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7 Debugging and Profiling Facilities
7.1 Recovery from NoMethodFound-Errors
7.1-1 ShowArguments
7.1-2 ShowArgument
7.1-3 ShowDetails
7.1-4 ShowMethods
7.1-5 ShowOtherMethods
7.2 Inspecting Applicable Methods
7.2-1 ApplicableMethod
7.3 Tracing Methods
7.3-1 TraceMethods
7.3-2 UntraceMethods
7.3-3 TraceImmediateMethods
7.4 Info Functions
7.4-1 NewInfoClass
7.4-2 DeclareInfoClass
7.4-3 SetInfoLevel
7.4-4 InfoLevel
7.4-5 Info
7.4-6 Customizing `Info` (7.4-5) statements
7.4-7 InfoWarning
7.5 Assertions
7.5-1 SetAssertionLevel
7.5-2 AssertionLevel
7.5-3 Assert
7.6 Timing
7.6-1 Runtimes
7.6-2 Runtime
7.6-3 time
7.7 Profiling
7.7-1 ProfileGlobalFunctions
7.7-2 ProfileOperations
7.7-3 ProfileOperationsAndMethods
7.7-4 ProfileFunctions
7.7-5 UnprofileFunctions
7.7-6 ProfileMethods
7.7-7 UnprofileMethods
7.7-8 DisplayProfile
7.7-9 ClearProfile
7.7-10 An Example of Profiling
7.7-11 DisplayCacheStats
7.7-12 ClearCacheStats
7.8 Information about the version used
7.9 Test Files
7.9-1 ReadTest
7.9-2 Starting and stopping test
7.9-3 Test
7.10 Debugging Recursion
7.10-1 SetRecursionTrapInterval
7.11 Global Memory Information
7.11-1 GasmanStatistics
7.11-2 GasmanMessageStatus
7.11-3 GasmanLimits

### 7 Debugging and Profiling Facilities

This chapter describes some functions that are useful mainly for debugging and profiling purposes.

Probably the most important debugging tool in GAP is the break loop (see Section 6.4) which can be entered by putting an `Error` (6.6-1) statement into your code or by hitting Control-C. In the break loop one can inspect variables, stack traces and issue commands as usual in an interactive GAP session. See also the `DownEnv` (6.5-1), `UpEnv` (6.5-1) and `Where` (6.4-5) functions.

Sections 7.2 and 7.3 show how to get information about the methods chosen by the method selection mechanism (see chapter 78).

The final sections describe functions for collecting statistics about computations (see `Runtime` (7.6-2), 7.7).

#### 7.1 Recovery from NoMethodFound-Errors

When the method selection fails because there is no applicable method, an error as in the following example occurs and a break loop is entered:

    gap> IsNormal(2,2);
    Error, no method found! For debugging hints type ?Recovery from NoMethodFound
    Error, no 1st choice method found for `IsNormal' on 2 arguments called from
    <function>( <arguments> ) called from read-eval-loop
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you can 'return;' to continue
    brk>

This only says, that the method selection tried to find a method for `IsNormal` on two arguments and failed. In this situation it is crucial to find out, why this happened. Therefore there are a few functions which can display further information. Note that you can leave the break loop by the `quit` command (see 6.4-1) and that the information about the incident is no longer accessible afterwards.

##### 7.1-1 ShowArguments

`‣ ShowArguments`( ) | ( function )

This function is only available within a break loop caused by a "No Method Found"-error. It prints as a list the arguments of the operation call for which no method was found.

##### 7.1-2 ShowArgument

`‣ ShowArgument`( nr ) | ( function )

This function is only available within a break loop caused by a "No Method Found"-error. It prints the nr-th arguments of the operation call for which no method was found. `ShowArgument` needs exactly one argument which is an integer between 0 and the number of arguments the operation was called with.

##### 7.1-3 ShowDetails

`‣ ShowDetails`( ) | ( function )

This function is only available within a break loop caused by a "No Method Found"-error. It prints the details of this error: The operation, the number of arguments, a flag which indicates whether the operation is being traced, a flag which indicates whether the operation is a constructor method, and the number of methods that refused to apply by calling `TryNextMethod` (78.4-1). The last number is called `Choice` and is printed as an ordinal. So if exactly k methods were found but called `TryNextMethod` (78.4-1) and there were no more methods it says `Choice:` k `th`.

##### 7.1-4 ShowMethods

`‣ ShowMethods`( [verbosity] ) | ( function )

This function is only available within a break loop caused by a "No Method Found"-error. It prints an overview about the installed methods for those arguments the operation was called with (using 7.2. The verbosity can be controlled by the optional integer parameter verbosity. The default is 2, which lists all applicable methods. With verbosity 1 `ShowMethods` only shows the number of installed methods and the methods matching, which can only be those that were already called but refused to work by calling `TryNextMethod` (78.4-1). With verbosity 3 not only all installed methods but also the reasons why they do not match are displayed.

##### 7.1-5 ShowOtherMethods

`‣ ShowOtherMethods`( [verbosity] ) | ( function )

This function is only available within a break loop caused by a "No Method Found"-error. It prints an overview about the installed methods for a different number of arguments than the number of arguments the operation was called with (using 7.2. The verbosity can be controlled by the optional integer parameter verbosity. The default is 1 which lists only the number of applicable methods. With verbosity 2 `ShowOtherMethods` lists all installed methods and with verbosity 3 also the reasons, why they are not applicable. Calling `ShowOtherMethods` with verbosity 3 in this function will normally not make any sense, because the different numbers of arguments are simulated by supplying the corresponding number of ones, for which normally no reasonable methods will be installed.

#### 7.2 Inspecting Applicable Methods

##### 7.2-1 ApplicableMethod

`‣ ApplicableMethod`( opr, args[, printlevel[, nr]] ) | ( function )

`‣ ApplicableMethodTypes`( opr, args[, printlevel[, nr]] ) | ( function )

Called with two arguments, `ApplicableMethod` returns the method of highest rank that is applicable for the operation opr with the arguments in the list args. The default printlevel is `0`. If no method is applicable then `fail` is returned.

If a positive integer is given as the fourth argument nr then `ApplicableMethod` returns the nr-th applicable method for the operation opr with the arguments in the list args, where the methods are ordered according to descending rank. If less than nr methods are applicable then `fail` is returned.

If the fourth argument nr is the string `"all"` then `ApplicableMethod` returns a list of all applicable methods for opr with arguments args, ordered according to descending rank.

Depending on the integer value printlevel, additional information is printed. Admissible values and their meaning are as follows.

0

  no information,

1

  information about the applicable method,

2

  also information about the not applicable methods of higher rank,

3

  also for each not applicable method the first reason why it is not applicable,

4

  also for each not applicable method all reasons why it is not applicable.

6

  also the function body of the selected method(s)

When a method returned by `ApplicableMethod` is called then it returns either the desired result or the string `"TRY_NEXT_METHOD"`, which corresponds to a call to `TryNextMethod` (78.4-1) in the method and means that the method selection would call the next applicable method.

Note: The GAP kernel provides special treatment for the infix operations `\+`, `\-`, `\*`, `\/`, `\^`, `\mod` and `\in`. For some kernel objects (notably cyclotomic numbers, finite field elements and row vectors thereof) it calls kernel methods circumventing the method selection mechanism. Therefore for these operations `ApplicableMethod` may return a method which is not the kernel method actually used.

The function `ApplicableMethodTypes` takes the types or filters of the arguments as argument (if only filters are given of course family predicates cannot be tested).

#### 7.3 Tracing Methods

##### 7.3-1 TraceMethods

`‣ TraceMethods`( opr1, opr2, ... ) | ( function )

`‣ TraceMethods`( oprs ) | ( function )

After the call of `TraceMethods`, whenever a method of one of the operations opr1, opr2, ... is called, the information string used in the installation of the method is printed. The second form has the same effect for each operation from the list oprs of operations.

##### 7.3-2 UntraceMethods

`‣ UntraceMethods`( opr1, opr2, ... ) | ( function )

`‣ UntraceMethods`( oprs ) | ( function )

turns the tracing off for all operations opr1, opr2, ... or in the second form, for all operations in the list oprs.

    gap> TraceMethods( [ Size ] );
    gap> g:= Group( (1,2,3), (1,2) );;
    gap> Size( g );
    #I  Size: for a permutation group
    #I  Setter(Size): system setter
    #I  Size: system getter
    #I  Size: system getter
    6
    gap> UntraceMethods( [ Size ] );

##### 7.3-3 TraceImmediateMethods

`‣ TraceImmediateMethods`( flag ) | ( function )

If flag is true, tracing for all immediate methods is turned on. If flag is false it is turned off. (There is no facility to trace specific immediate methods.)

    gap> TraceImmediateMethods( true );
    gap> g:= Group( (1,2,3), (1,2) );;
    #I  immediate: Size
    #I  immediate: IsCyclic
    #I  immediate: IsCommutative
    #I  immediate: IsTrivial
    gap> Size( g );
    #I  immediate: IsNonTrivial
    #I  immediate: Size
    #I  immediate: IsFreeAbelian
    #I  immediate: IsTorsionFree
    #I  immediate: IsNonTrivial
    #I  immediate: GeneralizedPcgs
    #I  immediate: IsPerfectGroup
    #I  immediate: IsEmpty
    6
    gap> TraceImmediateMethods( false );
    gap> UntraceMethods( [ Size ] );

This example gives an explanation for the two calls of the "system getter" for `Size` (30.4-6). Namely, there are immediate methods that access the known size of the group. Note that the group `g` was known to be finitely generated already before the size was computed, the calls of the immediate method for `IsFinitelyGeneratedGroup` (39.15-17) after the call of `Size` (30.4-6) have other arguments than `g`.

#### 7.4 Info Functions

The `Info` (7.4-5) mechanism permits operations to display intermediate results or information about the progress of the algorithms. Information is always given according to one or more info classes. Each of the info classes defined in the GAP library usually covers a certain range of algorithms, so for example `InfoLattice` covers all the cyclic extension algorithms for the computation of a subgroup lattice.

The amount of information to be displayed can be specified by the user for each info class separately by a level, the higher the level the more information will be displayed. Ab initio all info classes have level zero except `InfoWarning` (7.4-7) which initially has level 1.

##### 7.4-1 NewInfoClass

`‣ NewInfoClass`( name ) | ( operation )

creates a new info class with name name.

##### 7.4-2 DeclareInfoClass

`‣ DeclareInfoClass`( name ) | ( function )

creates a new info class with name name and binds it to the global variable name. The variable must previously be writable, and is made readonly by this function.

##### 7.4-3 SetInfoLevel

`‣ SetInfoLevel`( infoclass, level ) | ( operation )

Sets the info level for infoclass to level.

##### 7.4-4 InfoLevel

`‣ InfoLevel`( infoclass ) | ( operation )

returns the info level of infoclass.

##### 7.4-5 Info

`‣ Info`( infoclass, level, info[, moreinfo, ...] ) | ( function )

If the info level of infoclass is at least level the remaining arguments, info and possibly moreinfo and so on, are evaluated. (Technically, `Info` is a keyword and not a function.)

By default, they are viewed, preceded by the string `"#I "` and followed by a newline. Otherwise the third and subsequent arguments are not evaluated. (The latter can save substantial time when displaying difficult results.)

The behaviour can be customized with `SetInfoHandler` (7.4-6).

    gap> InfoExample:=NewInfoClass("InfoExample");;
    gap> Info(InfoExample,1,"one");Info(InfoExample,2,"two");
    gap> SetInfoLevel(InfoExample,1);
    gap> Info(InfoExample,1,"one");Info(InfoExample,2,"two");
    #I  one
    gap> SetInfoLevel(InfoExample,2);
    gap> Info(InfoExample,1,"one");Info(InfoExample,2,"two");
    #I  one
    #I  two
    gap> InfoLevel(InfoExample);
    2
    gap> Info(InfoExample,3,Length(Combinations([1..9999])));

Note that the last `Info` call is executed without problems, since the actual level `2` of `InfoExample` causes `Info` to ignore the last argument, which prevents `Length(Combinations([1..9999]))` from being evaluated; note that an evaluation would be impossible due to memory restrictions.

A set of info classes (called an info selector) may be passed to a single `Info` statement. As a shorthand, info classes and selectors may be combined with `+` rather than `Union` (30.5-3). In this case, the message is triggered if the level of any of the classes is high enough.

    gap> InfoExample:=NewInfoClass("InfoExample");;
    gap> SetInfoLevel(InfoExample,0);
    gap> Info(InfoExample + InfoWarning, 1, "hello");
    #I  hello
    gap> Info(InfoExample + InfoWarning, 2, "hello");
    gap> SetInfoLevel(InfoExample,2);
    gap> Info(InfoExample + InfoWarning, 2, "hello");
    #I  hello
    gap> InfoLevel(InfoWarning);
    1

##### 7.4-6 Customizing `Info` (7.4-5) statements

`‣ SetInfoHandler`( infoclass, handler ) | ( function )

`‣ SetInfoOutput`( infoclass, out ) | ( function )

`‣ SetDefaultInfoOutput`( out ) | ( function )

Returns: nothing

This allows to customize what happens in an `Info(infoclass, level, ...)` statement.

In the first function handler must be a function with three arguments infoclass, level, list. Here list is the list containing the third to last argument of the `Info` (7.4-5) call.

The default handler is the function `DefaultInfoHandler`. It prints `"#I "`, then the third and further arguments of the info statement, and finally a `"\n"`.

If the first argument of an `Info` (7.4-5) statement is a sum of Info classes, the handler of the first summand is used.

The file or stream to which `Info` (7.4-5) statements for individual `Info` (7.4-5) classes print can be changed with `SetInfoOutput`. The initial default for all `Info` (7.4-5) classes is the string `"*Print*"` which means the current output file. The default can be changed with `SetDefaultInfoOutput`. The argument out can be a filename or an open stream, the special names `"*Print*"`, `"*errout*` and `"*stdout*` are also recognized.

For example, `SetDefaultInfoOutput("*errout*");` would send `Info` (7.4-5) output to standard error, which can be interesting if GAPs output is redirected.

##### 7.4-7 InfoWarning

`‣ InfoWarning` | ( global variable )

is an info class to which general warnings are sent at level 1, which is its default level. More specialised warnings are shown via calls of `Info` (7.4-5) at `InfoWarning` level 2, e.g. information about the autoloading of GAP packages and the initial line matched when displaying an on-line help topic.

#### 7.5 Assertions

Assertions are used to find errors in algorithms. They test whether intermediate results conform to required conditions and issue an error if not.

##### 7.5-1 SetAssertionLevel

`‣ SetAssertionLevel`( lev ) | ( function )

assigns the global assertion level to lev. By default it is zero.

##### 7.5-2 AssertionLevel

`‣ AssertionLevel`( ) | ( function )

returns the current assertion level.

##### 7.5-3 Assert

`‣ Assert`( lev, cond[, message] ) | ( function )

With two arguments, if the global assertion level is at least lev, condition cond is tested and if it does not return `true` an error is raised. Thus `Assert(lev, cond)` is equivalent to the code

    if AssertionLevel() >= lev and not <cond> then
      Error("Assertion failure");
    fi;

With the message argument form of the `Assert` statement, if the global assertion level is at least lev, condition cond is tested and if it does not return `true` then message is evaluated and printed.

Assertions are used at various places in the library. Thus turning assertions on can slow code execution significantly.

#### 7.6 Timing

##### 7.6-1 Runtimes

`‣ Runtimes`( ) | ( function )

`Runtimes` returns a record with components bound to integers or `fail`. Each integer is the cpu time (processor time) in milliseconds spent by GAP in a certain status:

`user_time`

  cpu time spent with GAP functions (without child processes).

`system_time`

  cpu time spent in system calls, e.g., file access (`fail` if not available).

`user_time_children`

  cpu time spent in child processes (`fail` if not available).

`system_time_children`

  cpu time spent in system calls by child processes (`fail` if not available).

Note that this function is not fully supported on all systems. Only the `user_time` component is (and may on some systems include the system time).

The following example demonstrates tasks which contribute to the different time components:

    gap> Runtimes(); # after startup
    rec( user_time := 3980, system_time := 60, user_time_children := 0,
      system_time_children := 0 )
    gap> Exec("cat /usr/bin/*||wc"); # child process with a lot of file access
     893799 7551659 200928302
    gap> Runtimes();
    rec( user_time := 3990, system_time := 60, user_time_children := 1590,
      system_time_children := 600 )
    gap> a:=0;;for i in [1..100000000] do a:=a+1; od; # GAP user time
    gap> Runtimes();
    rec( user_time := 12980, system_time := 70, user_time_children := 1590,
      system_time_children := 600 )
    gap> ?blabla  # first call of help, a lot of file access
    Help: no matching entry found
    gap> Runtimes();
    rec( user_time := 13500, system_time := 440, user_time_children := 1590,
      system_time_children := 600 )

##### 7.6-2 Runtime

`‣ Runtime`( ) | ( function )

`Runtime` returns the time spent by GAP in milliseconds as an integer. It is the same as the value of the `user_time` component given by `Runtimes` (7.6-1), as explained above.

See `StringTime` (27.9-9) for a translation from milliseconds into hour/minute format.

##### 7.6-3 time

`‣ time` | ( global variable )

In the read-eval-print loop, `time` stores the time the last command took.

#### 7.7 Profiling

Profiling of code can be used to determine in which parts of a program how much time has been spent and how much memory has been allocated during runtime. The idea is that

- first one switches on profiling for those GAP functions the performance of which one wants to check,

- then one runs some GAP computations,

- then one looks at the profile information collected during these computations,

- then one runs more computations (perhaps clearing all profile information before, see `ClearProfile` (7.7-9)),

- and finally one switches off profiling.

For switching on and off profiling, GAP supports entering a list of functions (see `ProfileFunctions` (7.7-4), `UnprofileFunctions` (7.7-5)) or a list of operations whose methods shall be (un)profiled (`ProfileMethods` (7.7-6), `UnprofileMethods` (7.7-7)), and `DisplayProfile` (7.7-8) can be used to show profile information about functions in a given list.

Besides these functions, `ProfileGlobalFunctions` (7.7-1), `ProfileOperations` (7.7-2), and `ProfileOperationsAndMethods` (7.7-3) can be used for switching on or off profiling for all global functions, operations, and operations together with all their methods, respectively, and for showing profile information about these functions.

Note that GAP will perform more slowly when profiling than when not.

##### 7.7-1 ProfileGlobalFunctions

`‣ ProfileGlobalFunctions`( [bool] ) | ( function )

Called with argument `true`, `ProfileGlobalFunctions` starts profiling of all functions that have been declared via `DeclareGlobalFunction` (79.18-7). Old profile information for all these functions is cleared. A function call with the argument `false` stops profiling of all these functions. Recorded information is still kept, so you can display it even after turning the profiling off.

When `ProfileGlobalFunctions` is called without argument, profile information for all global functions is displayed, see `DisplayProfile` (7.7-8).

##### 7.7-2 ProfileOperations

`‣ ProfileOperations`( [bool] ) | ( function )

Called with argument `true`, `ProfileOperations` starts profiling of all operations. Old profile information for all operations is cleared. A function call with the argument `false` stops profiling of all operations. Recorded information is still kept, so you can display it even after turning the profiling off.

When `ProfileOperations` is called without argument, profile information for all operations is displayed (see `DisplayProfile` (7.7-8)).

##### 7.7-3 ProfileOperationsAndMethods

`‣ ProfileOperationsAndMethods`( [bool] ) | ( function )

Called with argument `true`, `ProfileOperationsAndMethods` starts profiling of all operations and their methods. Old profile information for these functions is cleared. A function call with the argument `false` stops profiling of all operations and their methods. Recorded information is still kept, so you can display it even after turning the profiling off.

When `ProfileOperationsAndMethods` is called without argument, profile information for all operations and their methods is displayed, see `DisplayProfile` (7.7-8).

##### 7.7-4 ProfileFunctions

`‣ ProfileFunctions`( funcs ) | ( function )

starts profiling for all function in the list funcs. You can use `ProfileGlobalFunctions` (7.7-1) to turn profiling on for all globally declared functions simultaneously.

##### 7.7-5 UnprofileFunctions

`‣ UnprofileFunctions`( funcs ) | ( function )

stops profiling for all function in the list funcs. Recorded information is still kept, so you can display it even after turning the profiling off.

##### 7.7-6 ProfileMethods

`‣ ProfileMethods`( ops ) | ( function )

starts profiling of the methods for all operations in the list ops.

##### 7.7-7 UnprofileMethods

`‣ UnprofileMethods`( ops ) | ( function )

stops profiling of the methods for all operations in the list ops. Recorded information is still kept, so you can display it even after turning the profiling off.

##### 7.7-8 DisplayProfile

`‣ DisplayProfile`( [functions, ][mincount, mintime] ) | ( function )

`‣ GAPInfo.ProfileThreshold` | ( global variable )

Called without arguments, `DisplayProfile` displays the profile information for profiled operations, methods and functions. If an argument functions is given, only profile information for the functions in the list functions is shown. If two integer values mincount, mintime are given as arguments then the output is restricted to those functions that were called at least mincount times or for which the total time spent (see below) was at least mintime milliseconds. The defaults for mincount and mintime are the entries of the list stored in the global variable `GAPInfo.ProfileThreshold`.

The default value of `GAPInfo.ProfileThreshold` is `[ 10000, 30 ]`.

Profile information is displayed in a list of lines for all functions (including operations and methods) which are profiled. For each function, "count" gives the number of times the function has been called. "self/ms" gives the time (in milliseconds) spent in the function itself, "chld/ms" the time (in milliseconds) spent in profiled functions called from within this function, "stor/kb" the amount of storage (in kilobytes) allocated by the function itself, "chld/kb" the amount of storage (in kilobytes) allocated by profiled functions called from within this function, and "package" the name of the GAP package to which the function belongs; the entry "GAP" in this column means that the function belongs to the GAP library, the entry "(oprt.)" means that the function is an operation (which may belong to several packages), and an empty entry means that `FilenameFunc` (5.1-4) cannot determine in which file the function is defined.

The list is sorted according to the total time spent in the functions, that is the sum of the values in the columns "self/ms" and "chld/ms".

At the end of the list, two lines are printed that show the total time used and the total memory allocated by the profiled functions not shown in the list (label `OTHER`) and by all profiled functions (label `TOTAL`), respectively.

An interactive variant of `DisplayProfile` is the function `BrowseProfile` (Browse: BrowseProfile) that is provided by the GAP package Browse.

##### 7.7-9 ClearProfile

`‣ ClearProfile`( ) | ( function )

clears all stored profile information.

##### 7.7-10 An Example of Profiling

Let us suppose we want to get information about the computation of the conjugacy classes of a certain permutation group. For that, first we create the group, then we start profiling for all global functions and for all operations and their methods, then we compute the conjugacy classes, and then we stop profiling.

    gap> g:= PrimitiveGroup( 24, 1 );;
    gap> ProfileGlobalFunctions( true );
    gap> ProfileOperationsAndMethods( true );
    gap> ConjugacyClasses( g );;
    gap> ProfileGlobalFunctions( false );
    gap> ProfileOperationsAndMethods( false );

Now the profile information is available. We can list the information for all profiled functions with `DisplayProfile` (7.7-8).

    gap> DisplayProfile();
      count  self/ms  chld/ms  stor/kb  chld/kb  package  function
      17647        0        0      275        0  GAP      BasePoint
      10230        0        0      226        0  (oprt.)  ShallowCopy
      10139        0        0        0        0           PositionSortedOp: for*
      10001        0        0      688        0           UniteSet: for two int*
      10001        8        0       28      688  (oprt.)  UniteSet
      14751       12        0        0        0           =: for two families: *
      10830        8        4      182      276  GAP      Concatenation
       2700       20       12      313       55  GAP      AddRefinement
       2444       28        4     3924      317  GAP      ConjugateStabChain
       4368        0       32        7      714  (oprt.)  Size
       2174       32        4     1030      116  GAP      List
        585        4       32       45      742  GAP      RRefine
       1532       32        8      194       56  GAP      AddGeneratorsExtendSc*
       1221        8       32      349      420  GAP      Partition
     185309       28       12        0        0  (oprt.)  Length
        336        4       40       95      817  GAP      ExtendSeriesPermGroup
          4       28       20      488      454  (oprt.)  Sortex
       2798        0       52       54      944  GAP      StabChainForcePoint
        560        4       48       83      628  GAP      StabChainSwap
        432       16       40      259      461  GAP      SubmagmaWithInversesNC
     185553       48        8      915       94  (oprt.)  Add
         26        0       64        0     2023  (oprt.)  CentralizerOp
         26        0       64        0     2023  GAP      CentralizerOp: perm g*
         26        0       64        0     2023  GAP      Centralizer: try to e*
        152        4       64        0     2024  (oprt.)  Centralizer
       1605        0       68        0     2032  (oprt.)  StabilizerOfExternalS*
         26        0       68        0     2024  GAP      Meth(StabilizerOfExte*
        382        0       96       69     1922  GAP      TryPcgsPermGroup
       5130        4       96      309     3165  GAP      ForAll
       7980       24      116      330     6434  GAP      ChangeStabChain
      12076       12      136      351     6478  GAP      ProcessFixpoint
        192        0      148        4     3029  GAP      StabChainMutable: cal*
       2208        4      148        3     3083  (oprt.)  StabChainMutable
        217        0      160        0     3177  (oprt.)  StabChainOp
        217       12      148       60     3117  GAP      StabChainOp: group an*
        216       36      464      334    12546  GAP      PartitionBacktrack
       1479       12      668      566    18474  GAP      RepOpElmTuplesPermGro*
       1453       12      684       56    18460  GAP      in: perm class rep
        126        0      728       13    19233  GAP      ConjugacyClassesTry
          1        0      736        0    19671  GAP      ConjugacyClassesByRan*
          2        0      736        2    19678  (oprt.)  ConjugacyClasses
          1        0      736        0    19675  GAP      ConjugacyClasses: per*
      13400     1164        0        0        0  (oprt.)  Position
                 484             12052                    OTHER
                2048             23319                    TOTAL

We can restrict the list to global functions with `ProfileGlobalFunctions` (7.7-1).

    gap> ProfileGlobalFunctions();
      count  self/ms  chld/ms  stor/kb  chld/kb  package  function
      17647        0        0      275        0  GAP      BasePoint
      10830        8        4      182      276  GAP      Concatenation
       2700       20       12      313       55  GAP      AddRefinement
       2444       28        4     3924      317  GAP      ConjugateStabChain
       2174       32        4     1030      116  GAP      List
        585        4       32       45      742  GAP      RRefine
       1532       32        8      194       56  GAP      AddGeneratorsExtendSc*
       1221        8       32      349      420  GAP      Partition
        336        4       40       95      817  GAP      ExtendSeriesPermGroup
       2798        0       52       54      944  GAP      StabChainForcePoint
        560        4       48       83      628  GAP      StabChainSwap
        432       16       40      259      461  GAP      SubmagmaWithInversesNC
        382        0       96       69     1922  GAP      TryPcgsPermGroup
       5130        4       96      309     3165  GAP      ForAll
       7980       24      116      330     6434  GAP      ChangeStabChain
      12076       12      136      351     6478  GAP      ProcessFixpoint
        216       36      464      334    12546  GAP      PartitionBacktrack
       1479       12      668      566    18474  GAP      RepOpElmTuplesPermGro*
        126        0      728       13    19233  GAP      ConjugacyClassesTry
          1        0      736        0    19671  GAP      ConjugacyClassesByRan*
                1804             14536                    OTHER
                2048             23319                    TOTAL

We can restrict the list to operations with `ProfileOperations` (7.7-2).

    gap> ProfileOperations();
      count  self/ms  chld/ms  stor/kb  chld/kb  package  function
      10230        0        0      226        0  (oprt.)  ShallowCopy
      10001        8        0       28      688  (oprt.)  UniteSet
       4368        0       32        7      714  (oprt.)  Size
     185309       28       12        0        0  (oprt.)  Length
          4       28       20      488      454  (oprt.)  Sortex
     185553       48        8      915       94  (oprt.)  Add
         26        0       64        0     2023  (oprt.)  CentralizerOp
        152        4       64        0     2024  (oprt.)  Centralizer
       1605        0       68        0     2032  (oprt.)  StabilizerOfExternalS*
       2208        4      148        3     3083  (oprt.)  StabChainMutable
        217        0      160        0     3177  (oprt.)  StabChainOp
          2        0      736        2    19678  (oprt.)  ConjugacyClasses
      13400     1164        0        0        0  (oprt.)  Position
                 764             21646                    OTHER
                2048             23319                    TOTAL

We can restrict the list to operations and their methods with `ProfileOperationsAndMethods` (7.7-3).

    gap> ProfileOperationsAndMethods();
      count  self/ms  chld/ms  stor/kb  chld/kb  package  function
      10230        0        0      226        0  (oprt.)  ShallowCopy
      10139        0        0        0        0           PositionSortedOp: for*
      10001        0        0      688        0           UniteSet: for two int*
      10001        8        0       28      688  (oprt.)  UniteSet
      14751       12        0        0        0           =: for two families: *
       4368        0       32        7      714  (oprt.)  Size
     185309       28       12        0        0  (oprt.)  Length
          4       28       20      488      454  (oprt.)  Sortex
     185553       48        8      915       94  (oprt.)  Add
         26        0       64        0     2023  (oprt.)  CentralizerOp
         26        0       64        0     2023  GAP      CentralizerOp: perm g*
         26        0       64        0     2023  GAP      Centralizer: try to e*
        152        4       64        0     2024  (oprt.)  Centralizer
       1605        0       68        0     2032  (oprt.)  StabilizerOfExternalS*
         26        0       68        0     2024  GAP      Meth(StabilizerOfExte*
        192        0      148        4     3029  GAP      StabChainMutable: cal*
       2208        4      148        3     3083  (oprt.)  StabChainMutable
        217        0      160        0     3177  (oprt.)  StabChainOp
        217       12      148       60     3117  GAP      StabChainOp: group an*
       1453       12      684       56    18460  GAP      in: perm class rep
          2        0      736        2    19678  (oprt.)  ConjugacyClasses
          1        0      736        0    19675  GAP      ConjugacyClasses: per*
      13400     1164        0        0        0  (oprt.)  Position
                 728             20834                    OTHER
                2048             23319                    TOTAL

Finally, we can restrict the list to explicitly given functions with `DisplayProfile` (7.7-8), by entering the list of functions as an argument.

    gap> DisplayProfile( [ StabChainOp, Centralizer ] );
      count  self/ms  chld/ms  stor/kb  chld/kb  package  function
        152        4       64        0     2024  (oprt.)  Centralizer
        217        0      160        0     3177  (oprt.)  StabChainOp
                2044             23319                    OTHER
                2048             23319                    TOTAL

##### 7.7-11 DisplayCacheStats

`‣ DisplayCacheStats`( ) | ( function )

displays statistics about the different caches used by the method selection.

##### 7.7-12 ClearCacheStats

`‣ ClearCacheStats`( ) | ( function )

clears all statistics about the different caches used by the method selection.

#### 7.8 Information about the version used

The global variable `GAPInfo.Version` (see `GAPInfo` (3.5-1)) contains the version number of the version of GAP. Its value can be checked other version number using `CompareVersionNumbers` (76.3-6).

To produce sample citations for the used version of GAP or for a package available in this GAP installation, use `Cite` (76.3-15).

If you wish to report a problem to GAP Support or GAP Forum, it may be useful to not only report the version used, but also to include the GAP banner displays the information about the architecture for which the GAP binary is built, used libraries and loaded packages.

#### 7.9 Test Files

Test files are used to check that GAP produces correct results in certain computations. A selection of test files for the library can be found in the `tst` directory of the GAP distribution.

##### 7.9-1 ReadTest

`‣ ReadTest`( string ) | ( operation )

reads the test file with name string. The test file should contain lines of GAP input and corresponding output. The input lines start with the `gap>` prompt (or with the `>` prompt if commands exceed one line). The output is exactly as would result from typing in the input interactively to a GAP session (on a screen with 80 characters per line).

Optionally, `START_TEST` (7.9-2) and `STOP_TEST` (7.9-2) may be used in the beginning and end of test files to reinitialize the caches and the global random number generator in order to be independent of the reading order of several test files. Furthermore, `START_TEST` (7.9-2) increases the assertion level for the time of the test, and `STOP_TEST` (7.9-2) sets the proportionality factor that is used to output a "GAPstone" speed ranking after the file has been completely processed.

##### 7.9-2 Starting and stopping test

`‣ START_TEST`( id ) | ( function )

`‣ STOP_TEST`( file, fac ) | ( function )

`START_TEST` and `STOP_TEST` may be optionally used in files that are read via `ReadTest` (7.9-1). If used, `START_TEST` reinitialize the caches and the global random number generator, in order to be independent of the reading order of several test files. Furthermore, the assertion level (see `Assert` (7.5-3)) is set to 2 by `START_TEST` and set back to the previous value in the subsequent `STOP_TEST` call.

To use these options, a test file should be started with a line

    gap> START_TEST( "arbitrary identifier string" );

(Note that the `gap>` prompt is part of the line!)

and should be finished with a line

    gap> STOP_TEST( "filename", 10000 );

Here the string `"filename"` should give the name of the test file. The number is a proportionality factor that is used to output a "GAPstone" speed ranking after the file has been completely processed. For the files provided with the distribution this scaling is roughly equalized to yield the same numbers as produced by the test file `tst/combinat.tst`.

Note that the functions in `tst/testutil.g` temporarily replace `STOP_TEST` before they call `ReadTest` (7.9-1).

If you want to run a quick test of your GAP installation (though this is not required), you can read in a test script that exercises some GAP's capabilities.

    gap> Read( Filename( DirectoriesLibrary( "tst" ), "testinstall.g" ) );

The test requires about 750MB of memory and runs about one minute on an Intel Core 2 Duo / 2.53 GHz machine. You will get a large number of lines with output about the progress of the tests.

    test file         GAP4stones     time(msec)
    -------------------------------------------
    testing: ................/gap4r5/tst/zlattice.tst
    zlattice.tst               0              0
    testing: ................/gap4r5/tst/gaussian.tst
    gaussian.tst               0             10
    [ further lines deleted ]

If you want to run a more advanced check (this is not required and make take up to an hour), you can read `testall.g` which is an extended test script performing all tests from the `tst` directory.

    gap> Read( Filename( DirectoriesLibrary( "tst" ), "testall.g" ) );

The test requires about 750MB of memory and runs about one hour on an Intel Core 2 Duo / 2.53 GHz machine, and produces an output similar to the `testinstall.g` test.

##### 7.9-3 Test

`‣ Test`( fname[, optrec] ) | ( function )

Returns: `true` or `false`.

The argument fname must be the name of a file or an open input stream. The content of this file or stream should contain GAP input and output. The function `Test` runs the input lines, compares the actual output with the output stored in fname and reports differences. With an optional record as argument optrec details of this process can be adjusted.

More precisely, the content of fname must have the following format.
Lines starting with `"gap> "` are considered as GAP input, they can be followed by lines starting with `"> "` if the input is continued over several lines.
To allow for comments in fname the following lines are ignored by default: lines at the beginning of fname that start with `"#"`, and one empty line together with one or more lines starting with `"#"`.
All other lines are considered as GAP output from the preceding GAP input.

By default the actual GAP output is compared exactly with the stored output, and if these are different some information about the differences is printed.

If any differences are found then `Test` returns `false`, otherwise `true`.

If the optional argument optrec is given it must be a record. The following components of optrec are recognized and can change the default behaviour of `Test`:

`ignoreComments`

  If set to `false` then no lines in fname are ignored as explained above (default is `true`).

`width`

  The screen width used for the new output (default is `80`).

`compareFunction`

  This must be a function that gets two strings as input, the newly generated and the stored output of some GAP input. The function must return `true` or `false`, indicating if the strings should be considered equivalent or not. By default `\=` (31.11-1) is used.
  Two strings are recognized as abbreviations in this component: `"uptowhitespace"` checks if the two strings become equal after removing all white space. And `"uptonl"` compares the string up to trailing newline characters.

`reportDiff`

  A function that gets six arguments and reports a difference in the output: the GAP input, the expected GAP output, the newly generated output, the name of tested file, the line number of the input, the time to run the input. (The default is demonstrated in the example below.)

`rewriteToFile`

  If this is bound to a string it is considered as a file name and that file is written with the same input and comment lines as fname but the output substituted by the newly generated version (default is `false`).

`writeTimings`

  If this is bound to a string it is considered as a file name, that file is written and contains timing information for each input in fname.

`compareTimings`

  If this is bound to a string it is considered as name of a file to which timing information was stored via `writeTimings` in a previous call. The new timings are compared to the stored ones. By default only commands which take more than a threshold of 100 milliseconds are considered, and only differences of more than 20% are considered significant. These defaults can be overwritten by assigning a list `[timingfile, threshold, percentage]` to this component. (The default of `compareTimings` is `false`.)

`reportTimeDiff`

  This component can be used to overwrite the default function to display timing differences. It must be a function with 5 arguments: GAP input, name of test file, line number, stored time, new time.

`ignoreSTOP_TEST`

  By default set to `true`, in that case the output of GAP input starting with `"STOP_TEST"` is not checked.

`showProgress`

  If this is `true` then GAP prints position information and the input line before it is processed (default is `false`).

`subsWindowsLineBreaks`

  If this is `true` then GAP substitutes DOS/Windows style line breaks "\r\n" by UNIX style line breaks "\n" after reading the test file. (default is `true`).

    gap> tnam := Filename(DirectoriesLibrary(), "../doc/ref/demo.tst");;
    gap> mask := function(str) return Concatenation("| ",
    >          JoinStringsWithSeparator(SplitString(str, "\n", ""), "\n| "),
    >          "\n"); end;;
    gap> Print(mask(StringFile(tnam)));
    | # this is a demo file for the 'Test' function
    | #
    | gap> g := Group((1,2), (1,2,3));
    | Group([ (1,2), (1,2,3) ])
    |
    | # another comment following an empty line
    | # the following fails:
    | gap> a := 13+29;
    | 41
    gap> ss := InputTextString(StringFile(tnam));;
    gap> Test(ss);
    ########> Diff in test stream, line 8:
    # Input is:
    a := 13+29;
    # Expected output:
    41
    # But found:
    42
    ########
    false
    gap> RewindStream(ss);
    true
    gap> dtmp := DirectoryTemporary();;
    gap> ftmp := Filename(dtmp,"demo.tst");;
    gap> Test(ss, rec(reportDiff := Ignore, rewriteToFile := ftmp));
    false
    gap> Test(ftmp);
    true
    gap> Print(mask(StringFile(ftmp)));
    | # this is a demo file for the 'Test' function
    | #
    | gap> g := Group((1,2), (1,2,3));
    | Group([ (1,2), (1,2,3) ])
    |
    | # another comment following an empty line
    | # the following fails:
    | gap> a := 13+29;
    | 42

#### 7.10 Debugging Recursion

The GAP interpreter monitors the level of nesting of GAP functions during execution. By default, whenever this nesting reaches a multiple of 5000, GAP enters a break loop (6.4) allowing you to terminate the calculation, or enter Return`;` to continue it.

    gap> dive:= function(depth) if depth>1 then dive(depth-1); fi; return; end;
    function( depth ) ... end
    gap> dive(100);
    gap> OnBreak:= function() Where(1); end; # shorter traceback
    function(  ) ... end
    gap> dive(6000);
    recursion depth trap (5000)
     at
    dive( depth - 1 );
     called from
    dive( depth - 1 ); called from
    ...
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you may 'return;' to continue
    brk> return;
    gap> dive(11000);
    recursion depth trap (5000)
     at
    dive( depth - 1 );
     called from
    dive( depth - 1 ); called from
    ...
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you may 'return;' to continue
    brk> return;
    recursion depth trap (10000)
     at
    dive( depth - 1 );
     called from
    dive( depth - 1 ); called from
    ...
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you may 'return;' to continue
    brk> return;
    gap>

This behaviour can be controlled using the following procedure.

##### 7.10-1 SetRecursionTrapInterval

`‣ SetRecursionTrapInterval`( interval ) | ( function )

interval must be a non-negative small integer (between 0 and 2^28). An interval of 0 suppresses the monitoring of recursion altogether. In this case excessive recursion may cause GAP to crash.

    gap> dive:= function(depth) if depth>1 then dive(depth-1); fi; return; end;
    function( depth ) ... end
    gap> SetRecursionTrapInterval(1000);
    gap> dive(2500);
    recursion depth trap (1000)
     at
    dive( depth - 1 );
     called from
    dive( depth - 1 ); called from
    ...
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you may 'return;' to continue
    brk> return;
    recursion depth trap (2000)
     at
    dive( depth - 1 );
     called from
    dive( depth - 1 ); called from
    ...
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you may 'return;' to continue
    brk> return;
    gap> SetRecursionTrapInterval(-1);
    SetRecursionTrapInterval( <interval> ): <interval> must be a non-negative smal\
    l integer
    not in any function
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you can replace <interval> via 'return <interval>;' to continue
    brk> return ();
    SetRecursionTrapInterval( <interval> ): <interval> must be a non-negative smal\
    l integer
    not in any function
    Entering break read-eval-print loop ...
    you can 'quit;' to quit to outer loop, or
    you can replace <interval> via 'return <interval>;' to continue
    brk> return 0;
    gap> dive(20000);
    gap> dive(2000000);
    Segmentation fault

#### 7.11 Global Memory Information

The GAP environment provides automatic memory management, so that the programmer does not need to concern themselves with allocating space for objects, or recovering space when objects are no longer needed. The component of the kernel which provides this is called `GASMAN` (GAP Storage MANager). Messages reporting garbage collections performed by `GASMAN` can be switched on by the `-g` command line option (see section 3.1). There are also some facilities to access information from `GASMAN` from GAP programs.

##### 7.11-1 GasmanStatistics

`‣ GasmanStatistics`( ) | ( function )

`GasmanStatistics` returns a record containing some information from the garbage collection mechanism. The record may contain up to four components: `full`, `partial`, `npartial`, and `nfull`.

The `full` component will be present if a full garbage collection has taken place since GAP started. It contains information about the most recent full garbage collection. It is a record, with six components: `livebags` contains the number of bags which survived the garbage collection; `livekb` contains the total number of kilobytes occupied by those bags; `deadbags` contains the total number of bags which were reclaimed by that garbage collection and all the partial garbage collections preceding it, since the previous full garbage collection; `deadkb` contains the total number of kilobytes occupied by those bags; `freekb` reports the total number of kilobytes available in the GAP workspace for new objects and `totalkb` the actual size of the workspace.

These figures should be viewed with some caution. They are stored internally in fixed length integer formats, and `deadkb` and `deadbags` are liable to overflow if there are many partial collections before a full collection. Also, note that `livekb` and `freekb` will not usually add up to `totalkb`. The difference is essentially the space overhead of the memory management system.

The `partial` component will be present if there has been a partial garbage collection since the last full one. It is also a record with the same six components as `full`. In this case `deadbags` and `deadkb` refer only to the number and total size of the garbage bags reclaimed in this partial garbage collection and `livebags`and `livekb` only to the numbers and total size of the young bags that were considered for garbage collection, and survived.

The `npartial` and `nfull` components will contain the number of full and partial garbage collections performed since GAP started.

##### 7.11-2 GasmanMessageStatus

`‣ GasmanMessageStatus`( ) | ( function )

`‣ SetGasmanMessageStatus`( stat ) | ( function )

`GasmanMessageStatus` returns one of the strings `"none"`, `"full"`, or `"all"`, depending on whether the garbage collector is currently set to print messages on no collections, full collections only, or all collections, respectively.

Calling `SetGasmanMessageStatus` with the argument stat, which should be one of the three strings mentioned above, sets the garbage collector messaging level.

##### 7.11-3 GasmanLimits

`‣ GasmanLimits`( ) | ( function )

`GasmanLimits` returns a record with three components: `min` is the minimum workspace size as set by the `-m` command line option in kilobytes. The workspace size will never be reduced below this by the garbage collector. `max` is the maximum workspace size, as set by the '-o' command line option, also in kilobytes. If the workspace would need to grow past this point, GAP will enter a break loop to warn the user. A value of 0 indicates no limit. `kill` is the absolute maximum, set by the `-K` command line option. The workspace will never be allowed to grow past this limit.

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