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| Current File : //usr/share/gap/lib/vec8bit.gi |
############################################################################
##
#W vec8bit.gi GAP Library Steve Linton
##
##
#Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file mainly installs the kernel methods for 8 bit vectors
##
#############################################################################
##
#V `TYPES_VEC8BIT . . . . . . . . prepared types for compressed GF(q) vectors
##
## A length 4 list of length 257 lists. TYPES_VEC8BIT[1][q] will be the type
## of mutable vectors over GF(q), TYPES_VEC8BIT[2][q] is the type of
## immutable vectors and TYPES_VEC8BIT[3][q] the type of locked vectors
## The 257th position is bound to 1 to stop the lists
## shrinking.
##
## It is accessed directly by the kernel, so the format cannot be changed
## without changing the kernel.
##
InstallValue(TYPES_VEC8BIT , [[],[], [], []]);
TYPES_VEC8BIT[1][257] := 1;
TYPES_VEC8BIT[2][257] := 1;
TYPES_VEC8BIT[3][257] := 1;
TYPES_VEC8BIT[4][257] := 1;
#############################################################################
##
#F TYPE_VEC8BIT( <q>, <mut> ) . . computes type of compressed GF(q) vectors
##
## Normally called by the kernel, caches results in TYPES_VEC8BIT,
## which is directly accessed by the kernel
##
InstallGlobalFunction(TYPE_VEC8BIT,
function( q, mut)
local col,filts;
if mut then col := 1; else col := 2; fi;
if not IsBound(TYPES_VEC8BIT[col][q]) then
filts := IsHomogeneousList and IsListDefault and IsCopyable and
Is8BitVectorRep and IsSmallList and
IsNoImmediateMethodsObject and
IsRingElementList and HasLength;
if mut then filts := filts and IsMutable; fi;
TYPES_VEC8BIT[col][q] := NewType(FamilyObj(GF(q)),filts);
fi;
return TYPES_VEC8BIT[col][q];
end);
InstallGlobalFunction(TYPE_VEC8BIT_LOCKED,
function( q, mut)
local col,filts;
if mut then col := 3; else col := 4; fi;
if not IsBound(TYPES_VEC8BIT[col][q]) then
filts := IsHomogeneousList and IsListDefault and IsCopyable and
Is8BitVectorRep and IsSmallList and
IsNoImmediateMethodsObject and
IsLockedRepresentationVector and
IsRingElementList and HasLength;
if mut then filts := filts and IsMutable; fi;
TYPES_VEC8BIT[col][q] := NewType(FamilyObj(GF(q)),filts);
fi;
return TYPES_VEC8BIT[col][q];
end);
#############################################################################
##
#V TYPE_FIELDINFO_8BIT type of the fieldinfo bags
##
## These bags are created by the kernel and accessed by the kernel. The type
## doesn't really say anything, because there are no applicable operations.
##
InstallValue( TYPE_FIELDINFO_8BIT, TYPE_KERNEL_OBJECT);
#############################################################################
##
#M Length( <vec> )
##
InstallOtherMethod( Length, "For a compressed VecFFE",
true, [IsList and Is8BitVectorRep], 0, LEN_VEC8BIT);
#############################################################################
##
#M <vec> [ <pos> ]
##
InstallOtherMethod( \[\], "For a compressed VecFFE",
true, [IsList and Is8BitVectorRep, IsPosInt], 0, ELM_VEC8BIT);
#############################################################################
##
#M <vec> [ <pos> ] := <val>
##
## This may involve turning <vec> into a plain list, if <val> does
## not lie in the appropriate field.
##
## <vec> may also be converted back into vector rep over a bigger field.
##
InstallOtherMethod( \[\]\:\=, "For a compressed VecFFE",
true, [IsMutable and IsList and Is8BitVectorRep, IsPosInt, IsObject],
0, ASS_VEC8BIT);
#############################################################################
##
#M Unbind( <vec> [ <pos> ] )
##
## Unless the last position is being unbound, this will result in <vec>
## turning into a plain list
##
InstallMethod( Unbind\[\], "For a compressed VecFFE",
true, [IsMutable and IsList and Is8BitVectorRep, IsPosInt],
0, UNB_VEC8BIT);
#############################################################################
##
#M ViewObj( <vec> )
##
## Up to length 10, GF(q) vectors are viewed in full, over that a
## description is printed
##
InstallMethod( ViewObj, "For a compressed VecFFE",
true, [Is8BitVectorRep and IsSmallList], 0,
function( vec )
local len;
len := LEN_VEC8BIT(vec);
if (len = 0 or len > 10) then
Print("< ");
if not IsMutable(vec) then
Print("im");
fi;
Print("mutable compressed vector length ",
LEN_VEC8BIT(vec)," over GF(",Q_VEC8BIT(vec),") >");
else
PrintObj(vec);
fi;
end);
#############################################################################
##
#M PrintObj( <vec> )
##
## Same method as for lists in internal rep.
##
InstallMethod( PrintObj, "For a compressed VecFFE",
true, [Is8BitVectorRep and IsSmallList], 0,
function( vec )
local i,l;
Print("\>\>[ \>\>");
l := Length(vec);
if l <> 0 then
PrintObj(vec[1]);
for i in [2..l] do
Print("\<,\<\>\> ");
PrintObj(vec[i]);
od;
fi;
Print(" \<\<\<\<]");
end);
#############################################################################
##
#M ShallowCopy(<vec>)
##
## kernel method produces a copy in the same representation
##
InstallMethod(ShallowCopy, "For a compressed VecFFE",
true, [Is8BitVectorRep and IsSmallList], 0,
SHALLOWCOPY_VEC8BIT);
#############################################################################
##
#M <vec1> + <vec2>
##
## The method installation enforced same
## characteristic. Compatability of fields and vector lengths is
## handled in the method
InstallMethod( \+, "For two 8 bit vectors in same characteristic",
IsIdenticalObj, [IsRowVector and Is8BitVectorRep,
IsRowVector and Is8BitVectorRep], 0,
SUM_VEC8BIT_VEC8BIT);
InstallMethod( \+, "For a GF2 vector and an 8 bit vector of char 2",
IsIdenticalObj, [IsRowVector and IsGF2VectorRep,
IsRowVector and Is8BitVectorRep], 0,
function(v,w)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v,GF(Q_VEC8BIT(w)));
return v+w;
fi;
end);
InstallMethod( \+, "For an 8 bit vector of char 2 and a GF2 vector",
IsIdenticalObj, [IsRowVector and Is8BitVectorRep,
IsRowVector and IsGF2VectorRep ], 0,
function(w,v)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v,GF(Q_VEC8BIT(w)));
return w+v;
fi;
end);
#############################################################################
##
#M `PlainListCopyOp( <vec> )
##
## Make the vector into a plain list (in place)
##
InstallMethod( PlainListCopyOp, "For an 8 bit vector",
true, [IsSmallList and Is8BitVectorRep], 0,
function (v)
PLAIN_VEC8BIT(v);
return v;
end);
#############################################################################
##
#M ELM0_LIST( <vec> )
##
## alternatibe element access interface, returns fail when unbound
##
InstallMethod(ELM0_LIST, "For an 8 bit vector",
true, [IsList and Is8BitVectorRep, IsPosInt], 0,
ELM0_VEC8BIT);
#############################################################################
##
#M DegreeFFE( <vector> )
##
BindGlobal("Q_TO_DEGREE", # discrete logarithm list
MakeImmutable(
[0,1,1,2,1,0,1,3,2,0,1,0,1,0,0,4,1,0,1,0,0,0,1,0,2,0,3,0,1,0,1,5,0,0,0,0,
1,0,0,0,1,0,1,0,0,0,1,0,2,0,0,0,1,0,0,0,0,0,1,0,1,0,0,6,0,0,1,0,0,0,1,0,
1,0,0,0,0,0,1,0,4,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,
1,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,3,0,1,7,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,
0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,0,2,0,0,0,1,0,0,0,0,0,1,0,
1,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,
0,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,5,0,0,0,0,0,0,0,1,0,
0,0,0,8] ) );
InstallOtherMethod( DegreeFFE, "for 8 bit vectors", true,
[ IsRowVector and IsFFECollection and Is8BitVectorRep], 0,
function( vec )
local q, deg, i, maxdeg;
q:=Q_VEC8BIT(vec);
maxdeg:=Q_TO_DEGREE[q];
# the degree could be smaller. Check or prove.
if Length(vec) = 0 then
return 0;
fi;
deg := DegreeFFE( vec[1] );
for i in [ 2 .. Length( vec ) ] do
deg := LcmInt( deg, DegreeFFE( vec[i] ) );
if deg=maxdeg then
return deg;
fi;
od;
return deg;
end );
#############################################################################
##
#M <vec>{<poss>}
##
## multi-element access
##
InstallOtherMethod(ELMS_LIST, "For an 8 bit vector and a plain list",
true, [IsList and Is8BitVectorRep,
IsPlistRep and IsDenseList ], 0,
ELMS_VEC8BIT);
InstallOtherMethod(ELMS_LIST, "For an 8 bit vector and a range",
true, [IsList and Is8BitVectorRep,
IsRange and IsInternalRep ], 0,
ELMS_VEC8BIT_RANGE);
#############################################################################
##
#M <vec>*<ffe>
##
InstallMethod(\*, "For an 8 bit vector and an FFE",
IsCollsElms, [IsRowVector and Is8BitVectorRep,
IsFFE and IsInternalRep], 0,
PROD_VEC8BIT_FFE);
#############################################################################
##
#M <vec>*<mat>
##
InstallMethod(\*, "For an 8 bit vector and a compatible matrix",
IsElmsColls, [IsRowVector and Is8BitVectorRep and IsSmallList
and IsRingElementList,
IsRingElementTable and IsPlistRep], 0,
PROD_VEC8BIT_MATRIX);
#############################################################################
##
#M \*( <ffe>, <gf2vec> ) . . . . . . . . . . . product of FFE and GF2 vector
##
## This is here to catch the case of an element in GF(2^k) 1 < k <= 8,
## in which case we can convert to an 8 bit vector. There is a
## higher-priority method in vecmat.gi which handles GF(2) elements.
##
InstallMethod( \*,
"for FFE and GF2 vector",
IsElmsColls,
[ IsFFE,
IsRingElementList and IsRowVector and IsGF2VectorRep ],
0,
function( a, b )
if DegreeFFE(a) > 8 or IsLockedRepresentationVector(b) then
TryNextMethod();
else
ConvertToVectorRepNC(b,Field(a));
return a*b;
fi;
end );
#############################################################################
##
#M <ffe>*<vec>
##
InstallMethod(\*, "For an FFE and an 8 bit vector ",
IsElmsColls, [IsFFE and IsInternalRep,
IsRowVector and Is8BitVectorRep],
0,
PROD_FFE_VEC8BIT);
#############################################################################
##
#M \*( <ffe>, <gf2vec> ) . . . . . . . . . . . product of FFE and GF2 vector
##
## This is here to catch the case of an element in GF(2^k) 1 < k <= 8,
## in which case we can convert to an 8 bit vector. There is a
## higher-priority method in vecmat.gi which handles GF(2) elements.
##
InstallMethod( \*,
"for FFE and GF2 vector",
IsElmsColls,
[ IsFFE,
IsRingElementList and IsRowVector and IsGF2VectorRep ],
0,
function( b, a )
if DegreeFFE(b) > 8 or IsLockedRepresentationVector(a) then
TryNextMethod();
else
ConvertToVectorRepNC(a,Field(b));
return b*a;
fi;
end );
#############################################################################
##
#M <vecl> - <vecr>
##
InstallMethod(\-, "For two 8bit vectors",
IsIdenticalObj, [IsRowVector and Is8BitVectorRep,
IsRowVector and Is8BitVectorRep],
0,
DIFF_VEC8BIT_VEC8BIT );
InstallMethod( \-, "For a GF2 vector and an 8 bit vector of char 2",
IsIdenticalObj, [IsRowVector and IsGF2VectorRep ,
IsRowVector and Is8BitVectorRep], 0,
function(v,w)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v,GF(Q_VEC8BIT(w)));
return v-w;
fi;
end);
InstallMethod( \-, "For an 8 bit vector of char 2 and a GF2 vector",
IsIdenticalObj, [IsRowVector and Is8BitVectorRep ,
IsRowVector and IsGF2VectorRep], 0,
function(w,v)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v,GF(Q_VEC8BIT(w)));
return w-v;
fi;
end);
#############################################################################
##
#M -<vec>
##
InstallMethod( AdditiveInverseOp, "For an 8 bit vector",
true, [IsRowVector and Is8BitVectorRep],
0,
AINV_VEC8BIT_MUTABLE);
#############################################################################
##
#M -<vec>
##
InstallMethod( AdditiveInverseSameMutability, "For an 8 bit vector",
true, [IsRowVector and Is8BitVectorRep],
0,
AINV_VEC8BIT_SAME_MUTABILITY );
#############################################################################
##
#M -<vec>
##
InstallMethod( AdditiveInverseImmutable, "For an 8 bit vector",
true, [IsRowVector and Is8BitVectorRep],
0,
AINV_VEC8BIT_IMMUTABLE );
#############################################################################
##
#M ZeroOp( <vec> )
##
## A mutable zero vector of the same field and length
##
InstallMethod( ZeroOp, "For an 8 bit vector",
true, [IsRowVector and Is8BitVectorRep],
0,
ZERO_VEC8BIT);
#############################################################################
##
#M ZEROOp( <vec> )
##
## A zero vector of the same field and length and mutability
##
InstallMethod( ZeroSameMutability, "For an 8 bit vector",
true, [IsRowVector and Is8BitVectorRep],
0,
function(v)
local z;
z := ZERO_VEC8BIT(v);
if not IsMutable(v) then
MakeImmutable(z);
fi;
return z;
end );
#############################################################################
##
#M <vec1> = <vec2>
##
InstallMethod( \=, "For 2 8 bit vectors",
IsIdenticalObj, [IsRowVector and Is8BitVectorRep,
IsRowVector and Is8BitVectorRep],
0,
EQ_VEC8BIT_VEC8BIT);
#############################################################################
##
#M <vec1> < <vec2>
##
## Usual lexicographic ordering
##
InstallMethod( \<, "For 2 8 bit vectors",
IsIdenticalObj, [IsRowVector and Is8BitVectorRep,
IsRowVector and Is8BitVectorRep],
0,
LT_VEC8BIT_VEC8BIT);
#############################################################################
##
#M <vec1>*<vec2>
##
## scalar product
#'
InstallMethod( \*, "For 2 8 bit vectors",
IsIdenticalObj, [IsRingElementList and Is8BitVectorRep,
IsRingElementList and Is8BitVectorRep],
0,
PROD_VEC8BIT_VEC8BIT);
InstallMethod( \*, "For a GF2 vector and an 8 bit vector of char 2",
IsIdenticalObj, [IsRowVector and IsGF2VectorRep,
IsRowVector and Is8BitVectorRep], 0,
function(v,w)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v,GF(Q_VEC8BIT(w)));
return v*w;
fi;
end);
InstallMethod( \*, "For an 8 bit vector of char 2 and a GF2 vector",
IsIdenticalObj, [IsRowVector and Is8BitVectorRep,
IsRowVector and IsGF2VectorRep ], 0,
function(w,v)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v,GF(Q_VEC8BIT(w)));
return w*v;
fi;
end);
#############################################################################
##
#M AddRowVector( <vec1>, <vec2>, <mult>, <from>, <to> )
##
## add <mult>*<vec2> to <vec1> in place
##
InstallOtherMethod( AddRowVector, "For 2 8 bit vectors and a field element and from and to",
IsCollsCollsElmsXX, [ IsRowVector and Is8BitVectorRep,
IsRowVector and Is8BitVectorRep,
IsFFE and IsInternalRep, IsPosInt, IsPosInt ], 0,
ADD_ROWVECTOR_VEC8BITS_5);
#############################################################################
##
#M AddRowVector( <vec1>, <vec2>, <mult> )
##
## add <mult>*<vec2> to <vec1> in place
##
InstallOtherMethod( AddRowVector, "For 2 8 bit vectors and a field element",
IsCollsCollsElms, [ IsRowVector and Is8BitVectorRep,
IsRowVector and Is8BitVectorRep,
IsFFE and IsInternalRep ], 0,
ADD_ROWVECTOR_VEC8BITS_3);
#############################################################################
##
#M AddRowVector( <vec1>, <vec2> )
##
## add <vec2> to <vec1> in place
##
InstallOtherMethod( AddRowVector, "For 2 8 bit vectors",
IsIdenticalObj, [ IsRowVector and Is8BitVectorRep,
IsRowVector and Is8BitVectorRep], 0,
ADD_ROWVECTOR_VEC8BITS_2);
#############################################################################
##
#M MultRowVector( <vec>, <ffe> )
##
## multiply <vec> by <ffe> in place
##
InstallOtherMethod( MultRowVector, "For an 8 bit vector and an ffe",
IsCollsElms, [ IsRowVector and Is8BitVectorRep,
IsFFE and IsInternalRep], 0,
MULT_ROWVECTOR_VEC8BITS);
#############################################################################
##
#M PositionNot( <vec>, <zero )
#M PositionNot( <vec>, <zero>, <from>)
#M PositionNonZero( <vec> )
#M PositionNonZero( <vec>, <from> )
##
##
InstallOtherMethod( PositionNot, "for 8-bit vector and 0*Z(p)",
IsCollsElms, [Is8BitVectorRep and IsRowVector , IsFFE and
IsZero], 0,
POSITION_NONZERO_VEC8BIT);
InstallOtherMethod( PositionNonZero, "for 8-bit vector",true,
[Is8BitVectorRep and IsRowVector],0,
# POSITION_NONZERO_VEC8BIT ignores the second argument
v->POSITION_NONZERO_VEC8BIT(v,0));
InstallOtherMethod( PositionNot, "for 8-bit vector and 0*Z(p) and starting ix",
IsCollsElmsX, [Is8BitVectorRep and IsRowVector , IsFFE and
IsZero, IsInt], 0,
POSITION_NONZERO_VEC8BIT3);
InstallOtherMethod( PositionNonZero, "for 8-bit vector and starting point",true,
[Is8BitVectorRep and IsRowVector, IsInt],0,
# POSITION_NONZERO_VEC8BIT3 ignores the second argument
function(v,from) return POSITION_NONZERO_VEC8BIT3(v,0,from); end);
#############################################################################
##
#M Append( <vecl>, <vecr> )
##
InstallMethod( Append, "for 8bitm vectors",
IsIdenticalObj, [Is8BitVectorRep and IsMutable and IsList,
Is8BitVectorRep and IsList], 0,
APPEND_VEC8BIT);
#############################################################################
##
#M NumberFFVector(<<vec>,<sz>)
##
InstallMethod(NumberFFVector,"8bit-vector",true,
[Is8BitVectorRep and IsRowVector and IsFFECollection,IsPosInt],0,
function(v,n)
if n<>Q_VEC8BIT(v) then TryNextMethod();fi;
return NUMBER_VEC8BIT(v);
end);
#############################################################################
##
#M IsSubset(<finfield>,<8bitvec>)
##
InstallMethod(IsSubset,"field, 8bit-vector",IsIdenticalObj,
[ IsField and IsFinite and IsFFECollection,
Is8BitVectorRep and IsRowVector and IsFFECollection],0,
function(F,v)
local q;
q:=Q_VEC8BIT(v);
if Size(F)=q then
return true;
fi;
# otherwise we must be a bit more clever
if 0 = DegreeOverPrimeField(F) mod LogInt(q,Characteristic(F)) then
return true; # degrees ovber prime field OK
fi;
TryNextMethod(); # the vector still might be written over a too-large
# field, so we can't say `no'.
end);
#############################################################################
##
#M DistanceVecFFE(<vecl>,<vecr>)
##
InstallMethod(DistanceVecFFE,"8bit-vector",true,
[Is8BitVectorRep and IsRowVector,
Is8BitVectorRep and IsRowVector],0,
DISTANCE_VEC8BIT_VEC8BIT);
#############################################################################
##
#M AddCoeffs( <vec1>, <vec2>, <mult> )
##
InstallOtherMethod( AddCoeffs, "two 8 bit vectors", IsCollsCollsElms,
[Is8BitVectorRep and IsRowVector,
Is8BitVectorRep and IsRowVector,
IsFFE], 0,
ADD_COEFFS_VEC8BIT_3);
InstallOtherMethod( AddCoeffs, "8 bit vector and GF2 vector", IsCollsCollsElms,
[Is8BitVectorRep and IsRowVector,
IsGF2VectorRep and IsRowVector,
IsFFE], 0,
function(v,w, x)
if IsLockedRepresentationVector(w) then
TryNextMethod();
else
ConvertToVectorRepNC(w, Q_VEC8BIT(v));
return ADD_COEFFS_VEC8BIT_3(v,w,x);
fi;
end);
InstallOtherMethod( AddCoeffs, "GF2 vector and 8 bit vector", IsCollsCollsElms,
[IsGF2VectorRep and IsRowVector,
Is8BitVectorRep and IsRowVector,
IsFFE], 0,
function(v,w, x)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v, Q_VEC8BIT(w));
return ADD_COEFFS_VEC8BIT_3(v,w,x);
fi;
end);
#############################################################################
##
#M AddCoeffs( <vec1>, <vec2> )
##
InstallOtherMethod( AddCoeffs, "two 8 bit vectors", IsIdenticalObj,
[Is8BitVectorRep and IsRowVector,
Is8BitVectorRep and IsRowVector], 0,
ADD_COEFFS_VEC8BIT_2);
InstallOtherMethod( AddCoeffs, "8 bit vector and GF2 vector", IsIdenticalObj,
[Is8BitVectorRep and IsRowVector,
IsGF2VectorRep and IsRowVector], 0,
function(v,w)
if IsLockedRepresentationVector(w) then
TryNextMethod();
else
ConvertToVectorRepNC(w, Q_VEC8BIT(v));
return ADD_COEFFS_VEC8BIT_2(v,w);
fi;
end);
InstallOtherMethod( AddCoeffs, "GF2 vector and 8 bit vector", IsIdenticalObj,
[IsGF2VectorRep and IsRowVector,
Is8BitVectorRep and IsRowVector], 0,
function(v,w)
if IsLockedRepresentationVector(v) then
TryNextMethod();
else
ConvertToVectorRepNC(v, Q_VEC8BIT(w));
return ADD_COEFFS_VEC8BIT_2(v,w);
fi;
end);
#############################################################################
##
#M LeftShiftRowVector( <vec>, <shift> )
##
InstallMethod( LeftShiftRowVector, "8bit vector", true,
[IsMutable and IsRowVector and Is8BitVectorRep,
IsPosInt], 0,
SHIFT_VEC8BIT_LEFT);
#############################################################################
##
#M RightShiftRowVector( <vec>, <shift>, <zero> )
##
InstallMethod( RightShiftRowVector, "8bit vector, fill with zeros", IsCollsXElms,
[IsMutable and IsRowVector and Is8BitVectorRep,
IsPosInt,
IsFFE and IsZero], 0,
SHIFT_VEC8BIT_RIGHT);
#############################################################################
##
#M PadCoeffs( <vec>, <len> )
##
InstallMethod( PadCoeffs, "8 bit vector", true,
[IsMutable and IsRowVector and Is8BitVectorRep and IsAdditiveElementWithZeroCollection, IsPosInt ],
0,
function(vec, len)
if len > LEN_VEC8BIT(vec) then
RESIZE_VEC8BIT(vec, len);
fi;
end);
#############################################################################
##
#M ShrinkRowVector( <vec> )
InstallMethod( ShrinkRowVector, "8 bit vector", true,
[IsMutable and IsRowVector and Is8BitVectorRep ],
0,
function(vec)
local r;
r := RIGHTMOST_NONZERO_VEC8BIT(vec);
RESIZE_VEC8BIT(vec, r);
end);
#############################################################################
##
#M RemoveOuterCoeffs( <vec>, <zero> )
##
InstallMethod( RemoveOuterCoeffs, "vec8bit and zero", IsCollsElms,
[ IsMutable and Is8BitVectorRep and IsRowVector, IsFFE and
IsZero], 0,
function (v,z)
local shift;
shift := POSITION_NONZERO_VEC8BIT(v,z) -1;
if shift <> 0 then
SHIFT_VEC8BIT_LEFT( v, shift);
fi;
if v <> [] then
RESIZE_VEC8BIT(v,RIGHTMOST_NONZERO_VEC8BIT(v));
fi;
return shift;
end);
#############################################################################
##
#M ProductCoeffs( <vec>, <len>, <vec>, <len>)
##
##
InstallMethod( ProductCoeffs, "8 bit vectors, kernel method", IsFamXFamY,
[Is8BitVectorRep and IsRowVector, IsInt, Is8BitVectorRep and
IsRowVector, IsInt ], 0,
PROD_COEFFS_VEC8BIT);
InstallOtherMethod( ProductCoeffs, "8 bit vectors, kernel method (2 arg)",
IsIdenticalObj,
[Is8BitVectorRep and IsRowVector, Is8BitVectorRep and
IsRowVector ], 0,
function(v,w)
return PROD_COEFFS_VEC8BIT(v, Length(v), w, Length(w));
end);
#############################################################################
##
#M ReduceCoeffs( <vec>, <len>, <vec>, <len>)
##
##
BindGlobal("ADJUST_FIELDS_VEC8BIT",
function(v,w)
local p,e;
if Q_VEC8BIT(v)<>Q_VEC8BIT(w) then
p:=Characteristic(v);
e:=Lcm(LogInt(Q_VEC8BIT(v),p),LogInt(Q_VEC8BIT(w),p));
if p^e > 256 or
p^e <> ConvertToVectorRepNC(v,p^e) or
p^e <> ConvertToVectorRepNC(w,p^e) then
return fail;
fi;
fi;
return true;
end);
InstallMethod( ReduceCoeffs, "8 bit vectors, kernel method", IsFamXFamY,
[Is8BitVectorRep and IsRowVector and IsMutable, IsInt, Is8BitVectorRep and
IsRowVector, IsInt ], 0,
function(vl, ll, vr, lr)
local res;
if ADJUST_FIELDS_VEC8BIT(vl, vr) = fail then
TryNextMethod();
fi;
res := REDUCE_COEFFS_VEC8BIT( vl, ll,
MAKE_SHIFTED_COEFFS_VEC8BIT(vr, lr));
if res = fail then
TryNextMethod();
else
return res;
fi;
end);
InstallOtherMethod( ReduceCoeffs, "8 bit vectors, kernel method (2 arg)",
IsIdenticalObj,
[Is8BitVectorRep and IsRowVector and IsMutable, Is8BitVectorRep and
IsRowVector ], 0,
function(v,w)
if ADJUST_FIELDS_VEC8BIT(v, w) = fail then
TryNextMethod();
fi;
return REDUCE_COEFFS_VEC8BIT(v, Length(v),
MAKE_SHIFTED_COEFFS_VEC8BIT(w, Length(w)));
end);
#############################################################################
##
#M QuotremCoeffs( <vec>, <len>, <vec>, <len>)
##
##
InstallMethod( QuotRemCoeffs, "8 bit vectors, kernel method", IsFamXFamY,
[Is8BitVectorRep and IsRowVector and IsMutable, IsInt, Is8BitVectorRep and
IsRowVector, IsInt ], 0,
function(vl, ll, vr, lr)
local res;
if ADJUST_FIELDS_VEC8BIT(vl, vr) = fail then
TryNextMethod();
fi;
res := QUOTREM_COEFFS_VEC8BIT( vl, ll,
MAKE_SHIFTED_COEFFS_VEC8BIT(vr, lr));
if res = fail then
TryNextMethod();
else
return res;
fi;
end);
InstallOtherMethod( QuotRemCoeffs, "8 bit vectors, kernel method (2 arg)",
IsIdenticalObj,
[Is8BitVectorRep and IsRowVector and IsMutable, Is8BitVectorRep and
IsRowVector ], 0,
function(v,w)
if ADJUST_FIELDS_VEC8BIT(v, w) = fail then
TryNextMethod();
fi;
return QUOTREM_COEFFS_VEC8BIT(v, Length(v),
MAKE_SHIFTED_COEFFS_VEC8BIT(w, Length(w)));
end);
#############################################################################
##
#M PowerModCoeffs( <vec1>, <len1>, <exp>, <vec2>, <len2> )
##
InstallMethod( PowerModCoeffs,
"for 8 bit vectors",
IsFamXYFamZ,
[ Is8BitVectorRep and IsRowVector, IsInt, IsPosInt,
Is8BitVectorRep and IsRowVector, IsInt ],
0,
function( v, lv, exp, w, lw)
local wshifted, pow, lpow, bits, i,p,e;
# ensure both vectors are in the same field
if ADJUST_FIELDS_VEC8BIT(v, w) = fail then
TryNextMethod();
fi;
if exp = 1 then
pow := ShallowCopy(v);
ReduceCoeffs(pow,lv,w,lw);
return pow;
fi;
wshifted := MAKE_SHIFTED_COEFFS_VEC8BIT(w, lw);
pow := v;
lpow := lv;
bits := [];
while exp > 0 do
Add(bits, exp mod 2);
exp := QuoInt(exp,2);
od;
bits := Reversed(bits);
for i in [2..Length(bits)] do
pow := PROD_COEFFS_VEC8BIT(pow,lpow, pow, lpow);
lpow := Length(pow);
lpow := REDUCE_COEFFS_VEC8BIT( pow, lpow, wshifted);
if lpow = 0 then
return pow;
fi;
if bits[i] = 1 then
pow := PROD_COEFFS_VEC8BIT(pow, lpow, v, lv);
lpow := Length(pow);
lpow := REDUCE_COEFFS_VEC8BIT( pow, lpow, wshifted);
if lpow = 0 then
return pow;
fi;
fi;
od;
return pow;
end);
#############################################################################
##
#M ZeroVector( len, <vector> )
##
InstallMethod( ZeroVector, "for an int and an 8bit vector",
[IsInt, Is8BitVectorRep],
function( len, v )
local w;
w := ZeroMutable(v);
RESIZE_VEC8BIT(w,len);
return w;
end );
InstallMethod( ZeroVector, "for an int and an 8bit matrix",
[IsInt, Is8BitMatrixRep],
function( len, m )
local w;
w := ZeroMutable(m[1]);
RESIZE_VEC8BIT(w,len);
return w;
end );
#############################################################################
##
## Stuff to adhere to new vector/matrix interface:
##
InstallMethod( BaseDomain, "for an 8bit vector",
[ Is8BitVectorRep ], function( v ) return GF(Q_VEC8BIT(v)); end );
InstallMethod( BaseDomain, "for an 8bit matrix",
[ Is8BitMatrixRep ], function( m ) return GF(Q_VEC8BIT(m[1])); end );
InstallMethod( NumberRows, "for an 8bit matrix",
[ Is8BitMatrixRep ], m -> m![1]);
# FIXME: this breaks down for matrices with 0 rows
InstallMethod( NumberColumns, "for an 8bit matrix",
[ Is8BitMatrixRep ], function( m ) return Length(m[1]); end );
# FIXME: this breaks down for matrices with 0 rows
InstallMethod( Vector, "for a plist of finite field elements and an 8bitvector",
[ IsList and IsFFECollection, Is8BitVectorRep ],
function( l, v )
local r;
r := ShallowCopy(l);
ConvertToVectorRep(r,Q_VEC8BIT(v));
return r;
end );
InstallMethod( Randomize, "for a mutable 8bit vector",
[ Is8BitVectorRep and IsMutable ],
function( v )
local f,i;
f := GF(Q_VEC8BIT(v));
for i in [1..Length(v)] do v[i] := Random(f); od;
return v;
end );
InstallMethod( Randomize, "for a mutable 8bit vector and a random source",
[ Is8BitVectorRep and IsMutable, IsRandomSource ],
function( v, rs )
local l,i;
l := AsSSortedList(GF(Q_VEC8BIT(v)));
for i in [1..Length(v)] do v[i] := Random(rs,l); od;
return v;
end );
InstallMethod( MutableCopyMat, "for an 8bit matrix",
[ Is8BitMatrixRep ],
function( m )
local mm;
mm := List(m,ShallowCopy);
ConvertToMatrixRep(mm,Q_VEC8BIT(m[1]));
return mm;
end );
InstallMethod( MatElm, "for an 8bit matrix and two integers",
[ Is8BitMatrixRep, IsPosInt, IsPosInt ],
MAT_ELM_MAT8BIT );
InstallMethod( SetMatElm, "for an 8bit matrix, two integers, and a ffe",
[ Is8BitMatrixRep, IsPosInt, IsPosInt, IsFFE ],
SET_MAT_ELM_MAT8BIT );
InstallMethod( Matrix, "for a list of vecs, an integer, and an 8bit mat",
[IsList, IsInt, Is8BitMatrixRep],
function(l,rl,m)
local q,i,li;
if not IsList(l[1]) then
li := [];
for i in [1..QuoInt(Length(l),rl)] do
li[i] := l{[(i-1)*rl+1..i*rl]};
od;
else
li:= ShallowCopy(l);
fi;
q := Q_VEC8BIT(m[1]);
# FIXME: Does not work for matrices m with no rows
ConvertToMatrixRep(li,q);
return li;
end );
InstallMethod( ExtractSubMatrix, "for an 8bit matrix, and two lists",
[Is8BitMatrixRep, IsList, IsList],
function( m, rows, cols )
local mm;
mm := m{rows}{cols};
ConvertToMatrixRep(mm,Q_VEC8BIT(m[1]));
# FIXME: this does not work for empty matrices
return mm;
end );
InstallMethod( CopySubVector, "for two 8bit vectors, and two lists",
[Is8BitVectorRep, Is8BitVectorRep and IsMutable, IsList, IsList],
function( v, w, f, t )
w{t} := v{f};
end );
InstallMethod( CopySubMatrix, "for two 8bit matrices, and four lists",
[Is8BitMatrixRep, Is8BitMatrixRep, IsList, IsList, IsList, IsList],
function( a, b, frows, trows, fcols, tcols )
b{trows}{tcols} := a{frows}{fcols};
end );
InstallMethod( Randomize, "for a mutable 8bit matrix",
[Is8BitMatrixRep and IsMutable],
function( m )
local v;
for v in m do Randomize(v); od;
return m;
end );
InstallMethod( Randomize, "for a mutable 8bit matrix, and a random source",
[Is8BitMatrixRep and IsMutable, IsRandomSource],
function( m, rs )
local v;
for v in m do Randomize(v,rs); od;
return m;
end );
InstallMethod( Unpack, "for an 8bit matrix",
[Is8BitMatrixRep],
function( m )
return List(m,AsPlist);
end );
InstallMethod( Unpack, "for an 8bit vector",
[Is8BitVectorRep],
function( v ) return AsPlist(v); end );
InstallOtherMethod( KroneckerProduct, "for two 8bit matrices", # priority to kernel code, if matrices have same field
[Is8BitMatrixRep and IsMatrix, Is8BitMatrixRep and IsMatrix], 1,
KRONECKERPRODUCT_MAT8BIT_MAT8BIT );
InstallOtherMethod( KroneckerProduct, "for two 8bit matrices",
[Is8BitMatrixRep and IsMatrix, Is8BitMatrixRep and IsMatrix],
function ( mat1, mat2 )
local i, row1, row2, row, kroneckerproduct;
kroneckerproduct := [ ];
for row1 in mat1 do
for row2 in mat2 do
row := [ ];
for i in row1 do
Append( row, i * row2 );
od;
ConvertToVectorRepNC( row );
Add( kroneckerproduct, row );
od;
od;
ConvertToMatrixRepNC(kroneckerproduct,Q_VEC8BIT(mat1[1]));
# FIXME: fails for empty matrices
return kroneckerproduct;
end );
InstallMethod( Fold, "for an 8bit vector, a positive int, and an 8bit matrix",
[ IsVectorObj and Is8BitVectorRep, IsPosInt, Is8BitMatrixRep ],
function( v, rl, t )
local rows,i,tt,m;
m := [];
tt := ZeroVector(rl,v);
for i in [1..Length(v)/rl] do
CopySubVector(v,tt,[(i-1)*rl+1..i*rl],[1..rl]);
Add(m,ShallowCopy(tt));
od;
ConvertToMatrixRep(m,Q_VEC8BIT(m[1]));
return m;
end );
InstallMethod( ConstructingFilter, "for an 8bit vector",
[ Is8BitVectorRep ], function(v) return Is8BitVectorRep; end );
InstallMethod( ConstructingFilter, "for an 8bit matrix",
[ Is8BitMatrixRep ], function(v) return Is8BitMatrixRep; end );
InstallMethod( BaseField, "for a compressed 8bit matrix",
[Is8BitMatrixRep], function(m) return DefaultFieldOfMatrix(m); end );
InstallMethod( BaseField, "for a compressed 8bit vector",
[Is8BitVectorRep], function(v) return GF(Q_VEC8BIT(v)); end );
InstallMethod( NewVector, "for Is8BitVectorRep, GF(q), and a list",
[ Is8BitVectorRep, IsField and IsFinite, IsList ],
function( filter, f, l )
local v;
v := ShallowCopy(l);
ConvertToVectorRep(v,Size(f));
return v;
end );
InstallMethod( NewZeroVector, "for Is8BitVectorRep, GF(q), and an int",
[ Is8BitVectorRep, IsField and IsFinite, IsInt ],
function( filter, f, i )
local v;
v := ListWithIdenticalEntries(i,Zero(f));
ConvertToVectorRep(v,Size(f));
return v;
end );
InstallMethod( ZeroMatrix, "for a compressed 8bit matrix",
[IsInt, IsInt, Is8BitMatrixRep],
function( rows, cols, m )
local l,i;
l := [];
for i in [1..rows] do
Add(l,ZeroVector(cols,m[1]));
od;
ConvertToMatrixRep(l);
return l;
end );
InstallMethod( NewMatrix, "for Is8BitMatrixRep, GF(q), an int, and a list",
[ Is8BitMatrixRep, IsField and IsFinite, IsInt, IsList ],
function( filter, f, rl, l )
local m;
m := List(l,ShallowCopy);
ConvertToMatrixRep(m,Size(f));
return m;
end );
InstallMethod( NewZeroMatrix, "for Is8BitMatrixRep, GF(q), and two ints",
[ Is8BitMatrixRep, IsField and IsFinite, IsInt, IsInt ],
function( filter, f, rows, cols )
local m,i;
m := 0*[1..rows];
m[1] := NewZeroVector(Is8BitVectorRep,f,cols);
for i in [2..rows] do
m[i] := ShallowCopy(m[1]);
od;
ConvertToMatrixRep(m,Size(f));
return m;
end );
InstallMethod( IdentityMatrix, "for a compressed 8bit matrix",
[IsInt, Is8BitMatrixRep],
function(rows,m)
local f,n;
f := BaseField(m);
n := IdentityMat(rows,f);
ConvertToMatrixRep(n,Size(f));
return n;
end );
InstallMethod( NewIdentityMatrix, "for Is8BitMatrixRep, GF(q), and an int",
[ Is8BitMatrixRep, IsField and IsFinite, IsInt ],
function( filter, f, rows )
local m,i,o;
m := 0*[1..rows];
o := One(f);
m[1] := NewZeroVector(Is8BitVectorRep,f,rows);
for i in [2..rows] do
m[i] := ShallowCopy(m[1]);
m[i][i] := o;
od;
m[1][1] := o;
ConvertToMatrixRep(m,Size(f));
return m;
end );
InstallMethod( ChangedBaseDomain, "for an 8bit vector and a finite field",
[ Is8BitVectorRep, IsField and IsFinite ],
function( v, f )
local w;
w := Unpack(v);
ConvertToVectorRep(w,Size(f));
return w;
end );
InstallMethod( ChangedBaseDomain, "for an 8bit matrix and a finite field",
[ Is8BitMatrixRep, IsField and IsFinite ],
function( v, f )
local w,i;
w := [];
for i in [1..Length(v)] do
Add(w,ChangedBaseDomain(v[i],f));
od;
ConvertToMatrixRep(w,Size(f));
return w;
end );
InstallMethod( CompatibleVector, "for an 8bit matrix",
[ Is8BitMatrixRep ],
function( m )
# This will break for a matrix with no rows
return ShallowCopy(m[1]);
end );
InstallMethod( WeightOfVector, "for an 8bit vector",
[ Is8BitVectorRep ],
function( v )
return WeightVecFFE(v);
end );
InstallMethod( DistanceOfVectors, "for two 8bit vectors",
[ Is8BitVectorRep, Is8BitVectorRep ],
function( v, w )
return DistanceVecFFE(v,w);
end );
InstallMethod( NewCompanionMatrix,
"for Is8BitMatrixRep, a polynomial and a ring",
[ Is8BitMatrixRep, IsUnivariatePolynomial, IsRing ],
function( ty, po, bd )
local i,l,ll,n,one;
one := One(bd);
l := CoefficientsOfUnivariatePolynomial(po);
n := Length(l)-1;
if not IsOne(l[n+1]) then
Error("CompanionMatrix: polynomial is not monic");
return fail;
fi;
l := -l{[1..n]};
ConvertToVectorRep(l,Size(bd));
ll := NewMatrix(ty,bd,n,[l]);
for i in [1..n-1] do
Add(ll,ZeroMutable(l),i);
ll[i][i+1] := one;
od;
return ll;
end );
#############################################################################
##
#E
##