From: Matt Corallo <git@bluematt.me>
Date: Tue, 14 Sep 2021 19:04:04 +0000 (+0000)
Subject: Double hashtable bucket size, halve parallelism.
X-Git-Url: http://git.bitcoin.ninja/index.cgi?a=commitdiff_plain;h=81e2215518fa76a2dc0dc88105550bf26c86c27b;p=flowspec-xdp

Double hashtable bucket size, halve parallelism.

256-way parallelism should suffice for most use-cases, but 16-entry
buckets should allow for much lower collisions than 8-entry buckets.

This also adds calculation for hash table collision.
---

diff --git a/README.md b/README.md
index 6437197..5f6e917 100644
--- a/README.md
+++ b/README.md
@@ -18,6 +18,9 @@ encoding in that the last 4 octets are the floating-point rate limit. Instead of
 AS/ignored value, the third octet is the maximum number of source IPs tracked (plus one, times 4096)
 and the fourth octet is a prefix length mask, which is applied to the source IP before rate-limiting.
 
+See `collision_prob.py` for collision probabilities in the hash table to estimate the size you
+should use.
+
 `install.sh` provides a simple example script which will compile and install a generated XDP program
 from the rules in bird's `flowspec4` and `flowspec6` routing tables. It will drop any packets which
 match any flowspec filter.
diff --git a/collision_prob.py b/collision_prob.py
new file mode 100644
index 0000000..36df0c9
--- /dev/null
+++ b/collision_prob.py
@@ -0,0 +1,75 @@
+# Approximate collisions in an N-bucket hash table
+# Using suggested approximate formula from https://stats.stackexchange.com/questions/1308/extending-the-birthday-paradox-to-more-than-2-people
+
+import math
+
+def poisson_pdf(avg, k):
+	return (avg ** k) / (math.factorial(k) * math.e**avg)
+
+def poisson_cdf(avg, k):
+	# Lazy version of inclusive cdf from 0 through k
+	it = 0
+	for i in range(0, k+1):
+		it += poisson_pdf(avg, i)
+	return it
+
+def poisson_pow(n, b, k):
+	if k == 0:
+		return poisson_cdf(n/b, 0)**b
+	sub = 0
+	for i in range(0, k):
+		sub += poisson_pow(n, b, i)
+	return poisson_cdf(n/b, k)**b - sub
+
+def inv_poisson_pow(n, b, k):
+	it = 0
+	# This loop is equivalent to the below two-step:
+	#for i in range(1, k):
+	#	it += poisson_pow(n, b, i)
+	it -= poisson_cdf(n/b, 0)**b
+	it += poisson_cdf(n/b, k-1)**b
+	return 1 - it
+
+def print_entry(e, t, b):
+	# We have t/b buckets, and want the probability that no bucket has >= b+1 entries
+	print("\t%ldK entries, %ld-buckets: %.20f" % (e/1000, b, inv_poisson_pow(e, t/b, b+1)))
+
+# Base cases which can be compared with WolframAlpha
+# Note that we have to multiply by b to undo the division in print_entry
+# https://www.wolframalpha.com/input/?i=birthday+problem+calculator&assumption=%7B%22F%22%2C+%22BirthdayProblem%22%2C+%22pbds%22%7D+-%3E%2220000%22&assumption=%7B%22F%22%2C+%22BirthdayProblem%22%2C+%22n%22%7D+-%3E%22300%22&assumption=%22FSelect%22+-%3E+%7B%7B%22BirthdayProblem%22%7D%7D
+#print_entry(300, 20000, 1)
+#print_entry(300, 20000*2, 2)
+
+print("Table and bucket sizes mapped to rough element count which has a 1% bucket-overflow probability")
+print("Note that we currently have a hard-coded bucket size of 16 elements")
+print()
+
+print("128K table * 16 bytes = %dMiB." % (128*16/1024))
+print_entry(4000, 128*1024, 4)
+print_entry(15000, 128*1024, 8)
+print_entry(33000, 128*1024, 16)
+print_entry(53000, 128*1024, 32)
+
+print("256K table * 16 bytes = %dMiB." % (256*16/1024))
+print_entry(7000, 256*1024, 4)
+print_entry(28000, 256*1024, 8)
+print_entry(63000, 256*1024, 16)
+print_entry(104000, 256*1024, 32)
+
+print("512K table * 16 bytes = %dMiB." % (512*16/1024))
+print_entry(13000, 512*1024, 4)
+print_entry(52000, 512*1024, 8)
+print_entry(119000, 512*1024, 16)
+print_entry(200000, 512*1024, 32)
+
+print("1M table * 16 bytes = %dMiB." % (1024*16/1024))
+print_entry(23000, 1024*1024, 4)
+print_entry(95000, 1024*1024, 8)
+print_entry(227000, 1024*1024, 16)
+print_entry(387000, 1024*1024, 32)
+
+print("2M table * 16 bytes = %dMiB." % (2*1024*16/1024))
+print_entry(40000, 2*1024*1024, 4)
+print_entry(175000, 2*1024*1024, 8)
+print_entry(431000, 2*1024*1024, 16)
+print_entry(749000, 2*1024*1024, 32)
diff --git a/xdp.c b/xdp.c
index ad6ab82..62120d2 100644
--- a/xdp.c
+++ b/xdp.c
@@ -213,9 +213,17 @@ struct {
 // Then we build an array of MAX_ENTRIES/2**SRC_HASH_MAX_PARALLELISM_POW entries,
 // which are split into buckets of size SRC_HASH_BUCKET_COUNT. An entry can appear
 // in any of the SRC_HASH_BUCKET_COUNT buckets at it's hash value.
-#define SRC_HASH_MAX_PARALLELISM_POW 9
+//
+// Because we use buckets of size 16, see collision_prob.py, the number of
+// elements we can hold with only a 1% probability of overflowing a bucket is:
+//
+// 128K-entry hash table (2MiB): ~33K sources
+// 256K-entry hash table (4MiB): ~63K sources
+// 512K-entry hash table (8MiB): ~119K sources
+// 1M-entry hash table (16MiB): ~227K sources
+#define SRC_HASH_MAX_PARALLELISM_POW 8
 #define SRC_HASH_MAX_PARALLELISM (1 << SRC_HASH_MAX_PARALLELISM_POW)
-#define SRC_HASH_BUCKET_COUNT_POW 3
+#define SRC_HASH_BUCKET_COUNT_POW 4
 #define SRC_HASH_BUCKET_COUNT (1 << SRC_HASH_BUCKET_COUNT_POW)
 
 #include "rand.h"