net/dccp/ccids/lib/tfrc_equation.c

   1 // SPDX-License-Identifier: GPL-2.0-or-later
   2 /*
   3  *  Copyright (c) 2005 The University of Waikato, Hamilton, New Zealand.
   4  *  Copyright (c) 2005 Ian McDonald <ian.mcdonald@jandi.co.nz>
   5  *  Copyright (c) 2005 Arnaldo Carvalho de Melo <acme@conectiva.com.br>
   6  *  Copyright (c) 2003 Nils-Erik Mattsson, Joacim Haggmark, Magnus Erixzon
   7  */
   8
   9 #include <linux/module.h>
  10 #include "../../dccp.h"
  11 #include "tfrc.h"
  12
  13 #define TFRC_CALC_X_ARRSIZE 500
  14 #define TFRC_CALC_X_SPLIT   50000       /* 0.05 * 1000000, details below */
  15 #define TFRC_SMALLEST_P     (TFRC_CALC_X_SPLIT/TFRC_CALC_X_ARRSIZE)
  16
  17 /*
  18   TFRC TCP Reno Throughput Equation Lookup Table for f(p)
  19
  20   The following two-column lookup table implements a part of the TCP throughput
  21   equation from [RFC 3448, sec. 3.1]:
  22
  23                                      s
  24   X_calc  =  --------------------------------------------------------------
  25              R * sqrt(2*b*p/3) + (3 * t_RTO * sqrt(3*b*p/8) * (p + 32*p^3))
  26
  27   Where:
  28         X      is the transmit rate in bytes/second
  29         s      is the packet size in bytes
  30         R      is the round trip time in seconds
  31         p      is the loss event rate, between 0 and 1.0, of the number of loss
  32                       events as a fraction of the number of packets transmitted
  33         t_RTO  is the TCP retransmission timeout value in seconds
  34         b      is the number of packets acknowledged by a single TCP ACK
  35
  36   We can assume that b = 1 and t_RTO is 4 * R. The equation now becomes:
  37
  38                                      s
  39   X_calc  =  -------------------------------------------------------
  40              R * sqrt(p*2/3) + (12 * R * sqrt(p*3/8) * (p + 32*p^3))
  41
  42   which we can break down into:
  43
  44                       s
  45         X_calc  =  ---------
  46                     R * f(p)
  47
  48   where f(p) is given for 0 < p <= 1 by:
  49
  50         f(p)  =  sqrt(2*p/3) + 12 * sqrt(3*p/8) *  (p + 32*p^3)
  51
  52   Since this is kernel code, floating-point arithmetic is avoided in favour of
  53   integer arithmetic. This means that nearly all fractional parameters are
  54   scaled by 1000000:
  55     * the parameters p and R
  56     * the return result f(p)
  57   The lookup table therefore actually tabulates the following function g(q):
  58
  59         g(q)  =  1000000 * f(q/1000000)
  60
  61   Hence, when p <= 1, q must be less than or equal to 1000000. To achieve finer
  62   granularity for the practically more relevant case of small values of p (up to
  63   5%), the second column is used; the first one ranges up to 100%.  This split
  64   corresponds to the value of q = TFRC_CALC_X_SPLIT. At the same time this also
  65   determines the smallest resolution possible with this lookup table:
  66
  67     TFRC_SMALLEST_P   =  TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE
  68
  69   The entire table is generated by:
  70     for(i=0; i < TFRC_CALC_X_ARRSIZE; i++) {
  71         lookup[i][0]  =  g((i+1) * 1000000/TFRC_CALC_X_ARRSIZE);
  72         lookup[i][1]  =  g((i+1) * TFRC_CALC_X_SPLIT/TFRC_CALC_X_ARRSIZE);
  73     }
  74
  75   With the given configuration, we have, with M = TFRC_CALC_X_ARRSIZE-1,
  76     lookup[0][0]  =  g(1000000/(M+1))           = 1000000 * f(0.2%)
  77     lookup[M][0]  =  g(1000000)                 = 1000000 * f(100%)
  78     lookup[0][1]  =  g(TFRC_SMALLEST_P)         = 1000000 * f(0.01%)
  79     lookup[M][1]  =  g(TFRC_CALC_X_SPLIT)       = 1000000 * f(5%)
  80
  81   In summary, the two columns represent f(p) for the following ranges:
  82     * The first column is for   0.002  <= p <= 1.0
  83     * The second column is for  0.0001 <= p <= 0.05
  84   Where the columns overlap, the second (finer-grained) is given preference,
  85   i.e. the first column is used only for p >= 0.05.
  86  */
  87 static const u32 tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE][2] = {
  88         {     37172,   8172 },
  89         {     53499,  11567 },
  90         {     66664,  14180 },
  91         {     78298,  16388 },
  92         {     89021,  18339 },
  93         {     99147,  20108 },
  94         {    108858,  21738 },
  95         {    118273,  23260 },
  96         {    127474,  24693 },
  97         {    136520,  26052 },
  98         {    145456,  27348 },
  99         {    154316,  28589 },
 100         {    163130,  29783 },
 101         {    171919,  30935 },
 102         {    180704,  32049 },
 103         {    189502,  33130 },
 104         {    198328,  34180 },
 105         {    207194,  35202 },
 106         {    216114,  36198 },
 107         {    225097,  37172 },
 108         {    234153,  38123 },
 109         {    243294,  39055 },
 110         {    252527,  39968 },
 111         {    261861,  40864 },
 112         {    271305,  41743 },
 113         {    280866,  42607 },
 114         {    290553,  43457 },
 115         {    300372,  44293 },
 116         {    310333,  45117 },
 117         {    320441,  45929 },
 118         {    330705,  46729 },
 119         {    341131,  47518 },
 120         {    351728,  48297 },
 121         {    362501,  49066 },
 122         {    373460,  49826 },
 123         {    384609,  50577 },
 124         {    395958,  51320 },
 125         {    407513,  52054 },
 126         {    419281,  52780 },
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 128         {    443487,  54211 },
 129         {    455940,  54916 },
 130         {    468635,  55614 },
 131         {    481581,  56306 },
 132         {    494785,  56991 },
 133         {    508254,  57671 },
 134         {    521996,  58345 },
 135         {    536019,  59014 },
 136         {    550331,  59677 },
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 140         {    610619,  62279 },
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 143         {    659253,  64183 },
 144         {    676158,  64809 },
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 149         {    766266,  67882 },
 150         {    785464,  68486 },
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 152         {    825103,  69684 },
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 155         {    887805,  71456 },
 156         {    909606,  72041 },
 157         {    931873,  72623 },
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 161         {   1025777,  74923 },
 162         {   1050508,  75492 },
 163         {   1075761,  76058 },
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 166         {   1154739,  77741 },
 167         {   1182172,  78298 },
 168         {   1210173,  78852 },
 169         {   1238753,  79405 },
 170         {   1267922,  79955 },
 171         {   1297689,  80503 },
 172         {   1328066,  81049 },
 173         {   1359060,  81593 },
 174         {   1390684,  82135 },
 175         {   1422947,  82675 },
 176         {   1455859,  83213 },
 177         {   1489430,  83750 },
 178         {   1523671,  84284 },
 179         {   1558593,  84817 },
 180         {   1594205,  85348 },
 181         {   1630518,  85878 },
 182         {   1667543,  86406 },
 183         {   1705290,  86932 },
 184         {   1743770,  87457 },
 185         {   1782994,  87980 },
 186         {   1822973,  88501 },
 187         {   1863717,  89021 },
 188         {   1905237,  89540 },
 189         {   1947545,  90057 },
 190         {   1990650,  90573 },
 191         {   2034566,  91087 },
 192         {   2079301,  91600 },
 193         {   2124869,  92111 },
 194         {   2171279,  92622 },
 195         {   2218543,  93131 },
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 205         {   2740689,  98155 },
 206         {   2798110,  98651 },
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 210         {   3037850, 100626 },
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 214         {   3294263, 102586 },
 215         {   3361063, 103073 },
 216         {   3428966, 103560 },
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 218         {   3568131, 104530 },
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 220         {   3711860, 105498 },
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 222         {   3860253, 106462 },
 223         {   3936229, 106942 },
 224         {   4013410, 107422 },
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 227         {   4252306, 108858 },
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 230         {   4502501, 110287 },
 231         {   4588472, 110762 },
 232         {   4675750, 111236 },
 233         {   4764349, 111709 },
 234         {   4854283, 112182 },
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 236         {   5038206, 113126 },
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 239         {   5324432, 114537 },
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 241         {   5522299, 115474 },
 242         {   5623389, 115942 },
 243         {   5725934, 116409 },
 244         {   5829948, 116876 },
 245         {   5935446, 117342 },
 246         {   6042439, 117808 },
 247         {   6150943, 118273 },
 248         {   6260972, 118738 },
 249         {   6372538, 119202 },
 250         {   6485657, 119665 },
 251         {   6600342, 120128 },
 252         {   6716607, 120591 },
 253         {   6834467, 121053 },
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 255         {   7075025, 121976 },
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 273         {   9548529, 130202 },
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 275         {   9859782, 131108 },
 276         {  10018296, 131561 },
 277         {  10178755, 132014 },
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 279         {  10505569, 132917 },
 280         {  10671954, 133369 },
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 285         {  11534274, 135621 },
 286         {  11712924, 136071 },
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 288         {  12076536, 136969 },
 289         {  12261527, 137418 },
 290         {  12448664, 137867 },
 291         {  12637961, 138315 },
 292         {  12829435, 138763 },
 293         {  13023101, 139211 },
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 295         {  13417071, 140106 },
 296         {  13617407, 140553 },
 297         {  13819999, 140999 },
 298         {  14024862, 141446 },
 299         {  14232012, 141892 },
 300         {  14441465, 142339 },
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 302         {  14867346, 143230 },
 303         {  15083805, 143676 },
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 306         {  15747453, 145011 },
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 308         {  16201939, 145900 },
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 569         { 214588312, 262800 },
 570         { 216116586, 263270 },
 571         { 217652696, 263741 },
 572         { 219196666, 264211 },
 573         { 220748520, 264682 },
 574         { 222308282, 265153 },
 575         { 223875978, 265625 },
 576         { 225451630, 266097 },
 577         { 227035265, 266569 },
 578         { 228626905, 267041 },
 579         { 230226576, 267514 },
 580         { 231834302, 267986 },
 581         { 233450107, 268460 },
 582         { 235074016, 268933 },
 583         { 236706054, 269407 },
 584         { 238346244, 269881 },
 585         { 239994613, 270355 },
 586         { 241651183, 270830 },
 587         { 243315981, 271305 }
 588 };
 589
 590 /* return largest index i such that fval <= lookup[i][small] */
 591 static inline u32 tfrc_binsearch(u32 fval, u8 small)
 592 {
 593         u32 try, low = 0, high = TFRC_CALC_X_ARRSIZE - 1;
 594
 595         while (low < high) {
 596                 try = (low + high) / 2;
 597                 if (fval <= tfrc_calc_x_lookup[try][small])
 598                         high = try;
 599                 else
 600                         low  = try + 1;
 601         }
 602         return high;
 603 }
 604
 605 /**
 606  * tfrc_calc_x - Calculate the send rate as per section 3.1 of RFC3448
 607  * @s: packet size          in bytes
 608  * @R: RTT                  scaled by 1000000   (i.e., microseconds)
 609  * @p: loss ratio estimate  scaled by 1000000
 610  *
 611  * Returns X_calc           in bytes per second (not scaled).
 612  */
 613 u32 tfrc_calc_x(u16 s, u32 R, u32 p)
 614 {
 615         u16 index;
 616         u32 f;
 617         u64 result;
 618
 619         /* check against invalid parameters and divide-by-zero   */
 620         BUG_ON(p >  1000000);           /* p must not exceed 100%   */
 621         BUG_ON(p == 0);                 /* f(0) = 0, divide by zero */
 622         if (R == 0) {                   /* possible  divide by zero */
 623                 DCCP_CRIT("WARNING: RTT is 0, returning maximum X_calc.");
 624                 return ~0U;
 625         }
 626
 627         if (p <= TFRC_CALC_X_SPLIT)             {     /* 0.0000 < p <= 0.05   */
 628                 if (p < TFRC_SMALLEST_P) {            /* 0.0000 < p <  0.0001 */
 629                         DCCP_WARN("Value of p (%d) below resolution. "
 630                                   "Substituting %d\n", p, TFRC_SMALLEST_P);
 631                         index = 0;
 632                 } else                                /* 0.0001 <= p <= 0.05  */
 633                         index =  p/TFRC_SMALLEST_P - 1;
 634
 635                 f = tfrc_calc_x_lookup[index][1];
 636
 637         } else {                                      /* 0.05   <  p <= 1.00  */
 638                 index = p/(1000000/TFRC_CALC_X_ARRSIZE) - 1;
 639
 640                 f = tfrc_calc_x_lookup[index][0];
 641         }
 642
 643         /*
 644          * Compute X = s/(R*f(p)) in bytes per second.
 645          * Since f(p) and R are both scaled by 1000000, we need to multiply by
 646          * 1000000^2. To avoid overflow, the result is computed in two stages.
 647          * This works under almost all reasonable operational conditions, for a
 648          * wide range of parameters. Yet, should some strange combination of
 649          * parameters result in overflow, the use of scaled_div32 will catch
 650          * this and return UINT_MAX - which is a logically adequate consequence.
 651          */
 652         result = scaled_div(s, R);
 653         return scaled_div32(result, f);
 654 }
 655
 656 /**
 657  *  tfrc_calc_x_reverse_lookup  -  try to find p given f(p)
 658  *  @fvalue: function value to match, scaled by 1000000
 659  *
 660  *  Returns closest match for p, also scaled by 1000000
 661  */
 662 u32 tfrc_calc_x_reverse_lookup(u32 fvalue)
 663 {
 664         int index;
 665
 666         if (fvalue == 0)        /* f(p) = 0  whenever  p = 0 */
 667                 return 0;
 668
 669         /* Error cases. */
 670         if (fvalue < tfrc_calc_x_lookup[0][1]) {
 671                 DCCP_WARN("fvalue %u smaller than resolution\n", fvalue);
 672                 return TFRC_SMALLEST_P;
 673         }
 674         if (fvalue > tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][0]) {
 675                 DCCP_WARN("fvalue %u exceeds bounds!\n", fvalue);
 676                 return 1000000;
 677         }
 678
 679         if (fvalue <= tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][1]) {
 680                 index = tfrc_binsearch(fvalue, 1);
 681                 return (index + 1) * TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE;
 682         }
 683
 684         /* else ... it must be in the coarse-grained column */
 685         index = tfrc_binsearch(fvalue, 0);
 686         return (index + 1) * 1000000 / TFRC_CALC_X_ARRSIZE;
 687 }
 688
 689 /**
 690  * tfrc_invert_loss_event_rate  -  Compute p so that 10^6 corresponds to 100%
 691  * When @loss_event_rate is large, there is a chance that p is truncated to 0.
 692  * To avoid re-entering slow-start in that case, we set p = TFRC_SMALLEST_P > 0.
 693  */
 694 u32 tfrc_invert_loss_event_rate(u32 loss_event_rate)
 695 {
 696         if (loss_event_rate == UINT_MAX)                /* see RFC 4342, 8.5 */
 697                 return 0;
 698         if (unlikely(loss_event_rate == 0))             /* map 1/0 into 100% */
 699                 return 1000000;
 700         return max_t(u32, scaled_div(1, loss_event_rate), TFRC_SMALLEST_P);
 701 }