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Speed up CoefficientsQadic for long results #4186

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Dec 2, 2020
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Speed up CoefficientsQadic for long results #4186

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36 changes: 29 additions & 7 deletions lib/integer.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -425,7 +425,7 @@ end);
InstallMethod( CoefficientsQadic, "for two integers",
true, [ IsInt, IsInt ], 0,
function( i, q )
local v;
local i1, res, l, qq, i2;
if q <= 1 then
Error("2nd argument of CoefficientsQadic should be greater than 1\n");
fi;
Expand All @@ -435,12 +435,34 @@ function( i, q )
TryNextMethod();
fi;
# represent the integer <i> as <q>-adic number
v := [];
while i > 0 do
Add( v, RemInt( i, q ) );
i := QuoInt( i, q );
od;
return v;
if i = 0 then
return [];
elif i < q then
return [i];
elif i < q^2 then
i1 := QuoInt(i, q);
return [i - i1*q, i1];
elif Log2Int(q)*100 > Log2Int(i) then
# straight forward loop for result length < 100
res := [];
while i > 0 do
i1 := QuoInt(i, q);
Add(res, i - i1*q);
i := i1;
od;
else
# divide and conquer method for large i
l := QuoInt(LogInt(i, q), 2)+1;
qq := q^l;
i2 := QuoInt(i,qq);
i1 := i - i2*qq;
res := CoefficientsQadic(i1, q);
while Length(res) < l do
Add(res, 0);
od;
Append(res, CoefficientsQadic(i2, q));
fi;
return res;
end);


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10 changes: 10 additions & 0 deletions tst/testinstall/integer.tst
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Original file line number Diff line number Diff line change
Expand Up @@ -178,5 +178,15 @@ Error, You cannot loop over the integer 5 did you mean the range [1..5]
gap> for x in 5 do od;
Error, You cannot loop over the integer 5 did you mean the range [1..5]

#
gap> CoefficientsQadic(0,3);
[ ]
gap> CoefficientsQadic(2,3);
[ 2 ]
gap> CoefficientsQadic(3^5*2^7,3);
[ 0, 0, 0, 0, 0, 2, 0, 2, 1, 1 ]
gap> CoefficientsQadic(3^5*2^7,2);
[ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1 ]

#
gap> STOP_TEST("integers.tst", 1);