Added several tools for fib hashing function analysis. It turned out

we can use very simple function which is monotonic with respect
to re-hashing:

	n ^= n >> 16;
	n ^= n << 10;
	h = (n >> (16 - o)) & ((1 << o) - 1);

where o is table order. Statistical analysis for both backbone routing
table and local OSPF routing tables gives values near theoretical
optimum for uniform distribution (see ips.c for formulae).

The trick is very simple: We always calculate a 16-bit hash value n and
use o most significant bits (this gives us monotonity wrt. rehashing
if we sort the chains by the value of n). The first shift/xor pair
reduces the IP address to a 16-bit one, the second pair makes higher
bits of the 16-bit value uniformly distributed even for tables containing
lots of long prefixes (typical interior routing case with 24-bit or even
longer prefixes).

1 files changed, 94 insertions, 0 deletions

diff --git a/misc/ips.c b/misc/ips.c
new file mode 100644
index 0000000..ec7e673
--- /dev/null
+++ b/misc/ips.c
@@ -0,0 +1,94 @@
+#include <stdio.h>
+#include <math.h>
+#include <unistd.h>
+#include <stdlib.h>
+
+int h[65536];
+
+/*
+ *  Probability analysis of hashing function:
+ *
+ *  Let n be number of items and k number of boxes. For uniform distribution
+ *  we get:
+ *
+ *  Expected value of "item i is in given box": Xi = 1/k
+ *  Expected number of items in given box: a = EX = E(sum Xi) = sum E(Xi) = n/k
+ *  Expected square value: E(X^2) = E((sum Xi)^2) = E((sum_i Xi^2) + (sum_i,j i<>j XiXj)) =
+ *	= sum_i E(Xi^2) + sum_i,j i<>j E(XiXj) =
+ *	= sum_i E(Xi) [Xi is binary] + sum_i,j i<>j E(XiXj) [those are independent] =
+ *	= n/k + n*(n-1)/k^2
+ *  Variance: var X = E(X^2) - (EX)^2 = n/k + n*(n-1)/k^2 - n^2/k^2 =
+ *	= n/k - n/k^2 = a * (1-1/k)
+ *  Probability of fixed box being zero: Pz = ((k-1)/k)^n = (1-1/k)^n = (1-1/k)^(ak) =
+ *	= ((1-1/k)^k)^a which we can approximate by e^-a.
+ */
+
+unsigned int hf(unsigned int n)
+{
+#if 0
+	n = (n ^ (n >> 16)) & 0xffff;
+	n = (n ^ (n << 8)) & 0xffff;
+#elif 1
+	n = (n >> 16) ^ n;
+	n = (n ^ (n << 10)) & 0xffff;
+#elif 0
+	n = (n >> 16) ^ n;
+	n *= 259309;
+#elif 0
+	n ^= (n >> 20);
+	n ^= (n >> 10);
+	n ^= (n >> 5);
+#elif 0
+	n = (n * 259309) + ((n >> 16) * 123479);
+#else
+	return random();
+#endif
+	return n;
+}
+
+int
+main(int argc, char **argv)
+{
+	int cnt=0;
+	int i;
+
+	int bits = atol(argv[1]);
+	int z = 1 << bits;
+	int max = atol(argv[2]);
+
+	while (max--)
+	  {
+	    unsigned int i, e;
+	    if (scanf("%x/%d", &i, &e) != 2)
+	      if (feof(stdin))
+		break;
+	    else
+	      fprintf(stderr, "BUGGG\n");
+//	    i >>= (32-e);
+//	    i |= (i >> e);
+            cnt++;
+	    h[(hf(i) >> 1*(16 - bits)) & (z-1)]++;
+	  }
+//	printf(">>> %d addresses\n", cnt);
+#if 0
+	for(i=0; i<z; i++)
+		printf("%d\t%d\n", i, h[i]);
+#else
+{
+	int min=cnt, max=0, zer=0;
+	double delta=0;
+	double avg = (double) cnt / z;
+	double exdelta = avg*(1-1/z);
+	double exzer = exp(-avg);
+	for(i=0; i<z; i++) {
+		if (h[i] < min) min=h[i];
+		if (h[i] > max) max=h[i];
+		delta += (h[i] - avg) * (h[i] - avg);
+		if (!h[i]) zer++;
+	}
+	printf("size=%5d, min=%d, max=%2d, delta=%-7.6g (%-7.6g), avg=%-5.3g, zero=%g%% (%g%%)\n", z, min, max, delta/z, exdelta, avg, zer/(double)z*100, exzer*100);
+}
+#endif
+
+	return 0;
+}