Quelle collectors.cc Sprache: C

/****************************************************************************
**
** This file is part of GAP, a system for computational discrete algebra.
**
** 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 contains a single collector for finite polycyclic groups, as
** well as a combinatorial collector for finite p-groups.
**
** Unfortunately there are quite a lot of stacks required by the collectors.
** The collector functions will adjust the lists to have physical length
** equal to the maximum defined in 'maxStackSize'. Therefore it is
** possible to initialise all stacks with an empty list.
**
** There are also two temporary collector vectors 'cwVector' and
** 'cw2Vector', the functions 'CXBits_VectorWord' will adjust the string
** length to match the number of rws generators. Therefore it is possible
** to initialise these vectors with an empty string. WARNING: if you use
** such a vector, you *must* clear it afterwards, because all functions
** assume that the vectors are cleared.
*/

extern "C" {

#include "collectors.h"

#include "bool.h"
#include "error.h"
#include "gapstate.h"
#include "gvars.h"
#include "lists.h"
#include "modules.h"
#include "objccoll.h"
#include "objfgelm.h"
#include "plist.h"
#include "stringobj.h"

} // extern "C"

/****************************************************************************
**
*F * * * * * * * * * * * * * module specific state * * * * * * * * * * * * *
*/

struct CollectorsState_ {
 Obj SC_NW_STACK;
 Obj SC_LW_STACK;
 Obj SC_PW_STACK;
 Obj SC_EW_STACK;
 Obj SC_GE_STACK;
 Obj SC_CW_VECTOR;
 Obj SC_CW2_VECTOR;
 UInt SC_MAX_STACK_SIZE;
};

static ModuleStateOffset CollectorsStateOffset = -1;

extern inline struct CollectorsState_ * CollectorsState(void)
{
 return (struct CollectorsState_ *)StateSlotsAtOffset(CollectorsStateOffset);
}

/****************************************************************************
**
*F * * * * * * * * * * * * local defines and typedefs * * * * * * * * * * * *
*/

/****************************************************************************
**
** SC_PUSH_GEN( gen, exp )
** push a generator <gen> with exponent <exp> onto the stack.
**
** SC_PUSH_WORD( word, exp )
** push <word> with global exponent <exp> into the stack.
**
** SC_POP_WORD()
** remove topmost word from stack
*/
#define SC_PUSH_WORD( word, exp ) \
 if ( ++sp == max ) { \
 CollectorsState()->SC_MAX_STACK_SIZE *= 2; \
 return -1; \
 } \
 *++nw = DATA_WORD(word); \
 *++lw = *nw + NPAIRS_WORD(word) - 1; \
 *++pw = *nw; \
 *++ew = (**pw) & expm; \
 *++ge = exp

#define SC_PUSH_GEN( gen, exp ) \
 if ( ++sp == max ) { \
 CollectorsState()->SC_MAX_STACK_SIZE *= 2; \
 return -1; \
 } \
 *++nw = DATA_WORD(gen); \
 *++lw = *nw; \
 *++pw = *nw; \
 *++ew = exp; \
 *++ge = 1

#define SC_POP_WORD() \
 sp--; nw--; lw--; pw--; ew--; ge--

/****************************************************************************
**
*T FinPowConjCol
**
** 'FinPowConjCol' is a structure containing all the functions depending on
** the number of bits used in the a finite power/conjugate collector.
*/
typedef Int (*FuncIOOO) (Obj,Obj,Obj);
typedef Obj (*FuncOOOI) (Obj,Obj,Int);
typedef Int (*FuncIOOI) (Obj,Obj,Int);
typedef Obj (*FuncOOOO) (Obj,Obj,Obj);
typedef Int (*FuncIOOOF) (Obj,Obj,Obj,FuncIOOO);

typedef struct {

 FuncOOOI wordVectorAndClear;
 FuncIOOI vectorWord;
 FuncIOOO collectWord;
 FuncIOOOF solution;

} FinPowConjCol;

/****************************************************************************
**
*F * * * * * * * * * * * internal collector functions * * * * * * * * * * * *
*/

/****************************************************************************
**
*F WordVectorAndClear( <type>, <vv>, <num> )
*/
template <typename UIntN>
static Obj WordVectorAndClear(Obj type, Obj vv, Int num)
{
 Int ebits; // number of bits in the exponent
 UInt expm; // unsigned exponent mask
 Int i; // loop variable for gen/exp pairs
 Int j; // loop variable for exponent vector
 Int * qtr; // pointer into the collect vector
 UIntN * ptr; // pointer into the data area of <obj>
 Obj obj; // result

 // get the number of bits for exponents
 ebits = EBITS_WORDTYPE(type);

 // get the exponent mask
 expm = ((UInt)1 << ebits) - 1;

 // construct a new object
 obj = NewWord(type, num);

 // clear <vv>
 ptr = DATA_WORD(obj);
 qtr = (Int*)(ADDR_OBJ(vv)+1);
 for ( i = 1, j = 0; i <= num; i++, qtr++ ) {
 if ( *qtr != 0 ) {
 *ptr++ = ((i-1) << ebits) | (*qtr & expm);
 *qtr = 0;
 j++;
 }
 }

 // correct the size of <obj>
 ResizeBag( obj, 2*sizeof(Obj) + j * BITS_WORD(obj)/8 );
 ADDR_OBJ(obj)[1] = INTOBJ_INT(j);

 return obj;
}

/****************************************************************************
**
*F VectorWord( <vv>, <v>, <num> )
**
** WARNING: This function assumes that <vv> is cleared!
*/
template <typename UIntN>
static Int VectorWord(Obj vv, Obj v, Int num)
{
 Int ebits; // number of bits in the exponent
 UInt expm; // unsigned exponent mask
 UInt exps; // sign exponent mask
 Int i; // loop variable for gen/exp pairs
 Int pos; // generator number
 Int * qtr; // pointer into the collect vector
 const UIntN * ptr; // pointer into the data area of <obj>

 // <vv> must be a string
 RequireStringRep("VectorWord", vv);
 RequireMutable("VectorWord", vv, "string");

 // fix the length
 if ( SIZE_OBJ(vv) != num*sizeof(Int)+sizeof(Obj)+1 ) {
 ResizeBag( vv, num*sizeof(Int)+sizeof(Obj)+1 );
 memset(ADDR_OBJ(vv) + 1, 0, sizeof(Int) * num);
 }

 // if <v> is zero, return
 if ( v == 0 )
 return 0;

 // get the number of bits for exponents
 ebits = EBITS_WORD(v);

 // get the exponent masks
 exps = (UInt)1 << (ebits-1);
 expm = exps - 1;

 // unfold <v> into <vv>
 ptr = CONST_DATA_WORD(v);
 qtr = (Int*)ADDR_OBJ(vv);
 for ( i = NPAIRS_WORD(v); 0 < i; i--, ptr++ ) {
 pos = ((*ptr) >> ebits)+1;
 if ( pos > num ) {
 ErrorQuit("word contains illegal generators %d", (Int)i, 0);
 return 0;
 }
 if ( (*ptr) & exps )
 qtr[pos] = ((*ptr)&expm)-exps;
 else
 qtr[pos] = (*ptr)&expm;
 }
 return 0;
}

/****************************************************************************
**
** The following functions are used to add a word into the exponent vector
** without collection. Two different cases occur:
**
** Add a word into the exponent vector. Here we can use the global
** exponent.
**
** Add part of a word into the exponent vector. Here we cannot use the
** global exponent because the beginning of the word might not commute with
** the rest.
**/
template <typename UIntN>
static Int SAddWordIntoExpVec(Int * v,
 const UIntN * w,
 const UIntN * wend,
 Int e,
 Int ebits,
 UInt expm,
 const Obj * ro,
 const Obj * pow,
 Int lpow)
{
 Int i;
 Int ex;
 Int start = 0;

 for( ; w <= wend; w++ ) {
 i = ((*w) >> ebits) + 1;
 v[ i ] += ((*w) & expm) * e; // overflow check necessary?
 if ( INT_INTOBJ(ro[i]) <= v[i] ) {
 ex = v[i] / INT_INTOBJ(ro[i]);
 v[i] -= ex * INT_INTOBJ(ro[i]);
 if ( i <= lpow && pow[i] && 0 < NPAIRS_WORD(pow[i]) ) {
 const UIntN * sub = CONST_DATA_WORD(pow[i]);
 const UIntN * subend = sub + NPAIRS_WORD(pow[i]) - 1;
 start = SAddWordIntoExpVec(
 v, sub, subend, ex,
 ebits, expm, ro, pow, lpow );
 }
 }
 if( start 
static Int SAddPartIntoExpVec(Int * v,
 const UIntN * w,
 const UIntN * wend,
 Int ebits,
 UInt expm,
 const Obj * ro,
 const Obj * pow,
 Int lpow)
{

 Int i;
 Int ex;
 Int start = 0;

 for( ; w <= wend; w++ ) {
 i = ((*w) >> ebits) + 1;
 v[ i ] += ((*w) & expm); // overflow check necessary?
 if ( INT_INTOBJ(ro[i]) <= v[i] ) {
 ex = v[i] / INT_INTOBJ(ro[i]);
 v[i] -= ex * INT_INTOBJ(ro[i]);
 if ( i <= lpow && pow[i] && 0 < NPAIRS_WORD(pow[i]) ) {
 const UIntN * sub = CONST_DATA_WORD(pow[i]);
 const UIntN * subend = sub + NPAIRS_WORD(pow[i]) - 1;
 start = SAddWordIntoExpVec(
 v, sub, subend, ex,
 ebits, expm, ro, pow, lpow );
 }
 }
 if( start , <vv>, <w> )
**
** If a stack overflow occurs, we simply stop and return false.
*/
template <typename UIntN>
static Int SingleCollectWord(Obj sc, Obj vv, Obj w)
{
 Int ebits; // number of bits in the exponent
 UInt expm; // unsigned exponent mask
 UInt exps; // sign exponent mask

 Obj vnw; // word stack
 UIntN ** nw; // address of <vnw>
 Obj vlw; // last syllable stack
 UIntN ** lw; // address of <vlw>
 Obj vpw; // current syllable stack
 UIntN ** pw; // address of <vpw>
 Obj vew; // unprocessed exponent stack
 UIntN * ew; // address of <vew>
 Obj vge; // global exponent stack
 Int * ge; // address of <vge>

 Obj vpow; // rhs of power relations
 Int lpow; // length of <vpow>
 const Obj * pow; // address of <vpow>

 Obj vcnj; // rhs of conjugate relations
 Int lcnj; // length of <vcnj>
 const Obj * cnj; // address of <vcnj>

 const Obj * avc; // address of the avector
 const Obj * gns; // address of the list of generators
 const Obj * ro; // address of the list of relative orders
 const Obj * inv; // address of the list of inverses

 Int * v; // address of <vv>

 Int max; // maximal stack size
 Int sp; // stack pointer
 Int i, j; // loop variable
 Int gn; // current generator number
 Int ex; // current exponent
 Int start; // last non-trivial entry

 Obj tmp; // temporary obj for power

 Int resized = 0;// indicates whether a Resize() happened

 // <start> is the first non-trivial entry in <v>
 start = SC_NUMBER_RWS_GENERATORS(sc);

 // if <w> is the identity return now
 if ( NPAIRS_WORD(w) == 0 ) {
 return start;
 }

 // get the number of bits for exponents
 ebits = EBITS_WORDTYPE( SC_DEFAULT_TYPE(sc) );

 // get the exponent mask
 expm = ((UInt)1 << ebits) - 1;

 // get the exponent sign masks
 exps = (UInt)1 << (ebits-1);

 // <nw> contains the stack of words to insert
 vnw = CollectorsState()->SC_NW_STACK;

 // <lw> contains the word end of the word in <nw>
 vlw = CollectorsState()->SC_LW_STACK;

 // <pw> contains the position of the word in <nw> to look at
 vpw = CollectorsState()->SC_PW_STACK;

 // <ew> contains the unprocessed exponents at position <pw>
 vew = CollectorsState()->SC_EW_STACK;

 // <ge> contains the global exponent of the word
 vge = CollectorsState()->SC_GE_STACK;

 // get the maximal stack size
 max = CollectorsState()->SC_MAX_STACK_SIZE;

 // ensure that the stacks are large enough
 const UInt desiredStackSize = sizeof(Obj) * (max + 2);
 if ( SIZE_OBJ(vnw) < desiredStackSize ) {
 ResizeBag( vnw, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vlw) < desiredStackSize ) {
 ResizeBag( vlw, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vpw) < desiredStackSize ) {
 ResizeBag( vpw, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vew) < desiredStackSize ) {
 ResizeBag( vew, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vge) < desiredStackSize ) {
 ResizeBag( vge, desiredStackSize );
 resized = 1;
 }
 if( resized ) return -1;

 // from now on we use addresses instead of handles most of the time
 v = (Int*)ADDR_OBJ(vv);
 nw = (UIntN**)(ADDR_OBJ(vnw)+1);
 lw = (UIntN**)(ADDR_OBJ(vlw)+1);
 pw = (UIntN**)(ADDR_OBJ(vpw)+1);
 ew = (UIntN*)(ADDR_OBJ(vew)+1);
 ge = (Int*)(ADDR_OBJ(vge)+1);

 // conjugates, powers, order, generators, avector, inverses
 vpow = SC_POWERS(sc);
 lpow = LEN_PLIST(vpow);
 pow = CONST_ADDR_OBJ(vpow);

 vcnj = SC_CONJUGATES(sc);
 lcnj = LEN_PLIST(vcnj);
 (void) lcnj; // please compiler -- lcnj not actually used
 cnj = CONST_ADDR_OBJ(vcnj);

 avc = CONST_ADDR_OBJ( SC_AVECTOR(sc) );
 gns = CONST_ADDR_OBJ( SC_RWS_GENERATORS(sc) );

 ro = CONST_ADDR_OBJ( SC_RELATIVE_ORDERS(sc) );
 inv = CONST_ADDR_OBJ( SC_INVERSES(sc) );

 // initialize the stack with <w>
 sp = 0;
 SC_PUSH_WORD( w, 1 );

 // run until the stack is empty
 while ( 0 < sp ) {

 // if <ew> is negative use inverse
 if ( *ew & exps ) {
 gn = ((**pw) >> ebits) + 1;
 ex = ( *ew & (exps-1) ) - exps;
 *ew = 0;
 SC_PUSH_WORD( inv[gn], -ex );
 }

 // if <ew> is zero get next syllable
 else if ( 0 == *ew ) {

 // if <pw> has reached <lw> get next & reduce globale exponent
 if ( *pw == *lw ) {

 // if the globale exponent is greater one reduce it
 if ( 1 < *ge ) {
 (*ge)--;
 *pw = *nw;
 *ew = (**pw) & expm;
 }

 // otherwise get the next word from the stack
 else {
 SC_POP_WORD();
 }
 }

 // otherwise set <ew> to exponent of next syllable
 else {
 (*pw)++;
 *ew = (**pw) & expm;
 }
 }

 // now move the next generator to the correct position
 else {

 // get generator number
 gn = ((**pw) >> ebits) + 1;

 // we can move <gn> directly to the correct position
 if ( INT_INTOBJ(avc[gn]) == gn ) {
 /*
 *T This if-statement implies that the next two cases are never
 *T executed. This is intended for the time being because we
 *T need the single collector to work with pc-presentations
 *T whose rhs are not reduced while the next two if-case need
 *T reduced rhs. This will be fixed at a later stage.
 */
 v[gn] += *ew;
 *ew = 0;
 if ( start <= gn )
 start = gn;
 }

 // collect a whole word exponent pair
 else if( *pw == *nw && INT_INTOBJ(avc[gn]) == gn ) {
 gn = SAddWordIntoExpVec(
 v, *nw, *lw, *ge, ebits, expm, ro, pow, lpow );
 *pw = *lw;
 *ew = *ge = 0;

 if( start <= gn ) start = gn;
 continue;
 }

 // move the rest of a word directly into the correct positions
 else if( INT_INTOBJ(avc[gn]) == gn ) {
 gn = SAddPartIntoExpVec(
 v, *pw, *lw, ebits, expm, ro, pow, lpow );
 *pw = *lw;
 *ew = 0;

 if( start <= gn ) start = gn;
 continue;
 }

 // we have to move <gn> step by step
 else {
 (*ew)--; v[gn]++;

 i = INT_INTOBJ(avc[gn]);
 if ( start < i )
 i = start;

 /* Find the first position in v from where on ordinary
 collection has to be applied. */
 for( ; gn < i; i-- )
 if( v[i] && gn <= LEN_PLIST(cnj[i]) ) {
 tmp = ELM_PLIST( cnj[i], gn );
 if ( tmp != 0 && 0 < NPAIRS_WORD(tmp) )
 break;
 }

 /* Stack up this part of v if we run through the next
 for-loop or if a power relation will be applied */
 if( gn < i || (INT_INTOBJ(ro[gn]) <= v[gn] &&
 gn <= lpow && pow[gn] && 0 < NPAIRS_WORD(pow[gn])) ) {
 j = INT_INTOBJ(avc[gn]);
 for( ; i < j; j-- )
 if( v[j] ) {
 SC_PUSH_WORD( gns[j], v[j] );
 v[j] = 0;
 }
 }

 if( gn < i ) {
 for ( ; gn < i; i-- ) {
 if ( v[i] ) {
 if ( LEN_PLIST(cnj[i]) < gn )
 tmp = gns[i];
 else {
 tmp = ELM_PLIST( cnj[i], gn );
 if ( tmp == 0 || NPAIRS_WORD(tmp) == 0 )
 tmp = gns[i];
 }
 SC_PUSH_WORD( tmp, v[i] );
 v[i] = 0;
 }
 }
 if ( start <= INT_INTOBJ(avc[gn]) )
 start = gn;
 }
 if( start <= gn ) start = gn;
 }

 // check that the exponent is not too big
 if ( INT_INTOBJ(ro[gn]) <= v[gn] ) {
 i = v[gn] / INT_INTOBJ(ro[gn]);
 v[gn] -= i * INT_INTOBJ(ro[gn]);
 if ( gn <= lpow && pow[gn] && 0 < NPAIRS_WORD(pow[gn]) ) {
 SC_PUSH_WORD( pow[gn], i );
 }
 }
 }
 }
 return start;
}

/****************************************************************************
**
*F Solution( <sc>, <ww>, <uu>, <func> )
*/
template <typename UIntN>
static Int Solution(Obj sc, Obj ww, Obj uu, FuncIOOO func)
{
 Int ebits; // number of bits in the exponent
 UInt expm; // unsigned exponent mask
 Int num; // number of gen/exp pairs in <data>
 Int i; // loop variable for gen/exp pairs
 Int ro; // relative order
 Obj rod; // relative orders
 Obj g; // one generator word
 UIntN * gtr; // pointer into the data area of <g>
 Int * ptr; // pointer into the collect vector
 Int * qtr; // pointer into the collect vector

 // get the number of generators
 num = SC_NUMBER_RWS_GENERATORS(sc);
 rod = SC_RELATIVE_ORDERS(sc);

 // <ww> must be a string
 RequireStringRep("Solution", ww);
 RequireMutable("Solution", ww, "string");

 // <uu> must be a string
 RequireStringRep("Solution", uu);
 RequireMutable("Solution", uu, "string");

 // fix the length
 if ( SIZE_OBJ(ww) != num*sizeof(Int)+sizeof(Obj)+1 ) {
 i = (SIZE_OBJ(ww)-sizeof(Obj)-1) / sizeof(Int);
 ResizeBag( ww, num*sizeof(Int)+sizeof(Obj)+1 );
 qtr = (Int*)(ADDR_OBJ(ww)+1);
 for ( i = i+1; i < num; i++ )
 qtr[i] = 0;
 }

 // fix the length
 if ( SIZE_OBJ(uu) != num*sizeof(Int)+sizeof(Obj)+1 ) {
 i = (SIZE_OBJ(uu)-sizeof(Obj)-1) / sizeof(Int);
 ResizeBag( uu, num*sizeof(Int)+sizeof(Obj)+1 );
 qtr = (Int*)(ADDR_OBJ(uu)+1);
 for ( i = i+1; i < num; i++ )
 qtr[i] = 0;
 }

 // get the number of bits for exponents
 ebits = EBITS_WORDTYPE( SC_DEFAULT_TYPE(sc) );

 // get the exponent mask
 expm = ((UInt)1 << ebits) - 1;

 // use <g> as right argument for the collector
 g = NewWord(SC_DEFAULT_TYPE(sc), 1);

 // start clearing <ww>, storing the result in <uu>
 ptr = (Int*)(ADDR_OBJ(ww)+1);
 qtr = (Int*)(ADDR_OBJ(uu)+1);
 gtr = DATA_WORD(g);
 for ( i = 0; i < num; i++, ptr++, qtr++ ) {
 ro = INT_INTOBJ(ELMW_LIST(rod,i+1));
 *qtr = ( *qtr - *ptr ) % ro;
 if ( *qtr < 0 ) *qtr += ro;
 if ( *qtr != 0 ) {
 *gtr = ( i << ebits ) | ( *qtr & expm );
 if ( func(sc,ww,g) == -1 )
 return -1;
 }
 *ptr = 0;
 }
 return 0;
}

/****************************************************************************
**
*V C8Bits_SingleCollector
*/
static FinPowConjCol C8Bits_SingleCollector = {
 WordVectorAndClear<UInt1>,
 VectorWord<UInt1>,
 SingleCollectWord<UInt1>,
 Solution<UInt1>,
};

/****************************************************************************
**
*V C16Bits_SingleCollector
*/
static FinPowConjCol C16Bits_SingleCollector = {
 WordVectorAndClear<UInt2>,
 VectorWord<UInt2>,
 SingleCollectWord<UInt2>,
 Solution<UInt2>,
};

/****************************************************************************
**
*V C32Bits_SingleCollector
*/
static FinPowConjCol C32Bits_SingleCollector = {
 WordVectorAndClear<UInt4>,
 VectorWord<UInt4>,
 SingleCollectWord<UInt4>,
 Solution<UInt4>,
};

/****************************************************************************
**
*F * * * * * * * * * * * combinatorial collectors * * * * * * * * * * * * *
**
** Here the combinatorial collectors are set up. They behave like single
** collectors and therefore can be used in the same way.
*/

/****************************************************************************
**
** The following functions are used to add a word into the exponent vector
** without collection. There are three different cases that can occur:
**
** Add a word into the exponent vector. Here we can use the global
** exponent.
**
** Add a commutator into the exponent vector. In this case the first
** generator in the conjugate has to be skipped. Here we can use the global
** exponent.
**
** Add part of a word into the exponent vector. Here we cannot use the
** global exponent because the beginning of the word might not commute with
** the rest.
**/
template <typename UIntN>
static void AddWordIntoExpVec(Int * v,
 const UIntN * w,
 const UIntN * wend,
 Int e,
 Int ebits,
 UInt expm,
 Int p,
 const Obj * pow,
 Int lpow)
{
 Int i;
 Int ex;

 for( ; w <= wend; w++ ) {
 i = ((*w) >> ebits) + 1;
 v[ i ] += ((*w) & expm) * e; // overflow check necessary?
 if ( p <= v[i] ) {
 ex = v[i] / p;
 v[i] -= ex * p;
 if ( i <= lpow && pow[i] && 0 < NPAIRS_WORD(pow[i]) ) {
 const UIntN * sub = CONST_DATA_WORD(pow[i]);
 const UIntN * subend = sub + NPAIRS_WORD(pow[i]) - 1;
 AddWordIntoExpVec(
 v, sub, subend, ex,
 ebits, expm, p, pow, lpow );
 }
 }
 }
}

template <typename UIntN>
static void AddCommIntoExpVec(Int * v,
 Obj word,
 Int e,
 Int ebits,
 UInt expm,
 Int p,
 const Obj * pow,
 Int lpow)
{
 const UIntN * w = CONST_DATA_WORD(word);
 const UIntN * wend = w + NPAIRS_WORD(word) - 1;
 Int i;
 Int ex;

 // Skip the first generator because we need the commutator here.
 w++;
 for( ; w <= wend; w++ ) {
 i = ((*w) >> ebits) + 1;
 v[ i ] += ((*w) & expm) * e; // overflow check necessary?
 if ( p <= v[i] ) {
 ex = v[i] / p;
 v[i] -= ex * p;
 if ( i <= lpow && pow[i] && 0 < NPAIRS_WORD(pow[i]) ) {
 const UIntN * sub = CONST_DATA_WORD(pow[i]);
 const UIntN * subend = sub + NPAIRS_WORD(pow[i]) - 1;
 AddWordIntoExpVec(
 v, sub, subend, ex,
 ebits, expm, p, pow, lpow );
 }
 }
 }
}

template <typename UIntN>
static void AddPartIntoExpVec(Int * v,
 const UIntN * w,
 const UIntN * wend,
 Int ebits,
 UInt expm,
 Int p,
 const Obj * pow,
 Int lpow)
{

 Int i;
 Int ex;

 for( ; w <= wend; w++ ) {
 i = ((*w) >> ebits) + 1;
 v[ i ] += ((*w) & expm); // overflow check necessary?
 if ( p <= v[i] ) {
 ex = v[i] / p;
 v[i] -= ex * p;
 if ( i <= lpow && pow[i] && 0 < NPAIRS_WORD(pow[i]) ) {
 const UIntN * sub = CONST_DATA_WORD(pow[i]);
 const UIntN * subend = sub + NPAIRS_WORD(pow[i]) - 1;
 AddWordIntoExpVec(
 v, sub, subend, ex,
 ebits, expm, p, pow, lpow );
 }
 }
 }
}

/****************************************************************************
**
*F CombiCollectWord( <sc>, <vv>, <w> )
**
** If a stack overflow occurs, we simply stop and return false.
*/
template <typename UIntN>
static Int CombiCollectWord(Obj sc, Obj vv, Obj w)
{
 Int ebits; // number of bits in the exponent
 UInt expm; // unsigned exponent mask
 UInt exps; // sign exponent mask

 Obj vnw; // word stack
 UIntN ** nw; // address of <vnw>
 Obj vlw; // last syllable stack
 UIntN ** lw; // address of <vlw>
 Obj vpw; // current syllable stack
 UIntN ** pw; // address of <vpw>
 Obj vew; // unprocessed exponent stack
 UIntN * ew; // address of <vew>
 Obj vge; // global exponent stack
 Int * ge; // address of <vge>

 Obj vpow; // rhs of power relations
 Int lpow; // length of <vpow>
 const Obj * pow; // address of <vpow>

 Obj vcnj; // rhs of conjugate relations
 Int lcnj; // length of <vcnj>
 const Obj * cnj; // address of <vcnj>

 const Obj * avc; // address of the avector
 const Obj * avc2; // address of the avector 2
 const Obj * wt; // address of the weights array
 const Obj * gns; // address of the list of generators
 const Obj * ro; // address of the list of relative orders
 const Obj * inv; // address of the list of inverses

 Int * v; // address of <vv>

 Int max; // maximal stack size
 Int sp; // stack pointer
 Int i, j; // loop variable
 Int gn; // current generator number
 Int ex; // current exponent
 Int cl; // p-class of the collector
 Int p; // the prime

 Obj tmp; // temporary obj for power

 Int resized = 0;// indicates whether a Resize() happened

 // if <w> is the identity return now
 if ( NPAIRS_WORD(w) == 0 ) {
 return SC_NUMBER_RWS_GENERATORS(sc);
 }

 // get the number of bits for exponents
 ebits = EBITS_WORDTYPE( SC_DEFAULT_TYPE(sc) );

 // get the exponent mask
 expm = ((UInt)1 << ebits) - 1;

 // get the exponent sign masks
 exps = (UInt)1 << (ebits-1);

 // <nw> contains the stack of words to insert
 vnw = CollectorsState()->SC_NW_STACK;

 // <lw> contains the word end of the word in <nw>
 vlw = CollectorsState()->SC_LW_STACK;

 // <pw> contains the position of the word in <nw> to look at
 vpw = CollectorsState()->SC_PW_STACK;

 // <ew> contains the unprocessed exponents at position <pw>
 vew = CollectorsState()->SC_EW_STACK;

 // <ge> contains the global exponent of the word
 vge = CollectorsState()->SC_GE_STACK;

 // get the maximal stack size
 max = CollectorsState()->SC_MAX_STACK_SIZE;

 // ensure that the stacks are large enough
 const UInt desiredStackSize = sizeof(Obj) * (max + 2);
 if ( SIZE_OBJ(vnw) < desiredStackSize ) {
 ResizeBag( vnw, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vlw) < desiredStackSize ) {
 ResizeBag( vlw, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vpw) < desiredStackSize ) {
 ResizeBag( vpw, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vew) < desiredStackSize ) {
 ResizeBag( vew, desiredStackSize );
 resized = 1;
 }
 if ( SIZE_OBJ(vge) < desiredStackSize ) {
 ResizeBag( vge, desiredStackSize );
 resized = 1;
 }
 if( resized ) return -1;

 // from now on we use addresses instead of handles most of the time
 v = (Int*)ADDR_OBJ(vv);
 nw = (UIntN**)(ADDR_OBJ(vnw)+1);
 lw = (UIntN**)(ADDR_OBJ(vlw)+1);
 pw = (UIntN**)(ADDR_OBJ(vpw)+1);
 ew = (UIntN*)(ADDR_OBJ(vew)+1);
 ge = (Int*)(ADDR_OBJ(vge)+1);

 // conjugates, powers, order, generators, avector, inverses
 vpow = SC_POWERS(sc);
 lpow = LEN_PLIST(vpow);
 pow = CONST_ADDR_OBJ(vpow);

 vcnj = SC_CONJUGATES(sc);
 lcnj = LEN_PLIST(vcnj);
 (void) lcnj; // please compiler -- lcnj not actually used
 cnj = CONST_ADDR_OBJ(vcnj);

 avc = CONST_ADDR_OBJ( SC_AVECTOR(sc) );
 gns = CONST_ADDR_OBJ( SC_RWS_GENERATORS(sc) );

 cl = INT_INTOBJ( SC_CLASS(sc) );
 wt = CONST_ADDR_OBJ( SC_WEIGHTS(sc) );
 avc2 = CONST_ADDR_OBJ( SC_AVECTOR2(sc) );

 ro = CONST_ADDR_OBJ( SC_RELATIVE_ORDERS(sc) );
 p = INT_INTOBJ(ro[1]);
 inv = CONST_ADDR_OBJ( SC_INVERSES(sc) );

 // initialize the stack with <w>
 sp = 0;
 SC_PUSH_WORD( w, 1 );

 // run until the stack is empty
 while ( 0 < sp ) {

 // if <ew> is negative use inverse
 if ( *ew & exps ) {
 gn = ((**pw) >> ebits) + 1;
 ex = ( *ew & (exps-1) ) - exps;
 *ew = 0;
 SC_PUSH_WORD( inv[gn], -ex );
 }

 // if <ew> is zero get next syllable
 else if ( 0 == *ew ) {

 // if <pw> has reached <lw> get next & reduce globale exponent
 if ( *pw == *lw ) {

 // if the globale exponent is greater one reduce it
 if ( 1 < *ge ) {
 (*ge)--;
 *pw = *nw;
 *ew = (**pw) & expm;
 }

 // otherwise get the next word from the stack
 else {
 SC_POP_WORD();

 }
 }

 // otherwise set <ew> to exponent of next syllable
 else {
 (*pw)++;
 *ew = (**pw) & expm;
 }
 }

 // now move the next generator/word to the correct position
 else {

 // get generator number
 gn = ((**pw) >> ebits) + 1;

 // collect a single generator on the stack
 if( *lw == *nw && INT_INTOBJ(avc[gn]) == gn ) {
 v[gn] += *ew * *ge;
 *ew = *ge = 0;
 if ( p <= v[gn] ) {
 ex = v[gn] / p;
 v[gn] -= ex * p;
 if ( gn <= lpow && pow[gn] && 0 < NPAIRS_WORD(pow[gn]) ) {
 const UIntN * sub = CONST_DATA_WORD(pow[gn]);
 const UIntN * subend = sub + NPAIRS_WORD(pow[gn]) - 1;
 AddWordIntoExpVec(
 v, sub, subend, ex,
 ebits, expm, p, pow, lpow );
 }
 }

 continue;
 }

 // collect a whole word exponent pair
 else if( sp > 1 && *pw == *nw && INT_INTOBJ(avc[gn]) == gn ) {
 AddWordIntoExpVec(
 v, *nw, *lw, *ge, ebits, expm, p, pow, lpow );
 *pw = *lw;
 *ew = *ge = 0;

 continue;
 }

 // collect the rest of a word
 else if( sp > 1 && INT_INTOBJ(avc[gn]) == gn ) {
 AddPartIntoExpVec(
 v, *pw, *lw, ebits, expm, p, pow, lpow );
 *pw = *lw;
 *ew = 0;

 continue;
 }

 else if( sp > 1 && 3*INT_INTOBJ(wt[gn]) > cl ) {
 /* Collect <gn>^<ew> without stacking commutators.
 This is step 6 in (Vaughan-Lee 1990). */
 i = INT_INTOBJ(avc[gn]);
 for ( ; gn < i; i-- ) {
 if ( v[i] && gn <= LEN_PLIST(cnj[i]) ) {
 tmp = ELM_PLIST( cnj[i], gn );
 if ( tmp != 0 && 0 < NPAIRS_WORD(tmp) ) {
 AddCommIntoExpVec<UIntN>(
 v, tmp, v[i] * (*ew),
 ebits, expm, p, pow, lpow );
 }
 }
 }

 v[gn] += (*ew);
 (*ew) = 0;

 /* If the exponent is too big, we have to stack up the
 entries in the exponent vector. */
 if ( p <= v[gn] ) {
 ex = v[gn] / p;
 v[gn] -= ex * p;
 if ( gn <= lpow && pow[gn] && 0 < NPAIRS_WORD(pow[gn]) ) {
 // stack the exponent vector first.
 i = INT_INTOBJ(avc[gn]);
 for ( ; gn < i; i-- ) {
 if ( v[i] ) {
 SC_PUSH_GEN( gns[i], v[i] );
 v[i] = 0;
 }
 }
 const UIntN * sub = CONST_DATA_WORD(pow[i]);
 const UIntN * subend = sub + NPAIRS_WORD(pow[i]) - 1;
 AddWordIntoExpVec(
 v, sub, subend, ex,
 ebits, expm, p, pow, lpow );
 }
 }
 }
 // we have to move <gn> step by step
 else {

 (*ew)--;
 v[gn]++;

 i = INT_INTOBJ(avc[gn]);
 if( sp > 1 ) {
 // Do combinatorial collection as far as possible.
 j = INT_INTOBJ(avc2[gn]);
 for( ; j < i; i-- )
 if( v[i] && gn <= LEN_PLIST(cnj[i]) ) {
 tmp = ELM_PLIST( cnj[i], gn );
 if ( tmp != 0 && 0 < NPAIRS_WORD(tmp) )
 AddCommIntoExpVec<UIntN>(
 v, tmp, v[i],
 ebits, expm, p, pow, lpow );
 }
 }

 /* Find the first position in v from where on ordinary
 collection has to be applied. */
 for( ; gn < i; i-- )
 if( v[i] && gn <= LEN_PLIST(cnj[i]) ) {
 tmp = ELM_PLIST( cnj[i], gn );
 if ( tmp != 0 && 0 < NPAIRS_WORD(tmp) )
 break;
 }

 /* Stack up this part of v if we run through the next
 for-loop or if a power relation will be applied */
 if( gn < i || (p <= v[gn] &&
 gn <= lpow && pow[gn] && 0 < NPAIRS_WORD(pow[gn])) ) {
 j = INT_INTOBJ(avc[gn]);
 for( ; i < j; j-- )
 if( v[j] ) {
 SC_PUSH_GEN( gns[j], v[j] );
 v[j] = 0;
 }
 }

 // We finish with ordinary collection from the left
 for ( ; gn < i; i-- ) {
 if ( v[i] ) {
 if ( LEN_PLIST(cnj[i]) < gn ) {
 SC_PUSH_GEN( gns[i], v[i] );
 }
 else {
 tmp = ELM_PLIST( cnj[i], gn );
 if ( tmp == 0 || NPAIRS_WORD(tmp) == 0 ) {
 SC_PUSH_GEN( gns[i], v[i] );
 }
 else {
 SC_PUSH_WORD( tmp, v[i] );
 }
 }
 v[i] = 0;
 }
 }
 }

 // check that the exponent is not too big
 if ( p <= v[gn] ) {
 i = v[gn] / p;
 v[gn] -= i * p;
 if ( gn <= lpow && pow[gn] && 0 < NPAIRS_WORD(pow[gn]) ) {
 SC_PUSH_WORD( pow[gn], i );
 }
 }
 }
 }
 return SC_NUMBER_RWS_GENERATORS(sc);
}

/****************************************************************************
**
*V C8Bits_CombiCollector
*/
static FinPowConjCol C8Bits_CombiCollector = {
 WordVectorAndClear<UInt1>,
 VectorWord<UInt1>,
 CombiCollectWord<UInt1>,
 Solution<UInt1>,
};

/****************************************************************************
**
*V C16Bits_CombiCollector
*/
static FinPowConjCol C16Bits_CombiCollector = {
 WordVectorAndClear<UInt2>,
 VectorWord<UInt2>,
 CombiCollectWord<UInt2>,
 Solution<UInt2>,
};

/****************************************************************************
**
*V C32Bits_CombiCollector
*/
static FinPowConjCol C32Bits_CombiCollector = {
 WordVectorAndClear<UInt4>,
 VectorWord<UInt4>,
 CombiCollectWord<UInt4>,
 Solution<UInt4>,
};

/****************************************************************************
**
*V FinPowConjCollectors
*/
static FinPowConjCol * FinPowConjCollectors [6] =
{
#define C8Bits_SingleCollectorNo 0
 &C8Bits_SingleCollector,
#define C16Bits_SingleCollectorNo 1
 &C16Bits_SingleCollector,
#define C32Bits_SingleCollectorNo 2
 &C32Bits_SingleCollector,
#define C8Bits_CombiCollectorNo 3
 &C8Bits_CombiCollector,
#define C16Bits_CombiCollectorNo 4
 &C16Bits_CombiCollector,
#define C32Bits_CombiCollectorNo 5
 &C32Bits_CombiCollector
};

/****************************************************************************
**
*F * * * * * * * * * * * * reduce something functions * * * * * * * * * * * *
*/

/****************************************************************************
**
*F CollectWordOrFail( <fc>, <sc>, <vv>, <w> )
*/
static Obj CollectWordOrFail(FinPowConjCol * fc, Obj sc, Obj vv, Obj w)
{
 Int i; // loop variable
 Obj * ptr; // pointer into the array <vv>

 // convert <vv> into a list of C integers
 ptr = ADDR_OBJ(vv)+1;
 for ( i = LEN_PLIST(vv); 0 < i; i--, ptr++ )
 *ptr = (Obj)INT_INTOBJ(*ptr);

 // now collect <w> into <vv>
 if ( fc->collectWord( sc, vv, w ) == -1 ) {
 // If the collector fails, we return the vector clean.
 ptr = ADDR_OBJ(vv)+1;
 for ( i = LEN_PLIST(vv); 0 < i; i--, ptr++ )
 *ptr = INTOBJ_INT(0);

 return Fail;
 }

 // and convert back
 ptr = ADDR_OBJ(vv)+1;
 for ( i = LEN_PLIST(vv); 0 < i; i--, ptr++ )
 *ptr = INTOBJ_INT((Int)*ptr);

 return True;
}

/****************************************************************************
**
*F ReducedComm( <fc>, <sc>, <w>, )
*/
static Obj ReducedComm(FinPowConjCol * fc, Obj sc, Obj w, Obj u)
{
 Obj type; // type of the returned object
 Int num; // number of gen/exp pairs in <data>
 Obj vcw; // collect vector
 Obj vc2; // collect vector

 // use 'cwVector' to collect word *<w> to
 vcw = CollectorsState()->SC_CW_VECTOR;
 num = SC_NUMBER_RWS_GENERATORS(sc);

 // check that it has the correct length, unpack into it
 if ( fc->vectorWord( vcw, u, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // collect <w> into it
 if ( fc->collectWord( sc, vcw, w ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return ReducedComm( fc, sc, w, u );
 }

 // use 'cw2Vector' to collect word <w>* to
 vc2 = CollectorsState()->SC_CW2_VECTOR;

 // check that it has the correct length, unpack <w> into it
 if ( fc->vectorWord( vc2, w, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 memset(ADDR_OBJ(vc2) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // collect into it
 if ( fc->collectWord( sc, vc2, u ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 memset(ADDR_OBJ(vc2) + 1, 0, sizeof(Int) * num);
 return ReducedComm( fc, sc, w, u );
 }

 // now use 'Solution' to solve the equation, will clear <vcw>
 if ( fc->solution( sc, vcw, vc2, fc->collectWord ) == -1 )
 {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 memset(ADDR_OBJ(vc2) + 1, 0, sizeof(Int) * num);
 return ReducedComm( fc, sc, w, u );
 }

 // convert the vector <vc2> into a word and clear <vc2>
 type = SC_DEFAULT_TYPE(sc);
 return fc->wordVectorAndClear( type, vc2, num );
}

/****************************************************************************
**
*F ReducedForm( <fc>, <sc>, <w> )
*/
static Obj ReducedForm(FinPowConjCol * fc, Obj sc, Obj w)
{
 Int num; // number of gen/exp pairs in <data>
 Int i; // loop variable for gen/exp pairs
 Obj vcw; // collect vector
 Obj type; // type of the return objue

 // use 'cwVector' to collect word <w> to
 vcw = CollectorsState()->SC_CW_VECTOR;
 num = SC_NUMBER_RWS_GENERATORS(sc);

 // check that it has the correct length
 if ( fc->vectorWord( vcw, 0, num ) == -1 )
 return Fail;

 // and collect <w> into it
 while ( (i = fc->collectWord( sc, vcw, w )) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 }
 num = i;

 // get the default type
 type = SC_DEFAULT_TYPE(sc);

 // convert the vector <cvw> into a word and clear <vcw>
 return fc->wordVectorAndClear( type, vcw, num );
}

/****************************************************************************
**
*F ReducedLeftQuotient( <fc>, <sc>, <w>, )
*/
static Obj ReducedLeftQuotient(FinPowConjCol * fc, Obj sc, Obj w, Obj u)
{
 Obj type; // type of the return objue
 Int num; // number of gen/exp pairs in <data>
 Obj vcw; // collect vector
 Obj vc2; // collect vector

 // use 'cwVector' to collect word <w> to
 vcw = CollectorsState()->SC_CW_VECTOR;
 num = SC_NUMBER_RWS_GENERATORS(sc);

 // check that it has the correct length, unpack <w> into it
 if ( fc->vectorWord( vcw, w, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // use 'cw2Vector' to collect word to
 vc2 = CollectorsState()->SC_CW2_VECTOR;

 // check that it has the correct length, unpack into it
 if ( fc->vectorWord( vc2, u, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 memset(ADDR_OBJ(vc2) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // now use 'Solution' to solve the equation, will clear <vcw>
 if ( fc->solution( sc, vcw, vc2, fc->collectWord ) == -1 )
 {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 memset(ADDR_OBJ(vc2) + 1, 0, sizeof(Int) * num);
 return ReducedLeftQuotient( fc, sc, w, u );
 }

 // convert the vector <vc2> into a word and clear <vc2>
 type = SC_DEFAULT_TYPE(sc);
 return fc->wordVectorAndClear( type, vc2, num );
}

/****************************************************************************
**
*F ReducedProduct( <fc>, <sc>, <w>, )
*/
static Obj ReducedProduct(FinPowConjCol * fc, Obj sc, Obj w, Obj u)
{
 Obj type; // type of the return objue
 Int num; // number of gen/exp pairs in <data>
 Obj vcw; // collect vector

 // use 'cwVector' to collect word <w> to
 vcw = CollectorsState()->SC_CW_VECTOR;
 num = SC_NUMBER_RWS_GENERATORS(sc);

 // check that it has the correct length, unpack <w> into it
 if ( fc->vectorWord( vcw, w, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // collect <w> into it
 if ( fc->collectWord( sc, vcw, u ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return ReducedProduct( fc, sc, w, u );
 }

 // convert the vector <vcw> into a word and clear <vcw>
 type = SC_DEFAULT_TYPE(sc);
 return fc->wordVectorAndClear( type, vcw, num );
}

/****************************************************************************
**
*F ReducedPowerSmallInt( <fc>, <sc>, <w>, <pow> )
*/
static Obj ReducedPowerSmallInt(FinPowConjCol * fc, Obj sc, Obj w, Obj vpow)
{
 Obj type; // type of the return objue
 Int num; // number of gen/exp pairs in <data>
 Int i; // loop variable for gen/exp pairs
 Obj vcw; // collect vector
 Obj vc2; // collect vector
 Int pow; // power to raise <w> to
 Obj res; // the result

 // get the integer of <vpow>
 pow = INT_INTOBJ(vpow);

 // use 'cwVector' and 'cw2Vector to collect words to
 vcw = CollectorsState()->SC_CW_VECTOR;
 vc2 = CollectorsState()->SC_CW2_VECTOR;
 num = SC_NUMBER_RWS_GENERATORS(sc);
 type = SC_DEFAULT_TYPE(sc);

 // return the trivial word if <pow> is zero
 if ( pow == 0 ) {
 res = NewWord(type, 0);
 return res;
 }

 // invert <w> if <pow> is negative
 if ( pow < 0 ) {

 // check that it has the correct length, unpack <w> into it
 if ( fc->vectorWord( vcw, w, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // use 'Solution' to invert it, this will clear <vcw>
 if (fc->solution(sc,vcw,vc2,fc->collectWord) == -1) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 memset(ADDR_OBJ(vc2) + 1, 0, sizeof(Int) * num);
 return ReducedPowerSmallInt(fc, sc, w, vpow);
 }

 // and replace <pow> and <w> by its inverse
 pow = -pow;
 vpow = INTOBJ_INT(pow);
 w = fc->wordVectorAndClear( type, vc2, num );

 }

 // if <pow> is one, do nothing
 if ( pow == 1 ) {
 return w;
 }

 // catch small cases
 if ( pow < 6 ) {

 // check that it has the correct length, unpack <w> into it
 if ( fc->vectorWord( vcw, w, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // multiply <w> into <vcw>
 for ( i = pow; 1 < i; i-- ) {
 if ( fc->collectWord( sc, vcw, w ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return ReducedPowerSmallInt(fc,sc,w,vpow);
 }
 }

 // convert it back, this will clear <vcw>
 return fc->wordVectorAndClear( type, vcw, num );

 }

 // use "divide et impera" instead of repeated squaring r2l
 if ( pow % 2 ) {
 res = ReducedPowerSmallInt( fc, sc, w, INTOBJ_INT((pow-1)/2) );
 return ReducedProduct( fc, sc, w,
 ReducedProduct( fc, sc, res, res ) );
 }
 else {
 res = ReducedPowerSmallInt( fc, sc, w, INTOBJ_INT(pow/2) );
 return ReducedProduct( fc, sc, res, res );
 }

}

/****************************************************************************
**
*F ReducedQuotient( <fc>, <sc>, <w>, )
*/
static Obj ReducedQuotient(FinPowConjCol * fc, Obj sc, Obj w, Obj u)
{
 Obj type; // type of the return objue
 Int num; // number of gen/exp pairs in <data>
 Obj vcw; // collect vector
 Obj vc2; // collect vector

 // use 'cwVector' to collect word <w> to
 vcw = CollectorsState()->SC_CW_VECTOR;
 vc2 = CollectorsState()->SC_CW2_VECTOR;
 num = SC_NUMBER_RWS_GENERATORS(sc);
 type = SC_DEFAULT_TYPE(sc);

 // check that it has the correct length, unpack into it
 if ( fc->vectorWord( vcw, u, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // use 'Solution' to invert it, this will clear <vcw>
 if ( fc->solution( sc, vcw, vc2, fc->collectWord ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 memset(ADDR_OBJ(vc2) + 1, 0, sizeof(Int) * num);
 return ReducedQuotient( fc, sc, w, u );
 }

 // and replace by its inverse
 u = fc->wordVectorAndClear( type, vc2, num );

 // check that it has the correct length, unpack <w> into it
 if ( fc->vectorWord( vcw, w, num ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return Fail;
 }

 // collect <w> into it
 if ( fc->collectWord( sc, vcw, u ) == -1 ) {
 memset(ADDR_OBJ(vcw) + 1, 0, sizeof(Int) * num);
 return ReducedQuotient( fc, sc, w, u );
 }

 // convert the vector <vcw> into a word and clear <vcw>
 return fc->wordVectorAndClear( type, vcw, num );
}

/****************************************************************************
**
*F * * * * * * * * * * * * * exported GAP functions * * * * * * * * * * * * *
*/

/****************************************************************************
**
*F FuncFinPowConjCol_CollectWordOrFail( <self>, <sc>, <vv>, <w> )
*/
static Obj FuncFinPowConjCol_CollectWordOrFail(Obj self, Obj sc, Obj vv, Obj w)
{
 return CollectWordOrFail( SC_COLLECTOR(sc), sc, vv, w );
}

/****************************************************************************
**
*F FuncFinPowConjCol_ReducedComm( <self>, <sc>, <w>, )
*/
static Obj FuncFinPowConjCol_ReducedComm ( Obj self, Obj sc, Obj w, Obj u )
{
 return ReducedComm( SC_COLLECTOR(sc), sc, w, u );
}

/****************************************************************************
**
*F FuncFinPowConjCol_ReducedForm( <self>, <sc>, <w> )
*/
static Obj FuncFinPowConjCol_ReducedForm ( Obj self, Obj sc, Obj w )
{
 return ReducedForm( SC_COLLECTOR(sc), sc, w );
}

/****************************************************************************
**
*F FuncFinPowConjCol_ReducedLeftQuotient( <self>, <sc>, <w>, )
*/
static Obj FuncFinPowConjCol_ReducedLeftQuotient ( Obj self, Obj sc, Obj w, Obj u )
{
 return ReducedLeftQuotient( SC_COLLECTOR(sc), sc, w, u );
}

/****************************************************************************
**
*F FuncFinPowConjCol_ReducedProduct( <self>, <sc>, <w>, )
*/
static Obj FuncFinPowConjCol_ReducedProduct ( Obj self, Obj sc, Obj w, Obj u )
{
 return ReducedProduct( SC_COLLECTOR(sc), sc, w, u );
}

/****************************************************************************
**
*F FuncFinPowConjCol_ReducedPowerSmallInt( <self>, <sc>, <w>, <pow> )
*/
static Obj FuncFinPowConjCol_ReducedPowerSmallInt (Obj self,Obj sc,Obj w,Obj vpow)
{
 return ReducedPowerSmallInt( SC_COLLECTOR(sc), sc, w, vpow );
}

/****************************************************************************
**
*F FuncFinPowConjCol_ReducedQuotient( <self>, <sc>, <w>, )
*/
static Obj FuncFinPowConjCol_ReducedQuotient ( Obj self, Obj sc, Obj w, Obj u )
{
 return ReducedQuotient( SC_COLLECTOR(sc), sc, w, u );
}

/****************************************************************************
**
*F SET_SCOBJ_MAX_STACK_SIZE( <self>, <size> )
*/
static Obj FuncSET_SCOBJ_MAX_STACK_SIZE(Obj self, Obj size)
{
 CollectorsState()->SC_MAX_STACK_SIZE =
 GetPositiveSmallInt(SELF_NAME, size);
 return 0;
}

/****************************************************************************
**
*F * * * * * * * * * * * * * initialize module * * * * * * * * * * * * * * *
*/

/****************************************************************************
**
*V GVarFuncs . . . . . . . . . . . . . . . . . . list of functions to export
*/
static StructGVarFunc GVarFuncs [] = {

 GVAR_FUNC_3ARGS(FinPowConjCol_CollectWordOrFail, sc, list, word),
 GVAR_FUNC_3ARGS(FinPowConjCol_ReducedComm, sc, word, word),
 GVAR_FUNC_2ARGS(FinPowConjCol_ReducedForm, sc, word),
 GVAR_FUNC_3ARGS(FinPowConjCol_ReducedLeftQuotient, sc, word, word),
 GVAR_FUNC_3ARGS(FinPowConjCol_ReducedPowerSmallInt, sc, word, int),
 GVAR_FUNC_3ARGS(FinPowConjCol_ReducedProduct, sc, word, word),
 GVAR_FUNC_3ARGS(FinPowConjCol_ReducedQuotient, sc, word, word),
 GVAR_FUNC_1ARGS(SET_SCOBJ_MAX_STACK_SIZE, size),
 { 0, 0, 0, 0, 0 }

};

/****************************************************************************
**
*F InitKernel( <module> ) . . . . . . . . initialise kernel data structures
*/
static Int InitKernel (
 StructInitInfo * module )
{
 // init filters and functions
 InitHdlrFuncsFromTable( GVarFuncs );

 return 0;
}

/****************************************************************************
**
*F InitLibrary( <module> ) . . . . . . . initialise library data structures
*/
static Int InitLibrary (
 StructInitInfo * module )
{
 // export position numbers 'SCP_SOMETHING'
 ExportAsConstantGVar(SCP_UNDERLYING_FAMILY);
 ExportAsConstantGVar(SCP_RWS_GENERATORS);
 ExportAsConstantGVar(SCP_NUMBER_RWS_GENERATORS);
 ExportAsConstantGVar(SCP_DEFAULT_TYPE);
 ExportAsConstantGVar(SCP_IS_DEFAULT_TYPE);
 ExportAsConstantGVar(SCP_RELATIVE_ORDERS);
 ExportAsConstantGVar(SCP_POWERS);
 ExportAsConstantGVar(SCP_CONJUGATES);
 ExportAsConstantGVar(SCP_INVERSES);
 ExportAsConstantGVar(SCP_COLLECTOR);
 ExportAsConstantGVar(SCP_AVECTOR);
 ExportAsConstantGVar(SCP_WEIGHTS);
 ExportAsConstantGVar(SCP_CLASS);
 ExportAsConstantGVar(SCP_AVECTOR2);

 // export collector number
 AssConstantGVar( GVarName( "8Bits_SingleCollector" ),
 INTOBJ_INT(C8Bits_SingleCollectorNo) );
 AssConstantGVar( GVarName( "16Bits_SingleCollector" ),
 INTOBJ_INT(C16Bits_SingleCollectorNo) );
 AssConstantGVar( GVarName( "32Bits_SingleCollector" ),
 INTOBJ_INT(C32Bits_SingleCollectorNo) );

 AssConstantGVar( GVarName( "8Bits_CombiCollector" ),
 INTOBJ_INT(C8Bits_CombiCollectorNo) );
 AssConstantGVar( GVarName( "16Bits_CombiCollector" ),
 INTOBJ_INT(C16Bits_CombiCollectorNo) );
 AssConstantGVar( GVarName( "32Bits_CombiCollector" ),
 INTOBJ_INT(C32Bits_CombiCollectorNo) );

 // init filters and functions
 InitGVarFuncsFromTable( GVarFuncs );

 return 0;
}

static Int InitModuleState(void)
{
 // register global bags with the garbage collector
 InitGlobalBag( &CollectorsState()->SC_NW_STACK, "SC_NW_STACK" );
 InitGlobalBag( &CollectorsState()->SC_LW_STACK, "SC_LW_STACK" );
 InitGlobalBag( &CollectorsState()->SC_PW_STACK, "SC_PW_STACK" );
 InitGlobalBag( &CollectorsState()->SC_EW_STACK, "SC_EW_STACK" );
 InitGlobalBag( &CollectorsState()->SC_GE_STACK, "SC_GE_STACK" );
 InitGlobalBag( &CollectorsState()->SC_CW_VECTOR, "SC_CW_VECTOR" );
 InitGlobalBag( &CollectorsState()->SC_CW2_VECTOR, "SC_CW2_VECTOR" );

 const UInt maxStackSize = 256;
 const UInt desiredStackSize = sizeof(Obj) * (maxStackSize + 2);
 CollectorsState()->SC_NW_STACK = NewKernelBuffer(desiredStackSize);
 CollectorsState()->SC_LW_STACK = NewKernelBuffer(desiredStackSize);
 CollectorsState()->SC_PW_STACK = NewKernelBuffer(desiredStackSize);
 CollectorsState()->SC_EW_STACK = NewKernelBuffer(desiredStackSize);
 CollectorsState()->SC_GE_STACK = NewKernelBuffer(desiredStackSize);

 CollectorsState()->SC_CW_VECTOR = NEW_STRING(0);
 CollectorsState()->SC_CW2_VECTOR = NEW_STRING(0);
 CollectorsState()->SC_MAX_STACK_SIZE = maxStackSize;

 return 0;
}

/****************************************************************************
**
*F InitInfoCollectors() . . . . . . . . . . . . . . table of init functions
*/
static StructInitInfo module = {
/* type = */ MODULE_BUILTIN,
/* name = */ "collectors",
/* revision_c = */ 0,
/* revision_h = */ 0,
/* version = */ 0,
/* crc = */ 0,
/* initKernel = */ InitKernel,
/* initLibrary = */ InitLibrary,
/* checkInit = */ 0,
/* preSave = */ 0,
/* postSave = */ 0,
/* postRestore = */ 0,
/* moduleStateSize = */ sizeof(CollectorsState_),
/* moduleStateOffsetPtr = */ &CollectorsStateOffset,
/* initModuleState = */ InitModuleState,
/* destroyModuleState = */ 0,
};

StructInitInfo * InitInfoCollectors ( void )
{
 return &module;
}

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