handle rewards overflow

[djrtwo]

• Add EFFECTIVE_BALANCE_INCREMENT to avoid overflow in reward calculations
• Create bit analysis to show safety and precision
• Hand audit all multiplications in spec for overflows. The culprit in the two we make adjustments for were due to multiplying by the total active balance. I recommend a couple others do a similar audit

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Analysis generally looks good. Even at 10billion ETH deposited, the calculation only hits ~40 bits.

Because total_balance and attesting_balance are normalized with EFFECTIVE_BALANCE_INCREMENT, no precision in calculations is lost.

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todo (maybe future PR):

Figure out a way to test this... running a single rewards test in minimal config with 50k vals took 1 hour. Might look into using a config with "weird" values such as a MAX_EFFECTIVE_BALANCE equal to 32000 eth instead of 32.

[djrtwo]

cc: @hermanjunge

[ghost]

Took the new computations into this simulator https://github.com/hermanjunge/eth2-reward-simulation/blob/154130f7c712211c16483343916b70159681dade/src/process_epoch/get_attestation_deltas.rs#L56

Compiled using the --release flag. The latter is relevant, as rust won't yell at you about overflows in release mode, only on debug.

If we run the simulation at an online probability of .95 and 5 epochs against the initial stakes of 500k, 1M, 5M, 10M, and 100M and compare the results gotten (below the horizontal line, to improve readability) with a back-of-the-envelope calculation in a spreadsheet, we don't see major discrepancies in the total FFG rewards nor the total FFG penalties.

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[ ubuntu: reward ]$ ./target/release/simulation -i 500000 -e 5 -p 0.95
epoch number,FFG rewards,FFG penalties,proposer rewards,attester rewards,total staked balance,total effective balance,max balance,min balance,total validators,total active validatos,time μs
0,970160952,52067778,39753180,290278175,500001248124529,499242000000000,32001409887,31999931309,15625,15625,2618
1,965361000,56282520,42433024,288851720,500002488487753,499242000000000,32001495657,31999864715,15625,15625,597
2,968483352,52995792,41106992,289785980,500003734868285,499202000000000,32002906533,31999798121,15625,15625,641
3,968183043,53275236,41023652,289697659,500004980497403,499202000000000,32002991381,31999880312,15625,15625,559
4,970476948,50860569,41065322,290384034,500006231563138,499198000000000,32003076229,31999813715,15625,15625,617

[ ubuntu: reward ]$ ./target/release/simulation -i 1000000 -e 5 -p 0.95
epoch number,FFG rewards,FFG penalties,proposer rewards,attester rewards,total staked balance,total effective balance,max balance,min balance,total validators,total active validatos,time μs
0,1374141480,71300760,58134951,411170292,1000001772145963,998532000000000,32001935267,31999951430,31250,31250,2855
1,1368506826,76094286,54379674,409486464,1000003528424641,998532000000000,32001997110,31999904342,31250,31250,1252
2,1370202267,74309526,59777595,409993768,1000005294088745,998458000000000,32002057099,31999857254,31250,31250,1308
3,1368681216,75896964,58192425,409541606,1000007054607028,998458000000000,32002117092,31999915368,31250,31250,1105
4,1367702880,76926861,60069600,409248857,1000008814701504,998452000000000,32002177085,31999868284,31250,31250,1141

[ ubuntu: reward ]$ ./target/release/simulation -i 5000000 -e 5 -p 0.95
epoch number,FFG rewards,FFG penalties,proposer rewards,attester rewards,total staked balance,total effective balance,max balance,min balance,total validators,total active validatos,time μs
0,3061879260,170719200,109108610,916011470,5000003916280140,4992140000000000,32004223292,31999978280,156250,156250,6798
1,3059543778,170325912,130091035,915536950,5000007851125991,4992140000000000,32004250120,31999957220,156250,156250,6549
2,3062176530,167554296,129961199,916324774,5000011792034198,4991753000000000,32004276948,31999936160,156250,156250,7101
3,3059941368,169644618,129831363,915655928,5000015727818239,4991753000000000,32004303776,31999962150,156250,156250,5873
4,3059775531,169819200,125764714,915606303,5000019659145587,4991706000000000,32004330604,31999941090,156250,156250,5912

[ ubuntu: reward ]$ ./target/release/simulation -i 10000000 -e 5 -p 0.95
epoch number,FFG rewards,FFG penalties,proposer rewards,attester rewards,total staked balance,total effective balance,max balance,min balance,total validators,total active validatos,time μs
0,4334305536,237573120,189972480,1296846078,10000005583550974,9984533000000000,32005955598,31999984640,312500,312500,14281
1,4324605510,242375595,184035840,1294292985,10000011144109714,9984533000000000,32005974565,31999969751,312500,312500,14529
2,4325408868,241529802,177913680,1294533387,10000016700435847,9983781000000000,32005993532,31999954862,312500,312500,15261
3,4331683017,235547844,183293760,1296159441,10000022276024221,9983781000000000,32006012502,31999939970,312500,312500,13097
4,4327471080,239982192,183664800,1294899112,10000027842077021,9983699000000000,32006031472,31999958341,312500,312500,13277

[ ubuntu: reward ]$ ./target/release/simulation -i 100000000 -e 5 -p 0.95
epoch number,FFG rewards,FFG penalties,proposer rewards,attester rewards,total staked balance,total effective balance,max balance,min balance,total validators,total active validatos,time μs
0,13696331406,760465347,562204380,4096432020,100000017594502459,99843429000000000,32018746140,31999995143,3125000,3125000,149188
1,13686732822,756199224,521384260,4094009858,100000035140430175,99843429000000000,32018752138,31999990436,3125000,3125000,154040
2,13686842307,756083961,542350958,4094042615,100000052707582094,99835981000000000,32018758136,31999985729,3125000,3125000,153285
3,13682894079,759087837,580387888,4092868691,100000070304644915,99835981000000000,32018764134,31999981022,3125000,3125000,150937
4,13680966606,761117112,598571396,4092291962,100000087915357767,99835290000000000,32018770132,31999976315,3125000,3125000,148122

[hwwhww]

The analysis looks solid. LGTM! 👍