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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Frank Lübeck, Max Neunhöffer.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file declares variables for random sources.
##
#############################################################################
##
#C IsRandomSource( <rs> )
##
## <#GAPDoc Label="IsRandomSource">
## <ManSection>
## <Filt Name="IsRandomSource" Arg='obj' Type='Category'/>
##
## <Description>
## This is the category of random source objects.
## The <E>user interface</E> for these objects consists of the following
## functions.
## <P/>
## <Ref Oper="RandomSource"/> creates a new random source <A>rs</A>, say.
## <P/>
## <C>Random( <A>rs</A>, <A>list</A> )</C> yields a random element of the
## list <A>list</A>, and
## <C>Random( <A>rs</A>, <A>low</A>, <A>high</A> )</C> yields a random
## integer between <A>low</A> and <A>high</A> (inclusive),
## see <Ref Oper="Random" Label="for random source and list"/>.
## <P/>
## If <A>rs</A> supports resetting (see <Ref Oper="State"/>) then
## <C>State( <A>rs</A> )</C> yields a copy <A>state</A>, say,
## of the current state of <A>rs</A> such that
## <C>Reset( <A>rs</A>, <A>state</A> )</C> resets <A>rs</A> to the given
## state.
## <P/>
## One idea behind providing several independent (pseudo) random sources is
## to make algorithms which use some sort of random choices deterministic.
## They can use their own new random source created with a fixed seed and
## so do exactly the same in different calls.
## <P/>
## Random source objects lie in the family <C>RandomSourcesFamily</C>.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
BIND_GLOBAL( "RandomSourcesFamily", NewFamily( "RandomSourcesFamily" ) );
DeclareCategory( "IsRandomSource", IsComponentObjectRep );
#############################################################################
##
#O Random( <rs>, <list> ) . . . for random source and a dense, nonempty list
#O Random( <rs>, <low>, <high> ) . . . . for random source and two integers
##
## <#GAPDoc Label="Random">
## <ManSection>
## <Oper Name="Random" Arg='rs, list' Label="for random source and list"/>
## <Oper Name="Random" Arg='rs, coll'
## Label="for random source and collection"/>
## <Oper Name="Random" Arg='rs, low, high'
## Label="for random source and two integers"/>
##
## <Description>
## This operation returns a random element from the dense, nonempty list
## <A>list</A> or the nonempty collection <A>coll</A>,
## or an integer in the range from the given (possibly large) integers
## <A>low</A> to <A>high</A>, respectively.
## <P/>
## The choice should only depend on the random source <A>rs</A> and have no
## effect on other random sources.
## <P/>
## It is not defined what happens if <A>list</A> or <A>coll</A> is empty,
## <A>list</A> is not dense, or <A>low</A> is larger than <A>high</A>.
## <Example>
## gap> mysource := RandomSource(IsMersenneTwister, 42);;
## gap> Random(mysource, 1, 10^60);
## 999331861769949319194941485000557997842686717712198687315183
## </Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
# We keep the declaration for non-dense lists
# in order not to break existing code.
DeclareOperation( "Random", [IsRandomSource, IsListOrCollection] );
DeclareOperation( "Random", [IsRandomSource, IsInt, IsInt] );
#############################################################################
##
#O State( <rs> ) . . . . . . . . . . . . . . . . . . state of random source
#O Reset( <rs>[, <seed>] ) . . . . . . . . . . . . . reset a random source
##
## <#GAPDoc Label="State">
## <ManSection Label="State and Reset for Random Sources">
## <Heading>State and Reset for Random Sources</Heading>
## <Oper Name="State" Arg='rs'/>
## <Oper Name="Reset" Arg='rs[, seed]'/>
##
## <Description>
## These are the basic operations for random sources (see
## <Ref Filt="IsRandomSource"/>).
## <P/>
## <Ref Oper="State"/> returns a data structure which admits recovering
## the state of the random source such that a sequence of random calls
## using this random source can be reproduced.
## If a random source cannot be reset (say, it uses truly random physical
## data) then <Ref Oper="State"/> returns <K>fail</K>.
## <P/>
## <C>Reset( <A>rs</A>, <A>seed</A> )</C> resets the random source <A>rs</A>
## to a state described by <A>seed</A>, if the random source can be reset;
## otherwise it does nothing.
## Here <A>seed</A> can be an output of <Ref Oper="State"/> and then
## <A>rs</A> gets reset to that state.
## For historical reasons, random sources accept integer values as
## <A>seed</A>.
## We recommend that new code should not rely on this; always use the output
## of a prior call to <Ref Oper="State"/> as <A>seed</A>, or omit it.
## Without the <A>seed</A> argument a fixed default seed is used.
## <Ref Oper="Reset"/> returns the state of <A>rs</A> before the call.
## <P/>
## Most methods for <Ref Oper="Random" Label="for a list or collection"/>
## in the &GAP; library that do not take a random source as argument use the
## <Ref Var="GlobalMersenneTwister"/> as random source. It can be reset
## into a known state as in the following example.
## <Example><![CDATA[
## gap> seed := Reset(GlobalMersenneTwister);;
## gap> seed = State(GlobalMersenneTwister);
## true
## gap> List([1..10],i->Random(Integers));
## [ -3, 2, -1, -2, -1, -1, 1, -4, 1, 0 ]
## gap> List([1..10],i->Random(Integers));
## [ -1, -1, -1, 1, -1, 1, -2, -1, -2, 0 ]
## gap> Reset(GlobalMersenneTwister, seed);;
## gap> List([1..10],i->Random(Integers));
## [ -3, 2, -1, -2, -1, -1, 1, -4, 1, 0 ]
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "State", [IsRandomSource] );
DeclareOperation( "Reset", [IsRandomSource] );
DeclareOperation( "Reset", [IsRandomSource, IsObject] );
DeclareOperation( "Init", [IsRandomSource, IsObject] );
#############################################################################
##
#C IsMersenneTwister( <rs> )
#C IsGlobalRandomSource( <rs> )
#C IsGAPRandomSource( <rs> )
#V GlobalRandomSource
#V GlobalMersenneTwister
##
## <#GAPDoc Label="IsGlobalRandomSource">
## <ManSection Label="Kinds of Random Sources">
## <Heading>Kinds of Random Sources</Heading>
## <Filt Name="IsMersenneTwister" Arg='rs' Type='Category'/>
## <Filt Name="IsGAPRandomSource" Arg='rs' Type='Category'/>
## <Filt Name="IsGlobalRandomSource" Arg='rs' Type='Category'/>
## <Var Name="GlobalMersenneTwister"/>
## <Var Name="GlobalRandomSource"/>
##
## <Description>
## Currently, the &GAP; library provides three types of random sources,
## distinguished by the three listed categories.
## <P/>
## <Ref Filt="IsMersenneTwister"/> are random sources which use a fast
## random generator of 32 bit numbers, called the Mersenne twister. The
## pseudo random sequence has a period of <M>2^{19937}-1</M> and the
## numbers have a <M>623</M>-dimensional equidistribution. For more details
## and the origin of the code used in the &GAP; kernel, see:
## <URL>
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html</URL>.
## <P/>
## Use the Mersenne twister if possible, in particular for generating many
## large random integers.
## <P/>
## There is also a predefined global random source
## <Ref Var="GlobalMersenneTwister"/> which is used as the default
## random source by those library
## methods for <Ref Oper="Random" Label="for a list or collection"/>
## that do not take a random source as an argument.
## <P/>
## <Ref Filt="IsGAPRandomSource"/> uses the same number generator as
## <Ref Filt="IsGlobalRandomSource"/>, but you can create several of these
## random sources which generate their random numbers independently of
## all other random sources.
## <P/>
## <Ref Filt="IsGlobalRandomSource"/> gives access to the <E>classical</E>
## global random generator which was used by &GAP; in former releases.
## You do not need to construct new random sources of this kind which would
## all use the same global data structure. Just use the existing random
## source <Ref Var="GlobalRandomSource"/>. This uses the additive random number
## generator described in <Cite Key="TACP2"/> (Algorithm A in 3.2.2
## with lag <M>30</M>).
## <P/>
## Other kinds of random sources are implemented by &GAP; packages.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareCategory("IsGlobalRandomSource", IsRandomSource);
DeclareCategory("IsGAPRandomSource", IsRandomSource);
DeclareCategory("IsMersenneTwister", IsRandomSource);
if IsHPCGAP then
MakeThreadLocal( "GlobalRandomSource" );
MakeThreadLocal( "GlobalMersenneTwister" );
else
DeclareGlobalName( "GlobalRandomSource" );
DeclareGlobalName( "GlobalMersenneTwister" );
fi;
#############################################################################
##
#O RandomSource( <cat>[, <seed>] )
##
## <#GAPDoc Label="RandomSource">
## <ManSection>
## <Oper Name="RandomSource" Arg='cat[, seed]'/>
##
## <Description>
## This operation is used to create new random sources. The first argument
## <A>cat</A> is the category describing the type of the random generator,
## for example one of the categories listed in
## Section <Ref Subsect="Kinds of Random Sources"/>.
## <P/>
## An optional <A>seed</A> can be given to specify the initial state.
## For details,
## see Section <Ref Subsect="State and Reset for Random Sources"/>.
## <P/>
## <Example><![CDATA[
## gap> rs1 := RandomSource(IsMersenneTwister);
## <RandomSource in IsMersenneTwister>
## gap> l1 := List([1..10000], i-> Random(rs1, [1..6]));;
## gap> state1 := State(rs1);;
## gap> rs2 := RandomSource(IsMersenneTwister);;
## gap> l2 := List([1..10000], i-> Random(rs2, [1..6]));;
## gap> l1 = l2;
## true
## gap> l3 := List([1..10000], i-> Random(rs1, [1..6]));;
## gap> l1 = l3;
## false
## gap> rs3 := RandomSource(IsMersenneTwister, state1);;
## gap> l4 := List([1..10000], i-> Random(rs3, [1..6]));;
## gap> l3 = l4;
## true
## gap> n := Random(rs1, 1, 2^220);
## 1077726777923092117987668044202944212469136000816111066409337432400
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareOperation( "RandomSource", [IsOperation] );
DeclareOperation( "RandomSource", [IsOperation, IsObject] );
##############################################################################
##
## <#GAPDoc Label="RandomSource_develop">
## <Subsection Label="Implementing new kinds of random sources">
## <Heading>Implementing new kinds of random sources</Heading>
##
## If one wants to implement a new kind of random sources then
## the first step is the declaration of a new category <C>C</C>, say,
## that implies <Ref Filt="IsRandomSource"/>, analogous to the categories
## listed in Section <Ref Subsect="Kinds of Random Sources"/>,
## as follows.
## <P/>
## <C>DeclareCategory( "C", IsRandomSource );</C>.
## <P/>
## Then the following method installations are needed.
## <P/>
## <Index Key="Init"><C>Init</C> (initialize a random source object)</Index>
## <C>InstallMethod( Init, [ C, IsObject ], function( prers, seed )
## ... end );</C>
## <P/>
## Here <C>prers</C> is an empty component object (which has already the
## filter <C>C</C>), and <C>seed</C> is an integer or a state value
## as returned by <Ref Oper="State"/> that describes the initial state of
## the random source.
## The function should fill in the actual data and then return the
## (now initialized) object <C>prers</C>.
## The default used for <C>seed</C> is the integer <C>1</C>.
## A given state value need not be copied by the function.
## <P/>
## <C>InstallMethod( Random, [ C, IsInt, IsInt ], function( rs, low, high )
## ... end );</C>
## <P/>
## Here <C>rs</C> is an already initialized random source object in the
## category <C>C</C>, and the function returns an integer between <C>low</C>
## and <C>high</C> (inclusive).
## It is not defined what happens when <C>low</C> is larger than <C>high</C>.
## <P/>
## <C>InstallMethod( State, [ C ], function( rs ) ... end );</C>
## <P/>
## If <C>rs</C> supports resetting then the function must return an object
## that describes the current state of <C>rs</C>.
## This object must be an independent copy, that is,
## calling <Ref Oper="Random" Label="for random source and list"/>
## for <C>rs</C> must not change the object that was returned by
## <Ref Oper="State"/>;
## otherwise <Ref Func="ReturnFail"/> should be installed.
## <P/>
## <C>InstallMethod( Reset, [ C, IsObject ], function( rs, seed )
## ... end );</C>
## <P/>
## If <C>rs</C> supports resetting then the function must reinitialize
## <C>rs</C> to the integer or <Ref Oper="State"/> value <C>seed</C>
## and must return the <Ref Oper="State"/> value of <C>rs</C> before these
## changes; if resetting is not supported then <Ref Func="ReturnNothing"/>
## should be installed.
## Reset need not copy a given state.
## Note that the generic unary <Ref Oper="Reset"/> method uses the default
## seed <C>1</C>.
## <P/>
## Examples of implementations as described here are given by the
## random sources with defining filter <Ref Filt="IsMersenneTwister"/>
## or <C>IsRealRandomSource</C>.
## (For the latter, see <Ref Meth="RandomSource" BookName="io"/>
## in the &GAP; package <Package>IO</Package>.)
## </Subsection>
## <#/GAPDoc>
##############################################################################
##
## <#GAPDoc Label="InstallMethodWithRandomSource">
## <ManSection>
## <Func Name="InstallMethodWithRandomSource"
## Arg="opr,info[,famp],args-filts[,val],method"/>
## <Func Name="InstallOtherMethodWithRandomSource"
## Arg="opr,info[,famp],args-filts[,val],method"/>
##
## <Description>
## These functions are designed to simplify adding new methods for
## <Ref Oper="Random" Label="for a list or collection"/>,
## <Ref Oper="PseudoRandom"/>,
## and <Ref Oper="Randomize" Label="for a vector object"/> to &GAP;
## which can be called both with, and without, a random source.
## <P/>
## They accept the same arguments as <Ref Func="InstallMethod"/> and
## <Ref Func="InstallOtherMethod"/>, with
## the extra requirement that the first member of <A>args-filts</A> must
## be <Ref Filt="IsRandomSource"/>, and the <A>info</A> argument
## is compulsory and must begin 'for a random source and'.
## <P/>
## This function then installs two methods: first it calls
## <Ref Func="InstallMethod"/> (or <Ref Func="InstallOtherMethod"/>)
## with unchanged arguments.
## Then it calls <Ref Func="InstallMethod"/>
## (or <Ref Func="InstallOtherMethod"/>) a second time to install
## another method which lacks the initial random source argument; this
## additional method simply invokes the original method, with
## <Ref Var="GlobalMersenneTwister"/> added as first argument.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareGlobalFunction("InstallMethodWithRandomSource");
DeclareGlobalFunction("InstallOtherMethodWithRandomSource");
