/* [<][>][^][v][top][bottom][index][help] */
DEFINITIONS
This source file includes following definitions.
- tfrc_binsearch
- tfrc_calc_x
- tfrc_calc_x_reverse_lookup
/*
* 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 },
{ 163130, 29783 },
{ 171919, 30935 },
{ 180704, 32049 },
{ 189502, 33130 },
{ 198328, 34180 },
{ 207194, 35202 },
{ 216114, 36198 },
{ 225097, 37172 },
{ 234153, 38123 },
{ 243294, 39055 },
{ 252527, 39968 },
{ 261861, 40864 },
{ 271305, 41743 },
{ 280866, 42607 },
{ 290553, 43457 },
{ 300372, 44293 },
{ 310333, 45117 },
{ 320441, 45929 },
{ 330705, 46729 },
{ 341131, 47518 },
{ 351728, 48297 },
{ 362501, 49066 },
{ 373460, 49826 },
{ 384609, 50577 },
{ 395958, 51320 },
{ 407513, 52054 },
{ 419281, 52780 },
{ 431270, 53499 },
{ 443487, 54211 },
{ 455940, 54916 },
{ 468635, 55614 },
{ 481581, 56306 },
{ 494785, 56991 },
{ 508254, 57671 },
{ 521996, 58345 },
{ 536019, 59014 },
{ 550331, 59677 },
{ 564939, 60335 },
{ 579851, 60988 },
{ 595075, 61636 },
{ 610619, 62279 },
{ 626491, 62918 },
{ 642700, 63553 },
{ 659253, 64183 },
{ 676158, 64809 },
{ 693424, 65431 },
{ 711060, 66050 },
{ 729073, 66664 },
{ 747472, 67275 },
{ 766266, 67882 },
{ 785464, 68486 },
{ 805073, 69087 },
{ 825103, 69684 },
{ 845562, 70278 },
{ 866460, 70868 },
{ 887805, 71456 },
{ 909606, 72041 },
{ 931873, 72623 },
{ 954614, 73202 },
{ 977839, 73778 },
{ 1001557, 74352 },
{ 1025777, 74923 },
{ 1050508, 75492 },
{ 1075761, 76058 },
{ 1101544, 76621 },
{ 1127867, 77183 },
{ 1154739, 77741 },
{ 1182172, 78298 },
{ 1210173, 78852 },
{ 1238753, 79405 },
{ 1267922, 79955 },
{ 1297689, 80503 },
{ 1328066, 81049 },
{ 1359060, 81593 },
{ 1390684, 82135 },
{ 1422947, 82675 },
{ 1455859, 83213 },
{ 1489430, 83750 },
{ 1523671, 84284 },
{ 1558593, 84817 },
{ 1594205, 85348 },
{ 1630518, 85878 },
{ 1667543, 86406 },
{ 1705290, 86932 },
{ 1743770, 87457 },
{ 1782994, 87980 },
{ 1822973, 88501 },
{ 1863717, 89021 },
{ 1905237, 89540 },
{ 1947545, 90057 },
{ 1990650, 90573 },
{ 2034566, 91087 },
{ 2079301, 91600 },
{ 2124869, 92111 },
{ 2171279, 92622 },
{ 2218543, 93131 },
{ 2266673, 93639 },
{ 2315680, 94145 },
{ 2365575, 94650 },
{ 2416371, 95154 },
{ 2468077, 95657 },
{ 2520707, 96159 },
{ 2574271, 96660 },
{ 2628782, 97159 },
{ 2684250, 97658 },
{ 2740689, 98155 },
{ 2798110, 98651 },
{ 2856524, 99147 },
{ 2915944, 99641 },
{ 2976382, 100134 },
{ 3037850, 100626 },
{ 3100360, 101117 },
{ 3163924, 101608 },
{ 3228554, 102097 },
{ 3294263, 102586 },
{ 3361063, 103073 },
{ 3428966, 103560 },
{ 3497984, 104045 },
{ 3568131, 104530 },
{ 3639419, 105014 },
{ 3711860, 105498 },
{ 3785467, 105980 },
{ 3860253, 106462 },
{ 3936229, 106942 },
{ 4013410, 107422 },
{ 4091808, 107902 },
{ 4171435, 108380 },
{ 4252306, 108858 },
{ 4334431, 109335 },
{ 4417825, 109811 },
{ 4502501, 110287 },
{ 4588472, 110762 },
{ 4675750, 111236 },
{ 4764349, 111709 },
{ 4854283, 112182 },
{ 4945564, 112654 },
{ 5038206, 113126 },
{ 5132223, 113597 },
{ 5227627, 114067 },
{ 5324432, 114537 },
{ 5422652, 115006 },
{ 5522299, 115474 },
{ 5623389, 115942 },
{ 5725934, 116409 },
{ 5829948, 116876 },
{ 5935446, 117342 },
{ 6042439, 117808 },
{ 6150943, 118273 },
{ 6260972, 118738 },
{ 6372538, 119202 },
{ 6485657, 119665 },
{ 6600342, 120128 },
{ 6716607, 120591 },
{ 6834467, 121053 },
{ 6953935, 121514 },
{ 7075025, 121976 },
{ 7197752, 122436 },
{ 7322131, 122896 },
{ 7448175, 123356 },
{ 7575898, 123815 },
{ 7705316, 124274 },
{ 7836442, 124733 },
{ 7969291, 125191 },
{ 8103877, 125648 },
{ 8240216, 126105 },
{ 8378321, 126562 },
{ 8518208, 127018 },
{ 8659890, 127474 },
{ 8803384, 127930 },
{ 8948702, 128385 },
{ 9095861, 128840 },
{ 9244875, 129294 },
{ 9395760, 129748 },
{ 9548529, 130202 },
{ 9703198, 130655 },
{ 9859782, 131108 },
{ 10018296, 131561 },
{ 10178755, 132014 },
{ 10341174, 132466 },
{ 10505569, 132917 },
{ 10671954, 133369 },
{ 10840345, 133820 },
{ 11010757, 134271 },
{ 11183206, 134721 },
{ 11357706, 135171 },
{ 11534274, 135621 },
{ 11712924, 136071 },
{ 11893673, 136520 },
{ 12076536, 136969 },
{ 12261527, 137418 },
{ 12448664, 137867 },
{ 12637961, 138315 },
{ 12829435, 138763 },
{ 13023101, 139211 },
{ 13218974, 139658 },
{ 13417071, 140106 },
{ 13617407, 140553 },
{ 13819999, 140999 },
{ 14024862, 141446 },
{ 14232012, 141892 },
{ 14441465, 142339 },
{ 14653238, 142785 },
{ 14867346, 143230 },
{ 15083805, 143676 },
{ 15302632, 144121 },
{ 15523842, 144566 },
{ 15747453, 145011 },
{ 15973479, 145456 },
{ 16201939, 145900 },
{ 16432847, 146345 },
{ 16666221, 146789 },
{ 16902076, 147233 },
{ 17140429, 147677 },
{ 17381297, 148121 },
{ 17624696, 148564 },
{ 17870643, 149007 },
{ 18119154, 149451 },
{ 18370247, 149894 },
{ 18623936, 150336 },
{ 18880241, 150779 },
{ 19139176, 151222 },
{ 19400759, 151664 },
{ 19665007, 152107 },
{ 19931936, 152549 },
{ 20201564, 152991 },
{ 20473907, 153433 },
{ 20748982, 153875 },
{ 21026807, 154316 },
{ 21307399, 154758 },
{ 21590773, 155199 },
{ 21876949, 155641 },
{ 22165941, 156082 },
{ 22457769, 156523 },
{ 22752449, 156964 },
{ 23049999, 157405 },
{ 23350435, 157846 },
{ 23653774, 158287 },
{ 23960036, 158727 },
{ 24269236, 159168 },
{ 24581392, 159608 },
{ 24896521, 160049 },
{ 25214642, 160489 },
{ 25535772, 160929 },
{ 25859927, 161370 },
{ 26187127, 161810 },
{ 26517388, 162250 },
{ 26850728, 162690 },
{ 27187165, 163130 },
{ 27526716, 163569 },
{ 27869400, 164009 },
{ 28215234, 164449 },
{ 28564236, 164889 },
{ 28916423, 165328 },
{ 29271815, 165768 },
{ 29630428, 166208 },
{ 29992281, 166647 },
{ 30357392, 167087 },
{ 30725779, 167526 },
{ 31097459, 167965 },
{ 31472452, 168405 },
{ 31850774, 168844 },
{ 32232445, 169283 },
{ 32617482, 169723 },
{ 33005904, 170162 },
{ 33397730, 170601 },
{ 33792976, 171041 },
{ 34191663, 171480 },
{ 34593807, 171919 },
{ 34999428, 172358 },
{ 35408544, 172797 },
{ 35821174, 173237 },
{ 36237335, 173676 },
{ 36657047, 174115 },
{ 37080329, 174554 },
{ 37507197, 174993 },
{ 37937673, 175433 },
{ 38371773, 175872 },
{ 38809517, 176311 },
{ 39250924, 176750 },
{ 39696012, 177190 },
{ 40144800, 177629 },
{ 40597308, 178068 },
{ 41053553, 178507 },
{ 41513554, 178947 },
{ 41977332, 179386 },
{ 42444904, 179825 },
{ 42916290, 180265 },
{ 43391509, 180704 },
{ 43870579, 181144 },
{ 44353520, 181583 },
{ 44840352, 182023 },
{ 45331092, 182462 },
{ 45825761, 182902 },
{ 46324378, 183342 },
{ 46826961, 183781 },
{ 47333531, 184221 },
{ 47844106, 184661 },
{ 48358706, 185101 },
{ 48877350, 185541 },
{ 49400058, 185981 },
{ 49926849, 186421 },
{ 50457743, 186861 },
{ 50992759, 187301 },
{ 51531916, 187741 },
{ 52075235, 188181 },
{ 52622735, 188622 },
{ 53174435, 189062 },
{ 53730355, 189502 },
{ 54290515, 189943 },
{ 54854935, 190383 },
{ 55423634, 190824 },
{ 55996633, 191265 },
{ 56573950, 191706 },
{ 57155606, 192146 },
{ 57741621, 192587 },
{ 58332014, 193028 },
{ 58926806, 193470 },
{ 59526017, 193911 },
{ 60129666, 194352 },
{ 60737774, 194793 },
{ 61350361, 195235 },
{ 61967446, 195677 },
{ 62589050, 196118 },
{ 63215194, 196560 },
{ 63845897, 197002 },
{ 64481179, 197444 },
{ 65121061, 197886 },
{ 65765563, 198328 },
{ 66414705, 198770 },
{ 67068508, 199213 },
{ 67726992, 199655 },
{ 68390177, 200098 },
{ 69058085, 200540 },
{ 69730735, 200983 },
{ 70408147, 201426 },
{ 71090343, 201869 },
{ 71777343, 202312 },
{ 72469168, 202755 },
{ 73165837, 203199 },
{ 73867373, 203642 },
{ 74573795, 204086 },
{ 75285124, 204529 },
{ 76001380, 204973 },
{ 76722586, 205417 },
{ 77448761, 205861 },
{ 78179926, 206306 },
{ 78916102, 206750 },
{ 79657310, 207194 },
{ 80403571, 207639 },
{ 81154906, 208084 },
{ 81911335, 208529 },
{ 82672880, 208974 },
{ 83439562, 209419 },
{ 84211402, 209864 },
{ 84988421, 210309 },
{ 85770640, 210755 },
{ 86558080, 211201 },
{ 87350762, 211647 },
{ 88148708, 212093 },
{ 88951938, 212539 },
{ 89760475, 212985 },
{ 90574339, 213432 },
{ 91393551, 213878 },
{ 92218133, 214325 },
{ 93048107, 214772 },
{ 93883493, 215219 },
{ 94724314, 215666 },
{ 95570590, 216114 },
{ 96422343, 216561 },
{ 97279594, 217009 },
{ 98142366, 217457 },
{ 99010679, 217905 },
{ 99884556, 218353 },
{ 100764018, 218801 },
{ 101649086, 219250 },
{ 102539782, 219698 },
{ 103436128, 220147 },
{ 104338146, 220596 },
{ 105245857, 221046 },
{ 106159284, 221495 },
{ 107078448, 221945 },
{ 108003370, 222394 },
{ 108934074, 222844 },
{ 109870580, 223294 },
{ 110812910, 223745 },
{ 111761087, 224195 },
{ 112715133, 224646 },
{ 113675069, 225097 },
{ 114640918, 225548 },
{ 115612702, 225999 },
{ 116590442, 226450 },
{ 117574162, 226902 },
{ 118563882, 227353 },
{ 119559626, 227805 },
{ 120561415, 228258 },
{ 121569272, 228710 },
{ 122583219, 229162 },
{ 123603278, 229615 },
{ 124629471, 230068 },
{ 125661822, 230521 },
{ 126700352, 230974 },
{ 127745083, 231428 },
{ 128796039, 231882 },
{ 129853241, 232336 },
{ 130916713, 232790 },
{ 131986475, 233244 },
{ 133062553, 233699 },
{ 134144966, 234153 },
{ 135233739, 234608 },
{ 136328894, 235064 },
{ 137430453, 235519 },
{ 138538440, 235975 },
{ 139652876, 236430 },
{ 140773786, 236886 },
{ 141901190, 237343 },
{ 143035113, 237799 },
{ 144175576, 238256 },
{ 145322604, 238713 },
{ 146476218, 239170 },
{ 147636442, 239627 },
{ 148803298, 240085 },
{ 149976809, 240542 },
{ 151156999, 241000 },
{ 152343890, 241459 },
{ 153537506, 241917 },
{ 154737869, 242376 },
{ 155945002, 242835 },
{ 157158929, 243294 },
{ 158379673, 243753 },
{ 159607257, 244213 },
{ 160841704, 244673 },
{ 162083037, 245133 },
{ 163331279, 245593 },
{ 164586455, 246054 },
{ 165848586, 246514 },
{ 167117696, 246975 },
{ 168393810, 247437 },
{ 169676949, 247898 },
{ 170967138, 248360 },
{ 172264399, 248822 },
{ 173568757, 249284 },
{ 174880235, 249747 },
{ 176198856, 250209 },
{ 177524643, 250672 },
{ 178857621, 251136 },
{ 180197813, 251599 },
{ 181545242, 252063 },
{ 182899933, 252527 },
{ 184261908, 252991 },
{ 185631191, 253456 },
{ 187007807, 253920 },
{ 188391778, 254385 },
{ 189783129, 254851 },
{ 191181884, 255316 },
{ 192588065, 255782 },
{ 194001698, 256248 },
{ 195422805, 256714 },
{ 196851411, 257181 },
{ 198287540, 257648 },
{ 199731215, 258115 },
{ 201182461, 258582 },
{ 202641302, 259050 },
{ 204107760, 259518 },
{ 205581862, 259986 },
{ 207063630, 260454 },
{ 208553088, 260923 },
{ 210050262, 261392 },
{ 211555174, 261861 },
{ 213067849, 262331 },
{ 214588312, 262800 },
{ 216116586, 263270 },
{ 217652696, 263741 },
{ 219196666, 264211 },
{ 220748520, 264682 },
{ 222308282, 265153 },
{ 223875978, 265625 },
{ 225451630, 266097 },
{ 227035265, 266569 },
{ 228626905, 267041 },
{ 230226576, 267514 },
{ 231834302, 267986 },
{ 233450107, 268460 },
{ 235074016, 268933 },
{ 236706054, 269407 },
{ 238346244, 269881 },
{ 239994613, 270355 },
{ 241651183, 270830 },
{ 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 %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);