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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 },
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{ 118273, 23260 },
{ 127474, 24693 },
{ 136520, 26052 },
{ 145456, 27348 },
{ 154316, 28589 },
{ 163130, 29783 },
{ 171919, 30935 },
{ 180704, 32049 },
{ 189502, 33130 },
{ 198328, 34180 },
{ 207194, 35202 },
{ 216114, 36198 },
{ 225097, 37172 },
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{ 455940, 54916 },
{ 468635, 55614 },
{ 481581, 56306 },
{ 494785, 56991 },
{ 508254, 57671 },
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};
/* 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 */
/*
* In the congestion-avoidance phase p decays towards 0
* when there are no further losses, so this case is
* natural. Truncating to p_min = 0.01% means that the
* maximum achievable throughput is limited to about
* X_calc_max = 122.4 * s/RTT (see RFC 3448, 3.1); e.g.
* with s=1500 bytes, RTT=0.01 s: X_calc_max = 147 Mbps.
*/
tfrc_pr_debug("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 %u smaller than resolution\n", fvalue);
return TFRC_SMALLEST_P;
}
if (fvalue > tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][0]) {
DCCP_WARN("fvalue %u 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);
/**
* tfrc_invert_loss_event_rate - Compute p so that 10^6 corresponds to 100%
* When @loss_event_rate is large, there is a chance that p is truncated to 0.
* To avoid re-entering slow-start in that case, we set p = TFRC_SMALLEST_P > 0.
*/
u32 tfrc_invert_loss_event_rate(u32 loss_event_rate)
{
if (loss_event_rate == UINT_MAX) /* see RFC 4342, 8.5 */
return 0;
if (unlikely(loss_event_rate == 0)) /* map 1/0 into 100% */
return 1000000;
return max_t(u32, scaled_div(1, loss_event_rate), TFRC_SMALLEST_P);
}
EXPORT_SYMBOL_GPL(tfrc_invert_loss_event_rate);
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