Timing Functions

From Jacket Wiki

The user can set the minimum time over which the measurement is made. The longer time, the more reliable and reproducible the result is.
The code ensures that the minimum time set is actually met. It uses a predictor to estimate the needed number of repetitions but it also self updates this to ensure that the minimum time is met.
Warm-up is included for both MATLAB and Jacket variants.
Compensation for the repetition loop is included to focus on the function timing and not something irrelevant.

MATLAB Timing

Usage

The input-output relations for the TIMEFUN function is:

function [ TC, TELAPSC, RPTC ] = timefun( FUN, TMIN )
  % TIMEFUN Timing of MATLAB function
  %
  % INPUT:
  %   FUN      : Function handle.
  %   TMIN     : Minimum time over which the test is performed.
  %
  % OUTPUT:
  %   TC       : Execution time of one FUN evaluation.
  %   TELAPSC  : Total time over which the test is performed.
  %   RPTC     : Number of repetitions used to reach TELAPSC.
  %

Example 1: Creation of Random Matrix

To create a random matrix of size 400 times 400 in MATLAB and time this event the following is used:

>> [TC, TELAPSC, RPTC] = timefun(@() randn(400,400), 1)
 
TC =
 
    0.0052
 
 
TELAPSC =
 
    1.2272
 
 
RPTC =
 
   235
 
>>

Here, TC is the execution time of one instant of randn(400,400), TELAPSC is the total time over which the measurement is done, and RPTC is the number of repetitions the randn() function was executed to use TELAPSC seconds.

Example 2: Timing of Exponential

Suppose we want to know how much time Jacket needs to take the exponential values of a 300 by 300 matrix. In this case we need to make a function, which creates a matrix and does the exponential evaluation afterwards. But since this also includes time need to create the random matrix we need to subtract that time from the former one. The answer can therefore be given as:

>> timefun(@() exp(randn(300,300)), 4) - timefun(@() randn(300,300), 4)
 
ans =
 
    0.0025
 
>>

Here the evaluation is made over 4 seconds but it is of course possible to try other values. Further down, the same is done for Jacket, and it is thus very easy to compare MATLAB and Jacket performance.

MATLAB Code: TIMEFUN

function [ TC, TELAPSC, RPTC ] = timefun( FUN, TMIN )
  % TIMEFUN Timing of MATLAB function
  %
  % INPUT:
  %   FUN      : Function handle.
  %   TMIN     : Minimum time over which the test is performed.
  %
  % OUTPUT:
  %   TC       : Execution time of one FUN evaluation.
  %   TELAPSC  : Total time over which the test is performed.
  %   RPTC     : Number of repetitions used to reach TELAPSC.
  %
  % USE:
  %   TIMEFUN(FUN)
  %   Measure FUN repeatedly for at least 0.25 seconds (default).
  %
  %   TIMEFUN(FUN,TMIN)
  %   Measure FUN for at least TMIN seconds (TMIN larger => more accurate).
  %
  %   [TC, TELAPSC, RPTC] = TIMEFUN(FUN,TMIN)
  %   Measure FUN for at least TMIN seconds and return TC, which is the time
  %   for one execution, and TELAPSC is the totally measurement time.
  %
  % Examples:
  %   >> timefun(@() grand(64),1)
  %
  %   ans =
  %
  %      1.7167e-04
  %
  %   >> [TC,TELAPSC,RPTC] = timefun(@() rand(500,500)*randn(500,500), 0.9)
  %
  %   TC =
  %
  %       0.0340
  %
  %   TELAPSC =
  %
  %       0.9191
  %
  %   RPTC =
  %       27
  %
 
  % Generate error if FUN is not a function handle
  assert(isa(FUN, 'function_handle'))
 
  % Default time to average over
  if nargin < 2
    TMIN = 0.25;
  end
 
  % Estimate time and number of repetitions
  FUN();
  FUN();
  ts = tic;
    FUN();
    FUN();
  tend = toc(ts)/2;
  RPTi = max(ceil(0.75*TMIN/tend),2);
 
  % Warm up and adjust RPTi estimate
  ts = tic;
  for rpt=1:RPTi
    FUN();
  end
  tend = toc(ts)/RPTi;
  RPTi = max(ceil(TMIN/tend),2);
 
  % Measure time
  TELAPSC = -1;
  while TELAPSC < TMIN
    ts = tic;
    for rpt=1:RPTi
      FUN();
    end
    TELAPSC = toc(ts);
    RPTC = RPTi;
    RPTi = ceil(1.25*RPTi);
  end
 
  % Compensate for loop time
  y = FUN();
  ts = tic;
  for ii=1:ceil(1E6/RPTC)
    for rpt=1:RPTC
      y;
    end
  end
  tloop = toc(ts)/ceil(1E6/RPTC);
  TC = (TELAPSC-tloop)/RPTC;
end

Jacket Timing

Usage

The input-output relations for the GTIMEFUN function is:

function [ TG, TELAPSG, RPTG ] = gtimefun( FUN, TMIN )
  % GTIMEFUN Timing of Jacket function
  %
  % INPUT:
  %   FUN      : Function handle.
  %   TMIN     : Minimum time over which the test is performed.
  %
  % OUTPUT:
  %   TG       : Execution time of one FUN evaluation.
  %   TELAPSG  : Total time over which the test is performed.
  %   RPTG     : Number of repetitions used to reach TELAPSG.
  %

Example 1: Creation of Random Matrix

To create a random matrix of size 400 times 400 in Jacket and time this event the following is used:

>> [TG, TELAPSG, RPTG] = gtimefun(@() grandn(400,400), 1)
 
TG =
 
   4.8652e-04
 
 
TELAPSG =
 
    1.2375
 
 
RPTG =
 
        2507
 
>>

Here, TG is the execution time of one instant of grandn(400,400), TELAPSG is the total time over which the measurement is done, and RPTG is the number of repetitions the grandn() function was executed to use TELAPSG seconds.

Example 2: Timing of Exponential

Suppose we want to know how much time Jacket needs to take the exponential values of a 300 by 300 matrix. In this case we need to make a function, which creates a matrix and does the exponential evaluation afterwards. But since this also includes time need to create the random matrix we need to subtract that time from the former one. The answer can therefore be given as:

>> gtimefun(@() exp(grandn(300,300)), 4) - gtimefun(@() grandn(300,300), 4)
 
ans =
 
   1.7829e-04
 
>>

Here the evaluation is made over 4 seconds but it is of course possible to try other values.

Jacket Code: GTIMEFUN

function [ TG, TELAPSG, RPTG ] = gtimefun( FUN, TMIN )
  % GTIMEFUN Timing of Jacket function
  %
  % INPUT:
  %   FUN      : Function handle.
  %   TMIN     : Minimum time over which the test is performed.
  %
  % OUTPUT:
  %   TG       : Execution time of one FUN evaluation.
  %   TELAPSG  : Total time over which the test is performed.
  %   RPTG     : Number of repetitions used to reach TELAPSG.
  %
  % USE:
  %   GTIMEFUN(FUN)
  %   Measure FUN repeatedly for at least 0.25 seconds (default).
  %
  %   GTIMEFUN(FUN,TMIN)
  %   Measure FUN for at least TMIN seconds (TMIN larger => more accurate).
  %
  %   [TG, TELAPSG, RPTG] = GTIMEFUN(FUN,TMIN)
  %   Measure FUN for at least TMIN seconds and return TG, which is the time
  %   for one execution, and TELAPSG is the totally measurement time.
  %
  % EXAMPLES:
  %   >> gtimefun(@() grand(64),1)
  %
  %   ans = 1.7515e-04
  %
  %   >> [TG,TELAPSG,RPTG] = gtimefun(@() grand(500,500)*grandn(500,500), 0.9)
  %
  %   TG = 0.0095
  %
  %   TELAPSG = 1.1319
  %
  %   RPTG = 119
  %
 
  % Generate error if FUN is not a function handle
  assert(isa(FUN, 'function_handle'))
 
  % Default time to average over
  if nargin < 2
    TMIN = 0.25;
  end
 
  % Estimate time and number of repetitions
  geval(FUN());
  geval(FUN());
  gsync; ts = tic;
    geval(FUN());
    geval(FUN());
  gsync; tend = toc(ts)/2;
  RPTi = max(ceil(0.75*TMIN/tend),2);
 
  % Warm up and adjust RPTi estimate
  gsync, ts = tic;
  for rpt=1:RPTi
    geval(FUN());
  end
  gsync; tend = toc(ts)/RPTi;
  RPTi = max(ceil(TMIN/tend),2);
 
  % Measure time
  TELAPSG = -1;
  while TELAPSG < TMIN
    gsync; ts = tic;
    for rpt=1:RPTi
      geval(FUN());
    end
    gsync; TELAPSG = toc(ts);
    RPTG = RPTi;
    RPTi = ceil(1.25*RPTi);
  end
 
  % Compensate for loop time
  y = FUN();
  gsync, ts = tic;
  for ii=1:ceil(1E6/RPTG)
    for rpt=1:RPTG
      geval(y);
    end
  end
  gsync; tloop = toc(ts)/ceil(1E6/RPTG);
  TG = (TELAPSG-tloop)/RPTG;
end

Go Home: Torben's Corner

Timing Functions

From Jacket Wiki

Contents

MATLAB Timing

Usage

Example 1: Creation of Random Matrix

Example 2: Timing of Exponential

MATLAB Code: TIMEFUN

Jacket Timing

Usage

Example 1: Creation of Random Matrix

Example 2: Timing of Exponential

Jacket Code: GTIMEFUN

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