fast_mult.cc File Reference

#include "kernel/mod2.h"
#include "polys/monomials/ring.h"
#include "kernel/fast_mult.h"
#include "polys/kbuckets.h"

Go to the source code of this file.

Typedefs
typedef poly	fastmultrec(poly f, poly g, ring r)

Functions
int	Mults ()
static void	degsplit (poly p, int n, poly &p1, poly &p2, int vn, ring r)
static void	div_by_x_power_n (poly p, int n, int vn, ring r)
static poly	do_unifastmult (poly f, int df, poly g, int dg, int vn, fastmultrec rec, ring r)
static int	max (int a, int b)
static int	min (int a, int b)
poly	unifastmult (poly f, poly g, ring r)
poly	multifastmult (poly f, poly g, ring r)
poly	pFastPower (poly f, int n, ring r)
static void	p_MonMultMB (poly p, poly q, ring r)
static poly	p_MonMultCMB (poly p, poly q, ring r)
static void	buildTermAndAdd (int, number *, poly *, int *exp, int f_len, kBucket_pt, ring r, number coef, poly &zw, poly, poly **term_pot)
static void	MC_iterate (poly f, int n, ring r, int f_len, number *facult, int *exp, poly *f_terms, kBucket_pt erg_bucket, int pos, int sum, number coef, poly &zw, poly tmp, poly **term_pot)
poly	pFastPowerMC (poly f, int n, ring r)

Variables
static const int	pass_option =1
STATIC_VAR int	mults =0
STATIC_VAR omBin	lm_bin =NULL

Typedef Documentation

fastmultrec

typedef poly fastmultrec(poly f, poly g, ring r)

Definition at line 11 of file fast_mult.cc.

Function Documentation

buildTermAndAdd()

void buildTermAndAdd ( int , number * , poly * , int * exp, int f_len, kBucket_pt , ring r, number coef, poly & zw, poly , poly ** term_pot )

static

poly term=p_Copy(f_terms[i],r);

Definition at line 487 of file fast_mult.cc.

                                                                                                                                            {
 
  int i;
  //  poly term=p_Init(r);
 
   //  number denom=n_Init(1,r);
//   for(i=0;i<f_len;i++){
//     if(exp[i]!=0){
//       number trash=denom;
//       denom=n_Mult(denom,facult[exp[i]],r);
//       n_Delete(&trash,r);
//     }
 
//   }
//   number coef=n_IntDiv(facult[n],denom,r);   //right function here?
//   n_Delete(&denom,r);
//   poly erg=p_NSet(coef,r);
  poly erg=p_Init(r,lm_bin);
  p_SetCoeff0(erg, coef,r);
  //p_NSet(n_Copy(coef,r),r);
  for(i=0;i<f_len;i++){
    if(exp[i]!=0){
      ///poly term=p_Copy(f_terms[i],r);
      poly term=term_pot[i][exp[i]];
        //tmp;
        //p_ExpVectorCopy(term,f_terms[i],r);
        //p_SetCoeff(term, n_Copy(p_GetCoeff(f_terms[i],r),r),r);
 
      //term->next=NULL;
 
      //p_MonPowerMB(term, exp[i],r);
      p_MonMultMB(erg,term,r);
      //p_Delete(&term,r);
    }
 
  }
  zw=erg;
}

degsplit()

void degsplit ( poly p, int n, poly & p1, poly & p2, int vn, ring r )

static

Definition at line 18 of file fast_mult.cc.

{
  poly erg1_i, erg2_i;
  erg1_i=NULL;
  erg2_i=NULL;
  while(p)
  {
    if(p_GetExp(p,vn,r)>=n)
    {
      if (p1==NULL)
      {
        p1=p;
      }
      else
      {
        pNext(erg1_i)=p;
      }
      erg1_i=p;
    }
    else
    {
      if (p2==NULL)
      {
        p2=p;
      }
      else
      {
        pNext(erg2_i)=p;
      }
      erg2_i=p;
    }
    p=pNext(p);
  }
  if(erg2_i)
  {
    pNext(erg2_i)=NULL;
  }
  if (erg1_i)
  {
    pNext(erg1_i)=NULL;
  }
 
}

div_by_x_power_n()

void div_by_x_power_n ( poly p, int n, int vn, ring r )

static

Definition at line 61 of file fast_mult.cc.

{
  while(p)
  {
    assume(p_GetExp(p,vn,r)>=n);
    int e=p_GetExp(p,vn,r);
    p_SetExp(p,vn,e-n,r);
    p=pNext(p);
  }
}

do_unifastmult()

poly do_unifastmult ( poly f, int df, poly g, int dg, int vn, fastmultrec rec, ring r )

static

Definition at line 72 of file fast_mult.cc.

{
  int n=1;
  if ((f==NULL)||(g==NULL)) return NULL;
  //int df=pGetExp(f,vn);//pFDeg(f);
  //  int dg=pGetExp(g,vn);//pFDeg(g);
 
  int dm;
  if(df>dg)
  {
    dm=df;
  }
  else
  {
    dm=dg;
  }
  while(n<=dm)
    {
      n*=2;
    }
  if(n==1)
  {
    return(pp_Mult_qq(f,g,r));
  }
 
  int pot=n/2;
  assume(pot*2==n);
 
 
  //splitting
  poly f1=NULL;
  poly f0=NULL;//f-(x^(pot)*F1);
  degsplit(p_Copy(f,r),pot,f1,f0,vn,r);
  div_by_x_power_n(f1,pot,vn,r);
 
  poly g1=NULL;
  poly g0=NULL;
  degsplit(p_Copy(g,r),pot,g1,g0,vn,r);
  div_by_x_power_n(g1,pot,vn,r);
 
  //p00, p11
  poly p00=rec(f0,g0,r);//unifastmult(f0,g0);
  poly p11=rec(f1,g1,r);
 
  //construct erg, factor
  poly erg=NULL;
  poly factor=p_ISet(1,r);
 
  p_SetExp(factor,vn,n,r);
  erg=pp_Mult_mm(p11,factor,r);
  erg=p_Add_q(erg,p_Copy(p00,r),r);
 
 
 
 
 
  if((f1!=NULL) &&(f0!=NULL) &&(g0!=NULL) && (g1!=NULL))
  {
    //if(true){
    //eat up f0,f1,g0,g1
    poly s1=p_Add_q(f0,f1,r);
    poly s2=p_Add_q(g0,g1,r);
    poly pbig=rec(s1,s2,r);
    p_Delete(&s1,r);
    p_Delete(&s2,r);
 
 
    //eat up pbig
    poly sum=pbig;
    p_SetExp(factor,vn,pot,r);
 
    //eat up p00
    sum=p_Add_q(sum,p_Neg(p00,r),r);
 
    //eat up p11
    sum=p_Add_q(sum,p_Neg(p11,r),r);
 
 
    sum=p_Mult_mm(sum,factor,r);
 
 
    //eat up sum
    erg=p_Add_q(sum,erg,r);
  }
  else
  {
    //eat up f0,f1,g0,g1
    poly s1=rec(f0,g1,r);
    poly s2=rec(g0,f1,r);
    p_SetExp(factor,vn,pot,r);
    poly h=p_Mult_mm(((s1!=NULL)?s1:s2),factor,r);
    p_Delete(&f1,r);
    p_Delete(&f0,r);
    p_Delete(&g0,r);
    p_Delete(&g1,r);
    p_Delete(&p00,r);
    p_Delete(&p11,r);
    erg=p_Add_q(erg,h,r);
  }
 
 
  p_Delete(&factor,r);
 
 
 
  return(erg);
}

max()

int max ( int a, int b )

inlinestatic

Definition at line 264 of file fast_mult.cc.

{
  return (a>b)? a:b;
}

MC_iterate()

void MC_iterate ( poly f, int n, ring r, int f_len, number * facult, int * exp, poly * f_terms, kBucket_pt erg_bucket, int pos, int sum, number coef, poly & zw, poly tmp, poly ** term_pot )

static

Definition at line 528 of file fast_mult.cc.

                                                                                                                                                                                        {
  int i;
 
  if (pos<f_len-1)
  {
    poly zw_l=NULL;
    number new_coef;
    for(i=0;i<=n-sum;i++)
    {
      exp[pos]=i;
      if(i==0)
      {
        new_coef=n_Copy(coef,r->cf);
      }
      else
      {
        number old=new_coef;
        number old_rest=n_Init(n-sum-(i-1),r->cf);
        new_coef=n_Mult(new_coef,old_rest,r->cf);
        n_Delete(&old_rest,r->cf);
        n_Delete(&old,r->cf);
        number i_number=n_Init(i,r->cf);
        old=new_coef;
        new_coef=n_Div(new_coef,i_number,r->cf);
        n_Normalize(new_coef,r->cf);
        n_Delete(&old,r->cf);
        n_Delete(&i_number,r->cf);
      }
      //new_coef is
      //(n                          )
      //(exp[0]..exp[pos] 0 0 0 rest)
      poly zw_real=NULL;
      MC_iterate(f, n, r, f_len,facult, exp,f_terms,erg_bucket,pos+1,sum+i,new_coef,zw_real,tmp,term_pot);
      if (pos==f_len-2)
      {
        //get first small polys
 
        zw_real->next=zw_l;
        zw_l=zw_real;
      }
      //n_Delete(& new_coef,r->cf);
    }
    n_Delete(&new_coef,r->cf);
    if (pos==f_len-2)
    {
      int len=n-sum+1;
      kBucket_Add_q(erg_bucket,zw_l,&len);
    }
    return;
  }
  if(pos==f_len-1)
  {
    i=n-sum;
    exp[pos]=i;
    number new_coef=n_Copy(coef,r->cf);//n_IntDiv(coef,facult[i],r); //really consumed???????
    buildTermAndAdd(n,facult,f_terms,exp,f_len,erg_bucket,r, new_coef,zw, tmp,term_pot);
    // n_Delete(& new_coef,r);
  }
  assume(pos<=f_len-1);
}

min()

int min ( int a, int b )

inlinestatic

Definition at line 268 of file fast_mult.cc.

{
  return (a>b)? b:a;
}

multifastmult()

poly multifastmult	(	poly	f,
		poly	g,
		ring	r )

Definition at line 290 of file fast_mult.cc.

{
  mults++;
  if((f==NULL)||(g==NULL)) return NULL;
  if (pLength(f)*pLength(g)<100)
    return pp_Mult_qq(f,g,r);
  //find vn
  //determine df,dg simultaneously
  int i;
  int can_i=-1;
  int can_df=0;
  int can_dg=0;
  int can_crit=0;
  for(i=1;i<=rVar(r);i++)
  {
    poly p;
    int df=0;
    int dg=0;
    //max min max Strategie
    p=f;
    while(p)
    {
      df=max(df,p_GetExp(p,i,r));
      p=pNext(p);
    }
    if(df>can_crit)
    {
      p=g;
      while(p)
      {
        dg=max(dg,p_GetExp(p,i,r));
        p=pNext(p);
      }
      int crit=min(df,dg);
      if (crit>can_crit)
      {
        can_crit=crit;
        can_i=i;
        can_df=df;
        can_dg=dg;
      }
    }
  }
  if(can_crit==0)
    return pp_Mult_qq(f,g,r);
  else
    {
      poly erg=do_unifastmult(f,can_df,g,can_dg,can_i,multifastmult,r);
      p_Normalize(erg,r);
      return(erg);
    }
}

Mults()

int Mults

(

)

Definition at line 14 of file fast_mult.cc.

{
  return mults;
}

p_MonMultCMB()

poly p_MonMultCMB ( poly p, poly q, ring r )

static

Definition at line 455 of file fast_mult.cc.

{
  number x;
  poly res = p_Init(r,lm_bin);
 
  x = n_Mult(p_GetCoeff(p,r),p_GetCoeff(q,r),r->cf);
  p_SetCoeff0(res,x,r);
  p_ExpVectorSum(res,p, q,r);
  return res;
}

p_MonMultMB()

void p_MonMultMB ( poly p, poly q, ring r )

static

Definition at line 434 of file fast_mult.cc.

{
  number x, y;
  // int i;
 
  y = p_GetCoeff(p,r);
  x = n_Mult(y,pGetCoeff(q),r->cf);
  n_Delete(&y,r->cf);
  p_SetCoeff0(p,x,r);
  //for (i=(currRing->N); i!=0; i--)
  //{
  //  pAddExp(p,i, pGetExp(q,i));
  //}
  //p->Order += q->Order;
  p_ExpVectorAdd(p,q,r);
}

pFastPower()

poly pFastPower	(	poly	f,
		int	n,
		ring	r )

Definition at line 342 of file fast_mult.cc.

{
  if (n==1) return f;
  if (n==0) return p_ISet(1,r);
  assume(n>=0);
  int i_max=1;
  int pot_max=0;
  while(i_max*2<=n)
  {
    i_max*=2;
    pot_max++;
  }
  int field_size=pot_max+1;
  int* int_pot_array=(int*) omAlloc(field_size*sizeof(int));
  poly* pot_array=(poly*) omAlloc(field_size*sizeof(poly));
  int i;
  int pot=1;
  //initializing int_pot
  for(i=0;i<field_size;i++)
  {
    int_pot_array[i]=pot;
    pot*=2;
  }
  //calculating pot_array
  pot_array[0]=f; //do not delete it
  for(i=1;i<field_size;i++)
  {
    poly p=pot_array[i-1];
    if(rVar(r)==1)
      pot_array[i]=multifastmult(p,p,r);
    else
      pot_array[i]=pp_Mult_qq(p,p,r);
  }
 
 
 
  int work_n=n;
  assume(work_n>=int_pot_array[field_size-1]);
  poly erg=p_ISet(1,r);
 
 
  //forward maybe faster, later
  // for(i=field_size-1;i>=0;i--){
 
//       assume(work_n<2*int_pot_array[i]);
//       if(int_pot_array[i]<=work_n){
//         work_n-=int_pot_array[i];
//         poly prod=multifastmult(erg,pot_array[i],r);
//         pDelete(&erg);
//         erg=prod;
//       }
 
//       if(i!=0) pDelete(&pot_array[i]);
//   }
 
 
  for(i=field_size-1;i>=0;i--)
  {
 
      assume(work_n<2*int_pot_array[i]);
      if(int_pot_array[i]<=work_n)
      {
        work_n-=int_pot_array[i];
        int_pot_array[i]=1;
      }
      else int_pot_array[i]=0;
 
  }
  for(i=0;i<field_size;i++)
  {
    if(int_pot_array[i]==1)
    {
      poly prod;
      if(rVar(r)==1)
        prod=multifastmult(erg,pot_array[i],r);
      else
        prod=pp_Mult_qq(erg,pot_array[i],r);
      pDelete(&erg);
      erg=prod;
    }
    if(i!=0) pDelete(&pot_array[i]);
  }
  //free res
  omfree(pot_array);
  omfree(int_pot_array);
  return erg;
}

pFastPowerMC()

poly pFastPowerMC	(	poly	f,
		int	n,
		ring	r )

Definition at line 588 of file fast_mult.cc.

{
  //only char=0
 
  if(rChar(r)!=0)
    WerrorS("Char not 0, pFastPowerMC not implemented for this case");
  if (n<=1)
    WerrorS("not implemented for so small n, recursion fails");//should be length(f)
   if (pLength(f)<=1)
    WerrorS("not implemented for so small length of f, recursion fails");
  //  number null_number=n_Init(0,r);
  number* facult=(number*) omAlloc((n+1)*sizeof(number));
  facult[0]=n_Init(1,r->cf);
  int i;
  for(i=1;i<=n;i++)
  {
    number this_n=n_Init(i,r->cf);
    facult[i]=n_Mult(this_n,facult[i-1],r->cf);
    n_Delete(&this_n,r->cf);
  }
 
  lm_bin=omGetSpecBin(POLYSIZE + (r->ExpL_Size)*sizeof(long));
 
  kBucket_pt erg_bucket= kBucketCreate(currRing);
  kBucketInit(erg_bucket,NULL,0);
  const int f_len=pLength(f);
  int* exp=(int*)omAlloc(f_len*sizeof(int));
  //poly f_terms[f_len];
  poly* f_terms=(poly*)omAlloc(f_len*sizeof(poly));
  poly** term_potences=(poly**) omAlloc(f_len*sizeof(poly*));
 
  poly f_iter=f;
  for(i=0;i<f_len;i++)
  {
    f_terms[i]=f_iter;
    f_iter=pNext(f_iter);
  }
  for(i=0;i<f_len;i++)
  {
    term_potences[i]=(poly*)omAlloc((n+1)*sizeof(poly));
    term_potences[i][0]=p_ISet(1,r);
    int j;
    for(j=1;j<=n;j++){
      term_potences[i][j]=p_MonMultCMB(f_terms[i],term_potences[i][j-1],r);
    }
  }
  assume(f_iter==NULL);
  poly zw=NULL;
  poly tmp=p_Init(r);
  number one=n_Init(1,r->cf);
  MC_iterate(f,n,r,f_len,&facult[0], &exp[0], &f_terms[0],erg_bucket,0,0,one/*facult[n]*/,zw,tmp, term_potences);
 
 
  n_Delete(&one,r->cf);
 
 
 
  //free res
 
  //free facult
  for(i=0;i<=n;i++)
  {
    n_Delete(&facult[i],r->cf);
  }
  int i2;
  for (i=0;i<f_len;i++)
  {
    for(i2=0;i2<=n;i2++)
    {
      p_Delete(&term_potences[i][i2],r);
    }
    omfree(term_potences[i]);
 
  }
  omfree(term_potences);
  p_Delete(&tmp,r);
  omfree(exp);
  omfree(facult);
  omfree(f_terms);
  int len=0;
  poly erg;
  kBucketClear(erg_bucket,&erg, &len);
  kBucketDestroy(&erg_bucket);
  omUnGetSpecBin(&lm_bin);
  return erg;
}

unifastmult()

poly unifastmult	(	poly	f,
		poly	g,
		ring	r )

Definition at line 272 of file fast_mult.cc.

{
  int vn=1;
  if((f==NULL)||(g==NULL)) return NULL;
  int df=p_GetExp(f,vn,r);
  int dg=p_GetExp(g,vn,r);
  if ((df==0)||(dg==0))
    return pp_Mult_qq(f,g,r);
  if (df*dg<100)
    return pp_Mult_qq(f,g,r);
  // if (df*dg>10000)
  //  return
  //    do_unifastmult_buckets(f,g);
  //else
  return do_unifastmult(f,df,g,dg,vn,unifastmult,r);
 
}

Variable Documentation

lm_bin

STATIC_VAR omBin lm_bin =NULL

Definition at line 429 of file fast_mult.cc.

mults

STATIC_VAR int mults =0

Definition at line 13 of file fast_mult.cc.

pass_option

const int pass_option =1

static

Definition at line 12 of file fast_mult.cc.