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/****************************************
* Computer Algebra System SINGULAR *
****************************************/
#include "kernel/mod2.h"
#include "polys/monomials/ring.h"
#include "kernel/fast_mult.h"
#include "polys/kbuckets.h"
typedef poly fastmultrec(poly f, poly g, ring r);
static const int pass_option=1;
static int mults=0;
int Mults()
{
return mults;
}
static void degsplit(poly p,int n,poly &p1,poly&p2, int vn, ring r)
{
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;
}
}
static void div_by_x_power_n(poly p, int n, int vn, ring r)
{
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);
}
}
static poly do_unifastmult(poly f,int df,poly g,int dg, int vn, fastmultrec rec, ring r)
{
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);
}
// poly do_unifastmult_buckets(poly f,poly g){
// int n=1;
// if ((f==NULL)||(g==NULL)) return NULL;
// int df=pGetExp(f,1);//pFDeg(f);
// int dg=pGetExp(g,1);//pFDeg(g);
// int dm;
// if(df>dg){
// dm=df;
// }else{
// dm=dg;
// }
// while(n<=dm)
// {
// n*=2;
// }
// int pseudo_len=0;
// if(n==1){
// return ppMult_qq(f,g);
// }
// kBucket_pt erg_bucket= kBucketCreate(currRing);
// kBucketInit(erg_bucket,NULL,0 /*pLength(P.p)*/);
// int pot=n/2;
// assume(pot*2==n);
// //splitting
// poly f1=NULL;
// poly f0=NULL;//f-(x^(pot)*F1);
// degsplit(pCopy(f),pot,f1,f0);
// div_by_x_power_n(f1,pot);
// poly g1=NULL;
// poly g0=NULL;
// degsplit(pCopy(g),pot,g1,g0);
// div_by_x_power_n(g1,pot);
// //p00
// //p11
// poly p00=unifastmult(f0,g0);
// poly p11=unifastmult(f1,g1);
// //eat up f0,f1,g0,g1
// poly pbig=unifastmult(pAdd(f0,f1),pAdd(g0,g1));
// poly factor=pOne();//pCopy(erg_mult);
// pSetExp(factor,1,n);
// pseudo_len=0;
// kBucket_Add_q(erg_bucket,ppMult_mm(p11,factor),&pseudo_len);
// pseudo_len=0;
// kBucket_Add_q(erg_bucket,pCopy(p00),&pseudo_len);
// pSetExp(factor,1,pot);
// //eat up pbig
// pseudo_len=0;
// kBucket_Add_q(erg_bucket,pMult_mm(pbig,factor),&pseudo_len);
// pseudo_len=0;
// //eat up p00
// kBucket_Add_q(erg_bucket,pMult_mm(pNeg(p00),factor),&pseudo_len);
// pseudo_len=0;
// //eat up p11
// kBucket_Add_q(erg_bucket,pMult_mm(pNeg(p11),factor),&pseudo_len);
// pseudo_len=0;
// pDelete(&factor);
// int len=0;
// poly erg=NULL;
// kBucketClear(erg_bucket,&erg,&len);
// kBucketDestroy(&erg_bucket);
// return erg;
// }
static inline int max(int a, int b)
{
return (a>b)? a:b;
}
static inline int min(int a, int b)
{
return (a>b)? b:a;
}
poly unifastmult(poly f,poly g, ring r)
{
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);
}
poly multifastmult(poly f, poly g, ring r)
{
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);
}
}
poly pFastPower(poly f, int n, ring r)
{
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;
}
static omBin lm_bin=NULL;
/*3
* compute for monomials p*q
* destroys p, keeps q
*/
static void p_MonMultMB(poly p, poly q,ring r)
{
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);
}
/*3
* compute for monomials p*q
* keeps p, q
* uses bin only available in MCPower
*/
static poly p_MonMultCMB(poly p, poly q, ring r)
{
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;
}
// unused
#if 0
static poly p_MonPowerMB(poly p, int exp, ring r)
{
int i;
if(!n_IsOne(p_GetCoeff(p,r),r->cf))
{
number x, y;
y = p_GetCoeff(p,r);
n_Power(y,exp,&x,r->cf);
n_Delete(&y,r->cf);
p_SetCoeff0(p,x,r);
}
for (i=rVar(r); i!=0; i--)
{
p_MultExp(p,i, exp,r);
}
p_Setm(p,r);
return p;
}
#endif
static void buildTermAndAdd(int /*n*/,number* /*facult*/,poly* /*f_terms*/,int* exp,int f_len,kBucket_pt /*erg_bucket*/,ring r, number coef, poly & zw, poly /*tmp*/, poly** term_pot){
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;
}
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){
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);
}
poly pFastPowerMC(poly f, int n, ring r)
{
//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;
}
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