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Speed up AddToIgs and AddToIgsParallel #174

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80b43bc
Cache inverse powers in AddToIgs(Parallel)
stertooy Oct 22, 2026
b77a4ca
Use IgsNegativePower in more places
stertooy Oct 22, 2026
6fe05f3
Speed up AddToIgs and AddToIgsParallel
fingolfin Oct 22, 2026
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2 changes: 2 additions & 0 deletions CHANGES.md
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Expand Up @@ -48,6 +48,8 @@ This file describes changes in the GAP package 'polycyclic'.
- Allow a finite group fallback for `RepresentativeAction` and `IsConjugate` for
subgroups
- Optimise `NormalIntersection` and `EfaSeries`
- Speed up `AddToIgs` and `AddToIgsParallel`, in particular for many
generators and for large groups
- Avoid needlessly large powers when norming and sifting elements at a depth
of finite relative order; this also changes which power `NormedPcpElement`
returns
Expand Down
2 changes: 2 additions & 0 deletions gap/basic/collect.gd
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Expand Up @@ -128,3 +128,5 @@ BindGlobal( "PC_INVERSECOMMUTATORSINVERSE", 27 );
BindGlobal( "PC_NILPOTENT_COMMUTE", 28 );
BindGlobal( "PC_WEIGHTS", 29 );
BindGlobal( "PC_ABELIAN_START", 30 );

BindGlobal( "PC_COMMUTATOR_DEPTH_BOUNDS", 31 );
1 change: 1 addition & 0 deletions gap/basic/collect.gi
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Expand Up @@ -940,6 +940,7 @@ function( coll )
fi;

FromTheLeftCollector_SetCommute( coll );
Unbind( coll![PC_COMMUTATOR_DEPTH_BOUNDS] );

## We have to declare the collector up to date now because the following
## functions need to collect and are careful enough.
Expand Down
164 changes: 115 additions & 49 deletions gap/basic/pcppara.gi
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Expand Up @@ -73,13 +73,15 @@ end );

#############################################################################
##
#F ReduceExpoPara( ind, gen, indd, pgen, rel )
#F ReduceExpoPara( ind, gen, indd, pgen, rel, pows, ppows )
##
## Parallel version of ReduceExpo.
## Returns the positions changed in <gen>.
## Returns the positions changed in <ind> and in <gen>.
##
BindGlobal( "ReduceExpoPara", function ( ind, gen, indd, pgen, rel )
local i, j, a, b, q, cg;
BindGlobal( "ReduceExpoPara",
function ( ind, gen, indd, pgen, rel, pows, ppows )
local i, j, a, b, q, ci, cg;
ci := [];
cg := [];
for i in [ 1 .. Length( ind ) ] do
if not IsBool( ind[i] ) and rel[i] = 0 then
Expand All @@ -89,23 +91,47 @@ BindGlobal( "ReduceExpoPara", function ( ind, gen, indd, pgen, rel )
a := Exponents( ind[j] )[i];
q := QuoInt( a, b );
if q <> 0 then
ind[j] := ind[j] * ind[i] ^ (- q);
indd[j] := indd[j] * indd[i] ^ (- q);
ind[j] := ind[j] * IgsNegativePower(ind, pows, i, q);
indd[j] := indd[j] *
IgsNegativePower(indd, ppows, i, q);
AddSet( ci, j );
fi;
fi;
od;
for j in [ 1 .. Length( gen ) ] do
a := Exponents( gen[j] )[i];
q := QuoInt( a, b );
if q <> 0 then
gen[j] := gen[j] * ind[i] ^ (- q);
pgen[j] := pgen[j] * indd[i] ^ (- q);
gen[j] := gen[j] * IgsNegativePower(ind, pows, i, q);
pgen[j] := pgen[j] *
IgsNegativePower(indd, ppows, i, q);
AddSet( cg, j );
fi;
od;
fi;
od;
return cg;
return [ci, cg];
end );

#############################################################################
##
#F ReduceExpoElmPara( ind, g, indd, gg, rel, pows, ppows )
##
## Parallel version of ReduceExpoElm.
##
BindGlobal( "ReduceExpoElmPara",
function ( ind, g, indd, gg, rel, pows, ppows )
local i, q;
for i in [ Depth( g ) .. Length( ind ) ] do
if not IsBool( ind[i] ) and rel[i] = 0 then
q := QuoInt( Exponents( g )[i], LeadingExponent( ind[i] ) );
if q <> 0 then
g := g * IgsNegativePower(ind, pows, i, q);
gg := gg * IgsNegativePower(indd, ppows, i, q);
fi;
fi;
od;
return [ g, gg ];
end );

#############################################################################
Expand All @@ -114,11 +140,13 @@ end );
##
## This function adds the elements in <gens> to the induced pcs <pcs>.
## It acts simultaneously on <pcs> and <ppcs> as well as <gens> and <pgens>.
## See AddToIgs for the algorithm.
##
InstallGlobalFunction( AddToIgsParallel,
function( pcs, gens, ppcs, pgens )
local coll, rels, n, inf, todo, tododo, ind, indd, g, gg, d, h, hh, a, b,
q, k, c, i, r, sub, keep, val, j, f, nrmd, pairs, added, oldc, chg;
local coll, rels, n, inf, bnd, todo, tododo, ind, indd, pows, ppows, g,
gg, d, h, hh, a, b, q, k, c, i, r, sub, keep, idx, queue, pqueue,
qpos, val, j, f, nrmd, pairs, added, oldc, chg, t;

if Length( gens ) = 0 then return [pcs, ppcs]; fi;

Expand All @@ -127,39 +155,63 @@ function( pcs, gens, ppcs, pgens )
rels := RelativeOrders( coll );
n := NumberOfGenerators( coll );
inf := 0 in rels;
c := n+1;
bnd := fail;

# set up
# set up; pows[d] and ppows[d] cache negative powers of ind[d], indd[d]
ind := ListWithIdenticalEntries(n, false);
indd := ListWithIdenticalEntries(n, false);
for i in [1..Length(pcs)] do
d := Depth( pcs[i] );
ind[d] := pcs[i];
indd[d] := ppcs[i];
od;
pows := [];
ppows := [];
c := TailLimit(ind, n+1);

# initial gens still need to be reduced
added := true;

# do a reduction step
c := TailLimit(ind, c);
# gens wait in queue, keeping the first of equal elements and sorted by
# IGSValFun; todo holds powers and commutators
sub := Filtered([1..Length(gens)], i -> Depth(gens[i]) < c);
# Keep the first occurrence of each generator, in input order.
todo := gens{sub};
StableSortParallel(todo, sub);
keep := Filtered([1..Length(sub)], i -> i = 1 or todo[i] <> todo[i-1]);
queue := gens{sub};
StableSortParallel(queue, sub);
keep := Filtered([1..Length(sub)], i -> i = 1 or queue[i] <> queue[i-1]);
sub := Set(sub{keep});
todo := gens{sub};
tododo := pgens{sub};
val := List(todo, IGSValFun);

# loop over to-do list until it is empty
while Length( todo ) > 0 and c > 1 do
j := PositionMinimum(val);
g := Remove(todo, j);
gg := Remove(tododo, j);
Remove(val, j);
d := Depth( g );
queue := gens{sub};
pqueue := pgens{sub};
idx := [1..Length(sub)];
StableSortParallel(List(queue, IGSValFun), idx);
queue := queue{idx};
pqueue := pqueue{idx};
qpos := 1;
todo := [];
tododo := [];
val := [];
added := false;

while c > 1 do

# take the next element, from queue only once todo is empty
if Length( todo ) > 0 then
j := PositionMinimum(val);
g := Remove(todo, j);
gg := Remove(tododo, j);
Remove(val, j);
else
while qpos <= Length(queue) and Depth(queue[qpos]) >= c do
qpos := qpos+1;
od;
if qpos > Length(queue) then break; fi;
g := queue[qpos];
gg := pqueue[qpos];
qpos := qpos+1;
# sifting g unreduced can blow up its exponents
if inf then
pairs := ReduceExpoElmPara(ind, g, indd, gg, rels, pows, ppows);
g := pairs[1];
gg := pairs[2];
fi;
fi;
d := Depth( g );
f := [];

# shift g into ind
Expand All @@ -173,6 +225,8 @@ function( pcs, gens, ppcs, pgens )
nrmd := NormedPcpElementPara( g, gg );
ind[d] := nrmd[1];
indd[d] := nrmd[2];
Unbind(pows[d]);
Unbind(ppows[d]);
AddSet(f,d);
h := ind[d];
hh := indd[d];
Expand All @@ -186,8 +240,8 @@ function( pcs, gens, ppcs, pgens )
if a > 0 and b > 0 and a mod b = 0 then
# GcdPcpPara would leave h and hh unchanged.
q := SmallestResidue(a/b, rels[d]);
g := g * h^-q;
gg := gg * hh^-q;
g := g * IgsNegativePower(ind, pows, d, q);
gg := gg * IgsNegativePower(indd, ppows, d, q);
else
pairs := GcdPcpPara(g, h, gg, hh);
h := pairs[1];
Expand All @@ -198,6 +252,8 @@ function( pcs, gens, ppcs, pgens )
nrmd := NormedPcpElementPara( h, hh );
ind[d] := nrmd[1];
indd[d] := nrmd[2];
Unbind(pows[d]);
Unbind(ppows[d]);
AddSet(f, d);
fi;
fi;
Expand All @@ -213,12 +269,20 @@ function( pcs, gens, ppcs, pgens )
oldc := c;
c := TailLimit(ind, c);
chg := [];
if inf then chg := ReduceExpoPara(ind, todo, indd, tododo, rels); fi;
if inf then
t := ReduceExpoPara(ind, todo, indd, tododo, rels, pows, ppows);
for i in t[1] do
Unbind(pows[i]);
Unbind(ppows[i]);
od;
chg := t[2];
fi;
for i in chg do
if Depth(todo[i]) < c then val[i] := IGSValFun(todo[i]); fi;
od;

# add powers and commutators
# no need to clean up pows/ppows here
added := false;
for d in f do
g := ind[d];
Expand All @@ -234,26 +298,28 @@ function( pcs, gens, ppcs, pgens )
fi;
fi;
for j in [1..n] do
if j = d or Minimum( d, j ) >= c-1 then
# skip trivial commutators and those in the tail
if j = d or Minimum( d, j ) >= c-1 or IsBool(ind[j]) then
continue;
fi;
if not IsBool(ind[j]) then
k := Comm(g, ind[j]);
if bnd = fail then bnd := CommutatorDepthBounds(coll); fi;
if bnd[Minimum(d, j)][Maximum(d, j)] >= c then continue; fi;
k := Comm(g, ind[j]);
if Depth(k) < c then
Add(todo, k);
Add(tododo, Comm(gg, indd[j]));
Add(val, IGSValFun(k));
added := true;
fi;
if rels[j] = 0 then
k := Comm(g, IgsNegativePower(ind, pows, j, 1));
if Depth(k) < c then
Add(todo, k);
Add(tododo, Comm(gg, indd[j]));
Add(tododo, Comm(gg,
IgsNegativePower(indd, ppows, j, 1)));
Add(val, IGSValFun(k));
added := true;
fi;
if rels[j] = 0 then
k := Comm(g, ind[j]^-1);
if Depth(k) < c then
Add(todo, k);
Add(tododo, Comm(gg, indd[j]^-1));
Add(val, IGSValFun(k));
added := true;
fi;
fi;
fi;
od;
od;
Expand Down
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