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hypergeometric distribution CDF for PeerDAS (#6447)

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tersec 2024-07-25 01:59:24 +00:00 committed by GitHub
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commit 15cca5f93e
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3 changed files with 213 additions and 2 deletions
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5
AllTests-mainnet.md
View File

@ -833,9 +833,10 @@ OK: 1/1 Fail: 0/1 Skip: 0/1
## Spec helpers
```diff
+ build_proof - BeaconState OK
+ hypergeom_cdf OK
+ integer_squareroot OK
```
OK: 2/2 Fail: 0/2 Skip: 0/2
OK: 3/3 Fail: 0/3 Skip: 0/3
## Specific field types
```diff
+ root update OK
@ -1033,4 +1034,4 @@ OK: 2/2 Fail: 0/2 Skip: 0/2
OK: 9/9 Fail: 0/9 Skip: 0/9
---TOTAL---
OK: 690/695 Fail: 0/695 Skip: 5/695
OK: 691/696 Fail: 0/696 Skip: 5/696

23
beacon_chain/spec/helpers.nim
View File

@ -605,3 +605,26 @@ proc blockToBlockHeader*(blck: ForkyBeaconBlock): ExecutionBlockHeader =
proc compute_execution_block_hash*(blck: ForkyBeaconBlock): Eth2Digest =
rlpHash blockToBlockHeader(blck)
from std/math import exp, ln
from std/sequtils import foldl
func ln_binomial(n, k: int): float64 =
if k > n:
low(float64)
else:
template ln_factorial(n: int): float64 =
(2 .. n).foldl(a + ln(b.float64), 0.0)
ln_factorial(n) - ln_factorial(k) - ln_factorial(n - k)
func hypergeom_cdf*(k: int, population: int, successes: int, draws: int):
float64 =
if k < draws + successes - population:
0.0
elif k >= min(successes, draws):
1.0
else:
let ln_denom = ln_binomial(population, draws)
(0 .. k).foldl(a + exp(
ln_binomial(successes, b) +
ln_binomial(population - successes, draws - b) - ln_denom), 0.0)

187
tests/test_helpers.nim
View File

@ -67,3 +67,190 @@ suite "Spec helpers":
process(fieldVar, i shl childDepth)
i += 1
process(state, state.numLeaves)
test "hypergeom_cdf":
# Generated with SciPy's hypergeom.cdf() function
const tests = [
( 0, 2, 1, 1, 0.5),
( 8, 200, 162, 9, 0.85631007588636132),
( 2, 20, 11, 5, 0.39551083591331271),
( 2, 5, 4, 3, 0.59999999999999987),
( 16, 100, 71, 28, 0.050496322336354399),
( 1, 5, 2, 2, 0.90000000000000002),
( 0, 5, 4, 1, 0.20000000000000004),
( 27, 200, 110, 54, 0.24032479119039216),
( 0, 10, 2, 5, 0.22222222222222224),
( 3, 50, 27, 5, 0.77138514980460271),
( 2, 50, 24, 8, 0.15067269856977925),
( 4, 20, 16, 7, 0.10113519091847264),
( 13, 500, 408, 15, 0.79686197891279686),
( 0, 5, 3, 1, 0.40000000000000008),
( 0, 20, 14, 2, 0.078947368421052627),
( 49, 100, 62, 79, 0.6077614986362827),
( 2, 10, 3, 6, 0.83333333333333337),
( 0, 50, 31, 2, 0.13959183673469389),
( 2, 5, 4, 3, 0.59999999999999987),
( 4, 50, 21, 8, 0.81380887468704521),
( 0, 10, 7, 2, 0.066666666666666652),
( 0, 10, 1, 4, 0.59999999999999987),
( 0, 20, 4, 2, 0.63157894736842102),
( 0, 3, 2, 1, 0.33333333333333331),
( 39, 500, 427, 51, 0.05047757656076568),
( 2, 100, 6, 21, 0.89490672557682871),
( 5, 20, 11, 9, 0.68904501071683733),
( 0, 2, 1, 1, 0.5),
( 0, 3, 1, 1, 0.66666666666666674),
( 14, 50, 27, 30, 0.16250719969887772),
( 0, 5, 4, 1, 0.20000000000000004),
( 0, 5, 4, 1, 0.20000000000000004),
( 2, 10, 8, 4, 0.13333333333333333),
( 1, 5, 3, 2, 0.69999999999999996),
( 25, 100, 77, 31, 0.79699287800204943),
( 0, 3, 2, 1, 0.33333333333333331),
( 7, 20, 15, 8, 0.94891640866873062),
( 3, 50, 26, 7, 0.45339412360688952),
( 1, 10, 8, 2, 0.37777777777777771),
( 40, 200, 61, 134, 0.4491054454532335),
( 1, 5, 2, 4, 0.40000000000000008),
( 0, 10, 6, 1, 0.39999999999999991),
( 1, 50, 10, 13, 0.19134773839560071),
( 0, 2, 1, 1, 0.5),
( 1, 20, 5, 2, 0.94736842105263153),
( 7, 50, 12, 30, 0.57532691212157849),
( 0, 3, 1, 1, 0.66666666666666674),
( 6, 10, 7, 9, 0.69999999999999996),
( 0, 20, 2, 1, 0.90000000000000002),
( 2, 10, 5, 3, 0.91666666666666663),
( 0, 10, 8, 1, 0.19999999999999998),
(258, 500, 372, 347, 0.53219975096883698),
( 1, 3, 2, 2, 0.66666666666666674),
( 45, 200, 129, 68, 0.69415691010446789),
( 1, 10, 8, 2, 0.37777777777777771),
( 0, 10, 2, 1, 0.80000000000000004),
( 1, 10, 4, 5, 0.26190476190476192),
( 3, 50, 36, 4, 0.74422492401215801),
( 0, 20, 6, 1, 0.69999999999999996),
( 0, 5, 2, 3, 0.10000000000000002),
( 1, 200, 47, 9, 0.33197417194852796),
( 20, 50, 32, 30, 0.78323921453982637),
( 16, 50, 21, 34, 0.9149336897131396),
( 17, 50, 38, 22, 0.69599001425795692),
( 0, 5, 2, 3, 0.10000000000000002),
( 1, 5, 3, 2, 0.69999999999999996),
( 0, 10, 9, 1, 0.10000000000000001),
( 0, 5, 2, 3, 0.10000000000000002),
( 2, 10, 5, 6, 0.26190476190476192),
( 0, 5, 2, 1, 0.59999999999999987),
( 7, 20, 16, 9, 0.62538699690402466),
( 1, 100, 27, 2, 0.92909090909090908),
( 27, 100, 58, 50, 0.271780848715515),
( 47, 100, 96, 51, 0.063730084348641039),
( 1, 20, 6, 2, 0.92105263157894735),
( 1, 10, 6, 2, 0.66666666666666674),
( 0, 2, 1, 1, 0.5),
( 0, 20, 11, 1, 0.45000000000000001),
( 0, 3, 1, 1, 0.66666666666666674),
( 0, 2, 1, 1, 0.5),
( 0, 10, 1, 7, 0.29999999999999999),
( 0, 2, 1, 1, 0.5),
( 0, 100, 36, 1, 0.64000000000000001),
( 1, 100, 68, 2, 0.53979797979797983),
( 13, 200, 79, 29, 0.80029860188814683),
( 0, 10, 5, 1, 0.49999999999999994),
( 0, 3, 2, 1, 0.33333333333333331),
( 13, 100, 64, 21, 0.5065368728909565),
( 1, 10, 6, 4, 0.11904761904761905),
( 0, 2, 1, 1, 0.5),
( 0, 5, 1, 2, 0.59999999999999987),
( 0, 2, 1, 1, 0.5),
( 1, 5, 4, 2, 0.40000000000000008),
( 14, 50, 41, 17, 0.65850372332742224),
( 0, 2, 1, 1, 0.5),
( 0, 3, 1, 1, 0.66666666666666674),
( 1, 100, 2, 62, 0.61797979797979785),
( 0, 2, 1, 1, 0.5),
( 0, 2, 1, 1, 0.5),
( 12, 500, 312, 16, 0.91020698917397613),
( 0, 20, 2, 6, 0.47894736842105257),
( 0, 3, 2, 1, 0.33333333333333331),
( 1, 10, 3, 4, 0.66666666666666674),
( 0, 3, 1, 1, 0.66666666666666674),
( 0, 3, 2, 1, 0.33333333333333331),
( 6, 50, 20, 14, 0.72026241648862666),
( 3, 20, 14, 6, 0.22523219814241485),
( 0, 2, 1, 1, 0.5),
( 4, 100, 72, 7, 0.30429108474790234),
( 0, 5, 1, 2, 0.59999999999999987),
( 0, 10, 4, 1, 0.59999999999999998),
( 1, 3, 2, 2, 0.66666666666666674),
( 0, 3, 1, 1, 0.66666666666666674),
( 22, 50, 46, 24, 0.66413373860182379),
( 1, 5, 2, 4, 0.40000000000000008),
( 62, 100, 80, 79, 0.3457586020522983),
( 0, 3, 2, 1, 0.33333333333333331),
( 0, 10, 2, 7, 0.066666666666666666),
( 0, 2, 1, 1, 0.5),
( 0, 5, 2, 1, 0.59999999999999987),
( 42, 200, 145, 57, 0.65622325663713577),
( 1, 20, 12, 3, 0.34385964912280703),
( 0, 2, 1, 1, 0.5),
( 2, 10, 4, 7, 0.33333333333333331),
( 1, 5, 3, 2, 0.69999999999999996),
( 0, 10, 6, 2, 0.1333333333333333),
( 2, 10, 6, 5, 0.26190476190476192),
( 0, 5, 2, 1, 0.59999999999999987),
( 1, 3, 2, 2, 0.66666666666666674),
( 0, 50, 25, 2, 0.24489795918367349),
( 0, 50, 39, 1, 0.22),
( 2, 5, 3, 3, 0.90000000000000002),
( 9, 50, 46, 10, 0.60316977854971765),
( 0, 5, 2, 1, 0.59999999999999987),
( 72, 500, 324, 112, 0.49074275180525029),
( 0, 50, 9, 7, 0.22507959200836167),
( 0, 5, 2, 2, 0.30000000000000004),
( 17, 100, 35, 60, 0.067474411926413541),
( 15, 100, 83, 17, 0.83718038506483827),
( 0, 10, 7, 1, 0.29999999999999999),
( 28, 200, 87, 77, 0.071226044946921765),
(154, 500, 361, 212, 0.61327756805578304),
( 1, 10, 2, 3, 0.93333333333333335),
( 0, 10, 4, 4, 0.071428571428571425),
( 0, 5, 1, 1, 0.79999999999999993),
( 2, 5, 3, 4, 0.59999999999999987),
( 0, 10, 4, 1, 0.59999999999999998),
( 0, 3, 2, 1, 0.33333333333333331),
( 0, 10, 3, 1, 0.69999999999999996),
( 0, 50, 10, 1, 0.80000000000000004),
( 0, 2, 1, 1, 0.5),
( 0, 10, 1, 3, 0.69999999999999996),
( 2, 20, 12, 4, 0.53457172342621262),
( 0, 5, 4, 1, 0.20000000000000004),
( 4, 20, 9, 7, 0.89821981424148611),
( 2, 200, 188, 3, 0.17021775544388609),
(132, 500, 298, 215, 0.78880271135040059),
( 2, 5, 4, 3, 0.59999999999999987),
( 0, 2, 1, 1, 0.5),
( 2, 10, 6, 5, 0.26190476190476192),
( 0, 3, 1, 1, 0.66666666666666674),
(156, 200, 128, 174, 1),
( 1, 20, 6, 4, 0.65737874097007221),
( 0, 5, 0, 0, 1),
(488, 500, 198, 500, 1),
(143, 500, 8, 371, 1),
( 2, 10, 6, 5, 0.26190476190476192),
( 1, 5, 2, 4, 0.40000000000000008),
( 0, 3, 2, 0, 1),
( 12, 50, 7, 17, 1),
(129, 200, 43, 133, 1),
( 0, 5, 3, 0, 1),
( 0, 2, 1, 1, 0.5),
( 5, 20, 20, 17, 0),
( 4, 10, 4, 8, 1),
( 46, 500, 478, 58, 5.1715118817799218e-07),
( 0, 3, 2, 3, 0),
( 0, 3, 1, 1, 0.66666666666666674),
( 76, 500, 0, 120, 1),
( 1, 100, 41, 12, 0.011989696504564528),
]
for (k, population, successes, draws, val) in tests:
check: abs(hypergeom_cdf(k, population, successes, draws) - val) < 1e-11