tfrc_equation.c

/*
 *  Copyright (c) 2005 The University of Waikato, Hamilton, New Zealand.
 *  Copyright (c) 2005 Ian McDonald <[email protected]>
 *  Copyright (c) 2005 Arnaldo Carvalho de Melo <[email protected]>
 *  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 },
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	{    443487,  54211 },
	{    455940,  54916 },
	{    468635,  55614 },
	{    481581,  56306 },
	{    494785,  56991 },
	{    508254,  57671 },
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	{    536019,  59014 },
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	{    595075,  61636 },
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	{    626491,  62918 },
	{    642700,  63553 },
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	{    711060,  66050 },
	{    729073,  66664 },
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	{    785464,  68486 },
	{    805073,  69087 },
	{    825103,  69684 },
	{    845562,  70278 },
	{    866460,  70868 },
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	{    909606,  72041 },
	{    931873,  72623 },
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	{   1001557,  74352 },
	{   1025777,  74923 },
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	{   1101544,  76621 },
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	{   1210173,  78852 },
	{   1238753,  79405 },
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	{ 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);
}

/**
 *  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;
}

/**
 * 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);
}