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linux/net/dccp/ccids/lib/tfrc_equation.c
Gerrit Renker 50ab46c790 [DCCP] tfrc: Document boundaries and limits of the TFRC lookup table 
This adds documentation for the TCP Reno throughput equation which is at
the heart of the TFRC sending rate / loss rate calculations.

It spells out precisely how the values were determined and what they mean.
The equations were derived through reverse engineering and found to be
fully accurate (verified using test programs).

This patch does not change any code.

Signed-off-by: Gerrit Renker <gerrit@erg.abdn.ac.uk>
Signed-off-by: Ian McDonald <ian.mcdonald@jandi.co.nz>
Signed-off-by: Arnaldo Carvalho de Melo <acme@mandriva.com>
2006-12-03 14:51:29 -02:00

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/*
* net/dccp/ccids/lib/tfrc_equation.c
*
* Copyright (c) 2005 The University of Waikato, Hamilton, New Zealand.
* Copyright (c) 2005 Ian McDonald <ian.mcdonald@jandi.co.nz>
* Copyright (c) 2005 Arnaldo Carvalho de Melo <acme@conectiva.com.br>
* Copyright (c) 2003 Nils-Erik Mattsson, Joacim Haggmark, Magnus Erixzon
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*/
#include <linux/module.h>
#include <asm/div64.h>
#include "../../dccp.h"
#include "tfrc.h"
#define TFRC_CALC_X_ARRSIZE 500
#define TFRC_CALC_X_SPLIT 50000 /* 0.05 * 1000000, details below */
/*
TFRC TCP Reno Throughput Equation Lookup Table for f(p)
The following two-column lookup table implements a part of the TCP throughput
equation from [RFC 3448, sec. 3.1]:
s
X_calc = --------------------------------------------------------------
R * sqrt(2*b*p/3) + (3 * t_RTO * sqrt(3*b*p/8) * (p + 32*p^3))
Where:
X is the transmit rate in bytes/second
s is the packet size in bytes
R is the round trip time in seconds
p is the loss event rate, between 0 and 1.0, of the number of loss
events as a fraction of the number of packets transmitted
t_RTO is the TCP retransmission timeout value in seconds
b is the number of packets acknowledged by a single TCP ACK
We can assume that b = 1 and t_RTO is 4 * R. The equation now becomes:
s
X_calc = -------------------------------------------------------
R * sqrt(p*2/3) + (12 * R * sqrt(p*3/8) * (p + 32*p^3))
which we can break down into:
s
X_calc = ---------
R * f(p)
where f(p) is given for 0 < p <= 1 by:
f(p) = sqrt(2*p/3) + 12 * sqrt(3*p/8) * (p + 32*p^3)
Since this is kernel code, floating-point arithmetic is avoided in favour of
integer arithmetic. This means that nearly all fractional parameters are
scaled by 1000000:
* the parameters p and R
* the return result f(p)
The lookup table therefore actually tabulates the following function g(q):
g(q) = 1000000 * f(q/1000000)
Hence, when p <= 1, q must be less than or equal to 1000000. To achieve finer
granularity for the practically more relevant case of small values of p (up to
5%), the second column is used; the first one ranges up to 100%. This split
corresponds to the value of q = TFRC_CALC_X_SPLIT. At the same time this also
determines the smallest resolution.
The entire table is generated by:
for(i=0; i < TFRC_CALC_X_ARRSIZE; i++) {
lookup[i][0] = g((i+1) * 1000000/TFRC_CALC_X_ARRSIZE);
lookup[i][1] = g((i+1) * TFRC_CALC_X_SPLIT/TFRC_CALC_X_ARRSIZE);
}
With the given configuration, we have, with M = TFRC_CALC_X_ARRSIZE-1,
lookup[0][0] = g(1000000/(M+1)) = 1000000 * f(0.2%)
lookup[M][0] = g(1000000) = 1000000 * f(100%)
lookup[0][1] = g(TFRC_CALC_X_SPLIT/(M+1)) = 1000000 * f(0.01%)
lookup[M][1] = g(TFRC_CALC_X_SPLIT) = 1000000 * f(5%)
In summary, the two columns represent f(p) for the following ranges:
* The first column is for 0.002 <= p <= 1.0
* The second column is for 0.0001 <= p <= 0.05
Where the columns overlap, the second (finer-grained) is given preference,
i.e. the first column is used only for p >= 0.05.
*/
static const u32 tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE][2] = {
{ 37172, 8172 },
{ 53499, 11567 },
{ 66664, 14180 },
{ 78298, 16388 },
{ 89021, 18339 },
{ 99147, 20108 },
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{ 118273, 23260 },
{ 127474, 24693 },
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{ 521996, 58345 },
{ 536019, 59014 },
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{ 564939, 60335 },
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};
/**
* tfrc_calc_x - Calculate the send rate as per section 3.1 of RFC3448
*
* @s: packet size in bytes
* @R: RTT scaled by 1000000 (i.e., microseconds)
* @p: loss ratio estimate scaled by 1000000
* Returns X_calc in bytes per second (not scaled).
*
* Note: DO NOT alter this code unless you run test cases against it,
* as the code has been optimized to stop underflow/overflow.
*/
u32 tfrc_calc_x(u16 s, u32 R, u32 p)
{
int index;
u32 f;
u64 tmp1, tmp2;
if (p < TFRC_CALC_X_SPLIT) /* 0 <= p < 0.05 */
index = (p / (TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE)) - 1;
else /* 0.05 <= p <= 1.00 */
index = (p / (1000000 / TFRC_CALC_X_ARRSIZE)) - 1;
if (index < 0)
/* p should be 0 unless there is a bug in my code */
index = 0;
if (R == 0) {
DCCP_WARN("RTT==0, setting to 1\n");
R = 1; /* RTT can't be zero or else divide by zero */
}
BUG_ON(index >= TFRC_CALC_X_ARRSIZE);
if (p >= TFRC_CALC_X_SPLIT)
f = tfrc_calc_x_lookup[index][0];
else
f = tfrc_calc_x_lookup[index][1];
/* The following computes X = s/(R*f(p)) in bytes per second. Since f(p)
* and R are both scaled by 1000000, we need to multiply by 1000000^2.
* ==> DO NOT alter this unless you test against overflow on 32 bit */
tmp1 = ((u64)s * 100000000);
tmp2 = ((u64)R * (u64)f);
do_div(tmp2, 10000);
do_div(tmp1, tmp2);
return (u32)tmp1;
}
EXPORT_SYMBOL_GPL(tfrc_calc_x);
/*
* tfrc_calc_x_reverse_lookup - try to find p given f(p)
*
* @fvalue: function value to match, scaled by 1000000
* Returns closest match for p, also scaled by 1000000
*/
u32 tfrc_calc_x_reverse_lookup(u32 fvalue)
{
int ctr = 0;
int small;
if (fvalue < tfrc_calc_x_lookup[0][1])
return 0;
if (fvalue <= tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][1])
small = 1;
else if (fvalue > tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][0])
return 1000000;
else
small = 0;
while (fvalue > tfrc_calc_x_lookup[ctr][small])
ctr++;
if (small)
return TFRC_CALC_X_SPLIT * ctr / TFRC_CALC_X_ARRSIZE;
else
return 1000000 * ctr / TFRC_CALC_X_ARRSIZE;
}
EXPORT_SYMBOL_GPL(tfrc_calc_x_reverse_lookup);
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