/*
 *  net/dccp/ccids/lib/tfrc_equation.c
 *
 *  Copyright (c) 2005 The University of Waikato, Hamilton, New Zealand.
 *  Copyright (c) 2005 Ian McDonald <iam4@cs.waikato.ac.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/config.h>
#include <linux/module.h>

#include <asm/div64.h>

#include "tfrc.h"

#define TFRC_CALC_X_ARRSIZE 500

#define TFRC_CALC_X_SPLIT 50000
/* equivalent to 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 },
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	{ 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 },
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	{ 145322604, 238713 },
	{ 146476218, 239170 },
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	{ 177524643, 250672 },
	{ 178857621, 251136 },
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	{ 181545242, 252063 },
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	{ 185631191, 253456 },
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	{ 195422805, 256714 },
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	{ 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 }
};

/* Calculate the send rate as per section 3.1 of RFC3448
 
Returns send rate in bytes per second

Integer maths and lookups are used as not allowed floating point in kernel

The function for Xcalc as per section 3.1 of RFC3448 is:

X =                            s
     -------------------------------------------------------------
     R*sqrt(2*b*p/3) + (t_RTO * (3*sqrt(3*b*p/8) * p * (1+32*p^2)))

where 
X is the trasmit 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 acknowledgement

we can assume that b = 1 and t_RTO is 4 * R. With this the equation becomes:

X =                            s
     -----------------------------------------------------------------------
     R * sqrt(2 * p / 3) + (12 * R * (sqrt(3 * p / 8) * p * (1 + 32 * p^2)))


which we can break down into:

X =     s
     --------
     R * f(p)

where f(p) = sqrt(2 * p / 3) + (12 * sqrt(3 * p / 8) * p * (1 + 32 * p * p))

Function parameters:
s - bytes
R - RTT in usecs
p - loss rate (decimal fraction multiplied by 1,000,000)

Returns Xcalc in bytes per second

DON'T alter this code unless you run test cases against it as the code
has been manipulated to stop underflow/overlow.

*/
u32 tfrc_calc_x(u16 s, u32 R, u32 p)
{
	int index;
	u32 f;
	u64 tmp1, tmp2;

	if (p < TFRC_CALC_X_SPLIT)
		index = (p / (TFRC_CALC_X_SPLIT / TFRC_CALC_X_ARRSIZE)) - 1;
	else
		index = (p / (1000000 / TFRC_CALC_X_ARRSIZE)) - 1;

	if (index < 0)
		/* p should be 0 unless there is a bug in my code */
		index = 0;

	if (R == 0)
		R = 1; /* RTT can't be zero or else divide by zero */

	BUG_ON(index >= TFRC_CALC_X_ARRSIZE);

	if (p >= TFRC_CALC_X_SPLIT)
		f = tfrc_calc_x_lookup[index][0];
	else
		f = tfrc_calc_x_lookup[index][1];

	tmp1 = ((u64)s * 100000000);
	tmp2 = ((u64)R * (u64)f);
	do_div(tmp2, 10000);
	do_div(tmp1, tmp2); 
	/* Don't alter above math unless you test due to overflow on 32 bit */

	return (u32)tmp1; 
}

EXPORT_SYMBOL_GPL(tfrc_calc_x);

/*
 * args: fvalue - function value to match
 * returns: p closest to that value
 *
 * both fvalue and p are multiplied by 1,000,000 to use ints
 */
u32 tfrc_calc_x_reverse_lookup(u32 fvalue)
{
	int ctr = 0;
	int small;

	if (fvalue < tfrc_calc_x_lookup[0][1])
		return 0;

	if (fvalue <= tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][1])
		small = 1;
	else if (fvalue > tfrc_calc_x_lookup[TFRC_CALC_X_ARRSIZE - 1][0])
		return 1000000;
	else
		small = 0;

	while (fvalue > tfrc_calc_x_lookup[ctr][small])
		ctr++;

	if (small)
		return TFRC_CALC_X_SPLIT * ctr / TFRC_CALC_X_ARRSIZE;
	else
		return 1000000 * ctr / TFRC_CALC_X_ARRSIZE;
}

EXPORT_SYMBOL_GPL(tfrc_calc_x_reverse_lookup);