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Diffstat (limited to '')
| -rw-r--r-- | netem/.gitignore | 5 | ||||
| -rw-r--r-- | netem/Makefile | 32 | ||||
| -rw-r--r-- | netem/README.distribution | 97 | ||||
| -rw-r--r-- | netem/experimental.dat | 13448 | ||||
| -rw-r--r-- | netem/maketable.c | 234 | ||||
| -rw-r--r-- | netem/normal.c | 51 | ||||
| -rw-r--r-- | netem/pareto.c | 41 | ||||
| -rw-r--r-- | netem/paretonormal.c | 81 | ||||
| -rw-r--r-- | netem/stats.c | 77 |
9 files changed, 14066 insertions, 0 deletions
diff --git a/netem/.gitignore b/netem/.gitignore new file mode 100644 index 0000000..e36f396 --- /dev/null +++ b/netem/.gitignore @@ -0,0 +1,5 @@ +*.dist +maketable +normal +pareto +paretonormal diff --git a/netem/Makefile b/netem/Makefile new file mode 100644 index 0000000..ba4c5a7 --- /dev/null +++ b/netem/Makefile @@ -0,0 +1,32 @@ +# SPDX-License-Identifier: GPL-2.0 +include ../config.mk + +DISTGEN = maketable normal pareto paretonormal +DISTDATA = normal.dist pareto.dist paretonormal.dist experimental.dist + +HOSTCC ?= $(CC) +CCOPTS = $(CBUILD_CFLAGS) +LDLIBS += -lm + +all: $(DISTGEN) $(DISTDATA) + +$(DISTGEN): + $(HOSTCC) $(CCOPTS) -I../include -o $@ $@.c -lm + +%.dist: % + ./$* > $@ + +experimental.dist: maketable experimental.dat + ./maketable experimental.dat > experimental.dist + +stats: stats.c + $(HOSTCC) $(CCOPTS) -I../include -o $@ $@.c -lm + +install: all + mkdir -p $(DESTDIR)$(LIBDIR)/tc + for i in $(DISTDATA); \ + do install -m 644 $$i $(DESTDIR)$(LIBDIR)/tc; \ + done + +clean: + rm -f $(DISTDATA) $(DISTGEN) diff --git a/netem/README.distribution b/netem/README.distribution new file mode 100644 index 0000000..6d52785 --- /dev/null +++ b/netem/README.distribution @@ -0,0 +1,97 @@ +Notes about distribution tables from Nistnet +------------------------------------------------------------------------------- +I. About the distribution tables + +The table used for "synthesizing" the distribution is essentially a scaled, +translated, inverse to the cumulative distribution function. + +Here's how to think about it: Let F() be the cumulative distribution +function for a probability distribution X. We'll assume we've scaled +things so that X has mean 0 and standard deviation 1, though that's not +so important here. Then: + + F(x) = P(X <= x) = \int_{-inf}^x f + +where f is the probability density function. + +F is monotonically increasing, so has an inverse function G, with range +0 to 1. Here, G(t) = the x such that P(X <= x) = t. (In general, G may +have singularities if X has point masses, i.e., points x such that +P(X = x) > 0.) + +Now we create a tabular representation of G as follows: Choose some table +size N, and for the ith entry, put in G(i/N). Let's call this table T. + +The claim now is, I can create a (discrete) random variable Y whose +distribution has the same approximate "shape" as X, simply by letting +Y = T(U), where U is a discrete uniform random variable with range 1 to N. +To see this, it's enough to show that Y's cumulative distribution function, +(let's call it H), is a discrete approximation to F. But + + H(x) = P(Y <= x) + = (# of entries in T <= x) / N -- as Y chosen uniformly from T + = i/N, where i is the largest integer such that G(i/N) <= x + = i/N, where i is the largest integer such that i/N <= F(x) + -- since G and F are inverse functions (and F is + increasing) + = floor(N*F(x))/N + +as desired. + +II. How to create distribution tables (in theory) + +How can we create this table in practice? In some cases, F may have a +simple expression which allows evaluating its inverse directly. The +pareto distribution is one example of this. In other cases, and +especially for matching an experimentally observed distribution, it's +easiest simply to create a table for F and "invert" it. Here, we give +a concrete example, namely how the new "experimental" distribution was +created. + +1. Collect enough data points to characterize the distribution. Here, I +collected 25,000 "ping" roundtrip times to a "distant" point (time.nist.gov). +That's far more data than is really necessary, but it was fairly painless to +collect it, so... + +2. Normalize the data so that it has mean 0 and standard deviation 1. + +3. Determine the cumulative distribution. The code I wrote creates a table +covering the range -10 to +10, with granularity .00005. Obviously, this +is absurdly over-precise, but since it's a one-time only computation, I +figured it hardly mattered. + +4. Invert the table: for each table entry F(x) = y, make the y*TABLESIZE +(here, 4096) entry be x*TABLEFACTOR (here, 8192). This creates a table +for the ("normalized") inverse of size TABLESIZE, covering its domain 0 +to 1 with granularity 1/TABLESIZE. Note that even with the granularity +used in creating the table for F, it's possible not all the entries in +the table for G will be filled in. So, make a pass through the +inverse's table, filling in any missing entries by linear interpolation. + +III. How to create distribution tables (in practice) + +If you want to do all this yourself, I've provided several tools to help: + +1. maketable does the steps 2-4 above, and then generates the appropriate +header file. So if you have your own time distribution, you can generate +the header simply by: + + maketable < time.values > header.h + +2. As explained in the other README file, the somewhat sleazy way I have +of generating correlated values needs correction. You can generate your +own correction tables by compiling makesigtable and makemutable with +your header file. Check the Makefile to see how this is done. + +3. Warning: maketable, makesigtable and especially makemutable do +enormous amounts of floating point arithmetic. Don't try running +these on an old 486. (NIST Net itself will run fine on such a +system, since in operation, it just needs to do a few simple integral +calculations. But getting there takes some work.) + +4. The tables produced are all normalized for mean 0 and standard +deviation 1. How do you know what values to use for real? Here, I've +provided a simple "stats" utility. Give it a series of floating point +values, and it will return their mean (mu), standard deviation (sigma), +and correlation coefficient (rho). You can then plug these values +directly into NIST Net. diff --git a/netem/experimental.dat b/netem/experimental.dat new file mode 100644 index 0000000..3663a3e --- /dev/null +++ b/netem/experimental.dat @@ -0,0 +1,13448 @@ +211.6 +205.6 +203.0 +218.6 +213.9 +199.1 +208.7 +207.7 +203.4 +201.7 +200.3 +213.8 +213.4 +209.8 +204.3 +201.8 +196.3 +216.2 +208.9 +202.4 +205.2 +211.1 +210.9 +208.5 +199.9 +211.6 +211.9 +204.6 +215.4 +202.5 +206.5 +201.1 +198.4 +220.2 +203.7 +219.5 +199.1 +207.6 +205.3 +202.3 +219.7 +230.0 +211.0 +202.7 +209.9 +215.4 +202.9 +209.6 +200.5 +197.3 +212.3 +207.6 +210.5 +202.7 +205.7 +211.2 +208.0 +211.0 +209.4 +204.8 +204.8 +208.7 +210.1 +205.3 +202.5 +210.4 +209.4 +204.5 +204.7 +215.0 +202.6 +209.9 +220.2 +203.8 +206.3 +199.4 +221.8 +200.0 +199.6 +209.3 +206.2 +215.8 +196.9 +211.6 +198.4 +201.2 +209.4 +204.3 +219.0 +212.7 +214.6 +196.3 +202.0 +201.9 +197.5 +229.5 +207.5 +213.8 +209.2 +212.9 +193.9 +200.8 +208.6 +196.8 +201.3 +204.9 +204.7 +209.5 +211.3 +215.3 +203.7 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limit; + int n=0, i; + + if (!fstat(fileno(fp), &info) && + info.st_size > 0) { + limit = 2*info.st_size/sizeof(double); /* @@ approximate */ + } else { + limit = 10000; + } + + x = calloc(limit, sizeof(double)); + if (!x) { + perror("double alloc"); + exit(3); + } + + for (i=0; i<limit; ++i){ + if (fscanf(fp, "%lf", &x[i]) != 1 || + feof(fp)) + break; + ++n; + } + *number = n; + return x; +} + +void +arraystats(double *x, int limit, double *mu, double *sigma, double *rho) +{ + int n=0, i; + double sumsquare=0.0, sum=0.0, top=0.0; + double sigma2=0.0; + + for (i=0; i<limit; ++i){ + sumsquare += x[i]*x[i]; + sum += x[i]; + ++n; + } + *mu = sum/(double)n; + *sigma = sqrt((sumsquare - (double)n*(*mu)*(*mu))/(double)(n-1)); + + for (i=1; i < n; ++i){ + top += ((double)x[i]- *mu)*((double)x[i-1]- *mu); + sigma2 += ((double)x[i-1] - *mu)*((double)x[i-1] - *mu); + + } + *rho = top/sigma2; +} + +/* Create a (normalized) distribution table from a set of observed + * values. The table is fixed to run from (as it happens) -4 to +4, + * with granularity .00002. + */ + +#define TABLESIZE 16384/4 +#define TABLEFACTOR 8192 +#ifndef MINSHORT +#define MINSHORT -32768 +#define MAXSHORT 32767 +#endif + +/* Since entries in the inverse are scaled by TABLEFACTOR, and can't be bigger + * than MAXSHORT, we don't bother looking at a larger domain than this: + */ +#define DISTTABLEDOMAIN ((MAXSHORT/TABLEFACTOR)+1) +#define DISTTABLEGRANULARITY 50000 +#define DISTTABLESIZE (DISTTABLEDOMAIN*DISTTABLEGRANULARITY*2) + +static int * +makedist(double *x, int limit, double mu, double sigma) +{ + int *table; + int i, index, first=DISTTABLESIZE, last=0; + double input; + + table = calloc(DISTTABLESIZE, sizeof(int)); + if (!table) { + perror("table alloc"); + exit(3); + } + + for (i=0; i < limit; ++i) { + /* Normalize value */ + input = (x[i]-mu)/sigma; + + index = (int)rint((input+DISTTABLEDOMAIN)*DISTTABLEGRANULARITY); + if (index < 0) index = 0; + if (index >= DISTTABLESIZE) index = DISTTABLESIZE-1; + ++table[index]; + if (index > last) + last = index +1; + if (index < first) + first = index; + } + return table; +} + +/* replace an array by its cumulative distribution */ +static void +cumulativedist(int *table, int limit, int *total) +{ + int accum=0; + + while (--limit >= 0) { + accum += *table; + *table++ = accum; + } + *total = accum; +} + +static short * +inverttable(int *table, int inversesize, int tablesize, int cumulative) +{ + int i, inverseindex, inversevalue; + short *inverse; + double findex, fvalue; + + inverse = (short *)malloc(inversesize*sizeof(short)); + for (i=0; i < inversesize; ++i) { + inverse[i] = MINSHORT; + } + for (i=0; i < tablesize; ++i) { + findex = ((double)i/(double)DISTTABLEGRANULARITY) - DISTTABLEDOMAIN; + fvalue = (double)table[i]/(double)cumulative; + inverseindex = (int)rint(fvalue*inversesize); + inversevalue = (int)rint(findex*TABLEFACTOR); + if (inversevalue <= MINSHORT) inversevalue = MINSHORT+1; + if (inversevalue > MAXSHORT) inversevalue = MAXSHORT; + if (inverseindex >= inversesize) inverseindex = inversesize- 1; + + inverse[inverseindex] = inversevalue; + } + return inverse; + +} + +/* Run simple linear interpolation over the table to fill in missing entries */ +static void +interpolatetable(short *table, int limit) +{ + int i, j, last, lasti = -1; + + last = MINSHORT; + for (i=0; i < limit; ++i) { + if (table[i] == MINSHORT) { + for (j=i; j < limit; ++j) + if (table[j] != MINSHORT) + break; + if (j < limit) { + table[i] = last + (i-lasti)*(table[j]-last)/(j-lasti); + } else { + table[i] = last + (i-lasti)*(MAXSHORT-last)/(limit-lasti); + } + } else { + last = table[i]; + lasti = i; + } + } +} + +static void +printtable(const short *table, int limit) +{ + int i; + + printf("# This is the distribution table for the experimental distribution.\n"); + + for (i=0 ; i < limit; ++i) { + printf("%d%c", table[i], + (i % 8) == 7 ? '\n' : ' '); + } +} + +int +main(int argc, char **argv) +{ + FILE *fp; + double *x; + double mu, sigma, rho; + int limit; + int *table; + short *inverse; + int total; + + if (argc > 1) { + if (!(fp = fopen(argv[1], "r"))) { + perror(argv[1]); + exit(1); + } + } else { + fp = stdin; + } + x = readdoubles(fp, &limit); + if (limit <= 0) { + fprintf(stderr, "Nothing much read!\n"); + exit(2); + } + arraystats(x, limit, &mu, &sigma, &rho); +#ifdef DEBUG + fprintf(stderr, "%d values, mu %10.4f, sigma %10.4f, rho %10.4f\n", + limit, mu, sigma, rho); +#endif + + table = makedist(x, limit, mu, sigma); + free((void *) x); + cumulativedist(table, DISTTABLESIZE, &total); + inverse = inverttable(table, TABLESIZE, DISTTABLESIZE, total); + interpolatetable(inverse, TABLESIZE); + printtable(inverse, TABLESIZE); + return 0; +} diff --git a/netem/normal.c b/netem/normal.c new file mode 100644 index 0000000..90963f4 --- /dev/null +++ b/netem/normal.c @@ -0,0 +1,51 @@ +/* + * Normal distribution table generator + * Taken from the uncopyrighted NISTnet code. + */ +#include <stdio.h> +#include <stdlib.h> +#include <math.h> +#include <string.h> +#include <limits.h> + +#include <linux/types.h> +#include <linux/pkt_sched.h> + +#define TABLESIZE 16384 +#define TABLEFACTOR NETEM_DIST_SCALE + +static double +normal(double x, double mu, double sigma) +{ + return .5 + .5*erf((x-mu)/(sqrt(2.0)*sigma)); +} + + +int +main(int argc, char **argv) +{ + int i, n; + double x; + double table[TABLESIZE+1]; + + for (x = -10.0; x < 10.05; x += .00005) { + i = rint(TABLESIZE * normal(x, 0.0, 1.0)); + table[i] = x; + } + + + printf("# This is the distribution table for the normal distribution.\n"); + for (i = n = 0; i < TABLESIZE; i += 4) { + int value = (int) rint(table[i]*TABLEFACTOR); + if (value < SHRT_MIN) value = SHRT_MIN; + if (value > SHRT_MAX) value = SHRT_MAX; + + printf(" %d", value); + if (++n == 8) { + putchar('\n'); + n = 0; + } + } + + return 0; +} diff --git a/netem/pareto.c b/netem/pareto.c new file mode 100644 index 0000000..51d9437 --- /dev/null +++ b/netem/pareto.c @@ -0,0 +1,41 @@ +/* + * Pareto distribution table generator + * Taken from the uncopyrighted NISTnet code. + */ +#include <stdio.h> +#include <stdlib.h> +#include <math.h> +#include <limits.h> + +#include <linux/types.h> +#include <linux/pkt_sched.h> + +static const double a=3.0; +#define TABLESIZE 16384 +#define TABLEFACTOR NETEM_DIST_SCALE + +int +main(int argc, char **argv) +{ + int i, n; + double dvalue; + + printf("# This is the distribution table for the pareto distribution.\n"); + + for (i = 65536, n = 0; i > 0; i -= 16) { + dvalue = (double)i/(double)65536; + dvalue = 1.0/pow(dvalue, 1.0/a); + dvalue -= 1.5; + dvalue *= (4.0/3.0)*(double)TABLEFACTOR; + if (dvalue > 32767) + dvalue = 32767; + + printf(" %d", (int)rint(dvalue)); + if (++n == 8) { + putchar('\n'); + n = 0; + } + } + + return 0; +} diff --git a/netem/paretonormal.c b/netem/paretonormal.c new file mode 100644 index 0000000..9773e37 --- /dev/null +++ b/netem/paretonormal.c @@ -0,0 +1,81 @@ +/* + * Paretoormal distribution table generator + * + * This distribution is simply .25*normal + .75*pareto; a combination + * which seems to match experimentally observed distributions reasonably + * well, but is computationally easy to handle. + * The entries represent a scaled inverse of the cumulative distribution + * function. + * + * Taken from the uncopyrighted NISTnet code. + */ +#include <stdio.h> +#include <stdlib.h> +#include <string.h> +#include <math.h> +#include <limits.h> +#include <malloc.h> + +#include <linux/types.h> +#include <linux/pkt_sched.h> + +#define TABLESIZE 16384 +#define TABLEFACTOR NETEM_DIST_SCALE + +static double +normal(double x, double mu, double sigma) +{ + return .5 + .5*erf((x-mu)/(sqrt(2.0)*sigma)); +} + +static const double a=3.0; + +static int +paretovalue(int i) +{ + double dvalue; + + i = 65536-4*i; + dvalue = (double)i/(double)65536; + dvalue = 1.0/pow(dvalue, 1.0/a); + dvalue -= 1.5; + dvalue *= (4.0/3.0)*(double)TABLEFACTOR; + if (dvalue > 32767) + dvalue = 32767; + return (int)rint(dvalue); +} + +int +main(int argc, char **argv) +{ + int i,n; + double x; + double table[TABLESIZE+1]; + + for (x = -10.0; x < 10.05; x += .00005) { + i = rint(TABLESIZE*normal(x, 0.0, 1.0)); + table[i] = x; + } + printf( +"# This is the distribution table for the paretonormal distribution.\n" + ); + + for (i = n = 0; i < TABLESIZE; i += 4) { + int normvalue, parvalue, value; + + normvalue = (int) rint(table[i]*TABLEFACTOR); + parvalue = paretovalue(i); + + value = (normvalue+3*parvalue)/4; + if (value < SHRT_MIN) value = SHRT_MIN; + if (value > SHRT_MAX) value = SHRT_MAX; + + printf(" %d", value); + if (++n == 8) { + putchar('\n'); + n = 0; + } + } + + return 0; +} diff --git a/netem/stats.c b/netem/stats.c new file mode 100644 index 0000000..ed70f16 --- /dev/null +++ b/netem/stats.c @@ -0,0 +1,77 @@ +/* + * Experimental data distribution table generator + * Taken from the uncopyrighted NISTnet code (public domain). + * + * Rread in a series of "random" data values, either + * experimentally or generated from some probability distribution. + * From this, report statistics. + */ + +#include <stdio.h> +#include <stdlib.h> +#include <math.h> +#include <malloc.h> +#include <sys/types.h> +#include <sys/stat.h> + +void +stats(FILE *fp) +{ + struct stat info; + double *x; + int limit; + int n=0, i; + double mu=0.0, sigma=0.0, sumsquare=0.0, sum=0.0, top=0.0, rho=0.0; + double sigma2=0.0; + + fstat(fileno(fp), &info); + if (info.st_size > 0) { + limit = 2*info.st_size/sizeof(double); /* @@ approximate */ + } else { + limit = 10000; + } + x = (double *)malloc(limit*sizeof(double)); + + for (i=0; i<limit; ++i){ + fscanf(fp, "%lf", &x[i]); + if (feof(fp)) + break; + sumsquare += x[i]*x[i]; + sum += x[i]; + ++n; + } + mu = sum/(double)n; + sigma = sqrt((sumsquare - (double)n*mu*mu)/(double)(n-1)); + + for (i=1; i < n; ++i){ + top += ((double)x[i]-mu)*((double)x[i-1]-mu); + sigma2 += ((double)x[i-1] - mu)*((double)x[i-1] - mu); + + } + rho = top/sigma2; + + printf("mu = %12.6f\n", mu); + printf("sigma = %12.6f\n", sigma); + printf("rho = %12.6f\n", rho); + /*printf("sigma2 = %10.4f\n", sqrt(sigma2/(double)(n-1)));*/ + /*printf("correlation rho = %10.6f\n", top/((double)(n-1)*sigma*sigma));*/ +} + + +int +main(int argc, char **argv) +{ + FILE *fp; + + if (argc > 1) { + fp = fopen(argv[1], "r"); + if (!fp) { + perror(argv[1]); + exit(1); + } + } else { + fp = stdin; + } + stats(fp); + return 0; +} |