    
/***************************************************************************
 **
 *A  cvec.c               cvec-package                        Max Neunhoeffer
 **
 **  Copyright (C) 2007  Max Neunhoeffer, Lehrstuhl D f. Math., RWTH Aachen
 **  This file is free software, see license information at the end.
 **  
 */

#include <stdlib.h>

#include "src/compiled.h"          /* GAP headers                */

#undef PACKAGE
#undef PACKAGE_BUGREPORT
#undef PACKAGE_NAME
#undef PACKAGE_STRING
#undef PACKAGE_TARNAME
#undef PACKAGE_URL
#undef PACKAGE_VERSION

#include "pkgconfig.h"             /* our own configure results */

/* Note that SIZEOF_VOID_P comes from GAP's config.h whereas
 * SIZEOF_VOID_PP comes from pkgconfig.h! */
#if SIZEOF_VOID_PP != SIZEOF_VOID_P
#error GAPs word size is different from ours, 64bit/32bit mismatch
#endif


#ifdef SYS_IS_64_BIT
#include "gf2lib_64.c"
WORD myarena[(4096*1024+1024*1024)/8];      
/* we assume 4MB of cache, aligned to 1MB */
WORD *arenastart;
#else
#include "gf2lib_32.c"
WORD myarena[(2048*1024+1024*1024)/4];      
/* we assume 2MB of cache, aligned to 1MB */
WORD *arenastart;
#endif

#if SYS_IS_CYGWIN32
#include <cygwin/in.h>
#endif

/* Our basic unit is a C unsigned long: */
typedef unsigned long Word;  /* Our basic unit for operations, 32 or 64 bits */
#define Word32 UInt4

#define WORDALLONE (~(0UL))
#define BYTESPERWORD sizeof(Word)
#define CACHESIZE (512L*1024L)
#define CACHELINE 64
/* If you want to change the following limit, please also change the
 * corresponding value in cvec.gi in CVEC_NewCVecClass! */
#define MAXDEGREE 1024

/* Define this to empty if you want global access to functions: */
#define STATIC static
/* #define STATIC */

/* Define this to empty if your compiler does not support inlined functions: */
#define INLINE inline


/************************************/
/* Macros to access the data types: */
/************************************/

/* The following positions are exported into the record CVEC for use
 * within the GAP part: If you add a position, please document it
 * in gap/cvec.gd and export it in InitLibrary! */

#define IDX_p 1
#define IDX_d 2
#define IDX_q 3
#define IDX_conway 4
#define IDX_bitsperel 5
#define IDX_elsperword 6
#define IDX_wordinfo 7
#define IDX_bestgrease 8
#define IDX_greasetabl 9
#define IDX_filts 10
#define IDX_tab1 11
#define IDX_tab2 12
#define IDX_size 13
#define IDX_scafam 14
#define IDX_filtscmat 15

#define IDX_fieldinfo 1
#define IDX_len 2
#define IDX_wordlen 3
#define IDX_type 4
#define IDX_GF 5
#define IDX_lens 6
#define IDX_classes 7
#define IDX_typecmat 8

#define OFF_mask 0
#define OFF_offset 1
#define OFF_maskp 2
#define OFF_cutmask 3

#ifndef DATA_TYPE
#define DATA_TYPE(type)       ELM_PLIST( type, 3 )
#endif
#define DATA_OBJ(obj)         DATA_TYPE(TYPE_DATOBJ(obj))
/* Note: The index 3 is a magic constant taken from the GAP library and kernel.
Future GAP versions will provide the DATA_TYPE macro in the
kernel headers, so that we do not need to rely on magic constants anymore.
*/

/* currently unused, see below:
#define PREPARE(f) \
    Word *wi = (Word *) (CHARS_STRING(ELM_PLIST(f,IDX_wordinfo))); \
    register Word offset = wi[OFF_offset]; \
    register Word mask = wi[OFF_mask]; \
    register Int shift = INT_INTOBJ(ELM_PLIST(f,IDX_bitsperel))-1; \
    register Int p = INT_INTOBJ(ELM_PLIST(f,IDX_p))
#define REDUCE(x) (x - (((x + offset) & mask) >> shift) * p)
*/

/* The following is used for arithmetic: */
#define PREPARE(f) \
    Word *wi = (Word *) (CHARS_STRING(ELM_PLIST(f,IDX_wordinfo))); \
    register Word offset = wi[OFF_offset]; \
    register Word mask = wi[OFF_mask]; \
    register Int shift = INT_INTOBJ(ELM_PLIST(f,IDX_bitsperel))-1; \
    register Int ps = INT_INTOBJ(ELM_PLIST(f,IDX_p))*(mask>>shift)
#define REDUCE(x) x - ((((x+offset)&mask) - (((x+offset)&mask)>>shift))&ps)

#define PREPARE_cl(v,cl) \
    Obj cl = DATA_OBJ(v);
#define PREPARE_clfi(v,cl,fi) \
    Obj cl = DATA_OBJ(v); \
    Obj fi = ELM_PLIST(cl,IDX_fieldinfo)
#define PREPARE_p(fi) Int p = INT_INTOBJ(ELM_PLIST(fi,IDX_p))
#define PREPARE_d(fi) Int d = INT_INTOBJ(ELM_PLIST(fi,IDX_d))
#define PREPARE_q(fi) Int q = INT_INTOBJ(ELM_PLIST(fi,IDX_q))
#define PREPARE_cp(fi) Int *cp = \
            (Int *)CHARS_STRING(ELM_PLIST(fi,IDX_conway))
#define PREPARE_bpe(fi) Int bitsperel = \
            INT_INTOBJ(ELM_PLIST(fi,IDX_bitsperel))
#define PREPARE_epw(fi) Int elsperword = \
            INT_INTOBJ(ELM_PLIST(fi,IDX_elsperword))
#define PREPARE_type(fi) Obj type = ELM_PLIST(fi,IDX_type)
#define PREPARE_tab1(fi) Obj tab1 = ELM_PLIST(fi,IDX_tab1)
#define PREPARE_tab2(fi) Obj tab2 = ELM_PLIST(fi,IDX_tab2)
#define PREPARE_mask(fi) Word mask = \
            ((Word *)CHARS_STRING(ELM_PLIST(fi,IDX_wordinfo)))[OFF_mask]
#define PREPARE_offset(fi) Word offset = \
            ((Word *)CHARS_STRING(ELM_PLIST(fi,IDX_wordinfo)))[OFF_offset]
#define PREPARE_maskp(fi) Word maskp = \
            ((Word *)CHARS_STRING(ELM_PLIST(fi,IDX_wordinfo)))[OFF_maskp]
#define PREPARE_cutmask(fi) Word cutmask = \
            ((Word *)CHARS_STRING(ELM_PLIST(fi,IDX_wordinfo)))[OFF_cutmask]


#define DATA_CVEC(cvec) ((Word *)((ADDR_OBJ(cvec))+1))

/* The following macros is called IS_CVEC, but actually does not test
 * the complete type. It only does some cheap plausibility check. In
 * addition, it also covers the case of big FF scalars (CSca). */

#define IS_CVEC(obj) \
   (TNUM_OBJ(obj)==T_DATOBJ && \
    TNUM_OBJ(DATA_OBJ(obj))==T_POSOBJ)


  /*******************************/
 /* Internal or test functions: */
/*******************************/

STATIC Obj OurErrorBreakQuit(char *msg)
{
    ErrorReturnVoid(msg,0L,0L,
                    "    try 'return;' (which will not work here!)");
    ErrorQuit("You were told, 'return;' did not work!",0L,0L);
    return 0L;
}

STATIC Obj TEST_ASSUMPTIONS(Obj self)
/* Result 0 is OK, otherwise something is wrong... */
{
    /* Note in addition, that d * length of a vector must fit into a
     * C Int! */
    if (0UL - 1UL != WORDALLONE) return INTOBJ_INT(1);
    if ( WORDALLONE >> 0 != WORDALLONE ) return INTOBJ_INT(2);
    if ( sizeof(Word) != 8 && sizeof(Word) != 4) return INTOBJ_INT(3);
#ifdef SYS_IS_64_BIT
    if (sizeof(Word) != 8) return INTOBJ_INT(5);
#else
    if (sizeof(Word) != 4) return INTOBJ_INT(6);
#endif
    if (sizeof(Word32) != 4) return INTOBJ_INT(7);
#if !(__BYTE_ORDER == __LITTLE_ENDIAN) && !(__BYTE_ORDER == __BIG_ENDIAN)
    return INTOBJ_INT(4);
#else
    return INTOBJ_INT(0);
#endif
}

STATIC Obj COEFF_LIST_TO_C(Obj self, Obj po, Obj s)
{
    /* po is a list of (small) GAP integers, s a GAP string. */
    Int l,i;
    Int *p;

    l = LEN_PLIST(po);
    GrowString(s,sizeof(Int)*l);
    SET_LEN_STRING(s,sizeof(Int)*l);
    p = (Int *) CHARS_STRING(s);
    for (i = 1;i <= l;i++) *p++ = INT_INTOBJ(ELM_PLIST(po,i));
    return s;
}

STATIC Obj FINALIZE_FIELDINFO(Obj self, Obj f)
{
    Obj s;
    Word *po;
    Word w;
    Int j;
    
    PREPARE_p(f);
    PREPARE_bpe(f);
    PREPARE_epw(f);

    /* GARBAGE COLLECTION POSSIBLE */
    s = NEW_STRING(sizeof(Word) * 4);
    po = (Word *) CHARS_STRING(s);
    if (p & 1) {   /* Odd characteristic */
        for (w = 1UL,j = 1;j < elsperword;j++)
            w = (w << bitsperel)+1UL;
        po[OFF_mask] = w << (bitsperel-1);
        po[OFF_offset] = po[OFF_mask] - w * p;
        po[OFF_maskp] = (1UL << bitsperel)-1;
        po[OFF_cutmask] = w * po[OFF_maskp];
    } else {     /* Characteristic 2 */
        po[OFF_mask] = 0;
        po[OFF_offset] = 0;
        po[OFF_maskp] = 1;
        po[OFF_cutmask] = WORDALLONE;
    }
    SET_ELM_PLIST(f,IDX_wordinfo,s);
    CHANGED_BAG(f);
    return f;
}

Obj INIT_SMALL_GFQ_TABS(Obj self, Obj pp, Obj dd, Obj qq, Obj tab1, Obj tab2,
                        Obj primroot)
{
    extern unsigned long PolsFF[];
    UInt p = INT_INTOBJ(pp);
    UInt d = INT_INTOBJ(dd);
    UInt q = INT_INTOBJ(qq);
    UInt poly;           /* Conway polynomial of extension  */
    UInt i, l, f, n, e;  /* loop variables                  */
    /* We already know that tab1 and tab2 are lists of length q. */
    
    /* The following code is from finfield.c in the GAP kernel: */

    /* if q is a prime find the smallest primitive root $e$, use $x - e$   */
    if ( d == 1 ) {
        for ( e = 1, i = 1; i != p-1; ++e ) {
            for ( f = e, i = 1; f != 1; ++i )
                f = (f * e) % p;
        }
        poly = p-(e-1);
    }
    /* otherwise look up the polynomial used to construct this field       */
    else {
        for ( i = 0; PolsFF[i] != q; i += 2 ) ;
        poly = PolsFF[i+1];
    }

    /* We want ELM_PLIST(tab1,VAL_FFE(fe)+1) to be the small integer
     * whose p-adic expansion corresponds to fe in F_p[x]/cp where
     * cp is the Conway polynomial. tab2 works the opposite way, that is,
     * ELM_PLIST(tab2,e+1) = fe for the corresponding FFE. */
    SET_ELM_PLIST(tab1,1,INTOBJ_INT(0));
    SET_ELM_PLIST(tab2,1,NEW_FFE(FLD_FFE(primroot),0));
    for ( e = 1, n = 0; n < q-1; ++n ) {
        SET_ELM_PLIST(tab1,n+2,INTOBJ_INT(e));
        SET_ELM_PLIST(tab2,e+1,NEW_FFE(FLD_FFE(primroot),n+1));
        if ( p != 2 ) {
            f = p * (e % (q/p));  l = (p - (e/(q/p))) % p;  e = 0;
            for ( i = 1; i < q; i *= p )
                e = e + i * ((f/i + l * (poly/i)) % p);
        }
        else {
            if ( 2*e & q )  e = 2*e ^ poly ^ q;
            else            e = 2*e;
        }
    }
    return 0L;
}

// Given a FFE o, perform lookup in tab1
static inline Obj FFE_TO_INTOBJ(Obj tab1, Int q, Obj o)
{
    FFV v = VAL_FFE(o);
    if (v == 0)
        return INTOBJ_INT(0);

    return ELM_PLIST(tab1, (v-1) * (q-1) / (SIZE_FF(FLD_FFE(o))-1) + 2);
}


  /**********************/
 /* Sequential access: */
/**********************/

typedef struct SeqAcc {
    Int d;
    Int bitsperel;
    Int elsperword;
    Int pos;     /* one based */
    Word mask;   /* to extract */
    Int bitpos;
    Int offset;  /* in words */
} seqaccess;

/* For the following macros sa is *seqaccess, v is *Word, off is Int, s is Int,
 * which is a prime field scalar. */

/* Gets a prime field component: */
#define GET_VEC_ELM(sa,w,off) \
  (((w)[(sa)->offset+off] & (sa)->mask) >> (sa)->bitpos)

/* Sets a prime field component: */
#define SET_VEC_ELM(sa,w,off,s) \
  (((w)[((sa)->offset)+(off)])) = \
  ((((w)[((sa)->offset)+(off)]) & (~((sa)->mask))) | (s << ((sa)->bitpos)))

/* Moves the sequential access struct left (down): */
#define STEP_LEFT(sa) \
  (sa)->pos--; \
  if ((sa)->bitpos > 0) { \
      (sa)->bitpos -= (sa)->bitsperel; \
      (sa)->mask >>= (sa)->bitsperel; \
  } else { \
      (sa)->bitpos += (sa)->bitsperel*((sa)->elsperword-1); \
      (sa)->mask <<= (sa)->bitsperel*((sa)->elsperword-1); \
      (sa)->offset -= (sa)->d; \
  }

/* Moves the sequential access struct right (up): */
#define STEP_RIGHT(sa) \
  (sa)->pos++; \
  if ((sa)->bitpos < (sa)->bitsperel*((sa)->elsperword-1)) { \
      (sa)->bitpos += (sa)->bitsperel; \
      (sa)->mask <<= (sa)->bitsperel; \
  } else { \
      (sa)->bitpos -= (sa)->bitsperel*((sa)->elsperword-1); \
      (sa)->mask >>= (sa)->bitsperel*((sa)->elsperword-1); \
      (sa)->offset += (sa)->d; \
  }

/* Initializes the sequential access struct, v is a cvec: */
INLINE void INIT_SEQ_ACCESS(seqaccess *sa, Obj v, Int pos)
{
    PREPARE_clfi(v,cl,fi);
    PREPARE_d(fi);
    PREPARE_bpe(fi);
    PREPARE_epw(fi);
    
    sa->d = d;
    sa->bitsperel = bitsperel;
    sa->elsperword = elsperword;
    sa->pos = pos;
    sa->offset = d*((pos-1) / elsperword);
    sa->bitpos = ((pos-1)%elsperword) * bitsperel;
    sa->mask = ((1UL << bitsperel)-1) << sa->bitpos;
}

/* Initializes the sequential access struct, v is a cvec: */
#define MOVE_SEQ_ACCESS(sa,pos) \
    (sa)->offset = (sa)->d*(((pos)-1) / (sa)->elsperword); \
    (sa)->bitpos = (((pos)-1) % (sa)->elsperword) * (sa)->bitsperel; \
    (sa)->mask = ((1UL << (sa)->bitsperel)-1) << (sa)->bitpos;


  /*******************************************************/
 /* Interfacing stuff for the objects to the GAP level: */
/*******************************************************/

STATIC Obj NEW(Obj self, Obj cl, Obj type)
{
    Obj v;
    Int si;

    si = sizeof(Word) * INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
    /* GARBAGE COLLECTION POSSIBLE */
    v = NewBag( T_DATOBJ, sizeof( Obj ) + si );
    if (v == 0L) {
        return OurErrorBreakQuit("CVEC_NEW: Cannot allocate memory");
    }
    SET_TYPE_DATOBJ(v, type);
    return v;
}

STATIC Obj MAKEZERO(Obj self, Obj v)
{
    if (!IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_MAKEZERO: no cvec");
    }
    {
        Int si;
        PREPARE_cl(v,cl);
        si = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
        memset(DATA_CVEC(v),0,sizeof(Word)*si);
    }
    return 0L;
}
    
STATIC Obj COPY(Obj self, Obj v, Obj w)
{
    if (!IS_CVEC(v) || !IS_CVEC(w)) {
        return OurErrorBreakQuit("CVEC_COPY: no cvec");
    }
    {
        Int si,si2;
        PREPARE_cl(v,cl);
        PREPARE_cl(w,cl2);
        si = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
        si2 = INT_INTOBJ(ELM_PLIST(cl2,IDX_len));
        if (si != si2) {
            return OurErrorBreakQuit("CVEC_COPY: unequal length");
        }
        si = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
        memcpy(DATA_CVEC(w),DATA_CVEC(v),sizeof(Word)*si);
        return 0L;
    }
}

STATIC Obj CVEC_TO_INTREP(Obj self,Obj v,Obj l)
/* This function returns the vector in its integer representation. This
 * means, that for the case that q <= 65536 or d = 1 each integer
 * corresponds to one field entry (p-adic expansion for d>1). For bigger
 * q (and d), we fill a list of lists of length d containing d little
 * integers for each vector entry, giving the coefficients of the
 * polynomial over the prime field representing the residue class. */
{
    register Word *pw;
    Int len;
    Int size;

    if (!IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_CVEC_TO_INTREP: no cvec");
    }
    if (!IS_PLIST(l)) {
        return OurErrorBreakQuit("CVEC_CVEC_TO_INTREP: no plist");
    }

    {
        PREPARE_clfi(v,cl,fi);
        PREPARE_d(fi);
        len = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
        size = INT_INTOBJ(ELM_PLIST(fi,IDX_size));

        if (LEN_PLIST(l) != len) {
            return OurErrorBreakQuit("CVEC_CVEC_TO_INTREP: different lengths");
        }

        pw = DATA_CVEC(v);
        {
            PREPARE_p(fi);
            PREPARE_epw(fi);
            PREPARE_bpe(fi);
            PREPARE_maskp(fi);

            if (d == 1) {
                register Word y;
                register Word w = 0;
                Int i,ii;
                for (i = 1,ii = elsperword;i <= len;i++,ii++) {
                    if (ii == elsperword) { w = *pw++; ii = 0; }
                    y = w & maskp;
                    w >>= bitsperel;
                    SET_ELM_PLIST(l,i,INTOBJ_INT((Int) y));
                }
            } else {
                pw -= d;   /* This is corrected at i==0! */
                Int i;
                register Int j;
                register Int shift;
                register Word y;
                if (size <= 0) {
                    for (i = 0;i < len;i++) {
                        shift = (i % elsperword) * bitsperel;
                        if (shift == 0) pw += d;
                        y = 0;
                        for (j = d - 1;j >= 0;j--)
                            y = y * p + ((pw[j] >> shift) & maskp);
                        SET_ELM_PLIST(l,i+1,INTOBJ_INT((Int) y));
                    }
                } else {   /* size >= 1, we write coefficient lists */
                    for (i = 0;i < len;i++) {
                        Obj oo = ELM_PLIST(l,i+1);
                        shift = (i % elsperword) * bitsperel;
                        if (shift == 0) pw += d;
                        for (j = 0;j < d;j++)
                            SET_ELM_PLIST(oo,j+1,
                                 INTOBJ_INT((Int)((pw[j] >> shift) & maskp)));
                    }
                }
            }
        }
    }
    return 0L;
}

STATIC Obj INTREP_TO_CVEC(Obj self,Obj l,Obj v)
/* This function transfers data in integer representation to the vector. This
 * means, that for the case that q <= 65536 or d = 1, each integer
 * corresponds to one field entry (p-adic expansion for d > 1). For
 * bigger q (and d), we have a list of lists of length d of little
 * integers such that every d numbers give the coefficients of the
 * polynomial over the prime field representing the residue class.
 * The length of the list l must correspond to the length of v. As an
 * exception, the elements in integer representation may also be GAP
 * FFEs, if those are in the same field or a subfield. */
{
    register Word *pw;

    if (!IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_INTREP_TO_CVEC: no cvec");
    }

    {
      PREPARE_clfi(v,cl,fi);
      PREPARE_d(fi);
      Int len = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
      pw = DATA_CVEC(v);

      /* Check lengths: */
      if (!IS_PLIST(l) || LEN_PLIST(l) != len) {
          return OurErrorBreakQuit(
         "CVEC_INTREP_TO_CVEC: l must be a list of corresponding length to v");
      }

      {
          PREPARE_p(fi);
          PREPARE_q(fi);
          PREPARE_epw(fi);
          PREPARE_bpe(fi);
          PREPARE_tab1(fi);

          if (d == 1) {
              register Word y;
              register Word w;
              register Int j;
              register Obj o;
              Int i;
              for (i = 1;i <= len;i += elsperword) {
                  j = i+elsperword-1;
                  if (j > len) j=len;
                  w = 0;
                  while (j >= i) {
                      o = ELM_PLIST(l,j);
                      if (IS_INTOBJ(o))
                          y = (Word) INT_INTOBJ(o);
                      else if (IS_FFE(o) && CHAR_FF(FLD_FFE(o)) == p && 
                               DegreeFFE(o) == 1) {
                          y = (Word) INT_INTOBJ(FFE_TO_INTOBJ(tab1, q, o));
                      } else {
                          return OurErrorBreakQuit(
                                "CVEC_INTREP_TO_CVEC: invalid object in list");
                      }
                      w = (w << bitsperel) | y;
                      j--;
                  }
                  *pw++ = w;
              }
          } else {
              /* First clear the space: */
              memset(pw,0,sizeof(Word)*INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen)));
              pw -= d;   /* This is corrected at i==0! */
              Int i;
              register Int j;
              register Int shift;
              register Word y;
              register Obj o;
              for (i = 0;i < len;i++) {
                  shift = (i % elsperword) * bitsperel;
                  if (shift == 0) pw += d;
                  o = ELM_PLIST(l,i+1);
                  if (IS_INTOBJ(o)) {
                      y = (Word) INT_INTOBJ(o);
                      for (j = 0;j < d;j++) {
                          pw[j] |= ((y % p) << shift);
                          y /= p;
                      }
                  } else if (IS_FFE(o) && CHAR_FF(FLD_FFE(o)) == p && 
                           (d % DegreeFFE(o) == 0)) {
                      y = (Word) INT_INTOBJ(FFE_TO_INTOBJ(tab1, q, o));
                      for (j = 0;j < d;j++) {
                          pw[j] |= ((y % p) << shift);
                          y /= p;
                      }
                  } else if (IS_PLIST(o) && LEN_PLIST(o) == d) {
                      register Obj oo;
                      for (j = 0;j < d;j++) {
                          oo = ELM_PLIST(o,j+1);
                          if (IS_INTOBJ(oo))
                              pw[j] |= INT_INTOBJ(oo) << shift;
                              /* This should better be between 0 and p-1! */
                          else if (IS_FFE(oo) && CHAR_FF(FLD_FFE(oo)) == p &&
                                   d == 1) {
                              if (VAL_FFE(oo) != 0)
                                  pw[j] |= INT_INTOBJ(ELM_PLIST(tab1,
                                               (VAL_FFE(oo)+1))) << shift;
                              /* We assume that tab1 is for GF(p) here! */
                          } else {
                              return OurErrorBreakQuit(
                             "CVEC_INTREP_TO_CVEC: invalid object in list");
                          }
                      }
                  } else {
                      return OurErrorBreakQuit(
                             "CVEC_INTREP_TO_CVEC: invalid object in list");
                  }
              }
          }
      }
    }
    return 0L;
}

Obj INTLI_TO_FFELI(Obj self,Obj fi, Obj l)
/* Transforms a list of integers between 0 and q-1 into FFEs. */
{
    if (!IS_PLIST(l)) {
        return OurErrorBreakQuit(
      "CVEC_INTLI_TO_FFELI: Must be called with a field info and a plain list");
    }
    {
        Int len;
        Int i;
        Obj e;
        PREPARE_q(fi);
        PREPARE_tab2(fi);

        len = LEN_PLIST(l);
        for (i = 1;i <= len;i++) {
            e = ELM_PLIST(l,i);
            if (!IS_INTOBJ(e) || INT_INTOBJ(e) < 0 || INT_INTOBJ(e) >= q) {
                return OurErrorBreakQuit("CVEC_INTLI_TO_FFELI: Elements of l "
                                         "must be integers between 0 and q-1");
            }
            e = ELM_PLIST(tab2,INT_INTOBJ(e)+1);
            SET_ELM_PLIST(l,i,e);
        }
    }
    return 0L;
}

Obj FFELI_TO_INTLI(Obj self,Obj fi, Obj l)
/* Transforms a list of FFEs into integers between 0 and q-1. */
{
    if (!IS_PLIST(l)) {
        return OurErrorBreakQuit(
      "CVEC_FFELI_TO_INTLI: Must be called with a field info and a plain list");
    }
    {
        Int len;
        Int i;
        Obj e;
        PREPARE_p(fi);
        PREPARE_d(fi);
        PREPARE_q(fi);
        PREPARE_tab1(fi);

        len = LEN_PLIST(l);
        for (i = 1;i <= len;i++) {
            e = ELM_PLIST(l,i);
            if (!IS_FFE(e) || CHAR_FF(FLD_FFE(e)) != p || 
                (d % DegreeFFE(e)) != 0) {
                return OurErrorBreakQuit("CVEC_FFELI_TO_INTLI: Elements of l "
                                         "must be finite field elements over "
                                         "the right field");
            }
            e = FFE_TO_INTOBJ(tab1, q, e);
            SET_ELM_PLIST(l,i,e);
        }
    }
    return 0L;
}

STATIC Obj CVEC_TO_NUMBERFFLIST(Obj self, Obj v, Obj l, Obj split)
{
    PREPARE_clfi(v,cl,fi);
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_maskp(fi);
    PREPARE_p(fi);
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
    Word *vv = DATA_CVEC(v);
    Word wo;
    Word res;
    Int i,j;
    Int shift;

    for (i = 1;i <= wordlen;i++) {
        wo = *vv++;
        res = 0;
        shift = bitsperel * (elsperword-1);
        for (j = elsperword;j > 0;j--,shift -= bitsperel)
            res = res * p + ((wo >> shift) & maskp);
        if (split == True) {
            SET_ELM_PLIST(l,2*i-1,
                 INTOBJ_INT(res & ((1UL << (4*BYTESPERWORD)) - 1UL)));
            SET_ELM_PLIST(l,2*i,
                 INTOBJ_INT(res >> (4*BYTESPERWORD)));
        } else {
            SET_ELM_PLIST(l,i,INTOBJ_INT((Int) res));
        }
    } 
    return 0L;
}

STATIC Obj NUMBERFFLIST_TO_CVEC(Obj self, Obj l, Obj v, Obj split)
{
    PREPARE_clfi(v,cl,fi);
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_p(fi);
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
    Word *vv = DATA_CVEC(v);
    Word wo;
    Word res;
    Int i,j;
    Int shift;

    for (i = 1;i <= wordlen;i++) {
        if (split == True) {
            res = (Word) INT_INTOBJ(ELM_PLIST(l,2*i-1)) +
                  (((Word) INT_INTOBJ(ELM_PLIST(l,2*i))) << (4*BYTESPERWORD));
        } else {
            res = INT_INTOBJ(ELM_PLIST(l,i));
        }
        shift = 0;
        wo = 0;
        for (j = elsperword;j > 0;j--,shift += bitsperel) {
            wo |= (res % p) << shift;
            res /= p;
        }
        *vv++ = wo;;
    } 
    return 0L;
}

STATIC Obj GREASEPOS(Obj self, Obj v, Obj pivs)
{
    PREPARE_clfi(v,cl,fi);
    PREPARE_p(fi);
    PREPARE_d(fi);
    Int i,j;
    seqaccess sa;
    Int res;
    Word *ww = DATA_CVEC(v);

    i = LEN_PLIST(pivs);
    INIT_SEQ_ACCESS(&sa,v,INT_INTOBJ(ELM_PLIST(pivs,i)));
    res = 0;
    while (1) {   /* we use break */
        /* sa already points to position i! */
        for (j = d-1;j >= 0;j--) res = res * p + GET_VEC_ELM(&sa,ww,j);
        if (--i <= 0) break;
        MOVE_SEQ_ACCESS(&sa,INT_INTOBJ(ELM_PLIST(pivs,i)));
    }
    return INTOBJ_INT(res+1);
}

  /*******************/
 /* The arithmetic: */
/*******************/

 /* Now we have the real worker routines, they are meant to be called from   */
/* the C level.                                                             */

/* For multiplication with scalars with non-prime fields we need some
 * infrastructure: */
/* p-adic expansion of the scalar (mod Conway polynomial): */
/* (index 0 contains prime field entry) */
static Int scbuf[MAXDEGREE+1];
/* Number of entries actually used in sc (beginning with 0): */
/* Is always at least 1. */
static Int sclen; 
/* A buffer for elsperword consecutive field entries: */
static Word buf[MAXDEGREE+1]; 

   /*                                                          */
  /* First some internal inlined functions to do addition and */
 /* scalar multiplication:                                   */
/*                                                          */

static INLINE void ADD2_INL(Word *vv,Word *ww,Obj f,long i)
/* This internal inlined function adds i Words at *ww to the corresponding
 * Words at *vv. Characteristic 2 and odd characteristic are handled
 * separately. */
{
    PREPARE_p(f);
    if (p == 2) {
        /* Characteristic 2: */
        register Word *vv_r = vv;
        register Word *ww_r = ww;
        register long j = i;
        while (--j >= 0) *vv_r++ ^= *ww_r++;
    } else {
        /* Odd characteristic: */
        register Word wo;
        register Word *vv_r = vv;
        register Word *ww_r = ww;
        register long i_r = i;
        PREPARE(f);
        while (--i_r >= 0) {
            wo = *vv_r + *ww_r++;
            *vv_r++ = REDUCE(wo);
        }
    }
}

static INLINE void ADD3_INL(Word *uu,Word *vv,Word *ww,Obj f,long i)
/* This internal inlined function adds i Words at *ww to the corresponding
 * Words at *vv and stores them to *uu. Characteristic 2 and odd 
 * characteristic are handled separately. */
{
    PREPARE_p(f);
    if (p == 2) {
        /* Characteristic 2: */
        register Word *uu_r = uu;
        register Word *vv_r = vv;
        register Word *ww_r = ww;
        register long i_r = i;
        while (--i_r >= 0) *uu_r++ = (*vv_r++) ^ (*ww_r++);
    } else {
        /* Odd characteristic: */
        register Word wo;
        register long i_r = i;
        register Word *uu_r = uu;
        register Word *vv_r = vv;
        register Word *ww_r = ww;
        PREPARE(f);
        while (--i_r >= 0) {
            wo = *vv_r++ + *ww_r++;
            *uu_r++ = REDUCE(wo);
        }
    }
}

static INLINE void MUL_INL(Word *vv,Obj f,Word s,long i)
/* This interal inlined function multiplies i Words at *vv by the scalar
 * s from the prime field (0 <= s < p). Special cases 0, 1, p-1, and 2
 * are handled especially fast. 
 * This code is extremely similar to the code of MUL1_INL, MUL2_INL, ADDMUL_INL,
 * and ADDMUL1_INL, so changes should be made accordingly. */
{
    PREPARE_p(f);
    /* Note that the characteristic 2 case is handled properly, because
     * s is either 0 or 1. */
    /* Handle scalar 1: */
    if (s == 1) return;
    /* Handle scalar 0: */
    if (s == 0)
        memset(vv,0,sizeof(Word) * i);
    else if (s == p - 1) { 
        /* Here we can calculate p-x for all entries x. */
        PREPARE(f);
        PREPARE_bpe(f);
        register Word pm1 = (mask >> (bitsperel - 1)) * p;
        register long i_r = i;
        register Word *vv_r = vv;
        register Word wo;
        while (--i_r >= 0) {
            wo = pm1 - *vv_r;
            *vv_r++ = REDUCE(wo);
        }
    } else {
        /* From here on we need some extra variables: */
        PREPARE(f);
        register Word wo,res;
        register Word *vv_r = vv;
        register long i_r = i;

        if (s == 2) { /* Here we can add v to v */
            while (--i_r >= 0) {
                wo = *vv_r << 1;
                *vv_r++ = REDUCE(wo);
            }
        } else {
            /* Now to the ugly case: */
            while (--i_r >= 0) {
                /* Handle one word: */
                register Word ss = s;
                wo = *vv_r;
                res = 0;
                while (1) {
                    if (ss & 1) {
                        res += wo; 
                        res = REDUCE(res);
                    }
                    ss >>= 1;
                    if (!ss) break;
                    wo <<= 1; 
                    wo = REDUCE(wo);
                }
                *vv_r++ = res;
            }
        }
    }
}

static INLINE Word MUL1_INL(Word wo,Obj f,Word s)
/* This interal inlined function multiplies 1 Word wo by the scalar
 * s from the prime field (0 <= s < p). Special cases 0, 1, p-1, and 2
 * are handled especially fast. 
 * This code is extremely similar to the code of MUL_INL, MUL2_INL, ADDMUL_INL,
 * and ADDMUL1_INL, so changes should be made accordingly. */
{
    PREPARE_p(f);
    /* Note that the characteristic 2 case is handled properly, because
     * s is either 0 or 1. */
    /* Handle scalar 1: */
    if (s == 1) return wo;
    /* Handle scalar 0: */
    else if (s == 0) return (Word) 0UL;
    else if (s == p - 1) { 
        /* Here we can calculate p-x for all entries x. */
        PREPARE(f);
        PREPARE_bpe(f);
        register Word pm1 = (mask >> (bitsperel - 1)) * p;
        wo = pm1 - wo;
        return REDUCE(wo);
    } else {
        /* From here on we need some extra variables: */
        PREPARE(f);

        if (s == 2) { /* Here we can add v to v */
            wo <<= 1;
            return REDUCE(wo);
        } else {
            /* Now to the ugly case: */
            register Word res = 0;
            while (1) {
                if (s & 1) {
                    res += wo; 
                    res = REDUCE(res);
                }
                s >>= 1;
                if (!s) break;
                wo <<= 1; 
                wo = REDUCE(wo);
            }
            return res;
        }
    }
}

static INLINE void MUL2_INL(Word *vv,Word *ww,Obj f,Word s,long i)
/* This interal inlined function multiplies i Words at *ww by the scalar
 * s from the prime field (0 <= s < p) and stores the result to *vv. 
 * Special cases 0, 1, p-1, and 2 are handled especially fast. 
 * This code is extremely similar to the code of MUL_INL, MUL1_INL, ADDMUL_INL,
 * and ADDMUL1_INL, so changes should be made accordingly. */
{
    PREPARE_p(f);
    /* Note that the characteristic 2 case is handled properly, because
     * s is either 0 or 1. */
    /* Handle scalar 1: */
    if (s == 1) memcpy(vv,ww,sizeof(Word) * i);
    /* Handle scalar 0: */
    else if (s == 0) memset(vv,0,sizeof(Word) * i);
    else if (s == p - 1) { 
        PREPARE(f);
        PREPARE_bpe(f);
        /* Here we can calculate p-x for all entries x. */
        register Word pm1 = (mask >> (bitsperel - 1)) * p;
        register long i_r = i;
        register Word *ww_r = ww;
        register Word *vv_r = vv;
        register Word wo;
        while (--i_r >= 0) {
            wo = pm1 - *ww_r++;
            *vv_r++ = REDUCE(wo);
        }
    } else {
        /* From here on we need some extra variables: */
        PREPARE(f);
        register Word wo,res;
        register long i_r = i;
        register Word *ww_r = ww;
        register Word *vv_r = vv;

        if (s == 2) { /* Here we can add v to v */
            while (--i_r >= 0) {
                wo = *ww_r++ << 1;
                *vv_r++ = REDUCE(wo);
            }
        } else {
            /* Now to the ugly case: */
            while (--i_r >= 0) {
                /* Handle one word: */
                register Word ss = s;
                wo = *ww_r++;
                res = 0;
                while (1) {
                    if (ss & 1) {
                        res += wo; 
                        res = REDUCE(res);
                    }
                    ss >>= 1;
                    if (!ss) break;
                    wo <<= 1; 
                    wo = REDUCE(wo);
                }
                *vv_r++ = res;
            }
        }
    }
}

static INLINE void ADDMUL_INL(Word *vv,Word *ww,Obj f,Word s,long i)
/* This interal inlined function multiplies i Words at *ww by the scalar
 * s from the prime field (0 <= s < p) and adds the result to *vv. 
 * Special cases 0, 1, p-1, and 2 are handled especially fast. 
 * This code is extremely similar to the code of MUL_INL, MUL1_INL, MUL2_INL, 
 * and ADDMUL1_INL, so changes should be made accordingly. */
{
    PREPARE_p(f);
    /* Note that the characteristic 2 case is handled properly, because s
     * is either 0 or 1. */
    /* Handle scalar 1: */
    if (s == 1) ADD2_INL(vv,ww,f,i);
    /* Handle scalar 0: */
    else if (s == 0) return;
    else if (s == p - 1) { 
        /* Here we can calculate p-x for all entries x. */
        PREPARE(f);
        PREPARE_bpe(f);
        register Word pm1 = (mask >> (bitsperel - 1)) * p;
        register Word wo;
        register long i_r = i;
        register Word *ww_r = ww;
        register Word *vv_r = vv;
        while (--i_r >= 0) {
            wo = (pm1 - *ww_r++) + *vv_r;
            *vv_r++ = REDUCE(wo);
        }
    } else {
        /* From here on we need some extra variables: */
        PREPARE(f);
        register Word wo,res;
        register long i_r = i;
        register Word *ww_r = ww;
        register Word *vv_r = vv;

        if (s == 2) { /* Here we can add v to v */
            while (--i_r >= 0) {
                wo = (*ww_r++ << 1);
                wo = REDUCE(wo) + *vv_r;
                *vv_r++ = REDUCE(wo);
            }
        } else {
            /* Now to the ugly case: */
            while (--i_r >= 0) {
                /* Handle one word: */
                register Word ss = s;
                wo = *ww_r++;
                res = 0;
                while (1) {
                    if (ss & 1) {
                        res += wo; 
                        res = REDUCE(res);
                    }
                    ss >>= 1;
                    if (!ss) break;
                    wo <<= 1; 
                    wo = REDUCE(wo);
                }
                wo = *vv_r + res;
                *vv_r++ = REDUCE(wo);
            }
        }
    }
}

static INLINE Word ADDMUL1_INL(Word vv,Word ww,Obj f,Word s)
/* This interal inlined function multiplies one Word ww by the scalar
 * s from the prime field (0 <= s < p) and adds the result to the Word vv. 
 * Special cases 0, 1, p-1, and 2 are handled especially fast. 
 * This code is extremely similar to the code of MUL_INL, MUL1_INL, MUL2_INL, 
 * and ADDMUL_INL, so changes should be made accordingly. */
{
    PREPARE_p(f);
    if (p == 2) {  /* Even characteristic: */
        return s == 1 ? (vv ^ ww) : vv;
    } else {  /* Odd characteristic: */
        PREPARE(f);
        /* Handle scalar 1: */
        if (s == 1) { 
            vv += ww;
            return REDUCE(vv);
        }
        /* Handle scalar 0: */
        else if (s == 0) return vv;
        else if (s == p - 1) { 
            /* Here we can calculate p-x for all entries x. */
            PREPARE_bpe(f);
            register Word pm1 = (mask >> (bitsperel - 1)) * p;
            vv = (pm1 - ww) + vv;
            return REDUCE(vv);
        } else {
            /* From here on we need some extra variables: */
            register Word res;

            if (s == 2) { /* Here we can add v to v */
                ww = ww << 1;
                vv = REDUCE(ww) + vv;
                return REDUCE(vv);
            } else {
                /* Now to the ugly case: */
                res = 0;
                while (1) {
                    if (s & 1) {
                        res += ww; 
                        res = REDUCE(res);
                    }
                    s >>= 1;
                    if (!s) break;
                    ww <<= 1; 
                    ww = REDUCE(ww);
                }
                vv += res;
                return REDUCE(vv);
            }
        }
    }
}

/*
 * Element access, internally, we distinguish between prime field and
 * extension field. Also the cases for different representations of
 * scalars are distinguished. This is later used in the functions for the
 * GAP level: 
 */

static INLINE Int CVEC_Itemp(Obj fi, Word *v, Int i)
{
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_maskp(fi);
    i--;   /* we are now 1 based */
    return (Int) ((v[i/elsperword] >> (bitsperel * (i % elsperword))) & maskp);
}

static INLINE void CVEC_Itemq(Obj fi, Word *v, Int i)
/* Writes scalar into scbuf. */
{
    Int *sc = scbuf;
    Int j;
    i--;    /* we are now 1 based */

    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_d(fi);
    PREPARE_maskp(fi);
    Int shift = (i % elsperword) * bitsperel;

    v += d * (i / elsperword);
    sclen = 1;  /* at least that */
    for (j = d;j > 0;j--) {
        *sc = ((*v++) >> shift) & maskp;
        if (*sc) sclen = (sc-scbuf)+1;
        sc++;
    }
}

static INLINE void CVEC_AssItemp(Obj fi, Word *v, Int i, Word sc)
{
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_maskp(fi);
    i--;   /* we are now 1 based */
    v += i / elsperword;
    register Int shift = bitsperel * (i % elsperword);
    *v = (*v & (WORDALLONE ^ (maskp << shift))) | (sc << shift);
}

static INLINE void CVEC_AssItemq(Obj fi, Word *v, Int i, Int *sc)
{
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_maskp(fi);
    PREPARE_d(fi);
    Int j;
    i--;   /* we are now 1 based */
    Int shift = (i % elsperword) * bitsperel;
    Word mask = WORDALLONE ^ (maskp << shift);

    v += d * (i / elsperword);
    for (j = d;j > 0;j--,v++) {
        *v = (*v & mask) | (((Word) (*sc++)) << shift);
    }
}

static INLINE Int CVEC_Firstnzp(Obj fi, Word *v, Int len)
/* Returns the index of the first non-zero element in the vector or len+1
 * if the vector is equal to zero. This is only for prime fields. */
{
    register PREPARE_epw(fi);
    register PREPARE_bpe(fi);
    register PREPARE_maskp(fi);
    register Word *p = v;
    register Int i = 1;
    register Int im = 0;  /* i mod elsperword */
    register Word w = 0;

    while (i <= len) {
        if (im == 0) {
            w = *p++;
            if (w == 0) {
                i += elsperword;
                continue;
            }
        }
        if (w & maskp) return i;
        w >>= bitsperel;
        i++;
        if (++im == elsperword) im = 0;
    }
    return len+1;
}

static INLINE Int CVEC_Firstnzq(Obj fi, Word *v, Int len, Int wordlen)
/* Returns the index of the first non-zero element in the vector or 0,
 * if the vector is equal to zero. This is for extension fields. */
{
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_d(fi);
    register Word *p = v;
    register Int i = 0;
    register Int im = 0;

    /* First look for the first non-vanishing word: */
    im = wordlen;
    while (*p == 0 && i < im) { p++; i++; }
    if (i >= im) return len+1;   /* Vector is zero */

    /* Go back to beginning of the d Words: */
    im = i % d;
    p -= im;
    i = ((i-im) / d) * elsperword + 1;
    {
        register PREPARE_maskp(fi);
        while (1) {
            for (im = d-1;im >= 0;im--) if (p[im] & maskp) return i;
            maskp <<= bitsperel;
            i++;
        }
    }
    /* Never reached: */
    return 0;
}

static INLINE Int CVEC_Lastnzp(Obj fi, Word *v, Int len)
/* Returns the index of the last non-zero element in the vector or 0
 * if the vector is equal to zero. This is only for prime fields. */
{
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_maskp(fi);
    Int i = len-1;   /* code used to be zero based */
    Word *p = v + i / elsperword;
    register Word w = *p--;
    register Word y = maskp << (bitsperel * (i % elsperword));
    if (w == 0) {
        i = i - i % elsperword - 1;
        y = maskp << (bitsperel * (elsperword-1));
        w = *p--;
    }
    /* Quickly step over zeros: */
    while (i >= 0 && w == 0) {
        i -= elsperword;
        w = *p--;
    }
    while (i >= 0) {
        if ((y & w) != 0) return i+1;   /* we use one based convention */
        y >>= bitsperel;
        if (i % elsperword == 0) {
            w = *p--;
            y = maskp << (bitsperel * (elsperword-1));
        }
        i--;
    }
    return 0;
}
    
static INLINE Int CVEC_Lastnzq(Obj fi, Word *v, Int len, Int wordlen)
/* Returns the index of the last non-zero element in the vector or 0,
 * if the vector is equal to zero. This is for extension fields. */
{
    register PREPARE_maskp(fi);
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    PREPARE_d(fi);
    register Word *p;
    register Int i;
    register Int im;
    register Word mask;

    /* First look for the first non-vanishing word: */
    i = wordlen-1;
    p = v + i;  /* The last word */
    while (*p == 0 && i >= 0) { p--; i--; }
    if (i < 0) return 0;   /* Vector is zero */

    /* Go back to beginning of the d Words: */
    im = i % d;
    p -= im;
    i = ((i-im) / d) * elsperword + elsperword - 1;
    mask = maskp << ((elsperword-1) * bitsperel);
    while (1) {
        for (im = d-1;im >= 0;im--) if (p[im] & mask) return i+1;
        mask >>= bitsperel;
        i--;
    }
    /* Never reached: */
    return 0;
} 


  /****************************************/
 /* Arithmetic for finite field scalars: */
/****************************************/

static INLINE Int invert_modp(Int s,Int p)
{
    /* This is a standard extended Euclidean algorithm for p and s.
     * We start with x:=p and y:=s and assume p>s>0. We always keep
     * a,a',b,b' such that x = a'*p+a*s and y = b'*p+b*s.
     * As we are only interested in b at the time when y divides x,
     * we do not bother to calculate a' and b'. 
     * The function returns the result between 1 and p-1. */
    ldiv_t qr;
    register Int a = 0;
    register Int b = 1;
    register Int c;
    register Int x = p;
    register Int y = s;
    while (1) {
        qr = ldiv(x,y);
        if (!qr.rem) {
            if (b < 0) return b+p;
            else       return b;
        }
        x = y;
        y = qr.rem;
        c = a-qr.quot*b;
        a = b;
        b = c;
    }
    return 0;   /* Never reached */
}

static INLINE Int mulmodp(Int a, Int b, Int p)
{
    return (Int)( (((long long)a) * b) % p);
}

/* Now some functions to put vector arithmetic up to the GAP level, here 
 * is an overview. Note that scalar multiplication with non-
 * prime-field values is implemented only here!             
 * For all of the following functions u,v, and w must be vectors over the
 * same field of equal length, already allocated:
 *   CVEC_ADD2(u,v,fr,to)       does u += v
 *   CVEC_ADD3(u,v,w)           does u = v+w
 *   CVEC_MUL1(v,s,fr,to)       does v *= s
 *   CVEC_MUL2(u,v,s)           does u = v*s
 *   CVEC_ADDMUL(u,v,s,fr,to)   does u += v*s
 * They all return nothing. Scalars s can be immediate integers or finite
 * field elements where appropriate. fr and to are hints, that all elements
 * outside the range [fr..to] in v are known to be zero, such that operations
 * can be left undone to save CPU time. The functions round fr and to to
 * word boundaries and apply the low level functions only within the bounds. 
 * The copying functions do not have this feature, because they have to
 * copy anyway. Both fr and to can be 0, which indicates 1 and length of
 * the vector respectively. */

static INLINE Int handle_hints(Obj cl, Obj fi, Obj fr, Obj to, 
                               Int *start, Int *end)
{
    Int st,en;
    PREPARE_epw(fi);
    PREPARE_d(fi);
    /* A return value of zero indicates failure. */
    if (!IS_INTOBJ(fr) || !IS_INTOBJ(to)) {
        return (Int) OurErrorBreakQuit(
                    "CVEC_handle_hints: fr and to must be immediate integers");
    }
    st = INT_INTOBJ(fr); 
    if (st == 0) st = 1;
    en = INT_INTOBJ(to); 
    if (en == 0) en = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
    if (en == -1) en = 1;    /* a scalar! */
    *start = ((st-1) / elsperword) * d;
    *end = ((en+elsperword-1)/elsperword) * d;
    return 1;
}

STATIC Obj ADD2(Obj self, Obj u, Obj v,Obj fr, Obj to)
{
    if (!IS_CVEC(u) || !IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_ADD2: no cvec");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        PREPARE_clfi(u,ucl,ufi);
        PREPARE_clfi(v,vcl,vfi);
        Int start = 0;  /* Initialization to keep the compiler happy. */
        Int end = 0;

        if (ufi != vfi || ELM_PLIST(ucl,IDX_len) != ELM_PLIST(vcl,IDX_len)) {
            return OurErrorBreakQuit(
                        "CVEC_ADD2: incompatible fields or lengths");
        }

        /* Handle hints: */
        if (!handle_hints(ucl,ufi,fr,to,&start,&end)) return 0L;

        ADD2_INL(DATA_CVEC(u)+start,DATA_CVEC(v)+start,ufi,end-start);
    }
    return 0L;
}

STATIC Obj ADD3(Obj self, Obj u, Obj v,Obj w)
{
    if (!IS_CVEC(u) || !IS_CVEC(v) || !IS_CVEC(w)) {
        return OurErrorBreakQuit("CVEC_ADD3: no cvec");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        PREPARE_clfi(u,ucl,ufi);
        PREPARE_clfi(v,vcl,vfi);
        PREPARE_clfi(w,wcl,wfi);

        if (ufi != vfi || vfi != wfi ||
            ELM_PLIST(ucl,IDX_len) != ELM_PLIST(vcl,IDX_len) ||
            ELM_PLIST(vcl,IDX_len) != ELM_PLIST(wcl,IDX_len)) {
            return OurErrorBreakQuit(
                        "CVEC_ADD3: incompatible fields or lengths");
        }
        ADD3_INL(DATA_CVEC(u),DATA_CVEC(v),DATA_CVEC(w),ufi,
             INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen)));
    }
    return 0L;
}

static INLINE Int *prepare_scalar(Obj fi, Obj s)
/* A NULL pointer indicates failure. */
{
    Int sc;
    PREPARE_p(fi);

    if (IS_FFE(s)) {
        PREPARE_tab1(fi);
        PREPARE_d(fi);
        PREPARE_q(fi);
        if (CHAR_FF(FLD_FFE(s)) == p && (d % DegreeFFE(s)) == 0) {
            sc = INT_INTOBJ(FFE_TO_INTOBJ(tab1, q, s));
        } else {
            return (Int *) OurErrorBreakQuit(
                    "prepare_scalar: scalar from wrong field");
        }
    } else if (IS_INTOBJ(s)) {
        sc = INT_INTOBJ(s);
        /* goes on below, case distinction! */
    } else if (IS_PLIST(s)) {   /* Coefficients are either FFEs from the 
                                   prime field or integers < p */
        /* Note that we assume that we only see FFEs in such a list, if
         * p < 65536 < q, such that tab1 and tab2 are created, but for the
         * prime field for exactly this purpose here! */
        PREPARE_tab1(fi);
        PREPARE_d(fi);
        Int len = LEN_PLIST(s);
        Obj ss;
        sclen = 0;
        /* Note that the length can be 0 <= len <= d, which is <= MAXDEGREE */
        if (len > d) {
            return (Int *) OurErrorBreakQuit(
                    "prepare_scalar: coefficient list longer than d");
        }
        if (len == 0) {
            scbuf[0] = 0;
            sclen = 1;
            return scbuf;
        }
        while (sclen < len) {
            ss = ELM_PLIST(s,sclen+1);
            if (IS_INTOBJ(ss)) scbuf[sclen++] = INT_INTOBJ(ss);
            else if (IS_FFE(ss) && CHAR_FF(FLD_FFE(ss)) == p &&
                     DEGR_FF(FLD_FFE(ss)) == 1) {
                if (VAL_FFE(ss) == 0)
                    scbuf[sclen++] = 0L;
                else
                    scbuf[sclen++] = INT_INTOBJ(ELM_PLIST(tab1,VAL_FFE(ss)+1));
            } else {
                return (Int *) OurErrorBreakQuit(
                       "prepare_scalar: strange object in coefficient list");
            }
        }
        /* Find length of scalar: */
        for (/* nothing here */;sclen > 1 && scbuf[sclen-1] == 0;sclen--);
        return scbuf;
    } else {
        return (Int *) OurErrorBreakQuit(
                "CVEC_MUL*: strange object as scalar");
    }
    /* Now the scalar is in sc as integer between 0..q-1 */
    /* We write out the p-adic expansion into our buffer: */
    sclen = 0;  /* Length should be at least one. */
    do {
        scbuf[sclen++] = sc % p;
        sc /= p;
    } while(sc); 
    return scbuf;
}

STATIC INLINE void MUL1_INT(Obj u, Obj ucl, Obj ufi, Int d, Int *sc,
                            Int start, Int end)
/* This does the multiplication in place in the non-prime field case.
 * This is an internal function, called by MUL1 and possibly during
 * other primitive operations that are implemented in the kernel.
 * Note that this function is not exported to the GAP level and that
 * the global variable sclen must contain the length of the scalar. */
{
  register Word *vv;
  Int c = end-start;
  Int i;
  Int j;
  Int ss;
  register Word wo;
  Word *bb;
  PREPARE_cp(ufi);

  /* Now the ugly case involving conway polynomials: */
  for (i = 0,vv = DATA_CVEC(u)+start;i < c;i += d,vv += d) {
      /* Do one chunk of elsperword elements from F_q: */

      ss = 0;  /* This counts the nonzero entries in the scalar */

      /* Make one copy for further processing: */
      for (j = d,bb = buf;j > 0;j--) *bb++ = *vv++; 
      vv -= d;  /* Go back to beginning. */
      /* Now handle prime field component: */
      MUL2_INL(vv,buf,ufi,*sc,d);
      while (++ss < sclen) {
          /* Now we have to multiply the content of the buffer by the 
           * polynomial x modulo the conway polynomial. This means
           * shifting the Words in the buffer one up and multiplying
           * the Word falling out by the conway polynomial. We do that
           * now. */
          wo = buf[d - 1];   /* Keep this one */
          for (j = d - 1; j > 0; j--) buf[j] = buf[j-1];
          buf[0] = 0UL;
          for (j = 0,bb = buf;j < d;j++,bb++) {
              *bb = ADDMUL1_INL(*bb,wo,ufi,cp[j]);
          }
          /* Now add a multiple of that to the result: */
          ADDMUL_INL(vv,buf,ufi,sc[ss],d);
      }
  } 
}

STATIC Obj MUL1(Obj self, Obj u, Obj s, Obj fr, Obj to)
{
    if (!IS_CVEC(u)) {
        return OurErrorBreakQuit("CVEC_MUL1: no cvec");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        PREPARE_clfi(u,ucl,ufi);
        PREPARE_d(ufi);
        Int *sc;
        Int start = 0;  /* Just to please modern C compilers */
        Int end = 0;

        /* Now handle the scalar: */
        sc = prepare_scalar(ufi,s); if (!sc) return 0L;
        
        /* Handle hints: */
        if (!handle_hints(ucl,ufi,fr,to,&start,&end)) return 0L;
            
        if (sclen == 1) {  /* Good luck, scalar is in prime field! */
            MUL_INL(DATA_CVEC(u)+start,ufi,*sc,end-start);
            return 0L;
        }
        MUL1_INT(u,ucl,ufi,d,sc,start,end);
    }
    return 0L;
}

STATIC INLINE void MUL2_INT(Obj u, Obj ucl, Obj ufi, Obj v, 
                            Int d, Int wordlen, Int *sc)
/* This does the multiplication with result somewhere else in the non-prime 
 * field case.
 * This is an internal function, called by MUL2 and possibly during
 * other primitive operations that are implemented in the kernel.
 * Note that this function is not exported to the GAP level and that
 * the global variable sclen must contain the length of the scalar. */
{
  register Word *vv;
  register Word *uu;
  Int i;
  Int j;
  Int ss;
  register Word wo;
  Word *bb;
  PREPARE_cp(ufi);

  /* Now the ugly case involving conway polynomials: */
  for (i = 0,uu = DATA_CVEC(u),vv = DATA_CVEC(v);i < wordlen;
       i += d,uu += d) {
      /* Do one chunk of elsperword elements from F_q: */

      ss = 0;  /* This counts the nonzero entries in the scalar */

      /* Make one copy for further processing: */
      for (j = d,bb = buf;j > 0;j--) *bb++ = *vv++; 
      /* Now handle prime field component: */
      MUL2_INL(uu,buf,ufi,*sc,d);
      while (++ss < sclen) {
          /* Now we have to multiply the content of the buffer by the 
           * polynomial x modulo the conway polynomial. This means
           * shifting the Words in the buffer one up and multiplying
           * the Word falling out by the conway polynomial. We do that
           * now. */
          wo = buf[d - 1];   /* Keep this one */
          for (j = d - 1; j > 0; j--) buf[j] = buf[j-1];
          buf[0] = 0UL;
          for (j = 0,bb = buf;j < d;j++,bb++) {
              *bb = ADDMUL1_INL(*bb,wo,ufi,cp[j]);
          }
          /* Now add a multiple of that to the result: */
          ADDMUL_INL(uu,buf,ufi,sc[ss],d);
      }
  } 
}

STATIC Obj MUL2(Obj self, Obj u, Obj v, Obj s, Obj fr, Obj to)
{
    if (!IS_CVEC(u) || !IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_MUL1: no cvec");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        PREPARE_clfi(u,ucl,ufi);
        PREPARE_d(ufi);
        PREPARE_clfi(v,vcl,vfi);
        Int wordlen = INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen));
        
        Int *sc;

        /* Check fields and lengths: */
        if (ufi != vfi || 
            ELM_PLIST(ucl,IDX_len) != ELM_PLIST(vcl,IDX_len)) {
            return OurErrorBreakQuit(
                        "CVEC_MUL2: incompatible fields or lengths");
        }
        
        /* Now handle the scalar: */
        sc = prepare_scalar(ufi,s); if (!sc) return 0L;
        
        if (sclen == 1) {  /* Good luck, scalar is in prime field! */
            MUL2_INL(DATA_CVEC(u),DATA_CVEC(v),ufi,*sc,wordlen);
            return 0L;
        }
        MUL2_INT(u,ucl,ufi,v,d,wordlen,sc);
    }
    return 0L;
}

STATIC INLINE void ADDMUL_INT(Obj u, Obj ucl, Obj ufi, Obj v,
                              Int d, Int *sc, Int start, Int end)
/* This does the multiplication plus addition to something else in the 
 * non-prime field case.
 * This is an internal function, called by ADDMUL and possibly during
 * other primitive operations that are implemented in the kernel.
 * Note that this function is not exported to the GAP level and that
 * the global variable sclen must contain the length of the scalar. */
{
  register Word *uu;
  register Word *vv;
  Int c = end-start;
  Int i;
  Int j;
  Int ss;
  register Word wo;
  Word *bb;
  PREPARE_cp(ufi);

  /* Now the ugly case involving conway polynomials: */
  for (i = 0,uu = DATA_CVEC(u)+start,vv = DATA_CVEC(v)+start;
       i < c;i += d,uu += d) {
      /* Do one chunk of elsperword elements from F_q: */

      ss = 0;  /* This counts the nonzero entries in the scalar */

      /* Make one copy for further processing: */
      for (j = d,bb = buf;j > 0;j--) *bb++ = *vv++; 
      /* Now handle prime field component: */
      ADDMUL_INL(uu,buf,ufi,*sc,d);
      while (++ss < sclen) {
          /* Now we have to multiply the content of the buffer by the 
           * polynomial x modulo the conway polynomial. This means
           * shifting the Words in the buffer one up and multiplying
           * the Word falling out by the conway polynomial. We do that
           * now. */
          wo = buf[d - 1];   /* Keep this one */
          for (j = d - 1; j > 0; j--) buf[j] = buf[j-1];
          buf[0] = 0UL;
          for (j = 0,bb = buf;j < d;j++,bb++) {
              *bb = ADDMUL1_INL(*bb,wo,ufi,cp[j]);
          }
          /* Now add a multiple of that to the result: */
          ADDMUL_INL(uu,buf,ufi,sc[ss],d);
      }
  } 
}

STATIC Obj ADDMUL(Obj self, Obj u, Obj v, Obj s, Obj fr, Obj to)
{
    if (!IS_CVEC(u) || !IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_ADDMUL: no cvec");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        PREPARE_clfi(u,ucl,ufi);
        PREPARE_d(ufi);
        PREPARE_clfi(v,vcl,vfi);
        Int *sc;
        Int start = 0; /* Just to please modern C compilers */
        Int end = 0;

        /* Check fields and lengths: */
        if (ufi != vfi || 
            ELM_PLIST(ucl,IDX_len) != ELM_PLIST(vcl,IDX_len)) {
            return OurErrorBreakQuit(
                        "CVEC_ADDMUL: incompatible fields or lengths");
        }
        
        /* Now handle the scalar: */
        sc = prepare_scalar(ufi,s); if (!sc) return 0L;
        
        /* Handle hints: */
        if (!handle_hints(ucl,ufi,fr,to,&start,&end)) return 0L;
            
        if (sclen == 1) {  /* Good luck, scalar is in prime field! */
            ADDMUL_INL(DATA_CVEC(u)+start,DATA_CVEC(v)+start,ufi,*sc,end-start);
            return 0L;
        }
        ADDMUL_INT(u,ucl,ufi,v,d,sc,start,end);
    }
    return 0L;
}

STATIC Obj ASS_CVEC(Obj self, Obj v, Obj pos, Obj s)
{
    Int i;
    Int *sc;
    if (!IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_ASS_CVEC: no cvec");
    }
    if (!IS_INTOBJ(pos)) {
        return OurErrorBreakQuit("CVEC_ASS_CVEC: no integer");
    }
    i = INT_INTOBJ(pos);
    {
        PREPARE_clfi(v,cl,fi);
        PREPARE_d(fi);
        Int j;

        /* Check bounds: */
        if (i < 1 || i > INT_INTOBJ(ELM_PLIST(cl,IDX_len))) {
            return OurErrorBreakQuit("CVEC_ASS_CVEC: out of bounds");
        }

        /* Now handle the scalar: */
        sc = prepare_scalar(fi,s); if (!sc) return 0L;
        
        /* Fill unused space: */
        for (j = sclen;j < d;scbuf[j++] = 0) ;
         
        if (d == 1)
            CVEC_AssItemp(fi, DATA_CVEC(v), i, (Word) (*sc));
        else
            CVEC_AssItemq(fi, DATA_CVEC(v), i, sc);
    }
    return 0L;
}

STATIC Obj ELM_CVEC(Obj self, Obj v, Obj pos)
{
    Int i;
    if (!IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_ELM_CVEC: no cvec");
    }
    if (!IS_INTOBJ(pos)) {
        return OurErrorBreakQuit("CVEC_ELM_CVEC: no integer");
    }
    i = INT_INTOBJ(pos);
    {
        /* The following are all pointers to masterpointers and thus
         * survive a garbage collection: */
        PREPARE_clfi(v,cl,fi);
        PREPARE_p(fi);
        PREPARE_d(fi);
        PREPARE_tab2(fi);
        Int size = INT_INTOBJ(ELM_PLIST(fi,IDX_size));
        Int s;
        Obj sca;

        /* Check bounds: */
        if (i < 1 || i > INT_INTOBJ(ELM_PLIST(cl,IDX_len))) {
            return OurErrorBreakQuit("CVEC_ELM_CVEC: out of bounds");
        }

        if (size >= 1 && d > 1) {  /* The field has more than 65536 elements */
            /* Let's allocate a new scalar first: */
            /* GARBAGE COLLECTION POSSIBLE */
            sca = NEW_PLIST( T_PLIST, d );
            SET_LEN_PLIST( sca, d );
            /* Here, a garbage collection might occur, however, all our
             * variables survive this, as they are pointers to master
             * pointers! */
        } else sca = 0L;  /* just to please the compiler */

        if (d == 1) {
            s = CVEC_Itemp(fi, DATA_CVEC(v), i);
            if (p < 65536)    /* we do GAP FFEs */
                return ELM_PLIST(tab2,s+1);
            else
                return INTOBJ_INT(s);
        } else {
            CVEC_Itemq(fi, DATA_CVEC(v), i);
            if (size == 0) {
                register Int i;
                for (s = 0,i = d-1;i >= 0;i--) s = s * p + scbuf[i];
                return ELM_PLIST(tab2,s+1);
            } else {
                if (p < 65536) {
                    for (i = 0;i < d;i++)
                        SET_ELM_PLIST(sca, i+1, ELM_PLIST(tab2,scbuf[i]+1));
                } else {
                    for (i = 0;i < d;i++)
                        SET_ELM_PLIST(sca, i+1, INTOBJ_INT(scbuf[i]));
                }
                return sca;
            }
        }
    }
    return 0L;
}

STATIC Obj POSITION_NONZERO_CVEC(Obj self, Obj v)
{
    if (!IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_POSITION_NONZERO_CVEC: no cvec");
    }
    {
        PREPARE_clfi(v,cl,fi);
        PREPARE_d(fi);
        if (d == 1) {
            return INTOBJ_INT(CVEC_Firstnzp(fi,DATA_CVEC(v),
                                      INT_INTOBJ(ELM_PLIST(cl,IDX_len))));
        } else {
            return INTOBJ_INT(CVEC_Firstnzq(fi,DATA_CVEC(v),
                                      INT_INTOBJ(ELM_PLIST(cl,IDX_len)),
                                      INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen))));
        }
    }
}

STATIC Obj POSITION_LAST_NONZERO_CVEC(Obj self, Obj v)
{
    if (!IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_POSITION_LAST_NONZERO_CVEC: no cvec");
    }
    {
        PREPARE_clfi(v,cl,fi);
        PREPARE_d(fi);
        if (d == 1) {
            return INTOBJ_INT(CVEC_Lastnzp(fi,DATA_CVEC(v),
                                      INT_INTOBJ(ELM_PLIST(cl,IDX_len))));
        } else {
            return INTOBJ_INT(CVEC_Lastnzq(fi,DATA_CVEC(v),
                                      INT_INTOBJ(ELM_PLIST(cl,IDX_len)),
                                      INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen))));
        }
    }
}
    
STATIC Obj CVEC_LT(Obj self, Obj u, Obj v)
{
    if (!IS_CVEC(u) || !IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_CVEC_LT: no cvecs");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        register Int wordlen;
        register Word *p1;
        register Word *p2;
        PREPARE_clfi(u,ucl,ufi);
        PREPARE_clfi(v,vcl,vfi);

        /* Check fields and lengths: */
        if (ufi != vfi || 
            ELM_PLIST(ucl,IDX_len) != ELM_PLIST(vcl,IDX_len)) {
            return OurErrorBreakQuit(
                        "CVEC_CVEC_LT: incompatible fields or lengths");
        }
        wordlen = INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen));
        p1 = DATA_CVEC(u);
        p2 = DATA_CVEC(v);
        while (wordlen > 0) {
            if (*p1 < *p2) return True;
            else if (*p1 > *p2) return False;
            p1++; p2++; wordlen--;
        }
        return False;
    }
    /* Never reached: */
    return 0L;
}

STATIC Obj CVEC_EQ(Obj self, Obj u, Obj v)
{
    if (!IS_CVEC(u) || !IS_CVEC(v)) {
        return OurErrorBreakQuit("CVEC_CVEC_EQ: no cvecs");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        register Int wordlen;
        register Word *p1;
        register Word *p2;
        PREPARE_clfi(u,ucl,ufi);
        PREPARE_clfi(v,vcl,vfi);

        /* Check fields and lengths: */
        if (ufi != vfi || 
            ELM_PLIST(ucl,IDX_len) != ELM_PLIST(vcl,IDX_len)) {
            return OurErrorBreakQuit(
                        "CVEC_CVEC_EQ: incompatible fields or lengths");
        }
        wordlen = INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen));
        p1 = DATA_CVEC(u);
        p2 = DATA_CVEC(v);
        while (wordlen > 0) {
            if (*p1 != *p2) return False;
            p1++; p2++; wordlen--;
        }
        return True;
    }
    /* Never reached: */
    return 0L;
}

STATIC Obj CVEC_ISZERO(Obj self, Obj u)
{
    if (!IS_CVEC(u)) {
        return OurErrorBreakQuit("CVEC_CVEC_EQ: no cvec");
    }
    {  /* The PREPAREs define new variables, so we want an extra block! */
        register Int wordlen;
        register Word *p;
        PREPARE_cl(u,ucl);

        wordlen = INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen));
        p = DATA_CVEC(u);
        while (wordlen > 0) {
            if (*p != 0) return False;
            p++; wordlen--;
        }
        return True;
    }
    /* Never reached: */
    return 0L;
}

STATIC Obj EXTRACT(Obj self, Obj v, Obj ii, Obj ll)
/* Extracts ll field elements from the vector self at position ii into
 * one Word in a convenient way, fitting to FILL_GREASE_TAB.
 * Here is an example with l = 3, d = 2:
 * (on a potential machine with 25 bits wide Words   :-) )
 * |-|---|---|---|333|222|111|---|---| lower memory addresses   ^
 * |-|---|---|---|666|555|444|---|---| higher memory addresses  V
 * ==>
 * |-|---|---|666|555|444|333|222|111|
 * Here is an example where i is such that not all field elements are in
 * the same word:
 * |-|222|111|---|---|---|---|---|---| lower memory addresses   ^
 * |-|555|444|---|---|---|---|---|---|
 * |-|---|---|---|---|---|---|---|333|
 * |-|---|---|---|---|---|---|---|666| higher memory addresses  V
 * ==> 
 * |-|---|---|666|555|444|333|222|111| 
 * Note that 111 and 444 encode the coefficients of the leftmost extension
 * field element in the vector, 222 and 555 the next one and 333 and 666
 * the third. 
 */ 
{
    /* No checks here, because performance is mission critical! */ 
    PREPARE_clfi(v,cl,fi);
    PREPARE_bpe(fi);
    PREPARE_epw(fi);
    PREPARE_d(fi);
    Int overflow = 0;      /* Set to 1 if we read over the end of the vector */
    Int i = INT_INTOBJ(ii)-1; /* we are 1-based in GAP, here we want 0-based */
    Int l = INT_INTOBJ(ll);
    Word res = 0UL;
    Word *p = DATA_CVEC(v) + (i / elsperword) * d;
    Int rest = i % elsperword;
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));

    if (((i+l-1)/elsperword)*d >= wordlen) overflow = 1;
    /* In that case we do not look over the last word, fortunately, this
     * can only happen in the ugly cases and we only have to skip the
     * second step. */

    /* First the prime field case: */
    if (d == 1) {
        /* First decide, whether we are in the simple or the ugly case: */
        if (rest + l <= elsperword) {
            /* Good luck, everything is in the same word! */
            Int s1 = rest * bitsperel;
            Word mask1 = (1UL << (l * bitsperel)) - 1UL;
            res = (*p >> s1) & mask1;
        } else {
            /* Urgh! Field elements are distributed among two Words! */
            Int nrinfirstword = elsperword - i % elsperword;
            Int s1 = rest * bitsperel;
            Word mask1 = (1UL << (bitsperel * nrinfirstword)) - 1UL;
            Int s2 = nrinfirstword * bitsperel;
            Word mask2 = (1UL << (bitsperel * (l-nrinfirstword))) - 1UL;
            if (overflow)
                res = (p[0] >> s1) & mask1;
            else
                res = ((p[0] >> s1) & mask1) | ((p[1] & mask2) << s2);
        }
    } else {   /* Extension field case: */
        int k;
        /* First decide, whether we are in the simple or the ugly case: */
        if (rest + l <= elsperword) {
            /* Good luck, everything is in the same word! */
            Int pos = 0;
            Int inc = l * bitsperel;
            Int s1 = rest * bitsperel;
            Word mask1 = (1UL << inc) - 1UL;
            for (k = d;k > 0;k--) {
                res |= ((*p++ >> s1) & mask1) << pos;
                pos += inc;
            }
        } else {
            /* Urgh! Field elements are distributed among two Words! */
            Int inc = l * bitsperel;
            Int pos = 0;
            Int nrinfirstword = elsperword - i % elsperword;
            Int s1 = rest * bitsperel;
            Word mask1 = (1UL << (bitsperel * nrinfirstword)) - 1UL;
            Int s2 = nrinfirstword * bitsperel;
            Word mask2 = (1UL << (bitsperel * (l-nrinfirstword))) - 1UL;
            if (overflow) {
                for (k = d;k > 0;k--) {
                    res |= ((*p++ >> s1) & mask1) << pos;
                    pos += inc;
                }
            } else {
                Word *q = p + d;
                for (k = d;k > 0;k--) {
                    res |= (((*p++ >> s1) & mask1) | ((*q++ & mask2) << s2)) 
                           << pos;
                    pos += inc;
                }
            }
        }
    }
    return INTOBJ_INT( (Int) res );
}

/* The following routines do the same as EXTRACT, but more efficiently,
 * if one needs many similar lookups. We separate initialization and lookup. */

static Int VecEx_d;
static Int VecEx_inc;
static Int VecEx_offset;
static Int VecEx_rest;
static Int VecEx_s1, VecEx_s2;
static Word VecEx_mask1, VecEx_mask2;
static Int VecEx_overflow;  /* see EXTRACT */

static Word (*Vector_Extract_Worker)(Word *data);
/* Call this for repeated lookup. */

static Word VecEx_Worker_prime_simple(Word *data)
/* Extraction worker for prime fields in the simple case. */
{
    register Word *p = data + VecEx_offset;
    return (*p >> VecEx_s1) & VecEx_mask1;
}

static Word VecEx_Worker_ext_simple(Word *data)
/* Extraction worker for extension fields in the simple case. */
{
    register Word res = 0;
    register Word *p = data + VecEx_offset;
    register Int pos = 0;
    register Int k;
    for (k = VecEx_d;k > 0;k--) {
        res |= ((*p++ >> VecEx_s1) & VecEx_mask1) << pos;
        pos += VecEx_inc;
    }
    return res;
}

static Word VecEx_Worker_prime_bad(Word *data)
/* Extraction worker for prime fields in the bad case. */
{
    register Word *p = data + VecEx_offset;
    if (VecEx_overflow)
        return (p[0] >> VecEx_s1) & VecEx_mask1;
    else
        return ((p[0] >> VecEx_s1) & VecEx_mask1) | 
               ((p[1] & VecEx_mask2) << VecEx_s2);
}

static Word VecEx_Worker_ext_bad(Word *data)
/* Extraction worker for extension fields in the bad case. */
{
    register Word res = 0;
    register Word *p = data + VecEx_offset;
    register Int pos = 0;
    register Int k;
    if (VecEx_overflow) {
        for (k = VecEx_d;k > 0;k--) {
            res |= ((*p++ >> VecEx_s1) & VecEx_mask1) << pos;
            pos += VecEx_inc;
        }
    } else {
        register Word *q = p + VecEx_d;
        for (k = VecEx_d;k > 0;k--) {
            res |= (((*p++ >> VecEx_s1) & VecEx_mask1) |
                    ((*q++ & VecEx_mask2) << VecEx_s2)) << pos;
            pos += VecEx_inc;
        }
    }
    return res;
}

STATIC Obj EXTRACT_INIT(Obj self, Obj v, Obj ii, Obj ll)
/* See comment of EXTRACT. This initializes the extraction routines.
 * Use Vector_Extract_Worker(Word *data) afterwards. */
{
    PREPARE_clfi(v,cl,fi);
    PREPARE_bpe(fi);
    PREPARE_epw(fi);
    PREPARE_d(fi);
    Int i = INT_INTOBJ(ii)-1;  /* 0 based from here */
    Int l = INT_INTOBJ(ll);
    Int rest = i % elsperword;
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));

    if (((i+l-1)/elsperword)*d >= wordlen) 
        VecEx_overflow = 1;
        /* In that case we do not look over the last word, fortunately, this
         * can only happen in the ugly cases and we only have to skip the
         * second step. */
    else
        VecEx_overflow = 0; 

    /* Some global static things to remember: */
    VecEx_d = d;
    VecEx_rest = rest;

    /* First the prime field case: */
    if (d == 1) {
        /* First decide, whether we are in the simple or the ugly case: */
        if (rest + l <= elsperword) {
            /* Good luck, everything is in the same word! */
            VecEx_s1 = rest * bitsperel;
            VecEx_mask1 = (1UL << (l * bitsperel)) - 1UL;
            VecEx_offset = i / elsperword;
            Vector_Extract_Worker = VecEx_Worker_prime_simple;
        } else {
            /* Urgh! Field elements are distributed among two Words! */
            int nrinfirstword = elsperword - i % elsperword;
            VecEx_s1 = rest * bitsperel;
            VecEx_mask1 = (1UL << (bitsperel * nrinfirstword)) - 1UL;
            VecEx_s2 = nrinfirstword * bitsperel;
            VecEx_mask2 = (1UL << (bitsperel * (l-nrinfirstword))) - 1UL;
            VecEx_offset = i / elsperword;
            Vector_Extract_Worker = VecEx_Worker_prime_bad;
        }
    } else {   /* Extension field case: */
        /* First decide, whether we are in the simple or the ugly case: */
        if (rest + l <= elsperword) {
            /* Good luck, everything is in the same word! */
            VecEx_inc = bitsperel * l;
            VecEx_s1 = rest * bitsperel;
            VecEx_mask1 = (1UL << (l * bitsperel)) - 1UL;
            VecEx_offset = (i / elsperword) * d;
            Vector_Extract_Worker = VecEx_Worker_ext_simple;
        } else {
            /* Urgh! Field elements are distributed among two Words! */
            int nrinfirstword = elsperword - rest;
            VecEx_inc = l * bitsperel;
            VecEx_s1 = rest * bitsperel;
            VecEx_mask1 = (1UL << (bitsperel * nrinfirstword)) - 1UL;
            VecEx_s2 = nrinfirstword * bitsperel;
            VecEx_mask2 = (1UL << (bitsperel * (l-nrinfirstword))) - 1UL;
            VecEx_offset = (i / elsperword) * d;
            Vector_Extract_Worker = VecEx_Worker_ext_bad;
        }
    }
    return 0L;  /* return nothing */
}

STATIC Obj EXTRACT_DOIT(Obj self, Obj v)
{
    /* Dereference the function pointer and call the worker routine: */
    return INTOBJ_INT( (Int) ( (*Vector_Extract_Worker)(DATA_CVEC(v)) ) );
}

STATIC Obj FILL_GREASE_TAB(Obj self, Obj li, Obj i, Obj l, Obj tab, Obj tablen,
                          Obj offset)
/* This function does the precalculation for greasing. This is the internal
 * version to be called from GAP. tab must already be long enough, no
 * checks are done. "Long enough" means that there must be room for
 * all pre-computed linear combinations and for l+1 more vectors, used
 * during the calculation. 
 * 
 * li     is a plist of vectors
 * i      is the start index in li
 * l      is the grease level 
 * tablen is the length of the tab to fill here
 * offset is the first index in tab used 
 * tab    is a plist to cache the linear combinations, length must already
 *        be long enough, such that from offset on there is room for
 *        tablen+l+1 vectors, all those places must be filled with vectors
 * 
 * of course, all vectors must be prepared and be compatible. */
{
    Int j;          /* A counter */
    Int jj;         /* Another one */
    Int k,kk,kkk;   /* Further small counters */
    Obj v = ELM_PLIST(li,INT_INTOBJ(i));  /* one of the vectors */
    PREPARE_clfi(v,cl,fi);
    PREPARE_p(fi);
    PREPARE_d(fi);
    Obj u,x,y;
    Int len;
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
    Int offs = INT_INTOBJ(offset);
    Int start,end;
    Int *sc;

    /* First put the zero vector into the tab at the beginning: */
    memset(DATA_CVEC(ELM_PLIST(tab,offs)),0,sizeof(Word)*wordlen);

    /* We have one more vectors for intermediate results: */
    u = ELM_PLIST(tab,offs+INT_INTOBJ(tablen));

    /* We copy the vectors such that we can mess around with them, note
     * that we have enough space in the grease tab: */
    for (kk = 0;kk < INT_INTOBJ(l);kk++) {
        if (INT_INTOBJ(i)+kk > LEN_PLIST(li))
            /* Take the zero vector: */
            memset(DATA_CVEC(ELM_PLIST(tab,offs+INT_INTOBJ(tablen)+1+kk)),
                   0,sizeof(Word)*wordlen);
        else
            memcpy(DATA_CVEC(ELM_PLIST(tab,offs+INT_INTOBJ(tablen)+1+kk)),
                   DATA_CVEC(ELM_PLIST(li,INT_INTOBJ(i)+kk)),
                   sizeof(Word)*wordlen);
    }

    len = 1;  /* Current length of vector list */
    for (k = 0;k < d;k++) {
        for (kk = 0;kk < INT_INTOBJ(l);kk++) {
            /* was: v = ELM_PLIST(li,INT_INTOBJ(i)+kk); */
            v = ELM_PLIST(tab,offs+INT_INTOBJ(tablen)+1+kk);
            /* memcpy(DATA_CVEC(w),DATA_CVEC(v),sizeof(Word)*wordlen); */
            /* MUL1(self,w,INTOBJ_INT(po),INTOBJ_INT(0),INTOBJ_INT(0)); */
            memcpy(DATA_CVEC(u),DATA_CVEC(v),sizeof(Word)*wordlen);
            jj = len;
            for (kkk = p-1;kkk > 0;kkk--) {
                for (j = 0;j < len;j++) {
                    x = ELM_PLIST(tab,offs + jj++);
                    y = ELM_PLIST(tab,offs + j);
                    ADD3_INL(DATA_CVEC(x),DATA_CVEC(u),DATA_CVEC(y),fi,wordlen);
                }
                if (kkk > 1) ADD2_INL(DATA_CVEC(u),DATA_CVEC(v),fi,wordlen);
            }
            len = jj;
        }
        /* Multiply all input vectors by the primitive root if we are not
         * yet done: */
        if (k < d-1) {
            /* Prepare for multiplication with scalar: */
            sc = prepare_scalar(fi,INTOBJ_INT(p));
            handle_hints(cl,fi,INTOBJ_INT(0),INTOBJ_INT(0),&start,&end);
            for (kk = 0;kk < INT_INTOBJ(l);kk++) {
                MUL1_INT(ELM_PLIST(tab,offs+INT_INTOBJ(tablen)+1+kk),
                         cl,fi,d,sc,start,end);
            }
        }
    }
    return 0L;
}

STATIC Obj PROD_CVEC_CMAT_NOGREASE(Obj self, Obj u, Obj v, Obj m)
/* Note that m is the list of vectors with first component unbound. */
{
    PREPARE_clfi(u,ucl,ufi);
    PREPARE_cl(v,vcl);
    PREPARE_d(ufi);
    Int k = INT_INTOBJ(ELM_PLIST(vcl,IDX_len));
    Int wordlen = INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen));
    Word *uu = DATA_CVEC(u);
    Word *vv = DATA_CVEC(v);
    register Int i;

    if (d == 1) {
        Int s;
        for (i = 1;i <= k;i++) {
            s = CVEC_Itemp(ufi,vv,i);
            if (s) ADDMUL_INL(uu,DATA_CVEC(ELM_PLIST(m,i+1)),ufi,s,wordlen);
        }
    } else {   /* d > 1 */
        for (i = 1;i <= k;i++) {
            CVEC_Itemq(ufi,vv,i);
            if (sclen != 1 || scbuf[0] != 0) 
                ADDMUL_INT(u, ucl, ufi, ELM_PLIST(m,i+1), d, scbuf, 0, wordlen);
        }
    }
    return 0L;
}

STATIC Obj PROD_CVEC_CMAT_GREASED(Obj self, Obj u, Obj v, Obj mgreasetab,
                                  Obj spreadtab, Obj glev)
{
    PREPARE_clfi(u,ucl,ufi);
    PREPARE_cl(v,vcl);
    Int k = INT_INTOBJ(ELM_PLIST(vcl,IDX_len));
    Int lev = INT_INTOBJ(glev);
    Int wordlen = INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen));
    Word *uu = DATA_CVEC(u);
    register Int i;
    register Int pos;
    register Obj w;
    register Word val;

    for (i = 1,pos = 1;pos <= k;pos += lev,i++) {
        val = INT_INTOBJ(EXTRACT(self, v, INTOBJ_INT(pos), glev));
        if (val != 0) {
            val = INT_INTOBJ(ELM_PLIST(spreadtab,val+1));
            w = ELM_PLIST(ELM_PLIST(mgreasetab,i),val);
            ADD2_INL(uu,DATA_CVEC(w),ufi,wordlen);
        }
    }
    return 0;
}

STATIC Obj PROD_CMAT_CMAT_GREASED(Obj self, Obj l, Obj m, Obj ngreasetab, 
                                  Obj spreadtab, Obj len, Obj glev)
{  /* See mult. routine "for two cmats, second one greased" in cvec.gi */
    Int k = INT_INTOBJ(len);
    Int t = LEN_PLIST(l)-1;
    Int lev = INT_INTOBJ(glev);
    Int pos;
    Int i;
    Int j;
    Int val;
    Obj v,w;

    v = ELM_PLIST(l,2);  /* we know that the result is not empty */
    {
        PREPARE_clfi(v,cl,fi);
        Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
        for (i = 1,pos = 1;pos <= k;pos += lev,i++) {
            EXTRACT_INIT(self,ELM_PLIST(m,2),INTOBJ_INT(pos),glev);
            for (j = 2;j <= t+1;j++) {
                val = (*Vector_Extract_Worker)(DATA_CVEC(ELM_PLIST(m,j)));
                if (val != 0) {
                    val = INT_INTOBJ(ELM_PLIST(spreadtab,val+1));
                    v = ELM_PLIST(l,j);
                    w = ELM_PLIST(ELM_PLIST(ngreasetab,i),val);
                    ADD2_INL(DATA_CVEC(v),DATA_CVEC(w),fi,wordlen);
                }
            }
        }
    }
    return 0L;
}

STATIC Obj PROD_CMAT_CMAT_WITHGREASE(Obj self, Obj l, Obj m, Obj n,
                                     Obj greasetab, Obj spreadtab, Obj glev)
{
    Int k = LEN_PLIST(n)-1;    /* the empty element in front! */
    Int t = LEN_PLIST(m)-1;    /* again */
    Int lev = INT_INTOBJ(glev);
    Int pos;
    Int j;
    Int val;
    Obj v,w;

    v = ELM_PLIST(l,2);  /* we know that the result is not empty */
    {
        PREPARE_clfi(v,cl,fi);
        Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
        for (pos = 1;pos <= k;pos += lev) {
            /* First fill the greasetab: */
            FILL_GREASE_TAB(self,n,INTOBJ_INT(pos+1),glev,greasetab,
                            INTOBJ_INT(LEN_PLIST(greasetab)-1-lev),
                            INTOBJ_INT(1));
            EXTRACT_INIT(self,ELM_PLIST(m,2),INTOBJ_INT(pos),glev);
            for (j = 2;j <= t+1;j++) {
                val = (*Vector_Extract_Worker)(DATA_CVEC(ELM_PLIST(m,j)));
                if (val != 0) {
                    val = INT_INTOBJ(ELM_PLIST(spreadtab,val+1));
                    v = ELM_PLIST(l,j);
                    w = ELM_PLIST(greasetab,val);
                    ADD2_INL(DATA_CVEC(v),DATA_CVEC(w),fi,wordlen);
                }
            }
        }
    }
    return 0L;
}

STATIC INLINE void ld(WORD *reg, Obj mat,
                      int wordscp, int wordscl, int rowscp)
{
    int i,j;
    WORD *data;
    for (i = 2;i <= rowscp+1;i++) {
        data = (WORD *) DATA_CVEC(ELM_PLIST(mat,i));
        for (j = wordscp; j > 0; j--) *reg++ = *data++;
        for (j = wordscl; j > 0; j--) *reg++ = 0UL;
    }
}

STATIC INLINE void st(Obj mat, WORD *reg,
                      int wordscp, int wordsskip, int rowscp)
{
    int i,j;
    WORD *data;
    for (i = 2;i <= rowscp+1;i++) {
        data = (WORD *) DATA_CVEC(ELM_PLIST(mat,i));
        for (j = wordscp; j > 0; j --) *data++ = *reg++;
        reg += wordsskip;
    }
}

STATIC Obj PROD_CMAT_CMAT_GF2_SMALL(Obj self, Obj l, Obj m, Obj n, Obj maxd)
{
    Int maxdim;
    PREPARE_cl(ELM_PLIST(m,2),clm);
    PREPARE_cl(ELM_PLIST(n,2),cln);
    Int rowsm = LEN_PLIST(m)-1;
    Int rowsn = LEN_PLIST(n)-1;
    int wordlenm,wordlenn;

    maxdim = INT_INTOBJ(maxd);
#ifndef SYS_IS_64_BIT
    if (maxdim <= 32) {
        ld(regs_32[0],m,1,0,rowsm);
        ld(regs_32[1],n,1,0,rowsn);
        gf2_grease_32(1,1);
        gf2_mul_32(2,0,rowsm,1);
        st(l,regs_32[2],1,0,rowsm);
    } else 
#endif
    if (maxdim <= 64) {
        wordlenm = INT_INTOBJ(ELM_PLIST(clm,IDX_wordlen));
        wordlenn = INT_INTOBJ(ELM_PLIST(cln,IDX_wordlen));
        ld(regs_64[0],m,wordlenm,WPR_64-wordlenm,rowsm);
        ld(regs_64[1],n,wordlenn,WPR_64-wordlenn,rowsn);
        gf2_grease_64(1,wordlenm);
        gf2_mul_64(2,0,rowsm,wordlenm);
        st(l,regs_64[2],wordlenn,WPR_64-wordlenn,rowsm);
    } else if (maxdim <= 128) {
        wordlenm = INT_INTOBJ(ELM_PLIST(clm,IDX_wordlen));
        wordlenn = INT_INTOBJ(ELM_PLIST(cln,IDX_wordlen));
        ld(regs_128[0],m,wordlenm,WPR_128-wordlenm,rowsm);
        ld(regs_128[1],n,wordlenn,WPR_128-wordlenn,rowsn);
        gf2_grease_128(1,wordlenm);
        gf2_mul_128(2,0,rowsm,wordlenm);
        st(l,regs_128[2],wordlenn,WPR_128-wordlenn,rowsm);
    } else if (maxdim <= 256) {
        wordlenm = INT_INTOBJ(ELM_PLIST(clm,IDX_wordlen));
        wordlenn = INT_INTOBJ(ELM_PLIST(cln,IDX_wordlen));
        ld(regs_256[0],m,wordlenm,WPR_256-wordlenm,rowsm);
        ld(regs_256[1],n,wordlenn,WPR_256-wordlenn,rowsn);
        gf2_grease_256(1,wordlenm);
        gf2_mul_256(2,0,rowsm,wordlenm);
        st(l,regs_256[2],wordlenn,WPR_256-wordlenn,rowsm);
    } else if (maxdim <= 512) {
        wordlenm = INT_INTOBJ(ELM_PLIST(clm,IDX_wordlen));
        wordlenn = INT_INTOBJ(ELM_PLIST(cln,IDX_wordlen));
        ld(regs_512[0],m,wordlenm,WPR_512-wordlenm,rowsm);
        ld(regs_512[1],n,wordlenn,WPR_512-wordlenn,rowsn);
        gf2_grease_512(1,wordlenm);
        gf2_mul_512(2,0,rowsm,wordlenm);
        st(l,regs_512[2],wordlenn,WPR_512-wordlenn,rowsm);
    }
    return 0L;
}

STATIC Obj PROD_CMAT_CMAT_NOGREASE(Obj self, Obj l, Obj m, Obj n)
{
    Int k = LEN_PLIST(n)-1;    /* the empty element in front! */
    Int t = LEN_PLIST(l)-1;    /* dito */
    Int pos;
    Int j;
    Int val;
    Obj u,v;

    v = ELM_PLIST(l,2);  /* we know that the result is not empty */
    {
        PREPARE_clfi(v,cl,fi);
        PREPARE_d(fi);
        Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
        if (d == 1) {
            for (j = 2;j <= t+1;j++) {
                u = ELM_PLIST(l,j);
                v = ELM_PLIST(m,j);
                for (pos = 1;pos <= k;pos++) {
                    val = CVEC_Itemp(fi,DATA_CVEC(v),pos);
                    if (val != 0) {
                        ADDMUL_INL(DATA_CVEC(u),DATA_CVEC(ELM_PLIST(n,pos+1)),
                                   fi,val,wordlen);
                    }
                }
            }
        } else {
            for (j = 2;j <= t+1;j++) {
                u = ELM_PLIST(l,j);
                v = ELM_PLIST(m,j);
                for (pos = 1;pos <= k;pos++) {
                    CVEC_Itemq(fi,DATA_CVEC(v),pos);
                    if (sclen != 1 || scbuf[0] != 0) {
                       ADDMUL_INT(u,cl,fi,ELM_PLIST(n,pos+1),d,scbuf,0,wordlen);
                    }
                }
            }
        }
    }
    return 0L;
}

STATIC Obj PROD_CMAT_CMAT_NOGREASE2(Obj self, Obj l, Obj m, Obj n)
{
    Int k = LEN_PLIST(n)-1;    /* the empty element in front! */
    Int t = LEN_PLIST(l)-1;    /* dito */
    Int pos;
    Int j;
    Int val;
    Obj u,v;
    Obj buf;

    v = ELM_PLIST(l,2);  /* we know that the result is not empty */
    {
        PREPARE_clfi(v,cl,fi);
        PREPARE_d(fi);
        Int size = INT_INTOBJ(ELM_PLIST(fi,IDX_size));
        Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
        if (d == 1) {
            /* A temporary buffer */
            /* GARBAGE COLLECTION POSSIBLE */
            buf = NEW_PLIST( T_PLIST, k );
            SET_LEN_PLIST( buf, k );
            for (j = 2;j <= t+1;j++) {
                u = ELM_PLIST(l,j);
                v = ELM_PLIST(m,j);
                CVEC_TO_INTREP(self,v,buf);
                for (pos = 1;pos <= k;pos++) {
                    val = INT_INTOBJ(ELM_PLIST(buf,pos));
                    if (val != 0) {
                        ADDMUL_INL(DATA_CVEC(u),DATA_CVEC(ELM_PLIST(n,pos+1)),
                                   fi,val,wordlen);
                    }
                }
            }
        } else {
            /* A temporary buffer */
            if (size < 2) {
                /* GARBAGE COLLECTION POSSIBLE */
                buf = NEW_PLIST( T_PLIST, k );
                SET_LEN_PLIST( buf, k );
                for (j = 2;j <= t+1;j++) {
                    u = ELM_PLIST(l,j);
                    v = ELM_PLIST(m,j);
                    CVEC_TO_INTREP(self,v,buf);
                    for (pos = 1;pos <= k;pos++) {
                        prepare_scalar(fi,ELM_PLIST(buf,pos));
                        if (sclen != 1 || scbuf[0] != 0) {
                            ADDMUL_INT(u,cl,fi,ELM_PLIST(n,pos+1),d,scbuf,
                                       0,wordlen);
                        }
                    }
                }
            } else {
                /* GARBAGE COLLECTION POSSIBLE */
                buf = NEW_PLIST( T_PLIST, k*d );
                SET_LEN_PLIST( buf, k*d );
                for (j = 2;j <= t+1;j++) {
                    register Int pos2;
                    u = ELM_PLIST(l,j);
                    v = ELM_PLIST(m,j);
                    CVEC_TO_INTREP(self,v,buf);
                    for (pos = 1,pos2 = 1;pos <= k;pos++) {
                        register Int i;
                        for (i = 0,sclen = 1;i < d;i++) {
                            val = (Word) INT_INTOBJ(ELM_PLIST(buf,pos2++));
                            scbuf[i] = val;
                            if (val) sclen = i+1;
                        }
                        if (sclen != 1 || scbuf[0] != 0) {
                            ADDMUL_INT(u,cl,fi,ELM_PLIST(n,pos+1),d,scbuf,
                                       0,wordlen);
                        }
                    }
                }
            }
        }
    }
    return 0L;
}

/* Our contribution to slicing: */

STATIC void SLICE_INT(Word *src, Word *dst, Int fr, Int le, Int to,
                      Int d, Int elsperword, Int bitsperel)
{
    Word stamask,endmask,upmask,domask,kupmask,kdomask;
    Int stanr,endnr,shiftl,shiftr;

    fr--;   /* from here on zero based! */
    to--;

    /* A hint: 
     * If you want to understand this, first read the case "shiftl=0", which
     * basically means, that source and target are word-aligned. Then look
     * at the general case. */

    /* Some precalculations: */
    shiftl = (to-fr) % elsperword;
    if (shiftl < 0) shiftl += elsperword;
    if (shiftl == 0) {  /* this is the easy case */
        stanr = elsperword - (fr % elsperword);
        if (stanr > le) stanr = le;
        if (stanr*bitsperel == 8*BYTESPERWORD)
            stamask = WORDALLONE;
        else
            stamask = ((1UL << (stanr*bitsperel))-1UL) 
                                  << ((fr % elsperword) * bitsperel);
        endnr = (fr+le) % elsperword;
        endmask = (1UL << (endnr*bitsperel))-1UL;
        {
            register Word *v = src + (fr/elsperword)*d;
            register Word *w = dst + (to/elsperword)*d;
            register Int i;

            /* We do the start bit in any case, even if stanr = elsperword! */
            for (i = d;i > 0;i--,v++,w++) 
                *w = (*w & (~stamask)) | (*v & stamask);
            le -= stanr;

            /* The following is the code to move one word at the position
             * pointed to by v to its destination: */
            while (le >= elsperword) {
                for (i = d;i > 0;i--,v++,w++) *w = *v;
                le -= elsperword;
            }
            
            /* Finally maybe we have to do the rest: */
            if (le > 0) 
                for (i = d;i > 0;i--,v++,w++) 
                    *w = (*w & (~endmask)) | (*v & endmask);
        }
    } else {   /* shiftl != 0 : the hard case */
        shiftr = elsperword-shiftl;
        shiftl *= bitsperel;
        shiftr *= bitsperel;
        kdomask = ((1UL << shiftl)-1UL);
        upmask = kdomask << shiftr;
        kdomask = ~kdomask;
        domask = (1UL << shiftr)-1UL;
        kupmask = ~(domask << shiftl);
        stanr = elsperword - (fr % elsperword);
        if (stanr > le) stanr = le;
        if (stanr*bitsperel == 8*BYTESPERWORD)
            stamask = WORDALLONE;
        else
            stamask = ((1UL << (stanr*bitsperel))-1UL) 
                                  << ((fr % elsperword) * bitsperel);
        endnr = (fr+le) % elsperword;
        endmask = (1UL << (endnr*bitsperel))-1UL;

        {
            register Word *v = src + (fr/elsperword)*d;
            register Word *w = dst + (to/elsperword)*d;
            register Int i;
            register Word wo;
            Word mask;

            /* Handle the case that position to is only hit by the upper
             * part of the Word containing fr. In that case we have to
             * decrement w by d Words. In that case the first few commands
             * do not write because of the "if (wo)" clause. */
            if ((fr % elsperword) * bitsperel >= shiftr) w -= d; 
            
            /* We do the start bit in any case, even if stanr = elsperword! */
            for (i = d;i > 0;i--,v++,w++) {
                mask = domask & stamask;
                wo = (*v & mask) << shiftl;
                *w = (*w & (~(mask << shiftl))) | wo;
                mask = upmask & stamask;
                wo = (*v & mask) >> shiftr;
                w[d] = (w[d] & (~(mask >> shiftr))) | wo;
            }
            le -= stanr;

            /* The following is the code to move one word at the position
             * pointed to by v to its destination: */
            while (le >= elsperword) {
                for (i = d;i > 0;i--,v++,w++) {
                    wo = (*v & domask) << shiftl;
                    *w = (*w & kupmask) | wo;
                    wo = (*v & upmask) >> shiftr;
                    w[d] = (w[d] & kdomask) | wo;
                }
                le -= elsperword;
            }
            
            /* Finally maybe we have to do the rest: */
            if (le > 0) {
                for (i = d;i > 0;i--,v++,w++) {
                    mask = domask & endmask;
                    wo = (*v & mask) << shiftl;
                    *w = (*w & (~(mask << shiftl))) | wo;
                    mask = upmask & endmask;
                    wo = (*v & mask) >> shiftr;
                    w[d] = (w[d] & (~(mask >> shiftr))) | wo;
                }
            }
        }
    }
}

STATIC Obj SLICE(Obj self, Obj src, Obj dst, Obj srcpos, Obj len, Obj dstpos)
/* No checks are done at all. src and dst must be cvecs over the same field and
 * 1 <= srcpos <= srcpos+len-1 <= Length(src) and
 * 1 <= dstpos <= dstpos+len-1 <= Length(dst) must hold. */
{
    PREPARE_clfi(src,cl,fi);
    PREPARE_d(fi);
    PREPARE_epw(fi);
    PREPARE_bpe(fi);

    SLICE_INT(DATA_CVEC(src),DATA_CVEC(dst),INT_INTOBJ(srcpos),INT_INTOBJ(len),
              INT_INTOBJ(dstpos),d,elsperword,bitsperel);
    return 0L;
}
    
STATIC Obj SLICE_LIST(Obj self, Obj src, Obj dst, Obj srcposs, Obj dstposs)
/* srcposs and dstposs may each be ranges or dense plain lists. src and
 * dst must be cvecs over the same field (this is not checked!).
 * srcposs and dstposs must be lists of integers within 
 * [1..Length(src)] and [1..Length(dst)] respectively. This is checked.
 * */
{
    PREPARE_clfi(src,cl,fi);
    PREPARE_clfi(dst,cldst,fidst);
    PREPARE_d(fi);
    seqaccess sasrc,sadst;
    register Int i,j;
    Word *so = DATA_CVEC(src);
    Word *de = DATA_CVEC(dst);
    Int srcl = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
    Int dstl = INT_INTOBJ(ELM_PLIST(cldst,IDX_len));
    Int a,b;

    if (fi != fidst) {  /* we can do IsIdenticalObj here! */
        return OurErrorBreakQuit("CVEC_SLICE_LIST: " 
                                 "cvecs not over same field");
    }

    if (IS_RANGE(srcposs) && GET_INC_RANGE(srcposs) == 1 &&
        IS_RANGE(dstposs) && GET_INC_RANGE(dstposs) == 1) {
        PREPARE_epw(fi);
        PREPARE_bpe(fi);
        Int srcpos,len,dstpos;
        srcpos = GET_LOW_RANGE(srcposs);
        len = GET_LEN_RANGE(srcposs);
        dstpos = GET_LOW_RANGE(dstposs);
        if (srcpos < 1 || srcpos+len-1 > srcl) {
            return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                     "source positions not valid");
        }
        if (dstpos < 1 || dstpos+len-1 > dstl) {
            return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                     "destination positions not valid");
        }
        SLICE_INT(DATA_CVEC(src),DATA_CVEC(dst),srcpos,len,dstpos,
                  d,elsperword,bitsperel);
        return 0L;
    }

    /* In the other case we have to do it the nasty way, we still have
     * four cases (note that ranges always have length at least 2!): */
    if (IS_RANGE(srcposs)) {
        if (IS_RANGE(dstposs)) {
            Int srcpos = GET_LOW_RANGE(srcposs);
            Int dstpos = GET_LOW_RANGE(dstposs);
            Int srcinc = GET_INC_RANGE(srcposs);
            Int dstinc = GET_INC_RANGE(dstposs);
            i = GET_LEN_RANGE(srcposs);
            if (srcpos < 1 || srcpos > srcl || dstpos < 1 || dstpos > dstl ||
                srcpos + (i-1)*srcinc < 1 || srcpos + (i-1)*srcinc > srcl ||
                dstpos + (i-1)*dstinc < 1 || dstpos + (i-1)*dstinc > dstl ||
                i != GET_LEN_RANGE(dstposs)) {
                return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                         "index out of range or unequal lengths");
            }
            INIT_SEQ_ACCESS(&sasrc,src,srcpos);
            INIT_SEQ_ACCESS(&sadst,dst,dstpos);
            while (1) {
                for (j = 0;j < d;j++) {
                    SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                }
                if (--i <= 0) break;
                srcpos += srcinc;
                dstpos += dstinc;
                MOVE_SEQ_ACCESS(&sasrc,srcpos);
                MOVE_SEQ_ACCESS(&sadst,dstpos);
            }
        } else {   /* dstposs is a dense plain list */
            Int srcpos = GET_LOW_RANGE(srcposs);
            Int srcinc = GET_INC_RANGE(srcposs);
            i = GET_LEN_RANGE(srcposs);
            if (srcpos < 1 || srcpos > srcl ||
                srcpos + (i-1)*srcinc < 1 || srcpos + (i-1)*srcinc > srcl ||
                GET_LEN_RANGE(srcposs) != LEN_PLIST(dstposs)) {
                return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                          "index out of range or unequal lengths");
            }
            INIT_SEQ_ACCESS(&sasrc,src,srcpos);
            a = INT_INTOBJ(ELM_PLIST(dstposs,1));
            if (a < 1 || a > dstl) {
                return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                         "index out of range");
            }
            INIT_SEQ_ACCESS(&sadst,dst,a);
            i = 1;
            while (1) {
                for (j = 0;j < d;j++) {
                    SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                }
                if (++i > LEN_PLIST(dstposs)) break;
                srcpos += srcinc;
                MOVE_SEQ_ACCESS(&sasrc,srcpos);
                a = INT_INTOBJ(ELM_PLIST(dstposs,i));
                if (a < 1 || a > dstl) {
                    return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                             "index out of range");
                }
                MOVE_SEQ_ACCESS(&sadst,a);
            }
        }
    } else {   /* srcposs is a dense plain list */
        if (IS_RANGE(dstposs)) {
            Int dstpos = GET_LOW_RANGE(dstposs);
            Int dstinc = GET_INC_RANGE(dstposs);
            i = GET_LEN_RANGE(dstposs);
            if (dstpos < 1 || dstpos > dstl ||
                dstpos + (i-1)*dstinc < 1 || dstpos + (i-1)*dstinc > dstl ||
                GET_LEN_RANGE(dstposs) != LEN_PLIST(srcposs)) {
                return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                          "index out of range or unequal lengths");
            }
            a = INT_INTOBJ(ELM_PLIST(srcposs,1));
            if (a < 1 || a > srcl) {
                return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                         "index out of range");
            }
            INIT_SEQ_ACCESS(&sasrc,src,a);
            INIT_SEQ_ACCESS(&sadst,dst,dstpos);
            i = 1;
            while (1) {
                for (j = 0;j < d;j++) {
                    SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                }
                if (++i > LEN_PLIST(srcposs)) break;
                dstpos += dstinc;
                MOVE_SEQ_ACCESS(&sadst,dstpos);
                a = INT_INTOBJ(ELM_PLIST(srcposs,i));
                if (a < 1 || a > srcl) {
                    return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                             "index out of range");
                }
                MOVE_SEQ_ACCESS(&sasrc,a);
            }
        } else {   /* dstposs is a dense plain list */
            if (LEN_PLIST(srcposs) != LEN_PLIST(dstposs)) {
                return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                         "lengths not equal");
            }
            if (LEN_PLIST(srcposs) == 0) return 0L;
            a = INT_INTOBJ(ELM_PLIST(srcposs,1));
            b = INT_INTOBJ(ELM_PLIST(dstposs,1));
            if (a < 1 || a > srcl || b < 1 || b > dstl) {
                return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                         "index out of range");
            }
            INIT_SEQ_ACCESS(&sasrc,src,a);
            INIT_SEQ_ACCESS(&sadst,dst,b);
            i = 1;
            while (1) {
                for (j = 0;j < d;j++) {
                    SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                }
                if (++i > LEN_PLIST(srcposs)) break;
                a = INT_INTOBJ(ELM_PLIST(srcposs,i));
                b = INT_INTOBJ(ELM_PLIST(dstposs,i));
                if (a < 1 || a > srcl || b < 1 || b > dstl) {
                    return OurErrorBreakQuit("CVEC_SLICE_LIST: "
                                             "index out of range");
                }
                MOVE_SEQ_ACCESS(&sasrc,a);
                MOVE_SEQ_ACCESS(&sadst,b);
            }
        }
    }

    return 0L;
}

STATIC Obj COPY_SUBMATRIX(Obj self, Obj src, Obj dst, 
     Obj srcrows, Obj dstrows, Obj srcposs, Obj dstposs)
/* srcposs and dstposs may each be ranges or dense plain lists. src and
 * dst must be lists of cvecs over the same field (this is not checked!).
 * Position 1 is not used as for cmats. So position 2 is the first row.
 * srcposs and dstposs must be lists of integers within 
 * [1..Length(src[1])] and [1..Length(dst[1])] respectively. This is checked.
 * srcrows and dstrows must be plain lists of integers in the ranges
 * [1..Length(src)] and [1..Length(dst)] respectively. This is not checked.
 * src and dst must have exactly one row! */
{
    PREPARE_clfi(ELM_PLIST(src,2),cl,fi);
    PREPARE_clfi(ELM_PLIST(dst,2),cldst,fidst);
    PREPARE_d(fi);
    seqaccess sasrc,sadst;
    register Int i,j;
    Int srcl = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
    Int dstl = INT_INTOBJ(ELM_PLIST(cldst,IDX_len));
    Int a,b;
    Int k;
    Word *so,*de;

    if (fi != fidst) {  /* we can do IsIdenticalObj here! */
        return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: " 
                                 "cvecs not over same field");
    }

    if (IS_RANGE(srcposs) && GET_INC_RANGE(srcposs) == 1 &&
        IS_RANGE(dstposs) && GET_INC_RANGE(dstposs) == 1) {
        PREPARE_epw(fi);
        PREPARE_bpe(fi);
        Int srcpos,len,dstpos;
        srcpos = GET_LOW_RANGE(srcposs);
        len = GET_LEN_RANGE(srcposs);
        dstpos = GET_LOW_RANGE(dstposs);
        if (srcpos < 1 || srcpos+len-1 > srcl) {
            return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                     "source positions not valid");
        }
        if (dstpos < 1 || dstpos+len-1 > dstl) {
            return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                     "destination positions not valid");
        }
        for (k = 1;k <= LEN_PLIST(srcrows);k++) {
            so = DATA_CVEC(ELM_PLIST(src,INT_INTOBJ(ELM_PLIST(srcrows,k))+1));
            de = DATA_CVEC(ELM_PLIST(dst,INT_INTOBJ(ELM_PLIST(dstrows,k))+1));
            SLICE_INT(so,de,srcpos,len,dstpos,d,elsperword,bitsperel);
        }
        return 0L;
    }

    /* In the other case we have to do it the nasty way, we still have
     * four cases (note that ranges always have length at least 2!): */
    if (IS_RANGE(srcposs)) {
        if (IS_RANGE(dstposs)) {
            Int srcpos = GET_LOW_RANGE(srcposs);
            Int dstpos = GET_LOW_RANGE(dstposs);
            Int srcinc = GET_INC_RANGE(srcposs);
            Int dstinc = GET_INC_RANGE(dstposs);
            i = GET_LEN_RANGE(srcposs);
            if (srcpos < 1 || srcpos > srcl || dstpos < 1 || dstpos > dstl ||
                srcpos + (i-1)*srcinc < 1 || srcpos + (i-1)*srcinc > srcl ||
                dstpos + (i-1)*dstinc < 1 || dstpos + (i-1)*dstinc > dstl ||
                i != GET_LEN_RANGE(dstposs)) {
                return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                         "index out of range or unequal lengths");
            }
            INIT_SEQ_ACCESS(&sasrc,ELM_PLIST(src,2),srcpos);
            INIT_SEQ_ACCESS(&sadst,ELM_PLIST(dst,2),dstpos);
            while (1) {
                for (k = 1;k <= LEN_PLIST(srcrows);k++) {
                    so = DATA_CVEC(ELM_PLIST(src,
                                       INT_INTOBJ(ELM_PLIST(srcrows,k))+1));
                    de = DATA_CVEC(ELM_PLIST(dst,
                                       INT_INTOBJ(ELM_PLIST(dstrows,k))+1));
                    for (j = 0;j < d;j++) {
                        SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                    }
                }
                if (--i <= 0) break;
                srcpos += srcinc;
                dstpos += dstinc;
                MOVE_SEQ_ACCESS(&sasrc,srcpos);
                MOVE_SEQ_ACCESS(&sadst,dstpos);
            }
        } else {   /* dstposs is a dense plain list */
            Int srcpos = GET_LOW_RANGE(srcposs);
            Int srcinc = GET_INC_RANGE(srcposs);
            i = GET_LEN_RANGE(srcposs);
            if (srcpos < 1 || srcpos > srcl ||
                srcpos + (i-1)*srcinc < 1 || srcpos + (i-1)*srcinc > srcl ||
                GET_LEN_RANGE(srcposs) != LEN_PLIST(dstposs)) {
                return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                          "index out of range or unequal lengths");
            }
            INIT_SEQ_ACCESS(&sasrc,ELM_PLIST(src,2),srcpos);
            a = INT_INTOBJ(ELM_PLIST(dstposs,1));
            if (a < 1 || a > dstl) {
                return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                         "index out of range");
            }
            INIT_SEQ_ACCESS(&sadst,ELM_PLIST(dst,2),a);
            i = 1;
            while (1) {
                for (k = 1;k <= LEN_PLIST(srcrows);k++) {
                    so = DATA_CVEC(ELM_PLIST(src,
                                       INT_INTOBJ(ELM_PLIST(srcrows,k))+1));
                    de = DATA_CVEC(ELM_PLIST(dst,
                                       INT_INTOBJ(ELM_PLIST(dstrows,k))+1));
                    for (j = 0;j < d;j++) {
                        SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                    }
                }
                if (++i > LEN_PLIST(dstposs)) break;
                srcpos += srcinc;
                MOVE_SEQ_ACCESS(&sasrc,srcpos);
                a = INT_INTOBJ(ELM_PLIST(dstposs,i));
                if (a < 1 || a > dstl) {
                    return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                             "index out of range");
                }
                MOVE_SEQ_ACCESS(&sadst,a);
            }
        }
    } else {   /* srcposs is a dense plain list */
        if (IS_RANGE(dstposs)) {
            Int dstpos = GET_LOW_RANGE(dstposs);
            Int dstinc = GET_INC_RANGE(dstposs);
            i = GET_LEN_RANGE(dstposs);
            if (dstpos < 1 || dstpos > dstl ||
                dstpos + (i-1)*dstinc < 1 || dstpos + (i-1)*dstinc > dstl ||
                GET_LEN_RANGE(dstposs) != LEN_PLIST(srcposs)) {
                return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                          "index out of range or unequal lengths");
            }
            a = INT_INTOBJ(ELM_PLIST(srcposs,1));
            if (a < 1 || a > srcl) {
                return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                         "index out of range");
            }
            INIT_SEQ_ACCESS(&sasrc,ELM_PLIST(src,2),a);
            INIT_SEQ_ACCESS(&sadst,ELM_PLIST(dst,2),dstpos);
            i = 1;
            while (1) {
                for (k = 1;k <= LEN_PLIST(srcrows);k++) {
                    so = DATA_CVEC(ELM_PLIST(src,
                                       INT_INTOBJ(ELM_PLIST(srcrows,k))+1));
                    de = DATA_CVEC(ELM_PLIST(dst,
                                       INT_INTOBJ(ELM_PLIST(dstrows,k))+1));
                    for (j = 0;j < d;j++) {
                        SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                    }
                }
                if (++i > LEN_PLIST(srcposs)) break;
                dstpos += dstinc;
                MOVE_SEQ_ACCESS(&sadst,dstpos);
                a = INT_INTOBJ(ELM_PLIST(srcposs,i));
                if (a < 1 || a > srcl) {
                    return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                             "index out of range");
                }
                MOVE_SEQ_ACCESS(&sasrc,a);
            }
        } else {   /* dstposs is a dense plain list */
            if (LEN_PLIST(srcposs) != LEN_PLIST(dstposs)) {
                return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                         "lengths not equal");
            }
            if (LEN_PLIST(srcposs) == 0) return 0L;
            a = INT_INTOBJ(ELM_PLIST(srcposs,1));
            b = INT_INTOBJ(ELM_PLIST(dstposs,1));
            if (a < 1 || a > srcl || b < 1 || b > dstl) {
                return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                         "index out of range");
            }
            INIT_SEQ_ACCESS(&sasrc,ELM_PLIST(src,2),a);
            INIT_SEQ_ACCESS(&sadst,ELM_PLIST(dst,2),b);
            i = 1;
            while (1) {
                for (k = 1;k <= LEN_PLIST(srcrows);k++) {
                    so = DATA_CVEC(ELM_PLIST(src,
                                       INT_INTOBJ(ELM_PLIST(srcrows,k))+1));
                    de = DATA_CVEC(ELM_PLIST(dst,
                                       INT_INTOBJ(ELM_PLIST(dstrows,k))+1));
                    for (j = 0;j < d;j++) {
                        SET_VEC_ELM(&sadst,de,j,GET_VEC_ELM(&sasrc,so,j));
                    }
                }
                if (++i > LEN_PLIST(srcposs)) break;
                a = INT_INTOBJ(ELM_PLIST(srcposs,i));
                b = INT_INTOBJ(ELM_PLIST(dstposs,i));
                if (a < 1 || a > srcl || b < 1 || b > dstl) {
                    return OurErrorBreakQuit("CVEC_COPY_SUBMATRIX: "
                                             "index out of range");
                }
                MOVE_SEQ_ACCESS(&sasrc,a);
                MOVE_SEQ_ACCESS(&sadst,b);
            }
        }
    }

    return 0L;
}

STATIC Obj CVEC_TO_EXTREP(Obj self, Obj v, Obj s)
{
    PREPARE_clfi(v,cl,fi);
    PREPARE_d(fi);
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));

    /* Unfortunately there are four cases: LITTLE/BIG ENDIAN, 32bit/64bit: */
#ifndef SYS_IS_64_BIT
    /* Here we assume 32bit, see TEST_ASSUMPTIONS. */

    /* To get rid of a warning: */
    d=d;

    /* GARBAGE COLLECTION POSSIBLE */
    GrowString(s,wordlen*BYTESPERWORD);
    SET_LEN_STRING(s,wordlen*BYTESPERWORD);

# if __BYTE_ORDER == __LITTLE_ENDIAN
    /* We are on a little endian machine, we just copy: */
    memcpy(CHARS_STRING(s),DATA_CVEC(v),wordlen*BYTESPERWORD);
# else
    /* Big endian machine, swap bytes: */
    register unsigned char *p;
    register unsigned char *q;
    /* Do a byte copy: */
    p = (unsigned char *) DATA_CVEC(v);
    q = (unsigned char *) CHARS_STRING(s);
    while (--wordlen >= 0) {
        q[3] = p[0];
        q[2] = p[1];
        q[1] = p[2];
        q[0] = p[3];
        p += 4;
        q += 4;
    }
# endif
    
#else
    /* From here on 64bit machine, we need some more variables: */
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    Int len = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
    /* How would things be in a 32bit world? */
    Int elsperword32 = elsperword/2;
    /* note that elsperword is always even on 64bit machines! */
    Word wordlen32 = (len + elsperword32 - 1)/elsperword32;
    Word mask = (1UL << (elsperword32 * bitsperel))-1UL;
    register Word *p;
    register Word wo;
    register int shift = elsperword32 * bitsperel;
    register int k;

# if __BYTE_ORDER == __LITTLE_ENDIAN
    /* We are on a little endian machine, we copy, but have to
     * work for upper halves and lower halves separatedly. */

    register Word32 *q;

    wordlen /= d;   /* We remember the factor d ourselves! */

    /* GARBAGE COLLECTION POSSIBLE */
    GrowString(s,wordlen32*4*d);
    SET_LEN_STRING(s,wordlen32*4*d);

    if ((wordlen32 & 1) != 0) wordlen--;  /* Do not copy last word */
    p = DATA_CVEC(v);
    q = (Word32 *) CHARS_STRING(s);
    while (--wordlen >= 0) {
        for (k = d-1;k >= 0;k--) {
            wo = *p++;
            *q = (Word32) (wo & mask);
            q[d] = (Word32) (wo >> shift);
            q++;
        }
        q += d;   /* Skip upper halves in result */
    }
    if ((wordlen32 & 1) != 0) {  /* Handle last half of word: */
        for (k = d-1;k >= 0;k--)
            *q++ = (Word32) (*p++ & mask);
    }
# else
    /* Big endian machine with 64 bit, now it becomes ugly! */
    /* We have to work for upper halves and lower halves separatedly and
     * to swap bytes around! */

    register Word32 wo32;
    register unsigned char *q;
    
    wordlen /= d;   /* We remember the factor d ourselves! */
    
    /* GARBAGE COLLECTION POSSIBLE */
    GrowString(s,wordlen32*4*d);
    SET_LEN_STRING(s,wordlen32*4*d);

    if (wordlen32 & 1 != 0) wordlen--;  /* Do not copy last word */
    p = DATA_CVEC(v);
    q = (unsigned char *) CHARS_STRING(s);
    while (--wordlen >= 0) {
        for (k = d-1;k >= 0;k--) {
            wo = *p++;
            wo32 = (Word32) (wo & mask);
            *q = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[1] = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[2] = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[3] = (unsigned char) (wo32 & 0xff);
            q += d * 4;
            wo32 = (Word32) (wo >> shift);
            *q = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[1] = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[2] = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[3] = (unsigned char) (wo32 & 0xff);
            q -= d * 4 - 4;
        }
        q += d*4;   /* Skip upper halves in result */
    }
    if (wordlen32 & 1 != 0) {  /* Handle last half of word: */
        for (k = d-1;k >= 0;k--) {
            wo32 = (Word32) (*p++ & mask);
            *q = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[1] = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[2] = (unsigned char) (wo32 & 0xff); wo32 >>= 8;
            q[3] = (unsigned char) (wo32 & 0xff);
            q += 4;
        }
    }
# endif
#endif
    return 0L;
}

STATIC Obj EXTREP_TO_CVEC(Obj self, Obj s, Obj v)
{
    PREPARE_clfi(v,cl,fi);
    PREPARE_d(fi);
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));

    /* Unfortunately there are four cases: LITTLE/BIG ENDIAN, 32bit/64bit: */
#ifndef SYS_IS_64_BIT
    /* Here we assume 32bit, see TEST_ASSUMPTIONS. */

    /* To get rid of a warning: */
    d=d;

# if __BYTE_ORDER == __LITTLE_ENDIAN
    /* We are on a little endian machine, we just copy: */
    memcpy(DATA_CVEC(v),CHARS_STRING(s),wordlen*BYTESPERWORD);
# else
    /* Big endian machine, swap bytes: */
    register unsigned char *p;
    register unsigned char *q;
    /* Do a byte copy: */
    p = (unsigned char *) CHARS_STRING(s);
    q = (unsigned char *) DATA_CVEC(v);
    while (--wordlen >= 0) {
        q[3] = p[0];
        q[2] = p[1];
        q[1] = p[2];
        q[0] = p[3];
        p += 4;
        q += 4;
    }
# endif
    
#else
    /* From here on 64bit machine, we need some more variables: */
    PREPARE_epw(fi);
    PREPARE_bpe(fi);
    Int len = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
    /* How would things be in a 32bit world? */
    Int elsperword32 = elsperword/2;
    /* note that elsperword is always even on 64bit machines! */
    Word wordlen32 = (len + elsperword32 - 1)/elsperword32;
    register Word *q;
    register int shift = elsperword32 * bitsperel;
    register int k;

# if __BYTE_ORDER == __LITTLE_ENDIAN
    /* We are on a little endian machine, we copy, but have to
     * work for upper halves and lower halves separatedly. */

    register Word32 *p;

    wordlen /= d;   /* We remember the factor d ourselves! */

    if ((wordlen32 & 1) != 0) wordlen--;  /* Do not copy last word */
    p = (Word32 *) CHARS_STRING(s);
    q = DATA_CVEC(v);
    while (--wordlen >= 0) {
        for (k = d-1;k >= 0;k--) {
            *q++ = (((Word)(p[d])) << shift) | (Word) (*p);
            p++;
        }
        p += d;   /* Skip upper halves in result */
    }
    if ((wordlen32 & 1) != 0) {  /* Handle last half of word: */
        for (k = d-1;k >= 0;k--)
            *q++ = (Word) (*p++);
    }
# else
    /* Big endian machine with 64 bit, now it becomes ugly! */
    /* We have to work for upper halves and lower halves separatedly and
     * to swap bytes around! */

    register Word32 wo32;
    register unsigned char *p;
    register Word wo;
    
    wordlen /= d;   /* We remember the factor d ourselves! */
    
    if (wordlen32 & 1 != 0) wordlen--;  /* Do not copy last word */
    p = (unsigned char *) CHARS_STRING(s);
    q = DATA_CVEC(v);
    while (--wordlen >= 0) {
        for (k = d-1;k >= 0;k--) {
            wo = ( ( ( ( ( (Word)(p[3]) << 8)
                         | (Word)(p[2]) ) << 8)
                     | (Word)(p[1]) ) << 8)
                 | (Word)(p[0]);
            p += d * 4;
            wo |= ( ( ( ( ( ( (Word)(p[3]) << 8)
                            | (Word)(p[2]) ) << 8)
                        | (Word)(p[1]) ) << 8)
                    | (Word)(p[0]) ) << shift;
            p -= d * 4 - 4;
            *q++ = wo;
        }
        p += d*4;   /* Skip upper halves in result */
    }
    if (wordlen32 & 1 != 0) {  /* Handle last half of word: */
        for (k = d-1;k >= 0;k--) {
            *q++ = ( ( ( ( ( (Word)(p[3]) << 8)
                           | (Word)(p[2]) ) << 8)
                       | (Word)(p[1]) ) << 8)
                   | (Word)(p[0]);
            p += 4;
        }
    }
# endif
#endif
    return 0L;
}

Obj PROD_COEFFS_CVEC_PRIMEFIELD(Obj self, Obj u, Obj v, Obj w)
/* All four must be cvecs over the same (prime) field.
 * u is overwritten but has to be zero beforehand! 
 * u must have length len(v)+len(w)-1 */
{
    if (!IS_CVEC(u) || !IS_CVEC(v) || !IS_CVEC(w)) {
        return OurErrorBreakQuit("CVEC_COEFFS_CVEC_PRIMEFIELD: "
                   "no cvecs");
    }
    {
        PREPARE_clfi(u,ucl,fi);
        PREPARE_cl(v,vcl);
        PREPARE_cl(w,wcl);
        PREPARE_epw(fi);
        PREPARE_bpe(fi);
        Int lenv = INT_INTOBJ(ELM_PLIST(vcl,IDX_len));
        Int lenw = INT_INTOBJ(ELM_PLIST(wcl,IDX_len));
        /* First create a table for the first elsperword-1 shifted w: */
        Int wordlenw = INT_INTOBJ(ELM_PLIST(wcl,IDX_wordlen));
        Int wordlenu = INT_INTOBJ(ELM_PLIST(ucl,IDX_wordlen));
        Int tablen = elsperword < lenv ? elsperword-1 : lenv-1; 
                     /* Minimum */
        Obj tmp;
        Word *buf;
        register Int i, imodepw, j;
        
        /* GARBAGE COLLECTION POSSIBLE */
        tmp = NEW_STRING(sizeof(Word)*(wordlenw+1)*tablen);
        if (tmp == 0L) {
            return OurErrorBreakQuit("CVEC_COEFFS_CVEC_PRIMEFIELD: "
                                     "out of memory");
        }
        /* done with possible garbage collections, no references stored! */
        buf = (Word *) CHARS_STRING(tmp);

        /* Now do the slicing: */
        Word *ww = DATA_CVEC(w);
        for (i = 0;i < tablen;i++) {
            SLICE_INT(ww,buf + (i*(wordlenw+1)),1,lenw,i+2,
                      1 /* ==d */, elsperword, bitsperel);
        }
        
        {
            /* Now we are ready to prepare the result: */
            seqaccess sa;
            Word *vv = DATA_CVEC(v);
            Word *uu = DATA_CVEC(u);
            register Word s;

            i = 1; j = 0;  /* j is the word shift */
            INIT_SEQ_ACCESS(&sa,v,1);

            while (i <= lenv) {
                /* Do the (unshifted) thing: */
                s = GET_VEC_ELM(&sa,vv,0);
                if (s) ADDMUL_INL(uu+j,ww,fi,s,wordlenw);

                i++; imodepw = 1;
                STEP_RIGHT(&sa);
                while (i <= lenv && imodepw < elsperword) {
                    s = GET_VEC_ELM(&sa,vv,0);
                    if (s)
                        ADDMUL_INL(uu+j,buf + (wordlenw+1)*(imodepw-1),fi,s,
                            j+wordlenw+1 <= wordlenu ? wordlenw+1 : wordlenw);
                    /* Note that we know u is long enough. If 
                     * j+wordlenw+1 > wordlenu, then it can only be 1 more
                     * and things in the last word of the shifted vector
                     * cannot be significant. */
                    i++; imodepw++;
                    STEP_RIGHT(&sa);
                }
                j++;
            }
        }
    }
    return 0L;
}

STATIC Obj TRANSPOSED_MAT(Obj self, Obj m, Obj n)
{
    /* n is empty, correct size, >0 rows, >0 cols, right size, same field. */
    PREPARE_clfi(ELM_PLIST(m,2),cl,fi);
    PREPARE_d(fi);
    Int lenm = LEN_PLIST(m)-1;   /* Remember the shift by one */
    Int lenn = LEN_PLIST(n)-1;
    Word *v;
    register Int i,j,k;

    seqaccess sasrc;   /* For access in source */
    seqaccess sadst;   /* For access in destination */

    if (d == 1) {
        /* We read row-wise and write column-wise. */
        INIT_SEQ_ACCESS(&sadst,ELM_PLIST(n,2),1);
        for (i = 1;i <= lenm;i++) {
            INIT_SEQ_ACCESS(&sasrc,ELM_PLIST(m,2),1);
            v = DATA_CVEC(ELM_PLIST(m,i+1));
            for (j = 1;j <= lenn;j++) {
                SET_VEC_ELM(&sadst,DATA_CVEC(ELM_PLIST(n,j+1)),0,
                            GET_VEC_ELM(&sasrc,v,0));
                STEP_RIGHT(&sasrc);
            }
            STEP_RIGHT(&sadst);
        }
    } else {  /* d > 1 */
        /* We read row-wise and write column-wise. */
        INIT_SEQ_ACCESS(&sadst,ELM_PLIST(n,2),1);
        for (i = 1;i <= lenm;i++) {
            INIT_SEQ_ACCESS(&sasrc,ELM_PLIST(m,2),1);
            v = DATA_CVEC(ELM_PLIST(m,i+1));
            for (j = 1;j <= lenn;j++) {
                for (k = 0;k < d;k++) {
                    SET_VEC_ELM(&sadst,DATA_CVEC(ELM_PLIST(n,j+1)),k,
                                GET_VEC_ELM(&sasrc,v,k));
                }
                STEP_RIGHT(&sasrc);
            }
            STEP_RIGHT(&sadst);
        }
    }
    return 0L;
}

STATIC inline void InternalClean(Obj mi, Obj mc, seqaccess *sa, Int row, Int j,
        Obj cl, Obj fi, Int p, Int d, Int saver, Int wordlen, Word *helperdata)
{
    register Int k;
    register Word el = 0;
    
    /* Is entry non-zero? */
    for (k = d-1;k >= 0;k--) {
        el = GET_VEC_ELM(sa,DATA_CVEC(ELM_PLIST(mc,j+1)),k);
        if (el != 0)
            break;  /* Leave loop immediately to keep value of k! */
    }
    if (k > -1) {   /* A non-zero entry, we have to work! */
        if (k == 0) {    /* Only a prime field component! */
            el = p - el;   /* We know it is nonzero! */
            ADDMUL_INL(DATA_CVEC(ELM_PLIST(mc,j+1))+saver,
                       DATA_CVEC(ELM_PLIST(mc,row+1))+saver,
                       fi,el,wordlen-saver);
            ADDMUL_INL(DATA_CVEC(ELM_PLIST(mi,j+1)),
                       DATA_CVEC(ELM_PLIST(mi,row+1)),fi,el,wordlen);
        } else {   /* extension field case! */
            for (k = 0;k < d;k++) {
                el = GET_VEC_ELM(sa,DATA_CVEC(ELM_PLIST(mc,j+1)),k);
                if (el != 0) {
                    sclen = k;
                    helperdata[k] = p-el;
                } else
                    helperdata[k] = 0;
            }
            sclen++;
            ADDMUL_INT(ELM_PLIST(mc,j+1),cl,fi,ELM_PLIST(mc,row+1),
                       d,(Int *) helperdata, saver, wordlen);
            ADDMUL_INT(ELM_PLIST(mi,j+1),cl,fi,ELM_PLIST(mi,row+1),
                       d,(Int *) helperdata, 0, wordlen);
        }
    }
}

STATIC Obj CMAT_INVERSE(Obj self, Obj mi, Obj mc, Obj helperfun, Obj helper)
{
    PREPARE_clfi(ELM_PLIST(mi,2),cl,fi);  /* We know that the length is >=2 */
    PREPARE_p(fi);
    PREPARE_d(fi);
    PREPARE_epw(fi);
    Int saver = 0;
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
    Int dim = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
    Int col, row;
    register Int j, k;
    seqaccess sa;
    register Word el = 0;
    Word *helperdata = DATA_CVEC(helper);
    Obj dummy;

    INIT_SEQ_ACCESS(&sa,ELM_PLIST(mc,2),1);
    for (col = 1; col <= dim;col++) {
        row = col-1;
        k = -1;  /* just to please the compiler */
        while (row < dim && k == -1) {
            row++;
            for (k = d-1;k >= 0;k--) {
                el = GET_VEC_ELM(&sa,DATA_CVEC(ELM_PLIST(mc,row+1)),k);
                if (el != 0)
                    break;  /* Leave loop immediately to keep value of k! */
            }
        }
        if (k == -1) return Fail;
        /* Check whether the found element is not equal to one: */
        if (k > 0) {   /* A non-prime field entry which is not equal to 1 */
            /* Here we need an inversion of a field element: */
            for (k = 0;k < d;k++) 
                helperdata[k]=GET_VEC_ELM(&sa,DATA_CVEC(ELM_PLIST(mc,row+1)),k);
            /* GARBAGE COLLECTION POSSIBLE */
            CALL_1ARGS(helperfun,helper);
            helperdata = DATA_CVEC(helper);  /* this is the only ref we have */

            for (sclen = d-1;sclen >= 0 && helperdata[sclen] == 0;sclen--) ;
            sclen++;
            MUL1_INT(ELM_PLIST(mc,row+1),cl,fi,d,(Int *) helperdata,0,wordlen);
            MUL1_INT(ELM_PLIST(mi,row+1),cl,fi,d,(Int *) helperdata,0,wordlen);
        } else if (el != 1) {   /* A primefield entry which is not equal to 1 */
            el = invert_modp((Int) el,(Int) p);
            MUL_INL(DATA_CVEC(ELM_PLIST(mc,row+1)),fi,el,wordlen);
            MUL_INL(DATA_CVEC(ELM_PLIST(mi,row+1)),fi,el,wordlen);
        }
        /* Now clean: */
        j = 1; if (j == row) j++;   /* Extrawurst */
        while (j <= dim) {
            InternalClean(mi,mc,&sa,row,j,cl,fi,p,d,saver,wordlen,helperdata);
            j++;
            if (j == col || j == row) 
                j = row+1;   /* Jump over rows known to be zero and row */
        }
        dummy = ELM_PLIST(mc,col+1);
        SET_ELM_PLIST(mc,col+1,ELM_PLIST(mc,row+1)); 
        SET_ELM_PLIST(mc,row+1,dummy);
        dummy = ELM_PLIST(mi,col+1);
        SET_ELM_PLIST(mi,col+1,ELM_PLIST(mi,row+1)); 
        SET_ELM_PLIST(mi,row+1,dummy);
        /* No CHANGED_BAG necessary here, because things are only
         * interchanged. */

        STEP_RIGHT(&sa);
        if (col % elsperword == 0) {
            saver += d;
        }
    }
    return True;
}
    
STATIC Obj CMAT_INVERSE_GREASE(Obj self, Obj mi, Obj mc, Obj helperfun, 
                               Obj helper, Obj grease)
{
    PREPARE_clfi(ELM_PLIST(mi,2),cl,fi);  /* We known that the length is >=3 */
    PREPARE_p(fi);
    PREPARE_d(fi);
    PREPARE_epw(fi);
    Int saver = 0;
    Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
    Int dim = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
    Int col, row;
    register Int j, k;
    seqaccess sa,sa2;
    register Word el = 0;
    Word *helperdata = DATA_CVEC(helper);
    Obj dummy;
    Obj greasetab1 = ELM_PLIST(grease,1);
    Obj greasetab2 = ELM_PLIST(grease,2);
    Obj spreadtab = ELM_PLIST(grease,3);
    Int lev = INT_INTOBJ(ELM_PLIST(grease,4));
    Int tablen = INT_INTOBJ(ELM_PLIST(grease,5));
    Int startgreaseclean; /* Record minimum, where we have to begin cleaning */
    Int blockend, l, i;
    Int val;

    INIT_SEQ_ACCESS(&sa,ELM_PLIST(mc,2),1);
    col = 1;
    while (col <= dim) {
        blockend = col+lev-1;
        if (dim < blockend) blockend = dim;
        startgreaseclean = dim+1;
        for (l = col;l <= blockend;l++) {   /* First we collect cleaners: */
            row = l-1;
            k = -1;  /* just to please the compiler */
            while (row < dim && k == -1) {
                row++;
                /* First clean left of the current situation in the block: */
                INIT_SEQ_ACCESS(&sa2,ELM_PLIST(mc,2),col);
                for (i = col;i < l;i++) {
                    InternalClean(mi,mc,&sa2,i,row,cl,fi,p,d,0,
                                  wordlen,helperdata);
                    STEP_RIGHT(&sa2);
                }
                /* Now look in our column: */
                for (k = d-1;k >= 0;k--) {
                    el = GET_VEC_ELM(&sa,DATA_CVEC(ELM_PLIST(mc,row+1)),k);
                    if (el != 0)
                        break;  /* Leave loop immediately to keep value of k! */
                }
            }
            if (k == -1) return Fail;
            /* Check whether the found element is not equal to one: */
            if (k > 0) {   /* A non-prime field entry which is not equal to 1 */
                /* Here we need an inversion of a field element: */
                for (k = 0;k < d;k++) 
                    helperdata[k] = GET_VEC_ELM(&sa,
                              DATA_CVEC(ELM_PLIST(mc,row+1)),k);
                /* GARBAGE COLLECTION POSSIBLE */
                CALL_1ARGS(helperfun,helper);
                helperdata = DATA_CVEC(helper);  
                    /* this is the only ref we have */

                for (sclen = d-1;sclen >= 0 && helperdata[sclen] == 0;sclen--) ;
                sclen++;
                MUL1_INT(ELM_PLIST(mc,row+1),cl,fi,d,(Int *) helperdata,
                                   0,wordlen);
                MUL1_INT(ELM_PLIST(mi,row+1),cl,fi,d,(Int *) helperdata,
                                   0,wordlen);
            } else if (el != 1) {   
                /* A primefield entry which is not equal to 1 */
                el = invert_modp((Int) el,(Int) p);
                MUL_INL(DATA_CVEC(ELM_PLIST(mc,row+1)),fi,el,wordlen);
                MUL_INL(DATA_CVEC(ELM_PLIST(mi,row+1)),fi,el,wordlen);
            }
            /* Now swap up: */
            if (row != l) {
                dummy = ELM_PLIST(mc,l+1);
                SET_ELM_PLIST(mc,l+1,ELM_PLIST(mc,row+1)); 
                SET_ELM_PLIST(mc,row+1,dummy);
                dummy = ELM_PLIST(mi,l+1);
                SET_ELM_PLIST(mi,l+1,ELM_PLIST(mi,row+1)); 
                SET_ELM_PLIST(mi,row+1,dummy);
                /* No CHANGED_BAG necessary here because things are only
                 * interchanged. */
                if (row < startgreaseclean) startgreaseclean = row;
            } else {
                if (row+1 < startgreaseclean) startgreaseclean = row+1;
            }
            /* Finally clean within this block upwards: */
            for (i = col;i < l;i++) {
                InternalClean(mi,mc,&sa,l,i,cl,fi,p,d,saver,
                              wordlen,helperdata);
            }

            STEP_RIGHT(&sa);
            if (l % elsperword == 0) {
                saver += d;
            }
        }
        /* We now have found cleaner rows col..blockend (inclusively) and
         * moved them to positions col..blockend. We can now fill the
         * greasetab and clean out rows 1..col-1 and startgreaseclean..dim: */
        FILL_GREASE_TAB(self,mc,INTOBJ_INT(col+1),INTOBJ_INT(lev),greasetab1,
                        INTOBJ_INT(tablen),INTOBJ_INT(1));
        FILL_GREASE_TAB(self,mi,INTOBJ_INT(col+1),INTOBJ_INT(lev),greasetab2,
                        INTOBJ_INT(tablen),INTOBJ_INT(1));
        EXTRACT_INIT(self,ELM_PLIST(mc,2),INTOBJ_INT(col),INTOBJ_INT(lev));
        if (startgreaseclean <= blockend) startgreaseclean = blockend+1;
        j = 1; if (j == col) j = startgreaseclean;
        while (j <= dim) {
            val = (*Vector_Extract_Worker)(DATA_CVEC(ELM_PLIST(mc,j+1)));
            if (val != 0) {
                val = INT_INTOBJ(ELM_PLIST(spreadtab,val+1));
                ADDMUL_INL(DATA_CVEC(ELM_PLIST(mc,j+1)),
                           DATA_CVEC(ELM_PLIST(greasetab1,val)),
                           fi,p-1,wordlen);
                ADDMUL_INL(DATA_CVEC(ELM_PLIST(mi,j+1)),
                           DATA_CVEC(ELM_PLIST(greasetab2,val)),
                           fi,p-1,wordlen);
            }
            j++;
            if (j == col) j = startgreaseclean;
        }
        col = blockend+1;
    }
    return True;
}
    
/* Cleaning vectors: */

STATIC Obj CLEANROWKERNEL( Obj self, Obj basis, Obj vec, Obj extend, Obj dec )
{
  /* INPUT:
     basis: record with fields
            vectors : matrix of basis vectors in semi echelon form
                      must be a cmat here!
            pivots  : integer list of pivot columns of basis matrix
                      will be made into a plain list rep.
     vec : vector of same length as basis vectors
           must be a cvec here
     extend : either true or false, indicating, whether the basis is extended
           note that if extend=true, then we norm the new vector!
     dec : either fail for no decomposition
           or a cvec with length at least equal to the length of the basis for
           the not-extend case, otherwise length at least one longer to 
           store the norming factor
     OUTPUT
     returns either true or false, depending on whether the vector lies
     in the span of the basis
     if dec is a cvec, then the coefficients of the linear combination
     are put there, if extend=true, then the basis is extended
     NOTES
     destructive in all arguments basis, vec, and dec */
  PREPARE_clfi(vec,cl,fi);
  PREPARE_p(fi);
  PREPARE_d(fi);
  Obj cldec;
  Obj vectors = ElmPRec( basis, RNamName( "vectors" ) );
  Obj rows = ElmPRec( vectors, RNamName( "rows" ) );
  Obj pivots = ElmPRec( basis, RNamName( "pivots" ) );
  Obj helper = ElmPRec( basis, RNamName( "helper" ) );
  Int vlen = INT_INTOBJ(ELM_PLIST(cl,IDX_len));
  Int wordlen = INT_INTOBJ(ELM_PLIST(cl,IDX_wordlen));
  Int firstnz;
  Int len;
  Int j;
  Int newpiv;
  int fnzcounter = 0;

  PLAIN_LIST(pivots);
  if (TNUM_OBJ(pivots) < FIRST_PLIST_TNUM || 
      TNUM_OBJ(pivots) > LAST_PLIST_TNUM) {
      return OurErrorBreakQuit("CLEANROWKERNEL: pivots is not in plist rep");
  }

  if (dec == Fail)
      cldec = 0L;
  else {
      if (!IS_CVEC(dec)) {
          return OurErrorBreakQuit("CLEANROWKERNEL: dec is no cvec");
      }
      cldec = DATA_OBJ(dec);
      /* Zero the decomposition vector: */
      MUL_INL(DATA_CVEC(dec),fi,0,INT_INTOBJ(ELM_PLIST(cldec,IDX_wordlen)));
  }

  /* First a little shortcut: */
  if (d == 1)
      firstnz = CVEC_Firstnzp(fi,DATA_CVEC(vec),vlen);
  else
      firstnz = CVEC_Firstnzq(fi,DATA_CVEC(vec),vlen,wordlen);
  if (firstnz > vlen) return True;  /* The zero vector, all done */

  len = LEN_PLIST( rows )-1;  /* note that CMats start with a fail in pos 1 */
  /* we distinguish between prime field case and extension field case: */
  if (d == 1) {
      Word *vecvec = DATA_CVEC(vec);
      Word *decdec = 0L;
      Int c;
      if (cldec) decdec = DATA_CVEC(dec);
      for (j = 1;j <= len;j++) {
          Int piv = INT_INTOBJ(ELM_PLIST(pivots,j));
          if (++fnzcounter >= 10) {
              firstnz = CVEC_Firstnzp(fi,vecvec,vlen);
              fnzcounter = 0;
          }
          if (piv >= firstnz) {   /* otherwise a shortcut */
              c = CVEC_Itemp(fi,vecvec,piv);
              if (c) {
                  if (cldec) CVEC_AssItemp(fi,decdec,j,c);
                  ADDMUL_INL(vecvec,DATA_CVEC(ELM_PLIST(rows,j+1)),fi,
                             p-c,wordlen);
              }
              // firstnz = piv+1;
          }
      }
      newpiv = CVEC_Firstnzp(fi,vecvec,vlen);
      if (newpiv > vlen) return True;
      if (extend == True) {
          c = CVEC_Itemp(fi,vecvec,newpiv);
          if (cldec) CVEC_AssItemp(fi,decdec,len+1,c);
          if (c != 1) {
              c = invert_modp(c,p);
              MUL_INL(vecvec,fi,c,wordlen);
          }
          /* GARBAGE COLLECTION POSSIBLE HERE! */
          ASS_LIST(rows,len+2,vec);   /* Remember the fail in position 1! */
          AssPRec(vectors,RNamName("len"),INTOBJ_INT(len+1));
          ASS_LIST(pivots,len+1,INTOBJ_INT(newpiv));
          /* We do not use any longer any references we might have! */
      }
      return False;
  } else {   /* d > 1 */
      Word *vecvec = DATA_CVEC(vec);
      Word *decdec = 0L;
      if (cldec) decdec = DATA_CVEC(dec);
      for (j = 1;j <= len;j++) {
          Int piv = INT_INTOBJ(ELM_PLIST(pivots,j));
          if (++fnzcounter >= 10) {
              firstnz = CVEC_Firstnzq(fi,vecvec,vlen,wordlen);
              fnzcounter = 0;
          }
          if (piv >= firstnz) {   /* otherwise a shortcut */
              CVEC_Itemq(fi,vecvec,piv);
              if (sclen > 1 || scbuf[0] != 0) {
                  Int k;
                  if (cldec) CVEC_AssItemq(fi,decdec,j,scbuf);
                  for (k = sclen-1;k >= 0;k--)
                      scbuf[k] = scbuf[k] ? p-scbuf[k] : 0;
                  ADDMUL_INT(vec,cl,fi,ELM_PLIST(rows,j+1),d,scbuf,0,wordlen);
              }
              // firstnz = piv+1;
          }
      }
      newpiv = CVEC_Firstnzq(fi,vecvec,vlen,wordlen);
      if (newpiv > vlen) return True;
      if (extend == True) {
          /* Norm the vector: */
          CVEC_Itemq(fi,vecvec,newpiv);
          if (cldec) CVEC_AssItemq(fi,decdec,len+1,scbuf);
          if (sclen > 1 || scbuf[0] != 1) {
              Word *helperdata = DATA_CVEC(helper);
              Obj helperfun = VAL_GVAR(GVarName("CVEC_INVERT_FFE"));
              Int k;
              
              /* Here we need an inversion of a field element: */
              for (k = 0;k < d;k++) helperdata[k]=scbuf[k];
              /* GARBAGE COLLECTION POSSIBLE */
              CALL_1ARGS(helperfun,helper);  
              
              /* these are the only refs we have and still use: */
              helperdata = DATA_CVEC(helper);
              vecvec = DATA_CVEC(vecvec);
              
              for (sclen = d-1;sclen >= 0 && helperdata[sclen] == 0;sclen--) ;
              sclen++;
              MUL1_INT(vec,cl,fi,d,(Int *) helperdata,0,wordlen);
          }
          /* GARBAGE COLLECTION POSSIBLE HERE! */
          ASS_LIST(rows,len+2,vec);   /* Remember the fail in position 1! */
          AssPRec(vectors,RNamName("len"),INTOBJ_INT(len+1));
          ASS_LIST(pivots,len+1,INTOBJ_INT(newpiv));
          /* We do not use any longer any references we might have! */
      }
      return False;
  }
}

STATIC Obj CVEC_EQINT(Obj self, Obj a, Obj b)
{
    return (EQ( a, b ) ? True : False);
}

STATIC Obj CMAT_ENTRY_OF_MAT_PROD(Obj self, Obj m, Obj n, Obj i, Obj j)
{
    /* m and n must be cmats over the same prime field with #cols(m)=#rows(n).
     * i must be a row number of m and j a row number of n. */
    Int rnamrows = RNamName( "rows" );
    Obj mrows = ElmPRec( m, rnamrows );
    Obj nrows = ElmPRec( n, rnamrows );
    Int len;
    Int k;
    len = LEN_PLIST(mrows);
    if (len == 1) return Fail;
    k = INT_INTOBJ(i);
    if (k < 1 || k > len-1) {
        return 
          OurErrorBreakQuit("CMAT_ENTRY_OF_MAT_PROD: row index out of range");
    }
    Obj v = ELM_PLIST(mrows,INT_INTOBJ(i)+1);
    PREPARE_clfi(v,vcl,fi);
    len = INT_INTOBJ(ELM_PLIST(vcl,IDX_len));
    if (len != LEN_PLIST(nrows)-1) {
        return OurErrorBreakQuit("CMAT_ENTRY_OF_MAT_PROD: unequal length");
    }
    PREPARE_p(fi);
    PREPARE_d(fi);
    PREPARE_tab2(fi);
    if (LEN_PLIST(nrows) == 1) return ELM_PLIST(tab2,1);    /* Zero! */
    Obj w = ELM_PLIST(nrows,2);
    PREPARE_cl(w,wcl);
    k = INT_INTOBJ(j);
    if (k < 1 || k > INT_INTOBJ(ELM_PLIST(wcl,IDX_len))) {
        return 
          OurErrorBreakQuit("CMAT_ENTRY_OF_MAT_PROD: col index out of range");
    }
    seqaccess sa;
    seqaccess saw;
    Word res;
    Word *vv,*ww;
    Int size = INT_INTOBJ(ELM_PLIST(fi,IDX_size));

    if (fi != ELM_PLIST(wcl,IDX_fieldinfo)) {
        return OurErrorBreakQuit("CMAT_ENTRY_OF_MAT_PROD: "
                                 "cmats not over same field");
    }
    if (d > 1 || p >= (1UL << (BYTESPERWORD*4)) || size > 0) {
        return TRY_NEXT_METHOD;
    }
    INIT_SEQ_ACCESS( &sa, v, 1 );
    INIT_SEQ_ACCESS( &saw, w, INT_INTOBJ(j) );
    k = 1;
    res = 0;
    vv = DATA_CVEC(v);
    ww = DATA_CVEC(w);
    /* We distinguish 2 cases: 
     * (1) 2*(p-1)*(p-1) does not fit into a Word
     * (2) 2*(p-1)*(p-1) does fit into a Word */
    if ((p-1)*(p-1) > (WORDALLONE >> 1)) {
        while (1) {
            res += (GET_VEC_ELM(&sa,vv,0) * GET_VEC_ELM(&saw,ww,0)) % p;
            if (res >= p) res -= p;
            if (++k > len) break;
            STEP_RIGHT(&sa);
            w = ELM_PLIST(nrows,k+1);
            ww = DATA_CVEC(w);
        }
    } else {
        Word addsbeforereduce = WORDALLONE / ((p-1)*(p-1));
        Word jj = addsbeforereduce;
        while (1) {
            res += GET_VEC_ELM(&sa,vv,0) * GET_VEC_ELM(&saw,ww,0);
            if (--jj == 0) {
                jj = addsbeforereduce;
                res %= p;
            }
            if (++k > len) break;
            STEP_RIGHT(&sa);
            w = ELM_PLIST(nrows,k+1);
            ww = DATA_CVEC(w);
        }
        res %= p;
    }
    return ELM_PLIST(tab2,res+1);
}

STATIC Obj CVEC_SCALAR_PRODUCT(Obj self, Obj v, Obj w)
{
    /* v and w must be cvecs over the same prime field with equal length! */
    if (!IS_CVEC(v) || !IS_CVEC(w)) {
        return OurErrorBreakQuit("CVEC_SCALAR_PRODUCT: no cvecs");
    }
    {
        PREPARE_clfi(v,vcl,fi);
        PREPARE_cl(w,wcl);
        PREPARE_p(fi);
        PREPARE_d(fi);
        PREPARE_tab2(fi);
        Int len = INT_INTOBJ(ELM_PLIST(vcl,IDX_len));
        seqaccess sa;
        Int i;
        Word res;
        Word *vv,*ww;
        Int size;

        size = INT_INTOBJ(ELM_PLIST(fi,IDX_size));

        if (vcl != wcl) {
            return OurErrorBreakQuit("CVEC_SCALAR_PRODUCT: "
                                     "cvecs not in same class");
        }
        /* This is a special case which is even higher optimised: */
        if (p == 2 && d == 1) {
            vv = DATA_CVEC(v);
            ww = DATA_CVEC(w);
            Int wlen = INT_INTOBJ(ELM_PLIST(vcl,IDX_wordlen));
            Word w = 0L;
            for (i = wlen;i > 0;i--) w ^= (*vv++ & *ww++);
#ifdef SYS_IS_64_BIT
            w ^= (w >> 32);
#endif
            w ^= (w >> 16); w ^= (w >> 8); w ^= (w >> 4);
            w ^= (w >> 2);  w ^= (w >> 1); w &= 1L;
            return ELM_PLIST(tab2,(Int) w + 1);
        }
        if (d > 1 || p >= (1UL << (BYTESPERWORD*4)) || size > 0) {
            return TRY_NEXT_METHOD;
        }
        INIT_SEQ_ACCESS( &sa, v, 1 );
        i = 1;
        res = 0;
        vv = DATA_CVEC(v);
        ww = DATA_CVEC(w);
        /* We distinguish 2 cases: 
         * (1) 2*(p-1)*(p-1) does not fit into a Word
         * (2) 2*(p-1)*(p-1) does fit into a Word */
        if ((p-1)*(p-1) > (WORDALLONE >> 1)) {
            while (1) {
                res += (GET_VEC_ELM(&sa,vv,0) * GET_VEC_ELM(&sa,ww,0)) % p;
                if (res >= p) res -= p;
                if (++i > len) break;
                STEP_RIGHT(&sa);
            }
        } else {
            Word addsbeforereduce = WORDALLONE / ((p-1)*(p-1));
            Word j = addsbeforereduce;
            while (1) {
                res += GET_VEC_ELM(&sa,vv,0) * GET_VEC_ELM(&sa,ww,0);
                if (--j == 0) {
                    j = addsbeforereduce;
                    res %= p;
                }
                if (++i > len) break;
                STEP_RIGHT(&sa);
            }
            res %= p;
        }
        return ELM_PLIST(tab2,res+1);
    }
}

STATIC UInt rnam_rows = 0;

STATIC Obj CMAT_ELM_LIST(Obj self, Obj m, Obj p)
{
    if (!rnam_rows) {
       rnam_rows = RNamName("rows");
    } 
    return ELM_PLIST(ElmPRec(m,rnam_rows),INT_INTOBJ(p)+1);
}

STATIC UInt rnam_vecclass = 0;

Obj             SumFFEFFE ( Obj opL, Obj opR );

STATIC Obj CMATS_SCALAR_PRODUCTS_ROWS(Obj self, Obj m, Obj n, Obj l)
/* m and n must have equal row length l */
{
    Obj cl,fi;

    if (!rnam_vecclass) {
        rnam_vecclass = RNamName("vecclass");
    }
    cl = ElmPRec(m,rnam_vecclass);
    fi = ELM_PLIST(cl,IDX_fieldinfo);
    PREPARE_d(fi);
    PREPARE_p(fi);
    Int size = INT_INTOBJ(ELM_PLIST(fi,IDX_size));

    /* The following test has to be adjusted to the one in
     * CVEC_SCALAR_PRODUCT! */
    if (d > 1 || p >= (1UL << (BYTESPERWORD*4)) || size > 0) {
        return TRY_NEXT_METHOD;
    }

    if (!rnam_rows) {
        rnam_rows = RNamName("rows");
    } 
    
    Obj rowsm = ElmPRec(m,rnam_rows);
    Obj rowsn = ElmPRec(n,rnam_rows);
    
    Int i,ll;
    ll = INT_INTOBJ(l)+1;  /* Offset in !.rows! */

    if (ll < 2) {   /* Empty cmats */
        return Fail;
    }
    Obj sum = CVEC_SCALAR_PRODUCT(self,ELM_PLIST(rowsm,2),ELM_PLIST(rowsn,2));
    for (i = 3;i <= ll;i++) {
        /*sum = CVEC_SCALAR_PRODUCT(self,ELM_PLIST(rowsm,i),
                                               ELM_PLIST(rowsn,i));*/
        sum = SumFFEFFE(sum,CVEC_SCALAR_PRODUCT(self,ELM_PLIST(rowsm,i),
                                                     ELM_PLIST(rowsn,i)));
    }
    return sum;
}

static UInt RNAM_greasehint = 0;
static UInt RNAM_len = 0;
static UInt RNAM_rows = 0;
static UInt RNAM_scaclass = 0;
static UInt RNAM_vecclass = 0;

STATIC Obj CVEC_CMatMaker_C( Obj self, Obj l, Obj cl )
{
    /* Create a cmat object. This is internal, so no checks are done! */
    Obj m;
    Obj q;
    Int qq;
    Int qp;
    Obj fi;
    Int greasehint;
    Int len;
    Int i;

    if (RNAM_greasehint == 0) {
        RNAM_greasehint = RNamName("greasehint");
        RNAM_len = RNamName("len");
        RNAM_rows = RNamName("rows");
        RNAM_scaclass = RNamName("scaclass");
        RNAM_vecclass = RNamName("vecclass");
    }
    fi = ELM_PLIST(cl,IDX_fieldinfo);
    q = ELM_PLIST(fi,IDX_q);
    if (!IS_INTOBJ(q)) 
        greasehint = 0;
    else {
        greasehint = INT_INTOBJ(ELM_PLIST(fi,IDX_bestgrease));
        qq = INT_INTOBJ(q);
        qp = 1;
        for (i = greasehint;i > 0;i--) qp *= qq;
        len = LEN_PLIST(l);
        while (greasehint > 0 && len < qp) {
            greasehint--;
            qp /= qq;
        }
    }
    /* GARBAGE COLLECTION POSSIBLE */
    m = NEW_PREC(5);
    AssPRec(m,RNAM_greasehint,INTOBJ_INT(greasehint));
    AssPRec(m,RNAM_len,INTOBJ_INT(LEN_PLIST(l)-1));
    AssPRec(m,RNAM_rows,l);
    AssPRec(m,RNAM_scaclass,ELM_PLIST(cl,IDX_GF));
    AssPRec(m,RNAM_vecclass,cl);
    SET_TYPE_COMOBJ(m,ELM_PLIST(cl,IDX_typecmat));
    RetypeBag( m, T_COMOBJ );
    return m;
}

STATIC Obj CVEC_MAKE_ZERO_CMAT(Obj self, Obj nrrows, Obj cl)
{
    Int i;
    Obj cvectype;
    Int len;
    Obj l;

    len = INT_INTOBJ(nrrows);
    /* GARBAGE COLLECTION POSSIBLE */
    l = NEW_PLIST(T_PLIST,len+1);
    SET_LEN_PLIST(l,len+1);
    SET_ELM_PLIST(l,1,INTOBJ_INT(0));
    cvectype = ELM_PLIST(cl,IDX_type);
    for (i = 2;i <= len+1;i++) {
        /* GARBAGE COLLECTION POSSIBLE */
        SET_ELM_PLIST(l,i,NEW(self,cl,cvectype));
        CHANGED_BAG(l);
    }
    /* GARBAGE COLLECTION POSSIBLE */
    return CVEC_CMatMaker_C(self,l,cl);
}

static Obj CVEC_PROD_CMAT_CMAT_BIG;

STATIC Obj CVEC_PROD_CMAT_CMAT_DISPATCH(Obj self, Obj m, Obj n)
{
    /* This function is installed as the multiplication function for cmats.
     * It dispatches very quickly for small matrices and calls back
     * CVEC_PROD_CMAT_CMAT_BIG on the GAP level for bigger matrices
     * to sort out Winograd and so on. It also does the catching of
     * argument errors. */
    Obj clm,cln;
    Obj fi;
    Int max;
    Int dim;
    Obj q;
    Obj res;

    if (ElmPRec(m,RNAM_scaclass) != ElmPRec(n,RNAM_scaclass)) {
        return OurErrorBreakQuit(
             "CVEC_PROD_CMAT_CMAT: incompatible base fields");
    }
    dim = INT_INTOBJ(ElmPRec(n,RNAM_len));
    clm = ElmPRec(m,RNAM_vecclass);
    if (INT_INTOBJ(ELM_PLIST(clm,IDX_len)) != dim) {
        return OurErrorBreakQuit(
             "CVEC_PROD_CMAT_CMAT: matrix dimension not matching");
    }
    cln = ElmPRec(n,RNAM_vecclass);
    max = INT_INTOBJ(ELM_PLIST(cln,IDX_len));
    if (dim > max) max = dim;
    dim = INT_INTOBJ(ElmPRec(m,RNAM_len));
    if (dim > max) max = dim;
    /* dim is now the number of rows of m */
    fi = ELM_PLIST(clm,IDX_fieldinfo);
    q = ELM_PLIST(fi,IDX_q);
    if (IS_INTOBJ(q) && q == INTOBJ_INT(2) && max <= 512) {
        res = CVEC_MAKE_ZERO_CMAT(self,INTOBJ_INT(dim),cln);
        if (dim > 0)   /* Otherwise there is nothing to do. */
            PROD_CMAT_CMAT_GF2_SMALL(self,ElmPRec(res,RNAM_rows),
                                          ElmPRec(m,RNAM_rows),
                                          ElmPRec(n,RNAM_rows),INTOBJ_INT(max));
        if (!(IS_MUTABLE_OBJ(m) || IS_MUTABLE_OBJ(n)))
            MakeImmutable(res);
        return res;
    }
    /* Go back to the GAP level: */
    return CALL_2ARGS(CVEC_PROD_CMAT_CMAT_BIG,m,n);
}



/*F * * * * * * * * * * * * * initialize package * * * * * * * * * * * * * * */

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

  { "CVEC_TEST_ASSUMPTIONS", 0, "",
    TEST_ASSUMPTIONS,
    "cvec.c:TEST_ASSUMPTIONS" },

  { "CVEC_COEFF_LIST_TO_C", 2, "coefflist, st",
    COEFF_LIST_TO_C,
    "cvec.c:COEFF_LIST_TO_C" },

  { "CVEC_FINALIZE_FIELDINFO", 1, "fieldinfo",
    FINALIZE_FIELDINFO,
    "cvec.c:FINALIZE_FIELDINFO" },

  { "CVEC_INIT_SMALL_GFQ_TABS", 6, "p, d, q, tab1, tab2, primroot",
    INIT_SMALL_GFQ_TABS,
    "cvec.c:INIT_SMALL_GFQ_TABS" },

  { "CVEC_NEW", 2, "class, type",
    NEW,
    "cvec.c:NEW" },

  { "CVEC_MAKEZERO", 1, "v",
    MAKEZERO,
    "cvec.c:MAKEZERO" },

  { "CVEC_COPY", 2, "v, w",
    COPY,
    "cvec.c:COPY" },

  { "CVEC_CVEC_TO_INTREP", 2, "v, l",
    CVEC_TO_INTREP,
    "cvec.c:CVEC_TO_INTREP" },

  { "CVEC_INTREP_TO_CVEC", 2, "l, v",
    INTREP_TO_CVEC,
    "cvec.c:INTREP_TO_CVEC" },

  { "CVEC_INTLI_TO_FFELI", 2, "c, l",
    INTLI_TO_FFELI,
    "cvec.c:INTLI_TO_FFELI" },

  { "CVEC_FFELI_TO_INTLI", 2, "c, l",
    FFELI_TO_INTLI,
    "cvec.c:FFELI_TO_INTLI" },

  { "CVEC_CVEC_TO_NUMBERFFLIST", 3, "v, l, split",
    CVEC_TO_NUMBERFFLIST,
    "cvec.c:CVEC_TO_NUMBERFFLIST" },

  { "CVEC_NUMBERFFLIST_TO_CVEC", 3, "l, v, split",
    NUMBERFFLIST_TO_CVEC,
    "cvec.c:NUMBERFFLIST_TO_CVEC" },

  { "CVEC_ADD2", 4, "u, v, fr, to",
    ADD2,
    "cvec.c:ADD2" },

  { "CVEC_ADD3", 3, "u, v, w",
    ADD3,
    "cvec.c:ADD3" },

  { "CVEC_MUL1", 4, "u, s, fr, to",
    MUL1,
    "cvec.c:MUL1" },

  { "CVEC_MUL2", 3, "u, v, s",
    MUL2,
    "cvec.c:MUL2" },

  { "CVEC_ADDMUL", 5, "u, v, s, fr, to",
    ADDMUL,
    "cvec.c:ADDMUL" },

  { "CVEC_ASS_CVEC", 3, "v, pos, s",
    ASS_CVEC,
    "cvec.c:ASS_CVEC" },

  { "CVEC_ELM_CVEC", 2, "v, pos",
    ELM_CVEC,
    "cvec.c:ELM_CVEC" },

  { "CVEC_POSITION_NONZERO_CVEC", 1, "v",
    POSITION_NONZERO_CVEC,
    "cvec.c:POSITION_NONZERO_CVEC" },

  { "CVEC_POSITION_LAST_NONZERO_CVEC", 1, "v",
    POSITION_LAST_NONZERO_CVEC,
    "cvec.c:POSITION_LAST_NONZERO_CVEC" },

  { "CVEC_CVEC_LT", 2, "u, v",
    CVEC_LT,
    "cvec.c:CVEC_LT" },

  { "CVEC_CVEC_EQ", 2, "u, v",
    CVEC_EQ,
    "cvec.c:CVEC_EQ" },

  { "CVEC_EQINT", 2, "u, v",
    CVEC_EQINT,
    "cvec.c:CVEC_EQINT" },

  { "CVEC_CVEC_ISZERO", 1, "u",
    CVEC_ISZERO,
    "cvec.c:CVEC_ISZERO" },

  { "CVEC_EXTRACT", 3, "v, i, l",
    EXTRACT,
    "cvec.c:EXTRACT" },

  { "CVEC_EXTRACT_INIT", 3, "v, i, l",
    EXTRACT_INIT,
    "cvec.c:EXTRACT_INIT" },

  { "CVEC_EXTRACT_DOIT", 1, "v",
    EXTRACT_DOIT,
    "cvec.c:EXTRACT_DOIT" },

  { "CVEC_FILL_GREASE_TAB", 6, "li, i, l, tab, tablen, offset",
     FILL_GREASE_TAB,
     "cvec.c:FILL_GREASE_TAB" },

  { "CVEC_PROD_CVEC_CMAT_NOGREASE", 3, "u, v, m",
    PROD_CVEC_CMAT_NOGREASE,
    "cvec.c:PROD_CVEC_CMAT_NOGREASE" },

  { "CVEC_PROD_CVEC_CMAT_GREASED", 5, "u, v, mgreasetab, spreadtab, glev",
    PROD_CVEC_CMAT_GREASED,
    "cvec.c:PROD_CVEC_CMAT_GREASED" },

  { "CVEC_PROD_CMAT_CMAT_GREASED", 6, "l, m, ngreasetab, spreadtab, len, glev",
    PROD_CMAT_CMAT_GREASED,
    "cvec.c:PROD_CMAT_CMAT_GREASED" },

  { "CVEC_PROD_CMAT_CMAT_GF2_SMALL", 4, "l, m, n, maxdim",
    PROD_CMAT_CMAT_GF2_SMALL,
    "cvec.c:PROD_CMAT_CMAT_GF2_SMALL" },

  { "CVEC_PROD_CMAT_CMAT_NOGREASE", 3, "l, m, n",
    PROD_CMAT_CMAT_NOGREASE,
    "cvec.c:PROD_CMAT_CMAT_NOGREASE" },

  { "CVEC_PROD_CMAT_CMAT_NOGREASE2", 3, "l, m, n",
    PROD_CMAT_CMAT_NOGREASE2,
    "cvec.c:PROD_CMAT_CMAT_NOGREASE2" },

  { "CVEC_PROD_CMAT_CMAT_WITHGREASE", 6, "l, m, n, greasetab, spreadtab, glev",
    PROD_CMAT_CMAT_WITHGREASE,
    "cvec.c:PROD_CMAT_CMAT_WITHGREASE" },

  { "CVEC_SLICE", 5, "src, dst, srcpos, len, dstpos",
    SLICE,
    "cvec.c:SLICE" },

  { "CVEC_SLICE_LIST", 4, "src, dst, srcposs, dstposs",
    SLICE_LIST,
    "cvec.c:SLICE_LIST" },

  { "CVEC_COPY_SUBMATRIX", 6, "src, dst, srcrows, dstrows, srcposs, dstposs",
    COPY_SUBMATRIX,
    "cvec.c:COPY_SUBMATRIX" },

  { "CVEC_CVEC_TO_EXTREP", 2, "v, s",
    CVEC_TO_EXTREP,
    "cvec.c:CVEC_TO_EXTREP" },

  { "CVEC_EXTREP_TO_CVEC", 2, "s, v",
    EXTREP_TO_CVEC,
    "cvec.c:EXTREP_TO_CVEC" },

  { "CVEC_PROD_COEFFS_CVEC_PRIMEFIELD", 3, "u, v, w",
    PROD_COEFFS_CVEC_PRIMEFIELD,
    "cvec.c:PROD_COEFFS_CVEC_PRIMEFIELD" },

  { "CVEC_TRANSPOSED_MAT", 2, "m, n",
    TRANSPOSED_MAT,
    "cvec.c:TRANSPOSED_MAT" },

  { "CVEC_CMAT_INVERSE", 4, "mi, mc, helperfun, helper",
    CMAT_INVERSE,
    "cvec.c:CMAT_INVERSE" },

  { "CVEC_CMAT_INVERSE_GREASE", 5, "mi, mc, helperfun, helper, grease",
    CMAT_INVERSE_GREASE,
    "cvec.c:CMAT_INVERSE_GREASE" },

  { "CVEC_GREASEPOS", 2, "v, pivs",
    GREASEPOS,
    "cvec.c:GREASEPOS" },

  { "CVEC_CLEANROWKERNEL", 4, "basis, vec, extend, dec",
    CLEANROWKERNEL, 
    "cvec.c:CLEANROWKERNEL" },

  { "CMAT_ENTRY_OF_MAT_PROD", 4, "m, n, i, j",
    CMAT_ENTRY_OF_MAT_PROD,
    "cvec.c:CMAT_ENTRY_OF_MAT_PROD" },

  { "CVEC_SCALAR_PRODUCT", 2, "v, w",
    CVEC_SCALAR_PRODUCT,
    "cvec.c:CVEC_SCALAR_PRODUCT" },

  { "CMAT_ELM_LIST", 2, "m, p",
    CMAT_ELM_LIST,
    "cvec.c:CMAT_ELM_LIST" },

  { "CMATS_SCALAR_PRODUCTS_ROWS", 3, "m, n, l",
    CMATS_SCALAR_PRODUCTS_ROWS,
    "cvec.c:CMATS_SCALAR_PRODUCTS_ROWS" },

  { "CVEC_CMatMaker_C", 2, "l, cl",
    CVEC_CMatMaker_C,
    "cvec.c:CVEC_CMatMaker_C" },

  { "CVEC_MAKE_ZERO_CMAT", 2, "nrrows, cl",
    CVEC_MAKE_ZERO_CMAT,
    "cvec.c:CVEC_MAKE_ZERO_CMAT" },

  { "CVEC_PROD_CMAT_CMAT_DISPATCH", 2, "m, n",
    CVEC_PROD_CMAT_CMAT_DISPATCH,
    "cvec.c:CVEC_PROD_CMAT_CMAT_DISPATCH" },

  { 0 }

};

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

    /* Init gf2lib structures: */
    arenastart = (WORD *) 
        ((((unsigned long) myarena)+0x100000UL) & (~(0xfffffUL)));
#ifdef SYS_IS_64_BIT
    gf2_usemem_512(arenastart,4096*1024);
    gf2_usemem_256(arenastart,4096*1024);
    gf2_usemem_128(arenastart,4096*1024);
    gf2_usemem_64(arenastart,4096*1024);
#else
    gf2_usemem_512(arenastart,2048*1024);
    gf2_usemem_256(arenastart,2048*1024);
    gf2_usemem_128(arenastart,2048*1024);
    gf2_usemem_64(arenastart,2048*1024);
    gf2_usemem_32(arenastart,2048*1024);
#endif

    InitFopyGVar("CVEC_PROD_CMAT_CMAT_BIG", &CVEC_PROD_CMAT_CMAT_BIG);

    /* return success                                                      */
    return 0;
}

#define CVEC_PUBLISH(nam) gvar=GVarName("CVEC_"#nam); \
    AssGVar( gvar, INTOBJ_INT(nam)); MakeReadOnlyGVar(gvar)

/******************************************************************************
*F  InitLibrary( <module> ) . . . . . . .  initialise library data structures
*/
static Int InitLibrary ( StructInitInfo *module )
{
    Int             gvar;
    Obj             tmp;

    /* init filters and functions */
    /* init functions */
    InitGVarFuncsFromTable(GVarFuncs);
    gvar = GVarName("CVEC_BYTESPERWORD");
    AssGVar(gvar,INTOBJ_INT(BYTESPERWORD));
    MakeReadOnlyGVar(gvar);
    gvar = GVarName("CVEC_MAXDEGREE");
    AssGVar(gvar,INTOBJ_INT(MAXDEGREE));
    MakeReadOnlyGVar(gvar);

    /* Export position numbers: */
    CVEC_PUBLISH(IDX_p);
    CVEC_PUBLISH(IDX_d);
    CVEC_PUBLISH(IDX_q);
    CVEC_PUBLISH(IDX_conway);
    CVEC_PUBLISH(IDX_bitsperel);
    CVEC_PUBLISH(IDX_elsperword);
    CVEC_PUBLISH(IDX_wordinfo);
    CVEC_PUBLISH(IDX_bestgrease);
    CVEC_PUBLISH(IDX_greasetabl);
    CVEC_PUBLISH(IDX_filts);
    CVEC_PUBLISH(IDX_tab1);
    CVEC_PUBLISH(IDX_tab2);
    CVEC_PUBLISH(IDX_size);
    CVEC_PUBLISH(IDX_scafam);
    CVEC_PUBLISH(IDX_filtscmat);

    CVEC_PUBLISH(IDX_fieldinfo);
    CVEC_PUBLISH(IDX_len);
    CVEC_PUBLISH(IDX_wordlen);
    CVEC_PUBLISH(IDX_type);
    CVEC_PUBLISH(IDX_GF);
    CVEC_PUBLISH(IDX_lens);
    CVEC_PUBLISH(IDX_classes);
    CVEC_PUBLISH(IDX_typecmat);

    /*ImportFuncFromLibrary( "IsCVecRep", &IsCVecRep );*/

    tmp = NEW_PREC(0);
    gvar = GVarName("CVEC"); AssGVar( gvar, tmp ); MakeReadOnlyGVar(gvar);
    /* return success                                                      */
    return 0;
}

/******************************************************************************
*F  InitInfopl()  . . . . . . . . . . . . . . . . . table of init functions
*/
static StructInitInfo module = {
#ifdef CVECSTATIC
 /* type        = */ MODULE_STATIC,
#else
 /* type        = */ MODULE_DYNAMIC,
#endif
 /* name        = */ "cvec",
 /* revision_c  = */ 0,
 /* revision_h  = */ 0,
 /* version     = */ 0,
 /* crc         = */ 0,
 /* initKernel  = */ InitKernel,
 /* initLibrary = */ InitLibrary,
 /* checkInit   = */ 0,
 /* preSave     = */ 0,
 /* postSave    = */ 0,
 /* postRestore = */ 0
};

#ifndef CVECSTATIC
StructInitInfo * Init__Dynamic ( void )
{
  return &module;
}
#endif

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

/* Here is a sketch of a proof that there are no bugs in this file because
 * of garbage collections being triggered and in the sequel references
 * kept in the C-level are no longer valid:
 * All places where a garbage collection can be triggered are marked
 * with "GARBAGE COLLECTION POSSIBLE" (usage of functions "NewBag",
 * "NEW_STRING", "NEW_PLIST", "GrowString", "NEW_PREC", or "CALL_1ARGS"). 
 * All those places have to be checked that no absolute reference is 
 * reused after the garbage collection. This has been done. 
 * The following functions contain such places:
 *   FINALIZE_FIELDINFO
 *   NEW
 *   ELM_CVEC
 *   PROD_CMAT_CMAT_NOGREASE2
 *   CVEC_TO_EXTREP
 *   PROD_COEFFS_CVEC_PRIMEFIELD
 *   CMAT_INVERSE
 *   CMAT_INVERSE_GREASE
 *   CVEC_CMatMaker_C
 *   CVEC_MAKE_ZERO_CMAT
 *   CVEC_PROD_CMAT_CMAT_DISPATCH
 * Those functions are not called from any other functions in this file 
 * from the C level. So no other functions are "infected". */

/* Here is a sketch of a proof that there are no missing CHANGED_BAGs in
 * this file:
 * A CHANGED_BAG only has to be used after assigning a reference to
 * a masterpointer. This can only be done by using one of
 *   SET_ELM_PLIST, SET_TYPE_DATOBJ, AssPRec
 * AssPRec does the CHANGED_BAG on its own.
 * All occurrences of "SET_" have been checked, whether references to
 * masterpointers are assigned. No missing CHANGED_BAGs have been found. */

/*
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; version 2 of the License.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 *
 */



