  
  [1X8 [33X[0;0YParallel computing with [5XSCSCP[105X[101X[1X[133X[101X
  
  
  [1X8.1 [33X[0;0YManaging multiple requests[133X[101X
  
  [33X[0;0YUsing procedure calls explained in the previous section, the user can create
  several  requests  to  multiple  services to execute them in parallel, or to
  wait until the fastest result will be available.[133X
  
  [1X8.1-1 SynchronizeProcesses[101X
  
  [33X[1;0Y[29X[2XSynchronizeProcesses[102X( [3Xprocess1[103X, [3Xprocess2[103X, [3X...[103X, [3XprocessN[103X ) [32X function[133X
  [33X[1;0Y[29X[2XSynchronizeProcesses[102X( [3Xproclist[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ylist of records with components [10Xobject[110X and [10Xattributes[110X[133X
  
  [33X[0;0YThe  function  collects  results of from each process given in the argument,
  and  returns  the  list, [22Xi[122X-th entry of which is the result obtained from the
  [22Xi[122X-th  process.  The  function  accepts  both  one argument that is a list of
  processes, and arbitrary number of arguments, each of them being a process.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27Xa:=NewProcess( "WS_Factorial", [10], "localhost", 26133 );[127X[104X
    [4X[28X< process at localhost:26133 pid=2064 >[128X[104X
    [4X[25Xgap>[125X [27Xb:=NewProcess( "WS_Factorial", [20], "localhost", 26134 );[127X[104X
    [4X[28X< process at localhost:26134 pid=1975 >[128X[104X
    [4X[25Xgap>[125X [27XSynchronizeProcesses(a,b);[127X[104X
    [4X[28X[ rec( attributes := [ [ "call_id", "localhost:26133:2064:yCWBGYFO" ] ], [128X[104X
    [4X[28X      object := 3628800 ), [128X[104X
    [4X[28X  rec( attributes := [ [ "call_id", "localhost:26134:1975:yAAWvGTL" ] ], [128X[104X
    [4X[28X      object := 2432902008176640000 ) ][128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [1X8.1-2 FirstProcess[101X
  
  [33X[1;0Y[29X[2XFirstProcess[102X( [3Xprocess1[103X, [3Xprocess2[103X, [3X...[103X, [3XprocessN[103X ) [32X function[133X
  [33X[1;0Y[29X[2XFirstProcess[102X( [3Xproclist[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Yrecords with components [10Xobject[110X and [10Xattributes[110X[133X
  
  [33X[0;0YThe  function  waits for the result from each process given in the argument,
  and  returns the result coming first, terminating all remaining processes at
  the  same  time.  The  function  accepts both one argument that is a list of
  processes, and arbitrary number of arguments, each of them being a process.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27Xa:=NewProcess( "WS_Factorial", [10], "localhost", 26133 );[127X[104X
    [4X[28X< process at localhost:26133 pid=2064 >[128X[104X
    [4X[25Xgap>[125X [27Xb:=NewProcess( "WS_Factorial", [20], "localhost", 26134 );[127X[104X
    [4X[28X< process at localhost:26134 pid=1975 >[128X[104X
    [4X[25Xgap>[125X [27X FirstProcess(a,b); [127X[104X
    [4X[28Xrec( attributes := [ [ "call_id", "localhost:26133:2064:mdb8RaO2" ] ], [128X[104X
    [4X[28X  object := 3628800 )[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [1X8.1-3 SCSCPservers[101X
  
  [33X[1;0Y[29X[2XSCSCPservers[102X [32X global variable[133X
  
  [33X[0;0Y[2XSCSCPservers[102X  is  a  list  of  hosts  and ports to search for [5XSCSCP[105X services
  (which  may  be  not  only  represented by [5XGAP[105X services, but also by another
  [5XSCSCP[105X-compliant systems).[133X
  
  [33X[0;0YIt   is   used   by   parallel   skeletons   [2XParQuickWithSCSCP[102X  ([14X8.1-4[114X)  and
  [2XParListWithSCSCP[102X ([14X8.2-1[114X).[133X
  
  [33X[0;0YThe   initial   value   of   this   variable   is   specified  in  the  file
  [11Xscscp/configpar.g[111X and may be reassigned later.[133X
  
  [1X8.1-4 ParQuickWithSCSCP[101X
  
  [33X[1;0Y[29X[2XParQuickWithSCSCP[102X( [3Xcommands[103X, [3Xlistargs[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Yrecord with components [10Xobject[110X and [10Xattributes[110X[133X
  
  [33X[0;0YThis  function  is  constructed using the [2XFirstProcess[102X ([14X8.1-2[114X). It is useful
  when  it  is not known which particular method is more efficient, because it
  allows  to  call  in parallel several procedures (given by the list of their
  names  [3Xcommands[103X)  with  the same list of arguments [3Xlistargs[103X (having the same
  meaning  as  in  [2XEvaluateBySCSCP[102X  ([14X6.3-1[114X))  and  obtain  the  result of that
  procedure call which will be computed faster.[133X
  
  [33X[0;0YIn  the example below we call two factorisation methods from the [5XGAP[105X package
  [5XFactInt[105X to factorise [22X2^150+1[122X. The example is selected in such a way that the
  runtime of these two methods is approximately the same, so you should expect
  results from both methods in some random order from repeated calls.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XParQuickWithSCSCP( [ "WS_FactorsECM", "WS_FactorsMPQS" ], [ 2^150+1 ] );[127X[104X
    [4X[28Xrec( attributes := [ [ "call_id", "localhost:26133:53877:GQX8MhC8" ] ],[128X[104X
    [4X[28X  object := [ [ 5, 5, 5, 13, 41, 61, 101, 1201, 1321, 63901 ],[128X[104X
    [4X[28X      [ 2175126601, 15767865236223301 ] ] )[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [1X8.1-5 FirstTrueProcess[101X
  
  [33X[1;0Y[29X[2XFirstTrueProcess[102X( [3Xprocess1[103X, [3Xprocess2[103X, [3X...[103X, [3XprocessN[103X ) [32X function[133X
  [33X[1;0Y[29X[2XFirstTrueProcess[102X( [3Xproclist[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ylist of records[133X
  
  [33X[0;0YThe  function  waits for the result from each process given in the argument,
  and  stops  waiting  as  soon  as the first [9Xtrue[109X is returned, abandoning all
  remaining  processes. It returns a list containing a records with components
  [10Xobject[110X  and  [10Xattributes[110X  at  the  position corresponding to the process that
  returned  [9Xtrue[109X.  If  none  of  the processes returned true, it will return a
  complete list of procedure call results.[133X
  
  [33X[0;0YThe  function  accepts  both  one  argument that is a list of processes, and
  arbitrary number of arguments, each of them being a process.[133X
  
  [33X[0;0YIn the first example, the second call returns [9Xtrue[109X:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27Xa:=NewProcess( "IsPrimeInt", [2^15013-1], "localhost", 26134 );[127X[104X
    [4X[28X< process at localhost:26134 pid=42554 >[128X[104X
    [4X[25Xgap>[125X [27Xb:=NewProcess( "IsPrimeInt", [2^521-1], "localhost", 26133 );[127X[104X
    [4X[28X< process at localhost:26133 pid=42448 >[128X[104X
    [4X[25Xgap>[125X [27XFirstTrueProcess(a,b); [127X[104X
    [4X[28X[ , rec( attributes := [ [ "call_id", "localhost:26133:42448:Lz1DL0ON" ] ], [128X[104X
    [4X[28X      object := true ) ][128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YIn the next example both calls return [9Xfalse[109X:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27Xa:=NewProcess( "IsPrimeInt", [2^520-1], "localhost", 26133 );[127X[104X
    [4X[28X< process at localhost:26133 pid=42448 >[128X[104X
    [4X[25Xgap>[125X [27Xb:=NewProcess( "IsPrimeInt", [2^15013-1], "localhost", 26134 );[127X[104X
    [4X[28X< process at localhost:26134 pid=42554 >[128X[104X
    [4X[25Xgap>[125X [27XFirstTrueProcess(a,b); [127X[104X
    [4X[28X[ rec( attributes := [ [ "call_id", "localhost:26133:42448:nvsk8PQp" ] ], [128X[104X
    [4X[28X      object := false ), [128X[104X
    [4X[28X  rec( attributes := [ [ "call_id", "localhost:26134:42554:JnEYuXL8" ] ], [128X[104X
    [4X[28X      object := false ) ][128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  
  [1X8.2 [33X[0;0YMasterWorker skeleton[133X[101X
  
  [33X[0;0YIn  this  section  we  will  present  more general framework to run parallel
  computations, which has a number of useful features:[133X
  
  [30X    [33X[0;6Yit is implemented purely in [5XGAP[105X;[133X
  
  [30X    [33X[0;6Ythe client (i.e. master, which orchestrates the computation) will work
        in UNIX/Linux, Mac OS X and MS Windows;[133X
  
  [30X    [33X[0;6Yit may orchestrate both [5XGAP[105X and non-[5XGAP[105X [5XSCSCP[105X servers;[133X
  
  [30X    [33X[0;6Yif  one  of  servers  (i.e.  workers)  will be lost, it will retry the
        computation on another available server;[133X
  
  [30X    [33X[0;6Yit  allows  to  add  dynamically new workers during the computation on
        hostnames  and  ports from a range previously declared in [2XSCSCPservers[102X
        ([14X8.1-3[114X).[133X
  
  [33X[0;0YTo  configure  this  functionality,  the  file [11Xscscp/configpar.g[111X assigns the
  global  variable  [10XSCSCPservers[110X  which specifies a list of hosts and ports to
  search  for  [5XSCSCP[105X  services  (which  may  be  not  only  represented by [5XGAP[105X
  services, but also by another [5XSCSCP[105X-compliant systems). See comments in this
  file for further instructions.[133X
  
  [1X8.2-1 ParListWithSCSCP[101X
  
  [33X[1;0Y[29X[2XParListWithSCSCP[102X( [3Xlistargs[103X, [3Xprocname[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ylist[133X
  
  [33X[0;0Y[2XParListWithSCSCP[102X implements the well-known master-worker skeleton: we have a
  master  ([5XSCSCP[105X  client) and a number of workers ([5XSCSCP[105X servers) which obtain
  pieces  of  work  from  the client, perform the required job and report back
  with the result, waiting for the next job.[133X
  
  [33X[0;0YIt returns the list of the same length as [3Xlistargs[103X, [22Xi[122X-th element of which is
  the result of calling the procedure [3Xprocname[103X with the argument [3Xlistargs[i][103X.[133X
  
  [33X[0;0YIt  accepts  two  options  which  should  be given as non-negative integers:
  [10Xtimeout[110X  which  specifies  in  minutes how long the client must wait for the
  result  (if  not  given,  the default value is one hour) and [10Xrecallfrequency[110X
  which  specifies  the  number  of  iterations after which the search for new
  services  will  be performed (if not given the default value is zero meaning
  no such search at all). There is also a boolean option [10Xnoretry[110X which, if set
  to  [9Xtrue[109X,  means  that no retrying calls will be performed if the timeout is
  exceeded and an incomplete resut may be returned.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XParListWithSCSCP( List( [2..6], n -> SymmetricGroup(n)), "WS_IdGroup" );[127X[104X
    [4X[28X#I  master -> [ "localhost", 26133 ] : SymmetricGroup( [ 1 .. 2 ] )[128X[104X
    [4X[28X#I  master -> [ "localhost", 26134 ] : SymmetricGroup( [ 1 .. 3 ] )[128X[104X
    [4X[28X#I  [ "localhost", 26133 ] --> master : [ 2, 1 ][128X[104X
    [4X[28X#I  master -> [ "localhost", 26133 ] : SymmetricGroup( [ 1 .. 4 ] )[128X[104X
    [4X[28X#I  [ "localhost", 26134 ] --> master : [ 6, 1 ][128X[104X
    [4X[28X#I  master -> [ "localhost", 26134 ] : SymmetricGroup( [ 1 .. 5 ] )[128X[104X
    [4X[28X#I  [ "localhost", 26133 ] --> master : [ 24, 12 ][128X[104X
    [4X[28X#I  master -> [ "localhost", 26133 ] : SymmetricGroup( [ 1 .. 6 ] )[128X[104X
    [4X[28X#I  [ "localhost", 26133 ] --> master : [ 720, 763 ][128X[104X
    [4X[28X#I  [ "localhost", 26134 ] --> master : [ 120, 34 ][128X[104X
    [4X[28X[ [ 2, 1 ], [ 6, 1 ], [ 24, 12 ], [ 120, 34 ], [ 720, 763 ] ][128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [1X8.2-2 SCSCPreset[101X
  
  [33X[1;0Y[29X[2XSCSCPreset[102X(  ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ynothing[133X
  
  [33X[0;0YIf   an  error  occurs  during  a  call  of  [2XParQuickWithSCSCP[102X  ([14X8.1-4[114X)  and
  [2XParListWithSCSCP[102X  ([14X8.2-1[114X), some of parallel requests may be still running at
  the  remaining  services,  making  them  inaccessible  for further procedure
  calls. [2XSCSCPreset[102X resets them by closing all open streams to [5XSCSCP[105X servers.[133X
  
  [1X8.2-3 SCSCPLogTracesToGlobal[101X
  
  [33X[1;0Y[29X[2XSCSCPLogTracesToGlobal[102X( [3Xtestname[103X ) [32X function[133X
  [33X[1;0Y[29X[2XSCSCPLogTracesToGlobal[102X(  ) [32X function[133X
  
  [33X[0;0YTo  analyse  the performance of parallel [5XSCSCP[105X framework, we make use of the
  [5XEdenTV[105X  program  [BL07]  developed initially to visualize the performance of
  parallel  programs  written in functional programming language Eden, and now
  distributed    under   the   GNU   Public   License   and   available   from
  [7Xhttp://www.mathematik.uni-marburg.de/~eden/?content=EdenTV[107X.[133X
  
  [33X[0;0YCalled with the string containing the name of the test, this functions turns
  on writing information about key activity events into trace files in current
  directories  for  the  client  and  servers listed [2XSCSCPservers[102X ([14X8.1-3[114X). The
  trace  file  will  have  the  name  of the format [3Xtestname[103X[10X.client.tr[110X for the
  client  and  [3Xtestname[103X[10X.<hostname>.<port>.tr[110X  for  the  server. After the test
  these  files  should be collected from remote servers and concatenated (e.g.
  using   [11Xcat[111X)   together   with   the   standard   preamble   from  the  file
  [11Xscscp/tracing/stdhead.txt[111X  (we recommend to put after the preamble first all
  traces  from  servers  and then the client's traces to have nicer diagrams).
  The resulting file then may be opened with [5XEdenTV[105X.[133X
  
  [33X[0;0YIn the following example we use a dual core MacBook laptop to generate trace
  files for two tests and then show their corresponding trace diagrams:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[28XSCSCPLogTracesToGlobal("quillen100");[128X[104X
    [4X[28XParListWithSCSCP( List( [1..100], i->[512,i]), "QuillenSeriesByIdGroup" );[128X[104X
    [4X[28XSCSCPLogTracesToGlobal();[128X[104X
    [4X[28XSCSCPLogTracesToGlobal( "euler" );[128X[104X
    [4X[28XParListWithSCSCP( [1..1000], "WS_Phi" );[128X[104X
    [4X[28XSCSCPLogTracesToGlobal();[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0Y/See  diagrams in HTML and PDF versions of the manual/ The diagrams (made on
  an  dual core MacBook laptop), shows that in the first case parallelising is
  efficient  and master successfully distributes load to workers, while in the
  second  case  a single computation is just too short, so most of the time is
  spent   on  communication.  To  parallelize  the  Euler's  function  example
  efficiently,  tasks must rather be grouped in chunks, which should be enough
  large  to reduce the communication overload, but enough small to ensure that
  tasks are evenly distributed.[133X
  
  [33X[0;0YOf course, tracing can be used to investigate communication between a client
  and  a  single  server  in a non-parallel context as well. For this purpose,
  [2XSCSCPservers[102X ([14X8.1-3[114X) must be modified to contain only one server.[133X
  
  [33X[0;0Y[2XParListWithSCSCP[102X ([14X8.2-1[114X) can be easily modified to have parallel versions of
  other  list  operations  like [2XForAll[102X ([14XReference: ForAll[114X), [2XForAny[102X ([14XReference:
  ForAny[114X),  [2XFirst[102X  ([14XReference:  First[114X),  [2XNumber[102X  ([14XReference: Number[114X), [2XFiltered[102X
  ([14XReference:  Filtered[114X), and also to have the skeleton in which the queue may
  be modified during the computation (for example, to compute orbits). We plan
  to provide such tools in one of the next versions of the package.[133X
  
  
  [1X8.3 [33X[0;0YExample: parallelising Karatsuba multiplication for polynomials[133X[101X
  
  [33X[0;0YThe   file  [11Xscscp/example/karatsuba.g[111X  contains  an  implementation  of  the
  Karatsuba  multiplication  algorithm  for polynomials. This algorithm can be
  easily  parallelized since each recursive step creates three recursive calls
  of  the  same  function  for other polynomials. [13XWe will not parallelize each[113X
  recursive  call,  since this will create enormous data flow. Instead of this
  we  parallelize  only  the  top-level  function.  For  our  experiments with
  parallelising   Karatsuba   multiplication   for  polynomials  with  integer
  coefficients  we  used  the  multi-core workstation, on which we started one
  [5XSCSCP[105X   client  and  two  [5XSCSCP[105X  servers.  To  use  it,  modify  the  server
  configuration   file   adding   to   it   the   command  to  read  the  file
  [11Xscscp/example/karatsuba.g[111X, then define there the following function[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[28XKaratsubaPolynomialMultiplicationExtRepByString:=function(s1,s2)[128X[104X
    [4X[28X    return String( KaratsubaPolynomialMultiplicationExtRep( [128X[104X
    [4X[28X                   EvalString(s1), EvalString(s2) ) );[128X[104X
    [4X[28Xend;;[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0Yand  finally  add  the  following  lines  to  made  it available as an [5XSCSCP[105X
  procedure under the name [10XWS_Karatsuba[110X:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[28XInstallSCSCPprocedure( "WS_Karatsuba", [128X[104X
    [4X[28X                       KaratsubaPolynomialMultiplicationExtRepByString);[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0Y(we  do  not  include it into the default [11Xscscp/example/myserver.g[111X since the
  code contains a call to [2XEvalString[102X ([14XReference: EvalString[114X)).[133X
  
  [33X[0;0YThis   function   provides   a   "bridge"   between  the  client's  function
  [10XKaratsubaPolynomialMultiplicationWS[110X     and     the     server's    function
  [10XKaratsubaPolynomialMultiplicationExtRep[110X,  which  performs the actual work on
  the  server.  [10XWS_Karatsuba[110X  converts  its  string  arguments  into  internal
  representation  of univariate polynomials (basically, lists of integers) and
  then  converts  the result back into string (since such data exchange format
  was  chosen). We are going to parallelize the following part of the client's
  code:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[28X...[128X[104X
    [4X[28Xu := KaratsubaPolynomialMultiplicationExtRep(f1,g1);[128X[104X
    [4X[28Xv := KaratsubaPolynomialMultiplicationExtRep(f0,g0);[128X[104X
    [4X[28Xw := KaratsubaPolynomialMultiplicationExtRep([128X[104X
    [4X[28X       PlusLaurentPolynomialsExtRep(f1,f0),[128X[104X
    [4X[28X       PlusLaurentPolynomialsExtRep(g1,g0) );[128X[104X
    [4X[28X...[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0Yand this can be done straightforwardly - we replace two first calls by calls
  of  the  appropriate  [5XSCSCP[105X  services, then perform the 3rd call locally and
  then collect the results from the two remote calls:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[28X...[128X[104X
    [4X[28Xu := NewProcess( "WS_Karatsuba",[ String(f1), String(g1) ],"localhost", 26133);   [128X[104X
    [4X[28Xv := NewProcess( "WS_Karatsuba",[ String(f0), String(g0) ],"localhost", 26134);   [128X[104X
    [4X[28Xw := KaratsubaPolynomialMultiplicationExtRep([128X[104X
    [4X[28X       PlusLaurentPolynomialsExtRep(f1,f0),[128X[104X
    [4X[28X       PlusLaurentPolynomialsExtRep(g1,g0) );[128X[104X
    [4X[28Xwsresult:=SynchronizeProcesses2( u,v );[128X[104X
    [4X[28Xu := EvalString( wsresult[1].object );[128X[104X
    [4X[28Xv := EvalString( wsresult[2].object );[128X[104X
    [4X[28X...[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
  [33X[0;0YWe  obtain  almost  double  speedup  on  three  cores  on randomly generated
  polynomials of degree 32000:[133X
  
  [4X[32X  Example  [32X[104X
    [4X[28X[128X[104X
    [4X[25Xgap>[125X [27XReadPackage("scscp/example/karatsuba.g");[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xfam:=FamilyObj(1);;[127X[104X
    [4X[25Xgap>[125X [27Xf:=LaurentPolynomialByCoefficients( fam, [127X[104X
    [4X[25X>[125X [27X        List([1..32000],i->Random(Integers)), 0, 1 );;[127X[104X
    [4X[25Xgap>[125X [27Xg:=LaurentPolynomialByCoefficients( fam, [127X[104X
    [4X[25X>[125X [27X        List([1..32000],i->Random(Integers)), 0, 1 );;[127X[104X
    [4X[25Xgap>[125X [27Xt2:=KaratsubaPolynomialMultiplication(f,g);;time;[127X[104X
    [4X[28X5892[128X[104X
    [4X[25Xgap>[125X [27Xt3:=KaratsubaPolynomialMultiplicationWS(f,g);;time;[127X[104X
    [4X[28X2974[128X[104X
    [4X[28X[128X[104X
  [4X[32X[104X
  
