net/dccp/ccids/lib/tfrc_equation.c

   1 /*
   2  *  Copyright (c) 2005 The University of Waikato, Hamilton, New Zealand.
   3  *  Copyright (c) 2005 Ian McDonald <ian.mcdonald@jandi.co.nz>
   4  *  Copyright (c) 2005 Arnaldo Carvalho de Melo <acme@conectiva.com.br>
   5  *  Copyright (c) 2003 Nils-Erik Mattsson, Joacim Haggmark, Magnus Erixzon
   6  *
   7  *  This program is free software; you can redistribute it and/or modify
   8  *  it under the terms of the GNU General Public License as published by
   9  *  the Free Software Foundation; either version 2 of the License, or
  10  *  (at your option) any later version.
  11  */
  12
  13 #include <linux/module.h>
  14 #include "../../dccp.h"
  15 #include "tfrc.h"
  16
  17 #define TFRC_CALC_X_ARRSIZE 500
  18 #define TFRC_CALC_X_SPLIT   50000       /* 0.05 * 1000000, details below */
  19 #define TFRC_SMALLEST_P     (TFRC_CALC_X_SPLIT/TFRC_CALC_X_ARRSIZE)
  20
  21 /*
  22   TFRC TCP Reno Throughput Equation Lookup Table for f(p)
  23
  24   The following two-column lookup table implements a part of the TCP throughput
  25   equation from [RFC 3448, sec. 3.1]:
  26
  27                                      s
  28   X_calc  =  --------------------------------------------------------------
  29              R * sqrt(2*b*p/3) + (3 * t_RTO * sqrt(3*b*p/8) * (p + 32*p^3))
  30
  31   Where:
  32         X      is the transmit rate in bytes/second
  33         s      is the packet size in bytes
  34         R      is the round trip time in seconds
  35         p      is the loss event rate, between 0 and 1.0, of the number of loss
  36                       events as a fraction of the number of packets transmitted
  37         t_RTO  is the TCP retransmission timeout value in seconds
  38         b      is the number of packets acknowledged by a single TCP ACK
  39
  40   We can assume that b = 1 and t_RTO is 4 * R. The equation now becomes:
  41
  42                                      s
  43   X_calc  =  -------------------------------------------------------
  44              R * sqrt(p*2/3) + (12 * R * sqrt(p*3/8) * (p + 32*p^3))
  45
  46   which we can break down into:
  47
  48                       s
  49         X_calc  =  ---------
  50                     R * f(p)
  51
  52   where f(p) is given for 0 < p <= 1 by:
  53
  54         f(p)  =  sqrt(2*p/3) + 12 * sqrt(3*p/8) *  (p + 32*p^3)
  55
  56   Since this is kernel code, floating-point arithmetic is avoided in favour of
  57   integer arithmetic. This means that nearly all fractional parameters are
  58   scaled by 1000000:
  59     * the parameters p and R
  60     * the return result f(p)
  61   The lookup table therefore actually tabulates the following function g(q):
  62
  63         g(q)  =  1000000 * f(q/1000000)
  64
  65   Hence, when p <= 1, q must be less than or equal to 1000000. To achieve finer
  66   granularity for the practically more relevant case of small values of p (up to
  67   5%), the second column is used; the first one ranges up to 100%.  This split
  68   corresponds to the value of q = TFRC_CALC_X_SPLIT. At the same time this also
  69   determines the smallest resolution possible with this lookup table:
  70
  71     TFRC_SMALLEST_P   =  TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE
  72
  73   The entire table is generated by:
  74     for(i=0; i < TFRC_CALC_X_ARRSIZE; i++) {
  75         lookup[i][0]  =  g((i+1) * 1000000/TFRC_CALC_X_ARRSIZE);
  76         lookup[i][1]  =  g((i+1) * TFRC_CALC_X_SPLIT/TFRC_CALC_X_ARRSIZE);
  77     }
  78
  79   With the given configuration, we have, with M = TFRC_CALC_X_ARRSIZE-1,
  80     lookup[0][0]  =  g(1000000/(M+1))           = 1000000 * f(0.2%)
  81     lookup[M][0]  =  g(1000000)                 = 1000000 * f(100%)
  82     lookup[0][1]  =  g(TFRC_SMALLEST_P)         = 1000000 * f(0.01%)
  83     lookup[M][1]  =  g(TFRC_CALC_X_SPLIT)       = 1000000 * f(5%)
  84
  85   In summary, the two columns represent f(p) for the following ranges:
  86     * The first column is for   0.002  <= p <= 1.0
  87     * The second column is for  0.0001 <= p <= 0.05
  88   Where the columns overlap, the second (finer-grained) is given preference,
  89   i.e. the first column is used only for p >= 0.05.
  90  */
  91 static const u32 tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE][2] = {
  92         {     37172,   8172 },
  93         {     53499,  11567 },
  94         {     66664,  14180 },
  95         {     78298,  16388 },
  96         {     89021,  18339 },
  97         {     99147,  20108 },
  98         {    108858,  21738 },
  99         {    118273,  23260 },
 100         {    127474,  24693 },
 101         {    136520,  26052 },
 102         {    145456,  27348 },
 103         {    154316,  28589 },
 104         {    163130,  29783 },
 105         {    171919,  30935 },
 106         {    180704,  32049 },
 107         {    189502,  33130 },
 108         {    198328,  34180 },
 109         {    207194,  35202 },
 110         {    216114,  36198 },
 111         {    225097,  37172 },
 112         {    234153,  38123 },
 113         {    243294,  39055 },
 114         {    252527,  39968 },
 115         {    261861,  40864 },
 116         {    271305,  41743 },
 117         {    280866,  42607 },
 118         {    290553,  43457 },
 119         {    300372,  44293 },
 120         {    310333,  45117 },
 121         {    320441,  45929 },
 122         {    330705,  46729 },
 123         {    341131,  47518 },
 124         {    351728,  48297 },
 125         {    362501,  49066 },
 126         {    373460,  49826 },
 127         {    384609,  50577 },
 128         {    395958,  51320 },
 129         {    407513,  52054 },
 130         {    419281,  52780 },
 131         {    431270,  53499 },
 132         {    443487,  54211 },
 133         {    455940,  54916 },
 134         {    468635,  55614 },
 135         {    481581,  56306 },
 136         {    494785,  56991 },
 137         {    508254,  57671 },
 138         {    521996,  58345 },
 139         {    536019,  59014 },
 140         {    550331,  59677 },
 141         {    564939,  60335 },
 142         {    579851,  60988 },
 143         {    595075,  61636 },
 144         {    610619,  62279 },
 145         {    626491,  62918 },
 146         {    642700,  63553 },
 147         {    659253,  64183 },
 148         {    676158,  64809 },
 149         {    693424,  65431 },
 150         {    711060,  66050 },
 151         {    729073,  66664 },
 152         {    747472,  67275 },
 153         {    766266,  67882 },
 154         {    785464,  68486 },
 155         {    805073,  69087 },
 156         {    825103,  69684 },
 157         {    845562,  70278 },
 158         {    866460,  70868 },
 159         {    887805,  71456 },
 160         {    909606,  72041 },
 161         {    931873,  72623 },
 162         {    954614,  73202 },
 163         {    977839,  73778 },
 164         {   1001557,  74352 },
 165         {   1025777,  74923 },
 166         {   1050508,  75492 },
 167         {   1075761,  76058 },
 168         {   1101544,  76621 },
 169         {   1127867,  77183 },
 170         {   1154739,  77741 },
 171         {   1182172,  78298 },
 172         {   1210173,  78852 },
 173         {   1238753,  79405 },
 174         {   1267922,  79955 },
 175         {   1297689,  80503 },
 176         {   1328066,  81049 },
 177         {   1359060,  81593 },
 178         {   1390684,  82135 },
 179         {   1422947,  82675 },
 180         {   1455859,  83213 },
 181         {   1489430,  83750 },
 182         {   1523671,  84284 },
 183         {   1558593,  84817 },
 184         {   1594205,  85348 },
 185         {   1630518,  85878 },
 186         {   1667543,  86406 },
 187         {   1705290,  86932 },
 188         {   1743770,  87457 },
 189         {   1782994,  87980 },
 190         {   1822973,  88501 },
 191         {   1863717,  89021 },
 192         {   1905237,  89540 },
 193         {   1947545,  90057 },
 194         {   1990650,  90573 },
 195         {   2034566,  91087 },
 196         {   2079301,  91600 },
 197         {   2124869,  92111 },
 198         {   2171279,  92622 },
 199         {   2218543,  93131 },
 200         {   2266673,  93639 },
 201         {   2315680,  94145 },
 202         {   2365575,  94650 },
 203         {   2416371,  95154 },
 204         {   2468077,  95657 },
 205         {   2520707,  96159 },
 206         {   2574271,  96660 },
 207         {   2628782,  97159 },
 208         {   2684250,  97658 },
 209         {   2740689,  98155 },
 210         {   2798110,  98651 },
 211         {   2856524,  99147 },
 212         {   2915944,  99641 },
 213         {   2976382, 100134 },
 214         {   3037850, 100626 },
 215         {   3100360, 101117 },
 216         {   3163924, 101608 },
 217         {   3228554, 102097 },
 218         {   3294263, 102586 },
 219         {   3361063, 103073 },
 220         {   3428966, 103560 },
 221         {   3497984, 104045 },
 222         {   3568131, 104530 },
 223         {   3639419, 105014 },
 224         {   3711860, 105498 },
 225         {   3785467, 105980 },
 226         {   3860253, 106462 },
 227         {   3936229, 106942 },
 228         {   4013410, 107422 },
 229         {   4091808, 107902 },
 230         {   4171435, 108380 },
 231         {   4252306, 108858 },
 232         {   4334431, 109335 },
 233         {   4417825, 109811 },
 234         {   4502501, 110287 },
 235         {   4588472, 110762 },
 236         {   4675750, 111236 },
 237         {   4764349, 111709 },
 238         {   4854283, 112182 },
 239         {   4945564, 112654 },
 240         {   5038206, 113126 },
 241         {   5132223, 113597 },
 242         {   5227627, 114067 },
 243         {   5324432, 114537 },
 244         {   5422652, 115006 },
 245         {   5522299, 115474 },
 246         {   5623389, 115942 },
 247         {   5725934, 116409 },
 248         {   5829948, 116876 },
 249         {   5935446, 117342 },
 250         {   6042439, 117808 },
 251         {   6150943, 118273 },
 252         {   6260972, 118738 },
 253         {   6372538, 119202 },
 254         {   6485657, 119665 },
 255         {   6600342, 120128 },
 256         {   6716607, 120591 },
 257         {   6834467, 121053 },
 258         {   6953935, 121514 },
 259         {   7075025, 121976 },
 260         {   7197752, 122436 },
 261         {   7322131, 122896 },
 262         {   7448175, 123356 },
 263         {   7575898, 123815 },
 264         {   7705316, 124274 },
 265         {   7836442, 124733 },
 266         {   7969291, 125191 },
 267         {   8103877, 125648 },
 268         {   8240216, 126105 },
 269         {   8378321, 126562 },
 270         {   8518208, 127018 },
 271         {   8659890, 127474 },
 272         {   8803384, 127930 },
 273         {   8948702, 128385 },
 274         {   9095861, 128840 },
 275         {   9244875, 129294 },
 276         {   9395760, 129748 },
 277         {   9548529, 130202 },
 278         {   9703198, 130655 },
 279         {   9859782, 131108 },
 280         {  10018296, 131561 },
 281         {  10178755, 132014 },
 282         {  10341174, 132466 },
 283         {  10505569, 132917 },
 284         {  10671954, 133369 },
 285         {  10840345, 133820 },
 286         {  11010757, 134271 },
 287         {  11183206, 134721 },
 288         {  11357706, 135171 },
 289         {  11534274, 135621 },
 290         {  11712924, 136071 },
 291         {  11893673, 136520 },
 292         {  12076536, 136969 },
 293         {  12261527, 137418 },
 294         {  12448664, 137867 },
 295         {  12637961, 138315 },
 296         {  12829435, 138763 },
 297         {  13023101, 139211 },
 298         {  13218974, 139658 },
 299         {  13417071, 140106 },
 300         {  13617407, 140553 },
 301         {  13819999, 140999 },
 302         {  14024862, 141446 },
 303         {  14232012, 141892 },
 304         {  14441465, 142339 },
 305         {  14653238, 142785 },
 306         {  14867346, 143230 },
 307         {  15083805, 143676 },
 308         {  15302632, 144121 },
 309         {  15523842, 144566 },
 310         {  15747453, 145011 },
 311         {  15973479, 145456 },
 312         {  16201939, 145900 },
 313         {  16432847, 146345 },
 314         {  16666221, 146789 },
 315         {  16902076, 147233 },
 316         {  17140429, 147677 },
 317         {  17381297, 148121 },
 318         {  17624696, 148564 },
 319         {  17870643, 149007 },
 320         {  18119154, 149451 },
 321         {  18370247, 149894 },
 322         {  18623936, 150336 },
 323         {  18880241, 150779 },
 324         {  19139176, 151222 },
 325         {  19400759, 151664 },
 326         {  19665007, 152107 },
 327         {  19931936, 152549 },
 328         {  20201564, 152991 },
 329         {  20473907, 153433 },
 330         {  20748982, 153875 },
 331         {  21026807, 154316 },
 332         {  21307399, 154758 },
 333         {  21590773, 155199 },
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 335         {  22165941, 156082 },
 336         {  22457769, 156523 },
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 355         {  28564236, 164889 },
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 360         {  30357392, 167087 },
 361         {  30725779, 167526 },
 362         {  31097459, 167965 },
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 364         {  31850774, 168844 },
 365         {  32232445, 169283 },
 366         {  32617482, 169723 },
 367         {  33005904, 170162 },
 368         {  33397730, 170601 },
 369         {  33792976, 171041 },
 370         {  34191663, 171480 },
 371         {  34593807, 171919 },
 372         {  34999428, 172358 },
 373         {  35408544, 172797 },
 374         {  35821174, 173237 },
 375         {  36237335, 173676 },
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 377         {  37080329, 174554 },
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 379         {  37937673, 175433 },
 380         {  38371773, 175872 },
 381         {  38809517, 176311 },
 382         {  39250924, 176750 },
 383         {  39696012, 177190 },
 384         {  40144800, 177629 },
 385         {  40597308, 178068 },
 386         {  41053553, 178507 },
 387         {  41513554, 178947 },
 388         {  41977332, 179386 },
 389         {  42444904, 179825 },
 390         {  42916290, 180265 },
 391         {  43391509, 180704 },
 392         {  43870579, 181144 },
 393         {  44353520, 181583 },
 394         {  44840352, 182023 },
 395         {  45331092, 182462 },
 396         {  45825761, 182902 },
 397         {  46324378, 183342 },
 398         {  46826961, 183781 },
 399         {  47333531, 184221 },
 400         {  47844106, 184661 },
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 408         {  52075235, 188181 },
 409         {  52622735, 188622 },
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 411         {  53730355, 189502 },
 412         {  54290515, 189943 },
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 414         {  55423634, 190824 },
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 416         {  56573950, 191706 },
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 420         {  58926806, 193470 },
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 436         {  69058085, 200540 },
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 567         { 205581862, 259986 },
 568         { 207063630, 260454 },
 569         { 208553088, 260923 },
 570         { 210050262, 261392 },
 571         { 211555174, 261861 },
 572         { 213067849, 262331 },
 573         { 214588312, 262800 },
 574         { 216116586, 263270 },
 575         { 217652696, 263741 },
 576         { 219196666, 264211 },
 577         { 220748520, 264682 },
 578         { 222308282, 265153 },
 579         { 223875978, 265625 },
 580         { 225451630, 266097 },
 581         { 227035265, 266569 },
 582         { 228626905, 267041 },
 583         { 230226576, 267514 },
 584         { 231834302, 267986 },
 585         { 233450107, 268460 },
 586         { 235074016, 268933 },
 587         { 236706054, 269407 },
 588         { 238346244, 269881 },
 589         { 239994613, 270355 },
 590         { 241651183, 270830 },
 591         { 243315981, 271305 }
 592 };
 593
 594 /* return largest index i such that fval <= lookup[i][small] */
 595 static inline u32 tfrc_binsearch(u32 fval, u8 small)
 596 {
 597         u32 try, low = 0, high = TFRC_CALC_X_ARRSIZE - 1;
 598
 599         while (low < high) {
 600                 try = (low + high) / 2;
 601                 if (fval <= tfrc_calc_x_lookup[try][small])
 602                         high = try;
 603                 else
 604                         low  = try + 1;
 605         }
 606         return high;
 607 }
 608
 609 /**
 610  * tfrc_calc_x - Calculate the send rate as per section 3.1 of RFC3448
 611  * @s: packet size          in bytes
 612  * @R: RTT                  scaled by 1000000   (i.e., microseconds)
 613  * @p: loss ratio estimate  scaled by 1000000
 614  * Returns X_calc           in bytes per second (not scaled).
 615  */
 616 u32 tfrc_calc_x(u16 s, u32 R, u32 p)
 617 {
 618         u16 index;
 619         u32 f;
 620         u64 result;
 621
 622         /* check against invalid parameters and divide-by-zero   */
 623         BUG_ON(p >  1000000);           /* p must not exceed 100%   */
 624         BUG_ON(p == 0);                 /* f(0) = 0, divide by zero */
 625         if (R == 0) {                   /* possible  divide by zero */
 626                 DCCP_CRIT("WARNING: RTT is 0, returning maximum X_calc.");
 627                 return ~0U;
 628         }
 629
 630         if (p <= TFRC_CALC_X_SPLIT)             {     /* 0.0000 < p <= 0.05   */
 631                 if (p < TFRC_SMALLEST_P) {            /* 0.0000 < p <  0.0001 */
 632                         DCCP_WARN("Value of p (%d) below resolution. "
 633                                   "Substituting %d\n", p, TFRC_SMALLEST_P);
 634                         index = 0;
 635                 } else                                /* 0.0001 <= p <= 0.05  */
 636                         index =  p/TFRC_SMALLEST_P - 1;
 637
 638                 f = tfrc_calc_x_lookup[index][1];
 639
 640         } else {                                      /* 0.05   <  p <= 1.00  */
 641                 index = p/(1000000/TFRC_CALC_X_ARRSIZE) - 1;
 642
 643                 f = tfrc_calc_x_lookup[index][0];
 644         }
 645
 646         /*
 647          * Compute X = s/(R*f(p)) in bytes per second.
 648          * Since f(p) and R are both scaled by 1000000, we need to multiply by
 649          * 1000000^2. To avoid overflow, the result is computed in two stages.
 650          * This works under almost all reasonable operational conditions, for a
 651          * wide range of parameters. Yet, should some strange combination of
 652          * parameters result in overflow, the use of scaled_div32 will catch
 653          * this and return UINT_MAX - which is a logically adequate consequence.
 654          */
 655         result = scaled_div(s, R);
 656         return scaled_div32(result, f);
 657 }
 658
 659 /**
 660  *  tfrc_calc_x_reverse_lookup  -  try to find p given f(p)
 661  *  @fvalue: function value to match, scaled by 1000000
 662  *  Returns closest match for p, also scaled by 1000000
 663  */
 664 u32 tfrc_calc_x_reverse_lookup(u32 fvalue)
 665 {
 666         int index;
 667
 668         if (fvalue == 0)        /* f(p) = 0  whenever  p = 0 */
 669                 return 0;
 670
 671         /* Error cases. */
 672         if (fvalue < tfrc_calc_x_lookup[0][1]) {
 673                 DCCP_WARN("fvalue %u smaller than resolution\n", fvalue);
 674                 return TFRC_SMALLEST_P;
 675         }
 676         if (fvalue > tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][0]) {
 677                 DCCP_WARN("fvalue %u exceeds bounds!\n", fvalue);
 678                 return 1000000;
 679         }
 680
 681         if (fvalue <= tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][1]) {
 682                 index = tfrc_binsearch(fvalue, 1);
 683                 return (index + 1) * TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE;
 684         }
 685
 686         /* else ... it must be in the coarse-grained column */
 687         index = tfrc_binsearch(fvalue, 0);
 688         return (index + 1) * 1000000 / TFRC_CALC_X_ARRSIZE;
 689 }
 690
 691 /**
 692  * tfrc_invert_loss_event_rate  -  Compute p so that 10^6 corresponds to 100%
 693  * When @loss_event_rate is large, there is a chance that p is truncated to 0.
 694  * To avoid re-entering slow-start in that case, we set p = TFRC_SMALLEST_P > 0.
 695  */
 696 u32 tfrc_invert_loss_event_rate(u32 loss_event_rate)
 697 {
 698         if (loss_event_rate == UINT_MAX)                /* see RFC 4342, 8.5 */
 699                 return 0;
 700         if (unlikely(loss_event_rate == 0))             /* map 1/0 into 100% */
 701                 return 1000000;
 702         return max_t(u32, scaled_div(1, loss_event_rate), TFRC_SMALLEST_P);
 703 }