add: `get_extended_sample_count` with test (#6544)

* add: get_extended_sample_count with test

* drop return

* reviews

* review fix

* fixed

* fix doc

* hooked to all_tests

* rm bin

* add updated test file

* early return, maybe need results?

* refactor function intricacies

* drop columnsCount

AllTests-mainnet.md

@@ -531,6 +531,11 @@ OK: 10/12 Fail: 0/12 Skip: 2/12
 + snapshot_cases                                                                             OK
 ```
 OK: 5/5 Fail: 0/5 Skip: 0/5
+## EIP-7594 Sampling Tests
+```diff
++ EIP7594: Extended Sample Count                                                             OK
+```
+OK: 1/1 Fail: 0/1 Skip: 0/1
 ## EL Configuration
 ```diff
 + Empty config file                                                                          OK
@@ -1114,4 +1119,4 @@ OK: 2/2 Fail: 0/2 Skip: 0/2
 OK: 9/9 Fail: 0/9 Skip: 0/9
 
 ---TOTAL---
-OK: 759/764 Fail: 0/764 Skip: 5/764
+OK: 760/765 Fail: 0/765 Skip: 5/765

beacon_chain/spec/eip7594_helpers.nim

@@ -98,3 +98,29 @@ func get_custody_column_list*(node_id: NodeId,
       NUMBER_OF_COLUMNS div DATA_COLUMN_SIDECAR_SUBNET_COUNT
 
   sortedColumnIndexList(ColumnIndex(columns_per_subnet), subnet_ids)
+
+# https://github.com/ethereum/consensus-specs/blob/v1.5.0-alpha.5/specs/_features/eip7594/peer-sampling.md#get_extended_sample_count
+func get_extended_sample_count*(samples_per_slot: int,
+                                allowed_failures: int):
+                                int =
+  ## `get_extended_sample_count` computes the number of samples we
+  ## should query from peers, given the SAMPLES_PER_SLOT and 
+  ## the number of allowed failures
+
+  # If 50% of the columns are missing, we are able to reconstruct the data
+  # If 50% + 1 columns are missing, we cannot reconstruct the data
+  const worstCaseConditionCount = (NUMBER_OF_COLUMNS div 2) + 1
+
+  # Compute the false positive threshold
+  let falsePositiveThreshold = 
+    hypergeom_cdf(0, NUMBER_OF_COLUMNS, worstCaseConditionCount, samples_per_slot)
+
+  # Finally, compute the extended sample count
+  for i in samples_per_slot .. NUMBER_OF_COLUMNS:
+    if hypergeom_cdf(
+        allowed_failures,
+        NUMBER_OF_COLUMNS, 
+        worstCaseConditionCount, i) <= falsePositiveThreshold:
+      return i
+
+  NUMBER_OF_COLUMNS

tests/all_tests.nim

@@ -27,6 +27,7 @@ import # Unit test
   ./test_discovery,
   ./test_engine_api_conversions,
   ./test_engine_authentication,
+  ./test_eip7594_helpers,
   ./test_el_manager,
   ./test_el_conf,
   ./test_eth2_ssz_serialization,

tests/test_eip7594_helpers.nim

@@ -0,0 +1,46 @@
+# beacon_chain
+# Copyright (c) 2018-2024 Status Research & Development GmbH
+# Licensed and distributed under either of
+#   * MIT license (license terms in the root directory or at https://opensource.org/licenses/MIT).
+#   * Apache v2 license (license terms in the root directory or at https://www.apache.org/licenses/LICENSE-2.0).
+# at your option. This file may not be copied, modified, or distributed except according to those terms.
+
+{.push raises: [].}
+{.used.}
+
+import
+  unittest2,
+  ../beacon_chain/spec/[helpers, eip7594_helpers]
+
+suite "EIP-7594 Sampling Tests":
+  test "EIP7594: Extended Sample Count":
+    proc testExtendedSampleCount() =
+      let samplesPerSlot = 16
+      const tests = [
+        (0, 16),
+        (1, 20),
+        (2, 24),
+        (3, 27),
+        (4, 29),
+        (5, 32),
+        (6, 35),
+        (7, 37),
+        (8, 40),
+        (9, 42),
+        (10, 44),
+        (11, 47),
+        (12, 49),
+        (13, 51),
+        (14, 53),
+        (15, 55),
+        (16, 57),
+        (17, 59),
+        (18, 61),
+        (19, 63),
+        (20, 65)
+      ]
+
+      for (allowed_failures, extendedSampleCount) in tests:
+        check: get_extended_sample_count(
+            samplesPerSlot, allowed_failures) == extendedSampleCount
+    testExtendedSampleCount()