<P/>
A hash function in <Package>datastructures</Package> is a
function <M>H</M> which maps a value <M>X</M> to a small integer (where
a small integer is an integer in the range <C>[-2^28..2^28-1]</C>
on a 32-bit system, and <C>[-2^60..2^60-1]</C> on a 64-bit system),
under the requirement that if <M>X=Y</M>, then <M>H(X)=H(Y)</M>.
<P/>
A variety of hash functions is provided by <Package>datastructures</Package>,
with different behaviours. A bad choice of hash function can lead to serious
performance problems.
<P/>
<Package>datastructures</Package> does not guarantee consistency of hash
values across release or &GAP; sessions.
</Section>
<Section Label="Chapter_Hash_Functions_Section_Hash_Functions_for_Basic_Types">
<Heading>Hash Functions for Basic Types</Heading>
<ManSection>
<Func Arg="obj..." Name="HashBasic" />
<Returns>a small integer
</Returns>
<Description>
Hashes any values built inductively from
<List>
<Item> built-in types, namely integers, booleans,
permutations, transformations, partial permutations, and</Item>
<Item> constructors for lists and records. </Item>
</List>
<P/>
This function is variadic, treating more than one argument
as equivalent to a list containing the arguments, that is
<C>HashBasic(x,y,z) = HashBasic([x,y,z])</C>.
</Description>
</ManSection>
</Section>
<Section Label="Chapter_Hash_Functions_Section_Hash_Functions_for_Permutation_Groups">
<Heading>Hash Functions for Permutation Groups</Heading>
<P/>
<Package>datastructures</Package> provides two hash functions for permutation groups;
<Ref Func="Hash_PermGroup_Fast"/> is the faster one, with higher likelihood of collisions
and <Ref Func="Hash_PermGroup_Complete"/> is slower but provides a lower
likelihood of collisions.
<ManSection>
<Func Arg="group" Name="Hash_PermGroup_Fast" />
<Returns>a small integer
</Returns>
<Description>
<Ref Func="Hash_PermGroup_Fast"/> is faster than <Ref Func="Hash_PermGroup_Complete"/>,
but will return the same value for groups with the same size, orbits and degree of
transitivity.
</Description>
</ManSection>
<ManSection>
<Func Arg="group" Name="Hash_PermGroup_Complete" />
<Returns>a small integer
</Returns>
<Description>
<Ref Func="Hash_PermGroup_Complete"/> is slower than <Ref Func="Hash_PermGroup_Fast"/>,
but is extremely unlikely to return the same hash for two different groups.
</Description>
</ManSection>
</Section>
</Chapter>
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