of LL/DC. Again as we speak I have a PIV 3.4 Ghz doing ECM also in the 5M range. The estimates were about 5.5 hours while the actual times were about 13 hours. Unlike P-1, Stage 2 ECM is actually a little faster than Stage 1. This PC will output 2 GhzDays per day in any other work type but drops to about 1 per day with ECM (Fermat too). If there is some good news: when I upgraded to 26.2 the actual times dropped to 11 hours ... about 15% faster. P.S. On this same machine also after the upgrade P-1 was only about 5% faster even though I would have though it was the same basic code. Last fiddled with by petrw1 on 2010-10-18 at 05:48 Reason: Found one...

2010-10-18, 20:34	#5
Prime95 P90 years forever! Aug 2002 Yeehaw, FL 1D71₁₆ Posts	Do you find the estimate to be off by a factor of 2 for exponents below 1 million? For B1 = 250000 too?

2010-10-18, 21:31	#6
sdbardwick Aug 2002 North San Diego County 5·137 Posts	Lets find out: M823051 B1=50000 gives an ETA of around 16.75 hrs (150 curves). M1809209 B1=250000 gives ETA of around 3.25 hrs (3 curves). ECM is not my thing ( I haven't examined the relationships between the bounds, exponent size and number of curves), so if you wanted the <1MM exponent with B1=250000, let me know.