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linux/net/dccp/ccids/lib/tfrc_equation.c
Gerrit Renker d63d8364cf [DCCP]: Simplify TFRC calculation 
In migrating towards using the newer functions scaled_div/scaled_div32
for TFRC computations mapped from floating-point onto integer arithmetic,
this completes the last stage of modifications.

In particular, the overflow case for computing X_calc is circumvented by
 * breaking the computation into two stages
 * the first stage, res = (s*1E6)/R, cannot overflow due to use of u64
 * in the second stage, res = (res*1E6)/f, overflow on u32 is avoided due
   to (i) returning UINT_MAX in this case (which is logically appropriate)
   and (ii) issuing a warning message into the system log (since very likely
   there is a problem somewhere else with the parameters)

Lastly, all such scaling operations are now exported into tfrc.h, since
actually this form of scaled computation is specific to TFRC and not to CCID3.

Signed-off-by: Gerrit Renker <gerrit@erg.abdn.ac.uk>
Acked-by: Ian McDonald <ian.mcdonald@jandi.co.nz>
Signed-off-by: Arnaldo Carvalho de Melo <acme@mandriva.com>
2006-12-11 14:34:46 -08:00

698 lines
18 KiB
C
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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 "../../dccp.h"
#include "tfrc.h"
#define TFRC_CALC_X_ARRSIZE 500
#define TFRC_CALC_X_SPLIT 50000 /* 0.05 * 1000000, details below */
#define TFRC_SMALLEST_P (TFRC_CALC_X_SPLIT/TFRC_CALC_X_ARRSIZE)
/*
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 possible with this lookup table:
TFRC_SMALLEST_P = TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE
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_SMALLEST_P) = 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 },
{ 108858, 21738 },
{ 118273, 23260 },
{ 127474, 24693 },
{ 136520, 26052 },
{ 145456, 27348 },
{ 154316, 28589 },
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{ 198328, 34180 },
{ 207194, 35202 },
{ 216114, 36198 },
{ 225097, 37172 },
{ 234153, 38123 },
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{ 252527, 39968 },
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{ 280866, 42607 },
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{ 300372, 44293 },
{ 310333, 45117 },
{ 320441, 45929 },
{ 330705, 46729 },
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{ 351728, 48297 },
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{ 384609, 50577 },
{ 395958, 51320 },
{ 407513, 52054 },
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{ 431270, 53499 },
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{ 455940, 54916 },
{ 468635, 55614 },
{ 481581, 56306 },
{ 494785, 56991 },
{ 508254, 57671 },
{ 521996, 58345 },
{ 536019, 59014 },
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{ 243315981, 271305 }
};
/* return largest index i such that fval <= lookup[i][small] */
static inline u32 tfrc_binsearch(u32 fval, u8 small)
{
u32 try, low = 0, high = TFRC_CALC_X_ARRSIZE - 1;
while (low < high) {
try = (low + high) / 2;
if (fval <= tfrc_calc_x_lookup[try][small])
high = try;
else
low = try + 1;
}
return high;
}
/**
* 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).
*/
u32 tfrc_calc_x(u16 s, u32 R, u32 p)
{
u16 index;
u32 f;
u64 result;
/* check against invalid parameters and divide-by-zero */
BUG_ON(p > 1000000); /* p must not exceed 100% */
BUG_ON(p == 0); /* f(0) = 0, divide by zero */
if (R == 0) { /* possible divide by zero */
DCCP_CRIT("WARNING: RTT is 0, returning maximum X_calc.");
return ~0U;
}
if (p <= TFRC_CALC_X_SPLIT) { /* 0.0000 < p <= 0.05 */
if (p < TFRC_SMALLEST_P) { /* 0.0000 < p < 0.0001 */
DCCP_WARN("Value of p (%d) below resolution. "
"Substituting %d\n", p, TFRC_SMALLEST_P);
index = 0;
} else /* 0.0001 <= p <= 0.05 */
index = p/TFRC_SMALLEST_P - 1;
f = tfrc_calc_x_lookup[index][1];
} else { /* 0.05 < p <= 1.00 */
index = p/(1000000/TFRC_CALC_X_ARRSIZE) - 1;
f = tfrc_calc_x_lookup[index][0];
}
/*
* Compute 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. To avoid overflow, the result is computed in two stages.
* This works under almost all reasonable operational conditions, for a
* wide range of parameters. Yet, should some strange combination of
* parameters result in overflow, the use of scaled_div32 will catch
* this and return UINT_MAX - which is a logically adequate consequence.
*/
result = scaled_div(s, R);
return scaled_div32(result, f);
}
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 index;
if (fvalue == 0) /* f(p) = 0 whenever p = 0 */
return 0;
/* Error cases. */
if (fvalue < tfrc_calc_x_lookup[0][1]) {
DCCP_WARN("fvalue %d smaller than resolution\n", fvalue);
return tfrc_calc_x_lookup[0][1];
}
if (fvalue > tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][0]) {
DCCP_WARN("fvalue %d exceeds bounds!\n", fvalue);
return 1000000;
}
if (fvalue <= tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][1]) {
index = tfrc_binsearch(fvalue, 1);
return (index + 1) * TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE;
}
/* else ... it must be in the coarse-grained column */
index = tfrc_binsearch(fvalue, 0);
return (index + 1) * 1000000 / TFRC_CALC_X_ARRSIZE;
}
EXPORT_SYMBOL_GPL(tfrc_calc_x_reverse_lookup);
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